training - european commission · model building (reg. variables) ... – ansleyin specific cases...

TRAINING

ADVANCED

SEASONAL

ADJUSTMENT

WITH JD+

COURSE NOTES &

DOCUMENTATION

Date: 9-11 February 2015 Location: Eurostat, Luxembourg Trainers: Dominique Ladiray and Jean Palate

CONTENTS

JDemetra+ and the Time Series Laboratory

JDemetra+, an open framework for Seasonal Adjustment

The Cruncher

Temporal Disaggregation and Benchmarking

More on Time Series Modelling

Seasonality tests.

Quality of Seasonal Adjustment

Quality indicators in JDemetra+

State Space Modeling with JDemetra+

Time-varying coefficient models for trading-days

Nowcasting and Backcalculation with JDemetra+

The ESS guidelines for Seasonal Adjustment

Seasonal Adjustment of Chain Linked Data

JDEMETRA+, AN OPEN FRAMEWORK FOR SEASONAL

ADJUSTMENT

1

JDemetra+an open framework for Seasonal Adjustment

Outline

• Objectives of JDemetra+ (JD+)

– GeneralGeneral

– For seasonal adjustment (SA)

• What is really JD+ ?

• Architecture, design

• Seasonal adjustment framework

– Overview, pre‐processing, decompositionp p g p

• State space framework

– Goals, overview

• Some examples

• Final remarks

2

General Objectives

• Providing algorithms for the production/analysis of [official] statistics– Regular time series (from monthly to yearly)– Algorithms for

• Seasonal adjustment, business cycle analysis• Benchmarking, temporal disaggregation• Modelling (forecasting, estimation of missing values, outliers detection)

• Reusable modules, compatible with common IT infrastructure Java WEB services– Java, WEB services...

• Designed for the whole statistical process– From research to bulk production (flexible, high‐performance)

• Maintainable– Open source solution

Objectives for SA

• Java implementation of the leading algorithms– Tramo‐Seats, X12‐ARIMA...

• Flexible design– Easier modifications of the core engines– Developments of additional tools/algorithms

• Challenge– Keeping

• similar results• high performances

– with • flexible (more general) design and algorithms• slower technical solution

3

What is JD+ (I) ?

Rich graphical application (end-users)

Advanced Java toolkit for time series (SA) processing (IT-teams, researchers)

What is JD+ ? (II)

Open Source project(EUPL license)

S d b E• Supported by Eurostat

•Developers:•NBB•Bundesbank•...

•Originally based on:•Tramo-Seats•Tramo-Seats (BDE)•X12-Arima (USCB)

https://github.com/jdemetra

4

Architecture (I)

JTsToolkit In house Core algorithms

Peripheral modulesExternalpackages

developments

Jdemetra-core

Jdemetra app

Cruncher

JDemetra+ plug‐insNetBeansThird party plug‐ins

Jdemetra-app

Architecture (II). Algorithmic libraries (jtstoolkit…)

Basic data handling Basic econometrics

Matrix computation

Complex, polynomials

Linear filters

Function optimization

Arima Ucarima

VAR,Dynamic factor Seats

X11

Arima modelling

RegArima

Tramo

Seasonal adjustment

Structural models...

Benchmarking, temporal disaggregation

Time series, calendars, regression variables...

Basic statistics

Utilities...

Arima, Ucarimamodel

State space framework

5

Design (GUI)

• Many extension points (= features that can be enriched/modified)– Time series providersp

• Direct access to new sources of data

– Seasonal adjustment• Output, reports• Diagnostics

– Graphical interface• Panels• Actions• Menu items• Menu items

– Formatting• Clipboard, drag/drop

– Algorithms• Integration in the workspaces.

– …

Seasonal adjustment frameworkGeneric modules:•Analysis

•Seasonality tests•Revision analysis•Sliding spans

•I/O (common xml schema)

SA methods

•I/O (common xml schema)•Graphical components

•Charts•SI ratios...

Tramo-Seats, X12-Arima...

Specific modules

(X11...) REGARIMA pre-processing

REGARIMA modules:•Common model•Estimation tools•Automatic modelling routines•Analysis tools (residuals,

Model-based decomposition(canonical decomposition,

structural models...) Signal extraction tools:•Estimation•Analysis •Graphical components

Other filters(X11...)

y ( ,forecasts...)•Graphical components

6

REGARIMA modelling

• Common definitions for Calendar variables, outliers, intervention variables, user variables...

Model building(Reg. variables)

• Algorithms for likelihood estimation– Kalman filter (Tramo‐like),

– Ansley algorithm (Cholesky on banded matrix)

– (modified) Ljung‐Box algorithm (X12‐like)

• Equivalent results, different performances

• JD+ uses Kalman filter – Up to 4 x faster than Ljung‐Box

Estimation of the model(likelihood, residuals)

p j g

– Ansley in specific cases (outliers detection)

• Optimization procedure– Levenberg‐Marquardt. Tramo‐Seats, X12 and JD+ use

slightly different variants.

Estimation of the parameters (by ML)

Automatic model identification

• Independent blocks (d i ll difi bl )

Pre-test (seasonality...)

(dynamically modifiable)

• Specific implementation for Tramo‐Seats, X12

Example: X12 modelling with outliers detection from Tramo

Log/level

Calendar effects...

Outliers detection

Arima (diff. / Arma)

Final estimation

Models comparison

Model validation

7

Algorithms for signal extraction in JD+

• Wiener‐Kolmogorov filtersBurman's algorithm Maravall's analysis framework (Seats)– Burman s algorithm, Maravall s analysis framework (Seats)

• Kalman smoother– Koopman's initialization procedure (disturbance or ordinary smoother)

• Matrix computation– McElroy 's formulae

• Can be applied to any (valid) UCARIMA model

• Results– Estimates: identical– Standard deviations: WK approach yields negligible differences

(exception: quasi‐unit roots in MA polynomial → large differences)

WK Kalman Matrix

Performance ++ = + ‐‐

Flexibility ‐ + ‐

Main characteristics (in JD+ !)

Length of the series

WK(Burman)

Kalman (disturbances)

Kalman (ordinary) Matrix

120 0 5 0 7 12 7 23 1

Performances (average processing time in milliseconds, Intel T7500, 2.2 GHz)

Robustness ‐ + =

Analysis + = =

120 0.5 0.7 12.7 23.1

240 0.6 0.9 21.1 145.7

360 0.7 1.2 29.9 408.1

3600 5.3 12.3 235.8 n

8

State space framework

• Key solution for:– REGARIMA estimation– Signal extraction (Kalman smoother)– Alternative time series modelling (for SA or not)

• Structural models...

– Benchmarking• Cholette (including multi‐variate extension)

– Temporal disaggregation• Chow‐Lin, Fernandez...

M lti i t d l– Multi‐variate models• VAR, dynamic factor models, SUTSE…

• JD+ provides an advanced OO implementation of SSF

State space framework (II)

Models Algorithms

Atomic models:• Generic (time invariant

or not)• Ar(i)ma• Ucarima• Basic structural • White noise• Random walk• ...

gFiltering:• Ordinary filter• Fast filter (Chandrasekhar)• Array filter (Kailath...)

Diffuse initialization:• Koopman• Square root• Ad hoc

Others:• Univariate handling of

multi-variate models

Likelihood evaluation:Prediction errordecomposition

Derived models:• Composite • Regression variables• Aggregation constraints• ...

Smoothing:• Ordinary• Disturbance• Fixed point

• Augmented Kalmanfilter (for reg. model)

• Extended Kalman filter(for non linear models)

• ...

9

Example 1. Comparison tool for different SA algorithms

Example 2. Extensible application through plug‐ins

10

Example 3. Derivation of new outputs

Standard deviations of the seasonal component as estimated in SEATS (separate) and as they appear in the full model (stochastic and final=stochastic+calendar).Computation by means of the corresponding state space model

0.0085

0.0095

0.0105

0.0115

S (separate)

S (stochastic)

S (final)

Computation by means of the corresponding state space model.

0.0075

S (final)

Belgium. Imports of goods (monthly series, 1995-2007)Standard deviations of the seasonal components (in logs; includes forecasts)

Final remarks

• JD+ is a complete re‐factoring of Tramo‐Seats an of X12‐Arima in an open OO framework. In some cases, the new p ,algorithms may lead to (usually slightly) different results .

• JD+ is also designed for the handling of related time series problems, especially through a rich state space library.

• By developing it as an open source solution, we have tried to create an environment appropriate to external collaborations.

JDEMETRA+, THE CRUNCHER

JWSACruncher

Quick guide

Description

JWSACruncher is the Java implementation of the .NET application "WSACruncher". It is a console

tool that re-estimates all the multi-processing defined in a workspace. The workspace may have been generated by either by means of Demetra+ (.NET) or of JDemetra+ (Java).

Installation

The user has to unzip the separate package jwsacruncher-xxx.zip in a specific folder. The folder will contain all the necessary dependencies

Command line

JWSACruncher uses the same parameters as WSACruncher. The command line for launching the tool is the following: Jwsacruncher[.bat][-x <parameters file>] For instance: Jwsacruncher d:\ repository\MyWS.xml -x d:\ repository\MyWS.params Jwsacruncher is located in the “bin” sub-folder Be aware that some operating systems are case sensitive. The only mandatory1 parameter is the name of a workspace defined with JDemetra+. It is

supposed that the depending files are available. The second parameter, identified by "-x", is an xml file containing detailed information on the batch processing. See below for further explanations. If that file is unavailable, the default specifications will be used.

The other parameters used with WSACruncher are still operational but obsolete. See the documentation of WSACruncher for further information.

Output

The following output is generated:

The processing xxx.xml used as input is saved as xxx.bak and the new results replace the file xxx.xml

The series specified in the in the file of parameters are generated in separate csv files, named series_zzz.csv; by default, each row of the csv files contains the identifier of the series, its frequency, its starting year and period, its length and the data; however, they can

1 Users can launch jwsacruncher without parameters. In that special case, a default file of parameters

(called wsacruncher.params) will be generated in the active folder. That file can be modified for further processing.

be formatted in a way that can be immediately read by software like Excel (vertical or horizontal tables).

The csv file "demetra_m.csv", containing a matrix with all the results specified in the file of parameters is also generated.

The different outputs are located by default in the folder(s) <folder of the workspace file>/Output/<processing name>[_x] , where - "processing name" is the name of the processing in the workspace - the [_x] prefix ("_1", "_2"...) correspond to an automatic splitting of large processing in smaller

groups (see "bundle" option in the parameters file) So, if the workspace "d:\sa\myWs.xml" contains the large processing "Processing-1", "Processing-

2", the folder "d:\sa will contain:

Inputs: o myWs.xml o .\myWs\SAProcessing\Processing-1.xml o .\myWs \SAProcessing\Processing-2.xml o ...

Outputs: o .\myWs \Output\Processing-1_1\demetra_m.csv o .\myWs \Output\Processing-1_1\series_sa.csv o .\myWs \Output\Processing-1_1\... o .\myWs \Output\Processing-1_2\demetra_m.csv o .\myWs \Output\Processing-1_2\series_sa.csv o .\myWs \Output\Processing-1_2\... o .\myWs \Output\Processing-1_...\...... o .\myWs \Output\Processing-2_1\demetra_m.csv o .\myWs \Output\Processing-2_1\series_sa.csv o .\myWs \Output\Processing-2_1\... o .\myWs \Output\Processing-2_2\demetra_m.csv o .\myWs \Output\Processing-2_2\series_sa.csv o .\myWs \Output\Processing-2_2\... o .\myWs \Output\Processing-2_2\...

Use of JWSACruncher with Demetra+

JWSACruncher is designed to be used with (J)Demetra+. We present below a typical scenario for

the use of both applications. 1. Creation of the workspace with JDemetra+ You should use JDemetra+ to create a new workspace and to add in it the processing that should

be re-estimated. Tips Don't run the processing in JDemetra+ If need be, create as many processing as needed. 2. Copy of the complete workspace in a suitable folder You can copy the complete workspace at the folder where you want to process it using the

command: file->Save workspace as... You can also copy it manually: the files that belongs to a workspace xxx are - xxx.xml, which contains the description of the workspace - the folder ./xxx and all its sub-folders, which contain the description of processing, the

calendars...

3. Run JWSACruncher (as defined above) You can re-use JDemetra+ to visualize the results and/or to correct some of them.

Parameters file

Tips: launch jwsacruncher (without parameter) for generating a default parameters file The parameters file has the following structure: <?xml version="1.0" encoding="UTF-8" standalone="yes"?> <wsaConfig bundle="1000" csvlayout="list" csvseparator="," ndecs="6”> <policy>parameters</policy> <output>d:\saresults</output> <matrix> <item>span.start</item> <item>span.end</item> <item>span.n</item> <item>likelihood.neffectiveobs</item> ... </matrix> <tsmatrix> <series>y</series> <series>sa</series> ... </tsmatrix> <paths> <path>C:\Documents and Settings\me\Data\Excel</path> <path>C:\Documents and Settings\me\Data\Xml</path> ... </paths> </wsaConfig> The meaning of the different tags and their possible values are defined below

Tag Meaning Value

bundle Maximum size for a group of series (in output)

1000 by default

csvlayout Layout of the csv files (series only)

list (default) htable vtable

csvseparator List separator of the csv file (“,”) by default

ndecs Number of decimals used in the output

6 by default

policy refreshing policy of the processing

parameters: parameters are re-estimated (default)

outliers: outliers are identified and

parameters are re-estimated lastoutliers: last outliers (1 year) are re-

identified and parameters are re-estimated

stochastic: arima model, outliers are

identified and parameters are re-estimated complete: complete model is re-

estimated

output Output folder: Full path of the output folder Could be empty (by default, it is

<workspace>/Output

matrix.item Items of the matrix output2 span.start span.end span.n espan.start espan.end espan.n likelihood.neffectiveobs likelihood.np likelihood.logvalue likelihood.adjustedlogvalue likelihood.ssqerr likelihood.aic likelihood.aicc likelihood.bic likelihood.bicc residuals.ser residuals.ser-ml residuals.mean residuals.skewness residuals.kurtosis residuals.dh residuals.lb residuals.lb2 residuals.seaslb residuals.bp residuals.bp2 residuals.seasbp residuals.nruns residuals.lruns m-statistics.m1 m-statistics.m2 m-statistics.m3 m-statistics.m4 m-statistics.m5 m-statistics.m6 m-statistics.m7 m-statistics.m8 m-statistics.m9 m-statistics.m10 m-statistics.m11 m-statistics.q

2 The meaning of the different items will be documented in the users' manual of JDemetra+

m-statistics.q-m2 diagnostics.quality diagnostics.basic checks.definition:2 diagnostics.basic checks.annual totals:2 diagnostics.visual spectral

analysis.spectral seas peaks diagnostics.visual spectral

analysis.spectral td peaks diagnostics.regarima

residuals.normality:2 diagnostics.regarima

residuals.independence:2 diagnostics.regarima residuals.spectral td

peaks:2 diagnostics.regarima residuals.spectral

seas peaks:2 diagnostics.residual seasonality.on sa:2 diagnostics.residual seasonality.on sa (last

3 years):2 diagnostics.residual seasonality.on

irregular:2 diagnostics.seats.seas variance:2 diagnostics.seats.irregular variance:2 diagnostics.seats.seas/irr cross-

correlation:2 log adjust arima.mean arima.p arima.d arima.q arima.bp arima.bd arima.bq arima.phi(1) arima.phi(2) arima.phi(3) arima.phi(4) arima.th(1) arima.th(2) arima.th(3) arima.th(4) arima.bphi(1) arima.bth(1) regression.lp:3 regression.ntd regression.td(1):3 regression.td(2):3 regression.td(3):3 regression.td(4):3 regression.td(5):3 regression.td(6):3

regression.td(7):3 regression.nmh regression.easter:3 regression.nout regression.out(1):3 regression.out(2):3 regression.out(3):3 regression.out(4):3 regression.out(5):3 regression.out(6):3 regression.out(7):3 regression.out(8):3 regression.out(9):3 regression.out(10):3 regression.out(11):3 regression.out(12):3 regression.out(13):3 regression.out(14):3 regression.out(15):3 regression.out(16):3 decomposition.seasonality decomposition.trendfilter decomposition.seasfilter

tsmatrix.series

Generated series 3 y y_f y_ef yc yc_f yc_ef y_lin l ycal ycal_f l_f l_b t t_f sa sa_f s s_f i i_f det det_f cal cal_f tde tde_f mhe

3 The meaning of the different items will be documented in the users' manual of JDemetra+

mhe_f ee ee_f omhe omhe_f out out_f out_i out_i_f out_t out_t_f out_s out_s_f reg reg_f reg_t reg_t_f reg_s reg_s_f reg_i reg_i_f reg_sa reg_sa_f reg_y reg_y_f fullresiduals decomposition.y_lin decomposition.y_lin_f decomposition.t_lin decomposition.t_lin_f decomposition.sa_lin decomposition.sa_lin_f decomposition.s_lin decomposition.s_lin_f decomposition.i_lin decomposition.i_lin_f decomposition.si_lin decomposition.a-tables.axx (X13 only)* decomposition.b-tables.axx (X13 only) decomposition.c-tables.axx (X13 only) decomposition.d-tables.axx (X13 only) decomposition.e-tables.axx (X13 only) benchmarking.target benchmarking.result

paths.path Paths that correspond to input files (Excel, xml...)

Necessary only if the series used in a processing use relative addresses.

* for instance, decomposition.d-tables.d7

JDEMETRA+, TEMPORAL DISAGGREGATION AND

BENCHMARKING

NATIONAL BANK OF BELGIUM

JD+ Temporal disaggregation and benchmarking

Jean Palate

1/22/2015

0. Introduction

JD+ contains several routines for temporal disaggregation and benchmarking. As far as temporal disaggregation is concerned, the libraries provide implementations of the usual regression-based methods, like the Chow-Lin, Fernandez or Litterman algorithms. Considering benchmarking, the univariate Denton and Cholette methods are provided. A generalization to the multi-variate case is also proposed.

Most of the algorithms follow a “model-based” approach, using state space forms. A short summary of the way JD+ handles state space forms is provided in the first point of the paper. In the second point, we present the regression-based methods for temporal disaggregation, with a special attention to their underlying hypotheses (initialization, definition of the likelihood…). Finally, we consider in the last point the benchmarking techniques.

1. State space forms

1.1. General form The general linear gaussian state-space model can be written in many different ways. The measurement equation and the state equation considered in JD+ are presented below.

𝑦𝑡 = 𝑍𝑡𝛼𝑡

𝛼𝑡+1 = 𝑇𝑡𝛼𝑡 + 𝜀𝑡 , 𝜀𝑡~𝑁(0,𝜎2𝑉𝑡)

𝑦𝑡 is the observation at period t, is the state vector. 𝜀𝑡 are assumed to be serially independent at all time points.

The residuals of the state equation will be modelled as

𝜀𝑡 = 𝑆𝑡𝜉𝑡 , 𝜉𝑡~𝑁(0,𝜎2𝑄𝑡)

where 𝑄𝑡 is a non-singular matrix. In other words, 𝑉𝑡 = 𝑆𝑡𝑄𝑡𝑆𝑡′

The initial conditions of the filter are defined as follows:

𝛼0 = 𝑎0 + 𝐵0𝛿 + 𝜇0

𝛿~𝑁(0, 𝜅𝐼)

𝜇0~𝑁(0,𝜎2𝑃∗0)

where 𝜅 is arbitrary large.

𝑃∗0 is the variance of the stationary part of the initial state vector and 𝐵0𝐵0′ = 𝑃∞0 models the diffuse part.

Contrary to what is often used, the measurement equation doesn't contain residuals. It is always possible to achieve such a representation by moving the measurement errors in the state vector.

State-space models are efficiently treated by KF. The augmented KF of De Jong (91) and a variant due to Gomez and Maravall (93) could be used to get an exact solution when the model contains elements with unspecified distributions. However, we follow the approach of Durbin and Koopman (2001, DK hereafter), which provides simpler and more efficient algorithms.

1.2. Regression variables Regression variables, if any, are integrated into the measurement equation, which becomes then:

ttttt XZy εβα ++= ,

where tX is the matrix of regressors at time t, and β is the column-matrix of the coefficients. Other

parts of the model remain unchanged.

We don't deal explicitly with regressors effects in the state equation. However such effects may always

be moved in the measurement equation by properly modifying them.

The β can be viewed as fixed but unknown (Rosenberg, 1973) or as diffused (De Jong, 1991). Unlike

other potential undefined items of the initial state, which we always treat as diffuse, both cases are

handled.

DK propose two solutions for the estimation of that model (2001, § 6.2.2 and 6.2.3): by extending the

state vector with the coefficients of the regressors or by using an approach similar to the augmented

KF. JD+ provides implementations for both solutions.

Skipping items corresponding to missing values, the likelihood of a model is easily obtained by means of the so-called prediction error decomposition provided by the Kalman filter. Following the way the regression coefficients are considered, we shall get either the diffuse likelihood or the profile (or concentrated) likelihood.

2. General considerations Temporal disaggregation and benchmarking are closely related. In both cases, we try to estimate an unobserved high-frequency series that respects some low-frequency constraints. In the case of temporal disaggregation, we will model the target by means of high-frequency information. We will prefer the term benchmarking when the problem consists in modifying an initial approximation of the target to fulfil the constraints. Temporal disaggregation will usually rest on statistical modelling techniques, while benchmarking will usually be based on the minimization of some penalty functions. However, many benchmarking problems can also be put in a form that corresponds to some model-based problems, so that the last distinction is often irrelevant. Most of the solutions proposed in JD+ will use model-based (state-space forms) solutions.

We use below the following conventions / notations:

High-frequency series will be noted by means of lower case letters and low-frequency series will be noted by (corresponding) higher case letters.

We will consider below the case of aggregation by sum. Aggregations based on averages (prices) are similar. Aggregation based on the last observations (stock variables) corresponds to a simple problem of missing observations and are not treated here.

3. Temporal disaggregation

3.1. Regression-based models The regression-based temporal disaggregation is defined by the following model:

𝑦𝑡 = 𝑋𝑡𝛽 + 𝜇𝑡

under the constraint that

𝑌𝑇 = �𝑦𝑡𝑡∈𝑇

The residuals may be modelled as

𝜇𝑡 = 𝜌𝜇𝑡−1 + 𝜀𝑡 Chow-Lin 𝜇𝑡 = 𝜇𝑡−1 + 𝜀𝑡 Fernandez (𝜇𝑡 − 𝜇𝑡−1) = 𝜌(𝜇𝑡−1 − 𝜇𝑡−2) + 𝜀𝑡 Litterman

The initial conditions (t<0) may be handled in different ways:

𝜇−1[= 𝜇−2] = 0, 𝑓𝑖𝑥𝑒𝑑

0-initialized

𝜇−1~𝑁(0,𝜎2

1 − 𝜌2)

Chow-Lin Unconditional distribution

𝜇−1~𝑁(0, 𝑘𝜎2), 𝑘 𝑎𝑟𝑏𝑖𝑡𝑟𝑎𝑟𝑦 𝑙𝑎𝑟𝑔𝑒 𝜇−1 = ��, 𝑓𝑖𝑥𝑒𝑑 𝑢𝑛𝑘𝑛𝑜𝑤𝑛

Fernandez Diffuse initialization Fixed unknown initialization

𝜇−2~𝑁(0, 𝑘𝜎2), 𝑘 𝑎𝑟𝑏𝑖𝑡𝑟𝑎𝑟𝑦 𝑙𝑎𝑟𝑔𝑒

(𝜇−1 − 𝜇−2)~𝑁(0,𝜎2

1 − 𝜌2)

𝜇−2 = ��, 𝑓𝑖𝑥𝑒𝑑 𝑢𝑛𝑘𝑛𝑜𝑤𝑛

Litterman Diffuse initialization Fixed unknown initialization

The hypotheses related to the different models are summarized in the table below

Method Model (P D Q)

Initial conditions (residuals/non stationary part)

JD+ JEcotrim

Chow-Lin (1 0 0) 0-initialisation X Unconditional X X

Fernandez (0 1 0) 0-initialisation X X Diffuse X Fixed unknown

Litterman (1 1 0) 0-initialisation X X Diffuse X Fixed unknown

In italic: to be avoided In bold: preferred (or default) solution

Different choices concerning the initial conditions will lead to different covariance structures for the disaggregated series and usually to different likelihood functions and to different MMSE estimates.

However, it should be noted that the Fernandez method with diffuse initialization and the Fernandez method with 0-initialization and mean correction are strictly equivalent (see annex 2).

As mentioned in the paragraph 1, the regression coefficients can be treated in two ways. They can be considered as fixed unknown or they can have an initial diffuse distribution. The likelihood functions based on those hypotheses will differ and lead to different ML estimates of the parameter of the model (𝜌). It should be noted that the hypothesis on the coefficients of the regression has no direct impact on the MMSE estimates of the disaggregated series.

Hypothesis on the regression coefficients

Likelihood JD+ JEcotrim Fixed unknown Profile (or concentrated) X X Diffuse Diffuse (∝ marginal) X

Details on the likelihood function following the different hypotheses can be found in DK (2001) or in Franke (2010).

An example of the impact of that hypothesis on the likelihood function is presented below

Diffuse likelihood (-) Profile likelihood (-)

3.2. State space form

We shortly describe below the generic state space model used in JD+

Each period of the aggregated time series contains c periods of the high-frequency time series; the different time series start at the same date. All indices start at 0.

We consider that the unobserved disaggregated series has a state space form (SSF) identified by the state 𝛼𝑡 and the system matrices�𝑍𝑡 ,𝑇𝑡 ,𝑉𝑡 ,𝑃∗0,𝑃∞0�.

We write

𝑦𝑡𝐶 = � 𝑦𝑘

𝑡−1

𝑘=𝑡−𝑡%𝑐

It represents the cumulator variable, from the beginning of each benchmarking period (included) to the current period (excluded).

and

𝑦𝑡𝐶 = � 𝑦𝑘

𝑡

𝑘=𝑡−𝑡%𝑐

= 𝑦𝑡𝐶 + 𝑦𝑡

So that 𝑦𝑡𝐶 = 𝑌𝑇 when 𝑡 + 1 is a multiple of c and is unobserved otherwise.

The benchmarking SSF for 𝜇𝑡𝐶 is the original SSF extended by the cumulator variable

The state is

𝛼�t=�𝑦𝑡𝐶 𝛼𝑡�

′

and the (time varying) matrices of the system can be easily derived. See Palate (2005).

The equivalent regression model is now built on the cumulated series

𝑦𝑡𝐶 = 𝑋𝑡𝐶𝛽 + 𝜇𝑡𝐶

The problem is then a simple problem of missing observations, which can be easily computed by means of the Kalman smoother.

4. Benchmarking

We shortly describe in this point a procedure that provides an exact solution for the univariate and for the multivariate Cholette's method, which generalizes the Denton’s one.

The univariate Cholette's benchmarking problem can easily be put in a state space form. See for example Harvey (1989). In JD+, the estimation of that model follows the diffuse Kalman filter of DK.

The multivariate procedure is a straightforward extension of the univariate solution, using a diffuse restricted Kalman filter, as defined -for instance- in Pizzinga (2009).

We describe the model in a first point. The univariate case, which is the basis of the multivariate case, is handled in a second point. We finally consider the multivariate extension in the last paragraph.

4.1. Model and notations

Given a set of initial time series

{𝑧𝑖𝑡}𝑖∈𝐼

we have to find the corresponding

{𝑥𝑖𝑡}𝑖∈𝐼

that respect temporal aggregation constraints, represented by

𝑋𝑖𝑇 = �𝑥𝑖𝑡𝑡∈𝑇

and contemporaneous constraints given by

𝑞𝑘𝑡 = �𝑤𝑘𝑗𝑥𝑗𝑡𝑗∈𝐽𝑘

or, in matrix form:

𝑞𝑘𝑡 = 𝑤𝑘𝑥𝑡

The Cholette's method consists in minimizing a quadratic penalty function that can take different forms. We consider in this paper the usual form:

��𝑥𝑖,𝑡 − 𝑧𝑖,𝑡�𝑧𝑖,𝑡�

𝜆 � − 𝜌 �𝑥𝑖,𝑡−1 − 𝑧𝑖,𝑡−1�𝑧𝑖,𝑡−1�

𝜆 ��

2

𝑖,𝑡

4.2. Univariate benchmarking

It is easy to see that the quadratic function of Cholette corresponds, from a formal point of view, to the sum of the square residuals generated by the auto-regressive process:

�𝑥𝑡−𝑧𝑡|𝑧𝑡|𝜆

� =𝛿𝑡

|𝑧𝑡|𝜆= 𝜇𝑡

𝜇𝑡 = 𝜌𝜇𝑡−1 + 𝜀𝑡

To simplify the notations, we will use hereafter

|𝑧𝑡|𝜆 = 𝛾𝑡

Starting from that observation, we can derive the benchmarked series from the following state space model:

the state vector is

𝛼𝑡 = �𝛿𝑡𝐶 𝛿𝑡

𝛾𝑡�

the measurement equation, only defined for 𝑡 = 𝑐 ∙ 𝑇 − 1 , is

𝛿𝑡𝐶 = 𝑍𝑡 ∙ 𝛼𝑡

where

𝑍𝑡 = (1 𝛾𝑡)

The transition equation is

𝛼𝑡+1 = 𝑇𝑡 ∙ 𝛼𝑡 + 𝑄𝑡

where

𝑇𝑡 = ��0 0

0 1� if 𝑡 + 1 = 𝑐 ∗ 𝑇

�1 𝛾𝑡0 1 � otherwise

�

𝑄𝑡 = �0 00 1�

The initial state vector is

𝛼−1 = (0 1)

and the initial (diffuse) variance matrices(using the DK notations) are

𝑃∞ = �0 00 1� ,𝑃∗ = �0 0

0 0�

The aggregation constraints are modified as follows

𝑋�𝑖𝑇 = 𝑋𝑖𝑇 −�𝑧𝑖𝑡𝑡∈𝑇

= �𝛿𝑖𝑡𝑡∈𝑇

Finally, the benchmarked series (𝑥𝑡) can easily be derived from the smoothed states (𝛼�𝑡):

𝑥𝑡 = 𝑧𝑡 + (0 𝛾𝑡) ∙ 𝛼�𝑡

4.3. Multi-variate benchmarking

The state space representation of the multi-variate benchmarking model is obtained by juxtaposing the different matrices of the univariate models (one for each series involved in the model) and by adding, for each linear constraint, the corresponding "measurement" equation.

More precisely, the state vector is

𝛼�𝑡 = �𝛿0𝑡𝐶 𝛿0𝑡

𝛾0𝑡⋯ 𝛿𝑛𝑡

𝐶 𝛿𝑛𝑡𝛾𝑛𝑡

�

After that the constraints have been adapted to correspond to differences in comparison with the actual data, the vector of "observations" becomes

𝜐𝑡 =

⎝

⎜⎜⎜⎜⎜⎛

⋮𝑞�0𝑡⋮𝑞�𝑘𝑡⋮𝛿0𝑠𝐶⋮𝛿𝑛𝑠𝐶⋮ ⎠

⎟⎟⎟⎟⎟⎞

and the measurement matrix is

��𝑡 =

⎩⎪⎪⎨

⎪⎪⎧ �

1 𝛾0𝑡 0 00 ⋱ 00 0 1 𝛾𝑛𝑡

� if 𝑡 = 𝑐 ∗ 𝑇 − 1

�⋯ 0 𝑤0𝛾𝑖𝑡 ⋯ ⋯⋯ ⋯ ⋯ ⋯⋯ ⋯ 𝑤𝑘𝛾𝑗𝑡 ⋯

� otherwise

�

In other words, the vector of the "observations" is composed of a sequence of contemporaneous constraints (for each t that doesn't correspond to the end of an aggregation period) and of temporal constraints1

As mentioned above, the other matrices of the system are just the juxtaposition of the matrices defined in the univariate case.

(for each t that corresponds to the end of an aggregation period); the matrices of the measurement equation are defined accordingly.

1 Of course, the aggregation constraints must respect the contemporaneous constraints.

By construction, the smoothed states contain MMSE estimates of the 𝛿𝑖𝑡 that respect all the constraints of the model.

4.4. Implementation

DK developed several features that can be used for an efficient implementation of the problem.

The JD+ solution uses the following routines:

• The multivariate model is handled through its univariate transformation, as defined in DK(see § 6.4)

• The smoothed states are computed by means of the disturbance smoother of DK (see § 5.4)

The performance of the resulting algorithm is highly dependent on the number of variables involved in the model (∝ 𝑛3). The other components of the problem (number of constraints, frequency of the series, and length of the series) are much less important (∝ 𝑛).

From a theoretical point of view, it should be noted that this approach may handle any set of linear restrictions (equalities), endogenous (between variables) or exogenous (related to external values), provided that they don't contain incompatible equations. The restrictions can also be relaxed for any period by considering their "observation" as missing. However, in practice, it appears that several kinds of contemporaneous constraints may yield unstable results. This is more especially true for constraints that contain differences (which is the case for non binding constraints). By using a special square root initialization, those problems have been significantly reduced.

Bibliography

DAGUM, B.E. and CHOLETTE P.A. (2006): “Benchmarking, Temporal Distribution, and Reconciliation Methods for Time Series”, Springer.

DE JONG P. (1991): "Stable Algorithms For the State Space Model", Journal of Time Series Analysis, 12, 2, 143-157.

DE JONG P. AND CHU-CHUN-LIN S. (2003): "Smoothing with an Unknown Initial Condition", Journal of Time Series Analysis, 24, 2, 141-148.

DI FONZO T. (2003): "Temporal disaggregation of economic time series: towards a dynamic extension", Working papers and Studies, European Communities.

DURBIN J. AND KOOPMAN S.J. (2001): "Time Series Analysis by State Space Methods". Oxford University Press.

__________ (2003): "Filtering and smoothing of state vector for diffuse state space models", Journal of Time Series Analysis, vol. 24, n°1, 85 - 98.

FRANKE M.K., KOOPMAN S.J. AND DE VOS A.F. (2010): "Likelihood functions for state space models with diffuse initial conditions”, Journal of Time Series Analysis, 31, 407-414.

GOMEZ V. AND MARAVALL A. (1993): "Initializing the Kalman Filter with Incompletely Specified Initial Conditions", WORKING PAPER 93/7, European University Institute.

__________ (1994): "Estimation, Prediction, and Interpolation for Nonstationary Series With the Kalman Filter", Journal of the American Statistical Association, vol. 89, n° 426, 611-624.

HARVEY, A.C. (1989): "Forecasting, Structural Time Series Models and the Kalman Filter", Cambridge University Press.

KOHN R. AND ANSLEY C.F. (1985): "Efficient estimation and prediction in time series regression models", Biometrika, 72, 3, 694-697.

KOOPMAN S.J. (1993): "Disturbance smoother for state space models", Biometrika, 80, 1, 117-126.

KOOPMAN S.J. AND HARVEY A. (1999): "Computing Observation Weights for Signal Extraction and Filtering".

PALATE J. (2005): ‘Reusable Components for Benchmarking Using Kalman Filters”, working papers and studies, European Communities

PIZZINGA A. (2009). Diffuse Restricted Kalman Filtering. 31º Meeting of the Brazilian Econometric Society.(http://virtualbib.fgv.br/ocs/index.php/sbe/EBE09/paper/viewFile/938/296).

PROIETTI T. (2004): "Temporal disaggregation by State Space Methods: Dynamic Regression Methods Revisited", working papers and studies, European Communities.

http://virtualbib.fgv.br/ocs/index.php/sbe/EBE09/paper/viewFile/938/296�

Annexe 1. State space forms of the different models

(1 0 0) residuals (Chow-Lin, Cholette) 𝜀𝑡 = 𝜌𝜀𝑡−1 + 𝜇𝑡

SSF:

𝑎𝑡 = [𝑦𝑡]

𝑍𝑡 = [1]

𝑇𝑡 = [𝜌]

𝑆𝑡 = [1]

𝑄𝑡 = [1]

𝑃0∗ = � 11−𝜌2

� or 𝑃0∗ = [1]

𝑃0∞ = [0]

(0 1 0) residuals (Fernandez, Denton) 𝜀𝑡 = 𝜀𝑡−1 + 𝜇𝑡

SSF:

𝑎𝑡 = [𝑦𝑡]

𝑍𝑡 = [1]

𝑇𝑡 = [1]

𝑆𝑡 = [1]

𝑄𝑡 = [1]

𝑃0∗ = [1]

𝑃0∞ = [1] or 𝑃0∞ = [0]

(1 1 0) residuals (Litterman) ∆𝜀𝑡 = 𝜌∆𝜀𝑡−1 + 𝜇𝑡

SSF:

𝑎𝑡 = �𝑦𝑡−1

𝑦𝑡 − 𝑦𝑡−1�

𝑍𝑡 = [1 1]

𝑇𝑡 = �1 10 𝜌�

𝑆𝑡 = �01�

𝑄𝑡 = [1]

𝑃0∗ = �0 00 1

1−𝜌2� or 𝑃0∗ = �0 0

0 1�

𝑃0∞ = �1 00 0� or 𝑃0∞ = �0 0

0 0�

Annexe 2. Equivalence of different implementations of the Denton’s method

Any state space model can be represented as a linear regression model

𝑦 = 𝑋𝛽 + 𝜇, 𝜇~𝑁(0,𝜎2Ω)

In the case of time invariant models, we have more especially

𝑋𝑡 = 𝑍(𝑇𝑡)𝐵0

A general expression for Ω cannot be easily derived, because it depends on all the matrices of the system. However, it can be generated in a recursive way.

Model-based Denton For the “diffuse Denton”, we have 𝑍 = 𝑇 = 𝐵0 = [1], which yields:

𝑋𝑡 = 1

Ω = (∆′∆)−1 ∆= �

1 0 0−1 1 00 ⋱ ⋱

� 𝑜𝑟 ∆−1= �1 0 01 1 01 1 ⋱

�

so that

Ω =

⎣⎢⎢⎢⎡1 1 1 1 11 2 2 2 21 2 3 3 31 2 3 4 41 2 3 4 ⋱⎦

⎥⎥⎥⎤

It is immediate that that model corresponds to the model “Denton with 0-initialization + constant” (same state space form, except for the diffuse initialization).

Original Denton In the case of the matrix formulae, the original penalty function is written

𝑓(𝜃) = 𝜃′∆′∆𝜃, to be minimized under the aggregation constraints.

It corresponds in an obvious way to the “Denton with 0-initialization (no constant)” model.

Modified Denton The modified Denton corresponds to the penalty function

𝑓�𝜃�� = 𝜃�′∆𝑀′∆𝑀𝜃�

Where

∆𝑀= �−1 1 00 −1 10 ⋱ ⋱

�

The penalty function corresponding to the model-based Denton (0-initialization + mean) can also be written as (the aggregation constraints are omitted)

𝑓�𝜃,� 𝜇� = �𝜃�0 − 𝜇�2 + ��𝜃�𝑡 − 𝜇� − �𝜃�𝑡−1 − 𝜇�2�𝑇

𝑡=1

𝑓�𝜃,� 𝜇� = �𝜃�0 − 𝜇�2 + ��𝜃�𝑡 − 𝜃�𝑡−1�2

𝑇

𝑡=1

Which is minimal for 𝜃�0 = 𝜇. In other words, if we write

𝑓�𝜃�� = ∑ �𝜃�𝑡 − 𝜃�𝑡−1�𝑇𝑡=1 ,

we have:

min𝜃�𝑓�𝜃�� = min

𝜃,�𝜇𝑓�𝜃,� 𝜇�

min𝜃� 𝑓�𝜃�� is exactly the modified Denton method and is thus equivalent to the model-based Denton with 0-initialization + mean or to the diffuse model-based Denton.

In summary:

Original Denton

Modified Denton

Model-based Denton,

0 initialization

Model-based Denton,

0 initialization + mean

Model-based Denton,

Diffuse initialization

1.

2b - JD+, Calendarization.docx


JD+ Calendarization

Palate Jean

1/22/2015

2.


The “NbDemetra-Benchmarking” plug-in provides a module on calendarization (see Quenneville et al. for technical details).

A new calendarization module is created through the following command.

The calendarization problem

The calendarization is the problem of transforming values from a flow time series observed over varying time intervals into values that cover calendar intervals such as month, quarter and year. The solution presented in the graphical interface is based on the Denton’s benchmarking method. It is implemented by means of a state space model. From a technical point of view, a smoothed daily series (with an underlying random walk model) is first computed, using the constraints imposed by the observed values. The daily series is then transformed into the selected frequency. The software computes standard deviations for the daily and for the aggregated series.

Graphical interface

3.


The user can import data either by clipboard (format as below) or introduce the figures using the graphical interface. The time intervals for the observations don’t need to be contiguous. However, they have to be ordered and they can’t overlap.

Format for clipboard importation

03/03/2000 30/11/2000 33 17/01/2001 06/05/2001 28 09/05/2001 01/06/2001 -6 22/08/2001 02/01/2002 45 17/02/2002 09/09/2002 77

The user can also specify weights that will be attributed to the different days of the week. See the reference paper for more information.

Applications

Simple applications of the algorithm could be:

− Transforming non calendar yearly figures into calendar yearly figures (see screenshot below)

− Transforming weekly figures into monthly figures (perhaps taking into account the week-ends)

− …

4.


Bibliography

Quenneville, B., Picard, F., Fortier, S. (2013), “Calendarization with interpolating splines and state space models”, Journal of the Royal Statistical Society, Series C (Applied Statistics), vol. 62, Issue 3, pages 371-399.


JD+ Multivariate Cholette algorithm (GUI)

Jean Palate

1/22/2015

The “NbDemetra-Benchmarking” plug-in provides a module on the multi-variate Cholette method (see the technical document on Temporal Disaggregation and Benchmarking for more details).

A new benchmarking module is created through the following command.

The current GUI for the Multi-variate Cholette contains a very rudimentary editor for defining the constraints, which can be temporal or contemporaneous. The editor is available through the properties window.

We describe it shortly in this document.

Contemporaneous constraints

The weighted average of some series must be equal to a specified series or to a given value.

Users can use wild cards (?) for selecting series. A series cannot appear more than one time in the equation.

Syntax:

𝑦 = [𝑎1] ∗ 𝑥1 + ⋯+ [𝑎𝑛] ∗ 𝑥𝑛

𝑐 = [𝑎1] ∗ 𝑥1 + ⋯+ [𝑎𝑛] ∗ 𝑥𝑛

𝑥𝑖 𝑐𝑎𝑛 𝑐𝑜𝑛𝑡𝑎𝑖𝑛 𝑤𝑖𝑙𝑑 𝑐𝑎𝑟𝑑𝑠 (? 𝑜𝑛𝑙𝑦)

The binding series (if any) is not modified. It cannot appear in another equation, except as binding series.

Examples:

𝑠1 = 2 ∗ 𝑠2 + 3.2 ∗ 𝑠3 (1) 0 = 𝑠1 − 𝑠2 − 𝑠3 − 𝑠4 (2)

10000 = 𝑠? (3)

To be noted that equation 1 is incompatible with the other one (s1 is at the same time a binding series and a benchmarked series)

Temporal constraints

The sum of a given series must be equal to a given aggregated series.

Syntax:

𝑦 = 𝑠𝑢𝑚(𝑥)

Example

Suppose that we have the following model (upper cases for yearly series, lower case for quarterly series):

Y= C+G+I+S+X-M p1+m=p2+c+g+i+x

We should write the constraints as:

M=sum(m) C=sum(c) G=sum(g) I=sum(i) X=sum(x) 0=p1+m-p2-c-g-i-x

JDEMETRA+, SEASONALITY TESTS

1.

3b - JD+_Seasonality.docx


JD+ Seasonality tests

De Antonio David, Palate Jean

12/16/2014

2.


Introduction

JD+ contains numerous tests on seasonality. Some of them are used in the automatic model identification used in Tramo for testing the presence of a seasonal component in the Arima model. Other tests are used in the diagnostics panels of TramoSeats and of X13. All of them are proposed in the “Seasonality tests” panel of JD+, which is launched by means of the command “Statistical methods ->Seasonal adjustment->Tools->Seasonality tests”. So, we will describe the seasonality tests through that tool.

By default the tests are performed on the complete series in level, after a differencing of order 1. The user can select by means of the properties window a previous log transformation, another differencing order (0 should be used for stationary series like residuals…) or another time span (most tests in the diagnostics of X13 and of Tramo-Seats will take into account the last 8 years).

Description

3.


The tests are executed by dropping a time series in the upper part of the panel (or by a double click on some series, when that feature is enabled).

We describe shortly bellow the different tests (tests used in the AMI of Tramo are marked by an asterisk).

Auto-correlations at seasonal lags (*)

A Ljung-Box test is computed on the first two seasonal lags. The test is a Chi2 computed on the square of the auto-correlations at lags freq and 2*freq. Only positive auto-correlations are taken into account. Despite of its very simple structure, it has been found that this test is especially efficient and robust.

Friedman test (*)

The Friedman test is a non-parametric test based on the rank of the observations by year. It is computed as follows:

• The observations are replaced by their rank in each year • A statistic similar to a one-way ANOVA is computed, using the ranks as values and the

periods as groups.

In other words, the test will be positive if the rank of the observations in each year is significantly linked to their period.

Kruskall-Wallis test

The Kruskall-Wallis test is also a one-way analysis of the variance by rank. The ranks are computed in this case on all the observations and the one-way analysis of the variance tests their dependency against the period of the year they are related to.

Spectral peaks (*)

Two different diagnostics are considered. The first one is based on the estimation of the spectrum of a long auto-regressive model that fits the series. It is identical to the tests introduced in the X12/X13 algorithms. Further information can be found in the X13 reference manual.

The second diagnostic is based on the (smoothed) Fourier transform of the auto-correlations of the series.

The spectral peaks tests need sufficiently long series (>=8 years).

4.


Periodogram

The tests are performed on the periodogram (Fourier transformation) of the series at the Fourier frequencies. A first test is based on the maximum of the periodogram on or around the seasonal frequencies. Another one is based on the sum of the values of the periodogram on or around the seasonal frequencies.

Strictly speaking, the statistical tests are only valid against the hypothesis that the (transformed) series is a white noise. As the spectral peaks, they don’t perform well for short series.

F-Test (regression with fixed dummies)(*)

An ARIMA model (0 1 1) (0 0 0) with mean and with seasonal dummies is estimated on the original (or log-transformed) series. Differencing orders are not taken into account.

The test is a joint F-test on the coefficients of the seasonal dummies.

This test is not suited to long series, with moving seasonality. However, it performs especially well for short series (4-6 years)

Implementation of the seasonality tests

The seasonality tests are implemented in the classes indicated in the table below. People interested in the details of the tests should consult the corresponding files.

Test Short description Implementation classes

Qs Test Test on the seasonal auto-correlations ec.satoolkit.diagnostics.QsTest,

ec.satoolkit.diagnostics.

LjungBoxTest

F-test on seasonal dummies

Estimation of a model with seasonal dummies. Joint F-test on the coefficients of the dummies

ec.satoolkit.diagnostics.FTest

Friedman test Non parametric test

(“ANOVA”-type)


FriedmanTest

Kruskall-Wallis test

Non parametric test on the ranks ec.satoolkit.diagnostics.

KruskallWallisTest

“X12” test on seasonality

Combined test on the presence of identifiable seasonality


CombinedSeasonalityTest

5.


Test on a Tukey spectrum

Identification of seasonal peaks on a Tukey spectrum


TukeySpectrumPeaksTest,

ec.tstoolkit.data.

BlackmanTukeySpectrum

Test on the auto-regressive spectrum

Tests on auto-regressive spectrum (Tramo or X12-like)


AutoRegressiveSpectrumTest,

ec.tstoolkit.timeseries.analysis.SpectralDiagnostic

Test on periodogram

Tests on the sum or the max of a periodogram at seasonal frequencies


PeriodogramTest

Seasonality tests Entry point for several seasonality tests (Tramo-like)

ec.tstoolkit.modelling.arima.tramo.

SeasonalityTests

JDEMETRA+, DIAGNOSTICS


JD+ Quality diagnostics

Jean Palate

12/16/2014

Demetra+ provides a set of quality diagnostics on seasonal adjustment. In the first part of this document, we shortly describe them. In the second part, we consider the design of the classes that provide the diagnostics. We also explain how the current diagnostics can be extended.

Generalities

The quality diagnostics that can be built on the different seasonal adjustment procedures are very heterogeneous. Moreover, their interpretation might be difficult for many users. That is why we have chosen to give a summary of information they provide by means of a very simple qualitative indicator, which is defined in the next table. That indicator is used in the batch processing module of JD+. Such a simple approach doesn't prevent that much more complicated and much richer information could be provided to the user through more sophisticated interface. The interactive module offers many details on the different diagnostics.

Meaning of the quality indicator1

Value

Meaning Undefined The quality is undefined: unprocessed test, meaningless test, failure in the

computation of the test... Error There is an error in the results. The processing should be rejected (for

instance, it contains aberrant values or some numerical constraints are not fulfilled

Severe There is no logical error in the results but they should not be accepted for some statistical reasons

Bad The quality of the results is bad, following a specific criterion, but there is no actual error and the results could be used.

Uncertain The result of the test is uncertain. Consider it with caution Good The result of the test is good

Several qualitative indicators can be combined following the next rules.

Given a set of n diagnostics, the sum of the results is:

Sum Rules Undefined All diagnostics are Undefined Error There is at least 1 error Severe There is at least 1 "severe" diagnostic but no error Bad No error, no severe diagnostics; the average of the (defined) diagnostics

(Bad=1, Uncertain=2, Good=3) is < 1.5 Uncertain No error, no severe diagnostics; the average of the (defined) diagnostics

(Bad=1, Uncertain=2, Good=3) is in [1.5, 2.5[ Good No error, no severe diagnostics; the average of the (defined) diagnostics

(Bad=1, Uncertain=2, Good=3) is ≥ 2.5

1 The model also contain a flag "Accepted", which simply means that the statistician decided to accept the results, no matter what are the different diagnostics.

So, errors and severe diagnostics are absorbent results. The global "quality" indicator of the seasonal adjustments displayed in the multi-processing window is the sum of all the defined quality diagnostics, using the rules defined above.

Finally, diagnostics can throws warnings, which are indicated by exclamation marks and tooltips in the multi-processing output panel.

Users should consider the quality indicator as a tool to detect rapidly possible problems in a large set of processing. For important series, a more complete examination of the results should always be considered.

Description of the diagnostics of JD+

The different diagnostics are put in several groups, corresponding to different modules (classes).

The current software contains diagnostics on the coherence of the decomposition ("Basic checks" group), on visual spectral inspection ("Visual spectral analysis"), on the residuals of the RegArima pre-processing ("RegArima residuals" group), on the residual seasonality ("Residual seasonality" group) and on the decomposition ("Seats" group for Tramo-Seats, M-Statistics group for X12).

Most of them use parameters (usually thresholds) that can be modified by means of the options dialog box (TO DO). Finally, each group of diagnostics might be disabled, when it is considered as meaningless.

We describe below the different items of the diagnostics, using the default options.

Basic checks

Definition

A first set of diagnostics consists in verifying that the definition constraints implied by the model of the series are well respected (see the description of the model for more details).

The maximum of the absolute differences is computed for the different equations and related to the Euclidean norm of the initial series (Q).

Results of the test

Q (see above) Diagnostic > 0.000001 Error <= 0.000001 Good

Annual totals

The annuals totals of the original series and those of the seasonally adjusted series are compared.

The maximum of their absolute differences is computed and related to the Euclidean norm of the initial series.

Results of the test

Q (see above) Diagnostic > 0.5 Error ]0.1, 0.5] Severe ]0.05, 0.1] Bad ]0.01, 0.05] Uncertain <=0.01 Good

The fact the test above throws an error doesn’t mean that the computation is wrong. It could also indicate some limits of the method. See below for an actual example.

production of sugar in Belgium

Warnings

A warning is thrown when the series is short (less than 7 years)

Visual spectral analysis

The visual spectral analysis used in Demetra+ follows the method developed at the US Census Bureau. The default spectrum estimator used to detect seasonal and trading day effects is an autoregressive spectral estimator 𝑠�(𝜆), expressed in decibel units (see appendix 1).

The visual inspection method consider the frequencies 𝜆 = 𝜋𝑖60

, 0 ≤ 𝑖 ≤ 60. An empirically criterion

of ”visual significance” is determined as follows. To be ”visually significant”, the value 𝑠�(𝜆) at a trading day or seasonal frequency must be above the median of the plotted values of 𝑠�(𝜆) and must

be larger than both neighboring values by at least 𝛼 × (��𝑚𝑎𝑥 − ��𝑚𝑖𝑛), with 𝛼 = 652

by default.

It should be noted that the auto-regressive diagnostics of JD+ are computed on the last 8 years of each series as it is done in X12 (but contrary to the other diagnostics).

Results of the test

Presence of a visual peeks Diagnostic On irregular and on sa Severe On irregular or on sa Bad No visual peek Good

Warnings

A warning is displayed when the differenced original series doesn't contain seasonal peak, which means that it should probably not be seasonally adjusted.

Residuals diagnostics

Several tests are computed on the residuals of the RegArima model. The exact definition of what we mean by "residuals" should be clarified. Indeed, X12 and Tramo are based on different estimation procedures of the likelihood of the RegArima models, which lead to slightly different definitions of the residuals.

In most cases, the different sets of residuals yield slightly different diagnostics. However, their global messages are near always very similar.

JD+ uses a solution - "the full residuals" - which is also available in Tramo.

Normality test

The joint normality test (which combines skewness and kurtosis tests) is the Doornik-Hansen test (see appendix 3), which is distributed as a 𝜒2(2).

Results of the test

Pr(𝜒2(2)>val) Diagnostic <0.01 Bad [0.01, 0.1[ Uncertain ≥0.1 Good

Independence test

The independence test is the Ljung-Box test (see appendix 4), which is distributed as 𝜒2(𝑘 − 𝑛𝑝),

where k depends on the frequency of the series (24 for monthly series, 8 for quarterly series, 4*freq for other frequencies) and np is the number of hyper-parameters of the model (number of parameters in the Arima model)

Results of the test

Pr(𝜒2(𝑘 − 𝑛𝑝)>val) Diagnostic <0.01 Bad [0.01, 0.1[ Uncertain ≥0.1 Good

Spectral tests

The software provides tests based on the periodogram of the residuals, for the trading days frequencies and for the seasonal frequencies.

The periodogram is computed at the so-called Fourier frequencies, which present good statistical properties. Under the hypothesis of Gaussian white noise of the residual, it is possible to derive simple test on the periodogram, around specific (groups of) frequencies. The exact definition and the used test are described in the appendix 5.

Results of the test

P(stat>val) Diagnostic <0.001 Severe [0.001, 0.01[ Bad [0.01, 0.1[ Uncertain ≥0.1 Good

Out-of-sample diagnostics

The out-of-sample diagnostics follow the method developed in Tramo.

Using the linearized series of the model estimated on the whole series, the model (ARIMA [+ mean]) are re-estimated on a shorter time span (the last 1.5 year is dropped).

The in-sample errors (n2

The means tests compare the sample means to 0, using the in-sample variance.

-nback data) and of the out-of-sample errors (nback) are computed by the Kalman filter (one-step-ahead forecast errors). Their sample mean and variance are then computed.

The variance test is the usual F test of equality of two sample variances. That test should be used with caution (when the distribution of the residuals is far to be normal).

2 N is adjusted by -1 in the case of a mean effect.

Results of the test

Pr(𝒂𝒃𝒔(𝑇(𝑛 − 𝑛𝑏𝑎𝑐𝑘))>val) or Pr(𝐹(𝑛𝑏𝑎𝑐𝑘,𝑛 − 𝑛𝑏𝑎𝑐𝑘))>val) Diagnostic <0.01 Bad [0.01, 0.1[ Uncertain ≥0.1 Good

Seats diagnostics

JD+ provides some model-based diagnostics for Seats, similar to those provided in the original program. They correspond to measures of over/under estimation of the seasonal and of the irregular components and of their cross-correlation. The variances of the theoretical estimators of the (stationary) components and of their estimates are compared; the Bartlett's approximation is used to build statistical tests on those measures. More detailed information, on the other components and on their auto-correlation functions, can be found in the interactive module.

It should be noted that the considered models are those of the final estimators and that the complete time span of the estimates is used, though the (preliminary) models for the first and for the last observations can present significantly different properties.

Results of the test

Pr(N>val) Diagnostic <0.01 Bad [0.01, 0.05[ Uncertain ≥0.5 Good

Warnings

Warning are also displayed when parameters were modified (quasi-unit roots in the moving average polynomials) or/and when a non-decomposable model was changed by Seats.

X11 diagnostics (M-statistics)

The M-diagnostics correspond to the statistics “Q” and “Q-M2” developed by the US Census Bureau.

See for instance Ladiray-Quenneville [1999] for a complete description of the tests.

Results of the test

M Diagnostic ≥2 Severe [1, 2[ Bad <1 Good

Residual seasonality diagnostics

The residual seasonality diagnostic corresponds to the test developed in X12/X13

The F-Test on stable seasonality (see appendix 6) is computed on the differences of the seasonally adjusted series (component CSA, see above) and on the irregular component (CI, see above).

The differencing is done with a lag of 3 periods for monthly series and with a lag of 1 period in the other cases. For the seasonally adjusted series, one test is computed on the complete time span and another one on the last 3 years.

Results of the test

Pr(F>val) Diagnostic <0.01 Severe [0.01, 0.05[ Bad [0.05, 0.1[ Uncertain ≥0.1 Good

TO DO

Maravall has introduced in the last releases of Tramo numerous tests on seasonality, which should complete this diagnostics. See also D. Findley (internal document). Most of the new tests are already displayed in the details of the diagnostics. We could complete the current diagnostics by the QS test of Maravall and by the fixed seasonal effects test on the last years (F-test) of the US census Bureau (probably the two most robust tests).

Design

For each set of diagnostics, JD+ contains 3 classes. By convention, they names are XXXDiagnostics,

XXXDiagnostcsFactory, XXXDiagnosticsConfiguration

The configuration class contains the entire settings specific to a set of diagnostics; the factory, which contains a configuration object, must be able to create a corresponding diagnostics object for a given SA processing.

All the current diagnostic factories are stored in the central SaManger instance.

The definition of the different classes are formalized by several generic interfaces, as displayed in the next diagram

Implementation classes

We list below the current implementations of diagnostics on seasonal adjustment

Diagnostics Classes Residual seasonality diagnostics ec.tss.sa.ResidualSeasonalityDiagnostics Seats diagnostics ec.tss.sa.SeatsDiagnostics M_Statistics ec.tss.sa.MDiagnostics Out of sample diagnostics ec.tss.sa.OutOfSampleDiagnostics

Visual spectral peaks ec.tss.sa.SpectralDiagnostics Outliers ec.tss.sa.OutliersDiagnostics RegArima residuals diagnostics ec.tss.sa.ResidualsDiagnostics Basic checks ec.tss.sa.CoherenceDiagnostics

Adding a new diagnostic

We explain below the different steps to add a completely new set of diagnostics. The example will use the new seasonality tests of Tramo to provide Qs tests and F-tests on regression models with seasonal dummies applied to the seasonally adjusted and on the irregular series.

1. Define a configuration class that will contain the parameters of the test (to be displayed in the future in a graphical interface). That class should remain very light. Moreover, it should implement the Cloneable interface.

public class MyDiagnosticsConfiguration implements Cloneable { public static final double SEV = .001, BAD = .01, UNC = .05; private double sev_ = SEV, bad_ = BAD, unc_ = UNC; private boolean enabled_ = true; @Override public MyDiagnosticsConfiguration clone() { try { return (MyDiagnosticsConfiguration) super.clone(); } catch (CloneNotSupportedException ex) { return null; } } public double getSevereThreshold() { return sev_; } public double getBadThreshold() { return bad_; } public double getUncertainThreshold() { return unc_; } public boolean isEnabled() { return enabled_; } public void setEnabled(boolean enabled) { enabled_ = enabled; } …

}

2. Define a factory class that will create the actual diagnostics, using a given configuration

public class MyDiagnosticsFactory implements ISaDiagnosticsFactory { static final String NAME="New Seasonality tests", DESC="New Seasonality tests"; private MyDiagnosticsConfiguration config_; public MyDiagnosticsFactory() { config_ = new MyDiagnosticsConfiguration(); } public MyDiagnosticsFactory(MyDiagnosticsConfiguration config) { config_ = config; } @Override public Scope getScope() {//Used to organize the diagnostics return Scope.Final; } @Override public int getOrder() {{//Used to organize the diagnostics return 0; //High priority } @Override public void dispose() { } @Override public String getName() { return NAME; } @Override public String getDescription() { return DESC; } @Override public boolean isEnabled() { return config_.isEnabled(); } @Override public void setEnabled(boolean enabled) { config_.setEnabled(enabled); } @Override public Object getProperties() { // To be shown in a graphical interface return config_.clone(); } @Override public void setProperties(Object obj) {// Set the new configuration if (obj instanceof MyDiagnosticsConfiguration) { MyDiagnosticsConfiguration nconfig = (MyDiagnosticsConfiguration) obj; config_ = nconfig.clone(); } } @Override public IDiagnostics create(CompositeResults rslts) { // Generate the diagnostics return MyDiagnostics.create(rslts, config_); }

}

3. Define the actual diagnostics class

public class MyDiagnostics implements IDiagnostics { static final String QS_SA = "Qs test on SA", QS_I = "Qs test on I", FTEST_SA = "F-Test on SA (seasonal dummies)", FTEST_I = "F-Test on I (seasonal dummies)"; static final String[] ALL = new String[]{QS_SA, QS_I, FTEST_SA, FTEST_I}; private StatisticalTest qs_sa, qs_i, f_sa, f_i; // All the computations are done here static IDiagnostics create(CompositeResults rslts, MyDiagnosticsConfiguration config) { try { MyDiagnostics test = new MyDiagnostics(); TsData sa = rslts.getData(ModellingDictionary.SA_LIN, TsData.class); TsData i = rslts.getData(ModellingDictionary.I_LIN, TsData.class); if (sa == null && i == null) { return null; } if (sa != null) { SeasonalityTests satest = SeasonalityTests.seasonalityTest(sa, 1, true, true); test.qs_sa = satest.getQs(); FTest F = new FTest(); if (F.test(sa)) { test.f_sa = F.getFTest(); } } if (i != null) { SeasonalityTests itest = SeasonalityTests.seasonalityTest(i, 0, true, true); test.qs_i = itest.getQs(); FTest F = new FTest(); if (F.test(i)) { test.f_i = F.getFTest(); } } return test; } catch (Exception err) { return null; } } @Override public String getName() { // The name that will appear in the diagnostics return MyDiagnosticsFactory.NAME; } @Override public List<String> getTests() { // The tests that will appear in the diagnostics ArrayList<String> tests = new ArrayList<String>(); if (qs_sa != null) { tests.add(QS_SA); } if (f_sa != null) { tests.add(FTEST_SA); } if (qs_i != null) { tests.add(QS_I); } if (f_i != null) { tests.add(FTEST_I); } return tests; } @Override

public ProcQuality getDiagnostic(String test) { // The quality indicator of the given test switch (test) { case QS_SA: return quality(qs_sa); case FTEST_SA: return quality(f_sa); case QS_I: return quality(qs_i); case FTEST_I: return quality(f_i); default: return ProcQuality.Undefined; } } @Override public double getValue(String test) { // The value associated with the given test (displayed in the summary) switch (test) { case QS_SA: return pvalue(qs_sa); case FTEST_SA: return pvalue(f_sa); case QS_I: return pvalue(qs_i); case FTEST_I: return pvalue(f_i); default: return Double.NaN; } } @Override public List<String> getWarnings() { // Possible warnings return Collections.EMPTY_LIST; } // implementation details private ProcQuality quality(StatisticalTest test) { if (test == null) { return ProcQuality.Undefined; } double pval = test.getPValue(); if (pval < .001) { return ProcQuality.Severe; } else if (pval < .01) { return ProcQuality.Bad; } else if (pval < .05) { return ProcQuality.Uncertain; } else { return ProcQuality.Good; } } private double pvalue(StatisticalTest test) { return test == null ? Double.NaN : test.getPValue(); } }

4. Add an instance of the new diagnostics factory into the current SaManager. The example below uses a feature provided by NetBeans. Other solutions are possible.

public class Installer extends ModuleInstall{ @Override public void restored() { super.restored(); ec.tss.sa.SaManager.instance.add(new MyDiagnosticsFactory()); } }

// Don’t forget to add the following line in the manifest.mf file of the project // OpenIDE-Module-Install: be/nbb/demetra/tutorial/plugin/sadiags/Installer.class

The new diagnostics will be available for any seasonal adjustment processing.

Appendices

1. Auto-regressive spectrum

For the series 𝑥𝑡 (for example, the model residuals), autoregressive spectrum estimates (in decibel units) have the form

��(𝜆) = 10 log10 �𝜎𝑚2

2𝜋�1−∑ ��𝑗𝑒𝑖𝑗𝜆𝑚𝑗=1 �

2� , 0 ≤ 𝜆 ≤ 𝜋,

where the coefficient estimates ��𝑗 are those of the linear regression of 𝑥𝑡 − �� on 𝑥𝑡−𝑗 − ��

1 ≤ 𝑗 ≤ 𝑚, with �� = 1𝑛∑ 𝑥𝑗𝑛𝑗=1 and where 𝜎𝑚2 is the sample variance of the resulting regression

residuals.

JD+ uses, like X12, 𝑚 = 30.

2. Doornik-Hansen test.

The Doornik-Hansen is defined as follows:

let s = skweness, k=kurtosis of the n (non missing) residuals

We make the following transformations:

Transformation of the skewness (D'Agostino)

𝛽 =3(𝑛2 + 27𝑛 − 70)(𝑛 + 1)(𝑛 + 3)

(𝑛 − 2)(𝑛 + 5)(𝑛 + 7)(𝑛 + 9)

𝜔2 = −1 + �2(𝛽 − 1)

𝛿 =1

�0.5 log𝜔2

𝑦 = 𝑠�(𝜔2 − 1)(𝑛 + 1)(𝑛 + 3)

12(𝑛 − 2)

𝑧1 = 𝛿 log �𝑦 + �𝑦2 − 1�

Transformation of the kurtosis (Wilson-Hilferty)

𝛿 = (𝑛 − 3)(𝑛 + 1)(𝑛2 + 15𝑛 − 4)

𝑎 =(𝑛 − 2)(𝑛 + 5)(𝑛 + 7)(𝑛2 + 27𝑛 − 70)

6𝛿

𝑐 =(𝑛 − 7)(𝑛 + 5)(𝑛 + 7)(𝑛2 + 2𝑛 − 5)

6𝛿

𝑙 =(𝑛 + 5)(𝑛 + 7)(𝑛3 + 37𝑛2 + 11𝑛 − 313)

12𝛿

𝛼 = 𝑎 + 𝑐 ∙ 𝑠 ∙ 𝑠

𝜒 = 2𝑙(𝑘 − 1 − 𝑠2)

𝑧2 = �√9𝛼� �1

9𝛼− 1 + �

𝜒2𝛼

3�

𝐷𝐻 = 𝑧12 + 𝑧2 2 ~ 𝜒2(2)

3. Ljung-Box test.

The Ljung-Box test is defined as follows:

let 𝜌𝑗 = the sample autocorrelation at rank k, of the n residuals is

𝐿𝐵(𝑘) = 𝑛 ∙ (𝑛 + 2)�𝜌𝑗2

𝑛 − 𝑗

𝑘

𝑗−1

If the residuals are random, It should be distributed as 𝜒2(𝑘 − 𝑛𝑝) where np is the number of hyper-parameters of the model from which the residuals are derived.

4. Periodogram

Definition of the periodogram

The periodogram of the series {𝑦𝑡} 1<𝑡≤𝑛 is computed as follows:

1. The 𝑦𝑡 are standardized

𝑦� =∑ 𝑦𝑡𝑡≤𝑛𝑡=1𝑛

𝜎�𝑦2 =∑ (𝑦𝑡 − 𝑦�)2𝑡≤𝑛𝑡=1

𝑛

𝑧𝑡 =(𝑦𝑡 − 𝑦�)𝜎�𝑦

2. The periodogram is computed on the standardized 𝑧𝑡

𝐼𝑛,𝑧(𝜆) = 2𝑛�𝐶𝑛,𝑧

2 (𝜆) + 𝑆𝑛,𝑧2 (𝜆)�

where

𝐶𝑛,𝑧(𝜆) = ∑ 𝑐𝑜𝑠(𝜆𝑡)𝑛𝑡=1 𝑧𝑡 and 𝑆𝑛,𝑧(𝜆) = ∑ 𝑠𝑖𝑛(𝜆𝑡)𝑛

𝑡=1 𝑧𝑡

Periodogram at the Fourier frequencies

The Fourier frequencies are defined by

𝜆𝑗 =2𝜋𝑗𝑛

, 0 < 𝑗 ≤ ⌊𝑛/2⌋

If the 𝑧𝑡 are iid 𝑁(0,1), it is easy to see that the corresponding quantities 𝐼𝑛,𝑧�𝜆𝑗� are iid 𝜒2(2).

We have indeed that

�𝑒𝑖𝑡�𝜆𝑗−𝜆𝑘� = �𝑛 𝑖𝑓 𝑗 = 𝑘0 𝑖𝑓 𝑗 ≠ 𝑘

�𝑛

𝑡=1

and

∑ 𝑐𝑜𝑠2�𝜆𝑗𝑡�𝑛𝑡=1 = ∑ 𝑠𝑖𝑛2�𝜆𝑗𝑡�𝑛

𝑡=1 = 𝑛/2,

so that �2𝑛𝐶𝑛,𝑧�𝜆𝑗� and �2

𝑛𝑆𝑛,𝑧(𝜆𝑘) are uncorrelated 𝑁(0,1) random variables.

Test on the periodogram

Under the hypothesis that 𝑧𝑡 is a Gaussian white noise, and considering subset J of Fourier frequencies, we have:

𝑃𝑟 �maxj∈J

𝐼𝑛,𝑧�𝜆𝑗� ≤ 𝛼 � = �1 − 𝑒−𝛼/2�#𝐽

If we consider the sets of Fourier frequencies on or near the trading days frequencies on one side and on or near the seasonal frequencies on the other side, we can use the above formula as rough tests on the absence of trading days/seasonal effects in the considered series.

The software considers the Fourier frequencies which are on or near the following frequencies (the two nearest frequencies are chosen):

Annual frequency Seasonal Trading days 12 2π/12, 4π/12, 6π/12, 8π/12, 10π/12 d 6 2π/6, 4π/6 d 4 2π/4 d, 1.292, 1.850, 2.128 3 - d 2 - d

where d is computed as follows, if s is the frequency of the series:

𝑛 = 365.25/𝑠

𝑑 = 2𝜋/7 ∙ (𝑛 𝑚𝑜𝑑𝑢𝑙𝑜 7)

5. Stable seasonality test

The stable seasonality test is a F-test used in the context of a single-factor ANOVA model, where the different categories are defined by the different periods (month, quarter...) of the considered series.

The F-test measures the probability that the observations for each period come from distributions that have the same mean.

If we write 𝑠, the number of periods by year, 𝑛𝑘 the number of observations for the period 𝑘 ( ∑ 𝑛𝑘 = 𝑛𝑠𝑘=1 , the total number of observations), we have the following decomposition of the

variance:

1𝑛��𝑥𝑘,𝑖 − ��2

𝑛𝑘

𝑖=1

=1𝑛�𝑛(��𝑘 − ��)2𝑠

𝑘=1

𝑠

𝑘=1

+1𝑛��𝑥𝑘,𝑖 − ��𝑘�

2𝑛𝑘

𝑖=1

= 𝑆𝐴2 + 𝑆𝐵2

𝑛

𝑠

𝑘=1

The test is then

𝐹 = 𝑆𝐴2/(𝑠−1)𝑆𝐵2(𝑛−𝑠) ~ 𝐹(𝑠 − 1,𝑛 − 𝑠)

STATE-SPACE MODELLING WITH JDEMETRA+

Moving Trading-Day Effects with X-12-Arima and Tramo-Seats

Ketty ATTAL-TOUBERT

, Dominique LADIRAY

, Marco MARINI

A large part of economic indicators related to production, imports-exports, inventories and sales are

affected by trading-day or calendar variations. Trading-day effects reflect variations in monthly time

series due to the changing composition of months with respect to the numbers of times each day of the

week occurs in the month. These variations are systematic and can strongly influence the short-term

variations of the series and the month-to-month comparisons.

A trading-day regression model with Arima errors, derived from the simple model proposed by Young

(1965), is currently used by X-12-Arima version 0.3 and Tramo-Seats. This model assumes that the

trading-day coefficients are constant over time. As long as the relative weight of daily activities is

fixed on the span of the series, this deterministic model gives reasonable estimates. However, this is

not always a realistic assumption. In the European Union, Member states legislations used to prohibit

the opening of retail trade stores on Sunday. This situation, as well as consumers’ shopping patterns,

has changed substantially in recent years. Seasonal adjustment practitioners sometimes deal with this

issue by restricting the length of the series to which the trading-day model is fit. However, this can

provide only a crude approximation to trading-day effects that vary through time.

Stochastic models for time-varying trading-day coefficients have been proposed in the literature and

some of them are already implemented in seasonal adjustment procedures like STAMP, BAYSEA,

DECOMP and Reg-Component.

In this short paper we explore a very simple strategy to mimic time-varying coefficient models in X-

12-Arima and Tramo-Seats. It is important to note that Demetra+ already implements this strategy and

that the next version of Tramo-Seats should incorporate a time-varying coefficient trading-day model1.

1 Modeling Trading-Day Effects

1.1 The basic model with fixed coefficients

It will be assumed below, following the notation of Findley et al. (1998), that the jth day of the week

has an effect j where, for example, j=1 refers to Monday, j=2 refers to Tuesday, etc., and j=7 refers

to Sunday. Each j represents for example the average sales for one day j. If jtD represents the

number of days j in the month t, the length of the month will be

7

1j

jtt DN and the cumulative

effect for that month, the total sales of the month, will be:

7

1j

jtj D . We also have

7

17

1

j

j the

mean daily effect, the average sales for one day. Since by design we have

7

1

0j

j , we may

write:

INSEE, Short-Term Statistics Department, Paris, France. Emails: [email protected],

[email protected] ISTAT, Methods Development in Quarterly National Accounts, Rome, Italy. Email:

[email protected]

1 Agustin Maravall presented some results of this new feature during the ECB-Eurostat Workshop on

Seasonal Adjustment held in Frankfurt on July 6-7, 2010.

mailto:[email protected]



6

1

7

7

1

7

1 j

tjtjt

j

jtjt

j

jtj DDNDND (1)

Thus, the cumulative monthly effect is decomposed into an effect directly linked to the length of the

month and a net effect for each day of the week.

Note that the sum

7

1j

jtj D involves only the days of the week occurring five times in a

month; every month contains four complete weeks, for which by definition the effect linked to the

days is cancelled out, plus 0, 1, 2 or 3 days which contribute to the trading-day effect for the month.

Equation (1) must be adjusted to remove possible seasonality and trend.

Potentially, part tN of the equation contains such components because the months vary in length

and because, as we have seen, variable tN is periodic (period of 400 years). These effects can be

summarized by the quantity *

tN where *

tN represents the average, over 400 years, of the length

of the month t. In other words, *

tN is equal to 30 or 31 if the month in question is not the month

of February, and is equal to 28.25 otherwise. Thus, we have: )(**

tttt NNNN , an

equation whose second part is zero except for the month of February.

The second part of the equation includes jtD , the number of times that day j is present in month t.

These variables are periodic (period of 33600 months or 400 years) with equal means for a given

month. In the second part of the equation, the difference tjt DD 7 is used, and since these

variables show the same behaviour, the difference involves no seasonality and no trend.

The procedure used to adjust equation (1) for these effects depends on the decomposition model used.

For an additive model, *

tN must be subtracted logically from equation (1). We thus have:

t

j

tjtjttt eDDNNI

6

1

7

*

0 )()(ˆ

where 0 and jj for 61 j

This model is implemented in X-12-ARIMA using the Regression specification, and in Tramo-

Seats using the TD=7 parameter. Other specification of the model, week-day regressor and no leap

year regressor, are available in both softwares.

1.2 Stochastic models for time-varying trading-day coefficients

We find in the literature several proposals of models with time-varying coefficients for trading-day

effects. Monsell (1983) used random walk models for the coefficients. Dagum, Quenneville and

Sutradhar (1992) and Dagum and Quenneville (1993) considered a more general formulation,

including seasonal, trend and irregular components in the model along with time-varying trading-day

effects. Bell (2004) introduced the RegComponent model, a regression model whose errors follow an

ARIMA component time series model. This class of models is quite general and can be used to allow

for stochastic time-varying regression coefficients. This model encompasses the structural time series

model of Harvey (1989), which is the basic formulation of the software STAMP. As we will use

STAMP as a “benchmark”, we present in this section an extension of a well-known structural time

series model to include time-varying calendar (not only trading-day) effects.

A structural time series model is based on the principle that a time series consists of interpretable

unobserved components such as trend, seasonal, cycle and irregular (Harvey, 1989). One particular

useful model for seasonal adjustment is the Basic Structural Model (BSM). Let ty be a (monthly)

time series. The BSM is given by

nty tttt ,,1 , (1)

where t is the trend,

t is the seasonality and t is the irregular component. Such components are

unobserved and modelled by stochastic processes.

The trend component t is usually specified as

),0( ,

),0( ,

2

1

2

1

NID

NID

tttt

ttttt

(2)

with ),0(1 N and ),0(1 N where is large (Koopman et al., 1998). The initial conditions

for 1 and

1 indicate that no information is available. Model

Erreur ! Source du renvoi introuvable. is called a local linear trend. The term t is the slope of the

trend: when 2 0 , 1t t and Erreur ! Source du renvoi introuvable. becomes a local trend

model. When also 2 0 , then the trend is linear deterministic and

Erreur ! Source du renvoi introuvable. reduces to a deterministic linear trend model.

The seasonal component t can be specified in various ways. The trigonometric seasonal model

(Koopman et al., 1998, and Koopman and Franses, 2001) is given by

6

,

1

t j t

j

(2)

where

, 1 , ,

* * *

, 1 , ,

cos sin,

sin cos

j t j j j t j t

j t j j j t j t

(3)

with frequencies / 6j j , for 1, ,6j . The disturbances are mutually uncorrelated and normally

distributed with mean zero and variance matrix

2

,

* 2,

0

0

j t j

j t j

var

.

The terms associated with different frequencies have different variances. Each initial seasonal value

,1j and *

,1j , for 1, ,6j is initialized with a diffuse prior, that is ),0(1, Nj and

),0(*

1, Nj . The trigonometric seasonal model (2) has the property to evolve very smoothly over

time. Finally, the irregular term t follows a normal random variable with mean zero and variance 2

.

The BSM can be written in state space form, which is particularly useful for estimating time-varying

models. The following state space representation is chosen (adopted by the SsfPack package):

ntPaN

GGHG

GHHH

G

Hu

Z

T

c

d

NIDuuy

tttt

tttt

t

t

t

t

t

t

t

t

t

t

t

tttttt

t

t

,,1 ),,(

,

,,,

),0( ,

1

''

''

1

(5)

The ( 1m ) vector t is the state of the system, containing unobserved stochastic processes and fixed

effects. The ( 1N ) vector ty contains the observations at time t of the observed variables. The matrix

t , of dimension( ( )m N m ), defines the state and measurement equations. The deterministic

matrices tT , tZ , tH and tG are referred to as system matrices.

In our case the state vector t is defined as

* *

1, 1, 5, 5, 6,t t t t t t t t

and has dimension (13 1 )2, while the observational vector ty is one-dimensional.

The vector t is null, while is defined as

1 1

1 1

5 5

5 5

1 1 0 0 0 0 0 0 0

0 0 cos sin 0 0 0 0 0

0 0 sin cos 0 0 0 0 0

0

0 0 0 0 0 0 cos sin 0

0 0 0 0 0 0 sin cos 0

0 0 0 0 0 0 0 0 1

1 0 1 0 1 0 1 0 1 0 1 0 1

T

Z

T

Z

The matrix is diagonal with elements

2 2 2 2 2 2 2

1 1 5 5 6 . (4)

Note that the time index has been dropped by the notation of and . The initial state vector is

assumed to follow a diffuse distribution, that is

1 13(0, )N I

with arbitrarily large.

The classical BSM can be extended to include time-varying calendar effects. Model (1) is modified as

follows:

, 1, , ,t t t t t ty x t n (5)

where tx is the ( 1k ) vector of regressors with calendar effects at time t and

t is the ( 1k ) vector

containing the corresponding time-varying coefficients. We assume that these follow independent

random walk models:

, 1 , , , 1, , , 1, , .i t i t i t i k t n (6)

The ,i t ’s are mutually independent normally distributed processes with variance 2

i . When

2

, 1 ,0,i i t i t i : a coefficient is thus fixed when the corresponding innovation variance is zero.

The hypothesis of a random walk is particularly appealing for capturing possible time variation in

calendar effects: in fact, it avoids too much erratic variation around the average level, instead allowing

the coefficients to change more smoothly over long periods of time without being tied to fixed means

(Bell and Martin, 2004).

The state space representation of the BSM needs to be changed to introduce the regression effects tx .

The state vector is augmented at the top with the calendar effects:

*

1, 1, 6, .t t t t t t tx

With T and Z defined as above, the new matrix t becomes

8 0

0t

t

I

T

x Z

which is a time-varying matrix, for the presence of tx in the measurement equation. Time-varying

regression coefficients are introduced in the state space model by defining the diagonal matrix as

1 2 3

2 2 2 2 2 2 2 2 2 2 2

1 1 5 5 6kx x x x (7)

i.e. by augmenting the matrix t with the variances of each calendar effect.

2 The seasonal coefficient

*

6 , t is excluded from the state because

6 and

6sin 0 .

The BSM augmented with time-varying calendar effects tx can be estimated by maximum likelihood

through the software STAMP or the Ox package SsfPack, which is a collection of routines for

implementing, fitting and analysing models in state space forms (Koopman et al., 1998).

For people using the SAS system, PROC UCM gives a clone of STAMP using the following basic

code:

PROC UCM DATA=MySASfile;

ID MyDateVariable INTERVAL=12;

MODEL MyVariable;

IRREGULAR;

LEVEL;

SLOPE;

SEASON LENGTH=12 TYPE=TRIG;

ESTIMATE OUTEST=Stamp_Est;

FORECAST OUTFOR=Stamp_Comp;

RANDOMREG MyTDRegressors;

RUN;

2 Moving Trading-Day effects with X-12-Arima and Tramo-Seats

X-12-Arima provides the user with 2 ways to check for moving trading day effects: the change of

regime specification and the sliding-span specification. We use the idea behind sliding-spans to derive

a “Rolling window technique” to estimate moving trading day effects.

2.1 The X-12-Arima “change of regime” specification3

Change-of-regime regression variables can be specified for seasonal (seasonal), trigonometric seasonal

(sincos), trading day (td, tdnolpyear, or tdstock), leap year (lpyear), length-of-month (lom),and length-

of-quarter (loq) regression variables. Two types of change-of-regime regressors are available: full and

partial.

As the following table shows, change of regime regressors are specified by appending the change date,

surrounded by one or two slashes, to the name of a regression variable in the variables argument of the

regression spec. The date specified for the change of regime divides the series being modelled into two

spans, an early span containing the data for times prior to the change date and a late span containing

the data from on and after this date. Partial change of regime variables are restricted to one of these

two spans, being zero in the complementary span. The full change of regime variables estimate both

the basic regression of interest and the partial change of regime regression for the early span.

For example, the full change of regime specification variables = (td/1990.jan/) is equivalent to the

specification variables = (td td/1990.jan//). It causes the program to output the coefficients estimated

for td and for td/1990.jan// along with trading day factors for their combined effects.

Table: Change of Regime Regressor Types and Syntax

Type Syntax Example

Full change of regime regressor reg/date/ td/1990.jan/

Partial change of regime regressor, zero before change date reg//date/ td//1990.jan/

Partial change of regime regressor, zero on and after change date reg/date// td/1990.jan//

3 Extracted from the X-12-ARIMA Reference Manual, Version 0.3

The coefficients resulting from use of a full change of regime regression have convenient

interpretations: Let the basic regressors be denoted by jtX , and let 0t be the change point. Then the

partial change of regime regressors for the early regime are

0

0

for 0

for

tt

ttXX

jtE

jt

And those for the late regime can be calculated as E

jtit

L

jt XXX . For the data transformed as

indicated in the transform spec, the effect estimated by the full change of regime regression has the

form

j

E

jtjj

j

L

jtj

j

E

jtj

j

jtj XbaXaXbXa )(

From the right-hand-side formula, we observe that the coefficients ja of the basic regressors jtX can

be interpreted as the coefficients of the late-span regressors L

jtX , and the coefficients jb of the E

jtX

can be interpreted as measuring the change in the coefficients of the late-span regressors required to

obtain coefficients for the early-span effects. Therefore, statistically significant jb indicate the nature

of the change of regime.

A usual output of this change of regime is shown hereafter. This example shows a clear change in the

trading-day pattern: Sunday had no significant effect before 1990 and a clear negative effect on the

series after 1990.

2.2 The Sliding-Spans specification4

Optional spec providing sliding spans stability analysis. These compare different features of seasonal

adjustment output from overlapping subspans of the time series data. The user can specify options to

control the starting date for sliding spans comparisons (start), the length of the sliding spans (length),

the threshold values determining sliding spans statistics (cutsf, cuttd, cutchng), how the values of the

regARIMA model parameter estimates will be obtained during the sliding spans seasonal adjustment

runs (fixmdl), and whether regARIMA automatic outlier identification is performed (outlier).

2.3 Using Rolling Windows to estimate moving trading-day effects

2.3.1 The principle

The basic idea, which is very simple, is a direct extension of the “sliding span” specification. It can

therefore easily be done with both Tramo-seats or X-12-Arima. In fact, this strategy has already been

implemented in Demetra+.

Let us suppose for example a monthly time series with N observations.

The estimation is first done on the complete time series. That gives you the Arima model of

the series, the outliers and the estimation of the fixed trading day effect;

You now do the estimation on the first n observations, using or not the same Arima model and

the previously detected outliers;

You add the next observation to your span (observation n+1), remove the first one and

estimate the trading-day effect on this new series of n observations, using or not the same

Arima model and the previously detected outliers;

You do it again and again and get at the end N-12n+1 estimations of the trading day

coefficients.

Of course, you can use your own trading-day regressors, taking into account for example your national

calendar.

2.3.2 An example: The Finish retail trade index

In order to have enough observations to perform a relevant analysis, the data were extracted from the

OECD Main Economic Indicators database and covers the period from January 1969 to February

2010.

We use the total retail trade index, in volume and not seasonally adjusted.

We use the default calendar and 7 regressors (the 6 contrasts and the Leap Year regressor).

We use X12 and a 12-year running window.

We also estimate a time-varying TD effect using PROC UCM, the “SAS implementation” of

STAMP.

The following graph illustrates the results on the evolutions of the Wednesday and Friday effects.

The horizontal black line is the fixed effect; the dotted black lines are the confidence limits;

The green line shows the moving effect estimated with PROC UCM;

The red line is the “rolling window” effect. The blue line is the smoothed “rolling window”

effect. The smoothing was done using the loess smoother; A red circle indicates that the

coefficient was statistically significant.

4 Extracted from the X-12-ARIMA Reference Manual, Version 0.3

This graph can easily be commented:

The “rolling window” effect shows a clear increase of the Friday coefficient. This moving

effect is coherent with the effect obtained using the STAMP-like stochastic model. A rupture

can be noted roughly in 1997.

As shown by the confidence limits, the rolling window effect for Friday is statistically

different from the fixed effect and the hypothesis of a moving effect is therefore accepted.

On the opposite, the Wednesday coefficient appears to be stable across time.

The “rolling window” effect is anyway quite erratic and requires some smoothing. This can be

done as here using a specific smoother or by increasing the number of points to skip in the

rolling window process (here we add one point each time).

FRIDAY

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

date

JAN80 JAN82 JAN84 JAN86 JAN88 JAN90 JAN92 JAN94 JAN96 JAN98 JAN00 JAN02 JAN04 JAN06 JAN08 JAN10 JAN12

Friday (FINLAND)

WEDNESDAY

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

date

JAN80 JAN82 JAN84 JAN86 JAN88 JAN90 JAN92 JAN94 JAN96 JAN98 JAN00 JAN02 JAN04 JAN06 JAN08 JAN10 JAN12

Wednesday (FINLAND)

3 Bibliography

[1] Bell, W. R. (1984), Seasonal Decomposition of Deterministic Effects, Research Report,

Statistical Research Division, U.S. Bureau of the Census, Washington D.C., RR84/01.

[2] Bell, W. R. (1995), Correction to ‘Seasonal Decomposition of Deterministic Effects’ (n°

RR84/01), Research Report, Statistical Research Division, U.S. Bureau of the Census, Washington

D.C., RR95/01.

[3] Bell, William R. (2004), “On RegComponent Time Series Models and Their Applications,” in

State Space and Unobserved Component Models: Theory and Applications, eds. Andrew C.

Harvey, Siem Jan Koopman, and Neil Shephard, Cambridge, UK: Cambridge University Press

[4] Bell, W. R., Hillmer, S. C. (1983), Modeling Time series with Calendar Variation, Journal of

the American Statistical Association, 383, 78, 526-534.

[5] Bell, W. R., Hillmer, S. C. (1984), Issues Involved with the Seasonal Adjustment of Economic

Time Series, Journal of Business and Economic Statistics, 4, 2, 291-320.

[6] Bell, W. R., Martin, D. E. K. (2004), Modeling Time-Varying Trading-Day Effects in

Monthly Time Series, ASA Proceedings of the Joint Statistical Meetings.

[7] Dagum, E. B., Quenneville, B. (1988), Deterministic and stochastic models for the estimation

of trading-day variations, Working Paper, Time Series Research and Analysis Division, Statistics

Canada, Ottawa, 88-003E.

[8] Dagum, E. B., Quenneville, B. (1993), Dynamic linear models for time series components,

Journal of Econometrics, 1-2, 55, 333-351.

[9] Dagum, E. B., Quenneville, B., Sutradhar, B. (1992), Trading-day variations multiple

regression model with random parameters, International Statistical Review, 1, 60, 57-73.

[10] Findley, David. F., Monsell, Brian C., Bell, William R., Otto, Mark C., and Chen, Bor-Chung,

(1998), “New Capabilities and Methods of the X-12-ARIMA Seasonal Adjustment Program (with

discussion),” Journal of Business and Economic Statistics, 16, 127-177.

[11] Monsell, B. C. (1983), “Using the Kalman Smoother to Adjust for Moving Trading Day,”

Research Report 83/04, Statistical Research Division, U.S. Census Bureau.

[12] Quenneville, B., Cholette, P., Morry, M. (1999), Should Stores Be Open on Sunday? The

Impact of Sunday Opening on the Retail Trade Sector in New Brunswick, Journal of Official

Statistics, 3, 15, 449-463.

[13] U.S. Census Bureau (2006), X-12-ARIMA Reference Manual, Version 0.3 (Beta), Time Series

Staff, Statistical Research Division, Washington, DC

[14] Young, A. H. (1965), Estimating trading-day variations in monthly economic series, Technical

Paper, U.S. Department of Commerce, U.S. Bureau of the Census, Washington D.C.

JDEMETRA+, NOWCASTING

JDEMETRA+ Nowcasting1

Macroeconomic Monitoring and Visualizing News


Research & Development

Philippe Charles

David De Antonio Liedo2

Mats Maggi

Jean Palate

Abstract. This article presents the first open source IT solution for nowcasting

and reading news with dynamic factor models. As illustrated in our workhorse

example, the software allows us to extend the limits of currently established

practices. The nowcasting model proposed for the US economy is, to the best of

our knowledge, the first one that accounts for the joint behavior of quantities and

prices. The model also provides a join interpretation of the forecast revisions for

multiple horizons in terms of the unexpected part of both new data releases and

revisions to past data, which become available in real time. For instance, a

worse than expected inflation release will have an impact on the forecasting

updates for GDP, but the sign of that impact will depend on the remaining news

too. The reason is that we can have both positive supply and negative demand

disturbances underlying the bad surprise in inflation data.

Keywords: JDEMETRA+, GDP and inflation interactions, state-space, business

cycles, timeliness, data revisions, real-time, forecasting

JEL: C87, E31, E32, E37

1 Licensed under the EUPL (http://ec.europa.eu/idabc/eupl).

The last updated version of the JD+ software, which has been designed for the analysis of

seasonal data, can be downloaded here:

http://www.cros-portal.eu/content/jdemetra.

The nowcasting tool is distributed as a plug-in and resides in the web site of the National Bank

of Belgium: http://www.nbb.be/app/dqrd/jdemetra/jdplugins-1.5.3.zip

2 Corresponding author. Email: [email protected]. 1000 Boulevard de Berlaimont

14, 1000 Bruxelles, Belgium. This work has benefited from discussions with Raf Wouters, Geert

Langenus, Marta Banbura, and seminar participants at the NBB and the CFE 2014 in Pisa. All

errors are our own responsibility.

http://ec.europa.eu/idabc/eupl

http://www.cros-portal.eu/content/jdemetra

http://www.nbb.be/app/dqrd/jdemetra/jdplugins-1.5.3.zip



1 Introduction

The meteorological term nowcasting has become increasingly popular in economics

over the last years. Unlike nowcasting users in meteorology, who base their decisions

on the current weather along with forecasts for a period of zero to six hours ahead,

institutions responsible for economic policy need to make important decisions without

directly observing the current state of the economy.

The first papers that formalize the real-time forecasting process are due to Evans

(2005) and Giannone et al. (2008). They use the term nowcasts to refer to predictions

of the most recent past, the present, and the nearest future. In this paper, we describe a

set of open source modules for nowcasting and analyzing news with dynamic factor

models, as described by Banbura and Modugno (2010). These modules are integrated

in the JDEMETRA+ framework developed at the National Bank of Belgium.

Our nowcasting library3 aims to simplify the practice of forecasting in real-time by

helping analysts and researchers to communicate their forecasts revisions in real time.

Moreover, users are able to save the models and data vintages and share them with

other analysts. Our implementation is based on two pillars. First, users can easily

specify and estimate a broad range of dynamic factor models, which are internally

casted in state-space form and estimated via maximum likelihood. For this purpose,

we combine the EM algorithm proposed by Banbura and Modugno (2010) with

numerical optimization methods. The second pillar of our implementation is a user

friendly graphical interface that represents in a transparent manner how the model

based expectations for all variables change as a consequence of news embedded in

different data releases. This feature simplifies the use and interpretation of the model in

real-time forecasting applications regardless its complexity.

Understanding the role of news is a crucial point for analysts and policy institutions

that produce forecast and are requested to explain modifications in their assessment on

the basis of new information that becomes available. The nowcasting literature has

aimed since its origins to understand the impact of data releases in forecasts for

economic growth. Since the work by Giannone et al. (2008), much of the empirical

research has drawn conclusions on the usefulness of monthly surveys at nowcasting

economic growth without being able to quantify their precise role. In the framework

of a small model with only one factor, Camacho and Pérez-Quirós (2010) suggested

that the importance of a given data release could be measured by how much it

contributes in the estimation of the driving factor, following the contributions analysis

3 JDEMETRA+ is Open Source time series software written in Java. It is mostly used in

statistical agencies for the analysis of seasonality (X12, TRAMO-SEATS, or structural

models). This article focuses on the new Nowcasting library, which currently supports the use

dynamic factor models.

of Harvey and Koopman (2003). However, the formal analysis of news in the

nowcasting context was brought by Banbura and Modugno (2010) on the basis of

concepts originated in control engineering. Their approach to handle this problem has

been incorporated in the JDEMETRA+ module for news along with an interactive

graphical interface that allows the user to assess the contribution of all data releases

(including data revisions) at updating the expected evolution path for all variables in

the system. To the best of our knowledge, we are the first ones proposing a feasible

method to disentangle the impact of data revisions from the whole set of news.

Finally, the empirical application describes a nowcasting model for real activity growth

and inflation in the US. Although the idea has been proposed by Aruoba and Diebold

(2010), this paper contains the first implementation of a nowcasting application

providing a joint interpretation of the fluctuations in prices and quantities4. This

example serves well to illustrate that the JDEMETRA+ nowcasting platform aims to

extend the limits of the currently established practices and promote an exchange of

ideas. Users can easily introduce their own expertise in the form of models, which can

be saved along with the data vintages that are available in real time. Through this

platform, researchers will also be able to easily share their forecasting knowledge and

explore alternative datasets or model specifications.

Overall, this implies forecasters with different backgrounds, independently of their

technical expertise, can avoid dealing with complex algorithms and spend more of

their valuable time trying to better understand the large amount of information at their

disposal. This new technology can help to revisit classic applications such as studying

the role of financial markets data at forecasting inflation, e.g. see Stock and Watson

(2003) for a survey. Our choice to publish this software as an Open Source solution

also establishes the basis for cooperation with external participants, which could lead

to significant improvements in the library or the implementation of alternative methods

that are common in empirical macroeconomics and finance, such as Bayesian VARs

with mixed frequency data (e.g. Schorfheide and Song, 2014), models with Markov-

Switching parameters or stochastic volatility. Another topic that would be particularly

relevant to statistical agencies would be the introduction of techniques such as

temporal disaggregation, as in Frale et al. (2011), who propose to convert quarterly

national accounts into monthly frequency.

4 The model by Banbura et al. (2011) specifies a block of inflation variables linked to an

“inflation specific” factor which is assumed to be independent from real quantities. Thus, their

framework does not take into account the interactions between prices and quantities.

2 Basic Model Specification

Consider the following representation of the multivariate process { yt } governing the

dynamics of a given set of N observables over time, e.g. months, 𝑡 = 1,… , T:

yt = Z𝛼𝑡 + 𝜉𝑡 𝑤𝑖𝑡ℎ 𝜉𝑡 ∼ 𝑁(0, 𝑅)

[ 1]

𝛼𝑡 = 𝑇1𝛼𝑡−1 + ⋯+ 𝑇𝑝𝛼𝑡−𝑝 + 𝑢𝑡 𝑤𝑖𝑡ℎ 𝑢𝑡 ∼ 𝑁(0, 𝑄)

[ 2]

The first equation represents the observables as a function of the vector of k

unobserved factors αt plus a vector of idiosyncratic measurement errors ξt. The

second equation defines the dynamics of the factors, which follow a covariance

stationary VAR process of order p. Thus, the dynamic interactions between all the

factors are given by the matrices T1, … , Tp and the underlying shocks ut, which are

uncorrelated with the measurement errors. Interestingly, the idiosyncratic nature of the

measurement errors, whose covariance matrix R is diagonal, implies that all the co-

movements in the data can be accounted for by fluctuations in the latent factors.

More parsimonious parameterizations are possible, as it will be clarified in the

empirical application. For example one can assume that a given factor does not load on

specific variables, i.e. the matrix of loadings will have zeroes in the columns

corresponding to that factor. Alternative parameterizations are also possible. Consider

for instance the possibility that the number of stochastic terms in ut is smaller than the

size k of the state vector, suggesting a reduced number of shocks spreading throughout

the economy. In this case, we would need to parameterize Q and T in terms of the

actual number of shocks, q.

Concept

Size Definition

𝐲𝐭 𝐍 × 𝟏 Observed data

𝛂𝐭 𝐤 × 𝟏 Underlying factors

𝛏𝐭 𝐍 × 𝟏 Measurement Error

𝐮𝐭 𝐤 × 𝟏 Shocks to the factors

𝐙 𝐍 × 𝐤 Loadings

𝐓𝟏, … , 𝐓𝐩 𝐤 × 𝐤 VAR coefficients in the motion equation for the factors

𝐑 𝐍 × 𝐍 Covariance of the measurement error

𝐐 𝐤 × 𝐤 Covariance of the shocks to the factors

3 Estimation, Forecasting and Analysis of News

The data vector yt may contain missing observations simply because macroeconomic

indicators are not necessarily released at the same time. In the case that the model is

specified at the monthly frequency, the presence of quarterly data also generates

additional missing observations. In this context, which will be carefully described

below, a variable such as GDP is of course only available for each quarter and not for

each month. This variable, which aims to measure the flow of economic activity over

a quarter, is observed every three months, i.e. ytGDP

is missing for 𝑡 ≠ 3,6,9,12, … The

standard Kalman filter can handle this complication and evaluate the likelihood via

prediction-error decomposition. Estimating the parameter values that maximize the

likelihood is conceptually simple, but complex models may require a heavy use of the

optimization capabilities implemented in JDEMETRA+. Once the model has been

specified and estimated, the so-called Kalman smoother is used to calculate

projections, as highlighted for example by Durbin and Koopman (2001). The

projections for any variable k at any point in time t conditional on the information set

available at any date v will be represented throughout this document as E[yk,t | ℱv]

The practice of forecasting in real time requires incorporating changes in the

information set that involve news. The Kalman filter can also be used in this context to

formalize the impact of news in the forecast revisions. Thus, updates in forecasts can

be expressed as a linear combination of the news identified by the model (see

equations [ 1] and [ 2]):

E[yk,t |ℱupdated] − E[yk,t |ℱold] = ∑ wj

k,t(yij,tj− E [yij,tj

|ℱold])

J

j=1

[ 3]

where the weights wjk,t

associated to each one of the J news is specific to each variable

k and time period t. The news itself is defined by the difference between the released

indicator and its expected value conditional on the previous information set ℱold.

Banbura and Modugno (2012) explain in detail how to compute these weights. As

opposed to the solution proposed by Harvey and Koopman (2003) to understand the

impact of the variables in the forecasts5, the JDEMETRA+ implementation focuses on

the concept of news, which also fits within the state-space modeling framework.

5 Harvey and Koopman (2002)’s insight has been followed in nowcasting applications by

Banbura and Rünstler (2011) and Camacho and Pérez-Quirós (2010).

4 Advanced Specification Options

Concept

Representation of the link to the factors

JDEMETRA+

code

monthly growth 𝜶𝒕

M

quarterly growth

𝛂𝐭𝐐

≅ (

𝟏

𝟑𝛂𝐭 +

𝟐

𝟑𝛂𝐭−𝟏+ 𝛂𝐭−𝟐+

𝟐

𝟑𝛂𝐭−𝟑+

𝟏

𝟑𝛂𝐭−𝟒)

Q

year-on-year growth

𝜶𝒕𝐘 =𝜶𝒕 + 𝜶𝒕−𝟏 + 𝜶𝒕−𝟐 + 𝜶𝒕−𝟑 + 𝜶𝒕−𝟒 + 𝜶𝒕−𝟓 +

𝜶𝒕−𝟔 + 𝜶𝒕−𝟕 + 𝜶𝒕−𝟖 + 𝜶𝒕−𝟗 + 𝜶𝒕−𝟏𝟎 + 𝜶𝒕−𝟏𝟏

YoY

4.1 Measurement Equation Type “M”

All variables measuring the monthly growth rate of the economy will be directly linked

to the factors αt , exactly as specified in the measurement equation [ 1]:

yt

= Z αt + ξt

The next two subsections explain how to introduce variables expressed in terms of

percentage changes both with respect to the previous quarter and with respect to the

same month of the previous year.

4.2 Measurement Equation Type “Q”

This option will be very familiar to practitioners that exploit monthly indicators of

economic activity as regression variables to obtain a nowcast for GDP, which is

typically expressed in terms of growth rates over a whole quarter. Thus, the

measurement equation [ 2], which relates all monthly indicators with a latent factor

representing the underlying monthly growth rate of the economy, cannot be used. The

measurement equation for variables measuring quarterly growth rates will be defined

as follows:

ytGDP = ZGDPαt

Q

+ ξt

GDP

,

where αtQ

represents the underlying quarterly growth rate of the economy. A linear

approximation can be used under the assumption that one third of the economic flow of

added value registered over the quarter is given by the geometric average over the

three months. Thus, the approximation

αt

Q

≅ (

1

3αt +

2

3αt−1+ αt−2+

2

3αt−3+

1

3αt−4)

allows us to rewrite the measurement equation above as a linear combination of the

underlying monthly growth rates:

ytGDP = ZGDP

1

3(αt + 2αt−1+ 3αt−2+ 2αt−3+ αt−4) + ξt

GDP

Albeit may seem to be a complex representation even in the simplest case where αt

contains a single factor, the only parameters to be estimated in the measurement

equation for GDP are the loading ZGDP and the variance of the measurement error

component ξtGDP. The fact that yt

GDP is available only every three months, i.e. missing

for t ≠ 3,6,9,12, … does not pose any technical difficulty thanks to the availability of

alternative indicators.

Further Remarks

In contrast to our state-space approach where the full system is modeled

simultaneously, the commonly used bridge equations6 for nowcasting involves a simple

regression of the quarterly growth rate of GDP, ytGDP, on aggregated values of the

higher frequency indicators, i.e. αtQ

would be replaced by the quarterly growth rate of a

predictor variable. The drawback is that some of that higher frequency data may not be

available for the whole quarter, which requires the use of auxiliary forecasting models

to fill-in the gaps. This clearly adds an extra layer of complexity to the methodology.

The solution of using bridge equations to calculate direct forecasts without the need to

use auxiliary models for the indicators would be also problematic because the resulting

forecasting equation will change depending on the information set available. This is an

undesirable feature because this implies that updates in the forecasts are driven by both

new data releases and changes in the model. Thus, an analysis of news such as the one

I will present in Section 8 is not possible in the context of bridge equations. Finally,

inside the broad class of bridge equation models for nowcasting, the so-called MIDAS

approach introduced by Ghysels, Santa-Clara and Valkanov (2004) and its multiple

parameterizations7 provide a parsimonious solution to link our target low frequency

variable with indicators released at a higher frequency. The MIDAS aggregation for

monthly data is also consistent with the aggregation scheme presented above to link a

factor representing economic growth over the quarter with monthly factors, although

the original MIDAS formulation involves explanatory variables and not unobserved

factors8. The key advantage of MIDAS is that the aggregation can be implemented in a

much more flexible way. The drawback of this univariate approach is that the large-

scale analysis of news illustrated in this article would not be valid anymore.

6 See for example Ingentino and Trehan (1996), Baffigi, Golinelli and Parigi (2004) or Diron

(2008). 7 See the survey by Andreou, Ghysels and Kourtellos (2010) for an overview. 8 See Marcellino and Schumacher (2010) for an example where the MIDAS regressions are

augmented with factors extracted from large cross-section.

4.3 Measurement Equation Type “YoY”

Some variables, such as the results of many surveys that represent how business or

consumer sentiments have changed with respect to one year ago, are likely to have a

strong correlation with year-on-year growth rates. In our framework, this has the

implication that they should be linked to the cumulative sum of the factors for twelve

months, i.e. year-on-year growth rate of the factor, as in the nowcasting model

developed by Camacho and Pérez-Quirós (2010). The European Commission (2006)

explicitly states that the guiding principle for the selection of questions in the different

surveys is the aim to achieve as high as possible coincident correlation of the

confidence indicators with year-on-year growth of the reference series. De Greef and

Van Nieuwenhuyze (2009) also emphasize the coincident correlation of the NBB

Business Survey with year-on-year GDP growth rates. The measurement equation for

variables measuring year-on-year growth rates will be defined as follows:

ytSurvey

= ZSurveyαtYoY

+ ξt

Survey

where

αtYoY

= αt + αt−1 + αt−2 + αt−3 + αt−4 + αt−5 + αt−6 + αt−7 + αt−8

+ αt−9 + αt−10 + αt−11

As in the previous case, measurement equations of this type increase the complexity of

the model without the need to estimate more parameters. The only parameter that

needs to be estimated is the factor loading 𝑍𝑆𝑢𝑟𝑣𝑒𝑦 and the variance of the

measurement error.

Further Remarks

Variables concerning expectations about the future are useful because they may

contain relevant information about the current unobserved state, i.e. factors, of the

economy. However, rather than linking it to the current factors, one could consider the

possibility to link it directly to the expected state. This option is not currently available

in JDEMETRA+, but it could be a feasible extension.

Consider a measure of inflation expectations for the next twelve months, πt|t+12Survey

.

This variable should be linked to the latent inflation factor as follows:

πt+12|tSurvey

= ZSurvey E[αt+12YoY | αt ] + ξt+12

Survey

[4]

where αt+12YoY

is defined as the year-on-year growth rate of the factor:

αt+12YoY

= αt+12 + αt+11 + αt+10 + αt+9 + αt+8 + αt+7 + αt+6 + αt+5

+ αt+4 + αt+3 + αt+2 + αt+1

Without loss of generality, assuming that the transition equation in the state-space

model [ 2] is a first order VAR we obtain a very simple expression for the conditional

expectation required to specify measurement equation [4]:

E[αt+h| αt ] = Thαt => E[αt+12YoY

| αt ] = (T + T2 + ⋯+ T12) αt

This implies the measurement equation should be specified as follows:

πt+12|tSurvey

= ZSurvey (T + T2 + ⋯+ T12) αt + ξt+12Survey

[5]

Modeling expectations correctly helps to better estimate T, which determines the

transition dynamics of the whole economic system. Alternatively, it would also be

possible to estimate the reduced form expression

πt+12|tSurvey

= ZSurvey∗ αt + ξt+12

Survey,

where the state αt loads on ZSurvey∗ and not on ZSurvey, defined above. If you

consider for simplicity that αt and E[αt+12Y | αt ] where observed variables, both

loadings would be linked, i.e. ZSurvey∗ = ZSurvey (T + T2 + ⋯+ T12)

, and the fit for

πt+12|tSurvey

would be exactly the same in both equations [4] and [5]. However, the

motivation for introduction data on expectations is the suspicion that they add

fundamental information about the state of the economy that would be otherwise

missed by the model.. Because data on expectations is relevant for policy, we would

propose to specify the measurement equation as in [5]. Ideally, expectations for any

horizon h could be incorporated in the model’s information set. This would be possible

with an interface that allows the user to select the measurement type “YoY” together

with the option link the variable with expectations for a given forecast horizon, h,

which has been set equal to 12 in this case.

Table 1: Data Selection

_____

5 A Joint Model for Nowcasting US inflation and GDP

Aruoba and Diebold (henceforth A&D) (2010) have proposed to extract monthly

factors from two data sets containing macroeconomic prices and quantities,

respectively, and discuss the interactions between inflation and real activity. Instead of

extracting those factors separately from the two different datasets, as they propose, we

will show how JDEMETRA+ can be used to define the interaction between real

activity and inflation within a state-space model with two factors. This approach is

more suitable to formalize the discussion of whether supply or demand shocks are

Real Activity Inflation

Real Gross Domestic Product Consumer Price Index for All Urban Consumers: All Items

U.S. Department of Commerce: Bureau of Economic Analysis U.S. Department of Labor: Bureau of Labor Statistics

Quarterly; start: 1947Q1 Monthly; start: January 1947

Real personal income excluding current transfer receipts Producer Price Index: Finished Goods

U.S. Department of Commerce: Bureau of Economic Analysis U.S. Department of Labor: Bureau of Labor Statistics

Monthly; start: January 1959 Monthly; start: April 1947

All Employees: Total nonfarm Gross Domestic Product: Implicit Price Deflator

U.S. Department of Labor: Bureau of Labor Statistics U.S. Department of Commerce: Bureau of Economic Analysis

Monthly; start: January 1939 Quarterly; start: 1947Q1

Industrial Production Index Nonfarm Business Sector: Compensation Per Hour

Board of Governors of the Federal Reserve System U.S. Department of Labor: Bureau of Labor Statistics

Monthly; start: January 1919 Quarterly; start: 1947Q1

Real Manufacturing and Trade Industries SalesCrude Oil Prices: West Texas Intermediate (WTI) - Cushing,

Oklahoma

Federal Reserve Bank of St. Louis U.S. Department of Energy: Energy Information Administration

Monthly; start: January 1967 Monthly; start: January 1986

Initial Claims S&P GSCI Non-Energy Spot - PRICE INDEX

U.S. Department of Labor: Employment and Training

AdministrationMonthly; start: December 1969

Monthly; start: January 1967

"Advance" and "Prelimimary" releases available 30 and 60 days,

respectively, after the end of the quarter. "Final" release

available with a delay of 85 days.

Released about 14 days after the month ends

Released about 16 days after the month ends

Available about 60 days after the month ends

Released four days after the week ends Available daily

Available daily

First release 30 days after the end of the quarter; Second

release 60 days after the end of the quarter (subsequent

revisions may be significant)

"Advance" and "Prelimimary" releases available 30 and 60 days,

respectively, after the end of the quarter. "Final" release

available with a delay of 85 days, but subsequent revisions may

be large.

Released around 30 days after the end of the month

Released on the first Friday after the month ends

Available around 16 days after the end of the month

behind a given recession and quantify the historical contribution of supply shocks at

different stages of the business cycle. Table 1 presents the selection of variables made

by A&D, which contains some of the most monitored real activity and inflation

indicators at the monthly frequency.

5.1 Model Specification to Extract the Latent Real Activity Growth Rate

A&D use the indicators in the left panel of Table 1 to extract a smooth index of real

economic activity. Those indicators are also used by the so-called ADS Index

published by the Federal Reserve Bank of Philadelphia, which uses a simplified

implementation of the model proposed by Aruoba, Diebold and Scotti (2009). The

model used by A&D to extract that signal from the monthly data differs from the state-

space representation originally proposed in JDemetra+ not only because their

measurement equation contains lags of the observed variables, but also because their

approach requires the idiosyncratic errors of quarterly variables to be explicitly

disaggregated in terms of the monthly measurement errors, even if they are unobserved

(see Mariano and Murasawa, 2003). Nevertheless, our approach is not fundamentally

different, since JDEMETRA+ also aims to represent GDP growth as a weighted

average of latent factors, i.e. code “Q”, as described in section 4.3. For the rest of the

variables, we use the code “M”, which implies that the growth rate of each one of the

indicators loads contemporaneously on the factor representing the latent growth rate of

the economy.

The user simply needs drag and drop the series, as shown in Figure 1. Then, one

should simply tick those to be incorporated in the model, and transform them so that

they are consistent with the way they are linked to the factors, as explained in Section

4, i.e. “Q”, “M” or “YoY”. Figures 2 (a, b and c) below describes three simple

specifications of our measurement equation. In the case of Figure 2(a), we have

specified only one factor, and all series transformed in log differences “Log, Diff1”.

The series can also be seasonally adjusted by simply adding the option “sa” before or

after the “Log” instruction or converted in year-on-year growth rates by using the

option “Log, DiffY”. Figure 3 describes the specification of the transition equation.

By clicking on the icon highlighted in the screenshot below, users will choose the

number of factors here (i.e. “Equations count=1”) and the number of lags in the VAR

process that defines the transition equation. As in A&D, we choose three lags (i.e.

“Lags count=3”).

Figure 1: Drag and Drop the Data into the Model Space

The “Providers tab” allows you to access the source data so that you can drag and drop it into

the model space. Before selecting the series to be incorporated in the model, one can perform

some basic analysis. For example, by using the “GrowthChart” one can compare the monthly or

yearly growth rate of different time series even if they do not have the same frequency. The

“Periodogram” window can also be used to have an overview of the cyclical properties of the

data and check that the series have been correctly adjusted for seasonality and calendar effects

(frequencies corresponding to the blue and red shadow, respectively).

_____

Figure 2 (a): Model Specification to extract “Latent Real Activity”

Two steps are required to specify the measurement equation. The first step to extract the “latent real activity”

factor is to select all measures of real growth that are associated to it. Next, all series can be transformed into

growth rates (Log, Diff1), so that the factor actually represents the latent growth rate for each month. Thus,

we need to make sure that each series is correctly linked to either the monthly growth rate of the factors

(code “M”) or the quarterly rate (code “Q”), depending on whether it refers to a month or to the whole

quarter. The code “YoY” for the factors can be used to represent year-on-year growth rates of the series

(Log, DiffY), although that was not necessary in this example. The series can also be seasonally adjusted by

simply adding the option “sa” before or after the “Log” code.

_____

5.2 Model Specification to Extract the Latent Inflation Rate

Following A&D, we use the indicators in the right panel of Table 1 to extract a smooth

index of inflation. Figure 2(b) shows that all concepts related to inflation have been

ticked. All the details regarding the specification of the measurement and transition

equations have been described in the previous subsection, 5.1.

Figure 2 (b): Model Specification to extract “Latent Inflation”

Two steps are required to specify the measurement equation. The first step to extract the “latent inflation”

factor is to select all measures of inflation that are associated to it. Next, all indexes can be transformed into

growth rates (Log, Diff1), so that the factor actually represents the latent inflation rate for each month. Thus,

we need to make sure that each series is correctly linked to either the monthly growth rate of the factors (code

“M”) or the quarterly rate (code “Q”), depending on whether it refers to a month or to the whole quarter. The

code “YoY” for the factors can be used to represent year-on-year growth rates of the series (Log, DiffY),

although that was not necessary in this example. The series can also be seasonally adjusted by simply adding

the option “sa” before or after the “Log” code.

_____

5.3 Simultaneous Extraction of the Activity and Inflation Latent Factors

We will assume that variables measuring real activity, such as real GDP growth, will

load on two factors (select “Equations count=2”; Figure 3). The first factor specified in

Figure 2(c), “F1", can be interpreted as a deflator (βtQ

) while the second factor, which

is represented by “F2”, will be related to nominal activity (αtQ

)

ytGDP = ZGDPαt

Q− ΛGDPβt

Q

+ ξt

GDP, [5]

where the sign of the so-called factor loadings ZGDP and ΛGDP is left unrestricted.

Monthly variables such as industrial production, or employment, will be treated in the

same fashion:

yt = Z αt

− Λ βt + ξt

[6]

Conversely, all measures of inflation will load exclusively on the second factor:

πt = Λπβt

+ ξt

π [7]

Since both latent factors, αt and βt

follow an unrestricted VAR and their innovations

may be correlated with each other, as specified in equation [2], our restrictions in the

factor loadings do not represent a serious constrain. The assumption that βt , and not αt

,

has a contemporaneous effect in inflation simply implies that changes in prices driven

by changes in αt can already be accounted for by the latent inflation factor βt

. The

question now is whether we can identify the structural shocks underlying the

fluctuations in both factors.

Figure 2 (c): Model Specification to extract “Activity and Inflation Factors”

Two steps are required to specify the measurement equation. The first step to extract the latent “activity

growth” and “inflation” factors is to select all measures that are have a associated to them. Next, all series

can be transformed into growth rates (Log, Diff1), so that the factor actually represents the latent growth rate

for each month. Thus, we need to make sure that each series is correctly linked to either the monthly growth

rate of the factors (code “M”) or the quarterly rate (code “Q”), depending on whether it refers to a month or

to the whole quarter.

_____

Figure 3: Specifying the transition equation

Specifying the transition equation, at the current development stage, only allows for an

unrestricted VAR with a certain number of lags.

_____

5.4 Structural Analysis (SVAR)

A structural interpretation requires an orthogonalization of the covariance matrix of the

factor innovations Q in the transition equation [2] that is compatible with our definition

of supply and demand disturbances. JDEMETRA+ performs this decomposition using

a simple Choleski scheme that is consistent with the triangular structure we have

imposed on the factor loadings of the measurement equation:

( πt

yt) = (

Λπ 0Λ Z

) (βt

αt ) + (

ξtπ

ξt )

We will show that defining demand shocks as the underlying forces that push nominal

activity without having a contemporaneous effect on inflation, the resulting supply

shocks turn out to generate a negative correlation between output and inflation, which

is consistent with common wisdom. Note first that the transition equation for the

factors,

(βt

αt ) = (

T11 T12 T21 T22

) (βt−1

αt−1 ) + (

uβ,t

uα,t),

can be written in terms of the “structural” shocks uβ,t

∗ and uα,t∗ , which are now

independent and have unitary variance. This alternative VAR representation is

obtained by pre-multiplying all terms of the transition equation by the inverse of the

Cholesky factor C:

(βt

∗

αt∗ ) = (

C11 0 C21 C22

)−1

(βt−1

αt−1 )

(uβ,t

∗

uα,t∗

) = (C11 0 C21 C22

)−1

(uβ,t

uα,t)

Thus, we obtain:

(βt

∗

αt∗ ) = (

C11 0 C21 C22

)−1

(T11 T12 T21 T22

) (C11 0 C21 C22

) (βt−1

∗

αt−1∗

) + (

uβ,t∗

uα,t∗ ).

Next, the measurement equation is also written in terms of the transformed factors. It

turns out that the Cholesky factorization of the covariance of the reduced form

innovations uβ,t and uα,t , i.e. Q = CC′, is the only way in which the loadings

restrictions can be satisfied:

( πt

yt) = (

Λπ 0Λ Z

) (C11 0 C21 C22

) (βt

∗

αt∗ ) + (

ξtπ

ξt )

By looking at both blocks separately, we can easily show that the structural shock

underlying αt∗ , i.e. we will call uα,t

∗ a demand shock, does not have a contemporaneous

effect in inflation variables. Conversely, the shock underlying βt∗, i.e. we will denote

uβ,t∗ as a supply shock, does have an impact in both prices πt

and quantities yt :

πt

= ΛπC11βt∗ + ξt

π

yt = Z C22 αt

∗ + (ΛC11

+ ZC21) βt∗ + ξt

We insist that our naïve identification assumption does not impose any restriction in

the sign of the impulse response functions. We will come back to this issue in more

detail in the next section where the estimation results will be discussed.

JDEMETRA+ has the potential to incorporate alternative identification schemes, but

the current implementation will automatically run the Cholesky decomposition. The

structural interpretation will therefore remain valid only when the loadings conform to

the kind of triangular structure described above.

5.5 Estimation Process

Once the measurement and the transition equations [1]-[2] of the model have been

specified, we need to estimate the factor loadings Z , and the VAR parameters T1, T2

and T3 along with Q, the covariance matrix of the innovations, and the diagonal

covariance of the idiosyncratic measurement errors R. The Kalman filter algorithms

implemented in JDEMETRA+ can handle the particularities of the nowcasting problem

and evaluate the likelihood via prediction-error decomposition, for a given point in the

parameter space. The objective of the estimation process is to combine several

optimization methods that allow us to find the vector of parameters that maximizes the

likelihood.

Figure 4: Estimation options

The method of principal components can be used to obtain an estimator of the factors or simply to

have a starting value to initialize either the EM algorithm or the numerical optimization. The EM

algorithm itself can also be used either in isolation, as in Banbura and Modugno (2010), or as a

starting value for the numerical optimization. This is in our view the most sensible approach, since the

EM algirhtm can be very slow in the neibourhood of the maximum likelihood estimator. The

numerical optimization can be decomposed in two steps by using the option “Iterations by blocks”,

emulating the logic of the EM algorithm. Both the Broyden–Fletcher–Goldfarb–Shanno (BFGS) and

Levenberg-Marquardt algorithms are at the user’s disposal. The use of a final EM algorithm is

unnecessary.

_____

As shown in Figure 4, we can enable the option to estimate the model parameters by

using the principal components of our panel as estimates of the factors, as in Giannone,

Reichlin and Small (2008) or Stock and Watson (2002). In order to achieve a higher

degree of efficiency, one can use those estimates as starting value for a more elaborate

optimization procedure. In this case, we may want to enable the EM algorithm, as in

Banbura and Modugno (2010) or use directly a numerical optimization procedure, as in

Camacho and Pérez-Quirós (2010). This option has turned out to be much faster in all

the examples we have tested thanks to the multithreading ability of our software, which

is able to reduce the execution time by exploiting multiple processors in parallel.

However, big models (i.e. in our context this means hundreds of variables, and

multiple factors) are quickly estimated mixing both methods, i.e. using the EM

algorithm in a first step and subsequently proceed with numerical optimization.

Regarding the numerical optimization procedure, there are two features that can be

useful for complex models. First, the user can enable the option to estimate a

simplified model (only one lag in the VAR) to obtain starting values and then proceed

with numerical optimization for the estimation of the original model. Second, by

ticking the mixed estimation box, the numerical optimization can be decomposed in

two steps (“iterations by block”), emulating the logic of the EM algorithm. Both the

Broyden–Fletcher–Goldfarb–Shanno (BFGS) and Levenberg-Marquardt algorithms

are at the user’s disposal. The use of a final EM algorithm is unnecessary. This option

was introduced at an earlier development stage before the numerical procedure was

fully operational.

6 Estimation Results

Once the estimation process is complete, all the results can be displayed by clicking on

the output tab (Figure 5). The estimation results (see Estimation/Model) show that the

variables related to the real growth rate of economic activity, highlighted in grey, load

on the latent inflation factor βt with the opposite sign to the inflation variables

themselves. This result suggests that one can identify innovations to βt that can

generate a negative correlation between prices and quantities, i.e. supply shocks.

Estimation of the factors

Using only the real activity monthly indicators suggested by A&D, the expected value

of our factor conditional on the whole information set resembles the ADS economic

activity index (see Figure 6), which have been taken from the website of the

Philadelphia Fed. The JDEMETRA+ estimation of the activity factor turns out to be

very similar independently of whether inflation variables have been incorporated in the

model or not. Regarding the inflation factor itself, a visual examination suggests that

supply shocks have not played a major role over the last recession (see upper panel of

Figure 7). This contrasts with the inflationary dynamics registered by the indicator

during the recessions dated in the mid-seventies and early eighties, which informally

suggests the prevalence of supply factors.

Figure 5: The Output

The output is divided in three blocks. First, we keep all information regarding the original data

and estimation options inside “Input”. Second, all results related to the estimation are stored

inside “Estimation”. This includes a display of the estimated model, plots of a historical shock

decomposition, plots of all the series without the noise component, estimates of the factors, and

analysis based on a decomposition of the shocks. Finally, all results related to “Forecasts” are

included under a separate title.

_____

Figure 6: Comparison with the ADS Index

Note: The data vintage corresponds to the 30th of June, 2014. From July onwards, the factor is

forecasted. The factors with confidence intervals can be visualized in the “output” tab by

clicking on “Factors”.

_____

Figure 7: Inflation factor over the business cycle




_____

Figure 8: Activity factor over the business cycle




_____

Estimated factor loadings

Figure 9: Factor Loadings

The estimation results shows that the variables related to the real growth rate of economic

activity, highlighted in grey, load on the latent inflation factor 𝛽𝑡 with the opposite sign to the

inflation variables themselves. This result suggest that one can identify innovations to 𝛽𝑡 that

can generate a negative correlation between prices and quantities, i.e. supply shocks.

_____

F1

(βt)

F2

(αt)

Real Gross Domestic Product 0.008 0.010 0.02 0.07 0.39

Real personal income excluding current transfer receipts 0.002 0.006 0.15 0.30 0.80

All Employees: Total nonfarm 0.001 0.002 0.00 0.61 0.25

Industrial Production Index 0.002 0.008 0.10 0.54 0.44

Real Manufacturing and Trade Industries Sales 0.002 0.010 0.15 0.40 0.68

Initial Claims 0.001 0.049 -0.13 -0.31 0.80

Producer Price Index: Finished Goods 0.003 0.006 -0.53 - 0.46

Gross Domestic Product: Implicit Price Deflator 0.008 0.006 -0.08 - 0.25

Nonfarm Business Sector: Compensation Per Hour 0.012 0.009 -0.37 - 0.74

Crude Oil Prices: West Texas Intermediate (WTI) - Cushing, Oklahoma 0.004 0.085 -0.40 - 0.76

S&P GSCI Non-Energy Spot - PRICE INDEX 0.003 0.045 -0.02 - 1.00

Consumer Price Index for All Urban Consumers: All Items 0.003 0.003 -0.68 - 0.10

Estimates of the factor loadings for all seriesSample

meanStdev

Normalized

FactorsIdiosyncratic

Variance

Structural Identification

As discussed above, a formal quantification of the role of both supply and demand

determinants is possible within JDEMETRA+ if we are willing to explicitly account

for the interaction between both factors. Such model, which considers both factors as a

structural VAR with three lags (to be consistent with the original A&D formulation), is

estimated here with maximum likelihood. The model is so simple that it does not

matter whether you use the EM algorithm or a more sophisticated optimization

procedure. The resulting factors remain, as discussed above, unchanged with respect to

the ones obtained with the two separate panels. However, this joint model allows for a

structural interpretation of the VAR innovations.

The structural identification of supply and demand shocks is conducted here using the

empirical framework described in Section 5.4. Although, we recognize it is a very

naïve formulation, it does not impose that supply shocks generate a negative

correlation between inflation and real activity.

Figure 10: Historical Decomposition of Real GDP (de-meaned)

Note: The data vintage corresponds to the 30th of June, 2014. From July onwards, the factors

are forecasted. The data plotted in this graph corresponds to the “Historical Shock

Decomposition” graph provided by JDEMETRA+ (see Figure 11).

_____

We are simply assuming that a demand shock does not have a contemporaneous effect

in inflation variables, possibly because prices are sticky, while supply shocks can

freely impact both prices 𝜋𝑡 and quantities 𝑦𝑡

. Ignoring the presence quarterly

variables for the sake of simplicity, the structural model can therefore be written as

follows:

( 𝜋𝑡

𝑦𝑡) = (

Λ𝜋∗ 0

Λ ∗

𝑍∗ )(

𝑇11∗

𝑇12

∗

𝑇21∗

𝑇22

∗ )

𝑡

(𝛽0

∗

𝛼0∗) + (

Λ𝜋∗ 0

Λ ∗

𝑍∗ )∑(

𝑇11∗

𝑇12

∗

𝑇21∗

𝑇22

∗ )

𝑗

𝑡−1

𝑗=0

(𝑢𝛽,𝑡

∗

𝑢𝛼,𝑡∗

) + (𝜉𝑡

𝜋

𝜉𝑡 )

Thus, we can obtain a historical decomposition of out activity and inflation series in

terms of the structural shocks 𝑢𝛽,𝑡∗ (supply) and 𝑢𝛼,𝑡

∗ (demand). The contribution of the

initial state of the factors in stationary models is significant only at the beginning of the

sample, i.e. the transition matrix to the power of “t” converges to zero.

Figure 11: JDemetra+ Historical Shocks Decomposition Graph

Note: The data vintage corresponds to the 27th of October, 2014. From November onwards, the factors are

forecasted. This interactive graph corresponds to the actual shock decomposition provided by

JDEMETERA+. All the elements can be highlighed by cliking on them and removed, for the sake of

simplicity. As opposed to the simplified version plotted in Figure 10, where only the signal and its

contributions are plotted, what we show here is the actual data (demeaned). Thus, the decomposition

involves now the noise shocks in addition to the contributions of orthogonalized factor innovations (the

structural shocks). The contribution of the initial conditions is negligible in this case, but it could play a role

in models where the factors have a unit root.

_____

Figures 10 and 11 shows the resulting decomposition of the signal underlying GDP

growth rate in terms of the structural shocks, providing a quantitative support to the

A&D’s claim that the recessions in the mid-seventies and early eighties were largely

driven by supply shocks. In turn, the contribution of supply shocks during the last

recession is rather limited.

In-sample fit

So far, we have formalized A&D discussion on the source of business cycle

fluctuations with special emphasis on the factors and their behavior during recessions.

The JDEMETRA+ interface offers many other features that allow users to validate the

model in-sample and to perform out of sample forecasts in real time. By clicking on

Estimation/Fit/”Signals vs Data”, we display a graph of all series together with their

underlying signal. Figures 12 and 13 show the graph for GDP and employment growth.

Figure 12: JDEMETRA+ Analysis of Dynamic Factor Models (GDP)

Figure 13: JDEMETRA+ Analysis of Dynamic Factor Models (Employment)

Note: The data vintage corresponds to the 27th of October, 2014. From November onwards, the

data are forecasted. One can visualize the graph corresponding to any of the series that appear

in the model.

_____

The difference between both series, which is the so-called idiosyncratic measurement

error, is also analyzed in detail. By clicking on Estimation/Residuals we obtain a table

with the autocorrelation of the measurement errors, which will appear in red when they

are considered to be statistically significant. The sections Estimation/Residuals/Matrix

and …/Correlation provide an analysis of the cross correlation by using dynamic

visualization techniques that can help to identify hidden patterns in the residuals. When

the cross-correlation is pervasive, the model can be considered to be misspecified.

7 Forecasting

The nowcasting library has been optimized for its use in real time situations. However,

the evaluation of out-of-sample forecasts is possible only after a sufficiently large

forecasting record has been archived. The forecasts displayed in Figure 14 correspond

to 2014Q3 and beyond.

Figure 14: Real GDP growth forecast obtained on 27th of October, 2014

Note: The data vintage corresponds to the 27th of October, 2014. The forecasting interval

represents the aggregate effect of news uncertainty (future data releases) and measurement

errors.

_____

Currently, we are developing an independent evaluation library that takes into account

the calendar of macro-economic releases (see Figure 15) in order to provide realistic

simulations of forecast errors in multivariate and univariate time series models. This

will allow us to use pseudo out-of-sample forecasts can be used for evaluation

purposes.

8 A Credible Narrative to Account for Forecasting Revisions

Many of the results mentioned so far are based on the model estimated with the vintage

of data available on the 27th of October. Today, on the 12th

of November, we have

some new data available. We will show now the impact of that news on the forecasts

for GDP at several forecast horizons. Figure 15 shows an approximate calendar of

data releases. This will play a crucial role in the evaluation of forecasting accuracy.

Figure 15: Calendar of Data Releases

In this calendar, based on the information available in Table 1, we represent the approximate publication delay

of all the indicators incorporated in the model. Employment, for example, is available soon after the end of the

month. In order to represent data revisions in the national accounts, we make the distinction between the first

release (i.e. Advanced), the second release (i.e. Preliminary) and the third release (i.e. Final). In the model,

however, we simplify things by incorporating Preliminary and Final releases alone. This is a relevant

modification with respect to the ADS approach.

_____

For the moment, note that in order to represent data revisions in the national accounts,

we make the distinction between the first release (i.e. Advanced), the second release

(i.e. Preliminary) and the third release (i.e. Final). In the model, however, we will

simplify things by incorporating Preliminary and Final releases alone. This is a new

ingredient with respect to the ADS approach, where no distinction is made.

8.1 A story of news, data revisions, and inflation-output interactions

The following table summarizes the information that is going to be described in this

section. The first example analyses how the forecasts obtained on October 27 are

revised with the information set available on November 12. Although we have data

revisions, we ignore them to focus on the concept of news. The second example does

consider data revisions, but they turn out to be insignificant and the emphasis is placed

PREVIOUS QUARTER

List of Indicators

Crude Oil Prices: West Texas

Intermediate (WTI) - Cushing,

Oklahoma

S&P GSCI Non-Energy Spot -

PRICE INDEX

Initial Claims

All Employees: Total nonfarm

Producer Price Index: Finished

Goods

Consumer Price Index for All

Urban Consumers: All Items

Industrial Production Index

Real personal income excluding

current transfer receipts

Real Manufacturing and Trade

Industries Sales

F

Nonfarm Business Sector:

Compensation Per Hour

Gross Domestic Product: Implicit

Price Deflator

Real Gross Domestic Product

A

P

A

P P

F

F

A

P

F

A

CURRENT QUARTER NEXT QUARTER

first month second month third month first month second month third month

on the interactions between inflation and output. In the final example, data revisions

happen to play an important role:

Examples Weights Impacts

1: Simplified context

Figure 17

Figure 18

ℱold : October 27

ℱnew: November 12

2: Inflation and output interactions

Figures 19, 20

Figure 21

ℱold : September 11

ℱnew: October 27

3: The role of data revisions

Figure 22, 23, 24

Figure 25

ℱold : November 12

ℱnew: November 25

First of all, it is worth mentioning that in the three cases we follow the same procedure

to update the forecast. Such an update is decomposed in terms of news and revisions to

past data following four logical steps:

[1] . A given model based on the information set ℱold can be

archived, say on October 27. This implies both model and data are frozen and

we are not able to perform any modification. The forecasts and all functions

of this model are stored and can be retrieved at any time.

[2] . On November 12, we update our database incorporating all

the news and data revisions that have arrived since the last time we refreshed.

JDemetra+ will look for all variable incorporated in the model and update

their values for the whole time span.

[3] . By clicking on the green arrow in the processing tab, we will

run the Kalman filter and smoother to re-estimate the factors. Note that this

process is executed using the last available version of the model, i.e. the same

specification and parameters. Because we have refreshed the data in the

previous step, the Kalman filter will update the forecasts.

[4] . Our updated forecasts are meaningless without an economic

interpretation. Thus, we are going to re-calculate those updated forecasts by

expressing them as a function of the news and data revisions that have

entered our information set. Computational details are provided in the

appendix.

By clicking on the News tab (see Figure 16) and choosing Versions we can see the list

of datasets that have been archived. In our case, the last archive took place in October

27 at 19:22CET, while the current update has occurred on November 12 at 22:25CET.

Thus, our main goal is to compare the last archived (version 0) with the new forecast

obtained with our updated data (version 1).

Figure 16: Versions

The same model (and estimation) archived for the first time on the 27th of October, is now used

to analyse the news. The updating sequence consists of two steps: First, the data needs to be

refresed (click on “New Model Flash” above and Refresh). Once the data has been refreshed,

click on the tab “Processing” and run the model (by default, all estimation options have been

unchecked to avoid re-estimating the parameters). Finally, by clicking on the tab “News”, the

analysis of news is executed, as described in Section 3, for all variables and forecast horizons.

_____

Weights and Impacts in a Simplified Context

Figure 17 can be found in the tab “News”, by clicking on News/Weights. Here, all the

new data releases are compared with the forecasts of the model. From all the news (i.e.

forecast errors), the largest weight corresponds in this case to the employment release,

which was worse than expected by the model. Remember from Equation 3 that the sum

of all news times their respective weights determines the size of the revision for GDP.

Although we only show the analysis for the fourth quarter, all the subsequent quarters

can be found by moving the bar towards the right. By looking at the graph below,

where the updated forecasting path is compared with the old one, we can already

anticipate that most of the forecast revision remains within the fourth quarter.

Figure 17: Updating Advanced GDP Projections (November 12)

In the tab “News”, click on News/Weights to compare all the new data releases with the figures

expected by the model. From all the news, the largest weight (see Equation 3) corresponds in

this case to the employment release, which was worst than expected by the model. The sum of

all news times their respective weights equals -0.45, which corresponds to a modest downward

revision of the nowcast for the Advance release in the forth quarter of the year. The graph

below compares the updated forecasting path with the old one.

_____

The current version of the software computes the impacts of all news, including data

revisions, for all variables and forecast horizons. This computation took a couple of

seconds in this simple example, but it could take a few of minutes when there are

revisions to past data in all variables. Figure 18 contains the same information as

Figure 17, but it does the math for you. The forecasting revision for all series is

decomposed in terms of the impact of each piece of news. The plot of the forecasting

revision along with the contribution of all the news turns out particularly informative.

From all the news, the largest impact corresponds in this case to the employment,

followed by real personal income, real manufacturing and the advance GDP release.

The sum of those impacts equals -0.46 for the fourth quarter of 2014. The forecast for

2015Q1 is revised downards by -0.3, but revisions to subsequent quarters become very

small.

Figure 18: News Impacts at Updating the Advanced GDP Forecast (November 12)

In the tab “News”, click on News/Impacts to decompose the forecast revisions in terms of the

news. We have the information for all variables, but let’s focus on GDP. From all the news, the

largest impact corresponds in this case to the employment, followed by real personal income,

real manufacturing and the advance GDP release. The sum of those impacts equals -0.45 for the

forth quarter of 2014. The forecast for 2015Q1 is revised downards by -0.3, but subsequent

revisions become very small.

_____

Inflation-Output Interactions

The JDEMETRA+ news algorithm can also be used for the analysis of scenarios. Let’s

assume that we want to incorporate in our forecast the knowledge that CPI inflation

will be zero for the rest of the year, which would be clearly below the figures expected

by the model. If such an assumption aims to reflect an improvement in productivity,

then our forecasts for real GDP growth will improve. If on the other hand our inflation

scenario simply aims to represent a sudden deterioration of demand, growth

expectations will have to be revised downwards. Fortunately, the Kalman filter

provides the most likely response of the economy to the whole set of news

incorporated in the system. Those forecast do not require any structural interpretation

of the shocks such as the one proposed above.

Rather than building a scenario, let’s consider an example that has actually occurred in

real time. Figures 19 and 20 compare the old forecasts obtained on September 11 with

the new predictions for output and inflation obtained after refreshing the data on

October 27. We can see that real GDP growth expectations for 2014Q3 and 2014Q4

have been revised upwards by 0.5 and 2 percentage points respectively. The GDP

deflator projections for those periods have been revised in the opposite direction,

suggesting the presence of supply shocks. Figure 21 sheds light in the factors that

account for that upward revision in GDP in spite of the deflationary pressure, which

was mostly driven by oil prices. Not surprisingly, the consumer price indexes for

August and September, which were lower than expected by the model, had a positive

contribution in the GDP forecast revision for 2014Q3, 2014Q4 and beyond (yellow

and green colors). From all the news, the largest impact corresponds in this case to the

industrial production (blue) and unemployment claims (red).

The role of data revisions

In our examples, we have ignored the frequent situation in which new data releases for a

series i contain important modification in its history. This implies that we will have many

pieces of news for the series i, each one referring to a period tj in the history that has

been subject to revision: yij,tj− E [yij,tj

|ℱold]

Analyzing the impact of all those revisions at updating a given series is challenging.

However, our approach helps the user to quickly identify the revisions that have a major

impact. We propose to incorporate the aggregate impact of all revisions, in a new row,

which can be expanded. Only in the case such impact is worth being investigated, the

user will open a new window with the actual decomposition arranged by variable, in

chronological order.

Let’s consider a concrete example where the information set corresponding to November

12 ( ℱold) is updated on November 25 ( ℱnew). Figures 22-24 shows the updated

forecasts for the Advanced GDP, Deflator and Industrial production conditional on the

new information set. The first two figures (22-23) also reveal that the real growth and

inflation releases for Q3 were in line with the model forecasts. Thus, the forecast

revisions for Q4 and beyond must be due to other news. In turn, figure 24 shows that the

Industrial Production release for October has been clearly worse than expected by the

model. One can also observe that the official statistic for industrial production in the

month of September has suffered a downward revision too. The role played by all news

and data revisions at updating a given variable can be summarized by clicking on

Impacts. Figure 25 shows that the downward revision in GDP forecasts for Q4 and

beyond is mostly driven by the bad news contained in the releases of employment and

industrial production for October, and unemployment claims for November. Expanding

All Revisions allows us to analyse the role played by statistical data revisions. In this

case, the largest impact corresponds to industrial production in September and the

unemployment claims in October. The impact of the revisions at updating Q4 and

beyond is much smaller than the impact of news. We can also observe that data revisions

refering to a more distant past, i.e. very common in seasonal adjusted data, tend to have a

negligible impact.

9 Conclusions

This paper presents an innovative expert system that is suitable for real-time

forecasting and nowcasting applications, with a particular emphasis in decomposing

the forecast revisions in terms of the unexpected component of new data releases.

More than a translation of the models described in leading nowcasting applications

such as Banbura and Modugno (2010) or Camacho and Pérez-Quirós (2010), the

library described here proposes a re-factoring of those methods exploiting existing

routines of the JDEMETRA+ environment, originally developed for the analysis of

seasonal data. In particular, this library makes an extensive use of both the state-space

modeling framework and dynamic graphical analysis tools that have been developed

for multiple purposes.

The nowcasting model proposed for the US economy as an illustration is, to the best of

our knowledge, the first one that accounts for the joint behavior of quantities and

prices. It complements the business cycle analysis provided at the Philadelphia Fed by

allowing for inflation-output interactions. Users can easily introduce their own

expertise in the form of alternative methods within the class of dynamic factor models,

contributing to extend the limits of the currently established practices in the

nowcasting literature. All model specifications can be saved along with the data

vintages that are available in real time. Thus, we hope our tool will catalyze the

dissemination of research on nowcasting and real-time data analysis and provide

practitioners with the means to improve the state-of-the-art. From the methodological

point of view, it is also possible to implement the analysis of news and data revisions

using alternative models, such as the VAR with mixed frequencies. Recent

applications, such as the work by Schorfheide and Song (2014), for example,

document the extent to which information improves the forecasts in real time.

However, they do not provide an analytical decomposition of the forecasting revisions

in terms of news.

Figure 19: Updating Advanced GDP Projections (October 27)

Figure 20: Updating Advanced GDP Deflator Projections (October 27)

In the tab “News”, click on News/Weights. By expanding the folder All News we can compare all

the new data releases with the figures expected by the model, and see their weight (Equation 3) at

updating inflation expectations. The same holds for the data revisions. By expanding the folder All

Revisions we can compare the revised data with the previous version. The graphs in both figures

illustrate the downward and upward revisions of the forecasting path for inflation and output,

respectively.

____

2014Q3

400xlog Δ

2014Q3

log Δ

Figure 21: News Impacts at Updating Advanced GDP projections (October 27)


news and revisions. We have the information for all variables, but let’s focus on GDP. From all

the news, the largest impact corresponds in this case to the industrial production (blue),

unemployment claims (red) and the consumer price index (highlighed in yellow), which turned

out to lower than predicted. Expanding the All Revisions help us to analyse the role played by

statistical data revisions. However, their aggregate effect, summarized in the blue line, is very

small.

_____

RevisionsInsignificant

Figure 22: Updating Advance Release of GDP Projections (November 25)

Figure 23: Updating Advance Release of GDP Deflator Projections (November 25)

In the tab “News”, click on News/Weights. By expanding the folder All News we can compare

all the new data releases with the figures expected by the model, and see their weight (Equation

3) at updating inflation expectations. The same holds for the data revisions. By expanding the

folder All Revisions we can compare the revised data with the previous version. The graph in

Figure 21 illustrates the downward revision of GDP for Q4, while inflation expectations in

Figure 22 do not change by much.

____

2014Q4

2014Q4

log Δ

Figure 24: Updating Industrial Production Projections (November 25)

In the tab “News”, click on News/Weights. By expanding the folder All News we can compare all

the new data releases with the figures expected by the model, and see their weight (Equation 3) at

updating inflation expectations. The same holds for the data revisions. By expanding the folder

All Revisions we can compare the revised data with the previous version.

____

2014 Octlog Δ

Figure 25: News Impacts at Updating Advance GDP Projections (November 25)


news and revisions. We have the information for all variables, but let’s focus on GDP. From all

the news, the largest impact corresponds in this case to employment, industrial production,

unemployment claims, which are all highlighted in blue in the spreadsheet. Expanding the All

Revisions help us to analyse the role played by statistical data revisions. However, their

aggregate effect, summarized in the blue line is smaller than that corresponding to news, in blue.

_____

10 Download the JDEMETRA+ software in any platform

The last updated version of the software can be downloaded here


Download (and unzip) the plug-ins:


Run the main application: ./bin/nbdemetra[64.exe]

You may get an error message saying that you do not have the last version of

Java. In such case, just download it here:

http://www.oracle.com/technetwork/java/javase/downloads/jdk8-downloads-

2133151.html Install the plug-ins:

Main menu: « Tools Plugins »

Select tab « Downloaded »

Click « Add plugins… »

Select NbDemetra-Core2 and NbDemetra-Dfm

(from plugins repository)

Follow the instructions.

RevisionsIPI OctClaims Nov




http://www.oracle.com/technetwork/java/javase/downloads/jdk8-downloads-2133151.html

http://www.oracle.com/technetwork/java/javase/downloads/jdk8-downloads-2133151.html

11 References

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[16] Evans M. D. D. (2005). “Where are we now? Real-Time Estimates of the

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[17] Frale, C., M. Marcellino, G. L. Mazzi, and T. Proietti (2011): “EUROMIND: a

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[18] Ghysels, E., P. Santa-Clara, and R. Valkanov (2002). “The MIDAS touch:

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[19] Giannone, D., L. Reichlin and D. Small (2008). “Nowcasting: The Real-Time

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https://ideas.repec.org/a/fip/fedfer/y1996p3-11n3.html

https://ideas.repec.org/a/fip/fedfer/y1996p3-11n3.html

https://ideas.repec.org/s/fip/fedfer.html

12 APPENDIX A: News Decomposition

Consider the following representation of two given vintages of data:

ℱv contains all time series of Table 1 as available at a given date v.

ℱv+1 contains the same time series as available at a later date v + 1.

Using the same notation as Banbura and Modugno (2010), the news content of the

second vintage is defined by the 𝐽𝑣+1 –sized vector of forecast errors Iv+1. Let’s

remove the subindex and use J ≡ Jv+1 to denote the number of news:

Iv+1 = [

yi1,t1− E[yi1,t1

|ℱv]…

yiJ,tJ − E [yiJ,tJ |ℱv]] ,

This vector represents is the part of the release ℱv+1 that is orthogonal to the

information already present in ℱv . This notation can be easily understood by

examining the example presented in Figure 26. Here, we have a total of J =

5 innovations. Two of them correspond to two consecutive months, t1 and t2 that

become available for the same variable i1 = i2 = 1. The third innovation corresponds

to a release for variable i3 = 2 and refers to t3. Note that both t1 and t3 correspond in

this example to two innovations for the different variables but relative to the same

month, which is March. Finally, the forth and fifth innovations corresponds to the last

variable, N, which is revised for the months of March and April. Thus, data revisions

have and index i corresponding to the variable they refer to and a subindex j that

refers to the point in time. As a result, revisions can be represented with the same

notation as news resulting from additional data releases:

revision ij ∶ yij,tj − E [yij,tj

|ℱv], ij = N, and tj = March

revision ij+1 ∶ yij+1,tj+1− E [yij+1,tj+1

|ℱv], ij+1 = N, and tj+1 = April

The forecast revision for a given variable k, E[yk,tk

|ℱv+1] − E[yk,tk|ℱv] , is given by

its projection on the news information set Iv+1:

E[yk,tk

|Iv+1] = E[yk,tk Iv+1

′ ] E[Iv+1 Iv+1′ ]−1Iv+1 [9]

This linear projection determines the impact of the news. Thus, the revision can be

expressed, more explicitly, as a weighted average of the different pieces of news:

E[yk,tk|Iv+1] = ∑ wj (yij,t1

− E [yij,tj |ℱv])

Jv+1

j=1

[10]

The expectations shown in expression [9], which are required to compute the weights

in [10], are a function of the estimated state-space model parameters:

E[yk,tk Iv+1

′ ] =

[ Λk E [ (ftk − E(ftk|ℱv)) (ft1 − E(ft1|ℱv))

′

] Λi1′

Λk E [ (ftk − E(ftk|ℱv)) (ft2 − E(ft2|ℱv))′

] Λi2′

⋮

Λk E [ (ftk − E(ftk|ℱv)) (ftj − E(ftj|ℱv))′

] Λij′

⋮

Λk E [ (ftk − E(ftk|ℱv)) (ftJ − E(ftJ|ℱv))′

] ΛiJ′

] ′

[11]

Figure 26: Two data vintages

In this stylized representation of two consecutive information sets, we have also represent revisions in old data. Macroeconomic data revisions can change both

recent and historical values of a time series, which implies that a large number

of innovations needs to be incorporated in 𝐼𝑣+1

__________

i = 1 2 3 … N

old data old data old data old data

january …


february …

old data

march …

old data

april …

i = 1 2 3 … N


january …


february …

new data new data revision

march t1 t3 … t4

new data revision

april t2 … t5

The element j, l of matrix E[Iv+1 Iv+1′ ] represents the covariance of the two innovations

indexed by j and l:

𝐸[𝐼𝑣+1 𝐼𝑣+1

′ ]{𝑗,𝑙}

= Λ𝑖𝑗 𝐸 [ (𝑓

𝑡𝑗− 𝐸(𝑓

𝑡𝑗|ℱ𝑣)) (𝑓

𝑡𝑙− 𝐸(𝑓

𝑡𝑙|ℱ𝑣))

′

] Λ𝑖𝑙′ + 𝐸 [ 𝜉

𝑖𝑗𝑡𝑗𝜉𝑖𝑙𝑡𝑙

]

[12]

Here, we use the same notation as in Banbura and Modugno (2010), who provide

details on the derivations. Note that the assumption that measurement errors are

idiosyncratic implies:

E [ξijtjξiltl

] = {R{j,l} if j = l

0 if j ≠ l

The expression 𝐸 [ (𝑓𝑡𝑗− 𝐸(𝑓𝑡𝑗

|ℱ𝑣)) (𝑓𝑡𝑙− 𝐸(𝑓𝑡𝑙

|ℱ𝑣))′

] implies that we need to

compute the conditional covariance of the factors in the case that 𝑡𝑗 and 𝑡𝑙 refer to very

distant periods of time. The state-space representation of the model is automatically

enlarged in order to make sure that all those covariance terms are obtained directly by

executing the Kalman smoother algorithm, i.e. the transition equation will

include 𝑡𝑚𝑎𝑥 − 𝑡𝑚𝑖𝑛, where 𝑡𝑚𝑎𝑥 and 𝑡𝑚𝑖𝑛 represent the most recent and oldest time

period, respectively, among the set {𝑡1, … , 𝑡𝐽, 𝑡𝑘}. The time index 𝑡𝑘 represents the

month for which the reaction to news of our target variable ytk is being analyzed

ESS GUIDELINES FOR SEASONAL ADJUSTMENT

1

Dominique LadirayINSEE - France

The ESS Guidelines on Seasonal Adjustment

The ESS Guidelines on SA

Outline

› A Need for Guidelines on Seasonal Adjustment– The ESS specificities– The ECB-Eurostat Steering Group on Seasonal Adjustment

and its Sub-groups

› Tools for the Implementation of the Guidelines– A New Software: Demetra+– More is needed: Handbook, Tutorials, Research Papers,

Training etc.

› The Guidelines on Seasonal Adjustment–Presentation and Comments

2


ESS specificities (1)

› 27 Member States and a lot of Institutes–Different characteristics of national statistical systems–Different level of expertise–Different internal organizations

› Legal acts as the major instrument for harmonization of statistical production

–Rarely giving clear rules for seasonal adjustment

› Seasonal adjustment performed on the basis of sectoral (units) and national practices

–Lack of comparability



› European aggregates derived from national data–Aggregation–Estimation–Aggregation/estimation

› Crucial role of harmonization for the quality of European aggregates

› But relevant discrepancies in:–calendar adjustment –seasonal adjustment–revisions policies

3



› Several recommendations for the harmonization of seasonal adjustment practices

–ECOFIN Council–Economic and Financial Committee (EFC)–Committee for Monetary, Finance and Balance of payments

statistics (CMFB)› Key points:

–High degree of harmonization of seasonal and calendar adjustment practices for Principal European Economic Indicators (PEEIs) needed

–Convergence of revisions policy for seasonal adjusted data–Improvements on the communication on seasonally and

calendar adjusted data


0 0 -- Seasonal Adjustment: advantages and costsSeasonal Adjustment: advantages and costs

Advantages- Provide more smoothed and understandable series for analysts- Facilitate comparisons of long/short term movements- Supply users with necessary input for BC analysis, TC decomposition and

turning points detection

Cautions- SA depends on ‘a priori’ hypothesis- Quality of SA depends on quality of raw data- Lower degree of comparability of data among countries and across

statistical domains if clear policies are not defined- Usefulness of SA data for econometric modelling to be carefully considered

Costs- Time consuming, significant computer/human resources required- Common and well defined IT structure is needed- Inappropriate or low quality SA can give misleading results

4


1 – Pre-treatment

1.1 - Objectives of the pre-treatment of the series

1.2 - Graphical analysis of the series

1.3 - Calendar adjustment

1.3.1 - Methods for trading/working day adjustment

1.3.2 - Correction for moving holidays

1.3.3 - National and EU/Euro-area calendars

1.4 - Outlier detection and correction

1.5 - Model selection

1.6 - Decomposition scheme


1.1 Objectives of the pre1.1 Objectives of the pre--treatmenttreatment

Options:– Running detailed pre-treatment– Running an automatic pre-treatment– No pre-treatment

Evaluation of alternatives:A. Detailed pre-treatment for at least more important

indicatorsB. Pure automatic pre-treatmentC. No pre-treatment

5


1.2 Graphical analysis of the series1.2 Graphical analysis of the series

› Options:–Use of basic graph in the time domain–Use of sophisticated graphs (spectrum, autocorrelograms)–Use default run of the SA software

› Evaluation of alternatives:A.Detailed graphical analysis based on basic graphs, spectra,

autocorrelograms. The analysis could be complemented with a first explanatory run of the SA software on complete set of series

B.First graphical analysis of the most important series (with explanatory first run of the SA software) on most important series

C.No first explanatory analysis of important series


1.3 Calendar adjustment1.3 Calendar adjustment

› Options

– CA on all series showing significant and plausible calendar effect within a robust statistical approach (RegARIMA)

– CA with non standard statistical approach – Proportional adjustments – Do not perform any kind of CA

› Evaluation of alternatives

A. RegARIMA approach with check for significance and plausibility of effects

B. Regression approach based on the provisional irregular component

C. Proportional methods; other adjustments; no adjustment; CA on all series without any checking

6


1.3.1 Methods for trading/working day adjustment1.3.1 Methods for trading/working day adjustment

› Options– Proportional methods

– Regression methods in a multivariate regression framework‐ (with or without correction for the length of the month or Leap Year)

– RegArima correction (as before but with ARIMA residuals)

– No correction

› Evaluation of alternativesA. RegArima approach (in case of economic rationale for the

existence of calendar effect)- All pre-test for number of regressors, length and composition of month- Check for plausibility of effects

B. Regression approach based on provisional irregular component

C. Proportional methods, other adjustments or no adjustment


1.3.2 Correction for moving holidays1.3.2 Correction for moving holidays

› Options– Proportional adjustment– Automatic correction– Correction based on an estimation of the duration of the moving

holidays effects– No correction

› Evaluation of alternativesA. RegArima approach

Pre-test for Easter and other moving holidays effectsDefinition of the length of moving holiday effect on the basis of pre-tests Check of plausibility of effects

B. Regression approach based on the provisional irregular component

C. No tests/correction despite diagnostic evidence of such effects, proportional adjustment

7


1.3.3 National and EU/Euro area 1.3.3 National and EU/Euro area calendars calendars

› Options– Use of default calendars

– Use of national calendars or the EU/Euro-area one as appropriate

– Definition of series for which calendar adjustment is not required

› Evaluation of alternativesA.

Calendar information used to be available to the publicB. Use of default calendars (without any reference to national and

European public holidays), no calendar correction despite evidence

C. Use of default calendars complemented by historical list of national public holiday to be corrected for

European aggregates (Direct approach) EU/Euro-area calendars

MS or EU aggregate (Indirect approach) National calendars


1.4 Outlier detection and correction1.4 Outlier detection and correction

› Options– Types of outliers to be considered for pre-testing– Removal of outliers before seasonal adjustment– Including most important outliers in the regression model as

intervention variables› Evaluation of alternatives

A. The series should be checked for different outliers- Outliers due to data errors to be corrected before treatment - Outliers should be explained/modelled using all available information

– Outliers with a clear interpretation (severe strikes, changes in government policy, territory changes ..) included as regressors

– Particular attention at the end of the series

B. As A), but complete automatic procedure according to available tools

C. No preliminary treatment of outliers

8


1.5 Model selection1.5 Model selection

› Options – Automatic model selection– Model selection based on a set of predefined models– Manual model selection

› Evaluation of alternativesA. Automatic selection within a large number of models according

to tools:- Check for model adequacy using standard statistical tests (normality,

heteroskedasticity, serial correlation, …) and spectrum diagnostics

- Manual model selection for most important/problematic series

B. As before, but complete automatic procedureC. Selection based on a restricted number of pre-defined models

not tested for adequacy with the set of series being adjusted


1.6 Decomposition scheme1.6 Decomposition scheme

› Options– Automatic decomposition scheme selection– Manual decomposition scheme selection after graphical inspection– For series with zero or negative values adding a constant and select

the most appropriate scheme

– For stationary series: additive decomposition

› Evaluation of alternativesA. Automatic decomposition scheme selection using appropriate criteria

after graphical inspection of the series; Special investigation for non positive series (adding a constant and checking the impact on the seasonally adjusted series); Manual selection for more problematic series

B. Fully automatic decomposition scheme using information criteriaC. Use of a fixed decomposition scheme (multiplicative for positive

series, additive for non positive series)

9


2 Seasonal Adjustment2 Seasonal Adjustment

2.1 Choice of SA approach

2.2 Consistency between raw and SA data

2.3 Direct versus indirect approach

2.3.1 Direct versus indirect: dealing with data from different agencies


2.1 Choice of seasonal adjustment approach2.1 Choice of seasonal adjustment approach› Options

– X12ARIMA– Tramo-Seats – Structural time series models

› Evaluation of alternativesA. Tramo-Seats and X12ARIMA (plus well documented

interfaces)‐ Choice on the basis of past experiences, subjective appreciation,

characteristics of the series‐ Production tools updated on a regular basis after satisfactory

testing‐ Methods (and versions) used in data production to be clearly

communicated to usersB. Structural time series models within software that can estimate

calendar and outliers effects with diagnostics for all components and effects.

C. Other production tools

10


2.2 Consistency between raw and SA data2.2 Consistency between raw and SA data

› Options– Do not apply any constraint– Apply default constraining techniques – Constrain equality over the year of SA data to original data– Constrain equality over the year of SA data to calendar only

adjusted data

› Evaluation of alternativesA. Do not impose equality over the year to the row and seasonally

adjusted or calendar adjusted data (e.g. sum or average)B. Forcing the equality over the year between the calendar adjusted

and the seasonally and calendar adjusted data or between original and the only seasonally adjusted data under particular circumstances (i.e. requirements from users). Recognised benchmarking methods should be used

C. Always impose consistency (seasonally/calendar adjusted data and raw data) or use benchmarking technique that leaves seasonality


2.3 Direct versus indirect approach (1)2.3 Direct versus indirect approach (1)

› Options

� Direct approach: raw data are aggregated and the aggregates and components directly seasonally adjusted. Discrepancies across the aggregation structure not removed

� Direct approach with distribution of discrepancies across the aggregation structure

� Indirect approach: SA of components using the same approach and software, totals are derived by aggregation of SA components

� Mixed indirect approach: SA of components using different approaches and software, totals derived by aggregation of SA components without info on options/parameters used

11


2.3 Direct versus indirect approach (2)2.3 Direct versus indirect approach (2)


A. Application direct versus indirect carefully considered Direct approach preferred for transparency and accuracy, especially when component series have similar patterns;indirect approach preferred when component series show different patterns. Residual seasonality should always be checked in all indirectly seasonally adjusted aggregates

B. Either direct approach with benchmarking techniques or indirect approach in case of strong users requirements for consistency between lower and higher level aggregates. Residual seasonality should always be checked in all indirectly seasonally adjusted aggregates

C. Other alternative approaches not consistent or transparent for all individual time series


› Relevant for EU aggregates (horizontal aggregation)

› Options– SA performed either by local or central statistical institution on

disaggregated series with same method and software; totals derived by their aggregation (decentralised or centralised indirect approach)

– All time series including geographical aggregates seasonally adjusted on an individual basis

– As before but aggregation constraints imposed ex-post (multivariate benchmarking techniques)

– mixed indirect approach

2.3.1 Dealing with data from different agencies (1)2.3.1 Dealing with data from different agencies (1)

12



A. Direct approach is preferred for transparency if component series show similar patterns and in case of lack of harmonisation in the national approaches; Centralised indirect approach when delegated to centralised agency. Decentralised indirect approach also to be considered in presence of satisfactory degree of harmonisation in national practices and if series show different seasonal patterns

B. Decentralised indirect approach accepted in case of strong users requirements for consistency and in presence of a satisfactory degree of harmonisation in national practices. Indirectly adjusted EU aggregates should be checked for the presence of residual seasonality

C. Mixed indirect approach (each geographical components adjusted with different methods and software)

2.3.1 Dealing with data from different agencies (2)2.3.1 Dealing with data from different agencies (2)


3 Revision Policies3 Revision Policies

3.1 General revision policy

3.2 Concurrent versus current adjustment

3.3 Horizon for published revisions

13


3.1 3.1 General revision policy (1)

› Options

– Revise SA data according to a defined, publically available revisions policy and release calendar

– Revise both raw and SA data between 2 consecutive official releases

– Revise SA data once a year independently of any revision of past raw data

– Revise SA data once a year when past raw data don’t change when a new observation is added or revise SA data whenever past raw data are revised

– Do not use official release calendar, perform revision on irregular basis, do not revise


3.1 3.1 General revision policy (2)


A. Revisions to SA data in accordance with a coherent, transparent and officially published revision policy and release calendar (aligned with revision policy of raw data). Revisions to SA data not be released more often than raw data releases. Public to be informed on average revisions of important SA macroeconomic variables observed in the past

B. Revision to SA data published according independent revision policies that apply to particular data releases

C. No revision of SA data, absence of a clear and public revision policy, policies leading to the publication of misleading information for the current period

14


3.2 Concurrent versus current adjustment3.2 Concurrent versus current adjustment (1)(1)

› Current adjustmentModel/filters/outliers/regression parameters re-identified and respective parameters and factors re-estimated at appropriately set review periods. Seasonal and calendar factors used to adjust the new data in-between review periods are those estimated in the previous review period and forecasted up to the next review period

› Concurrent adjustmentModel, filters, outliers and regression parameters are re-identified andthe respective parameters and factors re-estimated every time new orrevised data become available

Extreme strategies; in practice balanced alternatives in-betweenare followed



› Partial Concurrent Adjustment (PCA)Models/filters/outliers/calendar regressors identified oncea year; the respective parameters and factors newlyestimated every time a new or revised data becomesavailable

› Controlled Current Adjustment (CCA)Forecasted seasonal and calendar factors used toseasonally adjust new or revised raw data. Whenevernew or revised raw data become available, an internalcheck is performed against the results of a newestimation of parameter and seasonal factors. Resultsobtained by the new estimation are preferred if aperceptible difference exists

15



› Options– Current adjustment with regular annual review– Current adjustment with review less frequent than one

year – Concurrent adjustment – Partial concurrent adjustment– Controlled current adjustment



› AlternativesA. Data revised for less than two years and/or new observations are

available:

PCA is preferred (new information, minimisation of the size of revisions)

If seasonal component is stable enough:

CCA could be considered (minimisation of frequency of revisions). Full review of all SA parameters at least once a year.

Revisions covering two or more years: model, filters, outliers and regression parameters to be re-identified and re-estimated

B. Current adjustment with a full review every year

C. Current adjustment without annual review, concurrent adjustment

16


3.3 Horizon for published revisions (1)3.3 Horizon for published revisions (1)

› Options– Define the extent of revisions according to series specificities (TS

and X12Arima information)– Limit the revision period to 3-4 years before revision period raw

data freezing older data– Revise the entire time series in the event of re-estimation of the

seasonal factors– Revise the whole series for major revisions on raw data– Do not perform any revision


3.3 Horizon for published revisions (2)3.3 Horizon for published revisions (2)


A. Revision period for SA data must cover extent of raw data revision. Acceptable to revise SA data from a point 3-4 years before the beginning of the revision period of raw data (earlier data frozen)

B. Revise the whole series

C. Do not revise, revise only the last year data, revise for a shorter period than the revision period of the raw data

17


4 Quality of Seasonal Adjustment4 Quality of Seasonal Adjustment

4.1 Validation of seasonal adjustment

4.2 Quality measures for seasonal adjustment

4.3 Comparing alternative approaches and strategies

4.4 Metadata template for seasonal adjustment


4.14.1 Validation of seasonal adjustmentValidation of seasonal adjustment (1)(1)

› Options– Set of graphical, descriptive, non parametric

and/or parametric criteria to check the suitable characteristics of SA data;

– Restrict validation to the use of standard measures proposed by SA tools;

– Use only graphical inspection and descriptive statistics

18


4.14.1 Validation of seasonal adjustmentValidation of seasonal adjustment (2)(2)

› Evaluation of alternativesA. Use detailed set of graphical, descriptive, non parametric and

parametric criteria to validate the seasonal adjustment and run again the SA with a different set of options in case of non acceptance of results.

Particular attention to:- absence residual seasonality/calendar effects- absence over-smoothing- absence autocorrelation of the irregular component- stability of the seasonal component

B. Use default criteria defined within different tools and run again the seasonal adjustment as in alternative A) if validation fails;

C. No validation, use of only basic graphical and descriptive statistics


4.2 4.2 Quality measures for SA (1)

› Options– To use full set diagnostics and graphical facilities to assess the whole

process (appropriate for individual series)

– To use selected set of diagnostics/graphics (massive treatment)

– Complement available diagnostics by additional tests (more robust quality assessment)

– Do not use any quality measures for the SA assessment

› Evaluation of alternativesA. Use of all available quality measures complemented with measures not

yet included in the tool. Appropriate selection of diagnostics for treatment large numbers of series (at least: significance and plausibility CA coefficients, presence/number outliers by type, model fit, absence of residual calendar effects/seasonality or over smoothing

B. Use only quality measures provided by the tool or a subset of them

C. No quality measures to evaluate seasonal adjustment

19


4.2 4.2 Quality measures for SA (2)


A. Use of all available quality measures complemented with measures not yet included in the tool. Appropriate selection of diagnostics for treatment large numbers of series (at least: significance and plausibility CA coefficients, presence/number outliers by type, model fit, absence of residual calendar effects/seasonality or over smoothing

B. Use only quality measures provided by the tool or a subset of them

C. No quality measures to evaluate seasonal adjustment


4.3 4.3 Comparing alternative approaches and strategies

› Options

– Use a common set of quality measures complemented by quality measures specific to each approach

– Use common diagnostics for both approaches– Use specific quality measures for each approach

› Evaluation of alternativesA. Use of common and specific measures/diagnostics

for assessing/comparing quality of alternative SA methods and strategies

B. Use of a subset of common quality diagnostics C. Use specific diagnostics to each software, no quality

measures/diagnostics to compare the quality of alternative SA methods and strategies

20


4.4 Metadata template for seasonal adjustment4.4 Metadata template for seasonal adjustment

› Options– Use of the standard metadata template for SA as presented in

the Annex of the guidelines

– Include SA information into the existing standard metadata templates

› Evaluation of alternativesA. Use of the metadata template for SA as presented in the Annex

for all groups of series or most relevant ones. Information included to be regularly updated to reflect changes in the SA process

B. Include SA information into the existing reference metadata files

C. No methodological information supplied for SA


5 Specific issues on seasonal Adjustment5 Specific issues on seasonal Adjustment

5.1 Seasonal adjustment of short time series

5.2 Treatment of problematic series

21


5.1 Seasonal adjustment of short time series5.1 Seasonal adjustment of short time series (1)(1)

› Options

- No adjustment of series shorter than the minimum requirement for T-S and X12

- Use of alternative procedures to SA of short time series

- Re-specify all parameters of pre-treatment and SA more often

- Comparative studies on relative performance of T-S and X12 for series 3-7 years long

- Inform users on instability problems for series shorter than 7 years


5.1 Seasonal adjustment of short time series5.1 Seasonal adjustment of short time series (2)(2)


A.Series shorter than 3 years not SA; series 3-7 years long standard tools whenever possible:- Extension of the sample and stabilisation of SA with back-recalculated time series- Simulations on relative performances of the existing standard tools for short series SA - Inform users on the greater instability of SA data and on used methods - Clear publication policy- Settings and parameters to be checked more than once per year

B.Do not performed any SA on quite short series (3-7 years)

C.Use of non standard tools for short time series

22


5.2 Treatment of problematic series (1)5.2 Treatment of problematic series (1)

› Options

– Seasonally adjust only recent years of the series (if this makes possible to find reasonable adjustment)

– Perform ad hoc SA on all problematic series– Perform ad hoc SA only on relevant problematic series– No ad hoc SA


5.2 Treatment of problematic series (2)5.2 Treatment of problematic series (2)


A. SA is performed for problematic series- Prefer a case by case approach to a standard one- Consult literature/manual/experts - Inform users on the adopted strategy

B. Perform SA only on relevant problematic series (when failure to adjust these series leads to residual seasonality in important higher level aggregates) and treat other problematic series in a standard way

C. Automatic SA for all series

23


6 Data presentation issues6 Data presentation issues

6.1 Data availability in data bases

6.2 Press releases


6.1 Data availability in databases (1)6.1 Data availability in databases (1)

› Options

- Storage and availability of raw and SA data

- Storage and availability of additional time series

- Storage of associated metadata info relating to individual time series

- Storage of data vintages to enable revision analysis

24


6.1 Data availability in databases (1)6.1 Data availability in databases (1)

› Evaluation of alternativesA. Systematic storage raw, SA and other time series

metadata, ideally data vintages. Metadata standard to be followed. Database secure and able to be extracted or accessed on request. Transparency and replicability of the SA process assured

B. Systematic storage of raw and SA data with associated metadata identifiers. Information available on request for replicating SA figures

C. No database solution or systematic storage of time series estimates


6.2 Data presentation issues (1) 6.2 Data presentation issues (1)

› Options

- Include only raw data in press releases

- Extend the informative content of press releases with SA series, SA plus CA series, T-C series

- Present only levels or different kinds of growth rates

- Include empirical revisions errors for the seasonally adjusted and/or trend-cycle series

25


6.2 Data presentation issues (2) 6.2 Data presentation issues (2)


A. SA data to be presented. Users should have access to full historical raw/SA/CA/TC times series on request, by reference or by internet download; Most recent values of TC not shown; analysis of real time revision error of at least SA series to be included

Period on period growth rates / changes in level computed on SA data and used with caution

Year on year comparison computed on CA data or in raw data

B. Present SA data; T-C in graphical way with the current end of the series (end-point problem made clear). Annualised growth rate could be used for justified reasons. Particular attention to volatile series. User informed on characteristic of annualised growth rates

C. Present raw or T-C data only; yearly period to period growth rates on raw or T-C data

JDEMETRA+, CHAIN-LINKING

INSTITUT NATIONAL DE LA STATISTIQUE ET DES ÉTUDES ÉCONOMIQUES

Série des documents de travail de la Direction des Études et Synthèses Économiques

NOVEMBRE 2014

Ce travail a été réalisé afin de contribuer à la discussion de la réédition du manuel du FMI sur les comptes trimestriels. Il a servi de base à la contribution des auteurs à un groupe de travail organisé par le FMI à Vienne en novembre 2014. Les auteurs remercient leurs collègues des comptes nationaux de l’Insee qui depuis 2007 ont contribué à l’accumulation des connaissances résumées ici et à leur mise en œuvre au quotidien.

_____________________________________________

* Département des Comptes Nationaux - Division des Comptes Trimestriels Timbre G430 - 15, bd Gabriel Péri - BP 100 - 92244 MALAKOFF CEDEX

** Département des Études Économiques - Division Études Macroéconomiques Timbre G220 - 15, bd Gabriel Péri - BP 100 - 92244 MALAKOFF CEDEX Crest-LMA & École Polytechnique

Département des Études Économiques - Timbre G201 - 15, bd Gabriel Péri - BP 100 - 92244 MALAKOFF CEDEX - France - Tél. : 33 (1) 41 17 60 68 - Fax : 33 (1) 41 17 60 45 - CEDEX - E-mail : [email protected] - Site Web Insee : http://www.insee.fr

Ces documents de travail ne reflètent pas la position de l’Insee et n'engagent que leurs auteurs. Working papers do not reflect the position of INSEE but only their author's views.

G 2014 / 12

Computing additive contributions to growth and other issues for chain-linked quarterly aggregates

Franck ARNAUD*, Jocelyn BOUSSARD* Aurélien POISSONNIER** et Hélène SOUAL*

2

Computing additive contributions and other issues for chain-linked quarterly aggregates

Abstract

Since 2007, the French Quarterly National Accounts use a chain-linking method to measure volumes in replacement of volumes in constant prices of the reference year. This paper gathers 7 years of experience of the Quarterly National Accounts unit on this particular topic.

We first recall the annual overlap method used in France in comparison with the one quarter overlap method sometimes preferred in other countries. Based on numerical simulations, we show the distribution of two well-known effects: trend effects when elemental prices have different dynamics and non-additivity. In particular, the variance of these effects increases away from the reference year.

We also expose two new reasons to prefer the annual overlap method to the one quarter overlap: first, additive contributions to growth can be computed; second, unpleasant interactions with seasonal and trading day adjustment can be avoided.

Keywords: chain-linking, annual overlap, one quarter overlap, contribution to growth, seasonal and trading day adjustment

Calcul de contributions additives et autres difficultés des comptes trimestriels en volumes chainés

Résumé

Depuis 2007, les comptes trimestriels français utilisent des volumes chainés en remplacement des volumes à prix constants de l’année de base. Ce document compile 7 années d’expérience de la division des comptes trimestriels sur ce sujet.

Nous présentons la méthode de recouvrement annuel utilisée en France en la comparant à la méthode de recouvrement trimestriel parfois préférée dans d’autres pays. Sur la base de simulations numériques, nous illustrons deux propriétés des volumes chainés : l’effet tendanciel lorsque les prix des composants d’un agrégat ont des dynamiques divergentes et la non-additivité. Notamment nous montrons que la variance de ces effets croît lorsqu’on s’écarte de l’année de base.

Nous détaillons également deux nouvelles raisons de préférer la méthode de recouvrement annuel au recouvrement trimestriel : tout d’abord il est possible de calculer précisément la contribution d’un composant à la croissance d’un agrégat ; ensuite des interactions indésirables avec la correction des variations saisonnières et des jours ouvrés peuvent être évitées.

Mots-clés : volumes chainés, annual overlap, one quarter overlap, contribution à la croissance, correction saisonnière et des jours ouvrés

Classification JEL : C43, C82, E01

1 Introdu tion

One of the major obje tives of the national a ounts is to des ribe the hanges

in the major e onomi aggregates, in parti ular after an elling out the ef-

fe ts of pri e variation, to analyse in volumes the growth of domesti output,

onsumption, et . These volumes give a learer idea of quantity ex hanged

or produ ed. However, simply adding up the quantities of elementary om-

ponents involved is irrelevant: the quantity of ars is not dire tly omparable

with the quantity of bi y les. These quantities need to be made ommensu-

rate. Cal ulating the volume of an aggregate requires to weight the volumes

of its omponents through pri es. The hoi e of a referen e period, whi h

will determine this stru ture of the pri es, is thus of ru ial importan e.

There are two available options:

• al ulating volumes using onstant pri es derived from the referen e

year;

• al ulating volumes of ea h year using the pri es observed in the previ-

ous year and then hain-linking. The idea behind these hained-linked

volumes is to umulate the growth rates in volumes starting from the

values established for a given referen e year. Doing so the evolutions

of volumes at previous year's pri es are preserved, and the hain-linked

volume a ounts form time series without breaks in the stru ture of

pri es every year.

The relative weight of ea h omponent in an aggregate in volume depends

on the pri es of a parti ular weight period. These pri es an be markedly mod-

i�ed with time. Estimating hained volumes based on previous year's pri es

thus o�ers the dual advantage of providing data suitable for onstru ting

time series and also a ounting for any hange in the relative pri e stru ture:

simply put, they provide a more satisfa tory des ription of the e onomi re-

ality when the pri es of some produ ts evolve very di�erently than others.

However, these hained volumes do pose spe i� problems. They an

prove misleading when pri es tend to os illate rather than evolve following

a oherent trend. This may be the ase, for example, with agri ultural and

energy pri es [Berthier, 2002℄. Furthermore, these volumes lose their addi-

tivity with regard to volumes al ulated more simply at onstant pri es of

the referen e year.

3

Fa ed with these omplex problems, until 2007, the Fren h quarterly a -

ounts used volumes al ulated at onstant pri es of the referen e year. In

Fran e, the di�eren e between hain-linked volumes and the volumes ob-

tained by using onstant pri es of the referen e year was relatively minor.

However, European harmonisation, and the in reasing disparity observed

between the hained volumes and volumes in referen e year pri es for some

produ t-operation pairs, led to a methodologi al hange: sin e 2007 the

Fren h quarterly a ounts are published in hain-linked volumes at the pre-

vious year's pri es, using the annual overlap method.

With the one quarter overlap method, the annual overlap method is one

of the most widespread te hnique to hain-link the QNA (see Table 2 in

appendix). For both te hniques we re all the algebra (se tion 2). The for-

mulae theoreti ally show that QNA in annual overlap exa tly oin ide with

the orresponding annual a ounts but there is a residual pri e e�e t every

�rst quarter. With the one quarter overlap method the opposite is true: the

pri e e�e t every �rst quarter is ontrolled for but onsisten y with annual

hained volumes must be restored through ben hmarking.

We display on a simulation exer ise (se tion 3) the ommon features of

these hain-linking te hniques: both produ e non additive volumes and a

trend e�e t appears when pri es of omponent have diverging dynami s.

Simulated varian es of these two e�e ts in reases away from the referen e

year and an be sizeable on both ends of time series. These simulations al-

low us to ompare the two te hniques and analyse the e�e t of ben hmarking

on the one quarter overlap.

With respe t to its one quarter overlap alternative, the annual overlap

method has two advantages that, to the best of our knowledge have not been

put forth until now in the literature on hain-linking.

First in se tion 4 we show how hain-linking an intera t, with some un-

pleasant out ome, with trading day or seasonal adjustment. With the annual

overlap, whi h uses an annual link fa tor, it is possible to avoid these issues.

With the one quarter overlap, whi h uses a quarterly hain-link fa tor, these

issues an not be ir umvented. The one quarter overlap hen e raises addi-

tional issues of revisability, pre ision and quality.

Se ond, in the ase of the annual overlap method, additive ontributions

to the growth rate of an aggregate an be omputed (se tion 5). The la k of

4

additivity makes drawing up and publishing the a ounts a omplex opera-

tion as some aggregates are unsuitable for hain-linking. Computing additive

ontributions of a omponent to the growth rate of an aggregate over omes

this di� ulty. But, for one quarter overlap volumes, these ontributions are

only approximative, whi h does not allow to a urately ompute the ontri-

bution of the trade balan e to GDP growth for instan e.

2 Computing hain-linked estimates

In this se tion we re all the algebra for hain-linking, �rst in the ase of an-

nual a ounts, then for quarterly a ounts in annual overlap and one quarter

overlap.

2.1 Volume indexes in annual a ounts

For sake of larity, we introdu e on epts of volume with elementary goods

or servi es, for whi h there exists a pri e and an be measured a quantity

(e.g. potatoes, books, hair uts...). Let X denote an aggregate, p a pri e,

q a quantity. Hereafter a shall refer to a generi year while 0 refers to the

referen e year. Later on, a, t refers to quarter t ∈ [1, 2, 3, 4] of year a.

Let V al refer to values (i.e. urrent pri es). We denote volumes as follows:

• Volumes at onstant pri es of the referen e year (Cst): XCsta = p0qa

• Chain-linked volumes at previous year's pri es (Ch): XCha = IV ol

a XCha−1,

where IV ola = X

Pypa

XV ala−1

is the growth rate index of volumes at previous

year's pri es and volumes at previous year's pri es (Pyp) are de�ned

by XPypa = pa−1qa

Volumes at previous year's pri es an not be treated as standard time series

sin e there is a hange of pri es and volumes every period. Chain-linking

over omes this di� ulty by haining the growth rates measured at previous

year's pri es.

Elementally, volumes oin ide:

IV olCsta =

XCsta

XCsta−1

=qa

qa−1=

XPypa

XV ala−1

= IV olCha

5

Imposing the referen e year at urrent pri es as the referen e for all volumes,

we have:

XCsta = XCst

0

a∏

k=1

IV olCstk = XCh

0

a∏

k=1

IV olChk = XV al

0

a∏

k=1

IV olk

that is hained-linked volumes and volumes at onstant pri es are equal.

Individual produ ts hardly exist (potatoes ome in di�erent varieties,

hair uts di�er from one hairdresser to another...) and su h a data olle tion

would be impossible. In pra ti e, National A ounts work on detailed levels

whi h are already aggregates of goods or servi es but the previous on epts

an be generalized to aggregates measured at urrent pri es and trends in

average pri es measured by pri e indexes. One simply has to hoose the

most detailed levels he is willing to work on and de�ne volumes as the ratio

of values with the orresponding pri e index. By onstru tion, there is no

ambiguity of volume on ept at this level, and the issue of measuring quan-

tities is then over ome.

On aggregate, volume growth indexes di�er due to their weights...

Let E denote an aggregate and i its omponents. The growth index in volumes

at onstant pri e of an aggregate is a weighted sum of the growth indexes

of the omponents, with weights at onstant pri e volumes (hereafter the

weight of i in E for year a in the on ept V is denoted ωVa (i, E)).

IV olCsta (E) =

∑

i∈E XCsta (i)

∑

i∈E XCsta−1(i)

=∑

i∈E

XCsta−1(i)

XCsta−1(E)

IV ola (i) =

∑

i∈E

ωCsta−1(i, E)I

V ola (i)

The growth index in volumes at previous year's pri es on aggregate is a

weighted sum of the growth indexes of the omponents, with weights at

urrent pri es for the previous period.

IV olCha (E) =

∑

i∈E XPypa (i)

∑

i∈E XV ala−1(i)

=∑

i∈E

XV ala−1(i)

XV ala−1(E)

IV ola (i) =

∑

i∈E

ωV ala−1(i, E)I

V ola (i)

...and volumes in level no longer oin ide

XCha = XCh

0

a∏

k=1

IV olChk 6= XCst

0

a∏

k=1

IV olCstk = XCst

a

6

Chain-linked volumes at the previous year's pri es are also initialized XCh0 =

XV al0 . Sin e XCst

0 = XV al0 as well, Ch and Cst only di�er by the stru ture

of weights in their respe tive growth index. In Ch weights evolve with time

a ording to both volume and pri e hanges. For this reasons, in omparison

with Cst, Ch are said to better a ount for the hange in the stru ture of

the e onomy.

2.2 Volumes in quarterly a ounts

Current pri es, onstant pri es and previous year's pri es an be general-

ized to higher frequen ies (quarterly or monthly). However, there are several

hain-linking te hniques. We do not treat in this do ument the ases for over

the quarter overlap and over the year overlap be ause these te hniques are

seldom used and not re ommended ([Eurostat, 2013℄, [Bloem et al., 2001℄).

We onsider the two ases of annual overlap and one quarter overlap whi h

are most ommonly used (see Table 2). Contrary to the former two te h-

niques, these two ases yield aggregates whi h are additive within a year.

2.2.1 The annual overlap method XCh

To ompute quarterly aggregates in annual overlap (hereafter denoted XCh),

one shall:

1. Compute quarterly volumes at previous year's pri es for elementary

omponents: XPypa,t (i) = XCst

a,t (i)XV al

a−1(i)

XCsta−1

(i)

2. Then by sum, ompute all aggregates at previous year's pri esXPypa,t (E) =

∑

i∈E XPypa,t (i)

3. For ea h aggregate, hain-link from the referen e year (for whi h Val=Cst=Ch,

urrently 2010 for Fran e):

XCha,t = X

Pypa,t

XCha−1

XV ala−1

=X

Pypa,t

XDefCha−1

(1)

with XDefCha the annual hained de�ator, also alled annual link fa tor. Note

that the link fa tor is based on annual a ounts so that in parti ular seasonal

7

adjustment has no e�e t on hain-linking.

1

Comparison with annual omputations shows that previous year pri e

estimates an be summed to retrieve their annual ounterpart: XPypa =

∑4t=1X

Pypa,t . It dire tly follows that hain-linked estimates an also be summed

to retrieve their annual ounterpart: XCha =

∑4t=1X

Cha,t .

Change of year e�e t

Between Q4 and Q1, the transition from volumes at previous year's pri es

to hain-linked volumes entails a pri e orre tion to the hain-linked volume

growth rate orresponding to the growth of the annual link fa tor:

XCha,1

XCha−1,4

=X

Pypa,1

XPypa−1,4

XCha−1

XV ala−1

XV ala−2

XCha−2

=X

Pypa,1

XPypa−1,4

XPypa−1

XV ala−1

XV ala−2

XV ala−2

sin e

XCha−1

XCha−2

=X

Pypa−1

XV ala−2

=X

Pypa,1

XPypa−1,4

1

IDefCha−1

with IDefCha = XV al

a

XPypa

= XDefCha

XDefCha−1

the annual de�ator. This pri e orre tion

eliminates the hange in pri es every year in orporated in previous year's

pri es estimates. However, in this pri e orre tion, there is a weighting e�e t:

XCha,1 (E)

XCha−1,4(E)

=X

Pypa,1 (E)

XPypa−1,4(E)

XPypa−1 (E)

XV ala−1(E)

=

∑

i∈E XPypa,1 (i)

∑

i∈E XPypa−1,4(i)

∑

i∈E XPypa−1 (i)

∑

i∈E XV ala−1(i)

=

∑

i∈E ωV ala−1(i, E)

XPypa,1 (i)

XV ala−1

(i)

∑

i∈E ωPypa−1(i, E)

XPypa−1,4(i)

XPypa−1

(i)

One part of the growth rate of the �rst quarter is therefore due to the di�er-

en e in weights between Q1 and Q4. This issue is spe i� to the �rst quarters

sin e for the following quarters, the weights are identi al.

1

Provided that seasonally adjusted a ounts are ben hmarked on their non-adjusted

ounterparts as re ommended by international standards [Eurostat, 2013℄.

8

2.2.2 The one quarter overlap method XCh

One may want to have no ponderation e�e t in the pri e orre tion between

Q4 and Q1. This is the purpose of the one quarter overlap method (hereafter

denoted XCh).

To do so, one simply has to rede�ne the annual link fa tor. The new link

fa tor is another annual hained pri e de�ator using Q4 ponderation at pre-

vious year's pri es (XDefCha ).

Its growth di�ers from that of the previous link fa tor as follows:

IDefCha =

∑

i∈E

ωPypa,4 (i, E)

XV ala (i)

XPypa (i)

(2)

instead of IDefCha =

XV ala

XPypa

=∑

i∈E

ωPypa (i, E)

XV ala (i)

XPypa (i)

One an then ompute the hain-linked volumes identi ally using XDefCha

instead of XDefCha . The hain-linking formula (1) be omes:

XCha,t =

XPypa,t

XDefCha−1

(3)

Proof that this orre tion is orre t

XCha,1 (E)

XCha−1,4(E)

=X

Pypa,1 (E)

XPypa−1,4(E)

1

IDefCha−1 (E)

=

∑

i∈E XPypa,1 (i)

XPypa−1,4(E)

∑

i∈E ωPypa−1,4(i, E)

XV ala−1

(i)

XPypa−1

(i)

=

∑

i∈E XPypa,1 (i)

∑

i∈E XPypa−1,4(i)

XV ala−1

(i)

XPypa−1

(i)

=

∑

i∈E XPypa,1 (i)

∑

i∈E XV ala−1(i)

XPypa−1,4(i)

XPypa−1

(i)

=

∑


XPypa,1 (i)

XV ala−1

(i)

∑


XPypa−1,4(i)

XPypa−1

(i)

�

Contrary to the annual overlap method, with the one quarter overlap

method, the sum of the four quarters do not mat h the annual estimate of

hain-linked volumes be ause the link fa tor is di�erent. For this reason one

quarter overlap estimates are usually ben hmarked ex-post on their annual

9

ounterpart. In the present paper, we do not ompare or expose the di�erent

te hniques to do so: this is done for instan e in [Eurostat, 2013℄.

3 A simulation exer ise

To assess the properties of hain-linking, we perform a simulation exer ise.

2

We simulate data sets for two elementary a ounts whi h we aggregate us-

ing the di�erent on epts of volume. The parameters of the simulation are

alibrated to repli ate standard elements of national a ounts in developed

e onomies.

3

The data are simulated over a time period onsistent with Eu-

rostat's minimal request, that is sin e 1995.

The simulations exemplify the following properties:

• the non additivity of hain-linked volumes

• how hain-linking an modify the trend of volume estimates ompared

to volumes at onstant pri es of the referen e year

• the di�eren es between annual and one quarter overlap

• the ex-post ben hmarking of one quarter overlap

Loss of additivity

The non-additivity asso iated with hain indi es has been a major point of

riti ism [S hreyer, 2004℄. Either in annual or quarterly a ounts, with any

on ept of hain-linking, hain-linked volumes of 2 aggregates an not be

added.

To aggregate (or subtra t) 2 a ounts, one must �rst un hain them, i.e.

ompute the previous year's pri es whi h are additive before hain-linking

the aggregate.

4

When bluntly adding up two hain-linked volumes, one makes an error

whi h we exemplify on Figure 1. In annual overlap, the error is null the

2

The orresponding R ode is available upon request.

3

The growth rates in volume and pri es are equal to 2% in annual in the standard ase,

the standard deviation is quarterly is 0.5%.

4

A pra ti al advantage of the annual overlap over the one quarter overlap te hnique

is that sin e the former are not ben hmarked ex-post on their annual ounterpart, �nal

users of the data an perform this operation themselves.

10

1995 2000 2005 2010 2015

−0.03

−0.02

−0.01

0.00

0.01

0.02

Annual Overlap

10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.03

−0.02

−0.01

0.00

0.01

0.02

One Quarter Overlap (Bench.)

10%20%30%40%50%60%70%80%90%

Figure 1: Error made when adding up hain-linked volumes dire tly

year after the referen e year (2010). Indeed, this year hain-linked volumes

are equal to volumes at previous year's pri es whi h are additive (that year

the hain-linking fa tor in equation (1) is equal to one by de�nition of the

referen e year). The varian e of the error in reases away from that date.

A de ade before (or after) the referen e point, the error has roughly a 50%

han e to be larger than 0.01% in absolute terms. The same diagnosti

holds in one quarter overlap, although the error is not null the year after the

referen e year.

Trend orre tion of hain-linking

Be ause the weights of the growth index of hain-linked volumes a ount

for both hanges in pri es and volumes, ompared to volumes at onstant

pri es, hain-linked volumes an display sizeable trend di�eren es. To better

exemplify this trend di�eren e, we simulate two aggregations:

• a symmetri one, where both of its omponents grow on average at a

0.5% quarterly rate in volume and pri es,

11

• an asymmetri one, where one omponent grows at 0.5% quarterly rate

in volume and pri es and the other in reases faster in volume (+0.75%

quarterly rate) and de reases in pri es (-0.25% quarterly rate).

This asymmetri aggregation mimi s the ase of durables and new te h-

nologies aggregated with otherwise standard goods and servi es, whi h is a

hara teristi example of the trend e�e t.

In level for the symmetri ase (Figure 2, top left and right), the e�e t

of hain-linking is entered around 0 with both methods but its varian e

in reases away from the referen e year. Roughly speaking, a de ade away

from the referen e year, hain-linked volumes have a 50% han e of being in

absolute terms 0.5% away from volumes at onstant pri es, whether it is a

positive or negative dis repan y. At the same time, the e�e t of hain-linking

on growth rates (Figure 3) has a 50% han e of being larger than 0.01% in ab-

solute term. It is noteworthy that our simulations are alibrated on standard

deviations observed on Fren h data. Other simulations with higher varian es

show that for energy, ommodities, or developing ountries the distribution

e�e ts exposed throughout the present paper an be magni�ed more than

tenfold.

In the asymmetri ase the onsequen e of hain-linking is also het-

eroskedasti , but there is an additional trend orre tion. Chain-linked vol-

umes grow more rapidly than volumes at onstant pri es before the referen e

year and the opposite is true after this year. The median of this trend or-

re tion is 0.5% a de ade away from the referen e year.

Comparison of annual and one quarter overlap

As expe ted from the theory, the di�eren e between the two hain-linking

method in growth rate appears only on the �rst quarters of every year (Fig-

ure 3, bottom left).

In level, this di�eren e between the two hain-linking methods are smaller

than the di�eren e between onstant pri es and hained linked aggregates

(Figure 2, bottom left). This di�eren e derives from the di�eren e between

the hain-link fa tors of the two te hniques whi h are umulated by the hain-

linking pro ess. Also, sin e the annual overlap method is onsistent with the

annual hain-linking, this di�eren e, in annual terms, is equal to the ben h-

marking residual whi h an be eliminated ex-post to impose onsisten y with

12

annual a ounts in the one quarter overlap ase.

Ben hmarking the one quarter overlap

Ben hmarking one quarter overlap has, with the method used here,

5

a lim-

ited e�e t on growth rates (Figure 3, bottom right).

It is however noteworthy that in level this ex-post ben hmarking is a �rst

order integrated orre tion. As for the other e�e ts we exemplify with our

simulations, the varian e of the orre tion in reases away from the referen e

year (Figure 2, bottom right). On both ends of hain-linked volume time se-

ries, possible sizeable level orre tion may ensue. In this ase the orre tion

in level will ne essarily modify the short term �u tuations either in delta or

in growth rates, magnifying or lessening them depending on the dire tion of

the level orre tion and the use of an additive or multipli ative ben hmark-

ing method. Be ause they modify the homogeneity of the varian e one may

extra t from the QNA, the hoi e of one ben hmarking te hnique or another

is not neutral for e onomi analysis, whether one wishes to analyse the busi-

ness y le, run statisti al tests...

5

Ben hamrking is based on additive Denton method [Denton, 1971℄.

13

1995 2000 2005 2010 2015

−0.10

−0.05

0.00

0.05

annual ovlp vs cst prices

10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.10

−0.05

0.00

0.05

1 quarter ovlp vs cst prices

10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.02

−0.01

0.00

0.01

0.02

1 quarter ovlp vs annual ovlp

10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.02

−0.01

0.00

0.01

0.02

benchmarked vs non benchmarked 1 quarter ovlp

10%20%30%40%50%60%70%80%90%

symmetri

1995 2000 2005 2010 2015

−0.6

−0.4

−0.2

0.0


10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.8

−0.6

−0.4

−0.2

0.0


10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.10

−0.08

−0.06

−0.04

−0.02

0.00

0.02

0.041 quarter ovlp vs annual ovlp

10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.04

−0.02

0.00

0.02

0.04

0.06

0.08

0.10


10%20%30%40%50%60%70%80%90%

asymmetri

Figure 2: Comparison of volumes in levels

14

1995 2000 2005 2010 2015

−0.02

−0.01

0.00

0.01

0.02


10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.02

−0.01

0.00

0.01

0.02


10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.010

−0.005

0.000

0.005

0.010


10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.006

−0.004

−0.002

0.000

0.002

0.004


10%20%30%40%50%60%70%80%90%

symmetri

1995 2000 2005 2010 2015

−0.05

0.00

0.05

0.10


10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.05

0.00

0.05

0.10


10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.03

−0.02

−0.01

0.00

0.01

0.02


10%20%30%40%50%60%70%80%90%

1995 2000 2005 2010 2015

−0.010

−0.005

0.000

0.005

0.010


10%20%30%40%50%60%70%80%90%

asymmetri

Figure 3: Comparison of volumes in growth rates

15

4 Chain-linking and seasonal or trading day

adjustment

With annual overlap, hain-linking and seasonal adjustment do not intera t

if quarterly a ounts are assumed to be ben hmarked on their annual oun-

terpart (as re ommended by international standards). Indeed, the hain-link

fa tor in annual overlap is based on annual estimates so is identi al whether

it is omputed with raw or seasonally adjusted data (see eq (1)).

However, in equation (1) the question arises of using a trading day ad-

justed hain-link fa tor in addition to trading-day adjusted previous year's

pri es quarterly estimates.

Using a trading day adjusted hain-link fa tor is rather intuitive and easy.

The hain-linked aggregate is then al ulated as follows:

XCh,TDAa,t (E) =

XPyp,TDAa,t (E)

XDefCh,TDAa−1 (E)

,

with XTDAtrading-day adjusted series.

Trading-day adjustment introdu es only a small modi� ation of the hain-

link fa tor but due to hain-linking, it is umulated over the sample. This

umulated trading-day e�e t is not always sizeable. For example, with this

naive hain-linking, the trading-day e�e t on Fren h GDP was not entered

on zero in 2013 (last publi ation with 2005 as the referen e year), but there

is no visible problem after the update of the data in 2014 (�rst publi ation

with referen e year 2010, see Figure 4). With this hain-linking method, the

update of trading-day adjustment models may result in a trend modi� ation,

while trading day adjustment should be a priori stationary. From one up-

date to another, trend modi� ations may be sizeable on di�erent aggregates,

be either upwards or downwards and of di�erent magnitudes.

To avoid these issues, an alternative way of hain-linking uses a raw hain-

link fa tor:

XCh,TDAa,t (E) =

XPyp,TDAa,t (E)

XDefCh,Ra−1 (E)

,

with XRraw series. In this ase, the trading-day e�e t on hain-linked aggre-

gate remains stationary: it is only due to trading-day adjustment of volumes

at previous year's pri es.

16

−0.

10−

0.05

0.00

0.05

0.10

0.15

0.20

1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013

Reference year 2010Reference year 2005

Source : French Quarterly National Accounts

Figure 4: Comparison of trading day e�e ts on Fren h GDP, hain-linked

volumes, naive hain-linking

To illustrate further the onsequen e of the hoi e between raw and

trading-day adjusted hain-link fa tor, we perform a bootstrap exer ise. The

trading-day e�e t on Fren h GDP at previous year's pri es is estimated

through an OLSmodel, and the residuals of the estimation are bootstrapped.

6

This allows us to simulate a sample whi h repli ates the empiri al un er-

tainty of trading day adjustment. These trading-day adjusted series are used

to al ulate two samples of hain-linked aggregates: the �rst one using a

trading-day adjusted hain-linking fa tor (naive hain-linking), and the se -

ond one using a raw fa tor ( orre t hain-linking). Then, the distributions

of the trading-day e�e ts on hain-linked aggregate an be plotted (Figure 5).

For the intuitive hain-linking, the varian e of the trading-day e�e t in-

reases away from the referen e year, whereas with the alternative hain-

linking, the trading-day e�e t is learly stationary. A �rst advantage of the

method based on a raw hain-link fa tor is that it an not introdu e an un-

desirable drift in the trading day adjusted data. In addition, bootstrapping

shows that naive hain-linking in reases the un ertainty of the estimates. It

does so by introdu ing a �rst order integrated orre tion in level. Compared

6

The trading day e�e t is omputed from trading-day and non trading day adjusted

GDP and regressed on the alendar. The residuals (that is, 408 points from January 1980

to De ember 2013) are bootstrapped, and then aggregated in yearly series. In ea h ase,

a sample of 1000 simulations is reated.

17

1980 1985 1990 1995 2000 2005 2010

−0.

3−

0.2

−0.

10.

00.

10.

20.

3

real trading day effect

5% confidence interval10% confidence interval50% confidence interval

naive chain−linking

1980 1985 1990 1995 2000 2005 2010

−0.

100.

000.

050.

100.

15

real trading day effect

5% confidence interval10% confidence interval50% confidence interval

correct chain−linking

Source : French Quarterly National Accounts

Figure 5: Simulated trading day e�e t on Fren h GDP, hain-linked volumes

to the similar e�e t observed between the annual and one quarter overlap

te hniques, this orre tion is however mu h larger (tenfold) and alteration

of the statisti al properties of the series will be problemati if this undesired

e�e t is orre ted through ben hmarking.

By onstru tion of the hain-link fa tor, the one quarter overlap te h-

nique umulates the two issues of trading-day and seasonal adjustment in

the de�nition of the hain-link fa tor (see eq (2)).

First, the issue of trading-day adjustment is the same as in the annual

overlap: the un ertainty of adjustment is ampli�ed by hain-linking if a

trading-day adjusted hain-link fa tor is used.

Se ond, a similar issue is added by seasonal adjustment, be ause the

hain-link fa tor is quarterly and not annual. For statisti al reasons, it seems

better to use a non seasonally-adjusted fa tor, in order not to amplify the

adjustment un ertainty and the alteration of the initial statisti al proper-

ties. On the other hand, a raw fa tor may be based on a weighting stru ture

whi h is not representative of the e onomy and a�e t the trend of the series

(espe ially if seasonality is hanging). None of the two options is fully satis-

18

fying: in both ases, the ben hmarking on annual series is a trend orre tion

whi h may modify the varian e of quarterly �u tuations, with onsequen es

for data users.

5 Computing additive ontributions to growth

We illustrated on the simulations that hain-linked volumes are not additive.

It follows that a ounting equalities are not veri�ed in hain-linked volumes

whi h an ause some di� ulties in aggregating, balan ing... and most im-

portantly for users. Moreover, hain-linking misbehaves for aggregates whi h

hange signs or are temporarily equal to zero. Hen e, hanges in inventories

or trade balan e are usually not hain-linked. To over ome these di� ul-

ties, it is possible to ompute a urately ontribution to the growth rate of

a larger aggregate.

5.1 Annual

As we noted earlier (subse tion 2.1), in hain-linked volumes ponderations

are based upon urrent pri es where they are based upon volumes at on-

stant pri es for this other on ept of volumes. This property shows in the

omputation of ontributions to growth.

Let ev() denote the growth rate operator. For additive on epts (e.g.

values and volumes at onstant pri es) the ontribution of the omponent i

to the aggregate E an be omputed easily:

Contrib

V ala (i, E) =

XV ala−1(i)

XV ala−1(E)

ev(XV ala (i)) = ωV al

a−1(i, E)ev(XV ala (i))

For additive on epts, the ontribution to growth is the omponent's growth

rate times its weight in the aggregate in the same additive on ept at the

previous period.

For hain-linked aggregates, ontributions to growth are slightly more

omplex. The growth rate of a hained-linked aggregate an be written as

follows:

ev(XCha (E)) =

XV ola (E)

XV ala−1(E)

− 1 =∑

i∈E

XV ola (i)−XV al

a−1(i)∑

i∈E XV ala−1(i)

19

Hen e the ontribution of i to the evolution of E in annual in hain-linked

volumes an be de�ned as

Contrib

Ch

a (i, E) =XV al

a−1(i)

XV ala−1(E)

(

XPypa (i)

XV ala−1(i)

− 1

)

= ωV ala−1(i, E) ev(XCh

a (i)) (4)

= Contrib

Cha (i, E)

+ContribCha (i, E)

(

XDefCha−1 (i)

XDefCha−1 (E)

− 1

)

(5)

As said, ponderations are in values, not in volumes (see equation (4)). Con-

tributions an also be omputed by applying a orre tion to the additive

formula whi h orresponds to the omponent's pri e relative drift (see equa-

tion (5)).

5.2 With annual overlap

5.2.1 For quarters 2 to 4 in annual overlap XCh

Within a year (t 6= 1), the growth rate of hain-linked volumes equals that of

previous year's pri es volumes. In addition, previous year's pri es volumes

are additive, so one an easily ompute the ontributions in hain-linked

volumes as those at previous year's pri es volumes:

Contrib

Ch

a,t (i, E) = Contrib

Pypa,t (i, E) =

XPypa,t (i)−X

Pypa,t−1(i)

XPypa,t−1(E)

These ontributions an be written in terms of hain-linked volumes using

equation (1):

XV ola,t = XCh

a,t ∗XDefCha−1 =⇒

Contrib

Ch

a,t (i, E) =XCh

a,t (i)XDefCha−1 (i)−XCh

a,t−1(i)XDefCha−1 (i)

XCha,t−1(E)X

DefCha−1 (E)

=X

DefCha−1 (i)

XDefCha−1 (E)

XCha,t (i)−XCh

a,t−1(i)

XCha,t−1(E)

20

We an then write

Contrib

Ch

a,t (i, E) = Contrib

Cha,t (i, E)

+ContribCha,t (i, E)

(

XDefCha−1 (i)

XDefCha−1 (E)

− 1

)

(6)

In this expression similar to the annual ase, the �rst term is the ontribution

in the additive ase, the se ond term a orre tion for non-additivity. This

orre tion will be sizeable only for omponents for whi h pri es departs from

those of the aggregate.

5.2.2 For the �rst quarter in annual overlap (XCh)

If t = 1 the hange in pri es between the two periods modi�es the omputa-

tion made above.

ev(XCha,1 (E)) =

XCha,1 (E)−XCh

a−1,4(E)

XCha−1,4(E)

=

XPypa,1 (E)

XDefCha−1

(E)−

XPypa−1,4(E)

XDefCha−2

(E)

XCha−1,4(E)

=

∑i∈E

XPypa,1 (i)

XDefCha−1

(E)−

∑i∈E

XPypa−1,4(i)

XDefCha−2

(E)

XCha−1,4(E)

One an then ompute the ontribution as

Contrib

Ch

a,1(i, E) =

XPypa,1 (i)

XDefCha−1

(E)−

XPypa−1,4(i)

XDefCha−2

(E)

XCha−1,4(E)

=XCh

a,1 (i)X

DefCha−1

(i)

XDefCha−1

(E)−XCh

a−1,4(i)X

DefCha−2

(i)

XDefCha−2

(E)

XCha−1,4(E)

=X

DefCha−1 (i)

XDefCha−1 (E)

XCha,1 (i)−XCh

a−1,4(i)

XCha−1,4(E)

+XCh

a−1,4(i)

XCha−1,4(E)

(

XDefCha−1 (i)

XDefCha−1 (E)

−X

DefCha−2 (i)

XDefCha−2 (E)

)

The �rst term is the same ontribution as in quarters 2 to 4, the se ond

term is a orre tion for the hange in relative pri es a ross the years. This

21

additional term an have a marked impa t every �rst quarter and even in

extreme ases modify the sign of the ontribution [Arnaud, 2007℄.

One an orre t this undesired e�e t neutrally over the aggregate with a

simple subtra tion:

XCha−1,4(i)

XCha−1,4(E)

(

XDefCha−1 (i)

XDefCha−1 (E)

−X

DefCha−2 (i)

XDefCha−2 (E)

)

be omes

(

XCha−1,4(i)

XCha−1,4(E)

−XCh

a−1(i)

XCha−1(E)

)(

XDefCha−1 (i)

XDefCha−1 (E)

−X

DefCha−2 (i)

XDefCha−2 (E)

)

Sin e XV ala−1 = XCh

a−1XDefCha−1 and X

Pypa−1 = XCh

a−1XDefCha−2 this new term is

the di�erential of ponderation of i in E in values and previous year's pri es

volumes (ωV ala−1(i, E) − ω

Pypa−1(i, E)), whi h sums to zero over the aggregate.

Hen e, this te hnique minimizes the over-the-year e�e ts on ontributions

as

XCha−1,4(i)

XCha−1,4(E)

−XCh

a−1(i)

XCha−1

(E)be omes a se ond order orre tion. In addition, these

ontributions are additive without any approximation.

5.3 General formula for ontributions in hain-linked

volumes

With annual overlap

All in all, the ontribution of i to the growth of E in annual overlap hain-

linked volumes is:

Contrib

Ch

a,t (i, E) =

Contrib

Cha,t (i, E)


(

XDefCha−1

(i)

XDefCha−1

(E)− 1

)

+δt=1

(

XCha−1,4(i)

XCha−1,4(E)

−XCh

a−1(i)

XCha−1

(E)

)

(

XDefCha−1

(i)

XDefCha−1

(E)−

XDefCha−2

(i)

XDefCha−2

(E)

)

(7)

with δt=1 a dummy for the �rst quarters.

In line with se tion 4, we point out that annual a ounts in this formula

stem from the annual hain-link fa tor, hen e if this fa tor is not trading

day adjusted, non-trading day adjusted de�ators and annual hain-linked

volumes must be used in this equation.

The distributions of the three terms from equation(7) are displayed on

Figure 6 for symmetri simulations. The �rst term is the main omponent of

22

1995 2000 2005 2010 2015

−0.2

0.0

0.2

0.4

Contibution term 1

10%

20%

30%

40%

50%60%

70%

80%

90%

1995 2000 2005 2010 2015

−0.005

0.000

0.005

Contribution term 2

10%

20%30%40%50%60%70%

80%

90%

2000 2005 2010 2015

−0.4

−0.2

0.0

0.2

0.4

Contribution term 3

10%20%30%40%50%60%70%80%90%

2000 2005 2010 2015

−5e−04

0e+00

5e−04

Contribution term 3 corr.

10%20%30%40%50%60%70%80%90%

Figure 6: Three omponents of ontribution to quarterly growth rate in

annual overlap for symmetri simulations

the ontribution and is on average one half of a 2% annual growth rate (0.25%

quarterly ontribution). The se ond term orrespond to a trend dis repan y

in de�ators whi h resembles hain-linking e�e t depi ted earlier. For this

symmetri simulation it is very small sin e the pri es of both omponents

grow at the same rate on average. The third term before orre tion, though

it is small on average, has a very large varian e ( omparable with the average

value of the main omponent) but an be redu ed more than a hundred fold

by the orre tion proposed in this paper. However, ontributions exa tly

amount to the growth rate of the aggregate with and without this orre tion.

Equation (7) an be adapted to ompute ontributions to over the year

23

growth rates:

Contrib

Ch,yoy

a,t (i, E) =

XCha,t (i)−XCh

a−1,t(i)

XCha−1,t(E)

+XCh

a,t (i)−XCha−1,t(i)

XCha−1,t(E)

(

XDefCha−1

(i)

XDefCha−1

(E)− 1

)

+(

XCha−1,t(i)

XCha−1,t(E)

−XCh

a−1(i)

XCha−1

(E)

)

(

XDefCha−1

(i)

XDefCha−1

(E)−

XDefCha−2

(i)

XDefCha−2

(E)

)

(8)

The same pre aution as for equation (7) applies on the use of non trading-

day adjusted hain-link fa tor.

With one quarter overlap

All the omputations made for annual overlap estimates apply to the one

quarter overlap estimates, with one ex eption, the addition of a term to the

�rst quarter orre tion whi h is neutral over the aggregate. So mu h so that

the ontribution of i to the growth of E in one quarter overlap hain-linked

volumes an be written:

Contrib

Ch

a,t (i, E) =

Contrib

Cha,t (i, E)


(

XDefCha−1

(i)

XDefCha−1

(E)− 1

)

+δt=1XCh

a−1,4(i)

XCha−1,4(E)

(

XDefCha−1

(i)

XDefCha−1

(E)−

XDefCha−2

(i)

XDefCha−2

(E)

)

(9)

with δt=1 a dummy for the �rst quarters. The three terms of ontributions

omputed on one quarter overlap, ben hmarked on their annual ounterparts

or not, have very similar distributions to the annual overlap ase (Figures 7

and 8). In parti ular, the third term has a large varian e ompared to the

�rst term. Hen e, the orre tion of the third term seems mandatory to have

interpretable ontributions on the �rst quarters of ea h year. Contributions

in one quarter overlap no longer add up to the growth rate of the aggregate.

Figure 9 displays the dis repan y between the sum of the ontributions

and the growth rate of the aggregate in one quarter overlap, with and with-

out the orre tion to the third term and with ben hmarked and non ben h-

marked one quarter overlap aggregates. Contributions given by equation (9)

are additive prior to ben hmarking one quarter overlap estimates on annual

hain-linked aggregates (Figure 9, top left). However, the ne essary orre -

tion to the third term of the ontribution formula makes ontributions no

24

1995 2000 2005 2010 2015

−0.2

0.0

0.2

0.4

Contibution term 1

10%

20%

30%

40%

50%60%

70%

80%

90%

1995 2000 2005 2010 2015

−0.005

0.000

0.005

Contribution term 2

10%

20%30%40%50%60%70%80%

90%

2000 2005 2010 2015

−0.4

−0.2

0.0

0.2

0.4

Contribution term 3

10%20%30%40%50%60%70%80%90%

2000 2005 2010 2015

−0.0015

−0.0010

−0.0005

0.0000

0.0005

0.0010


10%20%30%40%50%60%70%80%90%

Figure 7: Three omponents of ontribution to growth in one quarter overlap

for symmetri simulations

longer additive (Figure 9, top left). When ben hmarking one quarter over-

lap on annual hained linked volumes, be ause of the ben hmarking residual,

formula (9) is only an approximation (Figure 9, bottom left). However, the

orre tion to the third term limits the size of this approximation (Figure 9,

bottom right). Hen e even for one quarter overlap, ontributions are better

omputed with equation 7.

5.4 Comparison with an approximative formula

A ommon approximation for equation (7) and (9) is to apply the annual

formula (4) on quarterly data:

˜Contrib

Ch

a,t (i, E) = ωV ala,t−1(i, E) ev(XCh

a,t (i)) (10)

Figure 10 depi ts the di�eren e between the approximative formula (10)

and the exa t formula (7) on symmetri simulations. For the annual over-

25

1995 2000 2005 2010 2015

−0.2

0.0

0.2

0.4

Contibution term 1

10%

20%

30%

40%

50%60%

70%

80%

90%

1995 2000 2005 2010 2015

−0.005

0.000

0.005

Contribution term 2

10%

20%30%40%50%60%70%

80%

90%

2000 2005 2010 2015

−0.4

−0.2

0.0

0.2

0.4

Contribution term 3

10%20%30%40%50%60%70%80%90%

2000 2005 2010 2015

−5e−04

0e+00

5e−04


10%20%30%40%50%60%70%80%90%

Figure 8: Three omponents of ontribution to growth in one quarter overlap

after ben hmarking for symmetri simulations

26

2000 2005 2010 2015

−1.0

−0.5

0.0

0.5

1.0

One Q ovlp

10%20%30%40%50%60%70%80%90%

2000 2005 2010 2015

−0.003

−0.002

−0.001

0.000

0.001

0.002

One Q ovlp with corr.

10%20%30%40%50%60%70%80%90%

2000 2005 2010 2015

−0.0015

−0.0010

−0.0005

0.0000

0.0005

0.0010

0.0015

Bench. One Q ovlp

10%20%30%40%50%60%70%80%90%

2000 2005 2010 2015

−1e−03

−5e−04

0e+00

5e−04

1e−03

Bench. One Q ovlp with corr.

10%20%30%40%50%60%70%80%90%

Figure 9: Residuals in ontributions to growth of an aggregate in one quarter

overlap for symmetri simulations

27

2000 2005 2010 2015

−0.004

−0.002

0.000

0.002

0.004

Annual Overlap

10%

20%

30%

40%

50%60%

70%

80%

90%

2000 2005 2010 2015

−0.004

−0.002

0.000

0.002

0.004

One Quarter Overlap

10%

20%

30%

40%

50%60%

70%

80%

90%

2000 2005 2010 2015

−0.004

−0.002

0.000

0.002

0.004

One Q. Benchmarked

10%

20%

30%

40%

50%60%

70%

80%

90%

Figure 10: Comparison of approximation (10) with (7) for the omputation

of ontribution to growth (in %)

lap and the one quarter overlap method, whether it is ben hmarked or not,

the approximation is quite good: the di�eren e between the two methods

is smaller than 0.002% for a ontribution of 0.25% in quarterly growth rate.

Hen e, sin e formula (7) is only an approximation for the one quarter overlap

ase, this simpler method may be preferred. In addition to being simpler,

this formula has onvenient de omposition properties [Berthier, 2002℄.

28

Con lusion

With respe t to one quarter overlap, the annual overlap method has the well-

known advantage of naturally adding up to annual hained-linked estimates

and the drawba k of not orre ting for a weight e�e t in the �rst quarters

growth rates. We show in this paper it has two additional advantages.

First, the al ulation of trading-day and seasonally adjusted series is eas-

ier with annual overlap. With both hain-linking methods, the trading-day

adjustment of the hain-link fa tor may a�e t the series trend, but this issue

an easily be solved by using a non adjusted hain-link fa tor. However, the

issue of the hain-link fa tor seasonal adjustment, whi h on erns only the

one quarter overlap method, is more di� ult to solve. Indeed, using either a

seasonally-adjusted or a raw fa tor is unsatisfa tory, the former raises issues

of revisability and pre ision and the trend and y le of the series may be

altered while the latter uses weights in�uen ed by Christmas, winter tem-

peratures...

Se ond, it is possible in annual overlap to ompute perfe tly additive

ontributions to growth. Our experien e is that these ontributions are e o-

nomi ally relevant and the additivity enables to pre isely omment the on-

tribution of hanges in inventories or trade balan e to GDP for instan e.

This property is parti ularly useful for the dissemination of Quarterly Na-

tional A ounts.

With one quarter overlap, al ulation of ontributions is plagued with

more problems: exa tly additive ontributions an be omputed but their

interpretation on �rst quarters is doubtful. In this ase, the formula pro-

posed for annual overlap (Equation (7)) may be preferred but a simpler

approximation may also be onsidered. Additivity is then lost even though

this error is empiri ally small in the present simulations (generally of the or-

der of magnitude of a �rst de imal rounding error on quarterly growth rates).

We an summarize the omparative advantages of the two methods in

Table 1. The new properties exposed in this paper tend to tip the s ales in

favour of the annual overlap method, even though the relative importan e of

these properties remain a matter of judgement. In parti ular, we pointed out

that ben hmarking one quarter overlap hain-linked a ount on their annual

ounterpart, though it is ne essary for pra ti al reasons, should be onsid-

ered with are: espe ially when trading-day or seasonal adjustment omes

into play, this operation may substantially alter the statisti al properties of

29

Property Annual overlap One quarter overlap

Additive quarter N N

Additive omponents ▽ ▽

Consisten y with annual N ▽

Corre tion of weight e�e t in Q1 ▽ N

Neutrality of TD-SA N ▽

Additive ontributions to growth N ▽

Table 1: Comparative advantages of the one quarter and annual overlap

method

the data.

We have only onsidered Laspeyres type indexes here as only the United

States and Canada use the alternative Fisher indexes. However as they use

the one quarter overlap te hnique for hain-linking the same issues as the ones

pointed out here should apply: exa tly additive ontributions to growth an

not be omputed and hain-linking shall intera t with seasonal and trading

day adjustment, in reasing revisability and the alteration of the statisti al

properties of the data through ben hmarking. A thorough demonstration is

left for future resear h.

30

Referen es

Arnaud, F. (2007). Cal ul des ontributions en volumes haînés. Note aux

utilisateurs, 23 novembre(n 47/DG75-G430/FA).

Berthier, J.-P. I. (2002). Ré�exions sur les di�érentes notions de volume dans

les omptes nationaux. Do ument de travail de l'INSEE, (Juin).

Bloem, A., Dippelsman, R., and Mæhle, N. (2001).

Quarterly national a ounts manual: on epts, data sour es, and ompilation.

International Monetary Fund.

Denton, F. T. (1971). Adjustment of monthly or quarterly series to an-

nual totals: an approa h based on quadrati minimization. Journal of the

Ameri an Statisti al Asso iation, 66(333):99�102.

Eurostat (2013). Handbook on quarterly national a ounts. Eurostat Euro-

pean Commission, eurostat manuals and guidelines edition.

S hreyer, P. (2004). Chain index number formulae in the national a -

ounts. In do ument presentat the 8th OECD-NBS Workshop on National

A ounts, volume 6.

Appendix

Country Ref year and volume on ept Chain-linking method

OECD Member E onomies

Australia 2011-12 Chained Vol. Est. Quarter overlap

Austria 2010 Chained Vol. Est. Annual overlap

Belgium 2011 Chained Vol. Est. Annual overlap

Canada 2007 Chained Vol. Est. Quarter overlap

Chile 2008 Chained Vol. Est. Annual overlap

Cze h Republi 2010 Chained Vol. Est. Annual overlap

Denmark 2010 Chained Vol. Est. Annual overlap

Estonia 2010 Chained Vol. Est. Annual overlap

Finland 2000 Chained Vol. Est. Annual overlap

Fran e 2010 Chained Vol. Est. Annual overlap

Germany 2010 Chained Vol. Est. Annual overlap

Gree e 2005 Chained Vol. Est. Indire t method

Hungary 2005 Chained Vol. Est. Annual overlap

I eland 2005 Chained Vol. Est. Annual overlap

Ireland 2012 Chained Vol. Est. Annual overlap

Israel 2010 Chained Vol. Est.

Italy 2010 Chained Vol. Est. Annual overlap

Japan 2005 Chained Vol. Est. Quarter overlap

Korea 2010 Chained Vol. Est. Annual overlap

Luxembourg 2005 Chained Vol. Est. Annual overlap

Mexi o 2008 Fixed Ct.Pr. -

Netherlands 2010 Chained Vol. Est. Over the year (original values)

Annual overlap (seas. adj. values)

New Zealand 1995-96 Chained Vol. Est. Annual overlap

Norway 2011 Chained Vol. Est. Annual overlap

Poland 2005 Chained Vol. Est. Annual overlap

Portugal 2011 Chained Vol. Est. Indire t method

Slovak Republi 2005 Chained Vol. Est. Annual overlap

Slovenia 2000 Chained Vol. Est. Annual overlap

Spain 2008 Chained Vol. Est. Annual overlap

Sweden 2013 Chained Vol. Est. Annual overlap

Switzerland 2005 Chained Vol. Est. Annual overlap

Turkey 1998 Chained Vol. Est. Indire t method

United Kingdom 2010 Chained Vol. Est. Quarter overlap

United States 2009 Chained Vol. Est. Quarter overlap

Non-OECD Member E onomies

Brazil 1995 Chained Vol. Est. Annual overlap

Latvia 2010 Chained Vol. Est. Annual overlap

Russian Federation 2004 Chained Vol. Est. Annual overlap

Argentina 2004 Fixed Ct.Pr. -

India 2004-05 Fixed Ct.Pr. -

Indonesia 2005 Fixed Ct.Pr. -

South Afri a 2005 Fixed Ct.Pr. -

Table 2: Con ept of volumes and hain-linking methods in use in OECD and

non-OECD ountries

Sour e: OECD

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http://stats.oecd.org/wbos/fileview2.aspx?IDFile=479ecd3c-28ec-4b04-bf6b-a6903ce31c55

G 9001 J. FAYOLLE et M. FLEURBAEY Accumulation, profitabilité et endettement des entreprises

G 9002 H. ROUSSE Détection et effets de la multicolinéarité dans les modèles linéaires ordinaires - Un prolongement de la réflexion de BELSLEY, KUH et WELSCH

G 9003 P. RALLE et J. TOUJAS-BERNATE Indexation des salaires : la rupture de 1983

G 9004 D. GUELLEC et P. RALLE Compétitivité, croissance et innovation de produit

G 9005 P. RALLE et J. TOUJAS-BERNATE Les conséquences de la désindexation. Analyse dans une maquette prix-salaires

G 9101 Équipe AMADEUS Le modèle AMADEUS - Première partie -Présentation générale

G 9102 J.L. BRILLET Le modèle AMADEUS - Deuxième partie -Propriétés variantielles

G 9103 D. GUELLEC et P. RALLE Endogenous growth and product innovation

G 9104 H. ROUSSE Le modèle AMADEUS - Troisième partie - Le commerce extérieur et l'environnement international

G 9105 H. ROUSSE Effets de demande et d'offre dans les résultats du commerce extérieur manufacturé de la France au cours des deux dernières décennies

G 9106 B. CREPON Innovation, taille et concentration : causalités et dynamiques

G 9107 B. AMABLE et D. GUELLEC Un panorama des théories de la croissance endogène

G 9108 M. GLAUDE et M. MOUTARDIER Une évaluation du coût direct de l'enfant de 1979 à 1989

G 9109 P. RALLE et alii France - Allemagne : performances économi-ques comparées

G 9110 J.L. BRILLET Micro-DMS NON PARU

G 9111 A. MAGNIER Effets accélérateur et multiplicateur en France depuis 1970 : quelques résultats empiriques

G 9112 B. CREPON et G. DUREAU Investissement en recherche-développement : analyse de causalités dans un modèle d'accélé-rateur généralisé

G 9113 J.L. BRILLET, H. ERKEL-ROUSSE, J. TOUJAS-BERNATE "France-Allemagne Couplées" - Deux économies vues par une maquette macro-économétrique

G 9201 W.J. ADAMS, B. CREPON, D. ENCAOUA Choix technologiques et stratégies de dissuasion d'entrée

G 9202 J. OLIVEIRA-MARTINS, J. TOUJAS-BERNATE

Macro-economic import functions with imperfect competition - An application to the E.C. Trade

G 9203 I. STAPIC Les échanges internationaux de services de la France dans le cadre des négociations multila-térales du GATT Juin 1992 (1ère version) Novembre 1992 (version finale)

G 9204 P. SEVESTRE L'économétrie sur données individuelles-temporelles. Une note introductive

G 9205 H. ERKEL-ROUSSE Le commerce extérieur et l'environnement in-ternational dans le modèle AMADEUS (réestimation 1992)

G 9206 N. GREENAN et D. GUELLEC Coordination within the firm and endogenous growth

G 9207 A. MAGNIER et J. TOUJAS-BERNATE Technology and trade: empirical evidences for the major five industrialized countries

G 9208 B. CREPON, E. DUGUET, D. ENCAOUA et P. MOHNEN Cooperative, non cooperative R & D and optimal patent life

G 9209 B. CREPON et E. DUGUET Research and development, competition and innovation: an application of pseudo maximum likelihood methods to Poisson models with heterogeneity

G 9301 J. TOUJAS-BERNATE Commerce international et concurrence impar-faite : développements récents et implications pour la politique commerciale

G 9302 Ch. CASES Durées de chômage et comportements d'offre de travail : une revue de la littérature

G 9303 H. ERKEL-ROUSSE Union économique et monétaire : le débat économique

G 9304 N. GREENAN - D. GUELLEC / G. BROUSSAUDIER - L. MIOTTI Innovation organisationnelle, dynamisme tech-nologique et performances des entreprises

G 9305 P. JAILLARD Le traité de Maastricht : présentation juridique et historique

G 9306 J.L. BRILLET Micro-DMS : présentation et propriétés

G 9307 J.L. BRILLET Micro-DMS - variantes : les tableaux

G 9308 S. JACOBZONE Les grands réseaux publics français dans une perspective européenne

G 9309 L. BLOCH - B. CŒURE Profitabilité de l'investissement productif et transmission des chocs financiers

G 9310 J. BOURDIEU - B. COLIN-SEDILLOT Les théories sur la structure optimale du capital : quelques points de repère

G 9311 J. BOURDIEU - B. COLIN-SEDILLOT Les décisions de financement des entreprises

Liste des documents de travail de la Direction des Études et Synthèses Économiques ii

françaises : une évaluation empirique des théo-ries de la structure optimale du capital

G 9312 L. BLOCH - B. CŒURÉ Q de Tobin marginal et transmission des chocs financiers

G 9313 Équipes Amadeus (INSEE), Banque de France, Métric (DP) Présentation des propriétés des principaux mo-dèles macroéconomiques du Service Public

G 9314 B. CREPON - E. DUGUET Research & Development, competition and innovation

G 9315 B. DORMONT Quelle est l'influence du coût du travail sur l'emploi ?

G 9316 D. BLANCHET - C. BROUSSE Deux études sur l'âge de la retraite

G 9317 D. BLANCHET Répartition du travail dans une population hété-rogène : deux notes

G 9318 D. EYSSARTIER - N. PONTY AMADEUS - an annual macro-economic model for the medium and long term

G 9319 G. CETTE - Ph. CUNÉO - D. EYSSARTIER -J. GAUTIÉ Les effets sur l'emploi d'un abaissement du coût du travail des jeunes

G 9401 D. BLANCHET Les structures par âge importent-elles ?

G 9402 J. GAUTIÉ Le chômage des jeunes en France : problème de formation ou phénomène de file d'attente ? Quelques éléments du débat

G 9403 P. QUIRION Les déchets en France : éléments statistiques et économiques

G 9404 D. LADIRAY - M. GRUN-REHOMME Lissage par moyennes mobiles - Le problème des extrémités de série

G 9405 V. MAILLARD Théorie et pratique de la correction des effets de jours ouvrables

G 9406 F. ROSENWALD La décision d'investir

G 9407 S. JACOBZONE Les apports de l'économie industrielle pour dé-finir la stratégie économique de l'hôpital public

G 9408 L. BLOCH, J. BOURDIEU, B. COLIN-SEDILLOT, G. LONGUEVILLE Du défaut de paiement au dépôt de bilan : les banquiers face aux PME en difficulté

G 9409 D. EYSSARTIER, P. MAIRE Impacts macro-économiques de mesures d'aide au logement - quelques éléments d'évaluation

G 9410 F. ROSENWALD Suivi conjoncturel de l'investissement

G 9411 C. DEFEUILLEY - Ph. QUIRION Les déchets d'emballages ménagers : une analyse économique des politiques française et allemande

G 9412 J. BOURDIEU - B. CŒURÉ - B. COLIN-SEDILLOT Investissement, incertitude et irréversibilité Quelques développements récents de la théorie de l'investissement

G 9413 B. DORMONT - M. PAUCHET L'évaluation de l'élasticité emploi-salaire dépend-elle des structures de qualification ?

G 9414 I. KABLA Le Choix de breveter une invention

G 9501 J. BOURDIEU - B. CŒURÉ - B. SEDILLOT Irreversible Investment and Uncertainty: When is there a Value of Waiting?

G 9502 L. BLOCH - B. CŒURÉ Imperfections du marché du crédit, investisse-ment des entreprises et cycle économique

G 9503 D. GOUX - E. MAURIN Les transformations de la demande de travail par qualification en France Une étude sur la période 1970-1993

G 9504 N. GREENAN Technologie, changement organisationnel, qua-lifications et emploi : une étude empirique sur l'industrie manufacturière

G 9505 D. GOUX - E. MAURIN Persistance des hiérarchies sectorielles de sa-laires: un réexamen sur données françaises

G 9505 D. GOUX - E. MAURIN Bis Persistence of inter-industry wages differentials:

a reexamination on matched worker-firm panel data

G 9506 S. JACOBZONE Les liens entre RMI et chômage, une mise en perspective NON PARU - article sorti dans Économie et Prévision n° 122 (1996) - pages 95 à 113

G 9507 G. CETTE - S. MAHFOUZ Le partage primaire du revenu Constat descriptif sur longue période

G 9601 Banque de France - CEPREMAP - Direction de la Prévision - Érasme - INSEE - OFCE Structures et propriétés de cinq modèles macro-économiques français

G 9602 Rapport d’activité de la DESE de l’année 1995

G 9603 J. BOURDIEU - A. DRAZNIEKS L’octroi de crédit aux PME : une analyse à partir d’informations bancaires

G 9604 A. TOPIOL-BENSAÏD Les implantations japonaises en France

G 9605 P. GENIER - S. JACOBZONE Comportements de prévention, consommation d’alcool et tabagie : peut-on parler d’une gestion globale du capital santé ? Une modélisation microéconométrique empirique

G 9606 C. DOZ - F. LENGLART Factor analysis and unobserved component models: an application to the study of French business surveys

G 9607 N. GREENAN - D. GUELLEC La théorie coopérative de la firme

iii

G 9608 N. GREENAN - D. GUELLEC Technological innovation and employment reallocation

G 9609 Ph. COUR - F. RUPPRECHT L’intégration asymétrique au sein du continent américain : un essai de modélisation

G 9610 S. DUCHENE - G. FORGEOT - A. JACQUOT Analyse des évolutions récentes de la producti-vité apparente du travail

G 9611 X. BONNET - S. MAHFOUZ The influence of different specifications of wages-prices spirals on the measure of the NAIRU: the case of France

G 9612 PH. COUR - E. DUBOIS, S. MAHFOUZ, J. PISANI-FERRY The cost of fiscal retrenchment revisited: how strong is the evidence?

G 9613 A. JACQUOT Les flexions des taux d’activité sont-elles seule-ment conjoncturelles ?

G 9614 ZHANG Yingxiang - SONG Xueqing Lexique macroéconomique Français-Chinois

G 9701 J.L. SCHNEIDER La taxe professionnelle : éléments de cadrage économique

G 9702 J.L. SCHNEIDER Transition et stabilité politique d’un système redistributif

G 9703 D. GOUX - E. MAURIN Train or Pay: Does it Reduce Inequalities to En-courage Firms to Train their Workers?

G 9704 P. GENIER Deux contributions sur dépendance et équité

G 9705 E. DUGUET - N. IUNG R & D Investment, Patent Life and Patent Value An Econometric Analysis at the Firm Level

G 9706 M. HOUDEBINE - A. TOPIOL-BENSAÏD Les entreprises internationales en France : une analyse à partir de données individuelles

G 9707 M. HOUDEBINE Polarisation des activités et spécialisation des départements en France

G 9708 E. DUGUET - N. GREENAN Le biais technologique : une analyse sur don-nées individuelles

G 9709 J.L. BRILLET Analyzing a small French ECM Model

G 9710 J.L. BRILLET Formalizing the transition process: scenarios for capital accumulation

G 9711 G. FORGEOT - J. GAUTIÉ Insertion professionnelle des jeunes et proces-sus de déclassement

G 9712 E. DUBOIS High Real Interest Rates: the Consequence of a Saving Investment Disequilibrium or of an in-sufficient Credibility of Monetary Authorities?

G 9713 Bilan des activités de la Direction des Études et Synthèses Économiques - 1996

G 9714 F. LEQUILLER Does the French Consumer Price Index Over-state Inflation?

G 9715 X. BONNET Peut-on mettre en évidence les rigidités à la baisse des salaires nominaux ? Une étude sur quelques grands pays de l’OCDE

G 9716 N. IUNG - F. RUPPRECHT Productivité de la recherche et rendements d’échelle dans le secteur pharmaceutique français

G 9717 E. DUGUET - I. KABLA Appropriation strategy and the motivations to use the patent system in France - An econometric analysis at the firm level

G 9718 L.P. PELÉ - P. RALLE Âge de la retraite : les aspects incitatifs du ré-gime général

G 9719 ZHANG Yingxiang - SONG Xueqing Lexique macroéconomique français-chinois, chinois-français

G 9720 M. HOUDEBINE - J.L. SCHNEIDER Mesurer l’influence de la fiscalité sur la locali-sation des entreprises

G 9721 A. MOUROUGANE Crédibilité, indépendance et politique monétaire Une revue de la littérature

G 9722 P. AUGERAUD - L. BRIOT Les données comptables d’entreprises Le système intermédiaire d’entreprises Passage des données individuelles aux données sectorielles

G 9723 P. AUGERAUD - J.E. CHAPRON Using Business Accounts for Compiling National Accounts: the French Experience

G 9724 P. AUGERAUD Les comptes d’entreprise par activités - Le pas-sage aux comptes - De la comptabilité d’entreprise à la comptabilité nationale - A paraître

G 9801 H. MICHAUDON - C. PRIGENT Présentation du modèle AMADEUS

G 9802 J. ACCARDO Une étude de comptabilité générationnelle pour la France en 1996

G 9803 X. BONNET - S. DUCHÊNE Apports et limites de la modélisation « Real Business Cycles »

G 9804 C. BARLET - C. DUGUET - D. ENCAOUA - J. PRADEL The Commercial Success of Innovations An econometric analysis at the firm level in French manufacturing

G 9805 P. CAHUC - Ch. GIANELLA - D. GOUX - A. ZILBERBERG Equalizing Wage Differences and Bargaining Power - Evidence form a Panel of French Firms

G 9806 J. ACCARDO - M. JLASSI La productivité globale des facteurs entre 1975 et 1996

G 9807 Bilan des activités de la Direction des Études et Synthèses Économiques - 1997

iv

G 9808 A. MOUROUGANE Can a Conservative Governor Conduct an Ac-comodative Monetary Policy?

G 9809 X. BONNET - E. DUBOIS - L. FAUVET Asymétrie des inflations relatives et menus costs : tests sur l’inflation française

G 9810 E. DUGUET - N. IUNG Sales and Advertising with Spillovers at the firm level: Estimation of a Dynamic Structural Model on Panel Data

G 9811 J.P. BERTHIER Congestion urbaine : un modèle de trafic de pointe à courbe débit-vitesse et demande élastique

G 9812 C. PRIGENT La part des salaires dans la valeur ajoutée : une approche macroéconomique

G 9813 A.Th. AERTS L’évolution de la part des salaires dans la valeur ajoutée en France reflète-t-elle les évolutions individuelles sur la période 1979-1994 ?

G 9814 B. SALANIÉ Guide pratique des séries non-stationnaires

G 9901 S. DUCHÊNE - A. JACQUOT Une croissance plus riche en emplois depuis le début de la décennie ? Une analyse en compa-raison internationale

G 9902 Ch. COLIN Modélisation des carrières dans Destinie

G 9903 Ch. COLIN Évolution de la dispersion des salaires : un essai de prospective par microsimulation

G 9904 B. CREPON - N. IUNG Innovation, emploi et performances

G 9905 B. CREPON - Ch. GIANELLA Wages inequalities in France 1969-1992 An application of quantile regression techniques

G 9906 C. BONNET - R. MAHIEU Microsimulation techniques applied to inter-generational transfers - Pensions in a dynamic framework: the case of France

G 9907 F. ROSENWALD L’impact des contraintes financières dans la dé-cision d’investissement

G 9908 Bilan des activités de la DESE - 1998

G 9909 J.P. ZOYEM Contrat d’insertion et sortie du RMI Évaluation des effets d’une politique sociale

G 9910 Ch. COLIN - Fl. LEGROS - R. MAHIEU Bilans contributifs comparés des régimes de retraite du secteur privé et de la fonction publique

G 9911 G. LAROQUE - B. SALANIÉ Une décomposition du non-emploi en France

G 9912 B. SALANIÉ Une maquette analytique de long terme du marché du travail

G 9912 Ch. GIANELLA Bis Une estimation de l’élasticité de l’emploi peu

qualifié à son coût

G 9913 Division « Redistribution et Politiques Sociales » Le modèle de microsimulation dynamique DESTINIE

G 9914 E. DUGUET Macro-commandes SAS pour l’économétrie des panels et des variables qualitatives

G 9915 R. DUHAUTOIS Évolution des flux d’emplois en France entre 1990 et 1996 : une étude empirique à partir du fichier des bénéfices réels normaux (BRN)

G 9916 J.Y. FOURNIER Extraction du cycle des affaires : la méthode de Baxter et King

G 9917 B. CRÉPON - R. DESPLATZ - J. MAIRESSE Estimating price cost margins, scale economies and workers’ bargaining power at the firm level

G 9918 Ch. GIANELLA - Ph. LAGARDE Productivity of hours in the aggregate production function: an evaluation on a panel of French firms from the manufacturing sector

G 9919 S. AUDRIC - P. GIVORD - C. PROST Évolution de l’emploi et des coûts par quali-fication entre 1982 et 1996

G 2000/01 R. MAHIEU Les déterminants des dépenses de santé : une approche macroéconomique

G 2000/02 C. ALLARD-PRIGENT - H. GUILMEAU - A. QUINET The real exchange rate as the relative price of nontrables in terms of tradables: theoretical investigation and empirical study on French data

G 2000/03 J.-Y. FOURNIER L’approximation du filtre passe-bande proposée par Christiano et Fitzgerald

G 2000/04 Bilan des activités de la DESE - 1999

G 2000/05 B. CREPON - F. ROSENWALD Investissement et contraintes de financement : le poids du cycle Une estimation sur données françaises

G 2000/06 A. FLIPO Les comportements matrimoniaux de fait

G 2000/07 R. MAHIEU - B. SÉDILLOT Microsimulations of the retirement decision: a supply side approach

G 2000/08 C. AUDENIS - C. PROST Déficit conjoncturel : une prise en compte des conjonctures passées

G 2000/09 R. MAHIEU - B. SÉDILLOT Équivalent patrimonial de la rente et souscription de retraite complémentaire

G 2000/10 R. DUHAUTOIS Ralentissement de l’investissement : petites ou grandes entreprises ? industrie ou tertiaire ?

G 2000/11 G. LAROQUE - B. SALANIÉ Temps partiel féminin et incitations financières à l’emploi

G2000/12 Ch. GIANELLA Local unemployment and wages

G2000/13 B. CREPON - Th. HECKEL - Informatisation en France : une évaluation à partir de données individuelles

v

- Computerization in France: an evaluation based on individual company data

G2001/01 F. LEQUILLER - La nouvelle économie et la mesure de la croissance du PIB - The new economy and the measure ment of GDP growth

G2001/02 S. AUDRIC La reprise de la croissance de l’emploi profite-t-elle aussi aux non-diplômés ?

G2001/03 I. BRAUN-LEMAIRE Évolution et répartition du surplus de productivité

G2001/04 A. BEAUDU - Th. HECKEL Le canal du crédit fonctionne-t-il en Europe ? Une étude de l’hétérogénéité des com-portements d’investissement à partir de données de bilan agrégées

G2001/05 C. AUDENIS - P. BISCOURP - N. FOURCADE - O. LOISEL Testing the augmented Solow growth model: An empirical reassessment using panel data

G2001/06 R. MAHIEU - B. SÉDILLOT Départ à la retraite, irréversibilité et incertitude

G2001/07 Bilan des activités de la DESE - 2000

G2001/08 J. Ph. GAUDEMET Les dispositifs d’acquisition à titre facultatif d’annuités viagères de retraite

G2001/09 B. CRÉPON - Ch. GIANELLA Fiscalité, coût d’usage du capital et demande de facteurs : une analyse sur données individuelles

G2001/10 B. CRÉPON - R. DESPLATZ Évaluation des effets des dispositifs d’allégements de charges sociales sur les bas salaires

G2001/11 J.-Y. FOURNIER Comparaison des salaires des secteurs public et privé

G2001/12 J.-P. BERTHIER - C. JAULENT R. CONVENEVOLE - S. PISANI Une méthodologie de comparaison entre consommations intermédiaires de source fiscale et de comptabilité nationale

G2001/13 P. BISCOURP - Ch. GIANELLA Substitution and complementarity between capital, skilled and less skilled workers: an analysis at the firm level in the French manufacturing industry

G2001/14 I. ROBERT-BOBEE Modelling demographic behaviours in the French microsimulation model Destinie: An analysis of future change in completed fertility

G2001/15 J.-P. ZOYEM Diagnostic sur la pauvreté et calendrier de revenus : le cas du “Panel européen des ménages »

G2001/16 J.-Y. FOURNIER - P. GIVORD La réduction des taux d’activité aux âges extrêmes, une spécificité française ?

G2001/17 C. AUDENIS - P. BISCOURP - N. RIEDINGER Existe-t-il une asymétrie dans la transmission du prix du brut aux prix des carburants ?

G2002/01 F. MAGNIEN - J.-L. TAVERNIER - D. THESMAR Les statistiques internationales de PIB par habitant en standard de pouvoir d’achat : une analyse des résultats


G2002/03 B. SÉDILLOT - E. WALRAET La cessation d’activité au sein des couples : y a-t-il interdépendance des choix ?

G2002/04 G. BRILHAULT - Rétropolation des séries de FBCF et calcul du

capital fixe en SEC-95 dans les comptes nationaux français

- Retropolation of the investment series (GFCF) and estimation of fixed capital stocks on the ESA-95 basis for the French balance sheets

G2002/05 P. BISCOURP - B. CRÉPON - T. HECKEL - N. RIEDINGER How do firms respond to cheaper computers? Microeconometric evidence for France based on a production function approach

G2002/06 C. AUDENIS - J. DEROYON - N. FOURCADE L’impact des nouvelles technologies de l’information et de la communication sur l’économie française - un bouclage macro-économique

G2002/07 J. BARDAJI - B. SÉDILLOT - E. WALRAET Évaluation de trois réformes du Régime Général d’assurance vieillesse à l’aide du modèle de microsimulation DESTINIE

G2002/08 J.-P. BERTHIER Réflexions sur les différentes notions de volume dans les comptes nationaux : comptes aux prix d’une année fixe ou aux prix de l’année précédente, séries chaînées

G2002/09 F. HILD Les soldes d’opinion résument-ils au mieux les réponses des entreprises aux enquêtes de conjoncture ?

G2002/10 I. ROBERT-BOBÉE Les comportements démographiques dans le modèle de microsimulation Destinie - Une comparaison des estimations issues des enquêtes Jeunes et Carrières 1997 et Histoire Familiale 1999

G2002/11 J.-P. ZOYEM La dynamique des bas revenus : une analyse des entrées-sorties de pauvreté

G2002/12 F. HILD Prévisions d’inflation pour la France

G2002/13 M. LECLAIR Réduction du temps de travail et tensions sur les facteurs de production

G2002/14 E. WALRAET - A. VINCENT - Analyse de la redistribution intragénérationnelle dans le système de retraite des salariés du privé - Une approche par microsimulation - Intragenerational distributional analysis in the french private sector pension scheme - A microsimulation approach

G2002/15 P. CHONE - D. LE BLANC - I. ROBERT-BOBEE Offre de travail féminine et garde des jeunes enfants

vi

G2002/16 F. MAUREL - S. GREGOIR Les indices de compétitivité des pays : inter-prétation et limites

G2003/01 N. RIEDINGER - E.HAUVY Le coût de dépollution atmosphérique pour les entreprises françaises : Une estimation à partir de données individuelles

G2003/02 P. BISCOURP et F. KRAMARZ Création d’emplois, destruction d’emplois et internationalisation des entreprises industrielles françaises : une analyse sur la période 1986-1992


G2003/04 P.-O. BEFFY - J. DEROYON - N. FOURCADE - S. GREGOIR - N. LAÏB - B. MONFORT Évolutions démographiques et croissance : une projection macro-économique à l’horizon 2020

G2003/05 P. AUBERT La situation des salariés de plus de cinquante ans dans le secteur privé

G2003/06 P. AUBERT - B. CRÉPON Age, salaire et productivité La productivité des salariés décline-t-elle en fin de carrière ?

G2003/07 H. BARON - P.O. BEFFY - N. FOURCADE - R. MAHIEU Le ralentissement de la productivité du travail au cours des années 1990

G2003/08 P.-O. BEFFY - B. MONFORT Patrimoine des ménages, dynamique d’allocation et comportement de consommation

G2003/09 P. BISCOURP - N. FOURCADE Peut-on mettre en évidence l’existence de rigidités à la baisse des salaires à partir de données individuelles ? Le cas de la France à la fin des années 90

G2003/10 M. LECLAIR - P. PETIT Présence syndicale dans les firmes : quel impact sur les inégalités salariales entre les hommes et les femmes ?

G2003/11 P.-O. BEFFY - X. BONNET - M. DARRACQ-PARIES - B. MONFORT MZE: a small macro-model for the euro area

G2004/01 P. AUBERT - M. LECLAIR La compétitivité exprimée dans les enquêtes trimestrielles sur la situation et les perspectives dans l’industrie

G2004/02 M. DUÉE - C. REBILLARD La dépendance des personnes âgées : une projection à long terme

G2004/03 S. RASPILLER - N. RIEDINGER Régulation environnementale et choix de localisation des groupes français

G2004/04 A. NABOULET - S. RASPILLER Les déterminants de la décision d’investir : une approche par les perceptions subjectives des firmes

G2004/05 N. RAGACHE La déclaration des enfants par les couples non mariés est-elle fiscalement optimale ?

G2004/06 M. DUÉE L’impact du chômage des parents sur le devenir scolaire des enfants

G2004/07 P. AUBERT - E. CAROLI - M. ROGER New Technologies, Workplace Organisation and the Age Structure of the Workforce: Firm-Level Evidence

G2004/08 E. DUGUET - C. LELARGE Les brevets accroissent-ils les incitations privées à innover ? Un examen microéconométrique

G2004/09 S. RASPILLER - P. SILLARD Affiliating versus Subcontracting: the Case of Multinationals

G2004/10 J. BOISSINOT - C. L’ANGEVIN - B. MONFORT Public Debt Sustainability: Some Results on the French Case

G2004/11 S. ANANIAN - P. AUBERT Travailleurs âgés, nouvelles technologies et changements organisationnels : un réexamen à partir de l’enquête « REPONSE »

G2004/12 X. BONNET - H. PONCET Structures de revenus et propensions différentes à consommer - Vers une équation de consommation des ménages plus robuste en prévision pour la France

G2004/13 C. PICART Évaluer la rentabilité des sociétés non financières

G2004/14 J. BARDAJI - B. SÉDILLOT - E. WALRAET Les retraites du secteur public : projections à l’horizon 2040 à l’aide du modèle de microsimulation DESTINIE

G2005/01 S. BUFFETEAU - P. GODEFROY Conditions de départ en retraite selon l’âge de fin d’études : analyse prospective pour les générations 1945 à1974

G2005/02 C. AFSA - S. BUFFETEAU L’évolution de l’activité féminine en France : une approche par pseudo-panel

G2005/03 P. AUBERT - P. SILLARD Délocalisations et réductions d’effectifs dans l’industrie française

G2005/04 M. LECLAIR - S. ROUX Mesure et utilisation des emplois instables dans les entreprises

G2005/05 C. L’ANGEVIN - S. SERRAVALLE Performances à l’exportation de la France et de l’Allemagne - Une analyse par secteur et destination géographique

G2005/06 Bilan des activités de la Direction des Études et Synthèses Économiques - 2004

G2005/07 S. RASPILLER La concurrence fiscale : principaux enseigne-ments de l’analyse économique

G2005/08 C. L’ANGEVIN - N. LAÏB Éducation et croissance en France et dans un panel de 21 pays de l’OCDE

G2005/09 N. FERRARI Prévoir l’investissement des entreprises Un indicateur des révisions dans l’enquête de conjoncture sur les investissements dans l’industrie.

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G2005/10 P.-O. BEFFY - C. L’ANGEVIN Chômage et boucle prix-salaires : apport d’un modèle « qualifiés/peu qualifiés »

G2005/11 B. HEITZ A two-states Markov-switching model of inflation in France and the USA: credible target VS inflation spiral

G2005/12 O. BIAU - H. ERKEL-ROUSSE - N. FERRARI Réponses individuelles aux enquêtes de conjoncture et prévision macroéconomiques : Exemple de la prévision de la production manufacturière

G2005/13 P. AUBERT - D. BLANCHET - D. BLAU The labour market after age 50: some elements of a Franco-American comparison

G2005/14 D. BLANCHET - T. DEBRAND - P. DOURGNON - P. POLLET L’enquête SHARE : présentation et premiers résultats de l’édition française

G2005/15 M. DUÉE La modélisation des comportements démogra-phiques dans le modèle de microsimulation DESTINIE

G2005/16 H. RAOUI - S. ROUX Étude de simulation sur la participation versée aux salariés par les entreprises

G2006/01 C. BONNET - S. BUFFETEAU - P. GODEFROY Disparités de retraite de droit direct entre hommes et femmes : quelles évolutions ?

G2006/02 C. PICART Les gazelles en France

G2006/03 P. AUBERT - B. CRÉPON -P. ZAMORA Le rendement apparent de la formation continue dans les entreprises : effets sur la productivité et les salaires

G2006/04 J.-F. OUVRARD - R. RATHELOT Demographic change and unemployment: what do macroeconometric models predict?

G2006/05 D. BLANCHET - J.-F. OUVRARD Indicateurs d’engagements implicites des systèmes de retraite : chiffrages, propriétés analytiques et réactions à des chocs démographiques types

G2006/06 G. BIAU - O. BIAU - L. ROUVIERE Nonparametric Forecasting of the Manufacturing Output Growth with Firm-level Survey Data

G2006/07 C. AFSA - P. GIVORD Le rôle des conditions de travail dans les absences pour maladie

G2006/08 P. SILLARD - C. L’ANGEVIN - S. SERRAVALLE Performances comparées à l’exportation de la France et de ses principaux partenaires Une analyse structurelle sur 12 ans

G2006/09 X. BOUTIN - S. QUANTIN Une méthodologie d’évaluation comptable du coût du capital des entreprises françaises : 1984-2002

G2006/10 C. AFSA L’estimation d’un coût implicite de la pénibilité du travail chez les travailleurs âgés

G2006/11 C. LELARGE Les entreprises (industrielles) françaises sont-elles à la frontière technologique ?

G2006/12 O. BIAU - N. FERRARI Théorie de l’opinion Faut-il pondérer les réponses individuelles ?

G2006/13 A. KOUBI - S. ROUX Une réinterprétation de la relation entre productivité et inégalités salariales dans les entreprises

G2006/14 R. RATHELOT - P. SILLARD The impact of local taxes on plants location decision

G2006/15 L. GONZALEZ - C. PICART Diversification, recentrage et poids des activités de support dans les groupes (1993-2000)

G2007/01 D. SRAER Allègements de cotisations patronales et dynamique salariale

G2007/02 V. ALBOUY - L. LEQUIEN Les rendements non monétaires de l’éducation : le cas de la santé

G2007/03 D. BLANCHET - T. DEBRAND Aspiration à la retraite, santé et satisfaction au travail : une comparaison européenne

G2007/04 M. BARLET - L. CRUSSON Quel impact des variations du prix du pétrole sur la croissance française ?

G2007/05 C. PICART Flux d’emploi et de main-d’œuvre en France : un réexamen

G2007/06 V. ALBOUY - C. TAVAN Massification et démocratisation de l’enseignement supérieur en France

G2007/07 T. LE BARBANCHON The Changing response to oil price shocks in France: a DSGE type approach

G2007/08 T. CHANEY - D. SRAER - D. THESMAR Collateral Value and Corporate Investment Evidence from the French Real Estate Market

G2007/09 J. BOISSINOT Consumption over the Life Cycle: Facts for France

G2007/10 C. AFSA Interpréter les variables de satisfaction : l’exemple de la durée du travail

G2007/11 R. RATHELOT - P. SILLARD Zones Franches Urbaines : quels effets sur l’emploi salarié et les créations d’établissements ?

G2007/12 V. ALBOUY - B. CRÉPON Aléa moral en santé : une évaluation dans le cadre du modèle causal de Rubin

G2008/01 C. PICART Les PME françaises : rentables mais peu dynamiques

G2008/02 P. BISCOURP - X. BOUTIN - T. VERGÉ The Effects of Retail Regulations on Prices Evidence form the Loi Galland

G2008/03 Y. BARBESOL - A. BRIANT Économies d’agglomération et productivité des

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entreprises : estimation sur données individuelles françaises

G2008/04 D. BLANCHET - F. LE GALLO Les projections démographiques : principaux mécanismes et retour sur l’expérience française

G2008/05 D. BLANCHET - F. TOUTLEMONDE Évolutions démographiques et déformation du cycle de vie active : quelles relations ?

G2008/06 M. BARLET - D. BLANCHET - L. CRUSSON Internationalisation et flux d’emplois : que dit une approche comptable ?

G2008/07 C. LELARGE - D. SRAER - D. THESMAR Entrepreneurship and Credit Constraints - Evidence from a French Loan Guarantee Program

G2008/08 X. BOUTIN - L. JANIN Are Prices Really Affected by Mergers?

G2008/09 M. BARLET - A. BRIANT - L. CRUSSON Concentration géographique dans l’industrie manufacturière et dans les services en France : une approche par un indicateur en continu

G2008/10 M. BEFFY - É. COUDIN - R. RATHELOT Who is confronted to insecure labor market histories? Some evidence based on the French labor market transition

G2008/11 M. ROGER - E. WALRAET Social Security and Well-Being of the Elderly: the Case of France

G2008/12 C. AFSA Analyser les composantes du bien-être et de son évolution Une approche empirique sur données individuelles

G2008/13 M. BARLET - D. BLANCHET - T. LE BARBANCHON Microsimuler le marché du travail : un prototype

G2009/01 P.-A. PIONNIER Le partage de la valeur ajoutée en France, 1949-2007

G2009/02 Laurent CLAVEL - Christelle MINODIER A Monthly Indicator of the French Business Climate

G2009/03 H. ERKEL-ROUSSE - C. MINODIER Do Business Tendency Surveys in Industry and Services Help in Forecasting GDP Growth? A Real-Time Analysis on French Data

G2009/04 P. GIVORD - L. WILNER Les contrats temporaires : trappe ou marchepied vers l’emploi stable ?

G2009/05 G. LALANNE - P.-A. PIONNIER - O. SIMON Le partage des fruits de la croissance de 1950 à 2008 : une approche par les comptes de surplus

G2009/06 L. DAVEZIES - X. D’HAULTFOEUILLE Faut-il pondérer ?… Ou l’éternelle question de l’économètre confronté à des données d’enquête

G2009/07 S. QUANTIN - S. RASPILLER - S. SERRAVALLE Commerce intragroupe, fiscalité et prix de transferts : une analyse sur données françaises

G2009/08 M. CLERC - V. MARCUS Élasticités-prix des consommations énergétiques des ménages

G2009/09 G. LALANNE - E. POULIQUEN - O. SIMON Prix du pétrole et croissance potentielle à long terme

G2009/10 D. BLANCHET - J. LE CACHEUX - V. MARCUS Adjusted net savings and other approaches to sustainability: some theoretical background

G2009/11 V. BELLAMY - G. CONSALES - M. FESSEAU - S. LE LAIDIER - É. RAYNAUD Une décomposition du compte des ménages de la comptabilité nationale par catégorie de ménage en 2003

G2009/12 J. BARDAJI - F. TALLET Detecting Economic Regimes in France: a Qualitative Markov-Switching Indicator Using Mixed Frequency Data

G2009/13 R. AEBERHARDT - D. FOUGÈRE - R. RATHELOT Discrimination à l’embauche : comment exploiter les procédures de testing ?

G2009/14 Y. BARBESOL - P. GIVORD - S. QUANTIN Partage de la valeur ajoutée, approche par données microéconomiques

G2009/15 I. BUONO - G. LALANNE The Effect of the Uruguay round on the Intensive and Extensive Margins of Trade

G2010/01 C. MINODIER Avantages comparés des séries des premières valeurs publiées et des séries des valeurs révisées - Un exercice de prévision en temps réel de la croissance trimestrielle du PIB en France

G2010/02 V. ALBOUY - L. DAVEZIES - T. DEBRAND Health Expenditure Models: a Comparison of Five Specifications using Panel Data

G2010/03 C. KLEIN - O. SIMON Le modèle MÉSANGE réestimé en base 2000 Tome 1 – Version avec volumes à prix constants

G2010/04 M.-É. CLERC - É. COUDIN L’IPC, miroir de l’évolution du coût de la vie en France ? Ce qu’apporte l’analyse des courbes d’Engel

G2010/05 N. CECI-RENAUD - P.-A. CHEVALIER Les seuils de 10, 20 et 50 salariés : impact sur la taille des entreprises françaises

G2010/06 R. AEBERHARDT - J. POUGET National Origin Differences in Wages and Hierarchical Positions - Evidence on French Full-Time Male Workers from a matched Employer-Employee Dataset

G2010/07 S. BLASCO - P. GIVORD Les trajectoires professionnelles en début de vie active : quel impact des contrats temporaires ?

G2010/08 P. GIVORD Méthodes économétriques pour l’évaluation de politiques publiques

G2010/09 P.-Y. CABANNES - V. LAPÈGUE - E. POULIQUEN - M. BEFFY - M. GAINI Quelle croissance de moyen terme après la crise ?

G2010/10 I. BUONO - G. LALANNE La réaction des entreprises françaises à la baisse des tarifs douaniers étrangers

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G2010/11 R. RATHELOT - P. SILLARD L’apport des méthodes à noyaux pour mesurer la concentration géographique - Application à la concentration des immigrés en France de 1968 à 1999

G2010/12 M. BARATON - M. BEFFY - D. FOUGÈRE Une évaluation de l’effet de la réforme de 2003 sur les départs en retraite - Le cas des enseignants du second degré public

G2010/13 D. BLANCHET - S. BUFFETEAU - E. CRENNER S. LE MINEZ Le modèle de microsimulation Destinie 2 : principales caractéristiques et premiers résultats

G2010/14 D. BLANCHET - E. CRENNER Le bloc retraites du modèle Destinie 2 : guide de l’utilisateur

G2010/15 M. BARLET - L. CRUSSON - S. DUPUCH - F. PUECH Des services échangés aux services échan-geables : une application sur données françaises

G2010/16 M. BEFFY - T. KAMIONKA Public-private wage gaps: is civil-servant human capital sector-specific?

G2010/17 P.-Y. CABANNES - H. ERKEL-ROUSSE - G. LALANNE - O. MONSO - E. POULIQUEN Le modèle Mésange réestimé en base 2000 Tome 2 - Version avec volumes à prix chaînés

G2010/18 R. AEBERHARDT - L. DAVEZIES Conditional Logit with one Binary Covariate: Link between the Static and Dynamic Cases

G2011/01 T. LE BARBANCHON - B. OURLIAC - O. SIMON Les marchés du travail français et américain face aux chocs conjoncturels des années 1986 à 2007 : une modélisation DSGE

G2011/02 C. MARBOT Une évaluation de la réduction d’impôt pour l’emploi de salariés à domicile

G2011/03 L. DAVEZIES Modèles à effets fixes, à effets aléatoires, modèles mixtes ou multi-niveaux : propriétés et mises en œuvre des modélisations de l’hétérogénéité dans le cas de données groupées

G2011/04 M. ROGER - M. WASMER Heterogeneity matters: labour productivity differentiated by age and skills

G2011/05 J.-C. BRICONGNE - J.-M. FOURNIER V. LAPÈGUE - O. MONSO De la crise financière à la crise économique L’impact des perturbations financières de 2007 et 2008 sur la croissance de sept pays industrialisés

G2011/06 P. CHARNOZ - É. COUDIN - M. GAINI Wage inequalities in France 1976-2004: a quantile regression analysis

G2011/07 M. CLERC - M. GAINI - D. BLANCHET Recommendations of the Stiglitz-Sen-Fitoussi Report: A few illustrations

G2011/08 M. BACHELET - M. BEFFY - D. BLANCHET Projeter l’impact des réformes des retraites sur l’activité des 55 ans et plus : une comparaison de trois modèles

G2011/09 C. LOUVOT-RUNAVOT L’évaluation de l’activité dissimulée des entre-

prises sur la base des contrôles fiscaux et son insertion dans les comptes nationaux

G2011/10 A. SCHREIBER - A. VICARD La tertiarisation de l’économie française et le ralentissement de la productivité entre 1978 et 2008

G2011/11 M.-É. CLERC - O. MONSO - E. POULIQUEN Les inégalités entre générations depuis le baby-boom

G2011/12 C. MARBOT - D. ROY Évaluation de la transformation de la réduction d'impôt en crédit d'impôt pour l'emploi de salariés à domicile en 2007

G2011/13 P. GIVORD - R. RATHELOT - P. SILLARD Place-based tax exemptions and displacement effects: An evaluation of the Zones Franches Urbaines program

G2011/14 X. D’HAULTFOEUILLE - P. GIVORD - X. BOUTIN The Environmental Effect of Green Taxation: the Case of the French “Bonus/Malus”

G2011/15 M. BARLET - M. CLERC - M. GARNEO - V. LAPÈGUE - V. MARCUS La nouvelle version du modèle MZE, modèle macroéconométrique pour la zone euro

G2011/16 R. AEBERHARDT - I. BUONO - H. FADINGER Learning, Incomplete Contracts and Export Dynamics: theory and Evidence form French Firms

G2011/17 C. KERDRAIN - V. LAPÈGUE Restrictive Fiscal Policies in Europe: What are the Likely Effects?

G2012/01 P. GIVORD - S. QUANTIN - C. TREVIEN A Long-Term Evaluation of the First Generation of the French Urban Enterprise Zones

G2012/02 N. CECI-RENAUD - V. COTTET Politique salariale et performance des entreprises

G2012/03 P. FÉVRIER - L. WILNER Do Consumers Correctly Expect Price Reductions? Testing Dynamic Behavior

G2012/04 M. GAINI - A. LEDUC - A. VICARD School as a shelter? School leaving-age and the business cycle in France

G2012/05 M. GAINI - A. LEDUC - A. VICARD A scarred generation? French evidence on young people entering into a tough labour market

G2012/06 P. AUBERT - M. BACHELET Disparités de montant de pension et redistribution dans le système de retraite français

G2012/07 R. AEBERHARDT - P GIVORD - C. MARBOT Spillover Effect of the Minimum Wage in France: An Unconditional Quantile Regression Approach

G2012/08 A. EIDELMAN - F. LANGUMIER - A. VICARD Prélèvements obligatoires reposant sur les ménages : des canaux redistributifs différents en 1990 et 2010

G2012/09 O. BARGAIN - A. VICARD Le RMI et son successeur le RSA découragent-ils certains jeunes de travailler ? Une analyse sur les jeunes autour de 25 ans

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G2012/10 C. MARBOT - D. ROY Projections du coût de l’APA et des caractéristiques de ses bénéficiaires à l’horizon 2040 à l’aide du modèle Destinie

G2012/11 A. MAUROUX Le crédit d’impôt dédié au développement durable : une évaluation économétrique

G2012/12 V. COTTET - S. QUANTIN - V. RÉGNIER Coût du travail et allègements de charges : une estimation au niveau établissement de 1996 à 2008

G2012/13 X. D’HAULTFOEUILLE - P. FÉVRIER - L. WILNER Demand Estimation in the Presence of Revenue Management

G2012/14 D. BLANCHET - S. LE MINEZ Joint macro/micro evaluations of accrued-to-date pension liabilities: an application to French reforms

G2013/01- T. DEROYON - A. MONTAUT - P-A PIONNIER F1301 Utilisation rétrospective de l’enquête Emploi à

une fréquence mensuelle : apport d’une modélisation espace-état

G2013/02- C. TREVIEN F1302 Habiter en HLM : quel avantage monétaire et

quel impact sur les conditions de logement ?

G2013/03 A. POISSONNIER Temporal disaggregation of stock variables - The

Chow-Lin method extended to dynamic models

G2013/04 P. GIVORD - C. MARBOT Does the cost of child care affect female labor

market participation? An evaluation of a French reform of childcare subsidies

G2013/05 G. LAME - M. LEQUIEN - P.-A. PIONNIER Interpretation and limits of sustainability tests in

public finance

G2013/06 C. BELLEGO - V. DORTET-BERNADET La participation aux pôles de compétitivité :

quelle incidence sur les dépenses de R&D et l’activité des PME et ETI ?

G2013/07 P.-Y. CABANNES - A. MONTAUT - P.-A. PIONNIER

Évaluer la productivité globale des facteurs en France : l’apport d’une mesure de la qualité du capital et du travail

G2013/08 R. AEBERHARDT - C. MARBOT Evolution of Instability on the French Labour

Market During the Last Thirty Years

G2013/09 J-B. BERNARD - G. CLÉAUD Oil price: the nature of the shocks and the impact

on the French economy

G2013/10 G. LAME Was there a « Greenspan Conundrum » in the

Euro area?

G2013/11 P. CHONÉ - F. EVAIN - L. WILNER - E. YILMAZ Introducing activity-based payment in the

hospital industry : Evidence from French data

G2013/12 C. GRISLAIN-LETRÉMY Natural Disasters: Exposure and Underinsurance

G2013/13 P.-Y. CABANNES - V. COTTET - Y. DUBOIS - C. LELARGE - M. SICSIC French Firms in the Face of the 2008/2009 Crisis

G2013/14 A. POISSONNIER - D. ROY Households Satellite Account for France in 2010.

Methodological issues on the assessment of domestic production

G2013/15 G. CLÉAUD - M. LEMOINE - P.-A. PIONNIER Which size and evolution of the government

expenditure multiplier in France (1980-2010)?

G2014/01 M. BACHELET - A. LEDUC - A. MARINO Les biographies du modèle Destinie II : rebasage

et projection

G2014/02 B. GARBINTI L’achat de la résidence principale et la création

d’entreprises sont-ils favorisés par les donations et héritages ?

G2014/03 N. CECI-RENAUD - P. CHARNOZ - M. GAINI Évolution de la volatilité des revenus salariaux du

secteur privé en France depuis 1968

G2014/04 P. AUBERT Modalités d’application des réformes des

retraites et prévisibilité du montant de pension

G2014/05 C. GRISLAIN-LETRÉMY - A. KATOSSKY The Impact of Hazardous Industrial Facilities on

Housing Prices: A Comparison of Parametric and Semiparametric Hedonic Price Models

G2014//06 J.-M. DAUSSIN-BENICHOU - A. MAUROUX Turning the heat up. How sensitive are households to fiscal incentives on energy efficiency investments?

G2014/07 C. LABONNE - G. LAMÉ Credit Growth and Capital Requirements: Binding or Not?

G2014/08 C. GRISLAIN-LETRÉMY et C. TREVIEN The Impact of Housing Subsidies on the Rental Sector: the French Example

G2014 09 M. LEQUIEN et A. MONTAUT Croissance potentielle en France et en zone euro : un tour d’horizon des méthodes d’estimation

G2014/10 B. GARBINTI - P. LAMARCHE Les hauts revenus épargnent-ils davantage ?

G2014/11 D. AUDENAERT - J. BARDAJI - R. LARDEUX - M. ORAND - M. SICSIC Wage Resilience in France since the Great Recession

G2014/12 F. ARNAUD - J. BOUSSARD - A. POISSONNIER - H. SOUAL Computing additive contributions to growth and other issues for chain-linked quarterly aggregates