Download - User Guide - COMESA Monetary Institute (CMI)
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Panel Data Analysis With Special Application to Monetary
Policy Transmission Mechanism
User Guide
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Panel Data Analysis
With Special Application to Monetary Policy Transmission Mechanism
Prepared By
Dr Esman Nyamongo
Assistant Director
Research Department
Central Bank of Kenya
Published by
COMESA Monetary Institute (CMI)
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First Published 2019 by
COMESA Monetary Institute C/O Kenya School of Monetary Studies P.O. Box 65041 – 00618 Noordin Road Nairobi, KENYA Tel: +254 – 20 – 8646207 http://cmi.comesa.int
Copyright © 2019, COMESA Monetary Institute (CMI)
All rights reserved. Except for fully acknowledged short citations for purposes of research and teaching, no part of this publication may be reproduced or transmitted in any form or by any means without prior permission from COMESA.
Disclaimer
The views expressed herein are those of the author and do not in any way represent the official position of COMESA, its Member States, or the affiliated Institution of the Author.
Typesetting and Design
Mercy W. Macharia [email protected]
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TABLE OF CONTENTS
List of Figures ............................................................................................ viii
List of Tables ............................................................................................. viii
List of Acronyms ........................................................................................ ix
Preface ........................................................................................................... x
Acknowledgements ..................................................................................... xi
1. INTRODUCTION TO PANEL DATA ANALYSIS ...................1
1.0 Introduction.......................................................................................... 1
1.1 Types of Panel Data ............................................................................ 1
1.1.1 Dated vs. Undated Panels ..................................................................... 2
1.1.2 Regular vs. Irregular Dated Panels ........................................................ 2
1.1.3 Balanced vs. Unbalanced Panels ............................................................ 2
1.2 Advantages of Panel Data .................................................................. 4
2. GETTING STARTED IN EVIEWS SOFTWARE ..................... 9
2.0 Introduction.......................................................................................... 9
2.1 Getting Started in Eviews ................................................................... 9
2.2 Data preparation in Excel ................................................................. 11
2.3 To Create an Eviews Workfile ......................................................... 11
2.3.1 Importing the data into Eviews ............................................................ 12
2.3.2 Setting up a pool in a workfile ............................................................. 14
2.3.3 Data transformations .......................................................................... 19
2.4 Viewing Data ...................................................................................... 21
2.5 Basic Plots ........................................................................................... 22
2.6 Descriptive Statistics ......................................................................... 24
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3. POOLED REGRESSION ANALYSIS ................................... 29
3.0 Introduction ........................................................................................ 29
3.1 The pooled regression model ........................................................... 29
3.1.1 Limitations of Pooled regression ........................................................... 30
3.2 Estimation of the Pooled Regression Model ................................. 31
3.2.1 Illustration of pooled regression using general data ................................ 31
3.2.2 Organising data in Excel .................................................................... 32
3.2.3 Loading the data into Eviews .............................................................. 34
3.2.4 Pooled regression in Eviews.................................................................. 36
3.2.5 Pooled regressions in Eviews Environment ........................................... 37
3.3 Application of Pooled Regression Approach to Monetary Policy Transmission in Kenya .......................................................... 39
3.3.1 Case Study: Monetary Policy Transmission in Kenya: Evidence from bank level data ............................................................................ 39
3.3.2 The Model setup.................................................................................. 40
References ................................................................................................... 45
4. ERROR COMPONENT MODEL ANALYSIS: ONE WAY
ERROR COMPONENTS MODEL ...................................... 47
4.0 Introduction ........................................................................................ 47
4.1 The Error Components Model Specification ................................ 47
4.1.1 One-Way Error Component Model ..................................................... 48
4.1.2 The least squares dummy variable estimation method .......................... 49
4.2 Case Study: Monetary Policy Transmission in Kenya: Evidence from bank level data ......................................................... 57
4.2.1 Within-Q-estimation method .................................................................... 59
4.3 Pooled Estimation Method Versus the Fixed Effect Method................................................................................................. 65
4.4 Case Study: Monetary Policy Transmission in Kenya: Evidence from bank level data ......................................................... 68
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4.5 Random Effects Model ..................................................................... 70
4.5.1 Testing the validity of the random effects: Hausman test ............................ 71
References ................................................................................................... 73
5. ERROR COMPONENT MODEL ANALYSIS: TWO WAY
ERROR COMPONENTS MODEL ..................................... 75
5.0 Introduction ......................................................................................... 75
5.1 Estimation of the Error Components Model ................................. 76
5.1.1 Fixed effects model.................................................................................... 76
6. DYNAMIC PANEL DATA ANALYSIS ................................ 83
6.1 Arellano and Bond Estimator .......................................................... 84
6.2 Estimation of Dynamic Panel in Eviews ....................................... 85
6.3 Step by Step Implementation of the Dynamic GMM Procedure in Eviews .......................................................................... 86
References ................................................................................................... 95
7. NON-STATIONARY PANEL ANALYSIS ........................... 97
7.0 Panel Unit-root Tests ........................................................................ 97
7.1 Panel Unit-root Test with an Automatic Lag Selection Method .............................................................................................. 105
References ................................................................................................. 107
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LIST OF FIGURES Figure 1: Creating a work file .............................................................................. 34
Figure 2: Getting the data into Eviews .............................................................. 35
Figure 3: Estimation in a pool object ................................................................. 36
Figure 4: Estimation result .................................................................................. 37
Figure 5: BLC based on pooled regressions analysis ....................................... 44
Figure 6: GMM Model Specification ................................................................. 93
LIST OF TABLES Table 1.1: Panel data set: Normalised bank size for 5 banks ........................... 4
Table 3.1: Raw data on bank size and loan ....................................................... 32
Table 3.2: Stacked data on bank size and loan ................................................. 33
Table 3.3: Data on size and growth rate of loan with cross-section
identifiers ............................................................................................. 38
Table 4.1: Dummy variables ................................................................................ 51
Table 4.2: Demeaned data ................................................................................... 61
Table 5.1: Data ...................................................................................................... 77
Table 5.2: transformed data: ................................................................................ 77
Table 6.1: Stacked data on bank size and loan ................................................. 86
Table 6.2: The Estimation results ....................................................................... 94
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LIST OF ACRONYMS ADF Augmented Dickey-Fuller
AIC Akaike Information Criterion
BIC Bayesian Information Criteria
BLC Bank Lending Channel
CBR Central Bank Rate
DPD Dynamic Panel Data
GDP Gross Domestic Product
GLS Generalised Least Squares
GMM Generalised Method of Moments
IBR Interbank Rate
LSDV Least Squares Dummy Variable
MAIC Minimising the modified AIC
MIC Modified information criteria
OLS Ordinary Least Squares
VAR Vector Autoregression
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PREFACE
The preparation of this User’s Guide followed a directive to COMESA Monetary
Institute (CMI) by the 22nd Meeting of the COMESA Committee of Governors of
Central Banks which was held in Bujumbura, Burundi in March 2017. Governors
noted that panel data analysis of monetary policy is an important prerequisite for
implementing a sound monetary policy, as it allows a judgement to be formed as to
the extent and the timing of monetary policy decisions which are appropriate in
order to maintain price stability.
The overall objective of this User’s Guide is to equip Users with skills to undertake
analysis of all aspects of panel data analysis. The User’s Guide demonstrates all
steps in panel data analysis from data organization to results interpretation,
applying bank level data using the EViews software.
Understanding panel data analysis is especially important in order to address
dynamics which cannot be addressed using purely cross-section or time series
analysis. In the central banking environment, the importance of panel data analysis
arises from the need to get answers to policy questions on a wide range of issues
on the banking sector such as the effectiveness of monetary policy and the
transmission mechanism using the bank lending channel (BLC); factors driving key
indicators for the banking sector such as interest rate spreads, profitability, non-
performing loans, governance etc. These issues require in-depth analysis of bank
level data. In addition, panel data analysis is useful in cross-country studies which
may provide an avenue to understand cross country differences which may inform
policy on matters related to regional economic integration.
It is hoped that the Guide will be a useful analytical tool on application of
advanced panel data analysis to transmission mechanism of monetary policy. It is
also hoped that the Guide will be used by COMESA member central banks as a
reference material to train their staff.
Ibrahim A. Zeidy Chief Executive Officer
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ACKNOWLEDGEMENTS
Although this User’s Guide is a sole work of the author, its present form is
a product of inputs from various training workshops organized by
COMESA Monetary Institute (CMI). The Author acknowledges all
participants of various CMI training workshops, who provided comments
that assisted in making the User’s Guide clearer and more User friendly.
The Author also thanks the Director, Mr. Ibrahim Abdullahi Zeidy and the
Senior Economist, Dr. Lucas Njoroge for providing technical and expert
assistance, and all the staff of the Institute for the facilitation and logistical
support towards the completion of the User’s Guide.
The Author especially acknowledges the rich comments from the
participants of the Validation Workshop held from 8th to 12th May, 2017 in
Nairobi, Kenya that provided the final inputs to the User’s Guide. The
workshop was attended by participants from the following COMESA
member countries’ Central Banks: Burundi, DR Congo, Ethiopia, Kenya,
Madagascar, Rwanda, Sudan, Swaziland, Zambia, and Zimbabwe.
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Chapter 1
Introduction to Panel Data Analysis
1.0 Introduction
Panel data, also known as longitudinal data or cross-sectional time series
data, in some special cases, refers to data containing time series
observations of a number of cross sections like individuals, households,
firms, or governments. This means that observations in panel data involve
at least two dimensions: a cross-sectional dimension, indicated by subscript
i, and a time series dimension, indicated by subscript t. In a more
complicated setup, panel data could have a more complicated clustering or
hierarchical structure. For example, variable y may be the measurement of
the share of government spending on budget item j (e.g. defense, education,
health etc.) in country i at time t.
There are two distinct sets of information that can be derived from cross-
sectional time series data. The cross-sectional component of the data set
reflects the differences observed between the individual subjects or entities
whereas the time series component which reflects the differences observed
for one subject over time. For instance, researchers could focus on the
differences in data between each person in a panel study and/or the
changes in observed phenomena for one person over the course of the
study (e.g., the changes in income over time of person 1 in Panel Data Set).
1.1 Types of Panel Data
Panel data may be characterized in a variety of ways. For purposes of
creating panel work files in EViews, there are several concepts that are of
particular interest.
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1.1.1 Dated vs. Undated Panels
A panel data set is said to be dated or undated depending on its cell ID.
When the observations of individual cross sections can be observed over
specific periods of time, we have a dated panel of the given frequency. If,
for example, our cell IDs are defined by a variable like QUARTER, we say
we have a quarterly frequency panel. Similarly, if the cell IDs are week or
year identifiers, we say we have a weekly or annual panel.
On the other hand, an undated panel uses group specific default integers as
cell IDs; by default, the cell IDs in each group are usually given by the
default integers (1, 2, ...N).
1.1.2 Regular vs. Irregular Dated Panels
Dated panels follow a regular or an irregular frequency. A panel is said to be
a regular frequency panel if the cell IDs for every group follow a regular
frequency. If one or more groups have cell ID values which do not follow a
regular frequency, the panel is said to be an irregular frequency panel.
However, it is possible to convert an irregular frequency panel into a regular
frequency panel by adding observations to remove gaps in the calendar for
all cross-sections.
1.1.3 Balanced vs. Unbalanced Panels
If every group in a panel has an identical set of cell ID values, we say that
the panel is fully balanced. All other panel datasets are said to be
unbalanced.
In the simplest form of balanced panel data, every cross-section follows the
same regular frequency, with the same start and end dates—for example,
data with 20 cross-sections, each with annual data from 1961 to 1970. In
this case, we say that the panel is balanced.
We may balance a panel by adding observations to the unbalanced data. The
procedure is quite simple—for each cross-section or group, we add
observations corresponding to cell IDs that are not in the current group,
but appear elsewhere in the data. By adding observations with these
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“missing” cell IDs, we ensure that all of the cross-sections have the same
set of cell IDs.
To complicate matters, we may partially balance a panel. There are three
possible methods—we may choose to balance between the starts and ends,
to balance the starts, or to balance the ends. In each of these methods, we
perform the procedure for balancing data described above, but with the set
of relevant cell IDs obtained from a subset of the data. Performing all three
forms of partial balancing is the same as fully balancing the panel.
Balancing data between the starts and ends involves adding observations
with cell IDs that are not in the given group, but are both observed
elsewhere in the data and lie between the start and end cell ID of the given
group. If, for example, the earliest cell ID for a given group is “2000” and
the latest ID is “2010”, the set of cell IDs to consider adding is taken from
the list of observed cell IDs that lie between these two dates. The effect of
balancing data between starts and ends is to create a panel that is internally
balanced, that is, balanced for observations with cell IDs ranging from the
latest start cell ID to the earliest end cell ID.
Assuming one is interested in analysing data for 5 banks over the period
2000 to 2016. A typical balanced panel dataset may appear as shown on
Table 1:
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Table 1.1: Panel data set: Normalised1 bank size for 5 banks
Bank1 Bank2 Bank3 Bank4 Bank5
2000 6.3 4.6 6.7 4.1 3.5
2001 5.8 5.1 6.7 2.9 3.2
2002 4.5 3.4 6.7 1.8 3.3
2003 2.1 2.2 9.3 -1.4 3.3
2004 2.0 2.0 9.8 -2.1 3.6
2005 1.9 1.7 9.8 -1.5 3.6
2006 2.0 1.5 9.8 -1.4 3.6
2007 1.5 -2.2 9.8 -2.4 3.6
2008 0.5 1.6 9.8 -2.2 3.6
2009 0.6 0.1 9.8 -1.4 1.1
2010 1.0 1.2 10.5 -1.3 0.8
2011 6.4 1.8 9.8 -1.8 0.8
2012 1.5 2.0 8.5 -1.1 2.8
2013 2.4 2.4 9.8 -0.7 2.8
2014 2.5 2.5 9.8 0.1 2.7
2015 3.7 1.5 9.8 0.5 2.7
2016 3.3 3.4 9.8 0.4 2.7
1.2 Advantages of Panel Data
Panel data, by blending the inter-individual differences and intra-individual
dynamics have several advantages over cross-sectional or time-series data:
More accurate inference of model parameters. Panel data usually contain
more degrees of freedom and more sample variability than cross-sectional
data which may be viewed as a panel with T = 1, or time series data which is
a panel with N = 1, hence improving the efficiency of econometric
estimates (e.g. Hsiao et al., 1995).
Greater capacity for capturing the complexity of human behaviour than a
single cross-section or time series data. These include:
1 Bank Size is measured by total assets. In order to control for the trend in size, total assets for
each bank is normalized by subtracting the log of total assets for each bank from the sample average. The result is a normalized bank size with banks whose size is larger than the sample average having a positive value and banks with a size smaller than the sample average having a negative value.
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Introduction to Panel Data Analysis
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i. Constructing and testing more complicated behavioural
hypotheses. For instance, consider the example of Ben-Porath
(1973) that a cross-sectional sample of married women was found to
have an average yearly labor-force participation rate of 50 percent.
These could be the outcome of random draws from a homogeneous
population or could be draws from heterogeneous populations in
which 50 percent were from the population who always work and 50
percent never work. If the sample was from the former, each woman
would be expected to spend half of her married life in the labor force
and half out of the labor force. The job turnover rate would be
expected to be frequent and the average job duration would be about
two years. If the sample was from the latter, there is no turnover. The
current information about a woman’s work status is a perfect
predictor of her future work status. A cross-sectional data is not able
to distinguish between these two possibilities, but panel data can
because the sequential observations for a number of women contain
information about their labor participation in different subintervals of
their life cycle.
Another example is the evaluation of the effectiveness of social
programs (e.g. Heckman et al., 1998; Hsiao et al., 2006; Rosenbaum
and Rubin, 1985). Evaluating the effectiveness of certain programs
using cross-sectional sample typically suffers from the fact that those
receiving treatment are different from those without. In other words,
one does not simultaneously observe what happens to an individual
when she receives the treatment or when she does not. An individual
is observed as either receiving treatment or not receiving treatment.
Using the difference between the treatment group and control group
could suffer from two sources of biases, selection bias due to
differences in observable factors between the treatment and control
groups and selection bias due to endogeneity of participation in
treatment. For instance, Northern Territory (NT) in Australia
decriminalized possession of small amount of marijuana in 1996.
Evaluating the effects of decriminalization on marijuana smoking
behavior by comparing the differences between NT and other states
that were still non-decriminalized could suffer from either or both
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sorts of bias. If panel data over this time period are available, it would
allow the possibility of observing the before- and effects on
individuals of decriminalization as well as providing the possibility of
isolating the effects of treatment from other factors affecting the
outcome.
ii. Controlling the impact of omitted variables. It is frequently
argued that the real reason one finds (or does not find) certain effects
is due to ignoring the effects of certain variables in one’s model
specification which are correlated with the included explanatory
variables. Panel data contain information on both the intertemporal
dynamics and the individuality of the entities may allow one to
control the effects of missing or unobserved variables. For instance,
MaCurdy’s (1981) life-cycle labor supply model under certainty
implies that because the logarithm of a worker’s hours worked is a
linear function of the logarithm of her wage rate and the logarithm of
worker’s marginal utility of initial wealth, leaving out the logarithm of
the worker’s marginal utility of initial wealth from the regression of
hours worked on wage rate because it is unobserved can lead to
seriously biased inference on the wage elasticity on hours worked
since initial wealth is likely to be correlated with wage rate. However,
since a worker’s marginal utility of initial wealth stays constant over
time, if time series observations of an individual are available, one can
take the difference of a worker’s labor supply equation over time to
eliminate the effect of marginal utility of initial wealth on hours
worked. The rate of change of an individual’s hours worked now
depends only on the rate of change of her wage rate. It no longer
depends on her marginal utility of initial wealth.
iii. Uncovering dynamic relationships. “Economic behavior is
inherently dynamic so that most econometrically interesting
relationship are explicitly or implicitly dynamic” (Nerlove, 2002).
However, the estimation of time adjustment pattern using time series
data often has to rely on arbitrary prior restrictions such as Koyck or
Almon distributed lag models because time series observations of
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Introduction to Panel Data Analysis
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current and lagged variables are likely to be highly collinear (e.g.
Griliches, 1967).
With panel data, we can rely on the inter-individual differences to
reduce the collinearity between current and lag variables to estimate
unrestricted time-adjustment patterns (e.g. Pakes and Griliches, 1984).
iv. Accurate predictions. Generating more accurate predictions for
individual outcomes by pooling the data rather than generating
predictions of individual outcomes using the data on the individual in
question. If individual behaviours are similar conditional on certain
variables, panel data provide the possibility of learning an individual’s
behaviour by observing the behaviour of others. Thus, it is possible to
obtain a more accurate description of an individual’s behaviour by
supplementing observations of the individual in question with data on
other individuals (e.g. Hsiao et al., 1993, 1989).
v. Providing micro foundations for aggregate data analysis.
Aggregate data analysis often invokes the “representative agent”
assumption. However, if micro units are heterogeneous, not only can
the time series properties of aggregate data be very different from
those of disaggregate data (e.g. Granger, 1990; Lewbel, 1994; Pesaran,
2003), but policy evaluation based on aggregate data may be grossly
misleading. Furthermore, the prediction of aggregate outcomes using
aggregate data can be less accurate than the prediction based on
micro-equations (e.g. Hsiao et al., 2005). Panel data containing time
series observations for a number of individuals is ideal for
investigating the “homogeneity” versus “heterogeneity” issue.
vi. Simplifying computation and statistical inference. Panel data
involve at least two dimensions, a cross-sectional dimension and a
time series dimension. Under normal circumstances one would expect
that the computation of panel data estimator or inference would be
more complicated than cross-sectional or time series data. However,
in certain cases, the availability of panel data actually simplifies
computation and inference. For instance:
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Analysis of nonstationary time series. When time series data are
not stationary, the large sample approximation of the distributions
of the least-squares or maximum likelihood estimators are no
longer normally distributed, (e.g. Anderson, 1959; Dickey and
Fuller, 1979, 1981; Phillips and Durlauf, 1986). But if panel data
are available, and observations among cross-sectional units are
independent, then one can invoke the central limit theorem across
cross-sectional units to show that the limiting distributions of
many estimators remain asymptotically normal (e.g. Binder et al.,
2005; Im et al., 2003; Levin et al., 2002; Phillips and Moon, 1999).
Measurement errors. Measurement errors can lead to under-
identification of an econometric model (e.g. Aigner et al., 1984).
The availability of multiple observations for a given individual or at
a given time may allow a researcher to make different
transformations to induce different and deducible changes in the
estimators, hence to identify an otherwise unidentified model (e.g.
Biørn, 1992; Griliches and Hausman, 1986; Wansbeek and
Koning, 1989).
Dynamic Tobit models. When a variable is truncated or
censored, the actual realized value is unobserved. If an outcome
variable depends on previous realized value and the previous
realized value are unobserved, one has to take integration over the
truncated range to obtain the likelihood of observables. In a
dynamic framework with multiple missing values, the multiple
integration is computationally unfeasible. With panel data, the
problem can be simplified by only focusing on the subsample in
which previous realized values are observed (e.g. Arellano et al.,
1999).
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Chapter 2
Getting Started in Eviews Software
2.0 Introduction
Data analysis within the context of panel may be conducted using a variety
of software currently available in the market. For the purpose of this User’s
Guide we demonstrate how to use EVIEWS to analyse panel data sets. In
addition, while acknowledging that we need to use bank data we, however,
use fictitious data to demonstrate how to get started in EVIEWS.
Therefore, in this chapter we will data generated purposely for
demonstration.
Panel data analysis is normally handled after learners have become
conversant with time series and cross section data analysis. Therefore, in
this User’s Guide we will largely abstract from detailed demonstration of
how to handle these two types of data sets. For purposes of this User’s
Guide we work with Eviews version 6. Most of the functionalities of the
different versions of Eviews have not changes over time. Therefore, any
version may be used for teaching purposes.
2.1 Getting Started in Eviews
The starting point towards understanding the
use of Eviews is to know how to access or
open Eviews software in a computer. In
most cases, if Eviews is installed on a
computer you will notice an icon on the
desktop which appears like the one here,
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depending on the version of the software. For you to open and operate
Eviews, take the cursor to this icon and double click the mouse.
Once you click on the
icon you will see the
window similar to the
one here below. Across
the top are Drop down
Menus that make
implementing EViews
procedures quite simple.
Below the menu items is
the Command window.
It can be used as an alternative to the menus, once you become familiar
with basic commands and syntax.
Across the bottom is the Current Path for reading data and saving files.
The EViews Help Menu is going to become a close friend. Use it when
you need guidance on how to navigate the software.
Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5
2000 6.3 4.6 6.7 4.1 3.5
2001 5.8 5.1 6.7 2.9 3.2
2002 4.5 3.4 6.7 1.8 3.3
2003 2.1 2.2 9.3 -1.4 3.3
2004 2.0 2.0 9.8 -2.1 3.6
2005 1.9 1.7 9.8 -1.5 3.6
2006 2.0 1.5 9.8 -1.4 3.6
2007 1.5 -2.2 9.8 -2.4 3.6
2008 0.5 1.6 9.8 -2.2 3.6
2009 0.6 0.1 9.8 -1.4 1.1
2010 1.0 1.2 10.5 -1.3 0.8
2011 6.4 1.8 9.8 -1.8 0.8
2012 1.5 2.0 8.5 -1.1 2.8
2013 2.4 2.4 9.8 -0.7 2.8
2014 2.5 2.5 9.8 0.1 2.7
2015 3.7 1.5 9.8 0.5 2.7
2016 3.3 3.4 9.8 0.4 2.7
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Getting Started in Eviews Software
~ 11 ~
2.2 Data preparation in Excel
Before we get data into Eviews for analysis there is data preparation which
needs to be done in excel. The first step in data preparation in excel is to get
data for all variables and prepare it using the following procedure. We
demonstrate data preparation using data using normalised Bank level data
on Bank size. After this has been demonstrated then any data set may be
prepared in the same version. The first step in data preparation in excel is to
get data for each individual cross sections, putting similar data together, that
is, if one is organising a range of data sets on banks, we require that, for
example, data on ‘Bank size’, be put together while noting the name of the
bank where the bank relates to. In our present case we have 5 cross sections
(five banks) as shown in the table. The second step is to provide cross
section identifiers. In the table you may notice that the variable name is
‘Size’. In order to identify the data with the bank we include an extension.
Here we add an underscore (_) followed by the unique name for each cross
section. In our present case the variable for the five cross sections are as
follows ‘Size_Bank1; Size_Bank2; Size_Bank3; Size_Bank4; Size_Bank5’. In
case one has more than one variable the same procedure is followed. We
will explain this further under the naming conventions in the pool object.
2.3 To Create an Eviews Workfile
Having known how to get started
in Eviews as shown in Section
2.1, we now proceed to explain
how to create a work file in
Eviews. To create a workfile in
Eviews, click File, New,
Workfile and you will see the
window similar to the one here.
In this window you need to
specify whether your data is dated or undated by selecting the appropriate
option under the workfile structure type. Our data is dated so we select Dated –
regular frequency. For now, let us leave out the Balanced panel frequency.
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Guidelines on Panel Data Analysis
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Additionally, we need to specify
the frequency using the drop
down menu under the Date
specification tab. In this case, our
data is annual so we select
accordingly. Under the same tab
we need to specify the start and
end date of our data. We can
provide a name to our workfile
say BANK_PANEL. You can
provide a page name of your choice, in our case we have named it SIZE.
Once you have populated the window as indicated above, click on ‘OK’ to
obtain the following screen. Now save your workfile in your preferred
location by clicking file, save.
2.3.1 Importing the data into Eviews
To import data, click Quick, Empty group (Edit series)
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Getting Started in Eviews Software
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Copy your data in excel excluding the year and paste as shown below;
Here we have imported data on Bank size as a group. For us to recognise
the group we give it a name. The name given is usually the variable name, in
our case ‘SIZE’.
Copy the series including
their names and paste here
from the series names.
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Guidelines on Panel Data Analysis
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Click ok and close the group. Your workfile now looks as follows;
2.3.2 Setting up a pool in a workfile
We shall be working with pooled data; therefore, the first thing we have to do
in order to work with pooled data is to create a Pool workfile. This is nothing
more than the Pool object in EViews found in Object, New Object, Pool. Note
that the Pool object operates within the EViews workfile, where all your data
must be stored; that is, the Pool object does not, in itself hold any of the
data. Note that the data range/sample is determined by the workfile, not the
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Getting Started in Eviews Software
~ 15 ~
Pool object. When working with pooled data, note that the series that are
being pooled need not be of the same dimension, so for example we can
have time series for various variables comprising different samples. The
data in our workfiles are balanced, that is, they have a common sample
period.
The Pool object serves two roles in EViews:
i. First, it allows you to perform certain aspects of data management;
that is, we can transform variables (e.g., take first differences) or even
create variables (e.g., define inflation from the price level, or create
dummy variables). In some cases, this is very useful, as it can save you
a lot of time when you need to create the same transformation for a
number of variables. Note, however, that the data transformations are
rather limited, for instance, you cannot apply the HP-filter or seasonal
adjustment to series.
ii. The second role of the Pool object is to provide procedures for the
estimation of econometric models (these will be discussed below).
To create a pool workfile we carry out the following simple steps;
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Guidelines on Panel Data Analysis
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Step 1: Click object, new object, and the following window emerges;
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Getting Started in Eviews Software
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Step 2: Select pool and give it a name as shown below;
Type the name of your pool object
here e.g. Pool1
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Guidelines on Panel Data Analysis
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Step 3: Click ok and the window below asking you to supply cross-sectional
identifiers emerges;
Step 4: Naming conventions
In a Pool object, we can have two types of definitions: cross-section identifiers
and definitions of groups (the latter is optional). In the workfile for, we
have defined our variable size_xx, where xx are the cross-section identifiers.
In this case, they are the different banks’ names. Bank1; Bank2; Bank3;
Bank1; and Bank5 as shown below.
Type cross section identifiers here
starting with underscore e.g. _Bank1
then enter to type the next identifier
e.g. _Bank2 and so on as shown
below in section 2.3.3
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Getting Started in Eviews Software
~ 19 ~
2.3.3 Data transformations
The Pool object provides a fast, efficient and useful way to manipulate and
manage data. Within the Pool object window, we have a tab PoolGenr which
allows us to transform the data within the Pool object. Our data is
normalized bank size. For example, we could compute the growth rates of a
variable of interest as follows;
Click PoolGenr, and a new window opens as shown below;
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Guidelines on Panel Data Analysis
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We would then proceed by typing the relevant equation to compute new
series (in this case, growth rate) as follows;
Click on the PoolGenr for
options on data transformation
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Getting Started in Eviews Software
~ 21 ~
Note the use of the ‘?’ character. The ? tells EViews to apply the
transformation to the cross-sectional series in the Pool. The lags of the
series (-1) must be placed after the ?. One can also define and/or adjust the
sample size under the sample window.
Note that this is just for demonstration on how to conduct data transformations. So we
are not going to perform this procedure. There are many other transformations which can
be done within the pool object, this is just one of them.
2.4 Viewing Data
At this stage, we can manipulate data as we would normally do. We can
even conduct unit root tests on the series and the cross-section without
having to consider the Pool object in EViews. The latter is EViews’ main
object for managing time-series/cross-section data. We shall do that first
and compare results with the Pool object later.
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Guidelines on Panel Data Analysis
~ 22 ~
In terms of viewing the data, we can either plot the series individually or
open them as a Group (note that a group is not the same as a Pool object
for EViews. A Group object is mainly used for working with collections of
series.) If you select all (or some of the) series and right click, you can open
them as a Group. Non-continuous time series are chosen by pressing the
Ctrl key and keeping it pressed while selecting individual time series.
In our case we have already created a group, SIZE. To open this group
double click on it. You will see the window below;
2.5 Basic Plots
Once that data has been successful imported into Eviews, the next step is to
know how to conduct basic analysis. Plot the series by selecting view,
graph. Select the Multiple graphs option in the Multiple series window
and click ok.
PANEL A PANEL B
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Getting Started in Eviews Software
~ 23 ~
Copy the figure by right clicking on it and selecting copy to clipboard.
The series are displayed in the figure below.
Whenever we begin working with a new data set, it is always a good idea to
take some time to simply examine the data. This will help ensure that there
were no mistakes in the data itself or in the process of reading in the data. It
also provides us with a chance to observe the general (time-series)
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Guidelines on Panel Data Analysis
~ 24 ~
behaviour of the series we will be working with. Points to look out for
include the possible existence of time trends or structural breaks in the
underlying data. The first thing one should always do is to plot the data to
make sure that it looks fine.
2.6 Descriptive Statistics
Once data has been entered into Eviews as indicated above and basic
graphical representations have been done. The next step is to conduct
descriptive statistics. In this case there are two avenues available: (i)
computing descriptive statistics for the group (ii) conducting descriptive
statistics for all the groups in the panel at one.
1. Descriptive statistics for the group
Step 1: Selecting the group: In our case, as shown in Panel A, we are
interested in the descriptive statistics for Bank Size. If you double click
on the group named ‘Size’ you will obtain the sheet shown on Panel B.
This sheet contains observations for the individual cross-sections for
Size for the period 2000-2016.
Step 2: Obtaining the descriptive statistics: Once the data has been
presented on the screen as shown on panel B, you then click ‘view’ on
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Getting Started in Eviews Software
~ 25 ~
the tool bar that contains the series. Then you will get a drop down
window which contains a number of options. In our case choose
‘Descriptive stat’. Once this is highlighted you will need to choose
whether you need statistics for individual series in the group or
common statistics. If you click on ‘individual series, you will obtain the
following:
2. Descriptive statistics within a panel environment: In case you are
interested in the descriptive statistics for all cross sections in the panel.
You may follow the following steps:
Step 1: create a pool object: Steps on creating a pool object are
explained in section 2.3.2. Follow these steps to create the pool object.
Once a pool object has been created, click View, Descriptive statistics…
A blank screen shown below pops-up. The next step is to list all the
variables of interest in the space provided. Remember to include ‘?’ after
listing the variable as shown below.
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Guidelines on Panel Data Analysis
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To obtain ‘descriptive statistics’ click on ‘OK’ to obtain the output shown
in below.
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Getting Started in Eviews Software
~ 27 ~
The descriptive statistics provided relate to the totality of the cross-sections
for each variable. For example, you may notice that for Variable X, the
Jarque-Bera test (p-value<0.05, therefore we reject the null hypothesis that
residuals are normal) shows that the variable is not normally distributed.
This finding contrasts with the one obtained for the individual cross
sections… but we are interested in panel data behaviour and not the
individual series!
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Chapter 3
Pooled Regression Analysis
3.0 Introduction
There are a number of methods of analysis of panel data. However, the
pooled regression analysis is the most basic. In this chapter we present the
theoretical workings of the pooled regression analysis, the data presentation
in the pooled regression framework and the estimation.
3.1 The pooled regression model
A pooled regression involves obtaining the data for all the cross sections of
interest over time and stacking them and run a simple ordinary least squares
(OLS) to obtain the estimates which are BEST. In this case we visualise the
pooled regression model as follows:
.
.....
.....
2222
111
ititiit
ttt
titt
exy
exy
exy
tititi XY ,,, 1
Where is Y, the dependent variable, is observed for all cross sections (i= 1,
2…. N), over time t, (t=1, 2 …T). X is the independent variable while it is
the error term. For a better representation of Equation 1, each of the
variables shown may be presented as for each cross section as follows:
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Guidelines on Panel Data Analysis
~ 30 ~
ik
i
kk
iTiTiT
k
iii
k
iii
iT
i
i
i
xxx
xxx
xxx
y
y
y
y
.
.
.
.
.
.
...
.
.
.
...
...
x
.
.
.
2
i1
i
2
1
21
2
2
2
1
2
1
2
1
1
1
i
2
1
where ity is the value of the dependent variable for cross-section unit i at
time t (i = 1, … , n; t = 1, … , T), it refers to the disturbance term for the
i-th unit at time t and j
itx is the value of the j-th explanatory variable for
cross-section unit i at time t. There are k explanatory variables indexed by j
= 1, …, k. Equation 1 is a giant model for all cross sections over time
which may then be estimated using OLS.
3.1.1 Limitations of Pooled regression
In the pooled regression analysis, the cross sections are assumed to be
homogenous. For that reason, it is assumed that the estimated coefficients
(intercept and slope) are common since there is no heterogeneity. However,
in the real life heterogeneity exists, meaning that if we assume a pooled
regression then we may have a bias, usually referred to as heterogeneous
bias. The heterogeneous bias is presented in the figure below. In this case
the pooled regression coefficients are B0 and B1. However, it is noted that
each individual cross-sections has its own and probably unique coefficients.
In our example, these individual and unique coefficients reflect the
heterogeneous (unique) nature of every individual bank.
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Pooled Regression Analysis
~ 31 ~
3.2 Estimation of the Pooled Regression Model
3.2.1 Illustration of pooled regression using general data
This User’s Guide seeks to demonstrate how to estimate a model in a panel
context based on the transmission of monetary policy transmission. Prior to
this, we realise that it is important to first demonstrate how the data is
organised and estimated using fictitious example. Once this is appreciated
then we can proceed to implement the example based on bank level data to
demonstrate the effectiveness of monetary policy transmission. In our case
we will seek to demonstrate whether the bank lending channel works in
Kenya.
In addition, the pooled model being the most basic of the known methods
of panel data analysis, we will devote time to explain how this approach
works. After that is done then it will be very clear on how data is organised
and model estimated in any panel specification. For convenience we seek to
illustrate the panel data estimation using the model shown in Equation 1,
reproduced here as:
tititi XY ,,,
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To estimate this model, we require data on Y (growth rate of loan) and X
(bank size) for all the cross sections. For illustration purposes we assume
that we have 5 cross sections (banks) namely Bank1-Bank5. For each cross
section we assume we are observing data for the period 2000- 2016.
3.2.2 Organising data in Excel
To estimate this model, we follow the following steps:
Step 1: Organising data in Excel: Consider a banking system consisting
of five (5) banks. Table 1 below shows two variables namely Bank Size
(measured by the normalized size of each banks’ assets) and Loan by bank.
The dataset therefore consists of two variables with three 5 cross-sections
observed over the period 2000-2016. In its primitive form, the data for
these two variables may be presented as shown in the table below:
Table 3.1: Raw data on bank size and loan
As shown in Table 1, we observe that data for bank size and loan are
observed for each cross section for the period 2000-2016. For example, in
the case of Bank1, the observed size and loan are 4.4 and 6.3, respectively in
2000. To estimate a panel model using this data we stack this data as shown
in Table 2. Stacking involves getting the data for size and loan for each
cross section and arranging them with size and its corresponding loan
arranged as follows:
Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5 Loan_Bank1 Loan_Bank2 Loan_Bank3 Loan_Bank4 Loan_Bank5
2000 6.3 4.6 6.7 4.1 3.5 4.4 5.7 5.3 15.9 4.6
2001 5.8 5.1 6.7 2.9 3.2 2.8 4.6 5.2 4.8 4.0
2002 4.5 3.4 6.7 1.8 3.3 12.9 6.1 6.6 5.3 6.2
2003 2.1 2.2 9.3 -1.4 3.3 9.2 6.9 1.3 3.5 6.9
2004 2.0 2.0 9.8 -2.1 3.6 3.5 4.4 6.1 4.9 8.3
2005 1.9 1.7 9.8 -1.5 3.6 3.4 8.0 7.5 1.6 5.5
2006 2.0 1.5 9.8 -1.4 3.6 2.4 7.1 17.1 3.0 5.5
2007 1.5 -2.2 9.8 -2.4 3.6 1.3 4.3 13.6 7.7 5.4
2008 0.5 1.6 9.8 -2.2 3.6 1.2 4.5 6.0 5.5 4.3
2009 0.6 0.1 9.8 -1.4 1.1 10.3 6.0 1.5 4.4 4.9
2010 1.0 1.2 10.5 -1.3 0.8 4.2 5.3 1.7 15.8 7.3
2011 6.4 1.8 9.8 -1.8 0.8 11.9 6.1 8.1 8.7 4.8
2012 1.5 2.0 8.5 -1.1 2.8 14.5 6.4 1.6 3.8 4.8
2013 2.4 2.4 9.8 -0.7 2.8 8.5 8.8 4.0 4.8 7.3
2014 2.5 2.5 9.8 0.1 2.7 7.8 5.2 5.0 1.6 7.7
2015 3.7 1.5 9.8 0.5 2.7 0.9 4.5 5.7 3.8 5.1
2016 3.3 3.4 9.8 0.4 2.7 1.0 6.1 3.8 4.9 7.5
LOAN BY BANKBANK SIZE
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Pooled Regression Analysis
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Table 3.2: Stacked data on bank size and loan
Loan Size
1 6.3 4.4
2 5.8 2.8
3 4.5 12.9
4 2.1 9.2
5 2.0 3.5
6 1.9 3.4
7 2.0 2.4
8 1.5 1.3
9 0.5 1.2
10 0.6 10.3
11 1.0 4.2
12 6.4 11.9
13 1.5 14.5
14 2.4 8.5
15 2.5 7.8
16 3.7 0.9
17 3.3 1.0
18 4.6 5.7
19 5.1 4.6
20 3.4 6.1
21 2.2 6.9
22 2.0 4.4
23 1.7 8.0
24 1.5 7.1
25 -2.2 4.3
26 1.6 4.5
27 0.1 6.0
28 1.2 5.3
29 1.8 6.1
30 2.0 6.4
31 2.4 8.8
32 2.5 5.2
33 1.5 4.5
34 3.4 6.1
35 6.7 5.3
36 6.7 5.2
37 6.7 6.6
38 9.3 1.3
39 9.8 6.1
40 9.8 7.5
41 9.8 17.1
42 9.8 13.6
43 9.8 6.0
44 9.8 1.5
45 10.5 1.7
46 9.8 8.1
47 8.5 1.6
48 9.8 4.0
49 9.8 5.0
50 9.8 5.7
51 9.8 3.8
52 4.1 15.9
53 2.9 4.8
54 1.8 5.3
55 -1.4 3.5
56 -2.1 4.9
57 -1.5 1.6
58 -1.4 3.0
59 -2.4 7.7
60 -2.2 5.5
61 -1.4 4.4
62 -1.3 15.8
63 -1.8 8.7
64 -1.1 3.8
65 -0.7 4.8
66 0.1 1.6
67 0.5 3.8
68 0.4 4.9
69 3.5 4.6
70 3.2 4.0
71 3.3 6.2
72 3.3 6.9
73 3.6 8.3
74 3.6 5.5
75 3.6 5.5
76 3.6 5.4
77 3.6 4.3
78 1.1 4.9
79 0.8 7.3
80 0.8 4.8
81 2.8 4.8
82 2.8 7.3
83 2.7 7.7
84 2.7 5.1
85 2.7 7.5
Bank1
Bank2
Bank3
Bank4
Bank5
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It is important to note that it does not matter which cross section is
arranged first. As shown in Table 2, we simply started with Bank1, but we
could have as well started with Bank2. You may now notice that in stacking
the data the time dimension is lost meaning that the data is now undated
with 85 observations (17x5). From Table 2, it is clear that we have two
variables: loan, the dependent variable and size, the independent variable.
This data is consistent with the model set up shown in Equation 1.
3.2.3 Loading the data into Eviews
Step 2: Getting started in Eviews: Considering that the data shown in
step 1 does not show any panel data features we will get it into Eviews
using the following procedure. Once Eviews work space is opened as
discussed in Chapter 1, we will follow the following steps.
File--New-- Workfile, to obtain Panel A, in Figure 1.
Figure 1: Creating a work file
Panel A Panel B
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Pooled Regression Analysis
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You may notice that in Panel A, a dialog box will emerge requiring you to
create workfile. If you click on the ‘Workfile Structure Type’ you will
obtain 3 options (Dated-regular frequency, Unstructured/Undated,
Balanced panel). However, as noted earlier, this dataset is undated,
therefore you need to choose ‘Unstructured/Undated’ in the drop down
menu named ‘Dated-regular frequency’. In addition, you are required to
choose the ‘Data Range’. In our case we have 85 observations. If you click
on ‘OK’ then you will obtain Panel B in Figure 2.
Step 3: Getting the Data into Eviews: Panel B in Figure 1 has been
configured to accept data with a range of 1-85… 85 obs for each bank).
The data we are interested in getting into Eviews as shown in Table 2 is
in Excel, therefore it needs to be copied from Excel and pasted into
Eviews as follows: In the Eviews workfile, on the main tool bar, click on
‘Quick’. Here you will find several options, but choose ‘empty Group’.
In the empty group, paste the data to obtain the following
Figure 2: Getting the data into Eviews
Variables Size and
loan appear here
Observations
for loan
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Guidelines on Panel Data Analysis
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You will notice that the workfile has 2 variables size and loan. This shows
that the data has been loaded into Eviews successfully and is ready for
further analysis.
3.2.4 Pooled regression in Eviews
Step 4: Estimation: You may recall in our model set up such that loan is
the dependent variable while size is the independent variable. To
estimate this model, you need to proceed to the main tool bar and click
on ‘Object’, followed by … New Object’ to obtain the output on Panel
A. You may notice that the New Object option gives you a range of
options to pick from. In our case, we are interested in an ‘Equation
Object’. Once you highlight the Equation Object and click ‘OK’ button
you will obtain the Box shown in Panel B of Figure 3. This provides you
with instructions on how to estimate the Equation. You will then
populate the blank space with the variable of interest, starting with the
dependent variable loan, followed by the rest including the constant, C as
shown in Panel B:
Figure 3: Estimation in a pool object
Panel A Panel B
You will notice that the estimation method is required. At the bottom of the
Box you will see a provision for ‘Estimation Setting’ – Method. The Default
method is the LS- Least Squares (NLS and ARMA). In the pooled regression
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Pooled Regression Analysis
~ 37 ~
approach, the estimation method is the LS, therefore if you click on ‘OK’,
you will obtain the following output:
Figure 4: Estimation result
3.2.5 Pooled regressions in Eviews Environment
Though informative, the step by step estimation of a pooled regression, may
be time consuming as it requires one to stack the data and depending on the
number of cross-sections and time dimension, errors may emerge. For
example, we had to limit our cross- sections to 5 and the number of
observations per cross section to 17 to be able to illustrate how the pooled
regression is done is Eviews.
In view of this, Eviews is configured to estimate a model within the panel
framework by following a certain procedure. In this part we discuss and
illustrate the procedure used in estimating a pooled regression in Eviews
based on the following steps:
Step 1: Data Preparation in Excel: The first step in the preparation of
data shown in Table 1 above, is to introduce cross-section identifiers.
Steps on how to introduce cross section identifiers in Eviews were
demonstrated in section 2.3.2. Cross-section identifiers are extensions
added to the variable names in order for Eviews to recognise in the stack
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Guidelines on Panel Data Analysis
~ 38 ~
procedure that data for a particular cross section started at a particular
point and ends at another point. In our case our variables of interest are
bank size and loan. We therefore add identifiers as explained in Chapter
1, in which case, the five cross sections: Bank1-Bank5 will be recorded as
follows:
Table 3.3: Data on size and growth rate of loan with cross-section identifiers
Step 2: Getting data into Eviews: As shown in Chapter 1, we need to
create a panel file structure with five cross sections for the period 2000 -
2016 as follows:
Loan_Bank1 Loan_Bank2 Loan_Bank3 Loan_Bank4 Loan_Bank5 Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5
2000 4.4 5.7 5.3 15.9 4.6 6.3 4.6 6.7 4.1 3.5
2001 2.8 4.6 5.2 4.8 4.0 5.8 5.1 6.7 2.9 3.2
2002 12.9 6.1 6.6 5.3 6.2 4.5 3.4 6.7 1.8 3.3
2003 9.2 6.9 1.3 3.5 6.9 2.1 2.2 9.3 -1.4 3.3
2004 3.5 4.4 6.1 4.9 8.3 2.0 2.0 9.8 -2.1 3.6
2005 3.4 8.0 7.5 1.6 5.5 1.9 1.7 9.8 -1.5 3.6
2006 2.4 7.1 17.1 3.0 5.5 2.0 1.5 9.8 -1.4 3.6
2007 1.3 4.3 13.6 7.7 5.4 1.5 -2.2 9.8 -2.4 3.6
2008 1.2 4.5 6.0 5.5 4.3 0.5 1.6 9.8 -2.2 3.6
2009 10.3 6.0 1.5 4.4 4.9 0.6 0.1 9.8 -1.4 1.1
2010 4.2 5.3 1.7 15.8 7.3 1.0 1.2 10.5 -1.3 0.8
2011 11.9 6.1 8.1 8.7 4.8 6.4 1.8 9.8 -1.8 0.8
2012 14.5 6.4 1.6 3.8 4.8 1.5 2.0 8.5 -1.1 2.8
2013 8.5 8.8 4.0 4.8 7.3 2.4 2.4 9.8 -0.7 2.8
2014 7.8 5.2 5.0 1.6 7.7 2.5 2.5 9.8 0.1 2.7
2015 0.9 4.5 5.7 3.8 5.1 3.7 1.5 9.8 0.5 2.7
2016 1.0 6.1 3.8 4.9 7.5 3.3 3.4 9.8 0.4 2.7
BANK SIZELOAN BY BANK
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Pooled Regression Analysis
~ 39 ~
Recall the steps in creating a pool workfile and cross section identifiers
from section 2.3.2
Step 3: Estimate model: You should use the Method dropdown menu to
choose between LS - Least Squares (LS and AR), TSLS - Two-Stage Least
Squares (TSLS and AR), and GMM / DPD – Generalized Method of
Moments / Dynamic Panel Data (DPD) techniques. In this case we are
interested in the LS - Least Squares (LS and AR). Click on ‘OK’ to obtain
the following:
Panel A Panel B
3.3 Application of Pooled Regression Approach to
Monetary Policy Transmission in Kenya
So far we have used variables bank size and growth rate of loans by bank to
illustrate how one navigates the Eviews software to generate output.
However, for illustration based on ‘monetary transmission mechanism’ it is
not possible to parade bank specific data. To meet this objective, however,
we present and interpret the results based on a study on Kenya:
3.3.1 Case Study: Monetary Policy Transmission in Kenya: Evidence
from bank level data
In study we investigate the existence, if any, and strength of the Bank
Lending Channel of monetary policy transmission in Kenya. We use micro-
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Guidelines on Panel Data Analysis
~ 40 ~
bank level data on 39 commercial banks using monthly data for 2001-2015.
To accomplish this task, we adopt a framework similar to that of Kashyap
and Stein (2000) and Walker (2013) which exploits the heterogeneous
nature of commercial banks to establish whether or not the BLC exists in
Kenya.
3.3.2 The Model setup
In this study, we estimate the following basic model:
tiiitttiti
ti
n
n
nttiti
vDXKAPLiq
SizeIRLL
,76,5,4
,3
0
21,1,
)log()ln()ln(
1
Where; )ln( ,tiL is the change in total lending by bank i at time t; IR is the
monetary policy variable, usually interest rate at t; )log( ,tiSize is a measure
of size of bank i at time t; tiLiq , is a measure of liquidity of bank i at time t;
tiKAP , is the total liquid assets to total assets of bank i at time t; tX is a
vector of macroeconomic variables which may affect the operating
environments for banks; tiD , is a various qualitative characteristics of
commercial banks such as private or public; domestic or foreign; iv is the
time invariant error component; ti , is the error term with the usual
properties.
Following the Kashyap and Stein (2000), tradition, the testable hypothesis
for the existence and strength of the BLC is stated as follows:
0/2 titit mBL where Lit is a measure of lending by bank i at time t, Bit is
a measure of strength of balance sheet of Bank i at time t while mt is a
measure of the monetary policy stance at time t. The implication of this
hypothesis is as follows: firstly, that the degree to which lending is liquidity-
constrained intensifies when monetary policy is tighter; secondly, that the sensitivity of
lending to monetary policy is greater for banks with weaker balance sheets. This
therefore suggest that it is important to understand the balance sheet items
which may impact on banks’ ability to lend and therefore impacting on the
BLC.
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Pooled Regression Analysis
~ 41 ~
The validity of the bank lending channels requires that commercial banks
which experience a change in their deposits or reserves on account of
monetary policy action should adjust their lending. Suggesting that a
negative relationship is expected between a monetary policy indicator and
commercial banks’ lending. However, as shown in the literature the choice
of a monetary policy variable is controversial. As shown by Kashyap and
Stein (2000), there is no general agreement on the appropriate choice of an
indicator of monetary policy. In the literature a set of possible indicators
have been suggested: change in short term interest rate under the control of
the central bank, the residuals from a vector autoregression (VAR)
representing the reaction function of the central bank (Bernanke and
Mihov, 1998), the narrative approach (Boschen and Mills, 1995). Etc. In
this study we proxy monetary policy by the Central Bank Rate (CBR)
and/or the interbank rate.
In the BLC literature the bank size is identified as a critical determinant of
the transmission of monetary policy signals to the real economy. As shown
in the literature, different bank sizes face varying degrees of access to
uninsured sources of finance. The role of size has been emphasized, for
example, in Kashyap and Stein (1995): small banks are assumed to suffer
from informational asymmetry problems more than large banks do, and
find it therefore more difficult to raise uninsured funds in times of
monetary tightening. Again, this should force them to reduce their bank
lending relatively more when compared to large banks. The sensitivity of
lending volume to monetary policy for a particular bank is greater for banks
with weaker balance sheets. Small banks tend to experience more friction
to raise uninsured finance. However, large banks have an easier time raising
uninsured finance, which would make their lending less dependent on
monetary policy shocks, irrespective of their internal liquidity positions. In
this study bank size (S) is defined as the natural logarithm of the total asset.
In order to control for the trend in size, total assets for each bank is
normalized by subtracting the log of total assets for each bank from the
sample average as:
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Guidelines on Panel Data Analysis
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t
N
i
it
itN
S
SS
1
log
log
;
Where
S the adjusted bank size and N is the number of banks in the
sample.
Following Kashyap and Stein (2000), it is shown that given the same
characteristics of banks, except the level of liquidity, the banks will react
differently to a monetary policy shock. That is assuming two banks which
both face difficulties in raising external finance, and are alike in all respects
except that one has a more liquid balance sheet (as measured by the ratio of
securities to assets) than the other. In the event of a monetary shock, it is
easier for the more liquid bank to protect its loan portfolio, as it can draw
down on its buffer stock of securities. In contrast, the less liquid bank will
have to cut its new loans to a greater extent to prevent its securities holdings
from falling too low. Whereas relatively liquid banks can draw down their
liquid assets to shield their loan portfolio, this is not feasible for less liquid
banks. This therefore suggests that more liquid banks tend to be less
sensitive to monetary policy shock compared with those with low liquidity.
Therefore, maintaining high liquidity levels is not conducive for monetary
policy transmission. How then do we measure liquidity? There are various
ways, in this study, however, we measure as a ratio of liquid assets to total
assets.
t
N
i
it
itN
L
LL
1
log
log
As shown in the literature (see Peek and Rosengren, 1995) poorly
capitalized banks have a more limited access to non-deposit financing and
as such should be forced to reduce their loan supply by more than well
capitalized banks do. Capitalization is defined as the ratio of equity to total
assets.
t
N
i it
it N
A
E
A
EK
1
log
log
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Pooled Regression Analysis
~ 43 ~
Where
K the adjusted capitalization of commercial banks, E is the total
equity and A is the total assets.
The distributional effects of monetary policy on banks are captured by the
interaction between the monetary policy indicators (interest rate and money
supply) and the individual bank characteristics. We now proceed to explain
our a priori expectations with respect to the signs of the interaction terms.
We expect the interaction between the size of the bank and the interest
rate/money supply to be positive because lending by large banks are less
sensitive to a change in monetary policy relative to small banks. Secondly,
we expect the interaction between monetary policy indicators and liquidity
to be positive because more liquid banks are less sensitive to changes in the
interest rate/money supply relative to small banks. This is because more
liquid banks are able to provide more lending by drawing down on their
stock of liquid assets. Finally, we also expect the interaction between bank
capitalization and the interest rates/money supply to be positive because
more capitalized banks are less sensitive to changes in monetary policy.
Ownership: The role of governments in the banking markets similarly
reduces the risk of depositors: An active role of the state in the banking
sector is obviously able to reduce the amount of informational asymmetries
significantly. Publicly owned or guaranteed banks are therefore unlikely to
suffer a disproportionate drain of funds after a monetary tightening, and
distributional effects in their loan reactions are hence unlikely to occur. On
the other hand, ownership on the basis of whether a bank is locally or
foreign versus local: The network arrangement between banks can also have
important consequences for the reaction of bank loan supply to monetary
policy. In networks with strong links between the head institutions and the
lower tier, the large banks in the upper tier can serve as liquidity providers
in times of a monetary tightening, such that the system would experience a
net flow of funds from the head institutions to the small member banks.
Ehrmann and Worms (2001) show that in Germany, indeed, small banks
receive a net inflow of funds from their head institutions following a
monetary contraction. This indicates that the size of a bank need not be a
good proxy to assess distributional effects of monetary policy across banks.
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Guidelines on Panel Data Analysis
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Figure 5: BLC based on pooled regressions analysis
As indicated earlier monetary policy is proxied by the interbank rate (IBR).
As shown in the basic model on panel A, the estimated coefficient of IBR is
found to be negative. A look at the standard error and the t-statistic reveals
that this coefficient is statistically significant at 1 percent level. This,
therefore suggests that there is evidence of the monetary policy in Kenya
impacting on the amounts that banks lend to the private sector. Including
other variables that is, Liquidity (LIQ); Inflation (CPI), and Capital (KAP),
in a manner similar to the existing studies, we obtain the results indicated in
panel B. It is also found that the estimated coefficient of the IBR is negative
as expected and significant at 1 percent level as indicated by the standard
error, t-statistic and p-value associated with IBR.
Panel A: Simple BLC Panel B: BLC based on Pooled regressions with control variables
IBR is negative and highly
significant
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Pooled Regression Analysis
~ 45 ~
References
Ashcraft, Adam B., 2006. New evidence on the lending channel. Journal of Money,
Credit and Banking, 38, 751-775.
Altunbas, Y., Fazylov, O., and Molyneux, P., (2002). Evidence on the Bank
Lending Channel in Europe. Journal of Banking and Finance. 26:11. 2093-
2110.
Bernanke, B.S. and Gertler, M., (1995). Inside the black box: The credit channel of
monetary policy. Journal of Economic Perspectives. 9:4. 27-48.
De Bondt, Gabe, J., 1999. Credit channels in Europe: Cross-country investigation.
Research Memorandum WO&E no. 569. De Nederlandsche Bank,
February.
Ehrmann, M., Gambacorta, L., Martinez-Pages, J., Sevestre, P., and Worms, A.,
(2001). Financial systems and the role of banks in monetary policy
transmission in the euro area. European Central Bank Working Paper No.
105.
Favero, Carlo A., Giavazzi, Francesco, Flabbi, Luca, 1999. The Transmission
mechanism of monetary policy in Europe: Evidence form banks’ balance
sheets. National Bureau of Economic Research, Working Paper no. 7231.
Gambacorta, Leonardo, 2005. Inside the bank lending channel. European
Economic Review, 49, 1737-1759.
Kashyap, A.K., and Stein, J.C, (2000). What Do a Million Observations on Banks
Say about the Transmission of Monetary Policy? American Economic
Review. 90:3. 407-428.
Kashyap, Anil K., Stein, Jeremy C., 1995. The impact of monetary policy on bank
balance sheets. Carnegie-Rochester Conference Series on Public Policy 42,
151-195.
Kashyap, Anil K., Stein, Jeremy C., 1997. The role of banks in monetary policy: A
survey with implications for the European Monetary Union. Economic
Perspectives, Federal Reserve Bank of Chicago 21, pp. 2–19.
Kishan, Ruby P., Opiela, Timothy P., 2000. Bank size, bank capital, and the bank
lending channel. Journal of Money, Credit and Banking, 32, 121-141.
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Guidelines on Panel Data Analysis
~ 46 ~
Sichei, M. (2005). Bank Lending Channel in South Africa: Bank-Level Dynamic
Panel Data Analysis. Working Paper: 2005-2010, Department of
Economics, University of Pretoria.
Sichei, M.M., and Njenga, G., (2012), Does Bank-Lending Channel Exist in
Kenya? Bank-Level Panel Data. AERC Research Paper No. 249.
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Chapter 4
Error Component Model Analysis: One Way Error Components Model
4.0 Introduction
In chapter 3, we demonstrated how the pooled regression is estimated. In
addition, we discussed the example based on the banking lending channel of
monetary policy transmission. Under the pooled regression approach we
estimated the regression model which takes the following form:
ititit uxy 10 1
The specification allows for estimation of common coefficients- the
intercept and the slope ( 10 , ). As pointed out this is very restrictive and is
susceptible to biased predictors. The bias is avoided by allowing for multiple
coefficients by appearing to the error components model.
4.1 The Error Components Model Specification
The error component model allows estimation of multiple coefficients for
each cross-section by exploiting the information content of the error term,
itu in Equation 1, which is expected to be well behaved. The error
components approach allows for decomposition of the error term, itu into
three distinct parts or components as follows:
ittiit vu 2
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Guidelines on Panel Data Analysis
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In Equation 2, iv , is the part or component of the error term that varies
across cross-sections but does not vary over time, which may be taken to
represent those unique characteristics of individual units which cannot be
found in the rest of the cross sections. On the other hand, t , is the error
component which varies over time but remains unchanged across the
various units, these may represent unique events/circumstances which may
have taken place in respective time periods which have no resemblance to
other events which took place in other periods under investigation.
For analysis, Equation 2 can be analysed as a two-way-error component or a
one-way-error components model. In each case the estimation is done using
the fixed effects or the random effects model. In order to understand how
the error components models are estimated using the fixed- and random
effects approaches we discuss in details how the two approaches are
implemented and how the output is interpreted.
4.1.1 One-Way Error Component Model
The one-way-error components model framework allows one to analyse the
error term, itu by abstracting one channel. For example, Equation 2, can be
converted to a one way error component by either assuming 0t , in
which case Equation 2 collapses to:
itiit vu 3a
In this formulation we allow for only cross section differences to be
investigated while assuming away the time variations. On the other hand, if
we assume 0iv , the Equation 2 becomes:
ittitu 3b
In this formulation we analyse the characteristics of the time periods while
abstracting from the cross section differences. Including these elements in
Equation 1 yields the following:
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Error Component Model Analysis
~ 49 ~
ittitit xy 10 4a
Or
itiitit vxy 10 4b
Equations 4a and 4b are expressed as one-way-error components models.
In order to analyses the time specific coefficients ( t ) and the cross-sections
specific coefficients ( iv ) we use either the fixed- or the random- effects
models.
Fixed effects assume that individual group/time have different intercept in
the regression equation, while random effects hypothesize individual
group/time have different disturbance. When the type of effects (group
versus time) and property of effects (fixed versus random) combined, there
are several specific models: fixed group effect model (one-way), fixed time
effect model (one-way), fixed group and time effect model (two-way),
random group effect model (one-way), random time effect (one-way), and
random group and time effect model (two-way).
4.1.1.1 Fixed Effects Model
The fixed effects model assumes that ( iv ) and ( t ) are separate parameters.
For illustration purposes we use the case where we estimate the ( iv ). In
estimating the separate parameters ( iv ) use the following two equivalent
methods: the Least Squares Dummy Variable (LSDV) method and the
Within-Q- Estimation method.
4.1.2 The least squares dummy variable estimation method
The least squares dummy variable estimation method calls for estimation of
the following model:
iiTii vXy 1
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Guidelines on Panel Data Analysis
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In this case the parameters for X are estimated. In addition, dummies for
each of the cross sections are estimated. In its non-compact form, it is
represented as follows:
inT
T
ni v
v
X
X
y
y
.
.
.
.
1000
00
00
0..1
.
.
.
.
1111
DvXvIXy Tn 1
This model is appealing but the number of parameters to be estimated is
large2. In the next section show a step by step estimation of this equation.
To estimate a model using this method the following steps are followed:
Step 1: Organise the data for the key variables size and growth of loan
as shown below:
2 The procedure is implemented using the Frisch-Waugh-Lovell (FWL) theorem on partitioned
regressions. For details see Davidson, R. and J.G. MacKinnon, 1993, Estimation and Inference in Econometrics (Oxford University Press, New York).
Loan_Bank1 Loan_Bank2 Loan_Bank3 Loan_Bank4 Loan_Bank5 Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5
2000 4.4 5.7 5.3 15.9 4.6 6.3 4.6 6.7 4.1 3.5
2001 2.8 4.6 5.2 4.8 4.0 5.8 5.1 6.7 2.9 3.2
2002 12.9 6.1 6.6 5.3 6.2 4.5 3.4 6.7 1.8 3.3
2003 9.2 6.9 1.3 3.5 6.9 2.1 2.2 9.3 -1.4 3.3
2004 3.5 4.4 6.1 4.9 8.3 2.0 2.0 9.8 -2.1 3.6
2005 3.4 8.0 7.5 1.6 5.5 1.9 1.7 9.8 -1.5 3.6
2006 2.4 7.1 17.1 3.0 5.5 2.0 1.5 9.8 -1.4 3.6
2007 1.3 4.3 13.6 7.7 5.4 1.5 -2.2 9.8 -2.4 3.6
2008 1.2 4.5 6.0 5.5 4.3 0.5 1.6 9.8 -2.2 3.6
2009 10.3 6.0 1.5 4.4 4.9 0.6 0.1 9.8 -1.4 1.1
2010 4.2 5.3 1.7 15.8 7.3 1.0 1.2 10.5 -1.3 0.8
2011 11.9 6.1 8.1 8.7 4.8 6.4 1.8 9.8 -1.8 0.8
2012 14.5 6.4 1.6 3.8 4.8 1.5 2.0 8.5 -1.1 2.8
2013 8.5 8.8 4.0 4.8 7.3 2.4 2.4 9.8 -0.7 2.8
2014 7.8 5.2 5.0 1.6 7.7 2.5 2.5 9.8 0.1 2.7
2015 0.9 4.5 5.7 3.8 5.1 3.7 1.5 9.8 0.5 2.7
2016 1.0 6.1 3.8 4.9 7.5 3.3 3.4 9.8 0.4 2.7
BANK SIZELOAN BY BANK
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Error Component Model Analysis
~ 51 ~
Step 2: Create cross section dummies. Here the dummies for each cross
section as if they are variables. In this case we have 5 cross-section,
therefore we need 5 dummies as follows:
Table 4.1: Dummy variables
As shown above we create a dummy for each cross section. For example, in
the case for Bank1, we create a dummy with 1 and zeroes elsewhere, for the
period 2000 to 20016.
Step 3: Getting data into Eviews: As shown in Chapter 1, we need to
create a panel file structure with five cross sections for the period 2000-
20016 as follows:
D1_Bank1 D1_Bank2 D1_Bank3 D1_Bank4 D1_Bank5 D2_Bank1 D2_Bank2 D2_Bank3 D2_Bank4 D2_Bank5 D3_Bank1 D3_Bank2 D3_Bank3 D3_Bank4 D3_Bank5
2000 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2001 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2002 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2003 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2004 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2005 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2006 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2007 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2008 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2009 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2010 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2011 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2012 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2013 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2014 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2015 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2016 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0
D4_Bank1 D4_Bank2 D4_Bank3 D4_Bank4 D4_Bank5 D5_Bank1 D5_Bank2 D5_Bank3 D5_Bank4 D5_Bank5
2000 0 0 0 1 0 0 0 0 0 1
2001 0 0 0 1 0 0 0 0 0 1
2002 0 0 0 1 0 0 0 0 0 1
2003 0 0 0 1 0 0 0 0 0 1
2004 0 0 0 1 0 0 0 0 0 1
2005 0 0 0 1 0 0 0 0 0 1
2006 0 0 0 1 0 0 0 0 0 1
2007 0 0 0 1 0 0 0 0 0 1
2008 0 0 0 1 0 0 0 0 0 1
2009 0 0 0 1 0 0 0 0 0 1
2010 0 0 0 1 0 0 0 0 0 1
2011 0 0 0 1 0 0 0 0 0 1
2012 0 0 0 1 0 0 0 0 0 1
2013 0 0 0 1 0 0 0 0 0 1
2014 0 0 0 1 0 0 0 0 0 1
2015 0 0 0 1 0 0 0 0 0 1
2016 0 0 0 1 0 0 0 0 0 1
Dummy for Bank1 Dummy for Bank2 Dummy for Bank3
Dummy for Bank4 Dummy for Bank5
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Guidelines on Panel Data Analysis
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Step 4: Getting data into Eviews: To get data into Eviews, click on the
‘Quick button’ followed by ‘Empty Group’. Then the following empty
box will appear:
This is the box where data for each individual variable will be entered. In
our case we have 2 variables (loan and bank size) and 5 dummy variables.
Therefore, in total we have seven variables to enter separately. For example,
we may start with bank size, in which case we cut the data on variable bank
size from Excel and paste it in this blank box to give:
Cross-section
identifiers are listed Data range is stated
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Error Component Model Analysis
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The same procedure is followed for the rest of the variables i.e. DLOAN,
D1, D2, D3, D4 and D5. Once all the variables have been pasted in Eviews,
Step 5: Estimation of the model: To estimate the model, you click on
‘Estimate’ button as shown above. This will result in the following box.
The 7 variables
are entered and
each is identified
as a group
To estimate this model, click on ‘estimate’
Give variable
name here
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Guidelines on Panel Data Analysis
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However, to avoid the Dummy variable trap, we exclude one cross section
dummy from the regression. In this particular regression you may notice we
have excluded D5. There is no rule regarding the dummy variable to
exclude from the regression. The parameter for excluded dummy variable
will be accounted for once the estimation procedure is completed. Once all
the variables have been entered as shown click on the ‘OK’ button and the
following result will show.
Enter Dependent variable here followed by ? Enter independent
variables here each followed by ?
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Error Component Model Analysis
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As you may notice, this is a long procedure for implementing the DVE
approach. However, Eviews has a shortcut which delivers on the same
results. In this case, when entering data for the independent variables do
not enter dummy variables in the space provided. Instead enter the constant
‘C’ in the space as shown below:
Entering ‘C’ in the space for ‘Cross-section specific coefficients’ allows
Eviews to recognise that DVE methods is applicable. Once this has been
done click on ‘OK’ button and you will see the following output:
Enter ‘C’ here
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Guidelines on Panel Data Analysis
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You may wish to compare the result from the long- and short- procedure
for implementing the DVEM as shown below. For instance, panels A and B
show that results for bank size (SIZE?) are exactly the same whether we use
dummy variable estimation or the short cut via cross-section identifiers.
Panel A Panel B
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Error Component Model Analysis
~ 57 ~
4.2 Case Study: Monetary Policy Transmission in Kenya:
Evidence from bank level data
As indicated in Chapter 3, where we demonstrated how the pooled
regression model is estimated and applied to the monetary policy
transmission, in this chapter we demonstrate using the same bank level data
to show how to estimate a one-way error components model. As before the
model set up is stated as:
tiiittti
titi
n
n
nttiti
vDXKAP
LiqSizeIRLL
,76,5
,4,3
0
21,1,
)log()ln()ln(
1
Where; )ln( ,tiL is the change in total lending by bank i at time t; IR is the
monetary policy variable, usually interest rate at t; )log( ,tiSize is a measure
of size of bank i at time t; tiLiq , is a measure of liquidity of bank i at time t;
tiKAP , is the total liquid assets to total assets of bank i at time t; tX is a
vector of macroeconomic variables which may affect the operating
environments for banks; tiD , is a various qualitative characteristics of
commercial banks such as private or public; domestic or foreign; iv is the
time invariant error component; ti , is the error term with the usual
properties. The discussion of the expected results is avoided in order to stay
clear of repetitions.
In this illustration we
abstract from the basic steps
in the data preparations and
creating an enabling
environment in Eviews for
panel data analysis.
Therefore, for us to show
how the Least Squares
Dummy Variable (LSDV)
estimation method is executed we follow the following steps:
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Guidelines on Panel Data Analysis
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Step 1: Setting up the LSDV. In the LSDV model set up, the important
aspect is the estimation of the individual specific coefficients. To
implement this, we perform only one modification to the estimation
procedure in the pooled regression approach. The dependent variable as
before is “tcad?”. To allow for cross section specific coefficients you
enter a ‘C’ in the space provided for Cross-section specific coefficients.
Step 2: Estimation of the LSDV: After entering a ‘C’ as indicated above
and ensuring that the estimation method is set as ‘LS-Least Squares (and
AR), you click on ‘OK’ to obtain the output shown in here. In this
particular example the following are observed:
The estimated coefficient of the monetary policy variable (IBR) is
negative and significant at 1 percent level of testing. The estimated
coefficient is 0.15, implying that a 1 percent change in monetary
policy stance will result in a 0.15 percent change in the total credit to
the private sector, in the opposite direction. The fact that the
estimated coefficient is negative and significant suggests that
monetary policy is effective in Kenya.
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Error Component Model Analysis
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The estimated coefficient of bank size is found to be positive and
significant at 1 percent as well, suggesting that larger banks lend to
change lending to the private sector more than the small banks.
The other coefficients, mainly those with an extension of ‘_C’ are the
cross section specific coefficients relate to whether the estimated
intercept for each individual bank is significant or not.
4.2.1 Within-Q-estimation method
In light of the limitations of the LSDV, regarding the number of parameters
to be estimated, the within estimation method overcomes this challenge by
computing the individual effects. Recall the fixed effects is applicable in the
case where there is potential endogeneity between the fixed effects ( iv ) and
Xit as stated here:
0
0
itit
iit
itiitit
XE
vXE
vXy
5
In this case the problem of endogeneity arises because of the correlation
between Xit and vi. To overcome this problem, we appeal to the Annihilator
matrix transformations. The transformation procedure involves eliminating
the Vi from Equation 5 in order to obtain reliable estimates of the slope
coefficient3.Once the estimates are obtained then the fixed effects are
computed. In terms of implementation of the transformations on the data,
we follow the following steps:
Step 1: Computation of the mean: Compute the mean of each variable
for all cross-sections as follows:
T
t
i
T
t
it
T
t
it
iiii
vT
vXT
XyT
y
vXy
111
1;
1;
1
3 The procedure involves transformations based on the Annihilator matrix transformations.
For detailed discussion see Liebler’s Basic Matrix Algebra with Algorithms and Applications
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Guidelines on Panel Data Analysis
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Step 2: Demeaning the data: For each variable subtract the mean
obtained from step 1 to obtain the following:
iitiiiitiit vvXXyy
In its compact form it may be presented as:
itititXy ~~~
Then stack by observation as follows:
nnn X
X
y
y
~.
.
~
~.
.
~
~.
.
~111
~~
~ Xy
The within-group fixed-effects estimator is pooled OLS on the transformed
regression that has been stacked by observations:
n
i
ii
n
i
iiFE yXXXyXXX1
1
1
1 ~~~
~~ ~~
~
This procedure may be implemented in Excel and Eviews by making the
following steps:
Step 1: Data preparation: Organise the data for the variables loan, and
bank size and also compute the mean value for each of the cross-
sections.
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Error Component Model Analysis
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Step 2: Demeaning the data: This transformation requires that you
subtract the mean for each cross-section from each observation to yield
the following:
Table 4.2: Demeaned data
Step 3: copy the transformed data and paste it in Eviews. But first
open a new file with the same dimensions as before. While following the
steps for creating a panel object, we estimate the equation with
transformed data (SizeT and DloanT) as shown below:
Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5 Loan_Bank1 Loan_Bank2 Loan_Bank3 Loan_Bank4 Loan_Bank5
2000 6.3 4.6 6.7 4.1 3.5 4.4 5.7 5.3 15.9 4.6
2001 5.8 5.1 6.7 2.9 3.2 2.8 4.6 5.2 4.8 4.0
2002 4.5 3.4 6.7 1.8 3.3 12.9 6.1 6.6 5.3 6.2
2003 2.1 2.2 9.3 -1.4 3.3 9.2 6.9 1.3 3.5 6.9
2004 2.0 2.0 9.8 -2.1 3.6 3.5 4.4 6.1 4.9 8.3
2005 1.9 1.7 9.8 -1.5 3.6 3.4 8.0 7.5 1.6 5.5
2006 2.0 1.5 9.8 -1.4 3.6 2.4 7.1 17.1 3.0 5.5
2007 1.5 -2.2 9.8 -2.4 3.6 1.3 4.3 13.6 7.7 5.4
2008 0.5 1.6 9.8 -2.2 3.6 1.2 4.5 6.0 5.5 4.3
2009 0.6 0.1 9.8 -1.4 1.1 10.3 6.0 1.5 4.4 4.9
2010 1.0 1.2 10.5 -1.3 0.8 4.2 5.3 1.7 15.8 7.3
2011 6.4 1.8 9.8 -1.8 0.8 11.9 6.1 8.1 8.7 4.8
2012 1.5 2.0 8.5 -1.1 2.8 14.5 6.4 1.6 3.8 4.8
2013 2.4 2.4 9.8 -0.7 2.8 8.5 8.8 4.0 4.8 7.3
2014 2.5 2.5 9.8 0.1 2.7 7.8 5.2 5.0 1.6 7.7
2015 3.7 1.5 9.8 0.5 2.7 0.9 4.5 5.7 3.8 5.1
2016 3.3 3.4 9.8 0.4 2.7 1.0 6.1 3.8 4.9 7.5
Average 2.8 2.1 9.1 -0.4 2.8 5.9 5.9 5.9 5.9 5.9
BANK SIZEINTEREST RATE Loan BY BANK
SizeT_Bank1 SizeT_Bank2 SizeT_Bank3 SizeT_Bank4 SizeT_Bank5 LoanT_Bank1 LoanT_Bank2 LoanT_Bank3 LoanT_Bank4 LoanT_Bank5
2000 3.4 2.5 -2.5 4.6 0.7 -1.5 -0.1 -0.6 10.1 -1.3
2001 3.0 3.1 -2.5 3.3 0.3 -3.1 -1.2 -0.7 -1.1 -1.9
2002 1.7 1.4 -2.5 2.3 0.5 7.0 0.3 0.7 -0.6 0.3
2003 -0.7 0.2 0.1 -1.0 0.5 3.3 1.0 -4.5 -2.3 1.0
2004 -0.8 0.0 0.6 -1.6 0.8 -2.4 -1.5 0.2 -0.9 2.4
2005 -0.9 -0.4 0.6 -1.1 0.8 -2.5 2.1 1.6 -4.2 -0.4
2006 -0.8 -0.5 0.6 -0.9 0.8 -3.5 1.2 11.2 -2.9 -0.4
2007 -1.3 -4.3 0.6 -1.9 0.8 -4.5 -1.6 7.7 1.8 -0.5
2008 -2.3 -0.5 0.6 -1.7 0.8 -4.7 -1.3 0.1 -0.4 -1.6
2009 -2.2 -2.0 0.6 -0.9 -1.7 4.4 0.1 -4.4 -1.5 -1.0
2010 -1.8 -0.8 1.3 -0.9 -2.0 -1.6 -0.6 -4.2 9.9 1.4
2011 3.6 -0.3 0.6 -1.4 -2.0 6.0 0.2 2.2 2.8 -1.0
2012 -1.3 0.0 -0.7 -0.6 0.0 8.6 0.5 -4.2 -2.1 -1.1
2013 -0.4 0.3 0.6 -0.3 0.0 2.6 2.9 -1.9 -1.0 1.4
2014 -0.3 0.5 0.6 0.5 -0.1 1.9 -0.7 -0.9 -4.3 1.8
2015 0.9 -0.6 0.6 0.9 -0.1 -5.0 -1.4 -0.2 -2.1 -0.8
2016 0.5 1.4 0.6 0.9 -0.1 -4.9 0.2 -2.0 -1.0 1.6
LOAN BY BANK BANK SIZE
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Guidelines on Panel Data Analysis
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Step 4: Estimation: Then click on the OK button to obtain the following
result.
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Error Component Model Analysis
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LSDV method, this is a long method, but it is useful in terms of
appreciating the inner workings of the method. Eviews has a shortcut to
this procedure in which you adjust the panel estimation screen to the
following:
Step 5: choice of estimation method: Next, click on the Panel Options
tab to specify additional panel specific estimation settings. First, you should
account for individual and period effects using the Effects specification
dropdown menus. By default, Eviews assumes that there are no effects so
that both dropdown menus are set to None. You may change the default
settings to allow for either Fixed or Random effects in either the cross-
section or period dimension, or both.
Since we are estimating a fixed effect within the context of cross-sections,
you click on the drop down arrow and select ‘Fixed’ while the regressors are
Size? You should be aware that when you select a fixed or random effects
specification, Eviews will automatically add a constant to the common
coefficients portion of the specification if necessary, to ensure that the
effects sum to zero.and C. Choosing ‘Fixed’ here tells Eviews that you are
estimating the model using the Within Q estimation method. If you click
“OK’ you will obtain the following result:
Click on drop
down and select
‘Fixed’
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Guidelines on Panel Data Analysis
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The LSDV and within-q- methods are equivalent: you may now see that
the LSDV and the Within-q- method are equivalent as shown in panels A
and B where the results for bank size (SIZE?) are exactly the same.
The fixed effects have no std. error etc. because they are computed.
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Error Component Model Analysis
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Panel A Panel B
4.3 Pooled Estimation Method Versus the Fixed Effect
Method
As indicated above the pooled regression allows for estimation of common
coefficients while the fixed effects model allows estimation individual
intercepts. It is therefore not possible to make a good guess as to which
model is appropriate. In this case we conduct the F-test to establish which
model is appropriate. To illustrate this, recall the following:
itiitit vxy 10
The test being implemented here calls seeks to establish whether ( iv ) exists
or not by testing the following hypothesis:
0...................: 1210 NvvvH
We test the null hypothesis of no individual effects within applied Chow or
F-test, combining the residual sum of squares for the regression both with
constraints (under the null) and without (under alternative). The F-statistics
is stated as:
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Guidelines on Panel Data Analysis
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KNNTNF
KNNTURSS
NURSSRSSF
1
/
1/
To implement the F-test we follow the following steps:
Step 1: Estimate the fixed effects model: In our example above we obtained
the following result based on cross-section effects:
Step 2: Once the result above is obtained, go to the tools bar and click on
‘view’ then choose ‘Fixed/Random Effects testing’ followed by
‘Redundant Fixed Effects—likelihood ratio’ and obtain the following:
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Error Component Model Analysis
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Step 3: The Decision rule: the part of the result which is critical to our
decision is indicated here below. The decision rule is as follows: if the P-
value < 0.05 we reject the null hypothesis, implying that the fixed effects are
not redundant. However, if P-value > 0.05, we fail to reject the null
hypothesis, implying that the fixed effects are redundant and therefore
pooled estimation is valid.
Redundant Fixed Effects Tests
Pool: POOL01
Test cross-section fixed effects Effects Test Statistic d.f. Prob. Cross-section F 88.223735 (4,79) 0.0000
Cross-section Chi-square 144.392433 4 0.0000
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Guidelines on Panel Data Analysis
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In this case it is observed that the Cross-Section F statistics is 88.2 with (4,
79) degrees of freedom whose associated p-value is 0.000, which is less than
0.05, therefore we reject the null hypothesis. In the present case fixed
effects are critical and need to be considered.
4.4 Case Study: Monetary Policy Transmission in Kenya:
Evidence from bank level data
As indicated in Chapter 2, where we demonstrated how the pooled
regression model is estimated and applied to the monetary policy
transmission, in this chapter we demonstrate using the same bank level data
to show how to estimate a one-way error components model. As before the
model set up is stated as:
tiiitttiti
ti
n
n
nttiti
vDXKAPLiq
SizeIRLL
,76,5,4
,3
0
21,1,
)log()ln()ln(
1
Where; )ln( ,tiL is the change in total lending by bank i at time t; IR is the
monetary policy variable, usually interest rate at t; )log( ,tiSize is a measure
of size of bank i at time t; tiLiq , is a measure of liquidity of bank i at time t;
tiKAP , is the total liquid assets to total assets of bank i at time t; tX is a
vector of macroeconomic variables which may affect the operating
environments for banks; tiD , is a various qualitative characteristics of
commercial banks such as private or public; domestic or foreign; iv is the
time invariant error component; ti , is the error term with the usual
properties. The discussion of the expected results are avoided in order to
stay clear of repetitions.
In this illustration we abstract from the basic steps in the data preparations
and creating an enabling environment in Eviews for panel data analysis.
Therefore, for us to show how the Least Squares Dummy Variable (LSDV)
estimation method is executed we follow the following steps:
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Error Component Model Analysis
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Step 1: Setting up- the Within Estimation. In the within model set up,
the important aspect is the computation of the individual specific
coefficients. Eviews is configured to implement this approach. To
implement the fixed effects, you check the Estimation Method - the Fixed
and Random effects are automated. The default shows cross-section:
‘None” and Period: ‘None’. First, you should account for individual and
period effects using the Effects specification dropdown menus. By
default, Eviews assumes that there are no effects so that both dropdown
menus are set to None. You may change the default settings to allow for
either Fixed or Random
effects in either the cross-
section or period dimension,
or both. The dependent
variable as before is “tcad?”.
To allow for fixed effects,
you click on Cross-section
and choose ‘Fixed’.
Step 2: Estimation: After choosing the estimation method as ‘Fixed’ and
ensuring that the estimation method is set as ‘LS-Least Squares (and
AR), you click on ‘OK’ to obtain the output shown in here. In this
particular example the following are observed:
The estimated
coefficient of the
monetary policy variable
(IBR) is negative and
significant at 1 percent
level of testing. The
estimated coefficient is
0.15, implying that a 1
percent change in
monetary policy stance
will result in a 0.15
percent change in the
total credit to the
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Guidelines on Panel Data Analysis
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private sector, in the opposite direction. The fact that the estimated
coefficient is negative and significant suggests that monetary policy is
effective in Kenya.
The estimated coefficient of bank size is found to be positive and
significant at 1 percent as well, suggesting that larger banks lend to
change lending to the private sector more than the small banks.
The other coefficients, mainly those with an extension of ‘_C’ are the
fixed effects. You may notice the fixed effects do not have –statistics
nor standard errors, meaning they are not estimated but computed.
Step 3: Testing the validity of the fixed effects: As indicated earlier we
run an F-test to obtain the result shown. The result of the test shows that
the estimated F-statistic is 3.56, with the p- value of 0.000. Based on the p-
value, we reject the null hypothesis, suggesting that the fixed effects are not
redundant. The implication of this test is that the model shown in Chapter
2, is invalid and therefore it cannot be used to make inferences regarding
the effectiveness of the bank lending channel in Kenya. With the F-test
allowing us to estimate the
fixed effects model, it
therefore means that the
estimated model in Step 2
above is valid and can be
used to make inferences
about the existence the
bank lending channel in
Kenya.
4.5 Random Effects Model
Recall the model in Equation 4a, stated as itiitit vxy 10
, in
the random effects approach the iv are said exist but are randomly
distributed and are not correlated with other regressors. In this case, the iv
are not a set of fixed parameters to be estimated but random variables,
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To estimate the random effects model we follow the same procedure like
the one for the fixed effects model. In this case we follow the following
steps:
4.5.1 Testing the validity of the random effects: Hausman test
Testing the validity of the Random effects uses the Hausman test. The test
tests whether the random effects are correlated with the other regressors.
Select random
effects option from
the drop-down menu
here
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Step 1: Estimate the random effects model:
Step 2: The Hausman test:
The Decision rule is as shown in the table.
Random Effects Fixed Effects
Hypothesis
0]/[ ii XuE 0]/[ ii XuE
Basis of test REFE
Decision If p-value > 0.05, fail to reject the null that the model is correctly specified as a RE
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References
Ashcraft, Adam B., 2006. New evidence on the lending channel. Journal of Money,
Credit and Banking, 38, 751-775.
Altunbas, Y., Fazylov, O., and Molyneux, P., (2002). Evidence on the Bank
Lending Channel in Europe. Journal of Banking and Finance. 26:11. 2093-
2110.
Bernanke, B.S. and Gertler, M., (1995). Inside the black box: The credit channel of
monetary policy. Journal of Economic Perspectives. 9:4. 27-48.
De Bondt, Gabe, J., 1999. Credit channels in Europe: Cross-country investigation.
Research Memorandum WO&E no. 569. De Nederlandsche Bank,
February.
Ehrmann, M., Gambacorta, L., Martinez-Pages, J., Sevestre, P., and Worms, A.,
(2001). Financial systems and the role of banks in monetary policy
transmission in the euro area. European Central Bank Working Paper No.
105.
Favero, Carlo A., Giavazzi, Francesco, Flabbi, Luca, 1999. The Transmission
mechanism of monetary policy in Europe: Evidence form banks’ balance
sheets. National Bureau of Economic Research, Working Paper no. 7231.
Gambacorta, Leonardo, 2005. Inside the bank lending channel. European
Economic Review, 49, 1737-1759.
Kashyap, A.K., and Stein, J.C, (2000). What Do a Million Observations on Banks
Say about the Transmission of Monetary Policy? American Economic
Review. 90:3. 407-428.
Kashyap, Anil K., Stein, Jeremy C., 1995. The impact of monetary policy on bank
balance sheets. Carnegie-Rochester Conference Series on Public Policy 42,
151-195.
Kashyap, Anil K., Stein, Jeremy C., 1997. The role of banks in monetary policy: A
survey with implications for the European Monetary Union. Economic
Perspectives, Federal Reserve Bank of Chicago 21, pp. 2–19.
Kishan, Ruby P., Opiela, Timothy P., 2000. Bank size, bank capital, and the bank
lending channel. Journal of Money, Credit and Banking, 32, 121-141.
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Guidelines on Panel Data Analysis
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Sichei, M. (2005). Bank Lending Channel in South Africa: Bank-Level Dynamic
Panel Data Analysis. Working Paper: 2005-2010, Department of
Economics, University of Pretoria.
Sichei, M.M., and Njenga, G., (2012), Does Bank-Lending Channel Exist in
Kenya? Bank-Level Panel Data. AERC Research Paper No. 249.
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Chapter 5
Error Component Model Analysis: Two Way Error Components Model
5.0 Introduction
In Chapter 4 we demonstrated how to estimate the one-way-error
components model using both the long- and short- cut methods
implemented in Eviews. In this part we now turn to the estimation of the
two-way-error components model. Recall the general panel model
specification
uXy 1
Where the error term u is represented as follows:
ittiit vu 2
Where: v… the cross –section effect (time invariant), t, time effect (cross-
section invariant) and e the error term with the usual properties (details to
be provided). In the case where both vi and ti are non-zero, i.e.:
ittiit vu 3c
This is referred to as a 2-way-error components model.
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Guidelines on Panel Data Analysis
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5.1 Estimation of the Error Components Model
Estimation of the two-way-error components model follows the same
approach as the one-way error components model. However, the mechanics
are more involving as we now demonstrate in this section. We now
demonstrate the fixed effect and random effect estimation methods in the
context of 2-way error components model.
5.1.1 Fixed effects model
The fixed effects model assumes that vi are separate parameters. To estimate
these separate parameters we use one of the following two equivalent
methods: the least squares dummy variable method and the within-q-
estimation method.
5.1.1.1 Two –way – error components model: The least squares dummy
variable estimation method
To estimate the two way-error components model we estimate the
following transformed model:
vvvv
xxxxyyyy
tiit
tiittiit
Is this complete???
The specific steps involved in estimating this equation are as follows:
Step 1: preparation of data: We present the data as shown in Table 5.1 and
also compute time- and cross-section means as shown in the green
columns for each variables Size and Loan. In addition, we compute the
mean of means shown on the year cell in the table.
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Error Component Model Analysis
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Table 5.1: Data
Step 2: data transformation: In this case the new data (transformed data) is
obtained by subtracting the mean of cross-sections, mean of time
periods and adding back the mean of means to obtain the following data:
Table 5.2: transformed data:
BANK SIZE
Size_Bank1 Size_Bank2 Size_Bank3 Size_Bank4 Size_Bank5 Spread_Bank1 Spread_Bank2 Spread_Bank3 Spread_Bank4 Spread_Bank5
2000 6.3 4.6 6.7 4.1 3.5 5.0 4.4 5.7 5.3 15.9 4.6 7.2
2001 5.8 5.1 6.7 2.9 3.2 4.7 2.8 4.6 5.2 4.8 4.0 4.3
2002 4.5 3.4 6.7 1.8 3.3 4.0 12.9 6.1 6.6 5.3 6.2 7.4
2003 2.1 2.2 9.3 -1.4 3.3 3.1 9.2 6.9 1.3 3.5 6.9 5.6
2004 2.0 2.0 9.8 -2.1 3.6 3.1 3.5 4.4 6.1 4.9 8.3 5.4
2005 1.9 1.7 9.8 -1.5 3.6 3.1 3.4 8.0 7.5 1.6 5.5 5.2
2006 2.0 1.5 9.8 -1.4 3.6 3.1 2.4 7.1 17.1 3.0 5.5 7.0
2007 1.5 -2.2 9.8 -2.4 3.6 2.1 1.3 4.3 13.6 7.7 5.4 6.5
2008 0.5 1.6 9.8 -2.2 3.6 2.7 1.2 4.5 6.0 5.5 4.3 4.3
2009 0.6 0.1 9.8 -1.4 1.1 2.0 10.3 6.0 1.5 4.4 4.9 5.4
2010 1.0 1.2 10.5 -1.3 0.8 2.4 4.2 5.3 1.7 15.8 7.3 6.9
2011 6.4 1.8 9.8 -1.8 0.8 3.4 11.9 6.1 8.1 8.7 4.8 7.9
2012 1.5 2.0 8.5 -1.1 2.8 2.7 14.5 6.4 1.6 3.8 4.8 6.2
2013 2.4 2.4 9.8 -0.7 2.8 3.3 8.5 8.8 4.0 4.8 7.3 6.7
2014 2.5 2.5 9.8 0.1 2.7 3.5 7.8 5.2 5.0 1.6 7.7 5.5
2015 3.7 1.5 9.8 0.5 2.7 3.6 0.9 4.5 5.7 3.8 5.1 4.0
2016 3.3 3.4 9.8 0.4 2.7 3.9 1.0 6.1 3.8 4.9 7.5 4.7
Average 2.8 2.1 9.1 -0.4 2.8 3.3 5.9 5.9 5.9 5.9 5.9 5.9
Average
INTEREST RATE SPREAD BY BANK
Average
SizeT2_Bank1 SizeT2_Bank2 SizeT2_Bank3 SizeT2_Bank4 SizeT2_Bank5 SpreadT2_Bank1 SpreadT2_Bank2 SpreadT2_Bank3 SpreadT2_Bank4 SpreadT2_Bank5
2000 1.7 0.8 -4.2 2.8 -1.0 -2.8 -1.4 -1.9 8.8 -2.6
2001 1.5 1.6 -3.9 1.9 -1.1 -1.5 0.3 0.9 0.5 -0.3
2002 1.0 0.7 -3.2 1.6 -0.2 5.5 -1.3 -0.8 -2.1 -1.3
2003 -0.6 0.4 0.3 -0.8 0.7 3.6 1.3 -4.2 -2.0 1.3
2004 -0.6 0.2 0.8 -1.4 1.0 -2.0 -1.1 0.6 -0.5 2.9
2005 -0.7 -0.2 0.8 -0.9 1.0 -1.8 2.8 2.3 -3.6 0.3
2006 -0.7 -0.3 0.8 -0.7 1.0 -4.7 0.1 10.0 -4.0 -1.5
2007 -0.1 -3.0 1.8 -0.7 2.0 -5.1 -2.1 7.1 1.2 -1.0
2008 -1.7 0.2 1.2 -1.1 1.4 -3.1 0.2 1.7 1.2 0.0
2009 -1.0 -0.7 1.9 0.3 -0.5 4.9 0.6 -3.9 -1.0 -0.5
2010 -1.0 0.0 2.2 -0.1 -1.2 -2.6 -1.6 -5.2 8.9 0.4
2011 3.5 -0.4 0.5 -1.5 -2.1 4.0 -1.9 0.2 0.8 -3.1
2012 -0.8 0.5 -0.1 -0.1 0.5 8.2 0.2 -4.6 -2.4 -1.4
2013 -0.5 0.3 0.6 -0.3 -0.1 1.8 2.1 -2.7 -1.8 0.6
2014 -0.5 0.2 0.4 0.3 -0.3 2.4 -0.3 -0.4 -3.9 2.3
2015 0.5 -0.9 0.3 0.5 -0.4 -3.1 0.5 1.7 -0.2 1.1
2016 -0.2 0.7 0.0 0.2 -0.7 -3.7 1.4 -0.8 0.2 2.8
INTEREST RATE SPREAD BY BANK BANK SIZE
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Guidelines on Panel Data Analysis
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Step 3: Copy and paste the data presented on Table 5.2 and paste it in
Eviews in a manner similar to the one discussed in Chapter 3 and 4. You
follow the steps by first going to the main tool bar and choose
‘Object’….. New object….pool’. Once you choose ‘pool’ you will be
prompted to list the ‘cross-section identifiers’ and you if you had settled
on some specific identifiers you then will be able to see an output similar
to the one below.
Step 4: Estimation: once the cross section identifiers have been listed then
process to the tool bar on that dialog box and click on ‘Estimate’ to obtain
the dialog box ‘pool estimation’ shown above. Then populate it with the
dependent variable ‘spreadt2’and regressors ‘SizeT2’ and a constant ‘C’ as
shown in Step 3. To obtain the estimation result click on ‘OK’ to obtain the
following output:
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Error Component Model Analysis
~ 79 ~
The output presented is based on a long method but is a step by step way of
demonstrating how the 2-way –error components model is estimated using
fixed effects. We now turn to a short cut when is implemented by copying
and pasting the raw data from Excel to Eviews (i.e. without transformation
‘Loan’(spread and ‘Size’). Once this is done, follow the process of creating a
pool object as discussed above to obtain the following screen:
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Guidelines on Panel Data Analysis
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Step 5: populating the ‘pool estimation’ dialog box. For one to implement
the 2 way fixed effects model we first need to input the dependent
variable in the space ‘Dependent variable’ in our case the dependent
variable is ‘Spread’ and also the space for regressors’ in our case the
regressors are ‘Size’ and C.
To indicate that this is a two-way- error component’ we go to ‘Estimation
Method’. Click on the arrow down in the area marked ‘cross-section’ and
select ‘Fixed’ and go the area indicated as Period and select ‘Fixed as well’.
Do not change any of the spaces provided as shown in Panel A. This will
result in the output in Panel B:
Panel A Panel B
Now you may notice that the result obtained above is similar to the one
obtained earlier. For comparison see the following set of output. Notice
that the coefficient for bank size is the same in both cases as shown below:
is this correct?
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Error Component Model Analysis
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Chapter 6
Dynamic Panel Data Analysis
So far we have estimated static panels. However, in the case were the lagged
dependent variable is included as an explanatory variable this results is
econometric problems. It does not sound right A simple dynamic model
may be presented as follows:
ittiittiit Xyy 1,
0
0
it
2
it
it
js
js
E
E
E
Here the choice between FE and RE formulation has implications for
estimations that are of a different nature than those associated with the
static panels. If the lagged dependent variable also appears as explanatory
variable then strict exogeneity of the regressors no longer holds. The lagged
variable introduces endogeneity problem in which case the LSDV is no
longer consistent when N tends to infinity and T is fixed.
The LSDV estimator is consistent for the static model whether the effects
are fixed or random. Therefore need to show that the LSDV is inconsistent
for a dynamic panel data with individual effects, whether the effects are
fixed or random. The bias of the LSDV estimator in a dynamic model is
generally known as dynamic bias or Nickell’s bias (1981).
To deal with this we use a number of estimators:
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Guidelines on Panel Data Analysis
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6.1 Arellano and Bond Estimator
To get consistent estimates in GMM for a dynamic panel model, Arellano
and Bond appeals to orthogonality condition that exists between Yit-1
and vit
to choose the instruments. Consider the following simple AR(1) model:
2
2
1
,0
,0
uit
vi
itiitit
iidu
iidv
uvyy
To get a consistent estimate of as N-> infinity with fixed T, we need to
difference this equation to eliminate individual effects.
23121 iiiiitit uuyyyy
Consider t=3 [first year with data]
231223 iiiiii uuyyyy
In this case yi1 is a valid instrument of (Y
i2-y
i1), since it is highly correlated
with (yi2-y
i1) and not correlated with (v
i3-v
i2)
Consider t=4
342334 iiiiii uuyyyy
For period T, set of instrument (w) will be:
221 ..., iTii yyyW
The combination of the instruments could be defined as
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Dynamic Panel Data Analysis
~ 85 ~
221
21
1
.........,0..0
0....
.....
...,0
0..0
iTii
ii
i
i
yyy
yy
y
W
Because the instruments are not correlated with the remaining error term,
then our moment condition is stated as:
0 ii uwE
Pre-multiplying our difference equation by WI yields:
vWyWyW 1
Estimating this equation by GLS yields the preliminary Arellano and Bond
one-step consistent estimator. In case there are other regressors then:
vWXWyWyW 1
6.2 Estimation of Dynamic Panel in Eviews
For illustration purposes we use the model stated as:
tiiittti
titi
n
n
nttiti
vDXKAP
LiqSizeIRLL
,76,5
,4,3
0
21,1,
)log()ln()ln(
Where; )ln( ,tiL is the change in total lending by bank i at time t; IR is the
monetary policy variable, usually interest rate at t; )log( ,tiSize is a measure
of size of bank i at time t; tiLiq , is a measure of liquidity of bank i at time t;
tiKAP , is the total liquid assets to total assets of bank i at time t; tX is a
vector of macroeconomic variables which may affect the operating
environments for banks; tiD , is a various qualitative characteristics of
commercial banks such as private or public; domestic or foreign; iv is the
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Guidelines on Panel Data Analysis
~ 86 ~
time invariant error component; ti , is the error term with the usual
properties.
6.3 Step by Step Implementation of the Dynamic GMM
Procedure in Eviews
To estimate a model using dynamic GMM we proceed as follows:
Step 1: Organising the data in Excel- Unlike the procedure we have been
using in the previous cases, here we stark the data as follows:
Table 6.1: Stacked data on bank size and loan
Spread Size
1 6.3 4.4
2 5.8 2.8
3 4.5 12.9
4 2.1 9.2
5 2.0 3.5
6 1.9 3.4
7 2.0 2.4
8 1.5 1.3
9 0.5 1.2
10 0.6 10.3
11 1.0 4.2
12 6.4 11.9
13 1.5 14.5
14 2.4 8.5
15 2.5 7.8
16 3.7 0.9
17 3.3 1.0
18 4.6 5.7
19 5.1 4.6
20 3.4 6.1
21 2.2 6.9
22 2.0 4.4
23 1.7 8.0
24 1.5 7.1
25 -2.2 4.3
26 1.6 4.5
27 0.1 6.0
28 1.2 5.3
29 1.8 6.1
30 2.0 6.4
31 2.4 8.8
32 2.5 5.2
33 1.5 4.5
34 3.4 6.1
35 6.7 5.3
36 6.7 5.2
37 6.7 6.6
38 9.3 1.3
39 9.8 6.1
40 9.8 7.5
41 9.8 17.1
42 9.8 13.6
43 9.8 6.0
44 9.8 1.5
45 10.5 1.7
46 9.8 8.1
47 8.5 1.6
48 9.8 4.0
49 9.8 5.0
50 9.8 5.7
51 9.8 3.8
52 4.1 15.9
53 2.9 4.8
54 1.8 5.3
55 -1.4 3.5
56 -2.1 4.9
57 -1.5 1.6
58 -1.4 3.0
59 -2.4 7.7
60 -2.2 5.5
61 -1.4 4.4
62 -1.3 15.8
63 -1.8 8.7
64 -1.1 3.8
65 -0.7 4.8
66 0.1 1.6
67 0.5 3.8
68 0.4 4.9
69 3.5 4.6
70 3.2 4.0
71 3.3 6.2
72 3.3 6.9
73 3.6 8.3
74 3.6 5.5
75 3.6 5.5
76 3.6 5.4
77 3.6 4.3
78 1.1 4.9
79 0.8 7.3
80 0.8 4.8
81 2.8 4.8
82 2.8 7.3
83 2.7 7.7
84 2.7 5.1
85 2.7 7.5
Bank1
Bank2
Bank3
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However, to be able to implement dynamic GMM in Eviews, the number
of cross sections should be sufficiently large compared to the time
dimension. In the present case we assume we have 84 banks with monthly
data spanning 2000M1- 2000M10.
Step 2: Getting started in Eviews: to conduct dynamic GMM in Eviews
you proceed as follows: click on: File New workfile this will lead you
to the screen in panel A. Then Click on : Workfile Structure type
Balanced panel, to obtain the screen in Panel B, which you then populate
with the Start data as 2000M1; End date 2000M10; and Number of cross
sections as 84 banks as shown in Panel B.
Spread Size
1 6.3 4.4
2 5.8 2.8
3 4.5 12.9
4 2.1 9.2
5 2.0 3.5
6 1.9 3.4
7 2.0 2.4
8 1.5 1.3
9 0.5 1.2
10 0.6 10.3
11 1.0 4.2
12 6.4 11.9
13 1.5 14.5
14 2.4 8.5
15 2.5 7.8
16 3.7 0.9
17 3.3 1.0
18 4.6 5.7
19 5.1 4.6
20 3.4 6.1
21 2.2 6.9
22 2.0 4.4
23 1.7 8.0
24 1.5 7.1
25 -2.2 4.3
26 1.6 4.5
27 0.1 6.0
28 1.2 5.3
29 1.8 6.1
30 2.0 6.4
31 2.4 8.8
32 2.5 5.2
33 1.5 4.5
34 3.4 6.1
35 6.7 5.3
36 6.7 5.2
37 6.7 6.6
38 9.3 1.3
39 9.8 6.1
40 9.8 7.5
41 9.8 17.1
42 9.8 13.6
43 9.8 6.0
44 9.8 1.5
45 10.5 1.7
46 9.8 8.1
47 8.5 1.6
48 9.8 4.0
49 9.8 5.0
50 9.8 5.7
51 9.8 3.8
52 4.1 15.9
53 2.9 4.8
54 1.8 5.3
55 -1.4 3.5
56 -2.1 4.9
57 -1.5 1.6
58 -1.4 3.0
59 -2.4 7.7
60 -2.2 5.5
61 -1.4 4.4
62 -1.3 15.8
63 -1.8 8.7
64 -1.1 3.8
65 -0.7 4.8
66 0.1 1.6
67 0.5 3.8
68 0.4 4.9
69 3.5 4.6
70 3.2 4.0
71 3.3 6.2
72 3.3 6.9
73 3.6 8.3
74 3.6 5.5
75 3.6 5.5
76 3.6 5.4
77 3.6 4.3
78 1.1 4.9
79 0.8 7.3
80 0.8 4.8
81 2.8 4.8
82 2.8 7.3
83 2.7 7.7
84 2.7 5.1
85 2.7 7.5
Bank4
Bank5
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Guidelines on Panel Data Analysis
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Panel A Panel B
Step 3: When you click on OK on the screen in Panel B, above you will
obtain the screen shown here. You may notice the screen has two new
elements namely the dateid and crossid. These elements are essential in
ensuring that data on a specific cross section at a particular time can be
identified with ease.
The crossid- this is the element for cross section identification. In
our case we have 84 cross sections, so the cross sections have
numbers with the first cross section being identified as ‘1’ and the 84th
cross section being identified as 84. In the case of Cross section 1, we
know that it has ten observations and assigned to each of these
observations is the identifier ‘1’. You may double click on the name
‘crossid’ to view the details as shown in the figure below.
The dateid- this is the element for date identification. Recall in our
case we have 10 time periods (2000M1: 2000M10). You may double
click on ‘dateid’ to appreciate the role of this element.
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Dynamic Panel Data Analysis
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Step 4: Getting the data from Excel to Eviews: The procedure for
getting data from Excel to Eviews is as explained in Chapter 1, on working
with ‘stacked data’. For illustration, we are working 3 variables: loans
disbursed by bank (Loans), bank size (Size) and policy rate (IBR). Following
the steps of getting stacked data from excel to Eviews you will obtain the
following (adjust for IBR which is cross section wide variable):
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Guidelines on Panel Data Analysis
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Step 5: the regression: in this case you will estimate the equation where
the dependent variable is ‘Loan’ and the independent variables are ‘size
and IBR’. The procedure for estimating a simple OLS equation applies
here. Once this is followed you will then obtain the screen shown below
with the dependent variable listed first followed by the independent
variables, size and ibr, and then the constant C. To estimate a dynamic
GMM model you will need to click on ‘Estimation settings’ and
choose the ‘GMM/DPD- Generalised Method of Moments/Dynamic
Panel’ method as shown here:
To estimate the dynamic GMM we use the ‘Dynamic Panel Wizard’
shown on the lower left of panel B in the figure above. If you click on the
‘Dynamic Panel Wizard’ button, it will prompt you to the next step of the
estimation procedure. You will observe the following screens:
The first screen welcomes you to the dynamic panel data model
wizard. As indicated in the screen, you are informed that the wizard
aids you in specifying a
member of the class of
dynamic panel data models
with fixed effects. You are
cautioned that this class of
models are designed for
panels with a large number
of cross-sections and a short
time series. In addition, you
Click here to start
estimating the dynamic
GMM
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Dynamic Panel Data Analysis
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are cautioned not to use the wizard to specify a static panel data
model. After this information set, you can then click on ‘Next’
button.
Step 1: Specify the dependent variable: The wizard then shows
you that there are 6 steps in
estimating a dynamic panel. The first
step, as shown in in the screen shot
is to specify the dependent variable.
As indicated, dynamic panel data
models have the feature that lags of
the dependent variable appear as
regressors. At this step, you are
required to specify the dependent variable. For our case we had
specified ‘loan’ as the dependent variable. As indicated earlier, the
dynamic panel uses lags of the dependent variable as regressors,
therefore you are required to specify the lags you want to use. Eviews
has set the lags at 1, however, if you click on the button provided you
will select the desired number of lags.
Step 2: specify any other
regressors: Ideally, without
specifying any other regressors a
dynamic panel will be estimated
since the lag of the dependent
variable has been included as a
regressor. However, at this step you
are required to include any other
regressors that you may consider necessary in the regression. In our
model we included ‘Size’ and ‘ibr’ as additional regressors as shown in
the screen above. In addition, you
are reminded that in case you need
period dummy variables (period
specific effects), you can click on
the box provided on ‘Include
period dummy variables (period
fixed effects)’.
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Guidelines on Panel Data Analysis
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Step 3: Select transformation method: This step allows you to
choose a transformation which will be applied to the specification of
a dynamic panel to remove cross-section fixed effects. There are two
method proposed namely, differences and orthogonal deviations.
Step 4-5: specify GMM level instruments and regular
instruments: In these two steps the wizard requires specification of
GMM level instruments in a manner consistent with the Arellano-
Bond type dynamic panel instruments with lags that vary by
observation as shown in Step 4 of 6 above. In addition, step 5 of 6
allows you to specify other instruments, if any. In case regular
instruments are required, then you are required to list those
instruments in the appropriate boxes depending on whether or not
you require to transform the instruments.
Step 6: Select the estimation
method. In this last step you are
reminded that the dynamic panel
data models are estimated by
GMM. In which case you are
expected to 1. Specify the
number of iterations. To do this
you click on the button libelled
‘GMM Iterations’, then choose
the number of iterations you need, (2) choose the GMM weighting
matrix. Here there are two options, namely Period SUR and White
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Dynamic Panel Data Analysis
~ 93 ~
Period. The default set is ‘White Period’. Unless you have reasons to
change the setting, you are advised to work with the default settings,
and (3) computation of standard errors.
After going through all the steps above click on the ‘Next’ button to obtain
screen shown in Panel A below. In this panel you are informed that the
wizard will transfer your specification to the GMM equation estimation
dialog. The finally, click on the button ‘Finish’ to conclude the procedure.
Otherwise, you have an option to go back by clicking on the ‘Back’ button
or abort the process by clicking on the ‘Cancel’ button. If you choose to
proceed by clicking on the ‘Finish’ button, you will obtain the screen
shown in Panel B below. In this last step you are shown the screen which is
similar to the one you started with.
Figure 6: GMM Model Specification
Step 6: viewing the estimation results: To view the estimation results you
click on ‘OK’ to obtain the following results:
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Guidelines on Panel Data Analysis
~ 94 ~
Table 6.2: The Estimation results
The table above shows the estimation results based on a dynamic GMM
procedure. The critical things to check out for in this output are the
following:
The estimated coefficients: in our case we used only two
variables: (1) Bank size- which is found to positive and significant
at the conventional levels of testing (ii) the policy rate- in which we
expected that tight monetary policy will reduce the quantity of
loans extended by banks. Here we find that the negative
relationship holds, however, the estimated coefficient is not
significant at the conventional levels of testing.
The J-statistic: To test whether the model fits the data well we
use the J-statistics. The J-test is a chi square with (M-K) degrees of
freedom, with M = number of instruments and K =the number of
endogenous variables. With the null hypothesis being that the
model is valid, when the computed J is less than the critical values.
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Dynamic Panel Data Analysis
~ 95 ~
References
Ahn, S C and Schmidt, P (1995), ‘Efficient estimation of models for dynamic panel
data’, Journal of Econometrics, Vol. 68, No. 1, pages 5-27.
Balestra, P and Nerlove, M (1966), ‘Pooling cross section and time series data in
the estimation of a dynamic model: the demand for natural gas’,
Econometrica, Vol. 34, No. 3, pages 585-612.
Baltagi, B H and Chihwa Kao, C (2000), ‘Nonstationary panels,
cointegration in panels and dynamic panels: a survey’, Chapter 1 in
Baltagi, B H (ed), Advances in econometrics, volume 15: nonstationary
panels, panel cointegration and dynamic panels, Amsterdam, JAI Press,
pages 7-51.
Hausman, J A and Taylor, W E (1981), ‘Panel data and unobservable individual
effects’, Econometrica, Vol. 49, No. 6, pages 1377-98.
Nerlove, M and Balestra, P (1992), ‘Formulation and estimation of econometric
models for panel data’, Chapter 1 in Mátyás, L and Sevestre, P (eds), The
econometrics of panel data: fundamentals and recent developments in theory and practice,
Amsterdam, Kluwer Academic Publishers, pages 3-18.
Pesaran, M H, Shin, Y and Smith, R (1999), ‘Pooled mean group estimation of
dynamic heterogeneous panels’, Journal of the American Statistical Association,
Vol. 94, No. 446, pages 621-34.
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Chapter 7
Non-Stationary Panel Analysis
7.0 Panel Unit-root Tests
Panel unit-root tests were originally considered by Levin and Lin
(1993) …and published as Levin et al. (2002). We can now look at some of
the tests that EViews performs, which include panel unit-root test. As such,
it will be interesting to compare the results from the panel unit-root tests
with the unit-root tests for the individual series. You may begin with the
individual augmented Dickey-Fuller (ADF) unit root tests on (the size for
each bank and examine whether they are I(0) or I(1).
What about the cross-sectional data? Are they I(0) or I(1)? To obtain an
answer, select the 5 bank size series and open them as a Group − note that
we have just done that! In the window for the Group, click on View and
select Unit Root Test…. A window will open that provides you with a set
of options emerge as shown below.
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Guidelines on Panel Data Analysis
~ 98 ~
EViews is set up to automatically calculate the following panel unit-root
tests: Levin et al. (2002), Breitung (2000), Hadri (1999), Im et al. (2003) and
the Fisher-ADF as well as Fisher-PP tests due to Maddala and Wu (1999)
and Choi (2001) respectively. Further references and explanations of these
tests can be found in, inter alia, Chapter 4 of Maddala and Kim (1998),
Chapter 7 of Harris and Sollis (2003) and Breitung and Pesaran (2005).
To begin with, we should note that the first three tests are different from
the remaining three. In particular, we can classify panel unit root tests on
the basis of whether there are restrictions on the autoregressive process
across cross-sections or series. To see this, consider an AR(1) process for
panel data:
itiittiiit xyy 1,
Where i = 1, 2, …, n are the number of series/countries (in this case the
number of base real GDP data series) and t = 1, 2, … , T are the observed
periods (in our case 1985 to 2011). Note that the xit represent exogenous
variables in the model, including any fixed effects or individual trends, and
the uit are iid error terms. We are interested, as in standard unit root tests, in
the value of the coefficient, ρi. As with standard univariate series, we say
that if |ρi| < 1, y is stationary, whereas if |ρi| = 1, yit contains a unit root.
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Non-Stationary Panel Analysis
~ 99 ~
Note the subscript i on the autoregressive term, ρi. There are two natural
assumptions we can make about the ρi. If we assume that ρi = ρ, then we
assume that the persistence parameters are common across cross-sections;
this is the test performed by Levin et al. (2002), Breitung (2000) and Hadri
(2000). Of those three tests, the null hypothesis for the first two is that the
series under investigation is I(1), i.e., non-stationary, whereas the Hadri4 test
is performed under the null of stationarity (no unit root).
Alternatively, we can allow ρi to vary freely across the cross-sections, in
which case the Im et al.’s (2003), Maddala and Wu’s (1999) Fisher-ADF and
Choi’s (2001) Fisher-PP panel unit-root tests are applicable. The null
hypothesis for these tests is that the series under investigation is I(1), i.e.,
non-stationary.
The different panel unit root tests available in EViews are summarised in
the Table below;
Test Null hypothesis
Alternative hypothesis
Possible deterministic components
Autocorrelation correction method
Levin et al. Unit root No unit root None, F, T Lags
Breitung Unit root No unit root None, F, T Lags
Im et al. Unit root No unit root F, T Lags
Fisher –
ADF
Unit root No unit root None, F, T Lags
Fisher –
PP
Unit root No unit root None, F, T Kernel
Hadri No unit
root
Unit root F, T Kernel
Notes: None denotes no exogenous variables, F denotes individual fixed
effect and T denotes individual fixed effect and individual trend.
What is the best test to perform? That really depends on what the overall
aim is, whether you wish to estimate cross-sectional regressions with the
same slope coefficients or with different coefficients accounting for the
4 The Hadri panel unit root test is similar to the KPSS unit root test, and has null hypothesis of
no unit root in any of the series in the panel.
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Guidelines on Panel Data Analysis
~ 100 ~
time-series or cross-section dimension (see later on). Note, however, that
Pesaran and Smith (1995) have shown that neglecting slope heterogeneity
will lead to inconsistent estimates.
For the time being, click on Summary (which is the default option) and select
the balanced panel option. Alternatively, you may use the drop-down menu
associated with Test type to select an individual panel unit-root test statistic.
Note that, as in the case of the individual series, we can include a constant
and/or a time trend i.e. select individual intercept and trend. You may choose
to exclude the deterministic time trend – but if the trend is included in one
equation, it should be included in all.
You will see the window below;
Unlike the standard EViews single series unit root tests, where t-statistics
are reported for the significance of the constant and/or the trend, the panel
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Non-Stationary Panel Analysis
~ 101 ~
unit tests in EViews report only the actual unit root test. Therefore, we
ought to perform all three tests to see whether we get different answers. We
now report the results from all these three tests, starting with the most
general and ending with the most specific. To start off with, we will assume
a fixed, user-specified lag length of one, so you should enter 1 in the User
specified box for the lag length as shown above. We note in passing that
depending on the specific set-up of the panel unit-root tests, not all six tests
are computed all the time.
For the test with a constant and trend, denoted Individual trend and intercept5,
we should find the results of the panel unit root tests shown in Table below.
As mentioned in the previous paragraph, in this particular case the Hadri
test is not computed.
5 Note that selecting Individual intercept is equivalent to including individual fixed effects,
while Individual trend and intercept is equivalent to both fixed effects and trends.
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Guidelines on Panel Data Analysis
~ 102 ~
Note that the panel unit-root tests are internally inconsistent, i.e., the five
tests that test the same null hypothesis (e.g., Levin et al. and Breitung), are in
agreement as to the rejection of the null hypothesis of a unit root in bank
size series.
For the test with a constant only (equivalent to individual fixed effects only), we
proceed as follows;
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Non-Stationary Panel Analysis
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The results of the panel unit root tests are given in the table below.
Similarly, the four available tests (we have lost Breitung’s test) are in
agreement as to the rejection of the null hypothesis of a unit root.
Finally, for the test with no constant and no trend, i.e., no deterministic
regressors, we proceed as follows;
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Guidelines on Panel Data Analysis
~ 104 ~
We should find the following results of the panel unit-root tests;
All the unit-root tests suggest that the cross-section series are stationary.
Note that we have allowed for only one lag in the tests. Good empirical
practice calls for some experimentation with alternative lags to determine
whether the results change in any way.
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Non-Stationary Panel Analysis
~ 105 ~
7.1 Panel Unit-root Test with an Automatic Lag Selection
Method
Alternative criteria for evaluating the optimal lag length may be selected via
the combo box (Akaike, Schwarz, Hannan-Quinn, Modified Akaike,
Modified Schwarz, Modified Hannan-Quinn), and you may limit the
number of lags to try in automatic selection by entering a number in the
Maximum lags box. This procedure sets the lag length to the value of p
that minimises the respective information criteria. Ng and Perron (2001)
stress that good size and power properties of all unit root tests rely on the
proper choice of the lag length p used for specifying the ADF test
regression. They argue, however, that traditional model selection criteria
such as the AIC and BIC are not well suited for determining p with
integrated data. Instead, they suggest modified information criteria (MIC).
On the basis of a series of simulation experiments, Ng and Perron
recommend selecting the lag length p by minimising the modified AIC
(MAIC) in the univariate context. On the basis of this advice, we will also
use the MAIC in a panel context. For a test results for a model with
constant and trend, denoted Individual trend and intercept, we proceed as
follows;
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Guidelines on Panel Data Analysis
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Make sure you uncheck the Use balanced sample box and we have
chosen 8 as the maximum lag length. The results are shown in the table
below
Consistent with the previous tests, the results assuming a common unit root
procedure indicate the absence of a unit root. Therefore we reject the null
hypothesis that the series are I(1). We, therefore, conclude that the series
under investigation are stationary.
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References
Ahn, S C and Schmidt, P (1995), ‘Efficient estimation of models for dynamic panel
data’, Journal of Econometrics, Vol. 68, No. 1, pages 5-27.
Arellano, M (1989), ‘A note on the Anderson-Hsiao estimator for panel data’,
Economics Letters, Vol. 31, No. 4, pages 337-41.
Arellano, M (1993), ‘On the testing of correlated effects with panel data’, Journal of
Econometrics, Vol. 59, No. 1-2, pages 87-97.
Arellano, M (2003), Panel data econometrics, Oxford, Oxford University Press.
Arellano, M and Bond, S R (1991), ‘Some tests of specification for panel
data: Monte Carlo evidence and an application to employment
equations’, Review of Economic Studies, Vol. 58, No. 2, pages 277-97.
Arellano, M and Bover, O (1995), ‘Another look at the instrumental variable
estimation of error-components models’, Journal of Econometrics, Vol. 68,
No. 1, pages 29-51.
Balestra, P and Nerlove, M (1966), ‘Pooling cross section and time series data in
the estimation of a dynamic model: the demand for natural gas’,
Econometrica, Vol. 34, No. 3, pages 585-612.
Baltagi, B H and Chihwa Kao, C (2000), ‘Nonstationary panels,
cointegration in panels and dynamic panels: a survey’, Chapter 1 in
Baltagi, B H (ed), Advances in econometrics, volume 15: nonstationary
panels, panel cointegration and dynamic panels, Amsterdam, JAI Press,
pages 7-51.
Breitung, J and Pesaran, M H (2005), ‘Unit roots and cointegration in panels’,
Chapter 9 in Matyas, L and Sevestre, P (eds), The econometrics of panel data:
fundamentals and recent developments in theory and practice, Amsterdam, Kluwer
Academic Publishers, pages 279-322. http://www.ect.uni-
bonn.de/mitarbeiter/joerg-
breitung/documents/breitung_pesaran.pdf/view.
Engle, R F and Granger, C W J (1987), ‘Co-integration and error correction:
representation, estimation and testing’, Econometrica, Vol. 55, No. 2,
pages 251-76.
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Guidelines on Panel Data Analysis
~ 108 ~
Harris, R and Sollis, R (2003), ‘Panel data models and cointegration’, Chapter 7 in
Applied time series modelling and forecasting, Oxford, John Wiley & Sons.
Hausman, J A (1978), ‘Specification tests in econometrics’, Econometrica, Vol. 46,
No. 6, pages 1251-71.
Hausman, J A and Taylor, W E (1981), ‘Panel data and unobservable individual
effects’, Econometrica, Vol. 49, No. 6, pages 1377-98.
Im, K S, Pesaran, M H and Shin, Y (2003), ‘Testing for unit roots in
heterogeneous panels’, Journal of Econometrics, Vol. 115, No. 1, pages
53-74.
Johansen, S (1988), ‘Statistical analysis of cointegrating vectors’, Journal of Economic
Dynamics and Control, Vol. 12, No. 2/3, pages 231-54.
Johansen, S (1991), ‘Estimation and hypothesis testing of cointegration vectors in
Gaussian vector autoregressive models’, Econometrica, Vol. 59, No. 6, pages
1551-80.
Levin, A and Lin, C-F (1993a), ‘Unit root tests in panel data: asymptotic and
finite sample properties’, Department of Economics, University of San
Diego Discussion Paper 93-23.
Levin, A and Lin, C-F (1993b), ‘Unit root tests in panel data: new results’,
Department of Economics, University of San Diego Discussion Paper 93-56.
Levin, A, Lin, C-F and Chu, C-S J (2002), ‘Unit root test in panel data: asymptotic
and finite-sample properties’, Journal of Econometrics, Vol. 108, No. 1, pages
1-24.
Maddala, G S and Wu, S (1999), ‘A comparative study of unit root tests with panel
data and a new simple test’, Oxford Bulletin of Economics and Statistics, Vol.
61, No. S1, pages 631-52.
Mundlak, Y (1978), ‘On the pooling of time series and cross-sectional data’,
Econometrica, Vol. 46, No. 1, pages 69-85.
Nerlove, M and Balestra, P (1992), ‘Formulation and estimation of econometric
models for panel data’, Chapter 1 in Mátyás, L and Sevestre, P (eds), The
econometrics of panel data: fundamentals and recent developments in theory and practice,
Amsterdam, Kluwer Academic Publishers, pages 3-18.
Neyman, J and Scott, E L (1948), ‘Consistent estimates based on partially
consistent observations’, Econometrica, Vol. 16, No. 1, pages 1-32.
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Non-Stationary Panel Analysis
~ 109 ~
Pedroni, P (1999), ‘Critical values for cointegration tests in heterogeneous
panels with multiple regressors’, Oxford Bulletin of Economics and
Statistics, Vol. 61, No. S1, pages 653-78.
Pedroni, P (2000), ‘Fully-modified OLS for heterogeneous cointegrated panels’,
Chapter 3 in Baltagi, B H (ed), Advances in econometrics, volume 15:
nonstationary panels, panel cointegration and dynamic panels, Amsterdam, JAI
Press, pages 93-130.
Pedroni, P (2001), ‘Purchasing power parity tests in cointegrated panels’, Review of
Economics and Statistics, Vol. 83, No. 4, pages 727-31.
Pedroni, P (2004), ‘Panel cointegration: asymptotic and finite sample
properties of pooled time series tests with an application to the PPP
hypothesis’, Econometric Theory, Vol. 20, No. 3, pages 597-625.
Pesaran, M H (1999), ‘On the interpretation of panel unit root tests’.
http://www.econ.cam.ac.uk/faculty/pesaran/imf-unit.pdf.
Pesaran, M H (2007), ‘A simple panel unit root test in the presence of cross-
section dependence’, Journal of Applied Econometrics, Vol. 22, No. 2, pages
265-312.
Pesaran, M H, Shin, Y and Smith, R (1999), ‘Pooled mean group estimation of
dynamic heterogeneous panels’, Journal of the American Statistical Association,
Vol. 94, No. 446, pages 621-34.