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Panel Data Nowcasting

Jack Fosten and Ryan Greenaway-McGrevy

September 2019

CENTRE FOR APPLIED RESEARCH IN ECONOMICS

WORKING PAPER NO. 006

DEPARTMENT OF ECONOMICS

UNIVERSITY OF AUCKLAND

Private Bag 92019

Auckland, New Zealand

www.business.auckland.ac.nz/CARE

http://www.business.auckland.ac.nz/CARE

Panel Data Nowcasting∗

Jack Fosten†‡ Ryan Greenaway-McGrevy§

September 20, 2019

Abstract

This paper promotes the use of panel data in nowcasting. We shift the existing focus of theliterature, which has almost exclusively used time series models to nowcast national aggregatevariables like gross domestic product (GDP). We propose a mixed-frequency panel VAR modeland a bias-corrected least squares (BCLS) estimator which attenuates the bias inherent tofixed effects dynamic panel settings. We demonstrate how existing panel model selectionand combination methods can be adapted to the mixed-frequency setting with different lagspecifications. Detailed Monte Carlo simulations find that these methods outperform naıveapproaches. We present a novel application of our methods to the case of nowcasting quarterlyU.S. state-level real GDP using timely employment data. Our results indicate that utilisingrelevant monthly information is important, while also highlighting the gains from poolinginformation across states and from the use of appropriate lag selection or combination methods.We also find particularly large gains from nowcasting in states such as California; a regionwhich has higher real GDP than most developed economies and deserves rigorous attention.

JEL Classification: C23, C52, C53Keywords: Panel Data, Nowcasting, Model Selection, Model Averaging, State-level GDP

1 Introduction

Nowcasting has become established as an important way to make timely near-term predictions,

particularly for economic output variables like gross domestic product (GDP) which are published

with a lag. However, the existing literature has almost exclusively focussed on the use of time

series methods for predicting national aggregate variables. In this paper, we propose new methods

for nowcasting using panel data models. There are several reasons why this is an important

∗The authors are grateful for very useful comments and discussions with Michael Clements, Ana Galvao, IvanPetrella, Gary Koop, Kalvinder Shields and participants at the workshop “Advances in Economic Modelling andForecasting” at Warwick Business School, July 2019.†King’s Business School, King’s College London, U.K. E-mail address: [email protected]‡Data Analytics in Finance and Macro (DAFM) Research Centre, King’s College London, U.K.§Department of Economics, The University of Auckland, New Zealand.

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advancement. Firstly, the increasing availability of regional output data has made panel nowcasting

feasible. At the same time, regional data are often reported in a less timely fashion than national

aggregates which further motivates the need for nowcasting. Secondly, it is often the case that

national policymakers care about regional and sectoral developments and not only the movements

that take place at the national-level. Finally, there are many cases when the target nowcast variable

is annual or quarterly where we might only have a very small number of time series observations.

Therefore, one could expect substantial benefits from pooling information across regions or sectors

to improve nowcast model estimation and allow for a meaningful historical reconstruction using

pseudo out-of-sample methods.

The main contribution of this paper is to propose a mixed-frequency panel VAR (MF-PVAR) for

nowcasting a target variable with higher-frequency predictors. The model accommodates limited

cross sectional heterogeneity through fixed effects, thereby permitting each time series in the panel

to have a different sample mean. It can also be generalised to allow for exogenous variables such as

national series which vary across time but not individuals. The use of mixed frequency approaches

to panel data can be seen as an extension of the existing time series MF-VAR approaches to

nowcasting (Mariano and Murasawa, 2010; Kuzin et al., 2011; Schorfheide and Song, 2015) and is

also related to MIDAS models (Ghysels et al., 2007; Clements and Galvao, 2008, 2009; Schumacher,

2016) and bridge equations (Baffigi et al., 2004; Aastveit et al., 2014; Bragoli and Fosten, 2018).

The issue of mixed frequencies in panel data methods has been addressed by Binder and Krause

(2014) and Khalaf et al. (2017) but not in the context of forecasting or nowcasting.

We then provide methods (i) to estimate the MF-PVAR and (ii) to select from (or combine)

different nowcasting model specifications. Both aspects of implementation are complicated by the

inclusion of fixed effects in the MF-PVAR. First, the fixed effects cause the ordinary least squares

(OLS) estimator to be biased (Nickell, 1981), which inflates measures of forecast loss (Greenaway-

McGrevy, 2019a). To attenuate the bias, we show how the bias-corrected least squares (BCLS)

procedure of Hahn and Kuersteiner (2002) can be adapted and applied to the mixed-frequency

setting. Second, because the estimated fixed effects themselves contribute to forecast loss, we

2

require model selection (or combination) methods that are specifically tailored to the purpose

of forecasting model selection, as opposed to model selection for the purpose of inference after

incidental parameters have been integrated out (Greenaway-McGrevy, 2019a). We therefore adopt

panel forecasting model selection methods such as the panel final prediction error (FPE) criterion,

the Mallows selection criterion, as well as panel Mallows model averaging (MMA) for forecast

combination (see Greenaway-McGrevy, 2019a,b,c). We explore how these methods perform when

adapted to the mixed-frequency setting through a detailed set of Monte Carlo simulations. We

show that our approaches compare favourably to other recent panel forecast selection criteria (Lee

and Phillips, 2015) and naıve criteria.

The final contribution of this paper is to apply our methodology with a novel empirical study

of nowcasting U.S. state-level GDP. We exploit the flow of monthly information on employment-

related series at the state level which are available in a more timely fashion than quarterly real

GDP. Using a pseudo out-of-sample experiment, we make several new findings: 1) the use of timely

employment data is important in nowcasting state-level GDP over and above naıve univariate

benchmarks, 2) the use of appropriate bias-correction and model selection or combination yields

improvements in nowcast model performance, 3) pooling data across all states to form a panel is

very useful and dominates over simple time series regressions where the sample size is very small,

and 4) the improvements from pooling across all states even dominate over allowing heterogeneity

of coefficients across geographical or economic subgroups. Another novelty of our application is

that we can begin to draw inferences about nowcasting in individual states. For instance, we see

that nowcast gains are particularly sizeable in the state of California which is larger than all other

U.S. states and, indeed, most developed economies in terms of real GDP. Our results provide a new

approach to the use of state-level employment data, which has recently been used in a different

context by Gonzalez-Astudillo (2019). We also build on very recent approaches to nowcasting

regional output such as Koop et al. (2018) which studies area-level gross value added (GVA) in

the United Kingdom.

Our paper gives a new direction to the growing body of empirical papers on time series fore-

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casting and nowcasting, as well as the more recent literature of panel data forecasting. Nowcasting

methodology has developed rapidly in recent years. Previously surveyed by Banbura et al. (2013),

the empirical literature on nowcasting individual countries’ GDP using time series methods has

exploded to a large number of papers (see Bok et al., 2018, for a full set of references). On the other

hand, relative to the very long and established literature of time series forecasting methodology, the

literature on panel forecasting has emerged more recently with perhaps the earliest survey being

Baltagi (2008). We envisage that the extension of these methods to the case of nowcasting may

have fruitful applications in many other contexts: sectoral-level GDP or output variables; predict-

ing multiple different measures of national inflation and providing an early warning for hospital

expenditure in public healthcare systems to name but a few.

The rest of this paper is organised as follows. Section 2 introduces the panel nowcasting

MF-PVAR model set-up and the BCLS estimation method. Section 3 provides various different

model selection and combination methods. Section 4 details an extensive Monte Carlo simulation

experiment and documents the results. Section 5 describes the data and empirical application to

U.S. state-level GDP nowcasting. Finally, 6 concludes the paper.

2 Bias-Corrected Least Squares Panel Data Nowcasting

In this section we outline the main methodology developed in this paper. We firstly describe the

set-up for the panel data nowcasting model we consider. We then demonstrate how to cast this

into a MF-PVAR and show how to estimate this model by bias corrected least squares. Finally,

we demonstrate how the set-up can be extended to allow for exogenous variables to enter the VAR

system.

2.1 Set-up

We are interested in nowcasting the single target variable yi,t which, for instructive purposes, we

assume is measured at the quarterly frequency with observations t = 1, ..., T across individuals

i = 1, ..., n. There is also a single predictor variable, xi,t, which is observed at a monthly frequency

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(corresponding to t = 1/3, 2/3, ..., T ) with data available in a more timely fashion than the target

variable. The framework can easily be extended to allow for different frequencies, and to allow yi,t

and xi,t to be vectors rather than scalars.

The nowcasting model for yi,t is given by:

yi,t = αi +∑ps=1 γ

′sYi,t−s + ui,t (1)

where Yi,t :=(yi,t, xi,t+1, xi,t+1− 1

3, xi,t+1− 2

3

)′and p denotes the lag order of the model. When

lagged one or more periods, the specification of the vector Yi,t allows yi,t to be predicted by the three

months of the current quarter of the monthly predictor, along with lagged quarters of both yi,t and

xi,t. Equation (1) is a panel extension of the unrestricted MIDAS model (see Schumacher, 2016;

Fosten and Gutknecht, 2019) and will allow this equation to be cast into a MF-PVAR framework.

We note that the specification of Equation (1) assumes homogeneity of the slope coefficients

when we pool across individuals. The issue of whether “to pool or not to pool” (see, for example,

Wang et al., 2019) is a long-standing question in panel data econometrics. While many methods

now exist to allow for heterogeneity in the slope coefficients, many studies dating back to Baltagi

and Griffin (1997) and Baltagi (2008) have found that simple pooling strategies can often dominate

in terms of mean squared forecast error (MSFE). Whether pooling is appropriate is an empirical

question which we will explore in detail later.

The OLS estimators of the parameters of models such as Equation (1) exhibit an O(T−1

)bias

due to the lagged dependent variable (see, among others, Nickell, 1981; Lee, 2012) and weak exo-

geneity in the monthly predictors xi,t. Thus, even if the lagged dependent variable is omitted from

Equation (1), the O(T−1

)bias will persist unless strict exogeneity is imposed on the monthly pre-

dictors. This assumption appears unrealistic in many applications. For example, in our empirical

application where monthly measures of employment are used to nowcast quarterly GDP growth, it

is advisable to permit innovations to GDP growth to have an effect on future employment growth.

The OLS bias inflates measures of out-of-sample MSFE, as seen in Hahn and Kuersteiner (2002)

and Greenaway-McGrevy (2019a). BCLS provides an effective way to attenuate the impact of the

5

OLS bias on MSFE. Firstly, in contrast to many IV and GMM approaches to the problem, the

bias correction does not inflate the asymptotic variance of the estimator (Hahn and Kuersteiner,

2002) which features in quadratic measures of forecast loss such as MSFE. Second, the asymptotic

MSFE of the OLS estimator can be reduced even when the set of candidate models is misspecified,

provided that the candidate set of models can grow large in the asymptotics and thus better

approximate the true DGP (Greenaway-McGrevy, 2019a).

2.2 Bias Corrected Least Squares Procedure

We adopt BCLS estimation of the model in Equation (1). Hahn and Kuersteiner (2002) provide

a general formulation for the bias correction that is based on the full specification of system of

equations. We therefore re-cast the nowcasting model in Equation (1) as the first equation from

the more general MF-PVAR of the form:

Yi,t = µi +∑ps=1 Λ′sYi,t−s + Ui,t, (2)

where µi = (αi, ξ′i)′, Λs = [γs : Φs] and Ui,t =

(ui,t, υ

′i,t

)′for each s, where υi,t, Φs and vi,t represent

the fixed effects, parameters and error terms in the equivalent models for the three xi,t equations

like in Equation (1). This MF-PVAR extends the time series MF-VAR specifications seen in the

traditional nowcasting literature (Mariano and Murasawa, 2010; Kuzin et al., 2011; Schorfheide

and Song, 2015) to the case of panel data.

We now present the bias correction expression for the nowcasting model for the MF-PVAR in

Equation (2). The bias correction here will be slightly different from the standard forecasting case

(for example Greenaway-McGrevy, 2013, 2019a) because xi,t is shifted forward one quarter in the

vector Yi,t. Specifically, though Equation (1) can be estimated using data spanning t = p+1, . . . , T ,

the full system (2) can only be estimated with data spanning t = p + 1, . . . , T − 1 because Yi,t

contains xi,t+1. Thus, as we show below, the bias-correction is implemented using an auxiliary

regression model that is estimated on fewer observations from the panel.

In deriving the bias-correction we first denote Λp =[Λ′1 : Λ′2 : · · · : Λ′p

]′. We can then express

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Equation (2) in companion form as follows:

Yi,t = µi + A′pYi,t−1 + Ui,t

where Yi,t :=(Y ′i,t−1, ..., Y

′i,t−p

)′, µi = (µ′i, 0

′)′, Ui,t =

(U ′i,t, 0

′)′ and, denoting m = dim(Yi,t):

Ap := [Λp : Lp] , Lp :=

Im(p−1)

0m×(p−1)m

.Returning to the parameters of the nowcasting model in Equation (1), letting γ denote the

OLS estimator, we can characterise the bias to the OLS estimates of the nowcasting equation as

(see Hahn and Kuersteiner, 2002):

E (γ − γ) = − 1T−pΓ−1p

(Imp −A′p

)−1Jpm,mΣJm,1+O

(T−2

)where Γp = cov (Yi,t) , Σ = cov (Ui,t) , and Jm2,m1 =

[Im1 : 0m1×(m2−m1)

]′for integers m2 ≥ m1.

With the analytic expression for the bias and the model cast into companion form, we can

now outline the BCLS procedure for making a nowcast for yi,T+1, given information on the same

quarter’s monthly predictors xi,T+1, xi,T+2/3 and xi,T+1/3, and further lags.

Bias Correction Procedure

1. Estimate Equation (1) for t = p+ 1, ..., T and i = 1, ..., n. Let γ = (γ′1, γ′2, ..., γ

′p)′ denote the

vector of OLS estimates.

2. Estimate the system of Equations (2) for t = p+ 1, ..., T − 1 and i = 1, ..., n. Let Λp denote

the OLS estimates of Λp and let µi denote the OLS estimates of µi. We also construct:

Q := 1n(T−p−1)

∑T−1t=p+1

∑ni=1 Yi,t−1Y

′i,t−1,

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where Yi,t := Yi,t − Yi; Yi := 1T−p−1

∑T−1t=p+1 Yi,t−1, and

Σ := 1n(T−p−1)

∑T−1t=p+1

∑ni=1 Ui,tU

′i,t,

where Ui,t = Yi,t −∑ps=1 Λ′sYi,t−s − µi.

3. The bias-corrected OLS estimator of γ is

γ := γ + 1(T−p)Q

−1(I− A

′p

)−1Jpm,mΣJm,1

where

A′p :=[Λp : Lp

]Then the bias-corrected fixed effects are αi := 1

(T−p)∑Tt=p+1

(yi,t − γ′Yi,t−1

).

4. The bias corrected nowcast is then:

yi,T+1 = αi +∑ps=1 γ

′sYi,T+1−s = αi + γ′Yi,T (3)

for all i = 1, ..., n.

2.3 Extension to Include Exogenous Variables

The baseline nowcasting model assumes that all of the xi,t variables in Equation (1) are endogenous

in the sense that they each appear as an equation of the MF-PVAR system in Equation (2). In

practice, however, there might be cases in which we want to allow for exogenous variables. In the

case of panel data nowcasting, this might include national (time series) variables being added into

a regional nowcasting model. This is motivated by the fact that national data are often produced

in a more timely fashion than regional data and therefore useful for nowcasting; something we

explore later in our empirical application.

We will briefly outline the adjustment which must be made to the BCLS procedure to allow us

8

to nowcast using exogenous variables. Suppose we now have additional regressor variable(s) zi,t

which we wish to use in nowcasting the target variable yi,t. We adapt Equation (1) to be:

yi,t = αi +∑ps=1 γ

′sYi,t−s + θ′zi,t + ui,t (4)

where zi,t is strictly exogenous in that E(zi,tui,t−s) = 0 for all t and s. It will be convenient to

combine the parameters into the vector η := [γ′ : θ′]′.

The OLS estimators of both γ and θ exhibit O(T−1

)bias (Phillips and Sul, 2007; Lee, 2012).

As above, we employ a bias-correction as follows. First, the mixed frequency panel VAR with

exogenous variables (MF-PVAR-X) is of the form:

Yi,t = µi +∑ps=1 Λ′sYi,t−s + Θ′zi,t + Ui,t (5)

We first estimate Equation (5) by least squares to obtain the estimates Λs,Θ and µi for s =

1, ..., p and i = 1, ..., n. We next construct:

QZ := 1n(T−p−1)

∑T−1t=p+1

∑ni=1 Zi,t−1Z

′i,t−1,

where Zi,t =(Y′i,t, z

′i,t

)′; Zi,t := Zi,t − Zi; Zi := 1

T−p−1∑T−1t=p+1 Zi,t−1, and:

Σ := 1n(T−p−1)

∑T−1t=p+1

∑ni=1 Ui,tU

′i,t,

where Ui,t = Yi,t −∑ps=1 Λ′sYi,t−s − Θ′zi,t − µi.

The bias-corrected OLS estimator of η, denoting mz = dim(zi,t), is then:

η := η + 1(T−p)Q

−1Z Jpm+mz,pm

(I− A

′p

)−1Jpm,mΣJm,1

and the nowcast for yi,T+1 can be found in the same way as before.

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3 Model Selection Methods

In the previous section, we detailed how to estimate the panel nowcasting model when we know the

number of lags p in Equation (1). In this section we outline three different methods to combine or

select between nowcasting models with different lag specifications, each estimated using the BCLS

procedure as detailed above. These methods are: panel MMA, a panel Mallows criterion and a

panel FPE criterion. The first method is a nowcast combination approach in which each model in

the candidate set is a assigned a different weight, whereas the other methods are model selection

approaches which assign a weight of zero to all models except one. We will also compare these

methods to existing panel model selection criteria of Lee and Phillips (2015).

We first require some additional notation. Let u (p) be an nTpmax × 1 vector of residuals from

the model with p lags fitted (by BCLS) to t = pmax + 1, . . . , T and i = 1, . . . , n. Here pmax denotes

the maximum lag order, and Tpmax:= T − pmax. Finally, let:

σ2 (p) := 1n(Tpmax−1)

u (p)′u (p)

3.1 Mallows Model Averaging

Forecast combination through model averaging often enhances forecast accuracy when compared

to selection of a single model (for surveys, see Clemen, 1989; Granger, 1989; Diebold and Lopez,

1996; Newbold and Harvey, 2002; Timmermann, 2006). Greenaway-McGrevy (2019b) generalizes

the MMA method proposed by Hansen (2008) to panel data VARs and shows that it generally

outperforms conventional averaging methods such as equal weights, exponentiated AIC and BIC

averaging, and Granger and Ramanathan (1984) cross validation in a set of Monte Carlo studies.

Let w be a pmax × 1 vector of arbitrary weights. Let p = (m, 2m, . . . , pmaxm)′, so that it is a

pmax × 1 vector consisting of the size of each model. Our estimator of MSFE based on w is

Ln,T (w) = 1nTpmax

w′u′n,T un,Tw + σ2 (pmax) ·[

2nTpmax

p′w+ 1T 2pmax

w′Pw],

10

where un,T := [u (1) : u (2) : · · · : u (pmax)]′

is an nTpmax × pmax matrix of residuals and P is a

pmax × pmax matrix with the (r, s) element set to min{r, s}. Panel MMA is finding a vector of

weights that minimizes Ln,T (w). This is the solution to quadratic programming problem:

w∗ = arg minw

(Ln,T (w)

). (6)

subject to:

1′Kw = 1, wk ∈ [0, 1]

3.2 Panel Mallows Criterion

The Mallows-type criterion can also be used to perform nowcast model selection rather than model

averaging. Greenaway-McGrevy (2019c) proposes lag selection by minimization of a panel version

of the Mallows estimator, specifically:

pmal = arg minp

(1

nTpmaxu (p)

′u (p) + σ2 (pmax) ·

[2mp

nTpmax+ 1

T−p

])(7)

Greenaway-McGrevy (2019c) outlines conditions under which the model selection rule is asymp-

totically efficient in that it minimizes the asymptotic MSFE as both n→∞ and T →∞. In this

paper we apply this criterion to the case of nowcast model selection.

3.3 Panel FPE Criterion

Another model selection criterion which can be adapted to this nowcasting setting is a panel version

of the final prediction error which was also explored by Greenaway-McGrevy (2019a). This can be

written as:

pfpe = arg minp

(1

nTpmaxu (p)

′u (p) + σ2 (p) ·

[2mp

nTpmax+ 1

T−p

])(8)

11

Note that the primary difference to Equation (7) is that the model complexity penalty is based

on the fitted VAR(p) and not VAR(pmax). Greenaway-McGrevy (2019a) outlines conditions under

which the model selection rule is asymptotically efficient.

We will apply all three of the above methods to our context of the panel data nowcasting model.

Detailed Monte Carlo simulation evidence will be presented to ascertain the performance of these

criteria in the mixed-frequency setting. We finally turn to two more panel model selection criteria

which have been proposed in the literature.

3.4 KLIC

Lee and Phillips (2015) generalize model selection via minimization of Kullback-Leibler information

loss to a panel setting. Their criterion chooses the lag length according to the following:

pklic = arg minp

(ln(σ2 (p)

)+ 2mp

nTpmax+ mp

T 2pmax

+ 1Tpmax

ω2(p)σ2(p)

)(9)

where ω (p) is an estimate of the long-run variance of the errors. The KLIC is designed for OLS

and thus the final term is a penalty that accounts for the impact of the fitted incidental parameters

on OLS bias. Whereas the Mallows and FPE criertia are tailored to minimizing the MSFE of the

model, the KLIC minimizes infomation loss with respect to the common parameters of the model

once the incidental parameters have been integrated out of the likelihood.

3.5 BIC

Lee and Phillips (2015) also generalize BIC model selection to panel data models with incidental

parameters, specifically:

pbic = arg minp

(ln(σ2 (p)

)+

mp ln(nTpmax )nTpmax

+ mpT 2pmax

+ 1Tpmax

ω2(p)σ2(p)

)(10)

The BIC is consistent for the true lag order when the data are generated according to model within

the candidate set.

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4 Monte Carlo Study

We conduct a battery of simulation experiments in order to explore the performance of the model

specification methods described above. Our goal is to provide practicial advice for choosing a

panel model nowcasting specification by exploring how the different methods perform in different

settings realistic to nowcasting.

For t = 1k ,

2k , ...,

k−1k , 1, 1 + 1

k , 1 + 2k , ..., T and i = 1, ... , n, we generate a bivariate panel

VARMA(1,1) process as follows:

y∗i,t

xi,t

=

ρ11 ρ12

ρ21 ρ22

y∗i,t−1/k

xi,t−1/k

+ vi,t,

vi,t =

θ1 0

0 θ2

εi,t−1/k + εi,t, εi,t ∼ iidN

0,

1 φ

φ 1

where k denotes the aggregation frequency. By setting k = 3 we can simulate quarterly aggregation

of monthly data which is the case of Equation (1). Meanwhile annual aggregation of quarterly data

corresponds to k = 4 and annual aggregation of monthly data corresponds to k = 12. We will

focus on the results for k = 3 which is the most common scenario in the nowcasting literature,

with results for k = 4 and k = 12 available upon request.

We treat y∗i,t as a latent variable in that we can only observe the aggregation of the time series

yi,t at t = 1, 2, ..., T , namely:

{yi,t}Tt=1 ={y∗i,t + y∗i,t−1/k + ...+ y∗i,t−(k−1)/k

}Tt=1

whereas we do directly observe the higher-frequency variable xi,t.

This gives us the data to run the nowcasting regressions described in Equations (1) and (2)

above. Since these nowcasting models are equivalent to mixed frequency VARs of different lag

orders p, all models within the candidate set will be misspecified relative to the DGP. Thus the

framework retains a trade-off between misspecification and model complexity when selecting the

13

size of a model even in large samples (c.f. Schorfheide, 2005).

We consider all combinations of ρ11 ∈ {0.2, 0.5, 0.8} and ρ22 ∈ {0.2, 0.5, 0.8}, which generates

a wide range of serial dependence in the VARMA(1,1). To ensure that the system remains stable

under combinations of ρ11 and ρ22 we set ρ12 = ρ21 = 0.1. We set φ = 0.5 so that there is a

moderate correlation between the innovations to the two time series. We set θ2 = θ1 = 0.8. For

the sample sizes, we consider n = 25, 50, 100, 200, 400 and T = 20, 40, 80, 160. This corresponds

to 5, 10, 20 and 40 years of data for the k = 3 monthly-to-quarterly aggregation. Our empirical

application is somewhere in the middle of these ranges for n and T . In setting the maximum lag

order we use the rule pmax = int(

max(√

2T ,min(√

2n, 12T)))

.1

We consider four different methods for selecting the lag order of the nowcasting model: panel

Mallows (Equation 7), panel final prediction error (FPE) (Equation 8), and the Lee and Phillips

(2015) KLIC and BIC criteria (Equations 9 and 10). We also report the MSFE of OLS nowcasts

based on the KLIC and BIC criteria. We compare the various lag order selection methods to panel

Mallows model averaging (Equation 6).

Tables A1 to A9 in the Appendix exhibit the MSFEs of the various model selection (and

averaging) methods. To facilitate comparisons between the various methods, we (i) normalize

each MSFE by subtracting off the unforecastable component of the MSFE,2 and (ii) express the

normalized MSFE relative to panel MMA (so that an entry greater than one indicates that panel

MMA had a lower MSFE across the simulations, on average).

The results show that panel MMA generally outperforms the model selection methods. The

advantage of MMA is particularly apparent in panels with moderate n ≥ 50. This result is perhaps

not surprising given that forecast combination methods that penalize the correlation between

forecast errors (such as MMA) require substantively more data in order to accurately estimate the

12pmax (pmax + 1) covariances of the forecast errors. Smith and Wallis (2009) argue that this is the

reason these methods perform poorly in time series applications, which inherently have fewer data

1Greenaway-McGrevy (2019a,c) shows that the maximum permissible rate of expansion in the lag order is just

slower than max(√

n,√T). This lag order selection rule ensures that pmax grows at a rate just above this maximum

permissible rate.2This is the MSFE of an infinitely large model with known (not estimated) parameters.

14

than panel applications.3

Results for the quarterly-to-annual (k = 4) and monthly-to-annual (k = 12) aggregations

are similar to that for the k = 3 case. Namely, panel MMA tends to perform best provided

n ≥ 50, particularly when the serial dependence parameters ρ11 and ρ22 are low. We do not

reports the results here but they are available upon request. For these simulations we consider

n = 25, 50, 100, 200, 400 and T = 5, 10, 20, 40, which corresponds to 5, 10, 20 and 40 years of data

for annual aggregations.

5 Empirical Application: Nowcasting State-Level GDP

In this section we will present a detailed empirical application of our methodology by nowcasting

the real GDP growth rate across the 50 U.S. states using employment data. This is a novel

contribution to the empirical nowcasting literature as all of the aforementioned studies of U.S. real

GDP nowcasting have taken place at a national level (for instance Giannone et al., 2016; Aastveit

et al., 2018; Fosten and Gutknecht, 2019). On the other hand, the ability to produce timely state-

level real GDP nowcasts could be of significant interest to national and regional policymakers.

Similar state-level data for unemployment have been used in a recent paper of Gonzalez-Astudillo

(2019), but this was in the context of using local data to predict national business cycles and not

for the purposes of making nowcasts of state-level GDP.

5.1 Data

Quarterly State-Level GDP Data

The target variable for this study is the real GDP growth rate for all U.S. states. The data are

available at the quarterly frequency, produced by the Bureau of Economic Analysis (BEA),4 and

the time span ranges from 2005Q1 to 2018Q1 for all 50 states. This defines the panel dimensions

3There are some outlying cases when n = 25 in which the relative MSFEs display very large values. In thosecases, panel MMA does particularly well, giving rise to a small number in the denominator of the relative MSFEwhich gives rise to the large entries seen in Tables A7 and A9.

4See https://www.bea.gov/data/gdp/gdp-state. [Last accessed: 25/10/18]

15

for the study as T = 52 and N = 50. In terms of the timeliness of data release, which is of critical

importance for nowcasting, the data for state-level GDP are only available around four to five

months (on average) after the end of the reference quarter. This is a substantial publication lag

relative to the national GDP figures where the preliminary estimate is available less than a month

after the end of the reference quarter. The lack of timely data in this setting gives a strong case

for the use of nowcasting.

Features of the GDP data are displayed in Table 1 which shows the largest and smallest four

states ranked by average real GDP over the sample period. Figure 1 provides a graphical depiction

of the real GDP data whereas Figure 2 shows the quarterly average real GDP growth rate. These

display the disparity in real GDP across states, with California having around 60% higher real

GDP than the next highest, Texas, on average over the sample period and more than 75 times the

real GDP of the lowest state, Vermont.

There is also considerable variability in terms of real GDP growth which can be seen in Figure

2. With the exception of Texas, the rankings in real GDP do not tend to match up with those of

real GDP growth over the sample period. For example, Florida’s growth is near the bottom of the

rankings and North Dakota (not seen in Table 1) is at the top of the GDP growth rankings (5.0%)

while being near the bottom in terms of the level of real GDP ($40bn).

This disparity in the real GDP growth rates across states gives motivation for the inclusion of

fixed effects in nowcasting Equation (1).

Table 1: Largest and Smallest Four States by Real GDP (Average 2005-2018)

State Real GDP ($billion, ann. SA) Real GDP Growth (%)

California 2073.9 1.89Texas 1290.3 3.13New York 1204.0 1.20Florida 770.6 0.69

Montana 38.3 1.73South Dakota 38.1 1.90Wyoming 35.2 1.54Vermont 26.7 0.68

16

Figure 1: Real GDP by State, average over 2005-2018

500

1000

1500

2000

Real GDP ($billion, ann. SA)

Figure 2: Real GDP Growth (%) by State, average over 2005-2018

0

1

2

3

4

5Real GDP Growth (%)

17

Monthly State-Level Employment Data

We will use employment-related series as the main source of predictor variables in the MF-PVAR

analysis. There are several reasons we use these in our analysis. Firstly, employment-type series are

amongst the most commonly-used predictors in previous empirical nowcasting studies. Secondly,

this can serve as a proxy to labour income which is one of the key ingredients of the BEA’s

methodology for constructing state-level GDP data. Finally, there are limited regional data on

other typical nowcast predictors such as industrial production.

The Bureau of Labour Statistics (BLS) produces monthly state-level data for employees on

nonfarm payrolls through the Current Employment Statistics (CES) programme, and state unem-

ployment through the Local Area Unemployment Statistics (LAUS) programme. The fact that

these data are monthly makes them ideal candidates for use in nowcasting. In addition, the data

are released in a much more timely fashion than real GDP, being available around a month and a

half after the end of the reference month. This flow of data, depicted in Figure 3, means that we

have data on all three months of a given quarter well in advance of the same quarter’s GDP data

release. This can allow us to build up an early picture of state-level GDP.

Figure 3: Graphical Illustration of the Data Flow in Nowcasting Q1

Jan Feb Mar Apr May Jun Jul

Data Release:

Q1 Q2

Emp(Dec)

Emp(Jan)

Emp(Feb)

Emp(M

ar)

Emp(Apr)

Emp(M

ay)

Emp(Jun)

GDP(Q

3)

GDP(Q

4)

GDP(Q

1)

5.2 Pseudo Out-of-Sample Set-up

We will perform a pseudo out-of-sample panel nowcast evaluation in the spirit of Diebold and

Mariano (1995) and West (1996). We transform the data to stationarity using the year-on-year

18

growth rates of the series which is the same growth rate as that presented by the BEA.5 This

gives a final time series dimension of T = 49 quarterly observations for real GDP growth (denoted

gdpi,t) and 3T = 147 for the monthly employment and unemployment variables (denoted empi,t

and unemi,t respectively).

To perform the out-of-sample evaluation we split the sample in the time series dimension into

T = R+P observations. We use the first R quarters of the data to make the nowcasts for quarter

R + 1 across the n states and then proceed in a recursive fashion, adding one quarter at a time

and re-estimating the parameters and the nowcasts throughout the sample. As a central scenario,

we start making out-of-sample nowcasts in 2012Q1 which splits the sample equally, giving a total

of P = 25 quarters of evaluation over the n states and an initial estimation window of R = 24

quarters. To assess robustness to the choice of sample split, we will also report present results

where nowcasting commences in 2010Q1 (R = 16, P = 33) and 2014Q1 (R = 32, P = 17). We will

also check robustness to the use of the rolling rather than recursive parameter estimation scheme.

For the endogenous explanatory variables in the MF-PVAR we will try both xi,t := empi,t and

xi,t := unemi,t.6 The lag specification we use will search over models up to pmax = 4 lags to allow

up to annual dynamics. For the BCLS MF-PVAR nowcasts we use three methods: lag selection

using the panel FPE criterion above, the Mallows model averaging method and a bias-corrected

panel VAR(1) which fixes the lag length at p = 1 and does not select lags optimally. In order to

compare BCLS with simple OLS (non-bias corrected) nowcasts, we will also present the MF-PVAR

results where OLS is used with a naıve BIC criterion to select the lag length:

pnbic = arg minp

(ln(σ2 (p)

)+

mp ln(nTpmax )nTpmax

)(11)

which is naıve in the sense that it ignores the impact of fixed effects (c.f. Lee and Phillips, 2015).

We will also report results for three benchmark methods. Firstly, in order to assess the im-

5While this imparts some serial correlation, we allow for this using up to annual lags in the model. We also trieda quarter-on-quarter versus month-on-month version of the models, however the data are quite noisy using thesegrowth rates. Results are available on request.

6Earlier versions of the paper also checked the results when both predictors were used and xi,t :=[empi,t, unemi,t]

′. The results did not improve over the main results and these models involved the estimationof more parameters.

19

portance of the pooled panel approach, we will report results where individual time series OLS

nowcasting regressions are run for each state. This is like an unrestricted version of the MIDAS

model of Clements and Galvao (2008, 2009) and corresponds to estimating Equation (1) state-by-

state instead of pooling across states. Since the sample size for time series regression will be as

low as R = 16, we restrict the number of parameters by fixing the lag length to be p = 1, which we

denote the MIDAS(1) model. Finally, we will use two univariate benchmarks: a panel AR(1) model

with homogeneous AR(1) coefficient estimated by OLS, and a time series AR(1) model which does

not pool the information across states. The AR(1) with no predictors is the most commonly-used

benchmark in nowcasting studies, and we will therefore assess the performance of our methods

relative to the panel and time series version of the AR benchmark.

In measuring the accuracy of the nowcasts across the various competing methods, we will use

the MSFE criterion which averages the squared nowcast errors across the n states and the P

evaluation periods.7 If we generically define ui,t = yi,t − yi,t as the nowcast errors from any of the

above methods, then we calculate MSFE as:

MSFE =1

nP

n∑i=1

T∑t=R+1

u2i,t (12)

We will also explore the results by way of a subgroup analysis, where we restrict the sample of

states to selected groups of size smaller than n. This is to check the impact of the homogeneous

coefficients assumption on the results. The groupings will be discussed in more detail later.

In all cases we use the ‘full information’ nowcast where the data on all variables in Yi,t−1 from

Equation (1) are available to make the nowcast at time period t. In other words we use the last

quarter’s real GDP growth and all months of the current quarter for the monthly variables. This

coincides with the point on Figure 1 at the beginning of the period after the reference quarter, so

this is in fact a ‘backcast’ rather than a ‘nowcast’.

7We do not assess the statistical significance of the MSFE differences between models as in Diebold and Mariano(1995) and West (1996). This is because almost no research has been done into constructing valid critical values inthe context of panel data forecast evaluation. One exception is the recent Working Paper of Timmermann and Zhu(2019) which rules out parameter estimation and is therefore not applicable in our context.

20

5.3 Results: Pseudo Out-of-Sample Nowcast Evaluation

Results across all States

We first present the main set of results where we compare the panel nowcasting methods estimated

on information pooled across all states. The results of the pseudo out-of-sample nowcast evaluation

are displayed in Table 2. This shows the MSFE by model on average across all states, first for

the employment version of the model (top panel) and then for the unemployment version (bottom

panel). Also presented are the relative MSFEs of each method with respect to the panel AR(1)

benchmark. There are several key findings to draw out of these results.

Table 2: MSFE Results - Recursive Estimation

Predictor Variable: empi,t

R = 16, P = 33 R = 24, P = 25 R = 32, P = 17

Panel BCLS MF-PVAR(FPE) 2.204 0.841 2.015 0.844 1.372 0.837MF-PVAR(MMA) 2.204 0.841 2.015 0.844 1.372 0.837MF-PVAR(1) 2.336 0.891 2.176 0.912 1.404 0.856

Panel OLS MF-PVAR(BIC) 2.303 0.878 2.056 0.861 1.408 0.859Panel AR(1) 2.622 1.000 2.387 1.000 1.639 1.000

TS OLS MIDAS(1) 3.036 1.158 2.447 1.025 1.670 1.019AR(1) 2.719 1.037 2.394 1.003 1.643 1.002

Predictor Variable: unemi,t

R = 16, P = 33 R = 24, P = 25 R = 32, P = 17



TS OLS MIDAS(1) 3.098 1.182 2.667 1.117 1.784 1.088AR(1) 2.719 1.037 2.394 1.003 1.643 1.002

Notes: The results for each set of R and P splits has two columns: the first column displays the MSFEof each method and the second column in italics displays the ratio of the MSFE to that of the PanelAR(1) method. A number in italics larger than one means that a given method has performed worsethan the Panel AR(1) method.

We firstly note that the idea of incorporating timely information for nowcasting is important.

We can see from the top panel of Table 2 that the MF-PVAR models with employment have

21

substantially lower MSFE on average than the panel or time series AR(1) versions of the model.

This result is robust to the choice of R and P . On the other hand, looking at the lower panel of

Table 2 we see that the unemployment version of the model fares much worse than the employment

version, relative to the benchmark AR models. This indicates that employment growth provides

a better timely signal than the unemployment rate, and we will focus on these results in what

follows.

In relation to the bias-corrected nowcasts there are two main points to draw out of Table 2. We

firstly note that the appropriate use of model selection or combination is, indeed, important as the

MSFE of the MF-PVAR methods is lower using the panel FPE and MMA methods relative to the

MF-PVAR(1) method which fixes the lag to be p = 1 in all pseudo out-of-sample periods. We also

see that the bias-correction appears to give lower MSFE when using the FPE and MMA methods

relative to the naıve use of OLS with the standard BIC selection criterion. The improvement is

relatively minor, though it is larger when the smaller initial estimation window R = 16 is used.

We expect gains from bias correction to be even larger in other applications where the overall time

series dimension T is yet smaller.

Finally, a very important result is that there appear to be substantial gains from pooling infor-

mation across states in our panel nowcasting approach. The MIDAS(1) model, using employment

information in state-by-state time series regressions, performs poorly even relative to the time

series AR(1) method. This result is particularly evident in the R = 16 case, and illustrates the

benefits from pooling information when the time series dimension is small, rather than attempting

to run time series models with few observations and many parameters.

In addition to displaying the robustness of the results to choice of R and P , in Table 3 we

also report results where we change to the rolling parameter estimation scheme. This is where the

estimation window is held fixed at R time series observations rather than expanding the window

one-by-one as in the recursive scheme. On making this change we see that the results are rather

robust in comparison to Table 2 with only minor changes to the MSFE results. Moreover, the use

of rolling estimation particularly highlights the poor performance of the time series MIDAS-type

22

model which has more than 40% worse MSFE than the panel AR(1) in some cases. This is even

greater than in the case of recursive estimation above, as the estimation window does not grow in

the rolling framework.

Table 3: MSFE Results - Rolling Estimation

Predictor Variable: empi,t

R = 16, P = 33 R = 24, P = 25 R = 32, P = 17



TS OLS MIDAS(1) 3.858 1.430 2.785 1.133 1.832 1.115AR(1) 2.846 1.055 2.451 0.997 1.684 1.025

Predictor Variable: unemi,t

R = 16, P = 33 R = 24, P = 25 R = 32, P = 17



TS OLS MIDAS(1) 4.039 1.498 2.946 1.199 1.990 1.212AR(1) 2.846 1.055 2.451 0.997 1.684 1.025

Notes: Same description as Table 2 where rolling parameter estimation is used instead of recursiveestimation.

State-Level Results

Rather than focussing on the nowcast model performance on average across states, it is interesting

to zoom in to see how the models perform within specific states. To achieve this we can also

compute MSFE results for individual states, acknowledging that this is based on a relatively small

quarterly time series sample. For this reason, we now turn attention to the results with the largest

evaluation window P = 33.

Returning to the four states with highest real GDP from Table 1 above, Table 4 presents

23

the benchmark results as in Table 2 but for these four states.8 We can see that the MF-PVAR

methods (for both BCLS and OLS) provide even more substantial gains over the benchmark AR(1)

predictions than those seen on average in Table 2. Again, we see that lag selection is important

when comparing with the BCLS VAR(1).

Table 4: MSFE Results - Largest 4 States

California Florida New York Texas

Panel BCLS MF-PVAR(FPE) 0.937 0.678 1.135 0.685 1.486 0.757 0.980 0.666MF-PVAR(MMA) 0.937 0.678 1.135 0.685 1.485 0.757 0.980 0.666MF-PVAR(1) 0.833 0.603 1.157 0.699 1.780 0.907 1.193 0.811

Panel OLS MF-PVAR(BIC) 0.967 0.699 1.205 0.727 1.568 0.800 1.001 0.681Panel AR(1) 1.382 1.000 1.657 1.000 1.962 1.000 1.471 1.000

TS OLS MIDAS(1) 1.104 0.799 1.450 0.875 2.222 1.133 1.455 0.989AR(1) 1.356 0.981 1.482 0.894 1.981 1.010 1.590 1.081

Notes: These numbers are the MSFE relative to the Panel AR(1) model with the relative MSFE to thepanel AR(1) in italics. Results are for the model with employment and for R = 16, P = 33 with recursiveestimation.

To give a graphical illustration of this, Figure 4 plots the Californian out-of-sample nowcasts

from the MMA method relative to the panel AR(1) benchmark. This shows how the nowcasting

method tracks real GDP growth in California much better than the naıve AR(1) benchmark,

particularly in picking up the acceleration in GDP growth since 2010.

As final remarks on the state-level results, we see that the MIDAS models do not perform as

badly in some of these larger states as they did on average as in Table 2. They still do not improve

over the nowcasts made from the MF-PVAR models estimated across all states, but this gives a

slight indication that there could be subgroup heterogeneity which we explore in a later section.

Indeed, we can also find individual states where we see even better results such as North Dakota,

which was the state with largest real GDP growth over the whole sample. There are also, of

course, individual states where the nowcasting methods perform worse than the AR(1) benchmark

but these are a minority.9

8The MSFE results for every individual state are not presented here but are available on request9Another possible explanation for this is that our panel methods fix the lag length to be the same across individual

states. If there is heterogeneity in the optimal lag length by state then it is possible that naıve methods dominatein some scenarios.

24

Figure 4: Out-of-Sample Predictions - California

Exogenous National-Level Predictors

It is possible that the nowcasts of real GDP growth across states can be improved by incorporating

variables related to national business cycle movements. Similar arguments are used in a different

context by Koop et al. (2018) who nowcast regional GVA in the U.K. using national GVA. On

the other hand, the opposite approach is taken in the U.S. by Gonzalez-Astudillo (2019) who uses

state-level data to estimate national business cycles.

We therefore add in national real GDP growth as an exogenous variable into the mixed frequency

VAR. This also gives us the opportunity to explore the modified bias correction which holds in the

presence of exogenous predictors, as outlined above. The results are displayed in Table 5 which

contains the MSFE results from Table 2 (excluding the AR(1) methods which do not use any

predictors) for the employment model and for the R = 16, P = 33 case as before, along with the

equivalent results including the exogenous national variable. We see that a lower MSFE is present

when we add in the exogenous national variable, though only by a factor of around 3% to 5%.

25

This indicates that there may be some small gains to be had from adding in national predictors to

regional nowcasting models in the U.S.

Table 5: MSFE Results - Exogenous National GDP

No Exog Exog

Panel BCLS MF-PVAR(FPE) 2.204 2.138MF-PVAR(MMA) 2.204 2.135MF-PVAR(1) 2.336 2.307

Panel OLS MF-PVAR(BIC) 2.303 2.213TS OLS MIDAS(1) 3.036 3.118

Notes: These numbers display the MSFE for the model withemployment and R = 16, P = 33. “No Exog” is the base-line version without exogenous national GDP variable (sameas Table 2) and “Exog” is the version with national GDP. ThePanel and Time Series AR(1) methods are excluded becausethey have the same MSFE across both versions as they do notuse any additional predictors.

Allowing Heterogeneity: Subgroup Pooling versus All-State Pooling

The results of the MF-PVAR nowcasting models up until now have used information pooled across

all n = 50 states under the assumption that each state has homogeneous slope coefficients in

Equations (1) and (2). We also found that it was not advisable to allow heterogeneity by estimating

individual time series equations when the sample size is prohibitively low. In this section we explore

whether there is any merit to pooling across specific subgroups of states, as an intermediate step

between all-state pooling and time series estimation.

In dividing the U.S. states into smaller subgroups there are many possibilities. The first,

and perhaps most obvious, way to categorise is based on geographical regions. We therefore

break down the states into the U.S. Census Bureau’s four census regions: Northeast (n = 9),

Midwest (n = 12), South (n = 16) and West (n = 13).10 Other categorisations we consider are

those discussed in Greenaway-McGrevy and Hood (2019) which are based on states with similar

production characteristics. As such we will look at energy-producing states (n = 7) as well as the

10See: https://www2.census.gov/geo/pdfs/maps-data/maps/reference/us regdiv.pdf [Last accessed: 17/07/2019].

26

so-called “Rust Belt” states (n = 7) which experienced common industrial decline since the 1980’s.

For completeness we will also report an “Other” subgroup (n = 34) which excludes both energy

and Rust Belt states. These groupings are displayed in Table A10 in the Appendix. To avoid only

using pre-determined groups, we will also use a data-driven method suggested by Su et al. (2016)

which identifies latent subgroup structures in panel data using a classifier-Lasso (C-Lasso).

Table 6 displays results from subgroup pooling versus all-state pooling for the model with

employment and recursive estimation with R = 16, P = 33. Specifically, we first estimate the MF-

PVAR models only on the subgroup data and then we report the MSFE measure as an average

over the states in that subgroup. To compare the results to those in Table 2 which uses all-

state pooling, we also compute the average MSFE across the subgroup from the all-state pooling

methods. The relative MSFE of subgroup to all-state pooling appears in the columns in italics

(so an entry greater than one means that all-state pooling had a smaller MSFE than sub-group

pooling for the particular model selection method). The time series methods from the tables above

are not reproduced here as they are the same for subgroup versus all-state pooling.

The striking result from Table 6 is that there appears to be no evidence in favour of using

subgroup pooling as a way to allow for heterogeneity in the coefficients. This result is in favour

of our baseline approach for modelling the panel by pooling across all states with homogeneous

coefficients. In virtually all cases in the top panel, the relative MSFE of subgroup pooling to all-

state pooling is greater than one, indicating that the nowcasts are worse when the model coefficients

are estimated on a restricted subgroup. This seems to indicate that, in relatively small panels like

this, the gains from pooling information across all states appear to outweigh any improvement from

permitting heterogeneity across subgroups. We also note that we find similar results when using

a data-driven selection of the subgroups using the C-Lasso approach of Su et al. (2016) instead of

these pre-determined subgroups.11

In looking across the geographical regions, the worsening from subgroup pooling is lowest in

11Specifically, we find that the C-Lasso approach predominantly picks out a very small subgroup of three energy-producing states when it is used to identify two latent sub-groups: Alaska, North Dakota and Wyoming. Whenwe run the results for this small subgroup the results are poor relative to the all-state pooled results, presumablydue to the very small sample size for estimation. The results are therefore not presented here, but are available onrequest.

27

Table 6: MSFE Results - Subgroup Pooling vs. All-State Pooling

Subgroup Pooling by Geographical Region

Northeast Midwest South West

Panel BCLS MF-PVAR(FPE) 2.844 1.503 3.480 1.252 1.873 1.071 3.013 1.230MF-PVAR(MMA) 2.094 1.107 3.292 1.185 1.841 1.053 2.759 1.127MF-PVAR(1) 2.044 1.053 3.262 1.018 2.007 1.014 2.373 1.056

Panel OLS MF-PVAR(BIC) 2.363 1.224 3.350 1.176 1.928 1.058 2.904 1.097Panel AR(1) 1.993 0.969 3.748 1.007 2.147 1.005 2.652 1.022

Subgroup Pooling by Category

Rust Belt Energy Other



Notes: These numbers display the MSFE by subgroup for the model with employmentand R = 16, P = 33, with the MF-PVAR methods estimated only using data from thatthat subgroup. The column in italics represents the MSFE of the subgroup poolingrelative to the MSFE of all-state pooling in the PVARs.

the South, which is the region with the largest number of states. This also gives evidence that

pooling across a large estimation sample size is more important than allowing heterogeneity in this

example. In the second panel, for rust belt and energy-producing states a similar story emerges,

although for the “Other” category the best method (MMA) is actually 3% better relative to all-

state pooling. As a final extension to explore subgroup pooling, we added in the inflation in the

West Texas Intermediate (WTI) crude oil price as an exogenous variable into the MF-PVAR for

energy-producing states to see if this yielded any MSFE improvements.12 However, we did not find

any consistent improvements in adding this as an exogenous predictor and so we do not pursue

this further.13

12Data accessed from FRED Economic Data: https://fred.stlouisfed.org/series/DCOILWTICO [Last Accessed:17/07/2019]

13The results are omitted here for the sake of brevity, but are available upon request.

28

6 Conclusion

In this paper, we look to shift the attention of the existing nowcasting literature away from time

series methods to the panel data context. This allows us to perform near-term prediction of regional

or sectoral data which typically suffer from even worse issues with data timeliness than national

aggregate data such as real GDP.

We propose a mixed-frequency panel VAR approach to nowcasting. We estimate the model

using a bias-corrected least squares approach and suggest several model selection and combination

methods, building on recent panel forecasting research by Greenaway-McGrevy (2019a,b,c). We are

careful to demonstrate, though Monte Carlo simulation, the effectiveness of these methods relative

to naıve benchmarks. We apply our methods to the case of U.S. state-level GDP nowcasting. This

yields further insights than previous national studies, such as the sizeable gains from nowcasting

in large states such as California. We envisage many further possible applications of our methods,

such as the prediction of sectoral GDP or nowcasting multiple different proxies for inflation.

Further work may look to enhance this panel nowcast model specification by allowing factors

to be estimated from a large set of external (time series) variables, or to estimate a common factor

from the panel of endogenous variables itself. This would extend existing factor-based time series

nowcasting methods (see: Giannone et al., 2008; Banbura et al., 2013; Antolin Diaz et al., 2017;

Fosten and Gutknecht, 2019) to the panel data context.

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7 Appendix

7.1 Graphs of Real GDP and Employment Growth

Figure 5: Real GDP and Employment Growth

34

Figure 6: Real GDP and Employment Growth

35

7.2 Monte Carlo Simulation Results

Table A1: Simulation Results ρ11 = 0.2, ρ22 = 0.2

n T pmax Kmax MMA PFPE PMal KLIC BIC KLICols BICols

25 20 5 20 1 1.095 1.050 0.975 0.971 1.005 0.99940 6 24 1 1.080 1.072 1.023 1.008 1.044 1.01880 9 36 1 1.124 1.138 1.055 1.323 1.076 1.323160 13 52 1 1.040 1.040 1.032 1.200 1.048 1.208

50 20 7 28 1 1.127 1.058 0.973 0.969 1.018 1.01140 7 28 1 1.075 1.069 1.050 1.054 1.092 1.07980 9 36 1 1.023 1.020 1.022 1.255 1.022 1.260160 13 52 1 1.063 1.048 1.052 1.946 1.065 1.953

100 20 10 40 1 1.202 1.123 0.975 0.975 1.005 1.00540 10 40 1 1.060 1.054 1.082 1.089 1.107 1.10680 10 40 1 1.004 1.000 1.008 1.280 1.049 1.297160 13 52 1 1.027 1.012 0.975 0.999 0.999 1.013

200 20 10 40 1 1.142 1.073 0.996 0.996 1.033 1.03340 14 56 1 1.030 1.025 1.071 1.075 1.091 1.09380 14 56 1 0.999 0.998 0.985 1.152 1.007 1.169160 14 56 1 1.021 1.018 1.019 1.008 1.044 1.030

400 20 10 40 1 1.137 1.070 1.001 1.001 1.038 1.03840 20 80 1 1.156 1.101 1.052 1.052 1.073 1.07380 20 80 1 1.000 0.999 0.985 1.009 1.007 1.029160 20 80 1 0.999 0.999 0.998 0.997 1.009 1.007

Notes: Here Kmax represents the total number of parameters in the model and is given byKmax = 4pmax for the quarterly-to-monthly aggregation frequency. MSFEs are normalized andexpressed as ratio to panel MMA (i.e. a ratio > 1 denotes panel MMA had a smaller MSFE).PFPE and PMal denote lag selection by Panel FPE and Panel Mallows. KLIC and BIC denoteslag selection by Lee and Phillips panel KLIC and BIC. KLICOLS and BICOLS denote Lee andPhillips KLIC and BIC lag selection but with the forecasting model fitted by OLS (not BCLS).

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25 20 5 20 1 1.141 1.079 1.034 1.007 1.075 1.03640 6 24 1 1.275 1.207 1.116 1.422 1.196 1.45180 9 36 1 0.999 0.992 0.985 1.554 0.991 1.549160 13 52 1 0.995 0.997 0.968 1.083 0.979 1.090

50 20 7 28 1 1.179 1.109 1.054 1.058 1.105 1.10940 7 28 1 1.060 1.056 1.058 1.296 1.092 1.30980 9 36 1 0.993 0.986 0.929 1.145 0.974 1.170160 13 52 1 1.175 1.219 0.987 0.835 0.903 0.740

100 20 10 40 1 1.157 1.087 1.049 1.049 1.087 1.08640 10 40 1 1.005 1.002 1.030 1.397 1.081 1.42780 10 40 1 1.000 0.994 0.983 0.981 1.027 1.019160 13 52 1 0.924 0.936 0.918 0.936 0.885 0.937

200 20 10 40 1 1.167 1.108 1.085 1.085 1.126 1.12640 14 56 1 0.997 0.981 1.049 1.363 1.090 1.38780 14 56 1 1.002 1.001 0.992 0.986 1.012 1.004160 14 56 1 1.007 1.007 1.007 1.005 1.025 1.018

400 20 10 40 1 1.152 1.103 1.088 1.088 1.127 1.12740 20 80 1 1.086 1.045 1.219 1.285 1.237 1.29980 20 80 1 1.004 1.002 0.998 0.998 1.029 1.027160 20 80 1 0.995 0.994 1.000 1.030 1.016 1.039

Notes: Same as for Table A1.

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25 20 5 20 1 1.148 1.110 1.114 1.183 1.162 1.21840 6 24 1 1.037 1.029 0.990 1.332 1.038 1.35480 9 36 1 0.998 0.934 0.877 0.860 0.926 0.902160 13 52 1 1.068 1.058 1.017 0.937 1.041 0.950

50 20 7 28 1 1.104 1.067 1.233 1.393 1.311 1.44740 7 28 1 1.036 1.029 0.998 1.089 1.069 1.14480 9 36 1 0.997 1.002 0.996 0.997 1.007 1.001160 13 52 1 1.180 1.160 1.140 1.220 1.175 1.233

100 20 10 40 1 1.194 1.105 1.305 1.325 1.346 1.36340 10 40 1 1.019 1.006 0.977 0.984 1.039 1.04480 10 40 1 1.013 1.006 0.996 0.979 1.046 1.020160 13 52 1 1.092 1.095 1.032 1.035 1.071 1.056

200 20 10 40 1 1.117 1.045 1.347 1.359 1.398 1.40840 14 56 1 1.025 1.013 0.984 0.984 1.032 1.03180 14 56 1 1.003 1.005 1.021 1.026 1.054 1.054160 14 56 1 1.008 1.009 1.023 1.117 1.046 1.136

400 20 10 40 1 1.120 1.055 1.393 1.398 1.440 1.44440 20 80 1 1.156 1.097 0.939 0.939 0.993 0.99380 20 80 1 1.005 1.004 1.019 1.016 1.051 1.044160 20 80 1 0.996 0.997 0.992 1.056 1.005 1.066


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25 20 5 20 1 1.120 1.102 1.047 1.051 1.104 1.08240 6 24 1 1.191 1.165 0.986 1.779 1.134 1.85080 9 36 1 1.070 1.014 0.976 1.601 0.983 1.592160 13 52 1 1.024 1.022 1.009 0.960 1.026 0.974

50 20 7 28 1 1.166 1.094 1.078 1.095 1.152 1.14040 7 28 1 1.058 1.051 1.008 1.300 1.050 1.31780 9 36 1 1.048 1.047 1.004 1.052 1.045 1.084160 13 52 1 2.195 2.283 1.536 1.300 1.075 0.901

100 20 10 40 1 1.165 1.084 1.093 1.092 1.136 1.13140 10 40 1 1.027 1.013 0.984 1.218 1.050 1.27280 10 40 1 1.036 1.041 1.038 0.992 1.085 1.036160 13 52 1 0.975 0.962 0.928 0.687 0.870 0.686

200 20 10 40 1 1.165 1.096 1.160 1.162 1.209 1.21040 14 56 1 1.015 1.001 0.975 1.054 1.030 1.10680 14 56 1 1.021 1.020 1.012 1.012 1.033 1.030160 14 56 1 1.011 1.010 1.007 1.042 1.028 1.057

400 20 10 40 1 1.144 1.090 1.167 1.167 1.211 1.21040 20 80 1 1.115 1.060 0.976 1.069 1.015 1.10580 20 80 1 1.013 1.012 1.031 1.030 1.065 1.061160 20 80 1 0.993 0.993 0.994 1.094 1.011 1.106


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25 20 5 20 1 1.178 1.117 1.076 1.084 1.145 1.12140 6 24 1 1.047 1.047 1.058 1.355 1.115 1.38880 9 36 1 1.053 1.047 1.040 1.117 1.050 1.125160 13 52 1 0.684 0.671 0.636 1.313 0.466 1.108

50 20 7 28 1 1.140 1.093 1.120 1.130 1.166 1.16640 7 28 1 1.060 1.044 1.023 1.212 1.071 1.24680 9 36 1 1.039 1.033 0.976 0.977 1.035 1.020160 13 52 1 1.030 1.032 1.033 1.044 1.046 1.050

100 20 10 40 1 1.146 1.083 1.168 1.171 1.202 1.20540 10 40 1 1.032 1.030 1.001 1.115 1.047 1.15380 10 40 1 1.003 1.004 1.009 1.015 1.032 1.032160 13 52 1 1.015 1.009 1.004 1.073 1.017 1.083

200 20 10 40 1 1.180 1.102 1.196 1.196 1.249 1.25040 14 56 1 1.025 1.012 0.975 1.008 1.027 1.06180 14 56 1 1.011 1.009 1.027 1.034 1.063 1.057160 14 56 1 1.013 1.012 0.998 1.104 1.028 1.128

400 20 10 40 1 1.117 1.065 1.233 1.233 1.276 1.27640 20 80 1 1.115 1.073 0.968 1.054 1.020 1.10480 20 80 1 0.993 0.991 1.023 1.065 1.070 1.104160 20 80 1 1.009 1.012 1.001 1.049 1.049 1.091


40



25 20 5 20 1 1.121 1.069 1.064 1.378 1.146 1.42240 6 24 1 1.223 1.194 1.058 1.267 1.224 1.37080 9 36 1 1.098 1.070 1.022 1.045 1.013 1.039160 13 52 1 0.976 0.977 0.967 1.132 1.010 1.150

50 20 7 28 1 1.164 1.084 1.075 1.459 1.202 1.54840 7 28 1 1.074 1.054 1.019 1.013 1.071 1.05680 9 36 1 1.070 1.060 1.029 1.053 1.086 1.090160 13 52 1 1.510 1.411 1.228 3.748 1.150 3.554

100 20 10 40 1 1.125 1.047 1.250 1.522 1.334 1.58340 10 40 1 1.039 1.032 1.014 1.022 1.100 1.09780 10 40 1 1.002 1.002 1.005 1.180 1.062 1.228160 13 52 1 0.952 0.956 0.994 0.439 0.928 0.386

200 20 10 40 1 1.134 1.066 1.352 1.655 1.449 1.73340 14 56 1 1.017 1.002 1.024 1.026 1.087 1.08780 14 56 1 1.001 0.998 0.994 1.107 1.024 1.134160 14 56 1 1.005 1.004 1.001 0.994 1.023 1.014

400 20 10 40 1 1.124 1.079 1.263 1.512 1.359 1.59340 20 80 1 1.105 1.064 1.003 1.003 1.047 1.04780 20 80 1 1.003 1.001 0.999 1.093 1.052 1.140160 20 80 1 1.009 1.006 0.994 1.005 1.015 1.023


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25 20 5 20 1 1.132 1.064 0.997 1.302 1.132 1.39940 6 24 1 1.083 1.075 1.026 1.033 1.094 1.09680 9 36 1 1.099 1.085 1.057 1.024 1.076 1.039160 13 52 1 12.166 13.631 10.411 29.163 14.307 34.874

50 20 7 28 1 1.091 1.04 0.993 1.203 1.108 1.29840 7 28 1 1.042 1.036 1.038 1.04 1.107 1.10580 9 36 1 1.024 1.026 1.026 1.122 1.071 1.162160 13 52 1 1.033 1.032 1.032 1.281 1.055 1.287

100 20 10 40 1 1.12 1.061 1.023 1.248 1.141 1.35140 10 40 1 1.067 1.071 1.059 1.06 1.134 1.13380 10 40 1 1.008 1.005 1.01 1.089 1.038 1.113160 13 52 1 1.008 1.008 0.993 1.072 1.01 1.081

200 20 10 40 1 1.109 1.063 0.99 1.026 1.163 1.19640 14 56 1 1.077 1.067 1.055 1.055 1.135 1.13480 14 56 1 1.003 1.005 1.01 1.175 1.063 1.216160 14 56 1 1.005 1.005 1.009 1.021 1.04 1.042

400 20 10 40 1 1.097 1.062 0.998 0.998 1.145 1.14540 20 80 1 1.116 1.078 1.036 1.036 1.113 1.11380 20 80 1 1.002 0.998 0.987 1.104 1.049 1.159160 20 80 1 1.003 1.004 1.02 1.083 1.102 1.147


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25 20 5 20 1 1.115 1.079 1.062 1.322 1.163 1.38440 6 24 1 1.045 1.039 1.018 1.073 1.085 1.13380 9 36 1 1.061 1.064 1.083 1.087 1.184 1.174160 13 52 1 1.057 1.041 1.052 1.278 1.120 1.321

50 20 7 28 1 1.112 1.059 1.066 1.381 1.183 1.45140 7 28 1 1.052 1.046 1.020 1.003 1.092 1.06880 9 36 1 1.026 1.019 1.042 1.136 1.051 1.145160 13 52 1 1.007 1.003 0.989 1.131 1.008 1.142

100 20 10 40 1 1.131 1.044 1.237 1.524 1.343 1.59140 10 40 1 1.052 1.040 1.040 1.052 1.116 1.12480 10 40 1 1.016 1.016 1.010 1.114 1.048 1.145160 13 52 1 1.008 1.008 1.003 1.049 1.021 1.068

200 20 10 40 1 1.129 1.080 1.257 1.560 1.407 1.66840 14 56 1 1.039 1.031 1.056 1.058 1.148 1.14780 14 56 1 1.011 1.008 1.010 1.110 1.046 1.142160 14 56 1 1.005 1.005 1.003 1.014 1.019 1.025

400 20 10 40 1 1.090 1.054 1.166 1.411 1.305 1.52140 20 80 1 1.115 1.073 1.033 1.033 1.110 1.10980 20 80 1 1.014 1.011 0.998 1.037 1.057 1.096160 20 80 1 1.007 1.007 1.006 1.012 1.029 1.032


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25 20 5 20 1 1.134 1.052 1.013 1.424 1.168 1.52940 6 24 1 1.061 1.046 1.043 1.023 1.118 1.08880 9 36 1 1.047 1.043 1.048 1.127 1.065 1.142160 13 52 1 3.010 2.681 1.853 7.473 2.629 8.593

50 20 7 28 1 1.095 1.042 1.001 1.275 1.137 1.39040 7 28 1 1.065 1.057 1.046 1.088 1.122 1.16080 9 36 1 1.027 1.020 0.985 1.181 1.035 1.234160 13 52 1 1.036 1.035 1.025 1.113 1.048 1.134

100 20 10 40 1 1.110 1.059 1.094 1.477 1.227 1.58540 10 40 1 1.023 1.026 1.055 1.150 1.164 1.24280 10 40 1 1.006 1.002 0.989 1.072 1.021 1.102160 13 52 1 1.015 1.016 1.020 1.011 1.037 1.022

200 20 10 40 1 1.099 1.049 1.001 1.160 1.187 1.33640 14 56 1 1.029 1.017 1.066 1.149 1.176 1.24580 14 56 1 1.012 1.009 1.014 1.022 1.071 1.073160 14 56 1 1.004 1.002 1.008 1.051 1.042 1.076

400 20 10 40 1 1.061 1.032 0.998 1.011 1.163 1.17540 20 80 1 1.109 1.071 1.109 1.129 1.204 1.22180 20 80 1 1.006 1.005 1.008 1.008 1.083 1.082160 20 80 1 1.021 1.022 1.023 1.160 1.103 1.233


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7.3 Additional Empirical Tables

Table A10: Subgroup Categories for States

Subgroups States

Rust Belt Illinois, Indiana, Michigan, Ohio, Pennsylvania, West Virginia,Wisconsin

Energy-producing Alaska, Colorado, Louisiana, North Dakota, Oklahoma, Texas,Wyoming

Northeast Connecticut, Maine, Massachusetts, New Hampshire, New Jersey,New York, Pennsylvania, Rhode Island, Vermont

Midwest Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota, Missouri,Nebraska, North Dakota, Ohio, South Dakota, Wisconsin

South Alabama, Arkansas, Delaware, Florida, Georgia, Kentucky,Louisiana, Maryland, Mississippi, North Carolina, Oklahoma,South Carolina, Tennessee, Texas, Virginia, West Virginia

West Alaska, Arizona, California, Colorado, Hawaii, Idaho, Montana,Nevada, New Mexico, Oregon, Utah, Washington, Wyoming

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