Estimating and Forecasting with a Dynamic Spatial Panel Data Model*
| Author | Badi H. Baltagi,Bernard Fingleton,Alain Pirotte |
| Published date | 01 February 2014 |
| DOI | http://doi.org/10.1111/obes.12011 |
| Date | 01 February 2014 |
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©2013 The Department of Economics, University of Oxford and John Wiley& Sons Ltd.
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 76, 1 (2014) 0305-9049
doi: 10.1111/obes.12011
Estimating and Forecasting with a Dynamic Spatial
Panel Data ModelÅ
Badi H. Baltagi†, Bernard Fingleton‡ and Alain Pirotte§,¶
†Department of Economics and Center for Policy Research, Syracuse University, Syracuse, NY,
USA (e-mail: bbaltagi@maxwell.syr.edu)
‡Department of Land Economy, University of Cambridge, Cambridge, UK
(e-mail: bf100@cam.ac.uk)
§ERMES (CNRS), University of Panthéon-Assas Paris II/Sorbonne University, Paris, France
(e-mail: alain.pirotte@u-paris2.fr)
¶IFSTTAR-DEST, French Institute of Science and Technology for Transport, Development
and Networks, Noisy-le-Grand, France (e-mail: alain.pirotte@ifsttar.fr)
Abstract
This study focuses on the estimation and predictive performance of several estimators
for the dynamic and autoregressive spatial lag panel data model with spatially correlated
disturbances. In the spirit of Arellano and Bond (1991) and Mutl (2006), a dynamic spatial
generalized method of moments (GMM) estimator is proposed based on Kapoor, Kelejian
and Prucha (2007) for the spatial autoregressive (SAR) error model. The main idea is to
mix non-spatial and spatial instruments to obtain consistent estimates of the parameters.
Then, a linear predictor of this spatial dynamic model is derived. Using Monte Carlo sim-
ulations, we compare the performance of the GMM spatial estimator to that of spatial and
non-spatial estimators and illustrate our approach with an application to new economic
geography.
I. Introduction
This study considers spatial panel data models in which there is variation across time and
space involving simultaneous spatial (network) dependence together with dynamic inter-
action. Spatial dependence models are popular in regional science and urban economics,
where the cross-sectional units are typically locations (cities, countries, regions) which are
affected by common factors or spillover effects from neighbouring locations. Forecasting
studies using spatial panel data models are rare, and those involving forecasting with a
dynamic component are almost absent from the literature. Recently, Baltagi and Pirotte
ÅThis paper was presented at the Economics Seminar Series, Strathclyde University, Glasgow, Scotland, 30 March
2011. Also, at the Vth Conference of the Spatial EconometricsAssociation, Toulouse University, France, 6–8 July,
2011. We would like to thank Patrick Sevestre, the participants of this seminar and this conference for their useful
comments and suggestions, and also the referees and editor of the journal, Anindya Banerjee, for their help and
advice.
JEL Classification number: C33.
Dynamic spatial Panels 113
(2010) showed that tests of hypotheses based on the usual panel data estimators that ignore
spatial dependence can produce misleading inference.
For dynamic panel data models with no spatial autocorrelation, it is well known that
the ordinary least squares (OLS) estimator is biased (see Trognon, 1978; Sevestre and
Trognon, 1983, 1985). Also, the fixed effects estimator is biased (see Nickell, 1981;
Kiviet, 1995). Anderson and Hsiao (1981, 1982) proposed an IV estimator which is con-
sistent. Subsequent developments focused on generalized method of moments (GMM)
estimators including Arellano and Bond (1991) and Blundell and Bond (1998) to mention
just a few. See Blundell, Bond andWindmeijer (2000), Arellano and Honor´e (2001), Hsiao
(2003), Harris et al. (2008) and Baltagi (2008) for good reviews and a textbook treatment
of this subject.
Spatial dependence models deal with spatial interaction and spatial heterogeneity (see
Anselin, 1988; LeSage and Pace, 2009). The structure of the spatial dependence can be
related to location and distance, both in a geographical space as well as a more general
economic or social network space (seeAnselin, Le Gallo and Jayet, 2008). Typically, cross-
section dependence is modelled as proportional to some observable distance (see Anselin,
1988; LeSage and Pace, 2009) introduced through an endogenous spatial lag variable or via
spatially correlated disturbances, or both. Combining cross-section dependence with auto-
regressive (temporal) dependence leads us to Elhorst (2005), who derives a maximum like-
lihood estimator (MLE).Another way to estimate autoregressive models with spatial depen-
dence is to extend the GMM approach to the spatial case in order to obtain consistent param-
eter estimates. Jacobs, Ligthart and Vrijburg(2009) focus on a dynamic autoregressive fixed
effects model which includes the spatial lag of the dependent variable together with spa-
tially correlated disturbances. They propose a three-step GMM approach. Elhorst (2010)
considers the same model except that the disturbances are not spatially autocorrelated. He
develops Bias-corrected least squares dummy variables (BCLSDV), unconditional ML and
GMM estimators. Mutl (2006) mixes the Arellano and Bond (1991) and Kapoor, Kelejian
and Prucha (2007) approaches to estimate a dynamic model with spatially correlated distur-
bances under less restrictive assumptions. Yu, de Jong and Lee (2008) propose a quasi max-
imum likelihood estimator (QMLE) for spatial dynamic panel data with fixed effects when
both Nand Tare large. Lee andYu (2010 a,b) extend this approach under different assump-
tions about Nand T. Kukenova and Monteiro (2009) consider a system-GMM to estimate
a dynamic spatial panel model (i.e. first order spatial autoregressive panel data model).
They compare its properties with those of the usual estimators (MLE, QMLE, LSDV, etc.).
In this study, we propose a spatial GMM estimator in the spirit of Arellano and Bond
(1991) and Mutl (2006) under the assumptions that the model includes temporal and spa-
tial lags on the endogenous variable together with SAR-RE disturbances. Only a few
articles study the predictive performance of spatial panel models. Baltagi and Li (2006),
Fingleton (2009, 2010) and Baltagi, Bresson and Pirotte (2012) focus on the particular
case of a static model under spatially correlated disturbances. In contrast, Longhi and
Nijkamp (2007) and Kholodilin, Siliverstovs and Kooths (2008) use dynamic spatial mod-
els. Longhi and Nijkamp (2007) compare different models designed to compute short-term
ex post forecasts of regional employment in a panel of 326 West German regions observed
over the period from 1987 to 2002. They show that forecasts can be improved by sim-
ply taking into account the distances across regions. Nevertheless, this study is specific
©2013 The Department of Economics, University of Oxford and John Wiley & Sons Ltd.
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