Abstract
The spatial Mundlak model first considered by Debarsy (2012) is an alternative to fixed effects and random effects estimation for spatial panel data models. Mundlak modelled the correlated random individual effects as a linear combination of the averaged regressors over time plus a random time-invariant error. This paper shows that if spatial correlation is present whether spatial lag or spatial error or both, the standard Mundlak result in panel data does not hold and random effects does not reduce to its fixed effects counterpart. However, using maximum likelihood one can still estimate these spatial Mundlak models and test the correlated random effects specification of Mundlak using Likelihood ratio tests as demonstrated by Debarsy for the Mundlak spatial Durbin model.
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Notes
Note that (Debarsy 2012) SDM does not have a spatial error model in the remainder disturbance and hence does not nest the SEM considered in this paper.
The same result, i.e., OLS is not equivalent to GLS can be similarly shown for the correlated random effects spatial Mundlak model when the remainder disturbance in SEM is a spatial moving average. This is not shown here to save space.
As an extension to this work, (Baltagi et al. 2003) derived the joint LM test for spatial error correlation as well as random country effects. Additionally, they derived conditional LM tests, which test for random country effects given the presence of spatial error correlation. Also, spatial error correlation given the presence of random country effects.
It is important to note that direct and indirect effects can be computed as described in LeSage and Pace (2009), Elhorst (2014), Debarsy (2012) and computed using Stata’s command xsmle by Belotti et al. (2017). These results were not reported here as the purpose of this application is to demonstrate the difference between fixed effects spatial and Mundlak random effects spatial models.
References
Anselin L (1988) Spatial econometrics: methods and models. Kluwer Academic Publishers, Dordrecht
Baltagi BH (2021) Econometric analysis of panel data, 6th edn. Springer, Switzerland
Baltagi BH (2006) An alternative derivation of Mundlak’s fixed effects results using system estimation. Econometr Theory 22:1191–1194
Baltagi BH, Song SH, Koh W (2003) Testing panel data regression models with spatial error correlation. J Econometr 117:123–150
Belotti F, Hughes G, Piano Mortari A (2017) Spatial panel data models using Stata. Stata J 17(1):139–180
Debarsy N (2012) The Mundlak approach in the spatial Durbin panel data model. Spatial Econ Anal 7:109–131
Elhorst JP (2014) Spatial econometrics: from cross-sectional data to spatial panels. Springer, Heidelberg
LeSage JP, Pace RK (2009) Introduction to spatial econometrics. Taylor & Francis, Boca Raton
Mundlak Y (1978) On the pooling of time series and cross-section data. Econometrica 46:69–85
Wansbeek TJ, Kapteyn A (1982) A simple way to obtain the spectral decomposition of variance components models for balanced data. Commun Statist A11:2105–2112
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Baltagi, B.H. The Mundlak spatial estimator. J Spat Econometrics 4, 6 (2023). https://doi.org/10.1007/s43071-023-00037-y
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DOI: https://doi.org/10.1007/s43071-023-00037-y