Abstract
This paper considers various estimators using panel data seemingly unrelated regressions (SUR) with spatial error correlation. The true data generating process is assumed to be SUR with spatial error of the autoregressive or moving average type. Moreover, the remainder term of the spatial process is assumed to follow an error component structure. Both maximum likelihood and generalized moments (GM) methods of estimation are used. Using Monte Carlo experiments, we check the performance of these estimators and their forecasts under misspecification of the spatial error process, various spatial weight matrices, and heterogeneous versus homogeneous panel data models.
Highlights
Since Zellner’s (1962) seminal paper on seemingly unrelated regressions (SUR) analyzing multiple equations with correlated disturbances, various extensions have been proposed, for e.g., to deal with the serially correlated case, the nonlinear case, the misspecified case, and SUR with unequal number of observations, see Srivastava and Dwivedi (1979).1 Of particular interest for this paper are the extensions of SUR to panel data utilizing the error component model, see Avery (1977), Baltagi (1980), Magnus (1982) and Prucha (1984) to mention a few
Some applications of SUR panel data with error components include Verbon (1980) who estimated a set of four labor demand equations, using data from the Netherlands on 18 industries over 10 semiannual periods covering the period 1972-79; Beierlein, Dunn and McConnon (1981) who estimated six equations describing the demand for electricity and natural gas in the northeastern United States using data on nine states comprising the Census Bureau’s northeastern region of the USA for the period 1967-77; Brown, Kleidon and Marsh (1983) who studied the size-related anomalies in stock returns using a panel of 566 firms observed quarterly over the period June 1967 to December 1975; Howrey and Varian (1984) who estimated a system of demand equations for electricity by time of day
It combines the simplicity of dealing with heterogeneity in the panel using an error component model and spatial correlation using a spatial autoregressive (SAR) or spatial moving average (SMA) disturbances
Summary
Since Zellner’s (1962) seminal paper on seemingly unrelated regressions (SUR) analyzing multiple equations with correlated disturbances, various extensions have been proposed, for e.g., to deal with the serially correlated case, the nonlinear case, the misspecified case, and SUR with unequal number of observations, see Srivastava and Dwivedi (1979). Of particular interest for this paper are the extensions of SUR to panel data utilizing the error component model, see Avery (1977), Baltagi (1980), Magnus (1982) and Prucha (1984) to mention a few. This paper extends Anselin’s (1988a,b) SUR spatial model to the panel data case This more general model allows for correlation across space, time and equations. It combines the simplicity of dealing with heterogeneity in the panel using an error component model and spatial correlation using a spatial autoregressive (SAR) or spatial moving average (SMA) disturbances. In this context, Wang and Kockelman (2007) derived the maximum likelihood estimator (under the normality assumption) of a SUR error component panel data model with SAR disturbances.
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