Abstract
A panel data regression model with heteroskedastic as well as spatially correlated disturbances is considered, and a joint LM test for homoskedasticity and no spatial correlation is derived. In addition, a conditional LM test for no spatial correlation given heteroskedasticity, as well as a conditional LM test for homoskedasticity given spatial correlation, are also derived. These LM tests are compared with marginal LM tests that ignore heteroskedasticity in testing for spatial correlation, or spatial correlation in testing for homoskedasticity. Monte Carlo results show that these LM tests, as well as their LR counterparts, perform well, even for small N and T . However, misleading inferences can occur when using marginal, rather than joint or conditional LM tests when spatial correlation or heteroskedasticity is present.
Highlights
The standard error component panel data model assumes that the disturbances have homoskedastic variances and no spatial correlation, see Hsiao (2003) and Baltagi (2005)
We do not explicitly derive the asymptotic distribution of our test statistics, they are likely to hold under a similar set of primitive assumptions developed by Kelejian and Prucha (2001)
The experimental design for the Monte Carlo simulations is based on the format extensively used in earlier studies in the spatial regression model by Anselin and Rey (1991) and Anselin and Florax (1995), and in the heteroskedastic panel data model by Roy (2002)
Summary
The standard error component panel data model assumes that the disturbances have homoskedastic variances and no spatial correlation, see Hsiao (2003) and Baltagi (2005). For a joint test of the absence of spatial correlation and random effects in a panel data model, see Baltagi, Song and Koh (2003) These tests ignore the heteroskedasticity in the disturbances. On the other hand, Holly and Gardiol (2000) derived an LM statistic which tests for homoskedasticity of the disturbances in the context of a one-way random effects panel data model This LM test ignores the spatial correlation in the disturbances. This paper extends the Holly and Gardiol (2000) model to allow for spatial correlation in the remainder disturbances It derives a joint LM test for homoskedasticity and no spatial correlation.
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