Testing for Serial Correlation, Spatial Autocorrelation and Random Effects

This paper considers a spatial panel data regression model with serial correlation on each spatial unit over time as well as spatial dependence between the spatial units at each point in time. In addition, the model allows for heterogeneity across the spatial units using random effects. The paper then derives several Lagrange Multiplier tests for this panel data regression model including a joint test for serial correlation, spatial autocorrelation and random effects. These tests draw upon two strands of earlier work. The first is the LM tests for the spatial error correlation model discussed in Anselin and Bera (1998) and in the panel data context by Baltagi, Song and Koh (2003). The second is the LM tests for the error component panel data model with serial correlation derived by Baltagi and Li (1995). Hence the joint LM test derived in this paper encompasses those derived in both strands of earlier works. In fact, in the context of our general model, the earlier LM tests become marginal LM tests that ignore either serial correlation over time or spatial error correlation. The paper then derives conditional LM and LR tests that do not ignore these correlations and contrast them with their marginal LM and LR counterparts. The small sample performance of these tests is investigated using Monte Carlo experiments. As expected, ignoring any correlation when it is significant can lead to misleading inference.panel data, spatial correlation

Testing Panel Data Regression Models with Spatial Error Correlation

This paper derives several Lagrange Multiplier tests for the panel data regression model with spatial error correlation. These tests draw upon two strands of earlier work. The first is the LM tests for the spatial error correlation model discussed in Anselin (1988, 1999) and Anselin, Bera, Florax and Yoon (1996), and the second is the LM tests for the error component panel data model discussed in Breusch and Pagan (1980) and Baltagi, Chang and Li (1992). The idea is to allow for both spatial error correlation as well as random region effects in the panel data regression model and to test for their joint significance. Additionally, this paper derives conditional LMtests, which test for random regional effects given the presence of spatial error correlation. Also, spatial error correlation given the presence of random regional effects. These conditional LM tests are an alternative to the one directional LM tests that test for random regional effects ignoring the presence of spatial error correlation or the one directional LM tests for spatial error correlation ignoring the presence of random regional effects. We argue that these joint and conditional LM tests guard against possible misspecification. Extensive Monte Carlo experiments are conducted to study the performance of these LM tests as well as the corresponding Likelihood Ratio tests.Panel data; Spatial error correlation, Lagrange Multiplier tests, Likelihood Ratio tests

Testing for Serial Correlation, Spatial Autocorrelation and Random Effects

This paper considers a spatial panel data regression model with serial correlation on each spatial unit over time as well as spatial dependence between the spatial units at each point in time. In addition, the model allows for heterogeneity across the spatial units using random effects. The paper then derives several Lagrange Multiplier tests for this panel data regression model including a joint test for serial correlation, spatial autocorrelation and random effects. These tests draw upon two strands of earlier work. The first is the LM tests for the spatial error correlation model discussed in Anselin and Bera (1998) and in the panel data context by Baltagi, Song and Koh (2003). The second is the LM tests for the error component panel data model with serial correlation derived by Baltagi and Li (1995). Hence the joint LM test derived in this paper encompasses those derived in both strands of earlier works. In fact, in the context of our general model, the earlier LM tests become marginal LM tests that ignore either serial correlation over time or spatial error correlation. The paper then derives conditional LM and LR tests that do not ignore these correlations and contrast them with their marginal LM and LR counterparts. The small sample performance of these tests is investigated using Monte Carlo experiments. As expected, ignoring any correlation when it is significant can lead to misleading inferencepanel data, spatial correlation

Testing for Heteroskedasticity and Spatial Correlation in a Random Effects Panel Data Model

A panel data regression model with heteroskedastic as well as spatially correlated disturbance 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 inference can occur when using marginal rather than joint or conditional LM tests when spatial correlation or heteroskedasticity is present

Testing for Heteroskedasticity and Serial Correlation in a Random Effects Panel Data Model

This paper considers a panel data regression model with heteroskedastic as well as serially correlated disturbances, and derives a joint LM test for homoskedasticity and no first order serial correlation. The restricted model is the standard random individual error component model. It also derives a conditional LM test for homoskedasticity given serial correlation, as well as a conditional LM test for no first order serial correlation given heteroskedasticity, all in the context of a random effects panel data model. Monte Carlo results show that these tests, along with their likelihood ratio alternatives, have good size and power under various forms of heteroskedasticity including exponential and quadratic functional forms

A note on S2 in a linear regression model based on two-stage sampling data

The ordinary least-squares-based estimator of the disturbance variance is shown to be asymptotically unbiased and weakly consistent irrespective of restrictions on the nonstochastic regressor matrix, when a regression model uses the data collected by a two-stage sampling.Ordinary least-squares estimator Disturbance variance Two-stage sampling Intracluster correlation

A note on S2 in a spatially correlated error components regression model for panel data

The ordinary least squares based estimator of the disturbance variance in a panel regression model with spatially correlated error component is shown to be asymptotically unbiased and weakly consistent without any restrictions on the regressor matrix.Spatial correlation errors Panel data OLSE Asymptotic unbiasedness Consistency