This paper proposes simple tests of error cross section dependence which are applicable to a variety of panel data models, including stationary and unit root dynamic heterogeneous panels with short T and large N. The proposed tests are based on average of pair-wise correlation coefficients of the OLS residuals from the individual regressions in the panel, and can be used to test for cross section dependence of any fixed order p, as well as the case where no a priori ordering of the cross section units is assumed, referred to as CD(p) and CD tests, respectively. Asymptotic distribution of these tests are derived and their power function analyzed under different alternatives. It is shown that these tests are correctly centred for fixed N and T, and are robust to single or multiple breaks in the slope coefficients and/or error variances. The small sample properties of the tests are investigated and compared to the Lagrange multiplier test of Breusch and Pagan using Monte Carlo experiments. It is shown that the tests have the correct size in very small samples and satisfactory power, and as predicted by the theory, quite robust to the presence of unit roots and structural breaks. The use of the CD test is illustrated by applying it to study the degree of dependence in per capita output innovations across countries within a given region and across countries in different regions. The results show significant evidence of cross dependence in output innovations across many countries and regions in the World.

General Diagnostic Tests for Cross Section Dependence in Panels

One important goal of this study is to develop a methodology of inference for a widely used Cliff-Ord type spatial model containing spatial lags in the dependent variable, exogenous variables, and the disturbance terms, while allowing for unknown heteroskedasticity in the innovations. We first generalize the generalized moments (GM) estimator suggested in Kelejian and Prucha (1998,1999) for the spatial autoregressive parameter in the disturbance process. We prove the consistency of our estimator; unlike in our earlier paper we also determine its asymptotic distribution, and discuss issues of efficiency. We then define instrumental variable (IV) estimators for the regression parameters of the model and give results concerning the joint asymptotic distribution of those estimators and the GM estimator under reasonable conditions. Much of the theory is kept general to cover a wide range of settings. We note the estimation theory developed by Kelejian and Prucha (1998, 1999) for GM and IV estimators and by Lee (2004) for the quasi-maximum likelihood estimator under the assumption of homoskedastic innovations does not carry over to the case of heteroskedastic innovations. The paper also provides a critical discussion of the usual specification of the parameter space.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1296549_code459177.pdf?abstractid=1296549&mirid=3

Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances

http://web.pdx.edu/~crkl/WISE/SEAUG/papers/Lee_Yu_JE10.pdf

Estimation of spatial autoregressive panel data models with fixed effects

http://econweb.umd.edu/~kelejian/Research/KP_0507.pdf

Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances

http://econweb.umd.edu/~prucha/Papers/JE140(2007a).pdf

Panel data models with spatially correlated error components

https://content.csbs.utah.edu/~ehrbar/erc2002/pdf/i046.pdf

Testing panel data regression models with spatial error correlation

http://repec.org/esAUSM04/up.3749.1080795402.pdf

Testing for serial correlation, spatial autocorrelation and random effects using panel data

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

Testing for Serial Correlation, Spatial Autocorrelation and Random Effects

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.

/pdf/testing-panel-data-regression-models-with-spatial-error-49a6xavxuf.pdf

Won Koh

Papers

Testing panel data regression models with spatial error correlation

Testing for serial correlation, spatial autocorrelation and random effects using panel data

Testing for Serial Correlation, Spatial Autocorrelation and Random Effects

Testing for Serial Correlation, Spatial Autocorrelation and Random Effects

Testing Panel Data Regression Models with Spatial Error Correlation