Abstract
We propose a random effects panel data model with both spatially correlated error components and spatially lagged dependent variables. We focus on diagnostic testing procedures and derive Lagrange multiplier (LM) test statistics for a variety of hypotheses within this model. We first construct the joint LM test for both the individual random effects and the two spatial effects (spatial error correlation and spatial lag dependence). We then provide LM tests for the individual random effects and for the two spatial effects separately. In addition, in order to guard against local model misspecification, we derive locally adjusted (robust) LM tests based on the Bera and Yoon principle (Bera and Yoon, 1993). We conduct a small Monte Carlo simulation to show the good finite sample performances of these LM test statistics and revisit the cigarette demand example in Baltagi and Levin (1992) to illustrate our testing procedures.
Highlights
Spatial econometric models have been extensively used to study regional effects and interdependence between different spatial units
We provide formulae for the standard Lagrange multiplier (LM) tests as well as formulae for the robust LM tests when necessary
We propose a panel data random effects models with both spatially correlated error components and spatially lagged dependent variables
Summary
Spatial econometric models have been extensively used to study regional effects and interdependence between different spatial units. For standard LM tests of spatial dependence in panel data models, Baltagi et al.,. Provide tests for random effects and/or spatial lag dependence. Debarsy and Ertur (2010) [9] derive tests in the spatial panel data model with individual fixed effects based on Lee and Yu (2010) [10]. (2013) [12] extend the model in Kapoor et al, (2007) [13] by allowing for different spatial correlation parameters in the individual random effects and in the disturbances, and they derive the corresponding. Yang (2015) [18] provides residual-based bootstrap procedure to obtain improved approximations to the finite sample critical values of the LM test statistics in spatial econometric models.
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