Testing for Spatial Autocorrelation in a Fixed Effects Panel Data Model

This paper derives several Lagrange Multiplier statistics and the corresponding likelihood ratio statistics to test for spatial autocorrelation in a fixed effects panel data model. These tests allow discriminating between the two main types of spatial autocorrelation which are relevant in empirical applications, namely endogenous spatial lag versus spatially autocorrelated errors. In this paper, five different statistics are suggested. The first one, the joint test, detects the presence of spatial autocorrelation whatever its type. Hence, it indicates whether specific econometric estimation methods should be implemented to account for the spatial dimension. In case they need to be implemented, the other four tests support the choice between the different specifications, i.e. endogenous spatial lag, spatially autocorrelated errors or both. The first two are simple hypothesis tests as they detect one kind of spatial autocorrelation assuming the other one is absent. The last two take into account the presence of one type of spatial autocorrelation when testing for the presence of the other one. We use the methodology developed in Lee and Yu (2008) to set up and estimate the general likelihood function. Monte Carlo experiments show the good performance of our tests. Finally, as an illustration, they are applied to the Feldstein-Horioka puzzle. They indicate a misspecification of the investment-saving regression due to the omission of spatial autocorrelation. The traditional saving-retention coefficient is shown to be upward biased. In contrast our results favor capital mobility.