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. |
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