Improved tests for spatial correlation

We consider testing the null hypothesis of no spatial autocorrelation against the alternative of first order spatial autoregression. A Wald test statistic has good first order asymptotic properties, but these may not be relevant in small or moderate-sized samples, especially as (depending on properties of the spatial weight matrix) the usual parametric rate of convergence may not be attained. We thus develop tests with more accurate size properties, by means of Edgeworth expansions and the bootstrap. The finite-sample performance of the tests is examined in Monte Carlo simulations.