REFINED TESTS FOR SPATIAL CORRELATION

We consider testing the null hypothesis of no spatial correlation against the alternative of pure first order spatial autoregression. A test statistic based on the least squares estimate 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. Although the least squares estimate is inconsistent for the correlation parameter, we show that under quite general conditions its probability limit has the correct sign, and that least squares testing is consistent; we also establish asymptotic local power properties. The finite-sample performance of our tests is compared with others in Monte Carlo simulations.