Robinson, Peter M. and Rossi, Francesca
(2015)
Refined tests for spatial correlation.
Econometric Theory, 31
(6).
pp. 1249-1280.
ISSN 0266-4666
Abstract
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.
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