A parametric specification test for linear spatial autoregressive models

We propose a new test for the specification of linear spatial autoregressive models where the spatial weights matrix is prespecified. Our test is built on the difference of two estimates of the spatial parameter where the two estimates are obtained by the parametric and nonparametric GMM estimation methods, respectively. Under mild assumptions, we derive the limiting null distribution and show consistency for our test. Unlike the general nonparametric test, our test can detect the local alternatives that approach the null at a rate n−1/2, where n is the sample size. Monte Carlo simulations are conducted to study the finite sample performance of our test. Finally, we apply our test to check the model specification for the economic growth rate example.