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Properties of Bootstrap Moran's I for Diagnostic Testing a Spatial Autoregressive Linear Regression Model

Moran’s I or Cliff-Ord test statistic has been widely used for diagnostic testing of spatial correlation in a linear regression model with or without spatial autoregressive lags. The latter simple model can be easily estimated with OLS, while the former spatial lag model relies on maximum likelihood or the instrumental variables method. Specification testing for spatial autocorrelation is typically performed with the asymptotic distribution of Moran’s I test statistic, which depends on the normality assumption of the model. For many real world applications, the asymptotic theory of the Moran test may not be applicable because the classical normality assumption is rarely satisfied. In this paper, we apply residual-based wild bootstrap methods for hypothesis testing of spatial autocorrelation in a linear regression model. For specification tests of a spatial autoregressive linear regression model, our simulation and bootstrap computations are presented with the consistent instrumental variables or 2SLS estimation method. Based on Moran’s I test statistic, the empirical size and power of bootstrap and asymptotic tests for spatial correlation are evaluated and compared. Under the normality assumption of the model, the performance of the bootstrap test is equivalent to or better than that of the asymptotic test. For more realistic heterogeneous non-normal models, the applicability of asymptotic tests is questionable. Bootstrap tests have shown superiority in smaller size distortion and higher power when compared to asymptotic counterparts, especially for cases with a small sample and dense spatial contiguity. Our Monte Carlo experiments indicate that based on Moran’s I test statistic, the bootstrap method is an effective alternative to the theoretical asymptotic approach when the classical normality assumption is not warranted.