Finite sample properties of Moran's I test for spatial autocorrelation in tobit models

In this note, we investigate the finite-sample properties of Moran's I test statistic for spatial autocorrelation in tobit models suggested by Kelejian and Prucha. We fill a void in the theoretical literature by investigating the finite sample properties of this test statistic in a series of Monte Carlo simulations, using data sets ranging from 49 to 15,625 observations. We find that the test is unbiased, has considerable power and approximates the asymptotic normal distribution even for medium-sized sample sizes, empirically confirming the theoretical results of Kelejian and Prucha. However, some caution is needed, since the statistic turns out to be sensitive to misspecification in the form of heteroscedasticity. In such instances the test over-rejects the null hypothesis, mistaking heteroscedasticity for spatial autocorrelation.