LM tests for spatial correlation in spatial models with limited dependent variables

Models of limited dependent variables are of great interest in econometrics. This paper focuses on the specification and hypothesis test of spatial models which have a Tobit structure. We derive an extended central limit theorem for statistics of a linear–quadratic form with multivariate random variables. We consider the LM statistics for testing spatial correlation and establish their asymptotic distributions. The tests are applied to an empirical example: we detect the presence of competition among school districts on school district income tax in Iowa.

► We derive five LM tests for spatial models with limited dependent variables.
► The asymptotic distribution of the LM statistic is based on an extended CLT.
► We use Monte Carlo studies to investigate finite sample properties of the tests.
► The tests indicate the existence of tax competition among Iowa school districts.