Robust outer product of gradients tests for testing spatial dependence

Abstract

In this paper, we suggest outer-product-of-gradient (OPG) variants of the Lagrange multiplier (LM) test statistic for testing spatial dependence under the local parametric misspecification in spatial models. Our OPG statistic for testing the presence of a spatial lag in the disturbance term remains valid irrespective of whether or not there is spatial dependence in the dependent variable. Similarly, our suggested OPG statistic for testing the presence of a spatial lag in the dependent variable is robust to the presence of spatial dependence in the disturbance term. We also suggest the OPG variants that are robust to the presence of an unknown form of heteroskedasticity in the disturbance terms. The computations of all suggested tests only require the least squares estimates from a linear regression model. In a Monte Carlo simulation, we investigate the finite sample properties of our tests and some alternative tests suggested in the literature. The simulation results show that our tests work well in finite samples.

Keywords

• Spatial autoregressive models
• SARAR
• Heteroskedasticity
• Testing
• Robust tests
• LM tests
• OPG tests
• Inference.

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