Improved inferences for spatial regression models

• We provide improved inferences for covariate effects of spatial models.
• Bias-correction method of Yang (2015) is used to improve t-ratios for covariates.
• Replace QMLEs by the bias-corrected versions, to improve t-ratios for covariates.
• We propose further corrections on the standard errors of the covariate estimates.
• Proposed methods are illustrated using three popular spatial regression models.

The quasi-maximum likelihood (QML) method is popular in the estimation and inference for spatial regression models. However, the QML estimators (QMLEs) of the spatial parameters can be quite biased and hence the standard inferences for the regression coefficients (based on t-ratios) can be seriously affected. This issue, however, has not been addressed. The QMLEs of the spatial parameters can be bias-corrected based on the general method of Yang (2015b, J. of Econometrics 186, 178–200). In this paper, we demonstrate that by simply replacing the QMLEs of the spatial parameters by their bias-corrected versions, the usual t-ratios for the regression coefficients can be greatly improved. We propose further corrections on the standard errors of the QMLEs of the regression coefficients, and the resulted t-ratios perform superbly, leading to much more reliable inferences.