Spatial Correlation Robust Inference in Linear Regression and Panel Models

Abstract

We consider inference about a scalar coefficient in a linear regression with spatially correlated errors. Recent suggestions for more robust inference require stationarity of both regressors and dependent variables for their large sample validity. This rules out many empirically relevant applications, such as difference-in-difference designs. We develop a robustified version of the recently suggested SCPC method that addresses this challenge. We find that the method has good size properties in a wide range of Monte Carlo designs that are calibrated to real world applications, both in a pure cross sectional setting, but also for spatially correlated panel data. We provide numerically efficient methods for computing the associated spatial-correlation robust test statistics, critical values, and confidence intervals.

Keywords:

• HAC
• HAR
• Matérn process

Supplementary Materials

The supplementary materials include (1) a description of the World Developments Indicator dataset and additional simulation results referenced in Section 4 of the article and (2) replication files for results reported in the article.

Acknowledgments

We thank two referees, the editor and associate editor, and participants at various workshops for helpful comments and suggestions.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

Müller acknowledges financial support from the National Science Foundation grant SES-191336.