Direct Standard Errors for Regressions with Spatially Autocorrelated Residuals

Regressions using data with known locations are increasingly used in empirical economics, and several standard error corrections are available to deal with the fact that their residuals tend to be spatially correlated. Unfortunately, different corrections commonly return significance levels that vary by several orders of magnitude, leaving the researcher uncertain as to which, if any, is valid. This paper proposes instead an extremely fast and simple procedure to derive standard errors directly from the spatial correlation structure of regression residuals. Importantly, because the estimated covariance matrix gives optimal weights to predict each residual as a linear combination of all residuals, the reliability of these standard errors is self-checking by construction. The approach extends immediately to instrumental variables, and balanced and unbalanced panels, as well as a wide class of nonlinear models. A step by step guide to estimating these standard errors is given in the accompanying tutorials.