Working Paper: CEPR ID: DP17429
Authors: Morgan Kelly
Abstract: With geographical observations, nearby places often have very similar treatments, controls, and outcomes. In such cases, even with perfect identification, difference in differences and synthetic controls return imprecise coefficients, while regression discontinuities and instrumental variables are prone to severe bias and spurious significance. This paper shows how this may be remedied by adding a spatial smoothing spline to the regression, something easily implemented in practice. The spline allows spatial structure to be separated out as a nuisance variable while simultaneously improving the bias-variance trade-off for the parameters of interest. For simulations and real examples, including a spline causes a marked shrinkage of coefficients, while standard errors change little for most types of cross-section but fall for panels.
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Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| traditional methods like difference in differences and synthetic controls (C90) | imprecise coefficient estimates (C51) |
| spatial correlation (C49) | biased coefficient estimates (C51) |
| spatial smoothing spline (C21) | improve causal inference (C32) |
| spatial smoothing spline (C21) | more accurate estimates (C13) |
| spline inclusion (C34) | marked shrinkage of coefficients (C29) |
| spline inclusion (C34) | stable standard errors for cross-sectional data (C23) |
| spline inclusion (C34) | decreased standard errors for panel data (C23) |
| Monte Carlo simulations (C15) | reveal coverage deterioration of least squares (C20) |
| adding a spline (Y60) | accurate coverage and unbiased coefficient estimates (C51) |