Working Paper: NBER ID: w15760
Authors: Thomas Barrios; Rebecca Diamond; Guido W. Imbens; Michal Kolesar
Abstract: It is standard practice in empirical work to allow for clustering in the error covariance matrix if the explanatory variables of interest vary at a more aggregate level than the units of observation. Often, however, the structure of the error covariance matrix is more complex, with correlations varying in magnitude within clusters, and not vanishing between clusters. Here we explore the implications of such correlations for the actual and estimated precision of least squares estimators. We show that with equal sized clusters, if the covariate of interest is randomly assigned at the cluster level, only accounting for non-zero covariances at the cluster level, and ignoring correlations between clusters, leads to valid standard errors and confidence intervals. However, in many cases this may not suffice. For example, state policies exhibit substantial spatial correlations. As a result, ignoring spatial correlations in outcomes beyond that accounted for by the clustering at the state level, may well bias standard errors. We illustrate our findings using the 5% public use census data. Based on these results we recommend researchers assess the extent of spatial correlations in explanatory variables beyond state level clustering, and if such correlations are present, take into account spatial correlations beyond the clustering correlations typically accounted for.
Keywords: Clustering; Spatial Correlations; Randomization Inference
JEL Codes: C01; C1; C31
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| substantial spatial correlations (C49) | log earnings (Q23) |
| substantial spatial correlations (C49) | years of education (I21) |
| substantial spatial correlations (C49) | hours worked (J22) |
| accounting for spatial correlations (C49) | confidence intervals for the effects of state-level regulations (C21) |
| accounting for spatial correlations (C49) | corrections for clustering at the state level (C38) |
| spatial correlations (C49) | precision in estimating confidence intervals for state-level regulations (C13) |
| if state-level regulations are randomly assigned (C90) | variance estimators are robust to misspecification of the error covariance matrix (C51) |
| importance of explicitly assessing spatial correlation structures (C21) | misleading inferences (D91) |