Bootstrap-Based Improvements for Inference with Clustered Errors

Abstract

Researchers have increasingly realized the need to account for within-group dependence in estimating standard errors of regression parameter estimates. The usual solution is to calculate cluster-robust standard errors that permit heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. Standard asymptotic tests can over-reject, however, with few (5-30) clusters. We investigate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the example of Bertrand, Duflo and Mullainathan (2004). Rejection rates of ten percent using standard methods can be reduced to the nominal size of five percent using our methods.

Local favoritism in at-large proportional representation systems

“…16 The p-value of the effect on municipalities with a leftwing representative only is 0.40, using the wild bootstrap procedure of Cameron, Gelbach, and Miller (2008) to account for within-region correlation. The p-value of the effect on municipalities with a rightwing representative only is 0.11.…”

“…However, with only 18 clusters inference may not be reliable. As a supplement to our municipality clustered standard errors, we therefore follow Cameron, Gelbach, and Miller (2008) and apply (wild) bootstrap resampling methods when clustering at the regional level. With a second order polynomial, the effect of being politically aligned is statistically significant at the 5 percent level both without and with municipality fixed effects (p = 0.03 and p = 0.04, respectively).…”

Access to treatment and educational inequalities in cancer survival

“…Our data follow the most recent health region structure. 7 Today, they both belong to the Oslo University Hospital, along with other teaching hospitals in the Oslo area. The decision to either treat patients at the local hospitals (to which they belong), or transfer them to more specialized care depended on an overall assessment of patients' age, cancer form and spread, likely outcomes, and the availability of specialized treatment, including surgical, radiation and chemotherapeutic options within the local hospital catchment area.…”

Inference with Large Clustered Datasets

“…For most values of G 1 , however, it is possible to obtain more accurate inferences by using the wild cluster bootstrap. This procedure was proposed by Cameron, Gelbach and Miller (2008) and studied in detail by MacKinnon and Webb (2016a).…”