The cluster robust variance estimator (CRVE) relies on the number of clusters being large. The precise meaning of 'large' is ambiguous, but a shorthand 'rule of 42' has emerged in the literature. We show that this rule depends crucially on the assumption of equal-sized clusters. Monte Carlo...

Inference based on cluster-robust standard errors is known to fail when the number of clusters is small, and the wild cluster bootstrap fails dramatically when the number of treated clusters is very small. We propose a family of new procedures called the sub- cluster wild bootstrap. In the case...

We study a cluster-robust variance estimator (CRVE) for regression models with clustering in two dimensions that was proposed in Cameron, Gelbach, and Miller (2011). We prove that this CRVE is consistent and yields valid inferences under precisely stated assumptions about moments and cluster...

Inference for estimates of treatment effects with clustered data requires great care when treatment is assigned at the group level. This is true for both pure treatment models and difference-in-differences regressions. Even when the number of clusters is quite large, cluster-robust standard...

Cluster-robust inference is widely used in modern empirical work in economics and many other disciplines. The key unit of observation is the cluster. We propose measures of "high-leverage" clusters and "influential" clusters for linear regression models. The measures of leverage and partial...

Many empirical projects are well suited to incorporating a linear difference-in-differences research design. While estimation is straightforward, reliable inference can be a challenge. Past research has not only demonstrated that estimated standard errors are biased dramatically downwards in...

Canada's Youth Hires program was a targeted employment subsidy that rebated employment insurance premiums to employers with net increases in insurable earnings for youth aged 18-24. Using a difference-in-differences approach, in each of two datasets statistically and economically significant...

This comment revisits the analysis in Christensen and Timmins (2022). We identify two critical errors used in the original analysis, one with the data and the other with coding. When either error is corrected several major results in the paper change, either in statistical significance or in...

This study pushes our understanding of research reliability by reproducing and replicating claims from 110 papers in leading economic and political science journals. The analysis involves computational reproducibility checks and robustness assessments. It reveals several patterns. First, we...

Immigrants in many Western countries have experienced poor economic outcomes. This has led to a lack of integration of child immigrants (the 1.5 generation) and the second generation in some countries. However, in Canada, child immigrants and the second generation have on average integrated very...