Jochmans, Koen (2023) Many (Weak) Judges in Judge-Leniency Designs. TSE Working Paper, n. 23-1481, Toulouse

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Abstract

Judge-lenciency designs are very popular. Evaluating whether conventional inference procedures apply to it is not immediate. We frame such designs as an inference problem from grouped data in a setting with a growing number of groups and limited variation between groups. Such an asymptotic approximation is well suited for the data sets encountered in practice. The two-stage least-squares estimator should never be used. The jackknife instrumental-variable estimator can present a reliable tool for inference, provided that a non-standard asymptotic-variance estimator is used along with it. Conventional decision rules to gauge instrument strength are typically not valid in our setting. An alternative such decision rule is provided and is found to perform well.