This study presents new evidence on the impacts of unionization using administrative data matching workers to employers in a regression discontinuity design. Close union elections exhibit substantial nonrandom selection or manipulation. Estimates accounting for this selection show that unionization substantially decreases payroll, employment, average worker earnings, and establishment survival. Payroll and earnings decreases are driven by composition changes, with older and higher-paid workers leaving unionizing establishments and younger workers joining or staying. Worker-level effects on earnings are small and are reconciled with large negative establishment-level effects in a model of employer and employee selection into union jobs.

The utility of machine learning (ML) for regression-based causal inference is illustrated by using lasso to select control variables for estimates of college characteristics’ wage effects. Post-double-selection lasso offers a path to data-driven sensitivity analysis. ML also seems useful for an instrumental variables (IV) first stage, since two-stage least squares (2SLS) bias reflects overfitting. While ML-based instrument selection can improve on 2SLS, split-sample IV and limited information maximum likelihood do better. Finally, we use ML to choose IV controls. Here, ML creates artificial exclusion restrictions, generating spurious findings. On balance, ML seems ill-suited to IV applications in labor economics.

Researchers commonly use jackknife-based instrumental variables estimators to eliminate the many-instruments bias of two-stage least squares. Where inference must be clustered, however, the jackknife fails to eliminate the bias. We propose a cluster-jackknife approach in which first-stage predicted values for each observation are constructed from a regression that leaves out the observation’s entire cluster. The cluster-jackknife instrumental variables estimator (CJIVE) eliminates many-instruments bias, and consistently estimates causal effects in the traditional linear model and local average treatment effects in the heterogeneous treatment effects framework. We illustrate the method in an application estimating the effects of pre-trial detention in Miami-Dade County.

We introduce a test of the rank invariance or rank similarity assumption common in treatment effects and instrumental variables models. The test probes the implication that the conditional distribution of ranks should be identical across treatment states using a regression-based test statistic. We apply the test to data from the Tennessee STAR class-size reduction experiment and show that systematic slippages in rank can be important statistically and economically.

This article provides empirical researchers with an introduction and guide to research designs based on variation in judge and examiner tendencies to administer treatments or other interventions. We review the basic theory behind this research design, outline the assumptions under which the design identifies causal effects, describe empirical tests of the conditions for identification, and discuss trade-offs associated with choices researchers must make for estimation. We demonstrate concepts and best practices in an empirical case study that uses an examiner tendency research design to study the effects of pretrial detention. (JEL C21, C26, K14, K41)

We propose a nonparametric test for the exclusion and monotonicity assumptions invoked in instrumental variable (IV) designs based on the random assignment of cases to judges. We show its asymptotic validity and demonstrate its finite-sample performance in simulations. We apply our test in an empirical setting from the literature examining the effects of pretrial detention on defendant outcomes in New York. When the assumptions are not satisfied, we propose weaker versions of the usual exclusion and monotonicity restrictions under which the IV estimator still converges to a proper weighted average of treatment effects. (JEL H76, K41)

Pharmacy benefit managers dominate the U.S. pharmaceutical market but are controversial and poorly understood. We analyze PBMs as market intermediaries that operate formulary contests in which on-patent brand-drug makers compete for favorable placement by offering rebates off list price. These formulary contests deliver efficiency gains compared to drug makers selling directly to consumers; PBMs capture some of these gains. Our approach answers key questions regarding the determinants of efficiency, rebates, list prices, and PBM market power in the pharmaceutical market. Our analysis also explains how common contracting practices, federal regulations, and incentives within formulary contests can undermine market efficiency.