# Treatment Effects and Regression Discontinuity

Paper Session

#### Friday, Jan. 5, 2018 10:15 AM - 12:15 PM

Marriott Philadelphia Downtown, Meeting Room 414
Hosted By: Econometric Society
• Chair: Joshua Angrist, MIT

### Identification of and Correction for Publication Bias

#### Abstract

Some empirical results are more likely to be published than others.
Such selective publication leads to biased estimators and distorted inference.
This paper proposes two approaches for identifying the conditional probability of publication as a function of a study's results, the first based on systematic replication studies and the second based on meta-studies.
For known conditional publication probabilities, we propose median-unbiased estimators and associated confidence sets that correct for selective publication.
We apply our methods to recent large-scale replication studies in experimental economics and psychology, and to meta-studies of the effects of minimum wages and de-worming programs.

### Inference on Breakdown Frontiers

#### Abstract

A breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value (e.g., nonnegative) and second that the proportion of units who benefit from treatment is at least a specific value (e.g., at least 50%). For these conclusions, we derive the breakdown frontier for two kinds of assumptions: one which indexes deviations from random assignment of treatment, and one which indexes deviations from rank invariance. These classes of assumptions nest both the point identifying assumptions of random assignment and rank invariance and the opposite end of no-constraints on treatment selection or the dependence structure between potential outcomes. This frontier provides a quantitative measure of robustness of conclusions to deviations in the point identifying assumptions. We derive $\sqrt{N}$-consistent sample analog estimators for these frontiers. We then provide an asymptotically valid bootstrap procedure for constructing lower uniform confidence bands for the breakdown frontier. As a measure of robustness, this confidence band can be presented alongside traditional point estimates and confidence intervals obtained under point identifying assumptions. We illustrate this approach in an empirical application to the effect of child soldiering on wages. We find that conclusions are fairly robust to failure of rank invariance, when random assignment holds, but conclusions are much more sensitive to both assumptions for small deviations from random assignment.

### Inference in Regression Discontinuity Designs With a Discrete Running Variable

#### Abstract

We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors that are clustered by the running variable. We derive theoretical results and present simulation and empirical evidence showing that these CIs have poor coverage properties and therefore recommend that they not be used in practice. We also suggest alternative CIs with guaranteed coverage properties under easily interpretable restrictions on the conditional expectation function.

### Multiple Treatments With Strategic Interaction

#### Abstract

We develop an empirical framework in which we identify and estimate the effects of treatments on outcomes of interest when the treatments are results of strategic interaction (e.g., bargaining, oligopolistic entry, decisions in the presence of peer effects). We consider a model where agents play a discrete game with complete information whose equilibrium actions (i.e., binary treatments) determine a post-game outcome in a nonseparable model with endogeneity. Due to the simultaneity in the first stage, the model as a whole is incomplete and the selection process fails to exhibit the conventional monotonicity. Without imposing parametric restrictions or large support assumptions, this poses challenges in recovering treatment parameters. To address these challenges, we first analytically characterize regions that predict equilibria in the first-stage game with possibly more than two players, whereby we find a certain monotonic pattern of these regions. Based on this finding, we derive bounds on the average treatment effects (ATE's) under nonparametric shape restrictions and the existence of excluded variables. We also introduce and point identify a multi-treatment version of local average treatment effects (LATE's).
##### JEL Classifications
• C21 - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions
• C14 - Semiparametric and Nonparametric Methods: General