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  5. Treatment Effects
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Treatment Effects

Paper Session

Saturday, Jan. 7, 2023 10:15 AM - 12:15 PM (CST)

Hilton Riverside, Durham
Hosted By: Econometric Society
  • Chair: Evan Munro, Stanford University

When is TSLS *Actually* LATE?

Christine Blandhol
,
Princeton University
John Bonney
,
Stanford University
Magne Mogstad
,
University of Chicago
Alexander Torgovitsky
,
University of Chicago

Abstract

Linear instrumental variable estimators, such as two-stage least squares (TSLS), are commonly interpreted as estimating positively weighted averages of causal effects, referred to as local average treatment effects (LATEs). We examine whether the LATE interpretation actually applies to the types of TSLS specifications that are used in practice. We show that if the specification includes covariates—which most empirical work does—then the LATE interpretation does not apply in general. Instead, the TSLS estimator will in general reflect treatment effects for both compilers and always/never-takers, and some of the treatment effects for the always/never-takers will necessarily be negatively weighted. We show that the only specifications that have a LATE interpretation are “saturated” specifications that control for covariates nonparametrically, implying that such specifications are both sufficient and necessary for TSLS to have a LATE interpretation, at least without additional parametric assumptions. This result is concerning because, as we document, empirical researchers almost never control for covariates nonparametrically, and rarely discuss or justify parametric specifications of covariates. We develop a decomposition that quantifies the extent to which the usual LATE interpretation fails. We apply the decomposition to four empirical analyses and find strong evidence that the LATE interpretation of TSLS is far from accurate for the types of specifications actually used in practice.

Treatment Effects in Market Equilibrium

Evan Munro
,
Stanford University
Stefan Wager
,
Stanford University
Kuang Xu
,
Stanford University

Abstract

When randomized trials are run in a marketplace equilibriated by prices, interference arises. To understand the impact on RCT analysis, we build a stochastic model of treatment effects in equilibrium. We characterize the average direct (ADE) and indirect treatment effect (AIE) asymptotically. A standard RCT can consistently estimate the ADE, but confidence intervals and estimation of the AIE require price elasticity estimates, which we provide using a novel experimental design. We define heterogeneous treatment effects and derive an optimal targeting rule that meets an equilibrium stability condition. We illustrate our results using a freelance labor market simulation and data from a cash transfer experiment.

Externally Valid Treatment Choice

Christopher Adjaho
,
New York University
Timothy Christensen
,
New York University

Abstract

We consider the problem of learning treatment (or policy) rules that are externally valid in the sense that they have welfare guarantees in target populations that are similar to, but possibly different from, the experimental population. We allow for shifts in both the distribution of potential outcomes and covariates between the experimental and target populations. This paper makes two main contributions. First, we show that policies that maximize social welfare in the experimental population remain optimal for the ``worst-case' social welfare when the distribution of potential outcomes (but not covariates) shifts. Hence, policy learning methods that have good regret guarantees in the experimental population, such as empirical welfare maximization, are externally valid with respect to shifts in potential outcomes. Second, we develop methods for policy learning that are robust to shifts in the joint distribution of potential outcomes and covariates. Our methods may be used with experimental or observational data.

Identification and Estimation of Average Marginal Treatment Effects with a Bunching Design

Carolina Caetano
,
University of Georgia
Gregorio Caetano
,
University of Georgia
Eric R. Nielsen
,
Federal Reserve Board

Abstract

We show that bunching on the treatment variable can be used for identification of the average marginal treatment effect at the bunching point. The approach requires no functional form or distributional assumptions, no exclusion restrictions, and no special data structures (e.g. panel data) and instead relies on continuity conditions that are similar to those imposed in Regression Discontinuity Designs with continuous treatment. Adding some types of parametric structures to the endogeneity bias allows the identification of all average marginal treatment effects. We provide estimators which can be implemented with off-the-shelf packaged software, and we apply the method to estimate the effects of watching television on children’s cognitive and non-cognitive skills.

Difference-in-Differences with a Continuous Treatment

Brantly Callaway
,
University of Georgia
Andrew Goodman-Bacon
,
Federal Reserve Bank of Minneapolis
Pedro H. C. Sant'Anna
,
Vanderbilt University and Microsoft

Abstract

This paper analyzes difference-in-differences setups with a continuous treatment. We show
that treatment effect on the treated-type parameters can be identified under a generalized parallel trends assumption that is similar to the binary treatment setup. However, interpreting differences in these parameters across different values of the treatment can be particularly challenging due to treatment effect heterogeneity. We discuss alternative, typically stronger, assumptions that alleviate these challenges. We also provide a variety of treatment effect decomposition results, highlighting that parameters associated with popular two-way fixed-effect specifications can be hard to interpret, even when there are only two time periods. We introduce alternative estimation strategies that do not suffer from these drawbacks. Our results also cover cases where (i) there is no available untreated comparison group and (ii) there are multiple periods and variation in treatment timing, which are both common in empirical work.
JEL Classifications
  • C1 - Econometric and Statistical Methods and Methodology: General
  • C2 - Single Equation Models; Single Variables