Inference under covariate-adaptive randomization with imperfect compliance

Federico A. Bugni*, Mengsi Gao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

This paper studies inference in a randomized controlled trial (RCT) with covariate-adaptive randomization (CAR) and imperfect compliance of a binary treatment. In this context, we study inference on the local average treatment effect (LATE), i.e., the average treatment effect conditional on individuals that always comply with the assigned treatment. As in Bugni et al. (2018, 2019), CAR refers to randomization schemes that first stratify according to baseline covariates and then assign treatment status so as to achieve “balance” within each stratum. In contrast to these papers, however, we allow participants of the RCT to endogenously decide to comply or not with the assigned treatment status. We study the properties of an estimator of the LATE derived from a “fully saturated” instrumental variable (IV) linear regression, i.e., a linear regression of the outcome on all indicators for all strata and their interaction with the treatment decision, with the latter instrumented with the treatment assignment. We show that the proposed LATE estimator is asymptotically normal, and we characterize its asymptotic variance in terms of primitives of the problem. We provide consistent estimators of the standard errors and asymptotically exact hypothesis tests. In the special case when the target proportion of units assigned to each treatment does not vary across strata, we can also consider two other estimators of the LATE, including the one based on the “strata fixed effects” IV linear regression, i.e., a linear regression of the outcome on indicators for all strata and the treatment decision, with the latter instrumented with the treatment assignment. Our characterization of the asymptotic variance of the LATE estimators in terms of the primitives of the problem allows us to understand the influence of the parameters of the RCT. We use this to propose strategies to minimize their asymptotic variance in a hypothetical RCT based on data from a pilot study. We illustrate the practical relevance of these results using a simulation study and an empirical application based on Dupas et al. (2018).

Original languageEnglish (US)
Article number105497
JournalJournal of Econometrics
Volume237
Issue number1
DOIs
StatePublished - Nov 2023

Keywords

  • Covariate-adaptive randomization
  • Imperfect compliance
  • Randomized controlled trial
  • Saturated regression
  • Strata fixed effects
  • Stratified block randomization
  • Treatment assignment

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics

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