A Generalized Approach to Power Analysis for Local Average Treatment Effects

TL;DR

This paper presents a new, simplified method for conducting power analysis in studies estimating local average treatment effects (LATE) with noncompliance, avoiding complex variance assumptions.

Contribution

It introduces a standardized effect size approach that bounds the power of the Wald IV estimator without requiring variance or distributional assumptions.

Findings

Provides bounds on power based on effect size and compliance rate.

Simplifies power analysis for LATE without variance assumptions.

Applicable with minimal parameters needed from researchers.

Abstract

This study introduces a new approach to power analysis in the context of estimating a local average treatment effect (LATE), where the study subjects exhibit noncompliance with treatment assignment. As a result of distributional complications in the LATE context, compared to the simple ATE context, there is currently no standard method of power analysis for the LATE. Moreover, existing methods and commonly used substitutes - which include instrumental variable (IV), intent-to-treat (ITT), and scaled ATE power analyses - require specifying generally unknown variance terms and/or rely upon strong and unrealistic assumptions, thus providing unreliable guidance on the power of tests of the LATE. This study develops a new approach that uses standardized effect sizes to place bounds on the power for the most commonly used estimator of the LATE, the Wald IV estimator, whereby variance terms and distributional parameters need not be specified nor assumed. Instead, in addition to the effect size, sample size, and error tolerance parameters, the only other parameter that must be specified by the researcher is the compliance rate. Additional conditions can also be introduced to further narrow the bounds on the power calculation. The result is a generalized approach to power analysis in the LATE context that is simple to implement.