Estimating Causal Effects Using Coarsened Treatments as Instruments

Abstract

Researchers often estimate causal effects in experimental or observational studies after coarsening continuous measures of treatments. In the statistical matching context, in particular, non-discrete interventions are frequently discretized to facilitate pair-stratification using traditional matching approaches for binary treatments. A well-known issue in studying coarsened interventions is that any coarsening induces measurement error that attenuates estimates, while inflating estimator standard errors. While this bias is known, there is yet no standard correction for it. This research note illustrates the error-in-variables structure underlying the use of discrete transformations of non-discrete (or dose) interventions. It also recommends the use of the standard IV estimator to recover an unbiased estimate of the uncoarsened treatment effect. Particular attention is given to the problem of matching with a continuous intervention, which motivates simulations.

Keywords: experiments, matching, continuous interventions, discrete data, instrumental variables, measurement error