Generalized Lee Bounds

TL;DR

This paper extends Lee bounds for causal inference to incorporate covariates, allowing for more flexible assumptions and multiple outcomes, with applications to job training program data.

Contribution

It introduces a generalized framework for Lee bounds that relaxes monotonicity assumptions using covariates and extends to multiple outcomes.

Findings

Covariates help tighten bounds in empirical applications.

Unconditional monotonicity is often violated in practice.

Theoretical asymptotic properties are established for the generalized bounds.

Abstract

Lee (2009) is a common approach to bound the average causal effect in the presence of selection bias, assuming the treatment effect on selection has the same sign for all subjects. This paper generalizes Lee bounds to allow the sign of this effect to be identified by pretreatment covariates, relaxing the standard (unconditional) monotonicity to its conditional analog. Asymptotic theory for generalized Lee bounds is proposed in low-dimensional smooth and high-dimensional sparse designs. The paper also generalizes Lee bounds to accommodate multiple outcomes. Focusing on JobCorps job training program, I first show that unconditional monotonicity is unlikely to hold, and then demonstrate the use of covariates to tighten the bounds.