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Logit-based alternatives to two-stage least squares

Denis Chetverikov, Jinyong Hahn, Zhipeng Liao, Shuyang Sheng

Abstract

We propose logit-based IV and augmented logit-based IV estimators that serve as alternatives to the traditionally used 2SLS estimator in the model where both the endogenous treatment variable and the corresponding instrument are binary. Our novel estimators are as easy to compute as the 2SLS estimator but have an advantage over the 2SLS estimator in terms of causal interpretability. In particular, in certain cases where the probability limits of both our estimators and the 2SLS estimator take the form of weighted-average treatment effects, our estimators are guaranteed to yield non-negative weights whereas the 2SLS estimator is not.

Logit-based alternatives to two-stage least squares

Abstract

We propose logit-based IV and augmented logit-based IV estimators that serve as alternatives to the traditionally used 2SLS estimator in the model where both the endogenous treatment variable and the corresponding instrument are binary. Our novel estimators are as easy to compute as the 2SLS estimator but have an advantage over the 2SLS estimator in terms of causal interpretability. In particular, in certain cases where the probability limits of both our estimators and the 2SLS estimator take the form of weighted-average treatment effects, our estimators are guaranteed to yield non-negative weights whereas the 2SLS estimator is not.
Paper Structure (11 sections, 11 theorems, 106 equations, 3 tables, 3 algorithms)

This paper contains 11 sections, 11 theorems, 106 equations, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Logit-Based IV Estimator
  3. Augmented Logit-Based IV Estimator
  4. Asymptotic Distribution Theory
  5. Hausman Specification Test
  6. Empirical Applications
  7. Regularity Conditions
  8. Proofs for Section \ref{['sec: estimator']}
  9. Proofs for Section \ref{['sec: augmented estimator']}
  10. Proofs for Section \ref{['sec: asymptotic distribution']}
  11. Auxiliary Lemma

Key Result

Theorem 2.1

Suppose that Assumptions as: conditional independence and as: monotonicity are satisfied. Then under appropriate regularity conditions,To avoid distractions, we provide the list of regularity conditions for this theorem and all other results in the Appendix. for any $s\in[0,1]$ and $a\in \{ \Lambda, and

Theorems & Definitions (30)

  • Theorem 2.1
  • Corollary 2.1
  • Corollary 2.2
  • Corollary 2.3
  • Corollary 2.4
  • Remark 2.1
  • Remark 2.2
  • Remark 2.3
  • Remark 2.4
  • Remark 2.5
  • ...and 20 more