The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables

Mogstad, Magne; Torgovitsky, Alexander; Walters, Christopher

doi:10.1257/aer.20190221

Cited by 80 publications

(59 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A major limitation of Lemma 3.1 and Theorem 3.2 is that empirical applications of IV methods rarely consider fully heterogeneous first stages and saturated specifications with discrete covariates. As mentioned above, in a survey of recent papers with multiple instruments, only 13% of applications interact covariates with an original instrument (Mogstad et al, 2020). Specifications using many overidentifying restrictions appear to have been more common in earlier work using IV methods (e.g., Angrist, 1990;Angrist and Krueger, 1991) but have effectively disappeared from empirical economics out of concern for weak instruments.…”

Section: Resultsmentioning

confidence: 99%

“…Such specifications are very rare in empirical work. For example, in a survey of recent papers with multiple instruments, only 13% of applications use covariate interactions with an original instrument (Mogstad, Torgovitsky, and Walters, 2020). This severely limits the applicability of Angrist and Imbens (1995)'s result to interpreting actual IV and 2SLS estimates.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

When Should We (Not) Interpret Linear IV Estimands as LATE?

Słoczyński¹

2020

Preprint

View full text Add to dashboard Cite

In this paper I revisit the interpretation of the linear instrumental variables (IV) estimand as a weighted average of conditional local average treatment effects (LATEs). I focus on a practically relevant situation in which additional covariates are required for identification while the reduced-form and first-stage regressions implicitly restrict the effects of the instrument to be homogeneous, and are thus possibly misspecified. I show that the weights on some conditional LATEs are negative and the IV estimand is no longer interpretable as a causal effect under conditional monotonicity, i.e. when there are compliers but no defiers at some covariate values and defiers but no compliers elsewhere. Even if monotonicity holds unconditionally, the IV estimand is not interpretable as the unconditional LATE parameter unless the groups with different values of the instrument are roughly equal sized.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

When Should We (Not) Interpret Linear IV Estimands as LATE?

Słoczyński¹

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…While we call τ * , τ * j , τ j (x) treatment effects here, we note that the causal interpretation of such quantities is not straightforward. Indeed, Mogstad et al (2019Mogstad et al ( , 2020 argue that estimating causal effects with multiple instruments requires more careful statements of assumptions and implied estimands, as well as alternative estimation strategies that go beyond simple (weighted) averages of two-stage least-squares estimates.…”

Section: Discussionmentioning

confidence: 99%

Improving Inference from Simple Instruments through Compliance Estimation

Coussens,

Spiess

2021

Preprint

View full text Add to dashboard Cite

Instrumental variables (IV) regression is widely used to estimate causal treatment effects in settings where receipt of treatment is not fully random, but there exists an instrument that generates exogenous variation in treatment exposure. While IV can recover consistent treatment effect estimates, they are often noisy. Building upon earlier work in biostatistics (Joffe and Brensinger, 2003) and relating to an evolving literature in econometrics (including Abadie et al., 2019;Huntington-Klein, 2020;Borusyak and Hull, 2020), we study how to improve the efficiency of IV estimates by exploiting the predictable variation in the strength of the instrument. In the case where both the treatment and instrument are binary and the instrument is independent of baseline covariates, we study weighting each observation according to its estimated compliance (that is, its conditional probability of being affected by the instrument), which we motivate from a (constrained) solution of the first-stage prediction problem implicit to IV. The resulting estimator can leverage machine learning to estimate compliance as a function of baseline covariates. We derive the large-sample properties of a specific implementation of a weighted IV estimator in the potential outcomes and local average treatment effect (LATE) frameworks, and provide tools for inference that remain valid even when the weights are estimated nonparametrically. With both theoretical results and a simulation study, we demonstrate that compliance weighting meaningfully reduces the variance of IV estimates when first-stage heterogeneity is present, and that this improvement often outweighs any difference between the compliance-weighted and unweighted IV estimands. These results suggest that in a variety of applied settings, the precision of IV estimates can be substantially improved by incorporating compliance estimation.

show abstract

“…3 Pairwise validity can be viewed as a generalization of the partial monotonicity assumption of Mogstad et al (2021). See Remark 2.1 for a discussion.…”

Section: Introductionmentioning

confidence: 99%

Pairwise Valid Instruments

Sun¹,

Wüthrich²

2022

Preprint

View full text Add to dashboard Cite

Finding valid instruments is difficult. We propose Validity Set Instrumental Variable (VSIV) regression, a method for estimating treatment effects when the instruments are partially invalid. VSIV regression exploits testable implications for instrument validity to remove invalid variation in the instruments. We show that the proposed VSIV estimators are asymptotically normal under weak conditions and always remove or reduce the asymptotic bias relative to standard IV estimators.

show abstract

The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables

Cited by 80 publications

References 56 publications

When Should We (Not) Interpret Linear IV Estimands as LATE?

When Should We (Not) Interpret Linear IV Estimands as LATE?

Improving Inference from Simple Instruments through Compliance Estimation

Pairwise Valid Instruments

Contact Info

Product

Resources

About