Instrument Residual Estimator for Any Response Variable with Endogenous Binary Treatment

Lee, Myoung‐jae

doi:10.1111/rssb.12442

Cited by 10 publications

(17 citation statements)

References 45 publications

(50 reference statements)

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“…To this question, Lee (2018) showed that the OLS of y on d − π x ("OLS PSR ") is consistent for E{ω(x)µ 1 (x)} without the restrictive condition. Going further, Lee (2021) showed that when d is endogenous with a binary instrument z, the IVE of y on d with instrument z − ζ x ("IVE ISR "), where ζ x ≡ E(z|x) is the instrument score (IS), is consistent for a modified OW average of µ 1 (x).…”

Section: Discussionmentioning

confidence: 99%

“…For exogenous d, Lee (2018) shows that the OLS of y on d − π x is consistent for E{ω(x)µ 1 (x)} for any form of y regardless of whether π x = λ x , as long as y 1 − y 0 makes sense. y 1 − y 0 makes sense for continuous, count, or binary y; for categorical y, turn each category to a dummy variable to use each dummy variable as an outcome.…”

Section: Ols With Ps Residualmentioning

confidence: 93%

“…y 1 − y 0 makes sense for continuous, count, or binary y; for categorical y, turn each category to a dummy variable to use each dummy variable as an outcome. In fact, Lee's (2018) OLS was suggested much earlier by Robins, Mark, and Newey (1992) for a constant-effect semilinear model y = µ 0 (x) + β d d + error with a continuous y and an unknown function µ 0 (x).…”

Section: Ols With Ps Residualmentioning

confidence: 99%

“…In contrast, the approach by Lee (2018Lee ( , 2021 presented below yields estimators that are always a weighted average of heterogeneous treatment effects, regardless of whether E(d|x) = L(d|x). Furthermore, their approach is applicable to any form of y and is straightforward to implement because it involves only linear regressions (for OLS and IVE) and widely used probit or logit.…”

Section: Introductionmentioning

confidence: 98%

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Ordinary least squares and instrumental-variables estimators for any outcome and heterogeneity

Lee,

Han

2024

The Stata Journal: Promoting communications on statistics and S

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Given an exogenous treatment d and covariates x, an ordinary least-squares (OLS) estimator is often applied with a noncontinuous outcome y to find the effect of d, despite the fact that the OLS linear model is invalid. Also, when d is endogenous with an instrument z, an instrumental-variables estimator (IVE) is often applied, again despite the invalid linear model. Furthermore, the treatment effect is likely to be heterogeneous, say, µ1(x), not a constant as assumed in most linear models. Given these problems, the question is then what kind of effect the OLS and IVE actually estimate. Under some restrictive conditions such as a “saturated model”, the estimated effect is known to be a weighted average, say, E{ ω(x) µ1(x)}, but in general, OLS and the IVE applied to linear models with a noncontinuous outcome or heterogeneous effect fail to yield a weighted average of heterogeneous treatment effects. Recently, however, it has been found that E{ ω(x) µ1(x)} can be estimated by OLS and the IVE without those restrictive conditions if the “propensity-score residual” d − E( d| x) or the “instrument-score residual” z−E( z| x) is used. In this article, we review this recent development and provide a command for OLS and the IVE with the propensity- and instrument-score residuals, which are applicable to any outcome and any heterogeneous effect.

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Section: Discussionmentioning

confidence: 99%

Section: Ols With Ps Residualmentioning

confidence: 93%

Section: Ols With Ps Residualmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Ordinary least squares and instrumental-variables estimators for any outcome and heterogeneity

Lee,

Han

2024

The Stata Journal: Promoting communications on statistics and S

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“…To drop this condition, we propose the "subsample OLS" of Y on D−E(D|X, D = 0, d), which turns out to be consistent for the "overlapweight average" of µ d (X) as in Lee (2018Lee ( , 2021.…”

Section: Introductionmentioning

confidence: 99%

Minimally capturing heterogeneous complier effect of endogenous treatment for any outcome variable

Lee

Choi

Lee

2023

Journal of Causal Inference

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When a binary treatment D D is possibly endogenous, a binary instrument δ \delta is often used to identify the “effect on compliers.” If covariates X X affect both D D and an outcome Y Y , X X should be controlled to identify the “ X X -conditional complier effect.” However, its nonparametric estimation leads to the well-known dimension problem. To avoid this problem while capturing the effect heterogeneity, we identify the complier effect heterogeneous with respect to only the one-dimensional “instrument score” E ( δ ∣ X ) E\left(\delta | X) for non-randomized δ \delta . This effect heterogeneity is minimal, in the sense that any other “balancing score” is finer than the instrument score. We establish two critical “reduced-form models” that are linear in D D or δ \delta , even though no parametric assumption is imposed. The models hold for any form of Y Y (continuous, binary, count, …). The desired effect is then estimated using either single index model estimators or an instrumental variable estimator after applying a power approximation to the effect. Simulation and empirical studies are performed to illustrate the proposed approaches.

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Overlap weight and propensity score residual for heterogeneous effects: A review with extensions

Choi

Lee

2023

Journal of Statistical Planning and Inference

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Instrument Residual Estimator for Any Response Variable with Endogenous Binary Treatment

Cited by 10 publications

References 45 publications

Ordinary least squares and instrumental-variables estimators for any outcome and heterogeneity

Ordinary least squares and instrumental-variables estimators for any outcome and heterogeneity

Minimally capturing heterogeneous complier effect of endogenous treatment for any outcome variable

Overlap weight and propensity score residual for heterogeneous effects: A review with extensions

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