Correcting Endogeneity without External Instruments: Four Estimators under the Mediation Constraint

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Autore principale: Araar, Abdelkrim
Natura: Recurso digital
Pubblicazione: Zenodo 2026
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author Araar, Abdelkrim
author_facet Araar, Abdelkrim
contents <p>Endogeneity correction without external instruments requires exploiting structure<br>within the model itself. This paper develops four estimators grounded in the mediation<br>constraint: the unobserved confounder has no direct effect on the outcome<br>beyond what it induces through the endogenous regressor.<br>Five results emerge. First, standard 2SLS diagnostics fail to detect when a contaminated<br>instrument causes 2SLS to amplify rather than correct OLS bias. Second,<br>the Structural Cubic Estimator (SCE) shows that under the mediation<br>constraint and equal-variance idiosyncratic shocks, the coefficient of interest is the<br>unique economically meaningful root of a cubic polynomial whose coefficients are<br>directly observable; it is consistent and outperforms recent distributional methods<br>(Gaussian copula, rank-based control function) under Gaussian data. Third, the<br>Higher-Moment Estimator (HME) drops the equal-variance assumption: under<br>non-Gaussianity of the confounder — ubiquitous in applications where the confounder<br>is income, ability, productivity, or firm size — the coefficient is identified<br>from third-order moments alone, with no restriction on the idiosyncratic shock variances.<br>Fourth, the Residual Purging IV (RPIV) reduces OLS bias by half without<br>any distributional assumption, though it remains asymptotically biased. Fifth,<br>an Adaptive Pre-test rule combines the estimators via an observable proxy for<br>endogeneity strength, and provides an endogeneity test with correct size — unlike<br>the Durbin–Wu–Hausman test, which rejects systematically even in the absence of<br>endogeneity.</p>
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id zenodo_https___doi_org_10_5281_zenodo_20315593
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publishDate 2026
publisher Zenodo
record_format zenodo
spellingShingle Correcting Endogeneity without External Instruments: Four Estimators under the Mediation Constraint
Araar, Abdelkrim
Endogeneity
Artificial IV
<p>Endogeneity correction without external instruments requires exploiting structure<br>within the model itself. This paper develops four estimators grounded in the mediation<br>constraint: the unobserved confounder has no direct effect on the outcome<br>beyond what it induces through the endogenous regressor.<br>Five results emerge. First, standard 2SLS diagnostics fail to detect when a contaminated<br>instrument causes 2SLS to amplify rather than correct OLS bias. Second,<br>the Structural Cubic Estimator (SCE) shows that under the mediation<br>constraint and equal-variance idiosyncratic shocks, the coefficient of interest is the<br>unique economically meaningful root of a cubic polynomial whose coefficients are<br>directly observable; it is consistent and outperforms recent distributional methods<br>(Gaussian copula, rank-based control function) under Gaussian data. Third, the<br>Higher-Moment Estimator (HME) drops the equal-variance assumption: under<br>non-Gaussianity of the confounder — ubiquitous in applications where the confounder<br>is income, ability, productivity, or firm size — the coefficient is identified<br>from third-order moments alone, with no restriction on the idiosyncratic shock variances.<br>Fourth, the Residual Purging IV (RPIV) reduces OLS bias by half without<br>any distributional assumption, though it remains asymptotically biased. Fifth,<br>an Adaptive Pre-test rule combines the estimators via an observable proxy for<br>endogeneity strength, and provides an endogeneity test with correct size — unlike<br>the Durbin–Wu–Hausman test, which rejects systematically even in the absence of<br>endogeneity.</p>
title Correcting Endogeneity without External Instruments: Four Estimators under the Mediation Constraint
topic Endogeneity
Artificial IV
url https://doi.org/10.5281/zenodo.20315593