EconBase
← All papers

Optimal Linear Instrumental Variables Approximations

Juan Carlos Escanciano, Wei Li

arXiv 8 May 2018 · Econometrics · publishedJournal of Econometrics (2020) · 8 citations (OpenAlex)

arXiv:1805.03275 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper studies the identification and estimation of the optimal linear approximation of a structural regression function. The parameter in the linear approximation is called the Optimal Linear Instrumental Variables Approximation (OLIVA). This paper shows that a necessary condition for standard inference on the OLIVA is also sufficient for the existence of an IV estimand in a linear model. The instrument in the IV estimand is unknown and may not be identified. A Two-Step IV (TSIV) estimator based on Tikhonov regularization is proposed, which can be implemented by standard regression routines. We establish the asymptotic normality of the TSIV estimator assuming neither completeness nor identification of the instrument. As an important application of our analysis, we robustify the classical Hausman test for exogeneity against misspecification of the linear structural model. We also discuss extensions to weighted least squares criteria. Monte Carlo simulations suggest an excellent finite sample performance for the proposed inferences. Finally, in an empirical application estimating the elasticity of intertemporal substitution (EIS) with US data, we obtain TSIV estimates that are much larger than their standard IV counterparts, with our robust Hausman test failing to reject the null hypothesis of exogeneity of real interest rates.

Citation extraction

51
references
118
in-text mentions
49
distinct cited
1
self-citations
10,825
main-text words

appendix boundary found by appendix_titled_section at “Appendix A: Notation, Assumptions and Preliminary Results” · 58% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Severini and Tripathi (2012) Efficency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors,\0.96510490%
2Santos (2011) Instrumental Variable Methods for Recovering Continuous Linear Functionals,\0.9285380%
3Imbens and Angrist (1994) Identification and Estimation of Local Average Treatment Effects,\0.87452100%
4Yogo (2004) Estimating the Elasticity of Intertemporal Substitution When Instruments Are Weak,\0.87452100%
5Engl, Hanke and Neubauer (1996) Regularization of Inverse Problems0.8434375%
6Lochner and Moretti (2015) Estimating and Testing Models with Many Treatment Levels and Limited Instruments0.84333100%
7Chen and Pouzo (2012) Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Gneralized Residuals,\0.79410350%
8Carrasco, Florens and Renault (2006) Linear Inverse Problem in Strucutral Econometrics Estimation Based on Spectral Decomposition and Regularization,\ in0.7374350%
9Hausman (1978) Specification Tests in Econometrics, \0.73732100%
10Severini and Tripathi (2006) Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors,\0.73732100%

Showing the top 10 of 49 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Inference on Strongly Identified Functionals of Weakly Identified Functions0.87462
2Is Completeness Necessary? Estimation in Nonidentified Linear Models0.51121
3Debiased Machine Learning for Unobserved Heterogeneity: High-Dimensional Panels and Measurement Error Models0.40511
4Mostly Harmless Machine Learning: Learning Optimal Instruments in Linear IV Models0.00011