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
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Severini and Tripathi (2012) Efficency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors,\ | 0.965 | 10 | 4 | 90% |
| 2 | Santos (2011) Instrumental Variable Methods for Recovering Continuous Linear Functionals,\ | 0.928 | 5 | 3 | 80% |
| 3 | Imbens and Angrist (1994) Identification and Estimation of Local Average Treatment Effects,\ | 0.874 | 5 | 2 | 100% |
| 4 | Yogo (2004) Estimating the Elasticity of Intertemporal Substitution When Instruments Are Weak,\ | 0.874 | 5 | 2 | 100% |
| 5 | Engl, Hanke and Neubauer (1996) Regularization of Inverse Problems | 0.843 | 4 | 3 | 75% |
| 6 | Lochner and Moretti (2015) Estimating and Testing Models with Many Treatment Levels and Limited Instruments | 0.843 | 3 | 3 | 100% |
| 7 | Chen and Pouzo (2012) Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Gneralized Residuals,\ | 0.794 | 10 | 3 | 50% |
| 8 | Carrasco, Florens and Renault (2006) Linear Inverse Problem in Strucutral Econometrics Estimation Based on Spectral Decomposition and Regularization,\ in | 0.737 | 4 | 3 | 50% |
| 9 | Hausman (1978) Specification Tests in Econometrics, \ | 0.737 | 3 | 2 | 100% |
| 10 | Severini and Tripathi (2006) Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors,\ | 0.737 | 3 | 2 | 100% |
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