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Home | Events | Optimal Linear Instrumental Variables Approximations

Optimal Linear Instrumental Variables Approximations

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    December 04, 2020
    12:00 - 13:15

This paper studies the identi…cation 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 su¢ cient for the existence of an IV estimand in a linear model. The instrument in the IV estimand is unknown and may not be identi…ed. 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 identi…cation of the instrument. As an important application of our analysis, we robustify the classical Hausman test for exogeneity against misspeci…cation of the linear structural model. We also discuss extensions to weighted least squares criteria. Monte Carlo simulations suggest an excellent …nite 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. Joint with Wei Li.

Keywords: Instrumental Variables; Nonparametric Identi…cation; Hausman Test.

JEL classi…cation: C26; C14; C21

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