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NONPARAMETRIC INSTRUMENTAL VARIABLES AND REGULAR ESTIMATION

Published online by Cambridge University Press:  14 March 2017

Jinyong Hahn  and
Zhipeng Liao
Jinyong Hahn*
Affiliation:
University of California, Los Angeles
Zhipeng Liao
Affiliation:
University of California, Los Angeles
*
*Address correspondence to Jinyong Hahn, Department of Economics, UCLA, Box 951477, Los Angeles, CA 90095-1477, USA; e-mail: [email protected].
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Abstract

This paper investigates whether there can exist regular estimators in models characterized by nonparametric instrumental variable (NPIV). We show by a number of examples that regular estimation is impossible in general for nonlinear functionals.

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 3 , June 2018 , pp. 574 - 597
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

We acknowledge helpful comments by anonymous referees. We are particularly grateful to the Editor and a Co-Editor for their considerable input.

References

REFERENCES

Ai, C. & Chen, X. (2003) Efficient estimation of conditional moment restrictions models containing unknown functions. Econometrica 71, 1795–1843.CrossRefGoogle Scholar
Ai, C. & Chen, X. (2007) Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables. Journal of Econometrics 141, 5–43.CrossRefGoogle Scholar
Ai, C. & Chen, X. (2012) The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions. Journal of Econometrics 170, 442–457.CrossRefGoogle Scholar
Bierens, H. (2013) The Hilbert space theoretical foundation of semi-nonparametric modeling. In Ullah, A., Racine, J., & Su, L. (eds.), Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics, pp. 3–37. Oxford University Press.Google Scholar
Carrasco, M., Florens, J.-P., & Renault, E. (2007) Linear inverse problems in structural econometrics. In Heckman, J.J. & Leamer, E.E. (eds.), Handbook of Econometrics 6B, pp. 5633–5751. Elsevier.CrossRefGoogle Scholar
Chamberlain, G. (1986) Asymptotic efficiency in semi-parametric models with censoring. Journal of Econometrics 32, 189–218.CrossRefGoogle Scholar
Chen, X. & Reiss, M. (2011) On rate optimality for ill-posed inverse problems in econometrics. Econometric Theory 27, 497–521.CrossRefGoogle Scholar
Florens, J.-P., Johannes, J., & van Bellegem, S. (2011) Identification and estimation by penalization in nonparametric instrumental regression. Econometric Theory 27, 472–496.CrossRefGoogle Scholar
d’Haultfoeuille, X. (2011) On the completeness condition in nonparametric instrumental problems. Econometric Theory 27, 460–471.CrossRefGoogle Scholar
Hahn, J. (1994) The efficiency bound of the mixed proportional hazard model. Review of Economic Studies 61, 607–629.CrossRefGoogle Scholar
Hall, P. & Horowitz, J.L. (2005) Nonparametric methods for inference in the presence of instrumental variables. Annals of Statistics 33, 2904–2929.CrossRefGoogle Scholar
Horowitz, J. (2011) Applied nonparametric instrumental variables estimation. Econometrica 79, 347–394.Google Scholar
Newey, W.K. (1990) Semiparametric efficiency bounds. Journal of Applied Econometrics 5, 99–135.Google Scholar
Newey, W.K. (1994) The asymptotic variance of semiparametric estimators. Econometrica 62, 1349–1382.CrossRefGoogle Scholar
Newey, W.P. & Powell, J.L. (2003) Instrumental variables for nonparametric models. Econometrica 71, 1565–1578.CrossRefGoogle Scholar
Johnston, W. (2014) The weighted Hermite polynomials form a basis for L 2(R). American Mathematical Monthly 121, 249–253.CrossRefGoogle Scholar
Schennach, S.M. (2004) Estimation of nonlinear models with measurement error. Econometrica 72, 33–75.CrossRefGoogle Scholar
Severini, T.A. & Tripathi, G. (2012) Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors. Journal of Econometrics 170, 491–498.CrossRefGoogle Scholar
Van der Vaart, A. (1991) On differentiable functionals. Annals of Statistics 19, 178–204.CrossRefGoogle Scholar
Van der Vaart, A. (2002) Semiparametric statistics. In Bernard, P. (ed.), Lectures on Probability Theory and Statistics (Ecole d’Eté de Probabilités de Saint-Flour XXIX - 1999), pp. 331–457. Springer.Google Scholar