Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-01-14T20:43:25.576Z Has data issue: false hasContentIssue false
  • English
  • Français

SEMIPARAMETRIC EFFICIENCY BOUNDS FOR CONDITIONAL MOMENT RESTRICTION MODELS WITH DIFFERENT CONDITIONING VARIABLES

Published online by Cambridge University Press:  15 April 2015

Marian Hristache  and
Valentin Patilea
Marian Hristache*
Affiliation:
CREST (Ensai)
Valentin Patilea
Affiliation:
CREST (Ensai) and Bucharest University of Economic Studies
*
*Address correspondence to Marian Hristache, CREST, Ecole Nationale de la Statistique et de l’Analyse de l’Information (Ensai), Campus de Ker-Lann, rue Blaise Pascal, BP 37203, 35172 Bruz cedex, France; e-mail: marian.hristache@ensai.fr.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper addresses the problem of semiparametric efficiency bounds for conditional moment restriction models with different conditioning variables. We characterize such an efficiency bound, that in general is not explicit, as a limit of explicit efficiency bounds for a decreasing sequence of unconditional (marginal) moment restriction models. An iterative procedure for approximating the efficient score when this is not explicit is provided. Our theoretical results provide new insight for the theory of semiparametric efficiency bounds literature and open the door to new applications. In particular, we investigate a class of regression-like (mean regression, quantile regression,…) models with missing data, an example of a supply and demand simultaneous equations model and a generalized bivariate dichotomous model.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 4 , August 2016 , pp. 917 - 946
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Valentin Patilea acknowledges financial support from the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, Project PN-II-ID-PCE-2011-3-0893.

Author’s name has been corrected since original publication. An erratum notice detailing this change was also published.

References

REFERENCES

Ahn, S.C. & Schmidt, P. (1999) Estimation of linear panel data models using GMM. In Mátyás, L. (ed.), Generalized Method of Moments Estimation. Cambridge University Press.Google Scholar
Ai, C. & Chen, X. (2003) Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica 71, 1795–1843.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
Bickel, P.J., Klaassen, C.A.J., Ritov, Y., & Wellner, J.A. (1993) Efficient and Adaptive Estimation for Semiparametric Models. The John Hopkins University Press.Google Scholar
Chamberlain, G. (1987) Asymptotic efficiency in estimation with conditional moment restrictions. Econometrica 34, 305–334.CrossRefGoogle Scholar
Chamberlain, G. (1992a) Efficiency bounds for semiparametric regression. Econometrica 60, 567–596.CrossRefGoogle Scholar
Chamberlain, G. (1992b) Comment: Sequential moment restrictions in panel data. Journal of Business & Economic Statistics 10, 20–26.Google Scholar
Chen, X. & Pouzo, D. (2009) Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals. Journal of Econometrics 152, 46–60.CrossRefGoogle Scholar
Gallant, A.R. (1975) Seemingly unrelated nonlinear regressions. Journal of Econometrics 3, 35–50.CrossRefGoogle Scholar
Graham, B. (2011) Efficiency bounds for missing data models with semiparametric restrictions. Econometrica 79, 437–452.Google Scholar
Hahn, J. (1997) Efficient estimation of panel data models with sequential moment restrictions. Journal of Econometrics 79, 1–21.CrossRefGoogle Scholar
Han, C. & Phillips, P.C.B. (2006) GMM with many moment conditions. Econometrica 74, 147–192.CrossRefGoogle Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.CrossRefGoogle Scholar
Hansen, L.P. (2008) Generalized method of moments. In Durlauf, S.N. & Blume, L.E. (eds.), The New Palgrave Dictionary of Economics, 2nd ed. Palgrave Macmillan.Google Scholar
Hansen, L.P. & Sargent, T.J. (1991) Rational Expectations Econometrics. Westview Press.Google Scholar
Ibragimov, I.A. & Has’minskii, R.Z. (1981) Statistical Estimation. Asymptotic Theory. Springer-Verlag.CrossRefGoogle Scholar
Jun, S. & Pinske, J. (2009) Efficient semiparametric seemingly unrelated quantile regression estimation. Econometric Theory 25, 1392–1414.CrossRefGoogle Scholar
Lavergne, P. (2008) A Cauchy-Schwarz inequality for expectation of matrices. http://econpapers.repec.org/RePEc:sfu:sfudps:dp08-07.Google Scholar
Lavergne, P. & Patilea, V. (2013) Smooth minimum distance estimation and testing with conditional estimating equations: Uniform in bandwidth theory. Journal of Econometrics 177, 47–59.CrossRefGoogle Scholar
Müller, U.U. (2009) Estimating linear functionals in nonlinear regression with responses missing at random. Annals of Statistics 37, 2245–2277.CrossRefGoogle Scholar
Müller, U.U. & Van Keilegom, I. (2012) Efficient parameter estimation in regression with missing responses. Electronic Journal of Statistics 6, 1200–1219.CrossRefGoogle Scholar
Newey, W.K. (1990) Semiparametric efficiency bounds. Journal of Applied Econometrics 5, 99–135.CrossRefGoogle Scholar
Newey, W.K. (1993) Efficient estimation of models with conditional moment restrictions. Handbook of Statistics, vol. 11, pp. 419–454.CrossRefGoogle Scholar
Newey, W.K. (2001) Conditional moment restrictions in censored and truncated regression models. Econometric Theory 17, 863–888.CrossRefGoogle Scholar
Newey, W.K. (2004) Efficient semiparametric estimation via moment restrictions. Econometrica 72, 1877–1897.CrossRefGoogle Scholar
Qian, H. & Schmidt, P. (1999) Improved instrumental variables and generalized method of moments estimators. Journal of Econometrics 91, 145–169.CrossRefGoogle Scholar
Robins, J.M., Rotnitzky, A., & Zhao, L.P. (1994) Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association 89, 846–866.CrossRefGoogle Scholar
Tan, Z. (2011) Efficient restricted estimators for conditional mean models with missing data. Biometrika 98, 663–684.CrossRefGoogle Scholar
Tsiatis, A.A. (2006) Semiparametric Theory and Missing Data. Springer.Google Scholar
van der Laan, M.J. & Robins, J.M. (2003) Unified Methods for Censored Longitudinal Data and Causality. Springer-Verlag.CrossRefGoogle Scholar
van der Vaart, A.W. (1998) Asymptotic Statistics. Cambridge University Press.CrossRefGoogle Scholar
Wei, Y., Ma, Y., & Carroll, R.J. (2012) Multiple imputation in quantile regression. Biometrika 99, 423–438.CrossRefGoogle ScholarPubMed
Wooldridge, J.M. (2010) Econometric Analysis of Cross Section and Panel Data, 2nd ed. MIT Press.Google Scholar