Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-27T04:38:16.673Z Has data issue: false hasContentIssue false
  • English
  • Français

CLOSED-FORM IDENTIFICATION OF DYNAMIC DISCRETE CHOICE MODELS WITH PROXIES FOR UNOBSERVED STATE VARIABLES

Published online by Cambridge University Press:  06 March 2017

Yingyao Hu  and
Yuya Sasaki
Yingyao Hu*
Affiliation:
Department of Economics, Johns Hopkins University
Yuya Sasaki
Affiliation:
Department of Economics, Johns Hopkins University
*
*Address correspondence to Yingyao Hu, Department of Economics, Wyman Park Building 544E, 3100 Wyman Park Drive, Baltimore, MD 21211; e-mail: yhu@jhu.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

Proxies for unobserved skills and technologies are increasingly available in empirical data. For dynamic discrete choice models of forward-looking agents where a continuous state variable is unobserved but its proxy is available, we derive closed-form identification of the structure by explicitly solving integral equations. In the first step, we derive closed-form identification of Markov components, including the conditional choice probabilities and the law of state transition. In the second step, we plug in these first-step identifying formulas to obtain primitive structural parameters of dynamically optimizing agents.

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 1 , February 2018 , pp. 166 - 185
Copyright
Copyright © Cambridge University Press 2017 

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

The authors can be reached at yhu@jhu.edu and sasaki@jhu.edu. We benefited from useful comments by the editor (Peter C.B. Phillips), the coeditor (Arthur Lewbel), three anonymous referees, seminar participants at Cambridge, Centre de Recherche en Économie et Statistique Paris, George Washington, London School of Economics, Oxford, Rice, Shanghai University of Finance and Economics, Texas A&M, Toulouse School of Economics, University College London, Wisconsin-Madison, 2013 Greater New York Metropolitan Area Econometrics Colloquium, and 2014 Shanghai Econometrics Workshop. The usual disclaimer applies.

References

REFERENCES

Aguirregabiria, V. & Mira, P. (2007) Sequential estimation of dynamic discrete games. Econometrica 75(1), 1–53.Google Scholar
Aguirregabiria, V. & Mira, P. (2013) Dynamic discrete choice structural models: A survey. Journal of Econometrics 156(1), 38–67.CrossRefGoogle Scholar
Arcidiacono, P. & Miller, R.A. (2011) Conditional choice probability estimation of dynamic discrete choice models with unobserved heterogeneity. Econometrica 79(6), 1823–1867.Google Scholar
Bissantz, N., Dümbgen, L., Holtzmann, H., & Munk, A. (2007) Non-parametric confidence bands in deconvolution density estimation. Journal of the Royal Statistical Society: Series B 69(3), 483–506.CrossRefGoogle Scholar
Cragg, J.G. & Donald, S.G. (1997) Inferring the rank of a matrix. Journal of Econometrics 76, 223–250.Google Scholar
Cunha, F., Heckman, J.J., & Schennach, S.M. (2010) Estimating the technology of cognitive and noncognitive skill formation. Econometrica 78(3), 883–931.Google ScholarPubMed
Hotz, V.J. & Miller, R.A. (1993) Conditional choice probabilities and the estimation of dynamic models. Review of Economic Studies 60(3), 497–529.CrossRefGoogle Scholar
Hotz, V.J., Miller, R.A., Sanders, S., & Smith, J. (1994) A simulation estimator for dynamic models of discrete choice. Review of Economic Studies 61(2), 265–289.CrossRefGoogle Scholar
Hu, Y. & Sasaki, Y. (2015) Closed-form estimation of nonparametric models with non-classical measurement errors. Journal of Econometrics 185(2), 392–408.Google Scholar
Hu, Y. & Schennach, S.M. (2008) Instrumental variable treatment of nonclassical measurement error models. Econometrica 76(1), 195–216.CrossRefGoogle Scholar
Hu, Y. & Shum, M. (2012) Nonparametric identification of dynamic models with unobserved state variables. Journal of Econometrics 171(1), 32–44.Google Scholar
Kasahara, H. & Shimotsu, K. (2009) Nonparametric identification of finite mixture models of dynamic discrete choices. Econometrica 77(1), 135–175.Google Scholar
Kato, K. & Sasaki, Y. (2016) Uniform confidence bands in deconvolution with unknown error distribution, arXiv:1608.02251v2.Google Scholar
Kleibergen, F. & Paap, R. (2006) Generalized reduced rank tests using the singular value decomposition. Journal of Econometrics 133(1), 97–126.Google Scholar
Li, T. (2002) Robust and consistent estimation of nonlinear errors-in-variables models. Journal of Econometrics 110, 1–26.CrossRefGoogle Scholar
Li, T. & Vuong, Q. (1998) Nonparametric estimation of the measurement error model using multiple indicators. Journal of Multivariate Analysis 65, 139–165.Google Scholar
Magnac, T. & Thesmar, D. (2002) Identifying dynamic discrete decision processes. Econometrica 70(2), 801–816.CrossRefGoogle Scholar
Pesendorfer, M. & Schmidt-Dengler, P. (2008) Asymptotic least squares estimators for dynamic games. Review of Economic Studies 75(3), 901–928.CrossRefGoogle Scholar
Robin, J.-M. & Smith, R.J. (2000) Tests of rank. Econometric Theory 16(2), 151–175.CrossRefGoogle Scholar
Rust, J. (1994) Structural estimation of Markov decision processes. In Engle, R. & McFadden, D. (eds.), Handbook of Econometrics, vol. 4, pp. 3081–3143. North Holland.Google Scholar
Sanches, F.A.M., Silva Junior, D., & Srisuma, S. (2015) Ordinary least squares estimation of a dynamic game model. International Economic Review 57(2), 623–634.Google Scholar
Schennach, S. (2004a) Estimation of nonlinear models with measurement error. Econometrica 72(1), 33–75.Google Scholar
Schennach, S. (2004b) Nonparametric regression in the presence of measurement errors. Econometric Theory 20(6), 1046–1093.CrossRefGoogle Scholar
Srisuma, S. (2015) Identification in discrete Markov decision models. Econometric Theory 31(3), 521–538.CrossRefGoogle Scholar
Srisuma, S. & Linton, O. (2012) Semiparametric estimation of Markov decision processes with continuous state space. Journal of Econometrics 166(2), 320–341.Google Scholar
Todd, P.E. & Wolpin, K.I. (2012) Estimating a Coordination Game in the Classroom. Working paper, University of Pennsylvania.Google Scholar
Supplementary material: PDF

Hu and Sasaki supplementary material

Appendix

Download Hu and Sasaki supplementary material(PDF)
PDF 409.1 KB