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IDENTIFICATION OF DISCRETE CHOICE DYNAMIC PROGRAMMING MODELS WITH NONPARAMETRIC DISTRIBUTION OF UNOBSERVABLES

Published online by Cambridge University Press:  21 March 2016

Le-Yu Chen
Le-Yu Chen*
Affiliation:
Academia Sinica
*
*Address correspondence to Le-Yu Chen, Institute of Economics, Academia Sinica, Nankang, Taipei, 115, Taiwan; e-mail: [email protected].
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Abstract

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This paper presents semiparametric identification results for the Rust (1994) class of discrete choice dynamic programming (DCDP) models. We develop sufficient conditions for identification of the deep structural parameters for the case where the per-period utility function ascribed to one choice in the model is parametric but the distribution of unobserved state variables is nonparametric. The proposed identification strategy does not rely on availability of the terminal period data and can therefore be applied to infinite horizon structural dynamic models. Identifying power comes from assuming that the agent’s per-period utilities admit continuous choice-specific state variables that are observed with sufficient variation and satisfy certain conditional independence assumptions on the joint time series of observables. These conditions allow us to formulate exclusion restrictions for identifying the primitive structural functions of the model.

Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 3 , June 2017 , pp. 551 - 577
Copyright
Copyright © Cambridge University Press 2016 

Footnotes

This paper is a significant revision of my earlier Cemmap working papers (Chen (2007, 2009)) and the first chapter of my doctoral thesis (Econometric Inference Involving Discrete Indicator Functions, 2009, University College London). I thank my advisor Sokbae Lee for his encouragement and insightful advice on this research work. I am grateful to the co-editor and two anonymous referees for valuable comments and suggestions on previous versions of the paper. I am indebted to the editor Peter Phillips for constructive advice and comments which have considerably improved the presentation of this paper. I also benefited from helpful comments provided by Richard Blundell, Andrew Chesher, Hidehiko Ichimura, Oliver Linton, Pedro Mira, Lars Nesheim, Adam Rosen, and seminar participants at Aarhus, University of St. Gallen, Alicante, Academia Sinica, UCL/Cemmap and 2009 Far East and South Asia Meeting of the Econometric Society.

References

REFERENCES

Aguirregabiria, V. (2010) Another look at the identification of dynamic discrete decision processes: An application to retirement behavior. Journal of Business and Economic Statistics 28, 201–218.CrossRefGoogle Scholar
Aguirregabiria, V. & Mira, P. (2002) Swapping the nested fixed point algorithm: A class of estimators for discrete Markov decision models. Econometrica 70, 1519–1543.Google Scholar
Aguirregabiria, V. & Mira, P. (2007) Sequential estimation of dynamic discrete games. Econometrica 75, 1–53.CrossRefGoogle Scholar
Aguirregabiria, V. & Mira, P. (2010) Dynamic discrete choice structural models: A survey. Journal of Econometrics 156, 38–67.CrossRefGoogle Scholar
Bajari, P., Benkard, C.L., & Levin, J. (2007) Estimating dynamic models of imperfect competition. Econometrica 75, 1331–1370.CrossRefGoogle Scholar
Bajari, P., Chernozhukov, V., Hong, H., & Nekipelov, D. (2009) Nonparametric and Semiparametric Analysis of a Dynamic Discrete Game. Working paper, University of Minnesota.Google Scholar
Blevins, J. (2014) Nonparametric identification of dynamic decision processes with discrete and continuous choices. Quantitative Economics 5, 531–554.CrossRefGoogle Scholar
Chen, L-Y. (2007) Semiparametric Identification of Structural Dynamic Optimal Stopping Time Models. Cemmap Working paper CWP06/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.CrossRefGoogle Scholar
Chen, L-Y. (2009) Identification of Structural Dynamic Discrete Choice Models. Cemmap Working paper CWP08/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.Google Scholar
Cho, S-J. (2011) An empirical model of mainframe computer investment. Journal of Applied Econometrics 26, 122–150.CrossRefGoogle Scholar
de Jong, R.M. & Woutersen, T. (2011) Dynamic time series binary choice. Econometric Theory 27, 673–702.Google Scholar
Denardo, E. (1967) Contraction mappings in the theory underlying dynamic programming. SIAM Review 9, 165–177.CrossRefGoogle Scholar
Eckstein, Z. & Wolpin, K. (1989) The specification and estimation of dynamic stochastic discrete choice models: A survey. Journal of Human Resources 24, 562–598.CrossRefGoogle Scholar
Fox, J.T. (2007) Semiparametric estimation of multinomial discrete-choice models using a subset of choices. RAND Journal of Economics 38, 1002–1019.CrossRefGoogle Scholar
Goeree, J.K., Holt, C.A., & Palfrey, T.R. (2005) Regular quantal response equilibrium. Experimental Economics 8, 347–367.CrossRefGoogle Scholar
Heckman, J. & Navarro, S. (2007) Dynamic discrete choice and dynamic treatment effects. Journal of Econometrics 136, 341–396.CrossRefGoogle Scholar
Horowitz, J. (1992) A maximum score estimator for the binary response model. Econometrica 60, 505–531.CrossRefGoogle Scholar
Horowitz, J. (1993) Optimal rates of convergence of parameter estimators in the binary response model with weak distributional assumptions. Econometric Theory 9, 1–18.CrossRefGoogle Scholar
Hotz, V. & Miller, R.A. (1993) Conditional choice probabilities and the estimation of dynamic models. Review of Economic Studies 60, 497–531.CrossRefGoogle Scholar
Hotz, V., Miller, R.A., Sanders, S., & Smith, J. (1994) A simulation estimator for dynamic models of discrete choice. Review of Economic Studies 61, 265–289.CrossRefGoogle Scholar
Hu, Y. & Shum, M. (2012) Nonparametric identification of dynamic models with unobserved state variables. Journal of Econometrics 171, 32–44.Google Scholar
Kasahara, H. & Shimotsu, K. (2009) Nonparametric identification of finite mixture models of dynamic discrete choices. Econometrica 77, 135–175.Google Scholar
Keane, M. & Wolpin, K. (2009) Empirical applications of discrete choice dynamic programming models. Review of Economic Dynamics 12, 1–22.CrossRefGoogle Scholar
Kennet, D.M. (1994) A structural model of aircraft engine maintenance. Journal of Applied Econometrics 9, 351–368.Google Scholar
Klein, R. & Spady, R. (1993) An efficient semiparametric estimator for binary response models. Econometrica 61, 387–421.CrossRefGoogle Scholar
Lewbel, A. (2000) Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables. Journal of Econometrics 97, 145–177.CrossRefGoogle Scholar
Lewbel, A. & Linton, O. (2007) Nonparametric matching and efficient estimators of homothetically separable functions. Econometrica 75, 1209–1227.CrossRefGoogle Scholar
Lewbel, A. (2014) An overview of the special regressor method. In Ullah, A., Racine, J., & Su, L. (eds.), Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics, Oxford University Press, pp. 38–62.Google Scholar
Lewbel, A. & Tang, X. (2015) Identification and estimation of games with incomplete information using excluded regressors. Journal of Econometrics 189, 229–244.CrossRefGoogle Scholar
Lippman, S. (1975) On dynamic programming with unbounded rewards. Management Science 21, 1225–1233.Google Scholar
Magnac, T. & Thesmar, D. (2002) Identifying dynamic discrete decision processes. Econometrica 70, 801–816.CrossRefGoogle Scholar
Manski, C.F. (1975) Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3, 205–228.CrossRefGoogle Scholar
Manski, C.F. (1985) Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator. Journal of Econometrics 27, 313–333.CrossRefGoogle Scholar
Manski, C.F. (1988) Identification of binary response models. Journal of the American Statistical Association 83, 729–738.CrossRefGoogle Scholar
Manski, C.F. (1993) Dynamic choice in social settings: Learning from the experiences of others. Journal of Econometrics 58, 121–136.CrossRefGoogle Scholar
Matzkin, R. (1991) Semiparametric estimation of monotone and concave utility functions for polychotomous choice models. Econometrica 59, 1315–1327.CrossRefGoogle Scholar
Matzkin, R. (1992) Nonparametric and distribution-free estimation of the binary threshold crossing and the binary choice models. Econometrica 60, 239–270.CrossRefGoogle Scholar
Matzkin, R. (1993) Nonparametric identification and estimation of polychotomous choice models. Journal of Econometrics 58, 137–168.CrossRefGoogle Scholar
McKelvey, R.D. & Palfrey, T.R. (1995) Quantal response equilibria for normal form games. Games and Economic Behavior 10, 6–38.Google Scholar
Miller, R. (1997) Estimating models of dynamic optimization with microeconomic data. In Pesaran, M. & Schmidt, P. (eds.), Handbook of Applied Econometrics, vol. 2, Oxford: Blackwell Publishers, pp. 246–299.Google Scholar
Norets, A. (2010) Continuity and differentiability of expected value functions in dynamic discrete choice models. Quantitative Economics 1, 305–322.CrossRefGoogle Scholar
Norets, A. & Tang, X. (2014) Semiparametric inference in dynamic binary choice models. Review of Economic Studies 81, 1229–1262.Google Scholar
Pakes, A., Ostrovsky, M., & Berry, S. (2007) Simple estimators for the parameters of discrete dynamic games (with entry/exit example). RAND Journal of Economics 38, 373–399.Google Scholar
Pesendorfer, M. & Schmidt-Dengler, P. (2008) Asymptotic least squares estimator for dynamic games. Review of Economic Studies 75, 901–928.CrossRefGoogle Scholar
Rust, J. (1987) Optimal replacement of GMC bus engines: An empirical model of Harold Zurcher. Econometrica 55, 999–1033.CrossRefGoogle Scholar
Rust, J. (1988) Maximum likelihood estimation of discrete control processes. SIAM Journal on Control and Optimization 26, 1006–1024.Google Scholar
Rust, J. (1994) Structural estimation of Markov decision processes. In Engle, R. & McFadden, D. (eds.), Handbook of Econometrics, vol. 4, pp. 3081–3143.Google Scholar
Sanches, F.A.M., Silva-Junior, D., & Srisuma, S. (2013) An Alternative Asymptotic Least Squares Estimator for Dynamic Games. Working paper, London School of Economics.Google Scholar
Sanches, F.A.M., Silva-Junior, D., & Srisuma, S. (2014) Identifying Dynamic Games with Switching Costs. Working paper, University of Surrey.Google Scholar
Srisuma, S. & Linton, O. (2012) Semiparametric estimation of Markov decision processes with continuous state space. Journal of Econometrics 166, 320–341.CrossRefGoogle Scholar
Srisuma, S. (2015) Identification in discrete Markov decision models. Econometric Theory 31, 521–538.CrossRefGoogle Scholar
Stokey, N. & Lucas, R. (1989) Recursive Methods in Economics Dynamics. Harvard University Press.Google Scholar
Taber, C. (2000) Semiparametric identification and heterogeneity in discrete choice dynamic programming models. Journal of Econometrics 96, 201–229.CrossRefGoogle Scholar
Thompson, T.S. (1989) Identification of semiparametric discrete choice models. Discussion paper, University of Minnesota.Google Scholar