IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v171y2012i1p32-44.html
   My bibliography  Save this article

Nonparametric identification of dynamic models with unobserved state variables

Author

Listed:
  • Hu, Yingyao
  • Shum, Matthew

Abstract

We consider the identification of a Markov process {Wt,Xt∗} when only {Wt} is observed. In structural dynamic models, Wt includes the choice variables and observed state variables of an optimizing agent, while Xt∗ denotes time-varying serially correlated unobserved state variables (or agent-specific unobserved heterogeneity). In the non-stationary case, we show that the Markov law of motion fWt,Xt∗∣Wt−1,Xt−1∗ is identified from five periods of data Wt+1,Wt,Wt−1,Wt−2,Wt−3. In the stationary case, only four observations Wt+1,Wt,Wt−1,Wt−2 are required. Identification of fWt,Xt∗∣Wt−1,Xt−1∗ is a crucial input in methodologies for estimating Markovian dynamic models based on the “conditional-choice-probability (CCP)” approach pioneered by Hotz and Miller.

Suggested Citation

  • Hu, Yingyao & Shum, Matthew, 2012. "Nonparametric identification of dynamic models with unobserved state variables," Journal of Econometrics, Elsevier, vol. 171(1), pages 32-44.
  • Handle: RePEc:eee:econom:v:171:y:2012:i:1:p:32-44
    DOI: 10.1016/j.jeconom.2012.05.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407612001479
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, June.
    2. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    3. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1059-1087.
    4. Susumu Imai & Neelam Jain & Andrew Ching, 2009. "Bayesian Estimation of Dynamic Discrete Choice Models," Econometrica, Econometric Society, vol. 77(6), pages 1865-1899, November.
    5. Igal Hendel & Aviv Nevo, 2006. "Measuring the Implications of Sales and Consumer Inventory Behavior," Econometrica, Econometric Society, vol. 74(6), pages 1637-1673, November.
    6. Tülin Erdem & Susumu Imai & Michael Keane, 2003. "Brand and Quantity Choice Dynamics Under Price Uncertainty," Quantitative Marketing and Economics (QME), Springer, vol. 1(1), pages 5-64, March.
    7. Doraszelski, Ulrich & Pakes, Ariel, 2007. "A Framework for Applied Dynamic Analysis in IO," Handbook of Industrial Organization, Elsevier.
    8. Flavio Cunha & James J. Heckman & Susanne M. Schennach, 2010. "Estimating the Technology of Cognitive and Noncognitive Skill Formation," Econometrica, Econometric Society, vol. 78(3), pages 883-931, May.
    9. V. Joseph Hotz & Robert A. Miller & Seth Sanders & Jeffrey Smith, 1994. "A Simulation Estimator for Dynamic Models of Discrete Choice," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 265-289.
    10. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    11. Thierry Magnac & David Thesmar, 2002. "Identifying Dynamic Discrete Decision Processes," Econometrica, Econometric Society, vol. 70(2), pages 801-816, March.
    12. Gregory S. Crawford & Matthew Shum, 2005. "Uncertainty and Learning in Pharmaceutical Demand," Econometrica, Econometric Society, vol. 73(4), pages 1137-1173, July.
    13. Allan Collard-Wexler, 2006. "Demand Fluctuations and Plant Turnover in the Ready-Mix Concrete Industry," Working Papers 06-25, New York University, Leonard N. Stern School of Business, Department of Economics.
    14. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    15. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 497-529.
    16. Bouissou, Michel B & Laffont, Jean-Jacques & Vuong, Quang H, 1986. "Tests of Noncausality under Markov Assumptions for Qualitative Panel Data," Econometrica, Econometric Society, vol. 54(2), pages 395-414, March.
    17. Hu, Yingyao & Shum, Matthew, 2012. "Nonparametric identification of dynamic models with unobserved state variables," Journal of Econometrics, Elsevier, vol. 171(1), pages 32-44.
    18. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-1297, November.
    19. Shiu, Ji-Liang & Hu, Yingyao, 2013. "Identification and estimation of nonlinear dynamic panel data models with unobserved covariates," Journal of Econometrics, Elsevier, vol. 175(2), pages 116-131.
    20. Han Hong & Matthew Shum, 2010. "Pairwise-Difference Estimation of a Dynamic Optimization Model," Review of Economic Studies, Oxford University Press, vol. 77(1), pages 273-304.
    21. Ackerberg, Daniel & Lanier Benkard, C. & Berry, Steven & Pakes, Ariel, 2007. "Econometric Tools for Analyzing Market Outcomes," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 63 Elsevier.
    22. Pakes, Ariel S, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," Econometrica, Econometric Society, vol. 54(4), pages 755-784, July.
    23. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    24. Daniel A. Ackerberg, 2003. "Advertising, learning, and consumer choice in experience good markets: an empirical examination," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(3), pages 1007-1040, August.
    25. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Oxford University Press, vol. 62(1), pages 53-82.
    26. Miller, Robert A, 1984. "Job Matching and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1086-1120, December.
    27. Arellano, Manuel & Honore, Bo, 2001. "Panel data models: some recent developments," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 53, pages 3229-3296 Elsevier.
    28. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
    29. repec:taf:gnstxx:v:22:y:2010:i:4:p:419-423 is not listed on IDEAS
    30. James Levinsohn & Amil Petrin, 2003. "Estimating Production Functions Using Inputs to Control for Unobservables," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 317-341.
    31. Sanghamitra Das & Mark J. Roberts & James R. Tybout, 2007. "Market Entry Costs, Producer Heterogeneity, and Export Dynamics," Econometrica, Econometric Society, vol. 75(3), pages 837-873, May.
    32. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    33. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    34. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    35. repec:taf:gnstxx:v:22:y:2010:i:4:p:379-399 is not listed on IDEAS
    36. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    37. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, January.
    38. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    39. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
    40. Victor Aguirregabiria & Pedro Mira, 2002. "Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models," Econometrica, Econometric Society, vol. 70(4), pages 1519-1543, July.
    41. Martin Pesendorfer & Philipp Schmidt-Dengler, 2008. "Asymptotic Least Squares Estimators for Dynamic Games -super-1," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 901-928.
    42. Andriy Norets, 2009. "Inference in Dynamic Discrete Choice Models With Serially orrelated Unobserved State Variables," Econometrica, Econometric Society, vol. 77(5), pages 1665-1682, September.
    43. Hu, Yingyao, 2008. "Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution," Journal of Econometrics, Elsevier, vol. 144(1), pages 27-61, May.
    44. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:171:y:2012:i:1:p:32-44. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.