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Identification of Dynamic Discrete Choice Models

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  • Jaap H. Abbring

    (CentER, Department of Econometrics and OR, Tilburg University, 5000 LE Tilburg, The Netherlands)

Abstract

Econometric models of dynamic discrete choice processes are applied to a wide variety of economic problems. Recent research on their empirical content has brought important new insights. It has clarified the conditions for their identification from choice and covariate panel data in the absence of dynamic selection on unobservables. It has provided important new identification results for discrete-time models with unobserved heterogeneity and unobserved states. Finally, it has enhanced the attractiveness of continuous-time models, by developing new insights on the identification of continuous-time optimal stopping models. Current developments in the literature promise to shed further light on the specification and identification of models with unobserved state variables, theory-based nonproportional hazard models, continuous-time optimal stopping models with time-varying covariates, and dynamic games in discrete and continuous time.

Suggested Citation

  • Jaap H. Abbring, 2010. "Identification of Dynamic Discrete Choice Models," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 367-394, September.
  • Handle: RePEc:anr:reveco:v:2:y:2010:p:367-394
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    as
    1. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-270, March.
    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. Stephen V. Cameron & James J. Heckman, 1998. "Life Cycle Schooling and Dynamic Selection Bias: Models and Evidence for Five Cohorts of American Males," Journal of Political Economy, University of Chicago Press, vol. 106(2), pages 262-333, April.
    4. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
    5. Jaap Abbring & James Heckman, 2008. "Dynamic policy analysis," CeMMAP working papers CWP05/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Pakes, Ariel & Ericson, Richard, 1998. "Empirical Implications of Alternative Models of Firm Dynamics," Journal of Economic Theory, Elsevier, vol. 79(1), pages 1-45, March.
    7. Rosen, Sherwin, 2007. "Studies in Labor Markets," National Bureau of Economic Research Books, University of Chicago Press, number 9780226726304, January.
    8. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    9. Flavio Cunha & James J. Heckman & Salvador Navarro, 2007. "The Identification And Economic Content Of Ordered Choice Models With Stochastic Thresholds," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1273-1309, November.
    10. Jaap H. Abbring, 2012. "Mixed Hitting‐Time Models," Econometrica, Econometric Society, vol. 80(2), pages 783-819, March.
    11. Jaap Abbring & Pierre-André Chiappori & Tibor Zavadil, 2008. "Better Safe than Sorry? Ex Ante and Ex Post Moral Hazard in Dynamic Insurance Data," Tinbergen Institute Discussion Papers 08-075/3, Tinbergen Institute.
    12. Taber, Christopher R., 2000. "Semiparametric identification and heterogeneity in discrete choice dynamic programming models," Journal of Econometrics, Elsevier, vol. 96(2), pages 201-229, June.
    13. Abbring, J.H., 2009. "Mixed Hitting-Time Models," Other publications TiSEM 6c745572-a041-4990-a767-6, Tilburg University, School of Economics and Management.
    14. Abbring, Jaap H. & Heckman, James J., 2007. "Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 72, Elsevier.
    15. Eckstein, Zvi & van den Berg, Gerard J., 2007. "Empirical labor search: A survey," Journal of Econometrics, Elsevier, vol. 136(2), pages 531-564, February.
    16. Flavio Cunha & James Heckman & Salvador Navarro, 2005. "Separating uncertainty from heterogeneity in life cycle earnings," Oxford Economic Papers, Oxford University Press, vol. 57(2), pages 191-261, April.
    17. Ulrich Doraszelski & Kenneth L. Judd, 2012. "Avoiding the curse of dimensionality in dynamic stochastic games," Quantitative Economics, Econometric Society, vol. 3(1), pages 53-93, March.
    18. Geert Ridder, 1990. "The Non-Parametric Identification of Generalized Accelerated Failure-Time Models," Review of Economic Studies, Oxford University Press, vol. 57(2), pages 167-181.
    19. Jaap H. Abbring & Pierre-André Chiappori & Jean Pinquet, 2003. "Moral Hazard and Dynamic Insurance Data," Journal of the European Economic Association, MIT Press, vol. 1(4), pages 767-820, June.
    20. Stephen V. Cameron & James J. Heckman, 1998. "Life Cycle Schooling and Dynamic Selection Bias: Models and Evidence for Five Cohorts," NBER Working Papers 6385, National Bureau of Economic Research, Inc.
    21. Geert Ridder & Tiemen M. Woutersen, 2003. "The Singularity of the Information Matrix of the Mixed Proportional Hazard Model," Econometrica, Econometric Society, vol. 71(5), pages 1579-1589, September.
    22. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 136(2), pages 341-396, February.
    23. 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.
    24. T. Anderson, 1954. "On estimation of parameters in latent structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 19(1), pages 1-10, March.
    25. Milton Friedman, 1957. "Introduction to "A Theory of the Consumption Function"," NBER Chapters, in: A Theory of the Consumption Function, pages 1-6, National Bureau of Economic Research, Inc.
    26. Hu, Yingyao & Shum, Matthew, 2012. "Nonparametric identification of dynamic models with unobserved state variables," Journal of Econometrics, Elsevier, vol. 171(1), pages 32-44.
    27. Bo E. Honor & Áureo De Paula, 2010. "Interdependent Durations," Review of Economic Studies, Oxford University Press, vol. 77(3), pages 1138-1163.
    28. 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.
    29. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    30. J. Heckman & B. Singer, 1984. "The Identifiability of the Proportional Hazard Model," Review of Economic Studies, Oxford University Press, vol. 51(2), pages 231-241.
    31. Bo E. Honoré, 1993. "Identification Results for Duration Models with Multiple Spells," Review of Economic Studies, Oxford University Press, vol. 60(1), pages 241-246.
    32. Flavio Cunha & James J. Heckman & Salvador Navarro, 2007. "The Identification & Economic Content of Ordered Choice Models with Stochastic Thresholds," Working Papers 200726, Geary Institute, University College Dublin.
    33. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, Oxford University Press, vol. 101(4), pages 707-727.
    34. Aguirregabiria, Victor, 2010. "Another Look at the Identification of Dynamic Discrete Decision Processes: An Application to Retirement Behavior," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 201-218.
    35. Van den Berg, Gerard J., 2001. "Duration models: specification, identification and multiple durations," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 55, pages 3381-3460, Elsevier.
    36. Milton Friedman, 1957. "A Theory of the Consumption Function," NBER Books, National Bureau of Economic Research, Inc, number frie57-1.
    37. 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.
    38. 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.
    39. Bo E. Honoré & Aureo de Paula, 2009. ""Interdependent Durations" Third Version," PIER Working Paper Archive 09-039, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Feb 2008.
    40. Keane, Michael P & Wolpin, Kenneth I, 1997. "The Career Decisions of Young Men," Journal of Political Economy, University of Chicago Press, vol. 105(3), pages 473-522, June.
    41. Boyarchenko, Svetlana & Levendorskii[caron], Sergei, 2007. "Optimal stopping made easy," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 201-217, February.
    42. Michael P. Keane & Kenneth I. Wolpin, 2009. "Empirical Applications of Discrete Choice Dynamic Programming Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(1), pages 1-22, January.
    43. Jaap H. Abbring, 0000. "Mixed Hitting-Time Models," Tinbergen Institute Discussion Papers 07-057/3, Tinbergen Institute, revised 11 Aug 2009.
    44. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    45. Ariel Pakes & Margaret Simpson, 1989. "Patent Renewal Data," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 20(1989 Micr), pages 331-410.
    46. James J. Heckman & Christopher R. Taber, 1994. "Econometric Mixture Models and More General Models for Unobservables in Duration Analysis," NBER Technical Working Papers 0157, National Bureau of Economic Research, Inc.
    47. Abbring, Jaap H., 2002. "Stayers versus defecting movers: a note on the identification of defective duration models," Economics Letters, Elsevier, vol. 74(3), pages 327-331, February.
    48. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
    49. Manski, Charles F., 1993. "Dynamic choice in social settings : Learning from the experiences of others," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 121-136, July.
    50. A. D. Roy, 1951. "Some Thoughts On The Distribution Of Earnings," Oxford Economic Papers, Oxford University Press, vol. 3(2), pages 135-146.
    51. Lancaster, Tony, 1979. "Econometric Methods for the Duration of Unemployment," Econometrica, Econometric Society, vol. 47(4), pages 939-956, July.
    52. Robert Shimer, 2008. "The Probability of Finding a Job," American Economic Review, American Economic Association, vol. 98(2), pages 268-273, May.
    53. 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.
    54. Flinn, C. & Heckman, J., 1982. "New methods for analyzing structural models of labor force dynamics," Journal of Econometrics, Elsevier, vol. 18(1), pages 115-168, January.
    55. László Mátyás & Patrick Sevestre (ed.), 2008. "The Econometrics of Panel Data," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75892-1, January-J.
    56. Bo E. Honore & Aureo de Paula, 2007. "Interdependent Durations, Second Version," PIER Working Paper Archive 08-044, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Nov 2008.
    57. Alexander Novikov & Albert Shiryaev, 2004. "On an Effective Solution of the Optimal Stopping Problem for Random Walks," Research Paper Series 131, Quantitative Finance Research Centre, University of Technology, Sydney.
    58. Zvi Eckstein & Kenneth I. Wolpin, 1999. "Why Youths Drop Out of High School: The Impact of Preferences, Opportunities, and Abilities," Econometrica, Econometric Society, vol. 67(6), pages 1295-1340, November.
    59. Jaap H. Abbring & Jeffrey R. Campbell, 2005. "A Firm's First Year," Tinbergen Institute Discussion Papers 05-046/3, Tinbergen Institute.
    60. Eckstein, Zvi & Wolpin, Kenneth I, 1990. "Estimating a Market Equilibrium Search Model from Panel Data on Individuals," Econometrica, Econometric Society, vol. 58(4), pages 783-808, July.
    61. Chris Elbers & Geert Ridder, 1982. "True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 403-409.
    62. James J. Heckman, 1981. "Heterogeneity and State Dependence," NBER Chapters, in: Studies in Labor Markets, pages 91-140, National Bureau of Economic Research, Inc.
    63. Heckman, James J. & Singer, Burton, 1986. "Econometric analysis of longitudinal data," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 29, pages 1689-1763, Elsevier.
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    Cited by:

    1. An, Yonghong & Hu, Yingyao & Xiao, Ruli, 2021. "Dynamic decisions under subjective expectations: A structural analysis," Journal of Econometrics, Elsevier, vol. 222(1), pages 645-675.
    2. Jaap H. Abbring, 2012. "Mixed Hitting‐Time Models," Econometrica, Econometric Society, vol. 80(2), pages 783-819, March.
    3. Sebastian Galiani & Juan Pantano, 2021. "Structural Models: Inception and Frontier," NBER Working Papers 28698, National Bureau of Economic Research, Inc.
    4. Zheng, Kun, 2019. "Essays on duration analysis and labour economics," Other publications TiSEM 6467229e-a10b-4d8d-acaf-c, Tilburg University, School of Economics and Management.
    5. Jaap H. Abbring & Øystein Daljord, 2020. "Identifying the discount factor in dynamic discrete choice models," Quantitative Economics, Econometric Society, vol. 11(2), pages 471-501, May.
    6. Sasaki, Yuya, 2015. "Heterogeneity and selection in dynamic panel data," Journal of Econometrics, Elsevier, vol. 188(1), pages 236-249.
    7. Wu, Tong & Lawell, C.Y. Cynthia Lin & Just, David R. & Zhao, Jiancheng & Fei, Zhangjun & Wei, Qiang, 2022. "Optimal Forest Management for Interdependent Products: A Nested Dynamic Bioeconomic Model and Application to Bamboo," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322164, Agricultural and Applied Economics Association.
    8. Schneider, Ulrich, 2019. "Identification of Time Preferences in Dynamic Discrete Choice Models: Exploiting Choice Restrictions," MPRA Paper 102137, University Library of Munich, Germany, revised 29 Jul 2020.
    9. Jaap H. Abbring & Tim Salimans, 2019. "The Likelihood of Mixed Hitting Times," Papers 1905.03463, arXiv.org, revised Apr 2021.
    10. Jean-Pierre Dubé & Günter Hitsch & Pranav Jindal, 2014. "The Joint identification of utility and discount functions from stated choice data: An application to durable goods adoption," Quantitative Marketing and Economics (QME), Springer, vol. 12(4), pages 331-377, December.
    11. Gabriel Ulyssea, 2018. "Firms, Informality, and Development: Theory and Evidence from Brazil," American Economic Review, American Economic Association, vol. 108(8), pages 2015-2047, August.
    12. Clemens, Michael A., 2021. "Violence, development, and migration waves: Evidence from Central American child migrant apprehensions," Journal of Urban Economics, Elsevier, vol. 124(C).
    13. Abbring, Jaap H. & Salimans, Tim, 2021. "The likelihood of mixed hitting times," Journal of Econometrics, Elsevier, vol. 223(2), pages 361-375.
    14. Jean-Pierre H. Dube & Günter J. Hitsch & Pranav Jindal, 2012. "The Joint Identification of Utility and Discount Functions From Stated Choice Data: An Application to Durable Goods Adoption," NBER Working Papers 18393, National Bureau of Economic Research, Inc.
    15. Taiga Tsubota, 2021. "Identifying Dynamic Discrete Choice Models with Hyperbolic Discounting," Papers 2111.10721, arXiv.org, revised Jul 2022.
    16. Jaap H. Abbring & {O}ystein Daljord, 2018. "Identifying the Discount Factor in Dynamic Discrete Choice Models," Papers 1808.10651, arXiv.org, revised Sep 2019.
    17. Philip Marx & Elie Tamer & Xun Tang, 2022. "Parallel Trends and Dynamic Choices," Papers 2207.06564, arXiv.org.
    18. Stéphane Gregoir & Tristan‐Pierre Maury, 2013. "The Impact Of Social Housing On The Labour Market Status Of The Disabled," Health Economics, John Wiley & Sons, Ltd., vol. 22(9), pages 1124-1138, September.
    19. Otero, Karina V., 2016. "Nonparametric identification of dynamic multinomial choice games: unknown payoffs and shocks without interchangeability," MPRA Paper 86784, University Library of Munich, Germany.
    20. Michele Fioretti & Alexander Vostroknutov & Giorgio Coricelli, 2022. "Dynamic Regret Avoidance," American Economic Journal: Microeconomics, American Economic Association, vol. 14(1), pages 70-93, February.

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    More about this item

    Keywords

    discrete decision process; optimal stopping; hazard; hitting time; heterogeneity;
    All these keywords.

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions

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