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Heterogeneity in dynamic discrete choice models

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  • Martin Browning
  • Jesus Carro

Abstract

We consider dynamic discrete choice models with heterogeneity in both the levels parameter and the state dependence parameter. We first analyse the purchase of full fat milk using a long consumer panel (T > 100) on many households. The large T nature of the panel allows us to consistently estimate the parameters of each household separately. This analysis indicates strongly that the levels and the state dependence parameter are heterogeneous and dependently distributed. This empirical analysis motivates the theoretical analysis which considers the estimation of dynamic discrete choice models on short panels, allowing for more heterogeneity than is usually accounted for. The theoretical analysis considers a simple two state, first order Markov chain model without covariates in which both transition probabilities are heterogeneous. Using such a model we are able to derive small sample analytical results for bias and mean squared error. We discuss the maximum likelihood approach, a novel bias corrected version of the latter and we also develop a new estimator that minimises the integrated mean square error, which we term MIMSE. The attractions of the latter estimator are that it is very easy to compute, it is always identified and it converges to maximum likelihood as T becomes large so that it inherits all of the desirable large sample properties of MLE. Our main finding is that in almost all short panel contexts the MIMSE significantly outperforms the other two estimators in terms of mean squared error.

Suggested Citation

  • Martin Browning & Jesus Carro, 2006. "Heterogeneity in dynamic discrete choice models," Economics Series Working Papers 287, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:287
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    File URL: http://www.economics.ox.ac.uk/materials/working_papers/paper287.pdf
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    References listed on IDEAS

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    1. Martin Browning & Mette Ejrnæs & Javier Alvarez, 2010. "Modelling Income Processes with Lots of Heterogeneity," Review of Economic Studies, Oxford University Press, vol. 77(4), pages 1353-1381.
    2. Bo E. Honoré & Elie Tamer, 2002. "Bounds on Parameters in Dynamic Discrete Choice Models," CAM Working Papers 2004-23, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics, revised Aug 2004.
    3. Hashem Pesaran, M. & Yamagata, Takashi, 2008. "Testing slope homogeneity in large panels," Journal of Econometrics, Elsevier, vol. 142(1), pages 50-93, January.
    4. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
    5. Manuel Arellano, 2003. "Discrete choices with panel data," Investigaciones Economicas, Fundación SEPI, vol. 27(3), pages 423-458, September.
    6. Carro, Jesus M., 2007. "Estimating dynamic panel data discrete choice models with fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 503-528, October.
    7. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    8. 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.
    9. Bo E. Honoré & Ekaterini Kyriazidou, 2000. "Panel Data Discrete Choice Models with Lagged Dependent Variables," Econometrica, Econometric Society, vol. 68(4), pages 839-874, July.
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    Citations

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    Cited by:

    1. Browning, Martin & Carro, Jesus M., 2014. "Dynamic binary outcome models with maximal heterogeneity," Journal of Econometrics, Elsevier, vol. 178(2), pages 805-823.
    2. Pauline Givord & Lionel Wilner, 2015. "When Does the Stepping‐Stone Work? Fixed‐Term Contracts Versus Temporary Agency Work in Changing Economic Conditions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 787-805, August.
    3. Tue Gørgens & Dean Hyslop, 2016. "The specification of dynamic discrete-time two-state panel data models," Working Papers 16_01, Motu Economic and Public Policy Research.
    4. Martin Browning & Jesus Carro, 2006. "Heterogeneity and Microeconometrics Modelling," CAM Working Papers 2006-03, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
    5. Hochguertel, Stefan & Ohlsson, Henry, 2011. "Wealth mobility and dynamics over entire individual working life cycles," Working Paper Series 1301, European Central Bank.
    6. Arthur Lewbel, 2006. "Modeling Heterogeneity," Boston College Working Papers in Economics 650, Boston College Department of Economics.
    7. Erik Biørn & Hild-Marte Bjørnsen, 2015. "What motivates farm couples to seek off-farm labour? A logit analysis of job transitions," European Review of Agricultural Economics, Foundation for the European Review of Agricultural Economics, vol. 42(2), pages 339-365.
    8. Fabio Berton & Francesco Devicienti & Lia Pacelli, 2011. "Are temporary jobs a port of entry into permanent employment?: Evidence from matched employer-employee," International Journal of Manpower, Emerald Group Publishing, vol. 32(8), pages 879-899, November.

    More about this item

    Keywords

    Unobserved Heterogeneity; Heterogeneous Slopes; Fixed Effects; Binary Choice; Panel Data;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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