Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-04-30T22:09:01.525Z Has data issue: false hasContentIssue false
  • English
  • Français

SEMIPARAMETRIC ESTIMATION OF DYNAMIC BINARY CHOICE PANEL DATA MODELS

Published online by Cambridge University Press:  11 March 2024

Fu Ouyang Open the ORCID record for Fu Ouyang [Opens in a new window]  and
Thomas Tao Yang Open the ORCID record for Thomas Tao Yang [Opens in a new window]
Fu Ouyang*
Affiliation:
University of Queensland
Thomas Tao Yang
Affiliation:
Australian National University
*
Address correspondence to Fu Ouyang, School of Economics, University of Queensland, St Lucia, QLD, Australia, e-mail: f.ouyang@uq.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose a new approach to the semiparametric analysis of panel data binary choice models with fixed effects and dynamics (lagged dependent variables). The model under consideration has the same random utility framework as in Honoré and Kyriazidou (2000, Econometrica 68, 839–874). We demonstrate that, with additional serial dependence conditions on the process of deterministic utility and tail restrictions on the error distribution, the (point) identification of the model can proceed in two steps, and requires matching only the value of an index function of explanatory variables over time, rather than the value of each explanatory variable. Our identification method motivates an easily implementable, two-step maximum score (2SMS) procedure – producing estimators whose rates of convergence, in contrast to Honoré and Kyriazidou’s (2000, Econometrica 68, 839–874) methods, are independent of the model dimension. We then analyze the asymptotic properties of the 2SMS procedure and propose bootstrap-based distributional approximations for inference. Evidence from Monte Carlo simulations indicates that our procedure performs satisfactorily in finite samples.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 40
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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

We thank the editor (Peter C. B. Phillips), the co-editor (Iván Fernández-Val), and the two anonymous referees for their valuable comments and suggestions, which have significantly improved the quality of this paper. We are grateful to Yonghong An, Shakeeb Khan, Arthur Lewbel, Takuya Ura, Hanghui Zhang, and Yichong Zhang for their insightful feedback and discussions. We also thank participants at the 2019 Asian Meeting of the Econometric Society, the 2019 Shanghai Workshop of Econometrics, and the 2022 Australasia Meeting of the Econometric Society for their helpful comments. Fu Ouyang acknowledges the financial support provided by the Faculty of Business, Economics, and Law (BEL) at the University of Queensland through the 2019 BEL New Staff Research Start-Up Grant. All errors are our responsibility.

References

REFERENCES

Abrevaya, J., & Huang, J. (2005). On the bootstrap of the maximum score estimator. Econometrica , 73, 1175–1204.CrossRefGoogle Scholar
Aguirregabiria, V., & Carro, J. M. (2021). Identification of average marginal effects in fixed effects dynamic discrete choice models. Preprint, arXiv:2107.06141.Google Scholar
Alessie, R., Hochguertel, S., & Soest, A. v. (2004). Ownership of stocks and mutual funds: A panel data analysis. Review of Economics and Statistics , 86, 783–796.CrossRefGoogle Scholar
Al-Sadoon, M. M., Li, T., & Pesaran, M. H. (2017). Exponential class of dynamic binary choice panel data models with fixed effects. Econometric Reviews , 36, 898–927.CrossRefGoogle Scholar
Altonji, J. G., & Matzkin, R. L. (2005). Cross section and panel data estimators for nonseparable models with endogenous regressors. Econometrica , 73, 1053–1102.CrossRefGoogle Scholar
Arellano, M., & Carrasco, R. (2003). Binary choice panel data models with predetermined variables. Journal of Econometrics , 115, 125–157.CrossRefGoogle Scholar
Arellano, M., & Honoré, B. (2001). Panel data models: Some recent developments. In Heckman, J. J., & Leamer, E. (Eds.), Handbook of econometrics , vol. 5 (pp. 3229–3296). Elsevier.Google Scholar
Aristodemou, E. (2021). Semiparametric identification in panel data discrete response models. Journal of Econometrics , 220, 253–271.CrossRefGoogle Scholar
Bartolucci, F., & Nigro, V. (2010). A dynamic model for binary panel data with unobserved heterogeneity admitting a $\sqrt{n}$ -consistent conditional estimator. Econometrica , 78, 719–733.Google Scholar
Bartolucci, F., & Nigro, V. (2012). Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data. Journal of Econometrics , 170, 102–116.CrossRefGoogle Scholar
Biewen, M. (2009). Measuring state dependence in individual poverty histories when there is feedback to employment status and household composition. Journal of Applied Econometrics , 24, 1095–1116.CrossRefGoogle Scholar
Cameron, S. V., & Heckman, J. J. (1998). Life cycle schooling and dynamic selection bias: Models and evidence for five cohorts of American males. Journal of Political economy , 106, 262–333.CrossRefGoogle Scholar
Cameron, S. V., & Heckman, J. J. (2001). The dynamics of educational attainment for black, hispanic, and white males. Journal of Political Economy , 109, 455–499.CrossRefGoogle Scholar
Cattaneo, M. D., Jansson, M., & Nagasawa, K. (2020). Bootstrap-based inference for cube root asymptotics. Econometrica , 88, 2203–2219.CrossRefGoogle Scholar
Chamberlain, G. (2010). Binary response models for panel data: Identification and information. Econometrica , 78, 159–168.Google Scholar
Charlier, E. (1997). Limited dependent variable models for panel data. Technical report. Tilburg University, School of Economics and Management.Google Scholar
Chay, K. Y., Hoynes, H. W., & Hyslop, D. (1999). A non-experimental analysis of true state dependence in monthly welfare participation sequences. American Statistical Association, 9–17.Google Scholar
Chen, S., Khan, S, & Tang, X. (2018). Exclusion restrictions in dynamic binary choice panel data models. Technical report. Boston College, Department of Economics.Google Scholar
Chen, S., Khan, S., & Tang, X. (2019). Exclusion Restrictions in Dynamic Binary Choice Panel Data Models: Comment on “Semiparametric Binary Choice Panel Data Models Without Strictly Exogenous Regressors”. Econometrica , 87, 1781–1785.CrossRefGoogle Scholar
Chernozhukov, V., Fernández-Val, I., Hahn, J., & Newey, W. (2013). Average and quantile effects in nonseparable panel models. Econometrica , 81, 535–580.Google Scholar
Chintagunta, P., Kyriazidou, E., & Perktold, J. (2001). Panel data analysis of household brand choices. Journal of Econometrics , 103, 111–153.CrossRefGoogle Scholar
Damrongplasit, K., Hsiao, C., & Zhao, X. (2018). Health status and labour market outcome: Empirical evidence from Australia. Pacific Economic Review , 24, 269–292.CrossRefGoogle Scholar
Dano, K. (2023). Transition probabilities and identifying moments in dynamic fixed effects logit models. Preprint, arXiv:2303.00083.Google Scholar
Davezies, L., D’Haultfoeuille, X., & Laage, L. (2022). Identification and estimation of average marginal effects in fixed effects logit models. Preprint arXiv:2105.00879.Google Scholar
Delgado, M., Rodríguez-Poo, J., & Wolf, M. (2001). Subsampling inference in cube root asymptotics with an application to Manski’s maximum score estimator. Economics Letters , 73, 241–250.CrossRefGoogle Scholar
Dobronyi, C., Gu, J., & Kim, K. I. (2021). Identification of dynamic panel logit models with fixed effects. Preprint, arXiv:2104.04590.Google 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
Halliday, T. J. (2008). Heterogeneity, state dependence and health. Econometrics Journal , 11, 499–516.CrossRefGoogle Scholar
Heckman, J. J. (1981a). The incidental parameters problem and the problem of initial condition in estimating a discrete time-discrete data stochastic process. In Manski, C. F. and McFadden, D. L. (Eds.), Structural analysis of discrete data and econometric applications . MIT Press, 179–195.Google Scholar
Heckman, J. J. (1981b). Statistical models for discrete panel data. In Manski, C. F., & McFadden, D. L. (Eds.), Structural analysis of discrete data and econometric applications . MIT Press, 114–178.Google Scholar
Hong, H., & Li, J. (2020). The numerical bootstrap. Annals of Statistics , 48, 397–412.CrossRefGoogle Scholar
Honoré, B. E., & De Paula, Á. (2021). Identification in simple binary outcome panel data models. Econometrics Journal , 24, C78–C93.CrossRefGoogle Scholar
Honoré, B. E., & Kyriazidou, E. (2000). Panel data discrete choice models with lagged dependent variables. Econometrica , 68, 839–874.CrossRefGoogle Scholar
Honoré, B. E., & Lewbel, A. (2002). Semiparametric binary choice panel data models without strictly exogeneous regressors. Econometrica , 70, 2053–2063.CrossRefGoogle Scholar
Honoré, B. E., & Tamer, E. (2006). Bounds on parameters in panel dynamic discrete choice models. Econometrica , 74, 611–629.CrossRefGoogle Scholar
Honoré, B. E., & Weidner, M. (2020). Moment conditions for dynamic panel logit models with fixed effects. Preprint, arXiv:2005.05942.Google Scholar
Horowitz, J. L. (1992). A smoothed maximum score estimator for the binary response model. Econometrica , 60, 505–531.CrossRefGoogle Scholar
Hsiao, C. (2022). Analysis of panel data , 4th ed. Econometric Society Monographs. Cambridge University Press.CrossRefGoogle Scholar
Kerr, W. R., Lincoln, W. F., & Mishra, P. (2014). The dynamics of firm lobbying. American Economic Journal: Economic Policy , 6, 343–79.Google Scholar
Khan, S., Ponomareva, M., & Tamer, E. (2020). Identification of dynamic panel binary response models. Boston College Working Papers in Economics 979. Boston College Department of Economics.Google Scholar
Kim, J., & Pollard, D. (1990). Cube root asymptotics. Annals of Statistics , 18, 191–219.CrossRefGoogle Scholar
Kitazawa, Y. (2022). Transformations and moment conditions for dynamic fixed effects logit models. Journal of Econometrics , 229, 350–362.CrossRefGoogle Scholar
Kyriazidou, E. (1997). Estimation of a panel data sample selection model. Econometrica , 65, 1335.CrossRefGoogle Scholar
Lee, S. M. S., & Pun, M. C. (2006). On m out of n bootstrapping for nonstandard m-estimation with nuisance parameters. Journal of American Statistical Association , 101, 1185–1197.CrossRefGoogle Scholar
Liu, L., Poirier, A., & Shiu, J.-L. (2023). Identification and estimation of average partial effects in semiparametric binary response panel models. Preprint, arXiv:2105.12891.Google 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. Journal of Econometrics , 27, 313–333.CrossRefGoogle Scholar
Manski, C. F. (1987). Semiparametric analysis of random effects linear models from binary panel data. Econometrica , 55, 357–362.CrossRefGoogle Scholar
McFadden, D. L. (1976). Quantal choice analysis: A survey. Annals of Economic and Social Measurement , 5, 363–390.Google Scholar
Pakes, A., & Porter, J. (2016). Moment inequalities for multinomial choice with fixed effects. Technical report. National Bureau of Economic Research.Google Scholar
Patra, R. K., Seijo, E., & Sen, B. (2018). A consistent bootstrap procedure for the maximum score estimator. Journal of Econometrics , 205, 488–507.CrossRefGoogle Scholar
Price, K. V., Storn, R. M., & Lampinen, J. A. (2006). A practical approach to global optimization . Springer-Verlag.Google Scholar
Seo, M. H., & Otsu, T. (2018). Local M-estimation with discontinuous criterion for dependent and limited observations. Annals of Statistics , 46, 344–369.CrossRefGoogle Scholar
Shi, X., Shum, M., & Song, W. (2018). Estimating semiparametric panel multinomial choice models using cyclic monotonicity. Econometrica , 86, 737–761.CrossRefGoogle Scholar
Silvapulle, M. J. (1981). On the existence of maximum likelihood estimators for the binomial response models. Journal of the Royal Statistical Society. Series B (Methodological) , 310–313.CrossRefGoogle Scholar
Storn, R. M., & Price, K. V. (1997). Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization , 11, 341–359.CrossRefGoogle Scholar
Torgovitsky, A. (2019). Nonparametric inference on state dependence in unemployment. Econometrica , 87, 1475–1505.CrossRefGoogle Scholar
van der Vaart, A., & Wellner, J. (1996). Weak convergence and empirical processes . Springer.CrossRefGoogle Scholar
Williams, B. (2019). Nonparametric identification of discrete choice models with lagged dependent variables. Journal of Econometrics 215, 286–304.CrossRefGoogle Scholar
Wooldridge, J. M. (2005). Simple solutions to the initial conditions problem in dynamic, nonlinear panel data models with unobserved heterogeneity. Journal of Applied Econometrics , 20, 39–54.CrossRefGoogle Scholar
Yan, J., & Yoo, H. I. (2019). Semiparametric estimation of the random utility model with rank-ordered choice data. Journal of Econometrics , 211, 414–438.CrossRefGoogle Scholar
Supplementary material: File

Ouyang and Yang supplementary material

Ouyang and Yang supplementary material
Download Ouyang and Yang supplementary material(File)
File 492.7 KB