- Volume 23 Issue 2
The fixed effects panel probit model faces "incidental parameters problem" because it has a property that the number of parameters to be estimated will increase with sample size. The maximum likelihood estimation fails to give a consistent estimator of slope parameter. Unlike the panel regression model, it is not feasible to find an orthogonal reparameterization of fixed effects to get a consistent estimator. In this note, a hierarchical Bayesian model is proposed. The model is essentially equivalent to the frequentist's random effects model, but the individual specific effects are estimable with the help of Gibbs sampling. The Bayesian estimator is shown to reduce reduced the small sample bias. The maximum likelihood estimator in the random effects model is also efficient, which contradicts Green (2004)'s conclusion.
panel probit model;Gibbs sampling;incidental parameters problem;fixed effects;random effects;individual-specific effects
- Albert JH and Chib S (1993). Bayesian analysis of binary and polychotomous response data, Journal of the American Statistical Association, 88, 669-679. https://doi.org/10.1080/01621459.1993.10476321
- ABmann C, GoBmann S, and Schonberger B (2014). Bayesian analysis of binary panel probit models: the case of measurement error and missing values in explaining factors, (NEPS Working Paper No 35), Bamberg: National Educational Panel Study.
- Baltagi B (2000). Econometric Analysis of Panel Data (2nd ed.), John Wiley & Sons, New York.
- Bruno G (2004). Limited dependent panel models: a comparative analysis of classical and Bayesian inference among econometrics packages, Retrieved March 1, 2016, from: http://fmwww.bc.edu/repec/sce2004/up.24654.1076487923.pdf
- Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, and Rubin DB (2013). Bayesian Data Analysis (3rd ed.), CRC Press, Boca Raton.
- Green W (2004). The behaviour of the maximum likelihood estimator of limited dependent variable models in the presence of fixed effects, Econometrics Journal, 7, 98-119. https://doi.org/10.1111/j.1368-423X.2004.00123.x
- Hahn J (2004). Does Jeffrey's prior alleviate the incidental parameter problem?, Economics Letters, 82, 135-138. https://doi.org/10.1016/j.econlet.2003.04.001
- Hamilton BH (1999). HMO selection and Medicare costs: Bayesian MCMC estimation of a robust panel data tobit model with survival, Health Economics, 8, 403-414. https://doi.org/10.1002/(SICI)1099-1050(199908)8:5<403::AID-HEC455>3.0.CO;2-D
- Harris MN, Macquarie LR, and Siouclis AJ (2000). A comparison of alternative estimators for binary panel probit models (Melbourne Institute Working Paper No. 3), Melbourne Institute of Applied Economic and Social Research, Melbourne.
- Heckman J (1981). The incidental parameters problem and the problem of initial conditions in estimating a discrete time-discrete data stochastic process. In CF Manski and D McFadden (Eds), Structural Analysis of Discrete Data with Econometric Applications (pp. 179-195), MIT Press, Cambridge.
- Hobert JP and Casella G (1996). The effect of improper priors on Gibbs sampling in hierarchical linear mixed models, Journal of the American Statistical Association, 91, 1461-1473. https://doi.org/10.1080/01621459.1996.10476714
- Hsiao C (1996). Logit and probit models. In L. Matyas and P Sevestre (Eds), The Econometrics of Panel Data: Handbook of Theory and Applications (pp. 410-428), Kluwer Academic Publisher, Dordrecht.
- Lancaster T (2000). The incidental parameter problem since 1948, Journal of Econometrics, 95, 391-413. https://doi.org/10.1016/S0304-4076(99)00044-5
- Lancaster T (2002). Orthogonal parameters and panel data, Review Economic Studies, 69, 647-666. https://doi.org/10.1111/1467-937X.t01-1-00025
- Lee SC and Choi B (2014). Bayesian inference for censored panel regression model, Communications for Statistical Applications and Methods, 21, 193-200. https://doi.org/10.5351/CSAM.2014.21.2.193
- Maddala GS (1983). Limited-Dependent and Qualitative Variables in Econometrics, Cambridge University Press, New York.
- McCulloch CE (1996). Fixed and random effects and best prediction, In Proceedings of the Kansas State Conference on Applied Statistics in Agriculture.
- Morawetz U (2006). Bayesian Modelling of Panel Data with Individual Effects Applied to Simulated Data, Institut fur Nachhaltige Wirtschaftsentwicklung, Wien.
- Neyman J and Scott EL (1948). Consistent estimates based on partially consistent observations, Econometrica, 16, 1-32. https://doi.org/10.2307/1914288
- Nickell S (1981). Biases in dynamic models with fixed effects, Econometrica, 49, 1417-1426. https://doi.org/10.2307/1911408
- R Core Team (2015). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
- Sarrias M (2015). Discrete choice models with random parameters in R: the Rchoice package, Retrieved March 1, 2016, from: http://msarrias.weebly.com/uploads/3/7/7/8/37783629/rchoicevignette.pdf
- Tanner MA and Wong WH (1987). The calculation of posterior distributions by data augmentation (with discussion), Journal of the American Statistical Association, 82, 528-550. https://doi.org/10.1080/01621459.1987.10478458
Supported by : Hanshin University