Abstract
Panel or longitudinal data are becoming increasingly popular in applied work as they offer a number of advantages over pure cross-sectional or pure time-series data. A particularly useful feature is that they allow researchers to model unobserved heterogeneity at the level of the observational unit, where the latter may be an individual, a household, a firm or a country. Standard practice in the econometric literature is to model this heterogeneity as an individual-specific effect which enters additively in the model, typically assumed to be linear, that captures the statistical relationship between the dependent and the independent variables. The presence of these individual effects may cause problems in estimation. In particular in short panels, that is, in panels where the time-series dimension is of smaller order than the cross-sectional dimension, their estimation in conjunction with the other parameters of interest usually yields inconsistent estimators for both. (Notable exceptions are the static linear and the Poisson count panel data models, where estimation of the individual effects along with the finite dimensional coefficient vector yields consistent estimators of the latter.) This is the well-known incidental parameters problem (Neyman and Scott, 1948). In linear regression models, this problem may be dealt with by taking transformations of the model, such as first differences or differences from time averages (‘within transformation’), which remove the individual effect from the equation under consideration. However they do not apply to nonlinear econometric models, that is, models which are nonlinear in the parameters of interest and which include models that arise frequently in applied work, such as discrete choice models, limited dependent variable models, and duration models, among others.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Ahn, H. and Powell, J.L. 1993. Semiparametric estimation of censored selection models with a nonparametric selection mechanism. Journal of Econometrics 58, 3–29.
Andersen, E. 1970. Asymptotic properties of conditional maximum likelihood estimators. Journal of the Royal Statistical Society, Series B 32, 283–301.
Anderson, T. and Hsiao, C. 1981. Estimation of dynamic models with error components. Journal of the American Statistical Association 76(375), 598–606.
Butler, J.S. and Moffitt, R. 1982. A computationally efficient quadrature procedure for the one-factor multinomial probit model. Econometrica 50, 761–1.
Chamberlain, G. 1984. Panel data. In Handbook of Econometrics, vol 2, ed. Z. Griliches and M. Intrilligator. Amsterdam: North-Holland.
Chamberlain, G. 1985. Heterogeneity, omitted variable bias, and duration dependence. In Longitudinal Analysis of Labor Market Data, ed. J.J. Heckman and B. Singer. Cambridge: Cambridge University Press.
Fristedt, B. and Gray, L. 1997. A Modern Approach to Probability Theory. Boston: Birkhauser.
Honoré, B.E. 1992. Trimmed LAD and least squares estimation of truncated and censored regression models with fixed effects. Econometrica 60, 533–65.
Honoré, B.E. 1993. Orthogonality conditions for Tobit models with fixed effects and lagged dependent variables. Journal of Econometrics 59, 35–61.
Honoré, B.E. and Kyriazidou, E. 2000a. Panel data discrete choice models with lagged dependent variables. Econometrica 68, 839–74.
Honoré, B.E. and Kyriazidou, E. 2000b. Estimation of Tobit-type models with individual specific effects. Econometric Reviews 19, 341–66.
Hu, L. 2002. Estimation of a censored dynamic panel data model. Econometrica 70, 2499–517.
Kyriazidou, E. 1997. Estimation of a panel data sample selection model. Econometrica 65, 1335–64.
Kyriazidou, E. 2001. Estimation of dynamic panel data sample selection models. Review of Economic Studies 68, 543–72.
Magnac, T. 2000. Subsidised training and youth employment: distinguishing unobserved heterogeneity from state dependence in labour market histories. Economic Journal 110, 805–37.
Manski, C. 1987. Semiparametric analysis of random effects linear models from binary panel data. Econometrica 55, 357–62.
Newey, W. 1994. The asymptotic variance of semiparametric estimators. Econometrica 62, 1349–82.
Neyman, J. and Scott, E.L. 1948. Consistent estimation from partially consistent observations. Econometrica 16, 1–32.
Powell, J.L. 2001. Semiparametric estimation of bivariate latent variable models. In Nonlinear Statistical Modeling: Proceedings of the Thirteenth International Symposium in Economic Theory and Econometrics: Essays in Honor of Takeshi Amemiya, ed. C. Hsiao, K. Morimune and J.L. Powell. Cambridge: Cambridge University Press.
Wooldridge, J.M. 2000. A framework for estimating dynamic, unobserved effects panel data models with possible feedback to future explanatory variables. Economics Letters 68, 245–50.
Editor information
Editors and Affiliations
Copyright information
© 2010 Palgrave Macmillan, a division of Macmillan Publishers Limited
About this chapter
Cite this chapter
Kyriazidou, E. (2010). Nonlinear Panel Data Models. In: Durlauf, S.N., Blume, L.E. (eds) Microeconometrics. The New Palgrave Economics Collection. Palgrave Macmillan, London. https://doi.org/10.1057/9780230280816_19
Download citation
DOI: https://doi.org/10.1057/9780230280816_19
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-0-230-23881-7
Online ISBN: 978-0-230-28081-6
eBook Packages: Palgrave Media & Culture CollectionLiterature, Cultural and Media Studies (R0)