Estimation of a Censored Dynamic Panel Data Model

PANEL DATA MODELS have a long history in econometrics and have become increasingly popular in empirical economics over the past two decades. Panel data expand our opportunities to study more complex economic relationships by, for example, allowing for individual heterogeneity and dynamic feedback. These goals are often achieved by including in the model individual specific effects and lagged dependent variables. These two features of the dynamic panel data model, however, often create difficulties in estimation. Although much progress has been made in the linear panel data model (see, among others, Hsiao (1986), Baltagi (1995), and Arellano and Honore (2001) for review), our knowledge of general nonlinear dynamic panel data models is very limited. In most nonlinear models, strict exogeneity of the explanatory variables is still the key assumption. The main difficulty is that with nonlinearity, it is not obvious how to "difference away" the individual specific effects and how to use instrumental variable type techniques.2 Despite these difficulties, some developments have been made on estimating certain nonlinear dynamic models using the "fixed-effects" approach, for example, the censored regression models (Honore (1993), Honore and Hu (2001)), the sample selection models (Kyriazidou (2001)), the discrete choice models (Honor6 and Kyriazidou (2000)), and the models with multiplicative individual effects (Chamberlain (1992), Wooldridge (1997)).