Nonlinear Models with Individual Effects

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Panel data, consisting of observations across time for individual economic agents, allows the possibility of controlling for unobserved individual heterogeneity. Such heterogeneity can arise from unobserved differences in tastes or technology and can be an important phenomenon. In such instances failure to control for it can result in misleading inferences. This problem is particularly severe when the unobserved heterogeneity affects explanatory variables. Situations of this sort arise naturally when some of the explanatory variables are decision variables, as is the case, for example, in dynamic panel data models. Models and methods of controlling for unobserved heterogeneity in linear models are well established. However, less is known about how to control for unobserved heterogeneity in nonlinear models. The methods that work for linear models do not carry over in a straightforward way to most nonlinear models. Except in special circumstances, it is not possible to eliminate individual effects by some data transformation, such as first differencing of time series observations which works in linear models. Also, fixed effects estimators of nonlinear models, which treat the individual effects as parameters to be estimated, encounter problems because of the short length of the typical time series in economic panel data. This research concerns two topics in controlling for unobserved heterogeneity in nonlinear models of panel data. The first topic deals with modelling the distribution of the individual effects, conditional on the explanatory variables. Such models can be used to specify random effects limited dependent variable models with a nonparametric conditional mean for the individual effect. The second topic investigates the use of the jacknife, applied to the time series dimension of panel data, for reduction of the bias of fixed effects estimators in nonlinear models. The research will examine the extent to which this nonparametric bias reduction method can alleviate the incidental parameters bias, in different models. The basic goals of the project are to assess the potential empirical impact of the models and methods to be considered, as well as derivation of asymptotic distributions for the various estimators.