Nonlinear panel and social interaction models are increasingly being used in empirical econometrics. However, solution to general nonlinear panel models with fixed effects, as well as formal and empirical results for identification in social interactions are not generally available in the literature. The development of formal models as well as empirical implementation of these models will be very useful to empirical economists.
The fixed effects model of panel data usually results in biased estimation due to the incidental parameters problem. The estimators of the parameters of interest will be inconsistent if the number of individuals goes to infinity with the time periods held fixed. This occurs because only a finite number of observations are available to estimate each individual effect; hence this estimate is random, even in the limit. This research considers two approaches to reducing the bias from fixed effects estimation in nonlinear models. The first approach is an analytical bias correction model using the bias formula obtained from an asymptotic expansion as T grows. The second approach is based on a jacknife in the time series dimension of the panel that produces an estimator with properties similar to the analytical approach without explicit computation of the bias term.
The research also uses panel data method to pseudo-panel data that arise in linear-in-means models of social interactions. Many individual outcomes, such as earnings, criminal behavior, and unemployment, vary more between groups than within them. This research develops an identification strategy that exploits the differences in between-group and within-group variation in the panel data. The between-group variation that contains information on the social multiplier is identified utilizing Hausman and Taylor's (1981) idea developed for panel models. Such quasi-panel formulation clarifies that identification requires sources of exogenous within- and between- group variation in the models covariate vector.
This research will have significant effect on empirical econometrics as well other social sciences.
