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Author: Johnson, Edward Graham
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Johnson, Edward Graham 
Panel Data Models with Discrete Dependent Variables Ph.D. Dissertation, Stanford University, October 2004. DAIA 65/04, p. 1464, Oct 2004 Cohort(s): NLSY79 Publisher: UMI  University Microfilms, Bell and Howell Information and Learning Keyword(s): Data Analysis; Educational Attainment; Family Models; Modeling; Modeling, Fixed Effects; Modeling, Logit; Modeling, Probit; Monte Carlo; Siblings; Statistical Analysis This dissertation makes two main contributions to the theory of panel data models with discrete dependent variables when the number of time periods is fixed. First, I present a new way of thinking about identification in these models and prove a necessary condition for identification of the common parameters. I show that under fairly general conditions, in a model of K discrete probabilities containing a nonparametric "fixed" effect, the common parameters can only be identified if the set of values that the K1 independent probabilities can take on (as the fixed effect varies) lies in a K2 dimensional subspace for some value of the explanatory variables. I show how this theorem can be used to derive results about identification in static binarychoice models with independence across time. This approach can be useful in understanding identification in many varieties of these types of models. For example, I prove that the parameters in a panel probit model are not identified. In another chapter, I present a method for estimating the parameters (including the threshold parameters) of an ordered logit model with fixed effects for panel data when the number of time periods is small. The method is based on the conditionallikelihood approach, but differs in that several conditional probabilities are derived, which together overidentify the model. These probabilities are used to construct moment conditions, which are then weighted using a standard GMM procedure. I also develop a method of evaluating population average marginal probability derivatives. This method requires a strong assumption about the distribution of the fixed effects, but Monte Carlo evidence suggests that the method gives good results even when this assumption is severely violated. I present an empirical application that uses these methods to investigate the factors that affect educational degree attainment by individuals, controlling for familyspecific fixed effects, using a sample of siblings from the National Longitudinal Survey of Youth. 

Bibliography Citation
Johnson, Edward Graham. Panel Data Models with Discrete Dependent Variables. Ph.D. Dissertation, Stanford University, October 2004. DAIA 65/04, p. 1464, Oct 2004. 