Estimation and testing in dynamic, nonlinear panel data models

This dissertation consists of three chapters that address issues of estimation and testing in dynamic, nonlinear panel data models. Chapter 1 deals with an example of the peculiar difficulties that can arise in estimation of nonlinear models. Many economic variables occur as fractions and percentages. In these cases, the fractions instead of the level values are the variables of interest. Estimating models with fractional response variables can present challenges due to the presence of corner solution outcomes at 0 and 1 and continuous outcomes in the interval (0,1). Most standard estimation techniques are inappropriate in this setting because they are designed for variables that are either entirely continuous or take on only a discrete number of values. This chapter demonstrates an easily implemented method for estimating fractional response variables and presents an application of the technique to the determination of firm dividend policy.;Chapter 2 studies the sensitivity and relative performance of average partial effect estimates. Typically, partial effects are the quantities of interest for policy analysis. For linear models, these are often simply the parameter estimates. However, obtaining partial effects is more complicated for nonlinear models because these estimates will depend on all of the model's explanatory variables in a way that is not separable, except in special cases. Therefore, when some important individual specific explanatory variables are unobserved, consistent estimates of the partial effects may not be available. Instead, estimates of the partial effects averaged over the distribution of the unobservables, average partial effects, may be used as the variables of interest for policy analysis. Current estimation techniques for dynamic, nonlinear panel data models require strong assumptions on economic models. Which assumptions are maintained affects generality, ease of computation, and even which quantities can be estimated, but little evidence exists on the relative performance of different estimation techniques for nonlinear panel data models. Since few economic models conform to such restrictive assumptions, it is important to know how sensitive estimates in these models are to econometric specifications. This chapter includes both simulations and empirical analysis.;Chapter 3 addresses a more general problem of testing the assumption of homoskedasticity in nonlinear models with unobserved effects. As a practical matter, heteroskedasticity is of little concern in linear models since it does not affect consistency or unbiasedness of estimators, and standard errors can easily be corrected to perform inference. However, in many nonlinear models the presence of heteroskedasticity is of greater consequence because it changes the functional form of the estimator. The class of tests known as score tests is ideal for cases in which the alternative hypothesis is complicated or computationally difficult because it only requires estimation under the null for implementation and is invariant to a many alternative hypotheses. Thus, such a test can be formulated for the null hypothesis of homoskedasticity against a general alternative that encompasses many prevalent specifications of the variance as special cases or locally invariant alternatives. In this chapter, a test for heteroskedasticity is proposed for two dynamic latent variable models, namely the panel probit and fractional response models, and applications of the test are presented for each.