This research addresses three important topics in applied econometrics, namely analysis of panel data, stability of time series data, and derivation of instrumental variables. Panel data, that is a set of data including both time series and cross sectional observations have become widely used in studies of consumer behavior, entrance into and exit from the labor market, and decision-making within the family. Time series data play a very important role in many analyses of the long term performance of an economy and the influence of government policy. Instrumental variables often come into econometric research when the variables required in a model are either not observable, or have statistical properties which interfere with the model's applicability. The work on estimation of models with panel data extends the existing literature on linear models to nonlinear models. In particular the logit and probit models are extended to include time varying and random parameters. Dynamic models with lagged dependent variables are also derived and analyzed. The research on time series analysis involves the derivation of tests for unit roots. The tests include allowance for autocorrelation in the variables. The power and robustness of the tests under varying assumptions concerning trend and stationarity are assessed. The work on instrumental variable estimators provides a simple and easily applicable method of improving the efficiency of estimators, and brings under one general principle the treatments of diverse estimators such as 3-Stage Least Squares and Full Information Maximum Likelihood. %%% This project bridges an important gap between theoretical and applied econometrics. It focuses on three important topics widely used in econometric research, namely analysis of panel data, stability of time series, and the derivation of instrumental variables. The term "panel data" refers to any data set of observations on a given group of individuals, firms, or organizations taken over time. In this respect a panel data set is comprised of both cross sectional data (on the different individuals) and time series data (observations on the same group of individuals taken at different times). Such data are widely used in economic analysis of the labor market, consumer behavior, and economic growth. Time series data are very prevalent in studies of the aggregate economy. This project provides tests for the stability of a given set of time series data, and examines the robustness and power of those tests under various assumptions about the correlation among the observations and the tendency of the entire series to change through time. Instrumental variables are often used in economic models in place of more relevant variables in order to bring desired statistical properties to the model. For instance, in many models the relevant variables are not observed, but instruments derived from them can be observed. This project provides efficient methods for deriving instrumental variables and applies them to several estimation techniques.
