There are cases in econometrics when the parameters of a model may not be easily identified making estimation and inference very difficult. This research will study and develop techniques for a number of related statistical and economic models that can be used to empirically investigate how economic agents (such as individual or firms) behave over time. These models have been used in many areas of economics: in labor economics to study the duration of employment or unemployment; in public economics to study participation in welfare programs; in marketing to study the long run effects of advertising; and in health economics to study differences in health status across demographic groups. These are all important questions, and to answer them it is important to have appropriate techniques. The main contribution of this project will be to investigate exactly what features of these models can be estimated, and how to estimate them. Even though it is often not possible to exactly estimate the parameters of interest, even if one had an infinite number of observations, it is in practice often possible to precisely find bounds for the parameters of such models. This research will provide techniques to provide such bounds of the parameters of interest. By providing methods to develop the bounds of parameters, the PI provides a way to estimate models that hitherto had been inestimable in a wide range of fields in economics. Although the main contributions of the research will be methodological, the project will also include applications of the methods that are developed. This research will be joint with more applied economists who are interested in the dynamics of unemployment and in health economics and thus provide ready applications of the theory developed in this research.
