Structural econometric models are essential tools for many empirical studies in fields such as industrial organization, labor and public economics, and development economics. The analysis of identification is a first necessary step in any such studies. In many of these models, such as those involving multidimensional optimization or equilibrium conditions, the variables of interest are determined simultaneously. A recent result by Benkard and Berry (2004) has shown that identification results that were used for a long time to determine identification, in simultaneous equations models, are incorrect. Hence, other than in the restrictive linear specification models with additive unobservable random terms, studied decades ago, little is known at present about the conditions for identification in structural simultaneous equation models. In this project, the PI will develop correct conditions for identification of systems of simultaneous equations, in parametric and nonparametric models, with additive and nonadditive unobservable variables. Since a large body of previous work in econometrics has relied on the previous incorrect conditions, the PI will also analyze under what additional conditions in the structural models, those previous results still hold. The identification conditions that will be developed will be used to guide the discovery of new methods for estimation in nonparametric simultaneous equations, which will be consistent, asymptotically normal, and easy to compute. Since in many of the structural econometric models encountered in applied fields in economics, one encounters situations where observations on the actual values of endogenous variables, such as profits or utility values, is limited, the identification and estimation results will be extended to such situations, where the endogenous variables is simultaneous equations models are latent. To guide the PI in the development of the new methods, and to facilitate the adoption and understanding of the new methods, she will consider applications to several leading models in applied economics, such as models of consumer demand, discrete choice models, hedonic equilibrium models, Nash equilibrium, and models of survey response errors.
Intellectual Merit of the Proposed Activity The results about identification of simultaneous equations that the PI will develop will allow applied econometricians to determine the elements that can be identified in an econometric model, given their available data. The results will be applicable to very general models, which do not specify parametric structures either for the unknown functions or for the distributions of the unobservable random terms, as well as to more restrictive, parametric models. The results about estimation of nonparametric models will allow researchers to estimate such models without imposing parametric restrictions. Since structural econometric models where the values of the variables of interest are determined simultaneously is widespread in most applied fields in economics, these results are predicted to have a very wide impact. Moreover, by opening the road to new ways of analyzing identification and estimation in nonparametric simultaneous equation models, it is expected that a wave of new theoretical results will follow, as a result of the research in this project.
Broader Impacts Models where several variables of interest are determined simultaneously are widespread in, among others, engineering and the social sciences. The methods that will be developed in this project will be suitable for applications in these sciences, and through them, they will benefit society at large. With this aim, the results of the project will be disseminated widely. By involving a graduate student in this research, it is expected that he/she will apply the new results in his/her dissertation and/or develop new related results.
