The research addresses three general topics: (1) nonparametric instrumental variables (IV) estimation, (2) estimation with high-dimensional data sets, and (3) imposing shape restrictions given by economic theory on nonparametric estimates of demand functions. Nonparametric IV estimation is a promising new econometric method that has received much recent attention in the econometrics literature. The research aims at solving two barriers that stand in the way of practical application of nonparametric IV methods in applied econometrics. The first is finding ways to choose the tuning parameters required to implement nonparametric IV estimators. The other is finding a way to construct confidence bands for functions estimated by nonparametric IV. The second topic is extending methods for estimating sparse, high-dimensional regression models in ways that make them more useful for economics and other social sciences. High-dimensional data sets are widely available in these fields. The statistical problem is to decide which variables to include in a model and to estimate the resulting model. Many existing methods for simultaneous model selection and estimation were motivated by problems in genomics. They are designed to identify empirically regression coefficients that are zero and estimate the ones that are not. In social science applications, however, it is more likely that some coefficients are "too small to matter," whereas others are "large." The proposed research will develop methods to discriminate empirically between "small" and "large" coefficients. The third topic is concerned with imposing the Slutsky condition of economic theory on nonparametric estimates of demand functions. Previous research has shown that imposing the Slutsky condition on a nonparametric estimate of average demand greatly improves the estimate's finite-sample performance and practical usefulness. The current research will develop ways to impose the Slutsky condition on estimates of non-separable demand functions. It also will develop ways to carry out estimation subject to the Slutsky condition when, as often happens, the income data are interval censored and, consequently, the demand function is not point identified.
The first research topic is important because it relaxes arbitrary assumptions that are frequently used in economic research, and thereby enables investigators to achieve results that are more accurate and realistic. The second topic is important because economic data often include many variables. It is rarely clear a priori which ones are relevant to the questions of interest, and decisions about which variables to use are often quite arbitrary. The research will provide systematic ways to make these decisions, enabling investigators in economics and other social sciences to achieve results of improved reliability. The third topic will yield improved methods for estimating demand functions. This is important for assessing the effects of economic policy interventions, including changes in taxes and prices.
