The project has two interrelated purposes: First, to analyze regularization techniques to impose shape restrictions in the estimation and numeric approximation of functions. More specifically, this part of the project studies techniques to impose monotonicity and other shape restrictions to regression, distribution, and quantile curves. The second purpose of the project consists of using regularized conditional quantile regression methods for policy analysis. In particular, this part develops inference methods to analyze the effect of counterfactual policies, or to decompose the effect of changes on the distribution of an outcome of interest across time or across subpopulations in differences of factors determining this outcome (composition effect) and differences on the effect of these factors (structure effect). For example, what would have been the distribution of infant birth weights for black mothers had they had the same economic and health characteristics as white mothers, what is the contribution of factors such as number of cigarettes smoked during pregnancy and pre?]natal care to the difference in infant birth weights between white and black mothers.
The project is focused on the following five parts: (1) Regularization techniques for distribution and quantile estimators; (2) Properties of regularization techniques for regression estimates; (3) Statistical applications: regularization of Edgeworth and Cornish Fisher expansions; (4) Economic applications of regularized estimates: yield curves, production and demand functions, and instrumental variables inference for distributional effects; (5) Inference on regularized counterfactual distributions.
Broader Impacts: The regularization techniques proposed are simple to implement and expected to be routinely used for practitioners. Thus, for example, a routine to monotonize quantile regression estimates based on the first part of the project is already available in the quantile regression package of freeware software R (which is publicly available at no cost). The inference methods for counterfactual analysis are also expected to have a broad impact since this type of analysis is commonly used in labor economics and other fields. A final purpose of the project is to produce public software in R that implements all the methods developed. The project will also have direct educational impact by involving help of two graduate students. One of the graduate students is already working as co-author of the parts (1), (2), and (3) of the project; and the other graduate student (to be funded by this project, if approved) will be coauthor for parts (4).
