EconStor Collection:
http://hdl.handle.net/10419/64637
2016-07-24T03:19:15ZDoubly robust uniform confidence band for the conditional average treatment effect function
http://hdl.handle.net/10419/130093
Title: Doubly robust uniform confidence band for the conditional average treatment effect function
Authors: Lee, Sokbae; Okui, Ryo; Wang, Yoon-Jae
Abstract: In this paper, we propose a doubly robust method to present the heterogeneity of the average treatment effect with respect to observed covariates of interest. We consider a situation where a large number of covariates are needed for identifying the average treatment effect but the covariates of interest for analyzing heterogeneity are of much lower dimension. Our proposed estimator is doubly robust and avoids the curse of dimensionality. We propose a uniform confidence band that is easy to compute, and we illustrate its usefulness via Monte Carlo experiments and an application to the effects of smoking on birth weights.2016-01-01T00:00:00ZIdentification and efficiency bounds for the average match function under conditionally exogenous matching
http://hdl.handle.net/10419/130097
Title: Identification and efficiency bounds for the average match function under conditionally exogenous matching
Authors: Graham, Bryan S.; Imbens, Guido W.; Ridder, Geert
Abstract: Consider two heterogenous populations of agents who, when matched, jointly produce an output, Y. For example, teachers and classrooms of students together produce achievement, parents raise children, whose life outcomes vary in adulthood, assembly plant managers and workers produce a certain number of cars per month, and lieutenants and their platoons vary in unit effectiveness. Let W 2 W = {w1, . . . ,wJ} and X 2 X = {x1, . . . ,xK} denote agent types in the two populations. Consider the following matching mechanism: take a random draw from the W = wj subgroup of the first population and match her with an independent random draw from the X = xk subgroup of the second population. Let ß (wj, xk), the average match function (AMF), denote the expected output associated with this match. We show that (i) the AMF is identified when matching is conditionally exogenous, (ii) conditionally exogenous matching is compatible with a pairwise stable aggregate matching equilibrium under specific informational assumptions, and (iii) we calculate the AMF's semiparametric efficiency bound.2016-01-01T00:00:00ZPractical and theoretical advances in inference for partially identified models
http://hdl.handle.net/10419/130095
Title: Practical and theoretical advances in inference for partially identified models
Authors: Canay, Ivan; Shaikh, Azeem
Abstract: This paper surveys some of the recent literature on inference in partially identified models. After reviewing some basic concepts, including the definition of a partially identified model and the identified set, we turn our attention to the construction of confidence regions in partially identified settings. In our discussion, we emphasize the importance of requiring confidence regions to be uniformly consistent in level over relevant classes of distributions. Due to space limitations, our survey is mainly limited to the class of partially identified models in which the identified set is characterized by a finite number of moment inequalities or the closely related class of partially identified models in which the identified set is a function of a such a set. The latter class of models most commonly arise when interest focuses on a subvector of a vectorvalued parameter, whose values are limited by a finite number of moment inequalities. We then rapidly review some important parts of the broader literature on inference in partially identified models and conclude by providing some thoughts on fruitful directions for future research.2016-01-01T00:00:00ZConfidence intervals for projections of partially identified parameters
http://hdl.handle.net/10419/130090
Title: Confidence intervals for projections of partially identified parameters
Authors: Kaido, Hiroaki; Molinari, Francesca; Stoye, Jörg
Abstract: This paper proposes a bootstrap-based procedure to build confidence intervals for single components of a partially identified parameter vector, and for smooth functions of such components, in moment (in)equality models. The extreme points of our confidence interval are obtained by maximizing/minimizing the value of the component (or function) of interest subject to the sample analog of the moment (in)equality conditions properly relaxed. The novelty is that the amount of relaxation, or critical level, is computed so that the component (or function) of Ø, instead of Ø itself, is uniformly asymptotically covered with prespecified probability. Calibration of the critical level is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attractive. Computation of the extreme points of the confidence interval is based on a novel application of the response surface method for global optimization, which may prove of independent interest also for applications of other methods of inference in the moment (in)equalities literature. The critical level is by construction smaller (in finite sample) than the one used if projecting confidence regions designed to cover the entire parameter vector. Hence, our confidence interval is weakly shorter than the projection of established confidence sets (Andrews and Soares, 2010), if one holds the choice of tuning parameters constant. We provide simple conditions under which the comparison is strict. Our inference method controls asymptotic coverage uniformly over a large class of data generating processes. Our assumptions and those used in the leading alternative approach (a profiling based method) are not nested. We explain why we employ some restrictions that are not required by other methods and provide examples of models for which our method is uniformly valid but profiling based methods are not.2016-01-01T00:00:00Z