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TITLE:
A Simple Ordered Data Estimator for Inverse Density Weighted Expectations

AUTHOR(S):
Arthur Lewbel , Boston College
Susanne M. Schennach, University of Chicago

DOCUMENT TYPE: Article

ABSTRACT:
We consider estimation of means of functions that are scaled by an unknown density, or equivalently, integrals of conditional expectations. The "ordered data" estimator we provide is root n consistent, asymptotically normal, and is numerically extremely simple, requiring little more than ordering the data and summing the results. A similarly simple estimator is provided for the limiting variance. Potential applications include endogenous binary choice, willingness to pay, selection, and treatment models.