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Unformatted text preview: Imbens/Wooldridge, Lecture Notes 9, Summer ’07 1 What’s New in Econometrics NBER, Summer 2007 Lecture 9, Tuesday, July 31th, 3.15-4.15pm Partial Identification 1. Introduction Traditionally in constructing statistical or econometric models researchers look for models that are (point-)identified : given a large (infinite) data set, one can infer without uncertainty what the values are of the objects of interest, the estimands. Even though the fact that a model is identified does not necessarily imply that we do well in finite samples, it would appear that a model where we cannot learn the parameter values even in infinitely large samples would not be very useful. Traditionally therefore researchers have stayed away from models that are not (point-)identified, often adding assumptions beyond those that could be justified using substantive arguments. However, it turns out that even in cases where we cannot learn the value of the estimand exactly in large samples, in many cases we can still learn a fair amount, even in finite samples. A research agenda initiated by Manski (an early paper is Manski (1990), monographs include Manski (1995, 2003)), referred to as partial identification , or earlier as bounds , and more recently adopted by a large number of others, notably Tamer in a series papers (Haile and Tamer, 2003, Ciliberto and Tamer, 2007; Aradillas-Lopez and Tamer, 2007), has taken this perspective. In this lecture we focus primarily on a number of examples to show the richness of this approach. In addition we discuss some of the theoretical issues connected with this literature, and some practical issues in implementation of these methods. The basic set up we adopt is one where we have a random sample of units from some population. For the typical unit, unit i , we observe the value of a vector of variables Z i . Sometimes it is useful to think of there being in the background a latent variable variable W i . We are interested in some functional θ of the joint distribution of Z i and W i , but, not observing W i for any units, we may not be able to learn the value of θ even in infinite samples because the estimand cannot be written as a functional of the distribution of Z i alone. The Imbens/Wooldridge, Lecture Notes 9, Summer ’07 2 three key questions are ( i ) what we can learn about θ in large samples (identification), ( ii ) how do we estimate this (estimation), and ( iii ) how do we quantify the uncertainty regarding θ (inference). The solution to the first question will typically be a set, the identified set . Even if we can characterize estimators for these sets, computing them can present serious challenges. Finally, inference involves challenges concerning uniformity of the coverage rates, as well as the question whether we are interested in coverage of the entire identified set or only of the parameter of interest....
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08