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Transcript
The University of Chicago
Department of Statistics
Seminar Series
AZEEM SHAIKH
Department of Economics
The University of Chicago
Inference for Partially Identified Econometrics
MONDAY, February 18, 2008 at 4:00 PM
133 Eckhart Hall, 5734 S. University Avenue
Refreshments following the seminar in Eckhart 110.
ABSTRACT
We develop computationally intensive, yet feasible methods for inference in a very general
class of partially identified econometric models. Let P denote the distribution of the observed
data. The class of models we consider are defined by a population objective function Q(θ, P )
for θ ∈ Θ. The point of departure from the classical extremum estimation framework is that
it is not assumed that Q(θ, P ) has a unique minimizer in the parameter space Θ. The goal
may be either to draw inferences about some unknown point in the set of minimizers of the
population objective function or to draw inferences about the set of minimizers itself. To
this end, we study two distinct definitions for confidence regions. In the first formulation,
the object of interest is some unknown point θ ∈ Θ0 (P ), where Θ0 (P ) = arg minθ∈Θ Q(θ, P ),
and so we seek random sets that contain each θ ∈ Θ0 (P ) with at least some prespecified
probability asymptotically. In the second formulation, the object of interest is Θ0 (P ) itself,
and so we seek random sets that contain this set with at least some prespecified probability
asymptotically. For each of these two notions of confidence regions, we construct random sets
satisfying the desired coverage property under weak assumptions. We also provide conditions
under which the confidence regions are uniformly consistent in level.
Please send email to Mathias Drton ([email protected]) for further information. Information about building
access for persons with disabilities may be obtained in advance by calling Karen Gonzalez (Department Administrator
and Assistant to Chair) at 773.702.8335 or by email ([email protected]).