Communication à un séminaire :
(LEI-ENSAE), « Nonparametric Identification using Group Theory »
, Econometrics Seminar
, TSE, Toulouse, 11 octobre 2011, 15:30-17:00, salle Amphi S.
This paper unifies and extends several recent nonparametric identification results on auctions, adverse selection or IV regression models by showing that all these models
satisfy what we call an induction property. This property states that if the structural function is identified at a given point, then it is also identified at another point. Using
results from group theory, we characterize the set where the structural function is identified under this property. The nature of this set depends on the dimensionality of the problem and on a property of the underlying group action, which is called
freeness. Full identification can be achieved in the one dimension case under freeness.
In the nonfree case, identification can be achieved but under a stronger induction
property. We obtain a partial characterization in the multivariate case. We illustrate
our framework to several settings, and provide new results on the identification of
sample selection models with discrete instruments.
Econométrie et Economie Empirique