Econometrica: May 2012, Volume 80, Issue 3

Set Identified Linear Models
p. 1129-1155

Christian Bontemps, Thierry Magnac, Eric Maurin

We analyze the identification and estimation of parameters satisfying the linear moment restrictions ((−)) = (()), where is a set of instruments and () an unknown bounded scalar function. We first provide empirically relevant examples of such a setup. Second, we show that these conditions set identify where the identified set is bounded and convex. We provide a sharp characterization of the identified set not only when the number of moment conditions is equal to the number of parameters of interest, but also in the case in which the number of conditions is strictly larger than the number of parameters. We derive a necessary and sufficient condition of the validity of supernumerary restrictions which generalizes the familiar Sargan condition. Third, we provide new results on the asymptotics of analog estimates constructed from the identification results. When is a strictly convex set, we also construct a test of the null hypothesis, ∈, whose size is asymptotically correct and which relies on the minimization of the support function of the set − {}. Results of some Monte Carlo experiments are presented.

Log In To View Full Content

Supplemental Material

Supplement to "Set Identified Linear Models"

This zip file contains replication files for the manuscript.

Read More View ZIP

Supplement to "Set Identified Linear Models"

This PDF contains proofs for the manuscript.

Read More View PDF