centre for microdata methods and practice

ESRC centre

cemmap is an ESRC research centre

ESRC

Keep in touch

Subscribe to cemmap news

Set identified linear models

Authors: Christian Bontemps , Thierry Magnac and Eric Maurin
Date: 10 April 2011
Type: cemmap Working Paper, CWP13/11
DOI: 10.1920/wp.cem.2011.1311

Abstract

We analyze the identification and estimation of parameters β satisfying the incomplete linear moment restrictions E(z T(x β−y)) = E(zTu(z)) where z is a set of instruments and u(z) an unknown bounded scalar function. We first provide empirically relevant examples of such a set-up. Second, we show that these conditions set identify β where the identified set B 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 B is a strictly convex set, we also construct a test of the null hypothesis, β0 ε B, whose size is asymptotically correct and which relies on the minimization of the support function of the set B − { β 0}. Results of some Monte Carlo experiments are presented.

Download full version
Now published:
Christian Bontemps, Thierry Magnac and Eric Maurin May 2012, Set identified linear models, Journal article, Wiley Online Library

Search cemmap

Search by title, topic or name.

Contact cemmap

Centre for Microdata Methods and Practice

How to find us

Tel: +44 (0)20 7291 4800

E-mail us