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Set identified linear models

  • Christian Bontemps

    (Institute for Fiscal Studies and Toulouse)

  • Thierry Magnac


    (Institute for Fiscal Studies and Toulouse)

  • Eric Maurin

    (Institute for Fiscal Studies)

We analyze the identification and estimation of parameters β satisfying the incomplete linear moment restrictions E(z T (x β−y)) = E(z Tu(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, β 0 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.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP13/11.

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Date of creation: Apr 2011
Date of revision:
Handle: RePEc:ifs:cemmap:13/11
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