Semialgebraic identification under polynomial moment restrictions
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2024-03-26
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Moreira, Marcelo Jovita
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We develop a general framework for models defined by multivariate polynomial moment restrictions and provide primitive and easily verifiable sufficient conditions for global identification within this class of models. Under mild regularity conditions, the problem of verifying global identification is reduced to the simple problem of counting the number of roots of a univariate polynomial. For just-identified models, the entire procedure is purely algebraic, thus allowing for theoretical proofs of global identification. For general over-identified models, the procedure shifts to numerical computations but is still guaranteed to give a correct verdict on identification, except for computational-related finite-precision issues. We also show how to analytically characterize sufficient global identifying restrictions in terms of semialgebraic restrictions on moments of observables, and how such characterizations can be leveraged for estimation and inference for this class of models. We illustrate the practical utility of our methods by introducing an identification-constrained efficient estimation procedure. Monte Carlo simulations indicate that the proposed procedure performs well in finite samples.