PML versus minimum $${\chi }^{2}$$ χ 2: the comeback

Dante Amengual (), Gabriele Fiorentini and Enrique Sentana
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Dante Amengual: CEMFI

SERIEs: Journal of the Spanish Economic Association, 2023, vol. 14, issue 3, No 3, 253-300

Abstract: Abstract Arellano (J Econ 42:247–265, 1989a) showed that valid equality restrictions on covariance matrices could result in efficiency losses for Gaussian PMLEs in simultaneous equations models. We revisit his two-equation example using finite normal mixtures PMLEs instead, which are also consistent for mean and variance parameters regardless of the true distribution of the shocks. Because such mixtures provide good approximations to many distributions, we relate the asymptotic variance of our estimators to the relevant semiparametric efficiency bound. Our Monte Carlo results indicate that they systematically dominate MD and that the version that imposes the valid covariance restriction is more efficient than the unrestricted one.

Keywords: Covariance restrictions; Distributional misspecification; Efficiency bound; Finite normal mixtures; Partial adaptivity; Sieves (search for similar items in EconPapers)
JEL-codes: C30 C36 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13209-023-00280-4

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