CONSISTENT PSEUDO-MAXIMUM LIKELIHOOD ESTIMATORS AND GROUPS OF TRANSFORMATIONS

In a transformation model yt = c[a(xt, β), ut], where the errors ut are i.i.d. and independent of the explanatory variables xt, the parameters can be estimated by a pseudo-maximum likelihood (PML) method, that is, by using a misspecified distribution of the errors, but the PML estimator of β is in g...

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Bibliographic Details
Published in:Econometrica 2019-01, Vol.87 (1), p.327-345
Main Authors: Gouriéroux, C., Monfort, A., Zakoïan, J-M.
Format: Article
Language:English
Subjects:
conditional heteroscedasticity
consistency
Economic models
identification
Mathematical models
Maximum likelihood method
NOTES AND COMMENTS
Pseudo‐maximum likelihood
spatial interactions
stochastic volatility
Transformation
transformation model
Usefulness
Volatility
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Summary:In a transformation model yt = c[a(xt, β), ut], where the errors ut are i.i.d. and independent of the explanatory variables xt, the parameters can be estimated by a pseudo-maximum likelihood (PML) method, that is, by using a misspecified distribution of the errors, but the PML estimator of β is in general not consistent. We explain in this paper how to nest the initial model in an identified augmented model with more parameters in order to derive consistent PML estimators of appropriate functions of parameter β. The usefulness of the consistency result is illustrated by examples of systems of nonlinear equations, conditionally heteroscedastic models, stochastic volatility, or models with spatial interactions.
ISSN:0012-9682
1468-0262
DOI:10.3982/ECTA14727