# Consistent Pseudo-Maximum Likelihood Estimators and Groups of Transformations

https://doi.org/10.3982/ECTA14727
p. 327-345

C. Gouriéroux, A. Monfort, J.‐M. Zakoïan

In a transformation model , where the errors are i.i.d. and independent of the explanatory variables , 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 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 . 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.

## Supplemental Material

### Supplement to "Consistent Pseudo-Maximum Likelihood Estimators and Groups of Transformations"

This document consists of two sections of additional results: i) Regularity conditions for Proposition 3 and sketch of proof; ii) Derivatives of functions based on exponential of matrices.