Parametric Identification of Multiplicative Exponential Heteroscedasticity

Harvey ( 1976 ) first proposed multiplicative exponential heteroscedasticity in the context of linear regression. These days it is more commonly seen in latent variable models such as Probit or Logit where correctly modelling the heteroscedasticity is imperative for consistent parameter estimates (Yatchew and Griliches, 1985 ). However, it appears the literature lacks a formal proof of point identification for the parametric model. This paper presents several examples that show the conditions presumed throughout the literature are not sufficient for identification. As a contribution, this paper discusses when identification can and cannot be easily obtained and provides proofs of point identification in common specifications.