Ambivalent about Ambivalence: A Re-examination of Heteroskedastic Probit Models

While the derivation and estimation of heterogeneous probit models appears straightforward, the properties of such models are not well understood. It is assumed that the properties of these models are identical to those of discrete choice models, but this may not be true. While these models are formally identified, we argue that they suffer from fragile identification. We first look for evidence of fragile identification using a series of Monte Carlo experiments. We then reanalyze data on abortion attitudes and use profile likelihood plots and a convergence analysis to look for signs of fragile identification. We find strong evidence that heteroskedastic probit models tend to be tenuously identified.