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.

Half of U.S. 50‐year‐olds will experience a nursing home stay before they die, and one in ten will incur out‐of‐pocket long‐term care expenses in excess of $200,000. Surprisingly, only about 10% of individuals over age 62 have private long‐term care insurance (LTCI) and LTCI takeup rates are low at all wealth levels. We analyze the contributions of Medicaid, administrative costs, and asymmetric information about nursing home entry risk to low LTCI takeup rates in a quantitative equilibrium contracting model. As in practice, the insurer in the model assigns individuals to risk groups based on noisy indicators of their nursing home entry risk. All individuals in frail and/or low‐income risk groups are denied coverage because the cost of insuring any individual in these groups exceeds that individual's willingness‐to‐pay. Individuals in insurable risk groups are offered a menu of contracts whose terms vary across risk groups. We find that Medicaid accounts for low LTCI takeup rates of poorer individuals. However, administrative costs and adverse selection are responsible for low takeup rates of the rich. The model reproduces other empirical features of the LTCI market including the fact that owners of LTCI have about the same nursing home entry rates as non‐owners.

This paper begins by observing that any reflexive binary (preference) relation (over risky prospects) that satisfies the independence axiom admits a form of expected utility representation. We refer to this representation notion as the coalitional minmax expected utility representation. By adding the remaining properties of the expected utility theorem, namely, continuity, completeness, and transitivity, one by one, we find how this representation gets sharper and sharper, thereby deducing the versions of this classical theorem in which any combination of these properties is dropped from its statement. This approach also allows us to weaken transitivity in this theorem, rather than eliminate it entirely, say, to quasitransitivity or acyclicity. Apart from providing a unified dissection of the expected utility theorem, these results are relevant for the growing literature on boundedly rational choice in which revealed preference relations often lack the properties of completeness and/or transitivity (but often satisfy the independence axiom). They are also especially suitable for the (yet overlooked) case in which the decision‐maker is made up of distinct individuals and, consequently, transitivity is routinely violated. Finally, and perhaps more importantly, we show that our representation theorems allow us to answer many economic questions that are posed in terms of nontransitive/incomplete preferences, say, about the maximization of preferences, the existence of Nash equilibrium, the preference for portfolio diversification, and the possibility of the preference reversal phenomenon.