This note proposes a necessary and sufficient condition on a utility function to guarantee that it generates a demand function satisfying the law of demand. This condition can be interpreted in terms of an agent's attitude towards lotteries in commodity space. As an application, we show that when an agent has an expected utility function, her demand for securities satisfies the law of demand if her coefficient of relative risk aversion does not vary by more than 4.

This paper analyzes the specification and identification of causal multivariate duration models. We focus on the case in which one duration concerns the point in time a treatment is initiated and we are interested in the effect of this treatment on some outcome duration. We define “no anticipation of treatment” and relate it to a common assumption in biostatistics. We show that (i) no anticipation and (ii) randomized treatment assignment can be imposed without restricting the observational data. We impose (i) but not (ii) and prove identification of models that impose some structure. We allow for dependent unobserved heterogeneity and we do not exploit exclusion restrictions on covariates. We provide results for both single-spell and multiple-spell data. The timing of events conveys useful information on the treatment effect.