Binary probit,tobit and hazard rate

This short note drows attention to an obvious although so far only partly noted relation between an inequality involving the hazard rate of the normal distribution and maximum likelihood estimation in the binary probit and in the Tobit model. Global concavity of the likelihood function for both the binary probit and the Tobit model can be proved by means of an inequality concerning the hazard rate of the standard normal distribution. As not yet noted in the literature this inequality may also be used to show that the hazard rate is monotonically increasing. Results of this paper are related to research which is financially supported by Thyssen-Stiftung. Comments on an earlier version by an anonymous referee are gratefully acknowledged.