Probability Feedback in a Recursive System of Probability Models

Abstract

This paper presents a general model for qualitative endogenous variables that is defined by a recursive system of conditional probability models in which the probabilities of some outcomes may depend on the probabilities of posterior outcomes. The model is related to, but conceptually different from C. D. Mallar's (1977) simultaneous probability model. It has as special cases the multivariate logit model (M. Nerlove and S. J. Press (1973, 1976)) and the constrained nested logit model (D. McFadden (1981)). The model can also be used to analyze outcomes of some game situations. Two examples are in particular considered: a game against Nature and a Stackelberg game under uncertainty. Identification of the structural parameters in the first example is seen to be related to the classical problem of stochastic revealed preference as studied by M. K. Richter and L. Shapiro (1978).