We investigate bargaining processes with two opponent parties, each consisting of two subjects. The parties negotiate about the distribution of a certain amount of money. The sum of the payoffs of the four subjects is not constant. The payoff situations are asymmetric. Between the two parties,...

We investigate identification of causal parameters in case-control and related studies. The odds ratio in the sample is our main estimand of interest and we articulate its relationship with causal parameters under various scenarios. It turns out that the odds ratio is generally a sharp upper...

This paper describes a method for carrying out non-asymptotic inference on partially identifi ed parameters that are solutions to a class of optimization problems. The optimization problems arise in applications in which grouped data are used for estimation of a model's structural parameters....

Multivalued treatment models have typically been studied under restrictive assumptions: ordered choice, and more recently unordered monotonicity. We show how treatment effects can be identified in a more general class of models that allows for multidimensional unobserved heterogeneity. Our...

This paper develops the method of local instrumental variables for models with multiple, unordered treatments when treatment choice is determined by a nonparametric version of the multinomial choice model. Responses to interventions are permitted to be heterogeneous in a general way and agents...