The paper develops and estimates a theoretical model of wage determination and union-nonunion wage differentials. In order to overcome the institutional criticisms of the formal bargaining literature, the paper generalizes the Nash-Zeuthen-Harsanyi model by linking the solution to the institutional concepts of bargaining power and fear or cost of disagreement and by making the outcome depend not only on endogenous but also on exogenous factors. An operational specification of bargaining power and fear of disagreement allows the model to be estimated with data covering twelve companies and trade unions during the period from mid-1950's to the late 1970's. While giving limited support to the Nash-Zeuthen-Harsanyi solution, the empirical analysis indicates that the bargaining outcome usually deviates from the Nash-Zeuthen-Harsanyi point and, in accordance with the institutionalist claim, that it varies significantly with exogenous factors. Contrary to the traditional labor economics view, the results do not support the general conclusion that the bargaining solution lies on the marginal revenue product curve of labor. Instead, the relevant coefficients suggest that for many firms and unions the outcome might be better characterized by the efficient contract (vertical contract curve).