The essential starting point of this dissertation presents an alternative approach for formulating simultaneous equation models for qualitative endogenous variables. To be explicit, the endogenous variables will be generated as Nash equilibria of a game between two players, and the statistical model will be generated by invoking the random utility framework introduced by McFadden (1974, 1981). Contrary to the earlier simultaneous equations models (Heckman (1978)), the approach presented in Chapter II will not ~pose logical consistency constraints on the parameters. A distinctive feature of the model is that it extends the usual simultaneous model with structural shift to cases where the parameters need not satisfy the logical consistency conditions.
Following the game theoretic formulation set out in Chapter II, Chapter III proposes an alternative model where the equilibrium concept is that of Stackelberg. As in Chapter II, we will still assume that each player maximizes his own utility, with the statistical model again being derived using McFadden's random utility approach. A distinctive feature of this model is that it contains as a special case the usual recursive model for discrete endogenous variables.
With Chapters II and III as a theoretical background, the purpose of Chapter IV is to present an empirical study of the Nash and Stackelberg equilibrium models. The problem we examine concerns a married couple's joint decision whether or not to participate in the labor. market. We examine three competing specifications. Chapter V concludes this dissertation with a discussion of which of the three empirical models most adequately describes the joint labor force participation decision of a random sample of married couples. Since none of the three models are completely nested in each other, we are not able to employ any of the classical tests. As such, we use an alternative method developed by Vuong (1985) for choosing the most adequate model.
