Two Essays on Stochastic Income Theory.

Abstract

Based on the overlapping generations model of Samuelson, an inter-temporal income transition rule can be derived through a utility maxmization process. Under weak assumptions, this income transition rule forms a Markov Process and the income distribution will eventually converge to a stationary distribution. This dissertation extends this type of Markov income theory in two different directions. In Chapter I, I study the effects of a social insurance tax on various welfare indexes of the stationary income distribution. Although the current generation will certainly be made better off by a social insurance tax, both theoretical and simulation analysis suggests that the welfare implication for "future generations" is sensitive to the effects of tax policy on savings behavior, as well as to the specification of social welfare indexes. Our result implies that, in addition to the incentive-insurance trade off considered in the conventional static analysis, the welfare trade off between current and future generations is a factor that should be considered in an optimal insurance tax structure. Chapter II extends the theoretical structure of the conventional Markov income models by including an endogenous fertility decision. Under weak assumptions, I prove the existence of a unique stationary state which implies both a constant population growth and a time-invariant income distribution. There are at least two distinguishing features of this result. First, it extends the Becker-Willis static fetility dem and structure to a dynamic theory of population growth. Second, the theory can be viewed as an income-specific stable population model which is different from the currently popular age-specific stable population theory associated with Lotka. Since our model is based on a two-period lifecycle framework, some interesting comparative statics questions which have not been addressed in one-period models are also analyzed.