A key economic issue is whether poor countries or regions tend to grow faster than rich ones: are there automatic forces that lead to convergence over time in the levels of per capita income and product? The authors use the neoclassical growth model as a framework to study convergence across the forty-eight contiguous U.S. states. They exploit data on personal income since 1840 and on gross state product since 1963. The U.S. states provide clear evidence of convergence, but the findings can be reconciled quantitatively with the neoclassical model only if diminishing returns to capital set in very slowly. Copyright 1992 by University of Chicago Press.(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)

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Convergence across States and Regions

https://www.nber.org/system/files/working_papers/w9270/w9270.pdf

Closing Small Open Economy Models

Regional cohesion: Evidence and theories of regional growth and convergence

We model a consumer's efforts to reduce the discount on future utilities. Our analysis shows how wealth, mortality, addictions, uncertainty, and other variables affect the degree of time preference. In addition to working out many implications of the model, we discuss evidence on consumption, savings, equilibrium, and the dynamics of inequality. We claim that most ofthat evidence is consistent with the predictions of our approach.

The Endogenous Determination of Time Preference

A stochastic differential formulation of recursive utility is given sufficient conditions for existence, uniqueness, time consistency, monotonicity, continuity, risk aversion, concavity, and other properties. In the setting of Brownian information, recursive and intertemporal expected utility functions are observationally distinguishable. However, one cannot distinguish between a number of non-expected-utility theories of one-shot choice under uncertainty after they are suitably integrated into an intertemporal framework. In a "smooth" Markov setting, the stochastic differential utility model produces a generalization of the Hamilton-Bellman-Jacobi characterization of optimality. A companion paper explores the implications for asset prices. Copyright 1992 by The Econometric Society.

/pdf/stochastic-differential-utility-2n7g5hp0f9.pdf

Stochastic differential utility

The problem of demand for money and other assets has been recently studied by Douglas (1966) and Sidrauski (1965) within the framework of a rational individual faced with the choice of a consumption schedule which is optimal with respect to the individual’s time preference structure. In both papers, the intertemporal utility function upon which the consumer’s choice is based is represented by a discounted integral of the stream of instantaneous utility levels, where future utilities are discounted by a rate which is kept constant independently of time profile of the utility stream associated with each consumption schedule. Thus, if a consumer is permitted to hold his assets either in the form of real cash balances or in the form of perpetuities yielding a constant rate of interest and if his instantaneous utility function is linear and homogeneous, he will either postpone his consumption until the very last moment or will consume as much as possible, according to whether the subject rate of discount is lower than the rate of interest. The only case in which the individual would desire to possess two types of assets simultaneously is one where his subject rate of discount is precisely equal to the rate of interest. Douglas has avoided this difficulty by having the level of bond holdings as one of the components for instantaneous utility level, while Sidrauski has introduced real capital as an alternative asset for which the rate of return varies with the amount held. In this paper, we shall instead start with an analysis of an individual’s time preference structure, to derive a certain specific formulation regarding the rate by which he discounts future levels. We shall then proceed to examine the behavior of an individual consumer who decides the allocation of his income between consumption and savings and the choice of portfolio balances in such manner that the resulting consumption stream is most preferred in terms of his time 486preference structure. The analysis will be first carried out for the simple case in which the individual is permitted to hold his assets only in the form of bonds for which the expected rate of interest is constant, and then for a more general case in which he may hold his assets in the form of money and bonds and other types for which the rates of return may vary.

Hirofumi Uzawa

Papers

Time Preference, the Consumption Function, and Optimum Asset Holdings