Optimality and Efficiency in
Open-Ended Dynamic Economies

Last Updated: 15 April 2017

Site Maintained By:
Leigh Tesfatsion
Professor of Econ, Math, and ECpE
Heady Hall 375
Iowa State University
Ames, IA 50011-1070
FAX: (515) 294-0221
http://www2.econ.iastate.edu/tesfatsi/
tesfatsi AT iastate.edu

Table of Contents:

Research Overview

This site collects together articles by myself and several collaborators focusing on the optimality and efficiency properties of economies represented by open-ended dynamic models, particularly by overlapping generations models. For each listed topic below, the articles are first summarized and then listed with full citations and with pointers to on-line preprints as available.

The First Welfare Theorem for Overlapping Generations Models

The overlapping generations (OG) model is an open-ended dynamic economic model that incorporates birth and death. The OG model thus facilitates the study of efficiency and distributional issues from an appealing microfoundations premise: Institutions may be long-lived, but people are mortal.

Nevertheless, the OG model raises a conundrum. The standard First Welfare Theorem found in most economic theory textbooks establishes under weak regularity conditions that all competitive equilibria are Pareto efficient for a particular class of economic models, namely, the standard Walrasian general equilibrium model. Two assumptions characterizing the latter model are that it has only finitely many goods and that it has only finitely many consumers. In contrast, the OG model has infinitely many goods and infinitely many consumers by the very nature of its construction. As shown by Paul Samuelson (JPE,1958) and David Gale (JET,1973), a first welfare theorem fails to exist for OG models as conventionally formulated.

The conclusion reached by Samuelson, Gale, and subsequent researchers is that the achievement of Pareto-efficiency for economies represented as OG models appears to require either a productive non-reproducible infinitely-lived asset ("land"), other-regarding preferences (altruism), or some form of non-market institution such as fiat money (with an appropriately set price) or a government tax-transfer system (with appropriately adjusted taxes and transfers).

In contrast, in a series of studies Pingle and Tesfatsion (1991;1997;1998a,b), Mark Pingle (Economics, U of Nevada-Reno) and I conclude that the non-existence of a first welfare theorem for OG models results from the incompleteness of the no-arbitrage conditions routinely used in these models to define competitive equilibrium. A key type of productive activity -- active seeking of profits through trade intermediation -- is not taken into account. Instead, trade intermediation is modeled as a coordination activity implemented by a passive "Walrasian Auctioneer," a fictitious clearinghouse construct whose goal is simply to ensure that prices are set to equate supply and demand.

More precisely, we consider three standard types of OG models frequently used in the economic theory literature: the pure-exchange OG model considered by Samuelson (JPE,1958); the Diamond (AER,1965) and Tirole (Econometrica,1985) OG production models; and the monetary OG model developed by Grandmont (Econometrica,1985). In each case we show that a First Welfare Theorem is restored for the OG model if trade intermediation is modeled as a contestable activity carried out by a profit-seeking corporate intermediary (a Walrasian Auctioneer in a corporate business suit) operating on behalf of its consumer-shareholders.

Growth and Human Capital Investment in Overlapping Generations Models

Overlapping generations models are now one of the main paradigms used to study the relationship between growth and human capital investment. Such studies typically make one of two polar assumptions. Either children are passive recipients of parental human capital investment, or children ("young agents") are lifetime utility maximizers who own resources (possibly augmented by parental bequests) and who decide for themselves how much of these resources to invest in their human capital. Given either polar case, distortion in educational investment in poorer children is typically attributed to credit market imperfections and hence to the unequal access of children to educational opportunity. One frequently considered remedy is government income redistribution through taxes and transfers.

In contrast, in Orazem and Tesfatsion (1997), my collaborator Peter Orazem (Economics, ISU) and I consider a middle-ground case with "neighborhood effects." Parents control all physical resources and make human capital investments in their children. However, children are able to affect the productivity of these investments by endogenously varying the degree of effort they exert in school.

In particular, we assume that the intensity of effort that children devote to schooling depends on their expected rate of return as proxied by the return to schooling experienced by their parents. The context of the investigation is an overlapping generations model consisting of multiple dynastic families with randomly determined ability levels for children. The main finding is that sole reliance on government income redistribution through taxes and transfers to improve human capital investment can result in suboptimal effort choices by children that counter or even offset the beneficial effects of the income transfers and sharply lower social welfare.

Time Inconsistency of Government Policy-Makers

Another basic microfoundations issue is the problem of "time-inconsistency." Decision-makers operating within a dynamic model are said to be time-inconsistent if their optimal intertemporal decision rules chosen at some time t cease to be optimal at some future time t+k. Time-inconsistency becomes an important issue whenever decision-makers are able to reoptimize their decisions at subsequent points in time.

In an influential study, Prescott and Kydland (JEDC,1980) construct examples demonstrating that government policy-makers in dynamic Walrasian economic models can be time-inconsistent even when there is no exogenous uncertainty, preferences are unchanging, all agents have perfect foresight, and the policy-makers benevolently attempt to maximize the lifetime utility of a representative consumer. These examples are based on special structures. Consequently, the question arises whether a general explanation for the demonstrated time-inconsistency can be provided.

This problem is addressed in Tesfatsion (1986) for a general class of dynamic Walrasian economic models that includes the Prescott-Kydland examples as special cases. It is first shown that the time-inconsistency of government policy-makers can be explained in this class of models as the consequence of successive structural changes in the constraints faced by the government policy-makers as private agents carry out decisions in each successive time period conditional on anticipated future government policy settings. Necessary and sufficient conditions for time-consistency are then determined and interpreted. These necessary and sufficient conditions turn out to be extremely stringent. Finally, it is shown that the Prescott-Kydland time inconsistency examples all fail to satisfy the necessary conditions.

Aggregation Issues in Overlapping Generations Models

Aggregation conditions permitting macro variables to be expressed as functions of other macro variables have long been sought in macroeconomics. For example, conditions have been sought permitting aggregate consumption to be expressed as a function of aggregate income, independently of the distribution of income across agents. In Tesfatsion (1982) I use a 3-period lived OG model to examine the extent to which macro variables such as aggregate consumption are invariant to government attempts to redistribute income across agents through selective tax-transfer policies. I show that conditions for invariance in this context are much stronger than found for standard Walrasian economic models.

In Tesfatsion (1984) I focus on the welfare properties of social security systems for the same class of OG models as in Tesfatsion (1982). Real net social security wealth (NSSW), the real present value of social security benefits received minus social security taxes paid, is frequently used as a direct proxy measure for the impact of a social security system on generation welfare. I demonstrate that NSSW can be a very poor proxy for the effects of a social security system on generation welfare. For example, NSSW can actually be negatively correlated with welfare for every generation due to price distortion effects.

Global Versus Bounded Rationality

In actual problem contexts the time horizon over which plans are formulated must generally be short in relation to the history of the process as a whole. What loss of return is entailed by the use of these relatively short planning horizons?

In Tesfatsion (1980) I develop a general discrete-time dynamic stochastic control model that encompasses many well-known economic models. I then derive sufficient conditions in this context for the equivalence of myopic (single period) and global (simultaneous multiple period) expected return maximization, and I provide a bound for the loss in global return when these conditions are not met. I also identify properties of proxy short-horizon return functions that can be used to partially order them in terms of overall expected return performance.

In Tesfatsion (1981) I consider a general class of dynamic investment models in which investors are not restricted to have constant risk aversion. After analytically establishing a number of different properties for the investors' globally optimal investment strategies, I use these properties to provide an upper bound on the loss in expected utility resulting when investors are boundedly rational and use a rolling n-period investment horizon shorter than the duration of the actual investment process. I then conduct computer experiments to explore the sensitivity of outcomes to changes in the horizon length n.