Optimality and Efficiency in
Open-Ended Dynamic Economies

Site Maintained By: Leigh Tesfatsion Research Professor & Professor Emerita of Economics Courtesy Research Professor of Electrical & Computer Engineering Heady Hall 260 Iowa State University Ames, Iowa 50011-1054 https://www2.econ.iastate.edu/tesfatsi/ tesfatsi AT iastate.edu

Table of Contents: Research Overview DSGL: DSG(~E) + Learning Agents First Welfare Theorem for Overlapping Generations (OLG) Models Growth/Human Capital Investment (OLG) Time Inconsistency of Government Policy-Makers Aggregation Issues for OLG Models Global Versus Bounded Rationality

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. 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.

DSGL = DSG(~E) + Learning Agents

Too often, in commentaries defending Dynamic Stochastic General Equilibrium (DSGE) modeling, one sees a complete lack of recognition that "GE" consists of conceptually distinct "G" and "E" aspects. The work cited in this section demonstrates the following important point.

The typically strong equilibrium assumptions constituting the "E" in DSGE models can be relaxed (or even altogether replaced) by an "L" assumption: specifically, by an assumption that decision-making agents have learning capabilities enabling them to adaptively update the strategies they use to participate in a generally specified collection of markets over time.

In short, the "E" in DSGE models can be replaced by an "L" for increased empirical credibility while leaving the "DSG" in place.

Another incorrect presumption dispelled by the work cited in this section is that computationally-modeled learning agents cannot be as rational (or irrational) as real people. To the contrary, exploiting the powerful capabilities of modern software, this work establishes that the decision methods used by computationally-modeled decision makers can range from simple behavioral rules to sophisticated anticipatory learning algorithms for the approximate achievement of intertemporal objectives.

• Leigh Tesfatsion, "Modeling Economic Systems as Locally-Constructive Sequential Games" [ (Preprint,pdf,654KB), (Slides,pdf,1MB)], Journal of Economic Methodology, Vol. 24, Issue 4, 2017, 384-409.

  Abstract: Real-world economies are open-ended dynamic systems consisting of heterogeneous interacting participants. Human participants are decision-makers who strategically take into account the past actions and potential future actions of other participants. All participants are forced to be locally constructive, meaning their actions at any given time must be based on their local states; and participant actions at any given time affect future local states. Taken together, these essential properties imply real-world economies are locally-constructive sequential games. This paper discusses a modeling approach, Agent-based Computational Economics (ACE), that permits researchers to study economic systems from this point of view. ACE modeling principles and objectives are first concisely presented and explained. The remainder of the paper then highlights challenging issues and edgier explorations that ACE researchers are currently pursuing.

• Leigh Tesfatsion, "Elements of Dynamic Economic Modeling: Presentation and Analysis" (WP,pdf,630KB), Eastern Economic Journal, Vol. 43, No. 2, 2016, 192-216. doi:10.1057/eej.2016.2

  Abstract: The primary goal of these introductory notes is to promote the clear presentation and rigorous analysis of dynamic economic models, whether expressed in equation or agent-based form. A secondary goal is to promote the use of initial-value state space modeling with its regard for historical process, for cause leading to effect without the external imposition of global coordination constraints on agent actions. Economists who claim to respect individual rationality should not be doing for their modeled economic agents what in reality these agents must do for themselves.

• Ekaterina Sinitskaya and Leigh Tesfatsion, "Macroeconomies as Constructively Rational Games" (WP Version,pdf,1.2MB), Journal of Economic Dynamics and Control, Vol. 61, 2015, 152-182.

  Abstract: Real-world decision-makers are forced to be locally constructive; that is, their decisions are necessarily constrained by their interaction networks, information, beliefs, and physical states. This study transforms an otherwise standard dynamic macroeconomic model into an open-ended dynamic game by requiring consumers and firms with intertemporal utility and profit objectives to be locally constructive. Tested locally-constructive decision processes for the consumers and firms range from simple reactive reinforcement learning to adaptive dynamic programming (ADP). Computational experiments are used to explore macroeconomic performance under alternative decision-process combinations relative to a social planner benchmark solution. A key finding is that simpler decision processes can outperform more sophisticated decision processes such as ADP. However, memory length permitting some degree of adaptive foresight is critical for good performance.

• Blake LeBaron and Leigh Tesfatsion, "Modeling Macroeconomies as Open-Ended Dynamic Systems of Interacting Agents" (pdf,45KB), American Economic Review (Papers & Proceedings), Vol. 98, No. 2, 2008, 246-250.

  Abstract: This study discusses the potential applicability of Agent-based Computational Economics (ACE) for macroeconomic modeling, with a particular stress on the following three issues: (1) taxonomy - what types of agents for macroeconomic models?; (2) scale robustness - how many agents for macroeconomic models?; and (3) empirical validation - connecting to data.

• Leigh Tesfatsion, "Agent-Based Computational Modeling and Macroeconomics" (pdf,148KB), Chapter 9 in David Colander (ed.), Post-Walrasian Macroeconomics: Beyond the Dynamic Stochastic General Equilibrium Model, Cambridge University Press, Cambridge, UK, 2006. A review of this book was published in the Eastern Economic Journal (2008).

  Abstract: Agent-based Computational Economics (ACE) is the computational study of economic processes modeled as dynamic systems of interacting agents. This essay discusses the potential of ACE modeling tools for the study of macroeconomic systems. Points are illustrated using an ACE model of a two-sector decentralized market economy.

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.

• Mark Pingle and Leigh Tesfatsion (1998a), "Active Intermediation in a Monetary Overlapping Generations Economy" (pdf,225K), Journal of Economic Dynamics and Control, Vol. 22, pp. 1533-1574. The published article is also available from Science Direct.

  Abstract: Why does the First Welfare Theorem fail in standard monetary overlapping generations economies such as Grandmont (Econometrica, 1985), and how is this failure related to business cycle fluctuations? This study argues that the failure of the First Welfare Theorem, and the potentially exotic nature of the resulting business cycle fluctuations that arise, can both be attributed to the passive intermediation role played by the Walrasian Auctioneer in these models. Specifically, the study demonstrates that when private intermediaries pursuing normal profit-maximizing activities are introduced into such models, a Pareto efficient outcome is ensured and only simple periodic types of business cycle fluctuations can occur in equilibrium.

• Mark Pingle and Leigh Tesfatsion (1998b), "Active Intermediation in Overlapping Generations Economies with Production and Unsecured Debt" (pdf,187K), Macroeconomic Dynamics, Vol. 2, pp. 183-212.

  Abstract: Why does the First Welfare Theorem fail in standard overlapping generations economies with production, such as Diamond (AER, 1965) and Tirole (Econometrica, 1985)? This study argues that the reason for this failure can be attributed to the passive intermediation role played by the Walrasian Auctioneer in these models. If intermediation is instead modeled as a contestable activity carried out by corporate intermediaries owned by consumer-shareholders, and operated in the interest of consumer-shareholders, then every equilibrium is Pareto efficient.

• Mark Pingle and Leigh Tesfatsion (1997), "Walras' Law in Overlapping Generations Economies" [ (pdf,68K), (ps,133K)], Economic Report No. 34, Iowa State University, revised October 1997

  Abstract: It is widely known that Walras' Law can fail for an overlapping generations economy. This report demonstrates that: (1) when this failure occurs, it represents an economic opportunity that can be exploited by the issuance of unsecured debt by private agents; and (2) when unsecured debt is issued, Walras' Law does not fail.

• Mark Pingle and Leigh Tesfatsion (1991), "Overlapping Generations, Intermediation, and the First Welfare Theorem" (pdf,1.4M), Journal of Economic Behavior and Organization, Vol. 15, pp. 325-345. The published article is available from Science Direct.

  Abstract: Why does the First Welfare Theorem fail in standard pure-exchange overlapping generations economies such as Samuelson (Journal of Political Economy, 1958)? This study argues that the failure can be attributed to the passive intermediation role played by the Walrasian Auctioneer in such models. Specifically, no agent actually residing within the model is permitted to exploit the earnings opportunities that can arise from mediating intertemporal trade. The study shows that the introduction of active profit-seeking private intermediaries in such models restores the First Welfare Theorem.

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.

• Peter Orazen and Leigh Tesfatsion (1997), "Macrodynamic Implications of Income Transfer Policies for Human Capital Investment and School Effort", Journal of Economic Growth, Vol. 2 (November), pp. 305-329. The published article is available from SpringerLink.

  Abstract: What happens when children are able to affect the productivity of human capital investment by endogenously varying the degree of effort they exert in school? This study explores the effectiveness of tax-financed human capital investment for the education of children when the intensity of effort which children devote to schooling depends on their expected rate of return as proxied by the rate of return experienced by their parents. The context of the investigation is an overlapping generations model consisting of multiple dynastic families with randomly determined ability levels. The main finding is that endogenous schooling effort choices by children can distort the intended effects of government income transfers meant to counter the imperfect access of poor families to credit markets.

  Note: The above article is a revised abridged version of "Human Capital Investment and the Locally Rational Child" [ (pdf,534K), (ps,255K)], Economic Report No. 31, Iowa State University, March 1997.

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.

• Leigh Tesfatsion (1986), "Time Inconsistency of Benevolent Government Economies" (pdf,1.7M), Journal of Public Economics, Vol. 31, pp. 25-52. The published article is available from Science Direct.

  Abstract: Why do government policymakers in open-ended dynamic economic models with period-by-period re-optimization tend to exhibit time inconsistency, in the sense that they systematically deviate in later periods from earlier planned policy paths? This article develops necessary and sufficient conditions for time consistency for a general class of dynamic Walrasian economies that includes many previous economic models (Brock, Calvo, Kydland-Prescott, Fischer, etc.) as special cases. It is shown that the time inconsistency of government policymakers can be explained in this class of models as the consequence of successive structural changes in the constraints faced by the government policymakers as private agents carry out decisions in each successive time period conditional on anticipated future government policy settings.

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.

• Leigh Tesfatsion (1982), "Macro Implications of Government Redistributive Tax-Transfer Policies" (pdf,1.6M), Journal of Public Economics, Vol. 19, No. 2 (November), pp. 139-169. The published article is available from Science Direct.

  Abstract: 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. This article uses a 3-period lived overlapping generations economy 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. It shows that conditions for invariance in this context are much stronger than found for the standard Walrasian general equilibrium economy.

• Leigh Tesfatsion (1984), "Welfare Implications of Net Social Security Wealth" (pdf,1.4M), Journal of Public Economics, Vol. 24, No. 1, pp. 1-27. The published article is available from Science Direct.

  Abstract: 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. This article examines the relationship between real NSSW and generation welfare in a 3-period lived overlapping generations economy. It demonstrates 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.

• Leigh Tesfatsion (1980), "Global and Approximate Global Optimality of Myopic Economic Decisions" (pdf,1.4m), Journal of Economic Dynamics and Control, Vol. 2, pp. 135-160. The published article is also available from Science Direct.

  Abstract: 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? This article develops a general discrete-time dynamic stochastic control model that encompasses many well-known economic models. It derives sufficient conditions in this context for the equivalence of myopic (single period) and global (simultaneous multiple period) expected return maximization, and it provides a bound for the loss in global return when these conditions are not met. It also identifies properties of proxy short-horizon return functions that can be used to partially order them in terms of overall expected return performance.

• Leigh Tesfatsion (1981), "Dynamic Investment, Risk Aversion, and Foresight Sensitivity" (pdf,1.5M), Journal of Economic Dynamics and Control, Vol. 3, pp. 65-96. The published article is available from Science Direct.

  Abstract: Since optimal investment strategies generally cannot be obtained in closed form when consumers exhibit non-constant risk aversion, many dynamic investment studies have focused on the constant risk aversion case. This study considers a general class of dynamic investment models in which agents are not restricted to have constant risk aversion. Existence, monotonicity, concavity, differentiability, and absolute risk aversion properties are established analytically for the optimal feedback investment strategies and dynamic progamming value functions. A bound is also obtained on the loss in expected utility resulting from the use of limited foresight horizons. Finally, results are reported for computer experiments conducted to explore the sensitivity of expected utility outcomes to changes in the length of the foresight horizon. For example, the results indicate the optimality of a rolling 2-period foresight horizon for a particular class of exponential utility functions exhibiting decreasing risk aversion.