Endogenous growth cycles in an overlapping generations model with investment gestation lags

Summary. A simple overlapping generations model with investment gestation lags is constructed. The model shows that, if the technology is of the AK type with capital-deepening externalities, the existence of investment gestation lags always generates permanent cyclical fluctuations in the economic growth rate. The mean growth rate is shown to be positive if the external effect is strong. The model also shows that, if the production technology takes the Cobb-Douglas form, there exists a unique steady state in which the economy exhibits neither cyclical fluctuations nor long-run growth.Received: 3 July 2003, Revised: 3 December 2003, JEL Classification Numbers: E32, B13. Correspondence to: Akiomi KitagawaAkiomi Kitagawa, Akihisa Shibata: The authors would like to thank Yasushi Iwamoto, Kazuo Mino, an anonymous referee and seminar participants at the Macroeconomics Workshop for their helpful comments and suggestions. Financial support from the Ministry of Education, Culture, Sports, Science and Technology of Japan is gratefully acknowledged.     

Too much of a good thing: Endogenous business cycles generated by bounded technological progress

Following Jones and Williams [Jones, C.I., Williams, J., 2000. Too much of a good thing? The economics of investment in R&D. Journal of Economic Growth vol. 5 (no. 1), 65–85], we assume that R&D is simultaneously subject to positive and to negative external effects (e.g., the non-rival nature of technology conflicts with congestion externalities). This observation allows to conceive an economy where two R&D sectors evolve without departing significantly from each other in terms of their productive results (society tends to penalize imbalances in technical progress, making negative external effects to appear associated to a sector when this outstands relatively to the other sector; the second sector, in turn, will be subject to positive externalities that reflect a catching up effect). The proposed framework, when associated to a growth setup, is able to replicate the existence of endogenous fluctuations and, therefore, it intends to be a contribution to the literature on endogenous business cycles.     

The endogenous formation of an environmental culture

This paper presents a mechanism explaining the surge in environmental culture across the globe. Based upon empirical evidence, we develop an overlapping generations model with environmental quality and endogenous environmental culture. Environmental culture may be costlessly transmitted intergenerationally, or via costly education.The model predicts that for low wealth levels, society is unable to free resources for environmental culture. In this case, society will only invest in environmental maintenance if environmental quality is sufficiently low. Once society has reached a certain level of economic development, then it may optimally invest a part of its wealth in developing an environmental culture. Environmental culture has not only a positive impact on environmental quality through lower levels of consumption, but it also improves the environment through maintenance expenditure for wealth-environment combinations at which, in a restricted model without environmental culture, no maintenance would be undertaken. Environmental culture leads to a society with a higher indirect utility at steady state in comparison to the restricted model.Our model leads us to the conclusion that, for societies trapped in a situation with low environmental quality, investments in culture may induce positive feedback loops, where more culture raises environmental quality which in turn raises environmental culture. We also discuss how environmental culture may lead to an Environmental Kuznets Curve.     

Indeterminacy of intertemporal equilibria under imperfect competition

Summary. It is known that overlapping generations models with imperfectly competitive firms may exhibit a continuum of stationary equilibria. The reason of this indeterminacy is that different price expectation functions of consumers lead to different objective demand functions against which firms maximize. All these expectation functions fulfill perfect foresight in the equilibrium, but they can be arbitrary off the equilibrium. In this paper it is shown that it is not this arbitrariness which is responsible for the indeterminacy, but that the continuum of stationary equilibria emerges even if expectation functions are rational. Received: March 25, 1999; revised version: February 16, 2000     

On local indeterminacy and endogenous cycles in Ramsey models with heterogeneous households

It is well-known that endogenous cycles can occur in Ramsey models with heterogeneous households and borrowing constraints. In this note, we address the issue of robustness in the more general case of endogenous labor supply and we explain the occurrence of local indeterminacy under progressive taxation.

Can market power sustain endogenous growth in overlapping-generations economies?

Summary. Sustained endogenous growth is known to be impossible in OLG one-sector models without non-convexities and externalities, unless income is redistributed to the young generation. No redistribution proper is however necessary, as shown in two simple examples, if positive profits accruing to young monopolistic entrepreneurs can be sustained in equilibrium, and/or if young unionised workers can guarantee a non-vanishing share of aggregate income. In this context, market power appears, in two different forms, as a significant source of sustained endogenous growth. Received: October 3, 2000; revised version: March 9, 2001     

Unemployment dynamics in an OLG economy with public pensions

Pension benefits in old age establish a disincentive to save in youth, thereby yielding lower levels of capital stock and the wage rate. As a result, the trade union has an incentive to change the composition of its two targets: employment and the wage rate. This paper develops a model that includes employment effects of public pensions via capital accumulation and union wage setting. Within this framework, we consider how contribution rates to the pension system influence the level and time path of the unemployment rate. It is demonstrated that (1) a higher contribution rate results in a lower unemployment rate, and (2) the economy with a high (low) contribution rate experiences monotone convergence towards (oscillatory convergence towards or a period-2 cycle around) the steady state. The author would like to thank an anonymous referee, Kazutoshi Miyazawa, and seminar participants at Osaka University for their useful comments and suggestions, and Masako Ikefuji and Hiroaki Yamagami for their research assistance. Financial support from the Japan Society for the Promotion of Science (JSPS) through a Grant-in-Aid for Young Scientists (B) (No.17730131), the Asahi Glass Foundation, the Japan Economic Research Foundation and the 21st Century COE Program (Osaka University) is gratefully acknowledged. All remaining errors are mine.     

Schumpeter's circular flow,learning by doing and cyclical growth

A two-sector growth model with endogenous technical change is presented. Concerning technical change, we assume that it is reflected by increases in the stock of human capital which are acquired through learning by doing. As a result, it turns out that transitory or, using the Hopf bifurcation theorem, persistent oscillations of the economic variables may be the outcome. Thus we are able to show that learning mechanisms alone may be sufficient to destroy the circular flow as described by Schumpeter.     

Social security and endogenous fertility: pensions and child allowances as siamese twins

This paper analyses public pensions and child support in a model with endogenous fertility. We show that the individual fertility choice may not coincide with the social optimum, due to the existence of external effects of children on society as a whole. The market outcome without government intervention is efficient, however, as the externalities exactly cancel out in that case. If the government wants to redistribute towards the old, it cannot replicate the command optimum by merely applying lump-sum transfers, but rather needs a child allowance scheme to effectively alter the number of offspring. Finally, we analyse whether a Pareto-improving social security reform is possible. It is shown that merely reducing the PAYG-scheme cannot be Pareto-improving, but the introduction of a child allowance scheme can be.     

On optimality in intergenerational risk sharing

Summary. This paper defines and studies optimality in a dynamic stochastic economy with finitely lived agents, and investigates the optimality properties of an equilibrium with or without sequentially complete markets. Various Pareto optimality concepts are considered, including interim and ex ante optimality. We show that, at an equilibrium with a productive asset (land) and sequentially complete markets, the intervention of a government may be justified, but only to improve risk sharing between generations. If markets are incomplete, constrained interim optimality is investigated in two-period lived OLG economies. We extend the optimality properties of an equilibrium with land and give conditions under which introducing a pay-as-you-go system at an equilibrium would not lead to any Pareto improvement. Received: October 5, 1998; revised version: April 3, 2001     

Forward and backward dynamics in implicitly defined overlapping generations models

In dynamic economic models derived from optimization principles, the forward equilibrium dynamics may not be uniquely defined, while the backward dynamics is well defined. We derive properties of the global forward equilibrium paths based on properties of the backward dynamics. We propose the framework of iterated function systems (IFSs) to describe the set of forward equilibria and apply the IFS framework to a one- and a two-dimensional version of the overlapping generations (OLG)-model. We show that if the backward dynamics is chaotic and has a homoclinic orbit (a “snap-back repeller”), the set of forward equilibrium paths converges to a fractal attractor. Forward equilibria may be interpreted as sunspot equilibria, where a random sunspot sequence determines equilibrium selection at each date.     

On the equivalence between the overlapping-generations model and cyclical general-equilibrium models

We show that equilibrium cycles in an overlapping-generations model are equivalent to asymmetric equilibria in a general-equilibrium model. We use this equivalence to find equilibrium cycles in the overlapping-generations model with two and three generations, respectively. For the example with two generations we show that for certain parameter values cycles of all periods occur.     

Evolutionary economics goes mainstream: A review of the theory of learning in games

The Theory of Learning in Games by Fudenberg and Levine surveys a key branch of evolutionary economics from a mainstream perspective. Its publication provides an opportunity to reassess the prospects and goals for evolutionary economics.     

Perpetual youth and endogenous labor supply: A problem and a possible solution

In the “perpetual youth” overlapping-generations model of Blanchard and Yaari, if leisure is a “normal” good then some agents will have negative labor supply. We suggest a solution to this problem by using a modified version of Greenwood, Hercowitz and Huffman’s utility function. The modification incorporates real money balances, so that the model may be used to analyze monetary as well as fiscal policy. In a Walrasian version of the economy, we show that increased government debt and increased government spending raise the interest rate and lower output, while an open-market operation to increase the money supply lowers the interest rate and raises output.     

Can evolutionary algorithms describe learning processes?

Evolutionary algorithms have attracted more and more the attention of economists in recent years. Repeatedly it is claimed that they are an adequate tool to describe learning processes within a population of individuals. The present paper examines this claim. To this end, a learning model is set up that contains the three elements of variation, elimination, and imitation that are claimed to correspond with the processes of mutation, selection, and replication of biological evolution. Subsequently, this model is compared with a formulation of evolutionary algorithms. The comparison reveals that although both processes have a similar structure there are crucial differences between the two dynamics.     

On the dynamics of an endogenous growth model with learning by doing

Summary. The paper studies the local dynamics of an endogenous growth model with externalities of investment. It is demonstrated that, in case of sustained per capita growth, the competitve economy is characterized by a situation with a unique balanced growth path which is saddle point stable or by a situation with two balanced growth paths. If there are two balanced growth paths, the one with the higher growth rate is a saddle point whereas the path with the lower growth rate is either completely stable, with convergence to a rest point or limit cycle, or completely unstable. In the social optimum the existence of a balanced growth path implies that it is unique and that this path is a saddle point. Received: May 15, 2000; revised version: December 14, 2001     

Cycling in a stochastic learning algorithm for normal form games

In this paper we study a stochastic learning model for 2×2 normal form games that are played repeatedly. The main emphasis is put on the emergence of cycles. We assume that the players have neither information about the payoff matrix of their opponent nor about their own. At every round each player can only observe his or her action and the payoff he or she receives. We prove that the learning algorithm, which is modeled by an urn scheme proposed by Arthur (1993), leads with positive probability to a cycling of strategy profiles if the game has a mixed Nash equilibrium. In case there are strict Nash equilibria, the learning process converges a.s. to the set of Nash equilibria.     

Multiple equilibria, coordination, and transitional growth

We study a small open economy with two sectors and two factors of production. In one of the sectors, external economies of scale are generated through the industry-level capital input. This leads to a divergence between private and social production possibility frontiers as well as to multiple equilibria. The equilibrium selection problem that arises is solved by agents who follow a simple trial-and-error learning rule. The growth path of the economy as agents learn lies below the production possibility frontier and may display cyclical transitional dynamics. We also show that coordination problems which may prevent the economy from attaining the “good” equilibrium may be alleviated by the temporary use of policy instruments that shape the allocation of resources.     

Environmental tax policy in a model of growth cycles

Summary. The purpose of this paper is to consider environmental taxation which would control emissions of firms in a model of growth cycles. In the model presented below, the economy may experience two phases of growth and environmental quality: “the no-innovation growth regime” and “the innovation-led growth regime”. Aggregate capital and environmental quality remain constant in the no-innovation growth regime, while they perpetually increase in the innovation-led growth regime. The paper shows that the tax plays a key role in determining whether the economy stably converges to one of the two regimes or fluctuates permanently between them. It also shows that there is a critical level of the tax and that the economy obtains higher growth rates of capital and environmental quality by raising (or reducing) the tax if the initial tax is below (or above) the critical level. Received: April 2, 2001; revised version: March 21, 2002 RID="*" ID="*" This research reported here was conducted within the research project “Project on Intergenerational Equity” at Institute of Economic Research, Hitotsubashi University. I am deeply grateful to an anonymous referee for his or her insightful comments, which greatly improved the paper. I also thank Hiroshi Honda, Yasuo Maeda, Yuji Nakayama, and participants in workshops at Hitotsubashi University, Kyoto University, Nagoya University, Osaka University, University of Tsukuba, Yokohama National University, and University of Tokyo for their valuable comments and suggestions. Any remaining errors are mine.     

On economic applications of evolutionary game theory

Evolutionary games have considerable unrealized potential for modeling substantive economic issues. They promise richer predictions than orthodox game models but often require more extensive specifications. This paper exposits the specification of evolutionary game models and classifies the possible asymptotic behavior for one and two dimensional models.