Debt, liquidity and dynamics

Summary. Money, which provides liquidity, is distinct from debt. The introduction of a bank that issues money in exchange for debt and pays out its profit as dividend to shareholders modifies the model of overlapping generations. The set of equilibrium paths, their dynamic properties, as well as the scope and effectiveness of monetary policy are significantly altered: though low rates of interest are associated with superior steady state allocations, stability of the steady state may require a nominal rate of interest above a certain minimum: without production, a decrease in the nominal rate of interest may result in explosive behavior or convergence to an endogenous cycle, while in an economy with production, an increase in the nominal rate of interest may lead to indeterminacy and fluctuations.Received: 5 October 2004, Revised: 5 November 2004 JEL Classification Numbers: E30, E32, E50, E52.C. Rochon, H.M. Polemarchakis: We thank Jean-Michel Grandmont for helpful comments. Correspondence to: C. RochonThis revised version was published online in May 2005 with a corrected abstract.     

Local Sunspot Equilibria Reconsidered

We generalize the usual notion of local sunspot equilibria. We say such equilibria exist around a steady state of an OLG economy whenever stationary sunspot equilibria of arbitrarily close economies exist within any neighborhood of the steady state. Unlike the usual notion, this generalization allows to address the following identification problem: Can an analyst distinguish empirically small fluctuations due to small shocks to the fundamentals from pure expectations-driven fluctuations? We study conditions under which these generalized local sunspot equilibria exist in OLG economies, and show that they may exist around not only indeterminate but also determinate steady states.     

Pollution and life expectancy: How environmental policy can promote growth

This article investigates the influence of environmental policy (EP) on growth in an AK-type growth model, when finite lifetime is introduced and the link between pollution and life expectancy (through the detrimental impact of pollution on health) is taken into account.Using an overlapping generations model à la Blanchard [Blanchard, O. (1985). Debt, deficits and finite horizon. Journal of Political Economy, 93:223-247], we demonstrate that finite lifetime introduces a “generational turnover effect” which modifies the influence of the EP on growth. Thus, when lifetime is finite and independent from pollution, we show that the “generational turnover effect” limits the detrimental impact of the EP on growth, if agents smooth their consumption over time. When pollution negatively influences life expectancy through health, we demonstrate that the “generational turnover effect” is magnified and that the EP and growth have an inverted U-shaped relationship in the steady-state. In this case, we show that the environmental policy is more likely to promote growth (i.e. it stimulates growth for a wider range of environmental taxes) when the impact of pollution on health is important and/or public expenditures in health are low. Finally, using numerical simulations, we find that for the value of parameters that we have chosen, the EP will be more likely to promote growth when agents smooth consumption over time.     

Signal-extracting education in an overlapping generations model

Summary. In order to get good positions in companies, people try to enter highly-ranked universities. However, abilities vary greatly between individuals. High-ability individuals have an incentive to send signals to firms by obtaining a higher level of education in order to distinguish themselves from low-ability individuals. This paper constructs an overlapping generations model in order to examine the macroeconomic consequences of such sorting behavior of individuals. There are two kinds of possible equilibria in our model. In one equilibrium, only the high-ability agent can obtain higher education and thus an elite society emerges. In the other equilibrium, all ability types have the chance to obtain higher education and thus a society with mass higher education emerges. We also discuss the possibility of multiple equilibria of these different steady states and the dynamic change in wage differentials.Received: 9 October 2002, Revised: 15 July 2003, JEL Classification Numbers: D82, J31, O10.The authors acknowledge Osamu Hayashida, Noriyoshi Hemmi, Hideshi Itoh, Michihiro Kandori, Toshihiro Matsumura, Takuya Nakaizumi, Osamu Nishimura, Ryoji Ohdoi, Tadashi Yagi, Noriyuki Yanagawa, and seminar participants at Doshisha University, the University of Tokyo, and Contract Theory Workshop at Kyoto University for helpful comments and suggestions. We would also like to thank an anonymous referee for valuable comments. This paper is part of the academic Project on Intergenerational Equity (PIE), funded by a scientific grant from Japans Ministry of Education, Culture, Sports, Science and Technology (grant number 603).     

Intergenerational policy and the measurement of tax incidence

We evaluate the ability of generational accounting to assess the potential welfare implications of policy reforms. In an intergenerational context policy reforms usually have redistributive, efficiency, and general equilibrium implications. Our analysis shows that when the policy reform implies changes in economic efficiency, generational accounts can be misleading not only about the magnitude of welfare changes, but also about the identity of who wins and who losses. In contrast, the generational accounts correctly identify welfare changes when the policy reform has only a pure intergenerational redistribution component. We illustrate and quantify this issue in the context of widely considered policy reforms (substitution of consumption for labor taxation, and the increase of retirement age) and in a more general context of optimal policy.     

The Japanese saving rate between 1960 and 2000: productivity,policy changes,and demographics

In this paper, we use an overlapping generations model to study the factors generating the saving rate in Japan between 1960–2000. The model economy allows for observed aging of the population, total factor productivity (TFP), and fiscal policy to affect the national saving rate. Our calibrated general equilibrium setup generates saving rates that are reasonably similar to the data during this period. Our counterfactual experiments indicate that observed TFP growth rates are the main reason for both the secular decline and the two humps in the saving rate during 1960–2000.      

The determinacy of equilibrium in economies of overlapping generations

We study the problem of uniqueness of equilibrium paths in the overlapping generations model. We show that, despite local calculation based on counting equations and unknowns, the equilibrium path may be unique. We do this by constucting an example of an economy of overlapping generations with just one equilibrium up to time shift, beside the steady states. Time is either discrete or continuous; in either case, it extend into the infinite future and, possibly, the infinite past. There is one, non-storable commodity at each date. The economy is stationary; intertemporal preferences are logarithmic; the endowments and discount factors of individuals need not depend continuously on time. With continuous time, equilibrium paths of prices are smooth; this, even for endowments and discount factors of individuals that do not depend continuously on time. With discrete time, as the number of periods in the life-span of individuals increases, equilibrium paths converge to the continuous time solutions. If time extends infinitely into the infinite past as well as into the infinite future, in continuous time, all non-stationary equilibrium paths of prices are time-shifts of a single path; in addition, there are two stationary solutions; in discrete time, there is a one dimensional family of non-stationary solutions, up to time-shift; however, the indeterminacy vanishes as the number of periods in the life span of individuals tends to infinity. If, alternatively, time has a finite starting point, in discrete time the degree of indeterminacy increases with the life-span of individuals, and, in continuous time, it is infinite; however, these are families of exponentially decreasing oscillations which, although they may exhibit pseudo-chaotic behaviour for a while, as time tends to infinity they all get damped, and asymptotic behaviour is that of the economy that originates in the infinite past. Stefano Lovo made interesting comments.     

Existence,uniqueness, and stability of equilibrium in an OLG economy

Summary. This paper presents sufficient conditions for the existence of a unique and globally stable steady state equilibrium for OLG economies with production. The conditions impose separate requirements on the utility and production functions. Moreover, the conditions do not require assumptions concerning the third order derivatives of the production and utility functions.Received: 12 August 2002, Revised: 7 January 2003, JEL Classification Numbers: D50, D91, E13, O41.I would like to thank Nick Baigent, Laurie Conway, Karl Farmer, Christian Gehrke, and Hideo Konishi for helpful comments. I am grateful to an anonymous referee for his or her comments.     

Welfare effects of bubbles in an endogenous growth model

This paper examines welfare effects of asset bubbles in an endogenous growth model with overlapping generations. In our model, a steady-state equilibrium with bubbles exists only if the presence of bubbles raises the welfare level of the initial generation. Bubbles can be beneficial to generations born at relatively early dates, whereas they reduce the welfare level of sufficiently distant future generations. Increasing the rate of supply of the useless asset improves the lifetime utilities of future generations.     

Sunspot cycles

Summary. This paper shows new properties about the equilibria of a stationary OG economy by establishing a connection between its stationary equilibria and those of a finite economy, with and without extrinsic uncertainty. Specifically, it shows the countability and local uniqueness with respect to the sup metric of the so-called sunspot cycles introduced here, that encompass both the deterministic cycles and the usual finite Markovian stationary sunspot equilibria. These sunspot cycles are, moreover, able to generate, at a lower cost in terms of assumptions than other sunspot equilibria, time series with the recurrent but irregular fluctuations typical of economic time series. Received: July 26, 2001; revised version: March 5, 2002 RID="*" ID="*" I want to thank an anonymous referee for comments that have helped greatly to improve this paper, as well as the comments about its contents received from several audiences in different seminars and conferences (the Economic Theory seminar of the University of Pennsylvania, the 2001 Meeting of the Econometric Society held at New Orleans, the 2000 Econometric Society World Congress, the 2000 Society for Economic Design Conference) and from comments to a previous paper, Dávila [10], specially from Jim Peck at the 1997 Workshop on General Equilibrium held at the University of Venice, that eventually lead to this one.     

Aggregate risk sharing and equivalent financial mechanisms in an endowment economy of incomplete participation

Summary. A pure endowment overlapping generations economy can be inefficient because of insufficient risk sharing. The introduction of an outside asset by a government or the existence of a clearing house can remedy the inefficiency by allowing some intergenerational risk sharing. While the typical outside asset is fiat money, many alternative financial mechanisms, such as social security, risk-free government bonds, mispriced deposit insurance, and income insurance can serve the same function as fiat money. Hence there are many equivalent financial mechanisms that provide intergenerational insurance. In the presence of uncertainty, there are several concepts of Pareto optimality that can be appropriately applied in an overlapping generations setting. I examine the risk-sharing arrangements associated with two different concepts of optimality, including how these arrangements are financed. The results are related to, and in some instances an extension of, the equivalence results obtained by Chamley and Polemarcharkis (1984), Weiss (1977), and Wallace (1981).Received: 4 March 2003, Revised: 30 January 2004JEL Classification Numbers: E40, E44, D51.P. Labadie: I would like to thank the participants of the Economic Theory Symposium Recent Developments in Money and Finance at Purdue University, May 2-4, 2003 and an anonymous referee for comments on this version. I am grateful to Bruce Smith for comments on an earlier version.     

The robustness of optimal equilibrium among overlapping generations

Summary. We combine and strengthen optimality and robustness theorems for the overlapping-generations model of money. Roughly, we find a Pareto-optimal monetary equilibrium of a generic stationary economy that is near an optimal monetary equilibrium of each nearby non-stationary economy. Since the nearby equilibria are monetary, the general problem of macroeconomic stabilization reduces to maintaining the money supply. And since the nearby equilibria are optimal, stabilization is socially desirable. Received: October 27, 1997; revised version: March 25, 1998     

Junior is rich: bequests as consumption

We explore the consequences for asset pricing of admitting a bequest motive into an otherwise standard overlapping generations economy where agents trade equity, a risk free asset and consol bonds. With low risk aversion, the calibrated model produces realistic values for the mean equity premium and the risk free rate, the variance of the equity premium, and the ratio of bequests to wealth. However, the variance of the risk free rate is unrealistically high. Security prices tend to be substantially higher in an economy with bequests as compared to an otherwise identical one where bequests are absent. We are able to keep the prices sufficiently low to generate reasonable returns and premia by stipulating that a portion of the bequests skips a generation and is received by the young.

“You never actually own a Patek Philippe. You merely take care of it for the next generation.” Patek Philippe & Co.

We thank John Cox, Jean Pierre Danthine, Felix Kubler, Edward Prescott and seminar participants at The Bank of Italy, Columbia, Lausanne, Mannheim, MIT, Lugano, SIFR, the University of New South Wales, USC, Yale and the University of Zurich for insightful xcomments. The usual caveat applies.     

Reconsidering the Impact of the Environment on Long-run Growth when Pollution Influences Health and Agents have a Finite-lifetime

Using an overlapping generation model à la Blanchard (1985, J Polit Econ 93:223–247) with human capital accumulation, we demonstrate that the influence of the environment on optimal growth in the long-run may be explained by the detrimental effect of pollution on life expectancy. We also show that, in such a case, greener preferences are growth- and welfare-improving in the long-run even if the ability of the agents to learn is independent of pollution and utility is additively separable. Finally, we establish that a minimum environmental policy is required to obtain a sustainable equilibrium in the market economy and that it is possible to implement a win–win environmental policy.     

Aging population and education finance

Conventional wisdom suggests that aging of population will increase political pressure to tilt the composition of social spending in favor of the elderly, while potentially sacrificing other publicly provided goods such as education. This view seems to be supported by recent empirical findings that per child public education spending tends to be lower in US jurisdictions with higher fraction of elderly residents. Do these cross-sectional findings also carry the dynamic implication that longevity will lead over time to waning political support for funding of public education? This paper challenges such implication. We present a model that is consistent with the aforementioned cross-sectional regressions yet predicts an overall positive impact of increasing longevity on public education funding and economic growth.     

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.