Markov rational expectations equilibria in an overlapping generations model

In this paper, we analyze rational expectations equilibrium paths in a stochastic overlapping generations model. The work presented here builds on results of S. E. Spear (J. Econ. Theory 35 (1985), 251–275), where is is shown that in a model with multiple goods and time non-separable preferences, a stochastic steady state equilibrium will generically fail to exist. A stochastic steady state is defined as an equilibrium in which the stochastic process of endogenously determined variables is measure isomorphic to the exogenous process driving the model. In this paper, we establish the existence of non-steady state equilibria and provide a characterization of their stochastic properties.     

Socially responsible investment in an environmental overlapping generations model

One of the problems associated with the conservation of the environment is that short-lived individuals fail to account for the long-term effects of pollution, which implies that future generations bear the costs imposed by the current generation. Such inter-generational externalities are usually tackled by (Pigovian) taxes, fiscal policy or environmental regulation. Alternatively, we propose that socially responsible investment funds create a role for the stock market to deal with intergenerational environmental externalities. We analyze the role of the stock market in an environmental overlapping generations model of the Diamond-type, in which agents choose between investing in “clean” government bonds or “polluting” firm equity. We show that although socially responsible investors are short-lived, the forward-looking nature of stock prices can help to resolve the conflict between current and future generations.     

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.     

Sunspot-like equilibria in an overlapping generations economy with strategic interactions

In this paper I analyze the effect of market uncertainty in an overlapping generations economy with strategic interactions among agents. I demonstrate the existence of sunspot-like equilibria, in which arbitrarily small amounts of intrinsic uncertainty in agents’ offers generate large fluctuations in equilibrium bids and prices. I would like to express my gratitude to Stephen Spear for his guidance during the realization of this project. I thank an anonymous referee for providing insightful comments and suggestions. I have benefited from comments by Alexander Elbittar, Cesar Guerrero, and Vivek Ramachandran.     

Fixed price equilibria in a multifirm model

In a simple temperary equilibrium model with three commodities (labour, goods and money) and two sectors, there are different firms, each having its own production function. There now exist four types of fixed price equilibria (Keynesian, classical, repressed inflation, undercounsumption). In the last type, consumers are not rationed, some producers are rationed on the goods market, and other producers on the labour market. There exist three different aggregate production functions, that have to be applied in Keynesian, classical, and repressed inflation situations respectively. For the fourth case no aggregate production function exists.     

Competitive equilibria in overlapping generations Experiments

Summary The paper presents the results of four overlapping generations experiments performed at the California Institute of Technology. Overlapping generations markets were created in which each agent had a two period life span. With the exception of the first period, there were eight agents trading in each period; four buyers (two young and two old) and four sellers (two young and two old). Parameters were selected so that a small set of equilibria existed. The markets were open for twenty-nine periods with a demand shift occurring at the fifteenth and sixteenth periods.This work provides a method of computing all competitive equilibria for a class of environments—called the opposing shift environments. The main conclusion of the experiments is that the experimental price data converge to near the stationary portions of the competitive equilibria. Demographic dynamics are also explored as part of the price adjustment process. Dynamic features found in non-overlapping environments are also observed in the overlapping generations case.We thank E. J. Nanale, a Caltech undergraduate student, who helped design and conduct the experiments. Special thanks are due to Hsing Yang Lee for his help in adapting the Multiple Unit Double Auction Program to accomodate the overlapping generations environment and for his help with the data processing. We also thank David Grether who found a serious problem with the statistical analysis in an early draft. The research assistance of Kay-Yut Chen was also very valuable to the completion of this work. The comments and suggestions of P. Rangazas were very helpful. The research of the second author was supported in part by a National Science Foundation Grant and the California Institute of Technology Laboratory for Experimental Economics and Political Science.     

Stationary Markov equilibria for overlapping generations

Summary.  At a stationary Markov equilibrium of a Markovian economy of overlapping generations, prices at a date-event are determined by the realization of the shock, the distribution of wealth and, with production, the stock of capital. Stationary Markov equilibria may not exist; this is the case with intra-generational heterogeneity and multiple commodities or long life spans. Generalized Markov equilibria exist if prices are allowed to vary also with the realization of the shock, prices and the allocation of consumption and production at the predecessor date-event. (Stationary) Markov -equilibria always exist; as allocations and prices converge to equilibrium prices and allocations that, however, need not be stationary.Received: 2 March 2004, Revised: 2 April 2004, JEL Classification Numbers:   D50, D52, D60, D80, D90.Correspondence to: Felix KublerWe thank participants in seminars in Athens and Lund, at Penn, at IMPA and at Stanford, the 2002 CEME (NBER) General Equilibrium Conference and the 2002 SED meetings, and especially Martin Hellwig, George Mailath and an anonymous referee for very helpful comments.     

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).     

Existence of equilibria in the overlapping generations model: the nontransitive case

Summary This paper investigates the existence of competitive equilibria in dynamic exchange models with countably many periods and countably many agents. At each period the commodity space can be finite or infinite dimensional. The preferences of agents are not assumed to be transitive or complete. A first equilibrium existence theorem is established under the classical assumption that there exists a finite set of non-negligible agents. In the particular case of an overlapping generations model, a second existence theorem allows simultaneously for finite-lived assets and infinite-lived assets and limits the previous assumption to infinite-lived assets. This theorem covers obviously the standard case of an overlapping generations model where the agents have no endowment outside their lifetime.     

Monetary equilibrium in an overlapping generations model with productive capital

Summary We study perfect foresight competitive equilibrium in an overlapping generations model with productive capital and a fixed nominal stock of money. We obtain almost-complete characterizations of (a) the existence of a monetary equilibrium from an arbitrary initial capital stock, and (b) the existence of anefficient monetary equilibrium from an arbitrary initial capital stock. When the initial capital stock is no larger than the golden rule stock, the necessary and sufficient condition for both (a) and (b) is the dynamic inefficiency (in the sense of Malinvaud) of the autarkic (or nonmonetary) equilibrium from the same initial stock. However, this condition, though necessary, isnot sufficient for the existence of a monetary equilibrium when the initial stock exceeds the golden rule stock (and still more conditions are needed for anefficient monetary equilibrium to exist). We provide characterizations for these cases, and as corollaries obtain examples in which (a) the nonmonetary equilibrium is inefficient but no monetary equilibrium exists, and (b) monetary equilibria exist but no efficient monetary equilibrium does.We are grateful to a co-editor and an anonymous referee for comments that greatly improved the exposition in the paper.     

Capital asset pricing in an overlapping generations model

This paper attempts to contribute to two rapidly growing branches in economic theory: asset pricing and “overlapping generations” models. The model is formulated and it is shown that equilibrium prices exist, and some of their properties are discussed. Then the model is applied to an asymmetric information environment to see if randomness in the number of informed agents could confuse the uninformed. Surprisingly, it could not.     

Asset bubbles in an overlapping generations model with endogenous labor supply

This paper examines the effects of asset bubbles in an overlapping generations model with endogenous labor supply. We show analytically that asset bubbles can lead to an expansion in steady-state capital, investment, employment and output under certain conditions.     

Fiscal incidence in an overlapping generations model with a fixed asset

We analyze a model of overlapping generations with a fixed factor (‘land’), malleable capital, and labor. We consider the dynamic effects of various fiscal policies including taxes on rent, wages, and creation of public debt on capital accumulation, land prices, and intergenerational welfare. Minimal assumptions (uniqueness and stability) imply that a land tax may initially raise land values, but the upper bound is less than one-half of the tax revenues. Assuming homothetic utility, the ratio between the long-run capital responses to a land tax and to a lump-sum transfer of equivalent revenue from the young to the old depends solely on the share of labor.     

Short run core equivalence in an overlapping generations model

This essay establishes the equality between the set of competitive equilibrium allocations and the set of allocations which belong to the cores of a sequence of short run economies for an overlapping generations model. A short run economy is a finite period economy obtained by truncating the original economy so that the truncated economy is irreducible.     

Equilibria in an overlapping generations model with transfer policies and exogenous growth

For an overlapping generations economy with varying life-cycle productivity, non-stationary endowments, continuous time starting at $-\infty $ (hence allowing for full anticipation), constant-returns-to-scale production and ces utility, we fully characterise equilibria where output is higher than investment, which is strictly positive. Net assets (aggregate savings minus the value of the capital stock) are constant in any equilibrium, and, for balanced growth equilibria (bge, defined for an economy with stationary endowments), net assets are non-zero only in the golden rule equilibrium, in accord with Gale (1973). The number of bge is finite. Their parity, however, depends on the life-cycle productivity, in particular, on the relation between the intertemporal elasticity of substitution, the minimal working age and the minimal tax age.     

Stationary equilibrium transition rules for an overlapping generations model with uncertainty

An overlapping generations model incorporating random production shocks is studied. Households have finite life spans. Futures markets are incomplete. Agents have full information in one case, and receive only a limited signal in another. In both instances the existence of a time-autonomous transition rule is proved such that if all agents forecast using it, the economy's actual growth will bear the predictions out. The rule corresponds to a steady state for a non-stochastic model. With limited information, it is seen to depend on all past signals. Several approximation theorems which may facilitate future applications are presented.     

Tax policy and aggregate stability in an overlapping generations model

In the context of a two-period non-monetary overlapping generations model with Cobb–Douglas preference and technological specifications, this paper explores the theoretical as well as quantitative interrelations between equilibrium (in)determinacy versus (i) a progressive tax schedule on wage income and (ii) a balanced-budget rule with endogenous labour taxation. In sharp contrast to previous studies on a one-sector representative-agent macroeconomy, we find that both fiscal formulations can possibly operate as stabilizing instruments against cyclical fluctuations driven by agents' self-fulfilling beliefs. The key policy implication of our no-indeterminacy result is that depending on what is the underlying analytical environment, countercyclical income taxation may stabilize or destabilize the business cycle.     

Aspirations and the transfer paradox in an overlapping generations model

This study examines the transfer problem between two countries when either the donor or the recipient has aspirations, based on parents’ standards of living, in a one-sector overlapping generations model. Focusing on whether and how aspirations impact the welfare effect of a transfer, we demonstrate the following results. First, when the donor forms aspirations, as the degree of his/her aspirations to their parents increases, a transfer is more likely to cause donor enrichment. However, this does not affect the recipient’s welfare at all. In contrast, when the recipient forms aspirations, whether the increase in the degree of these aspirations causes immiserization depends on whether the transfer raises the recipient’s consumption. Second, we show that if the donor’s or recipient’s marginal utility increases with their respective aspirations, the transfer is more likely to cause recipient immiserization. However, whether donor enrichment occurs depends on the situation. These results imply that there are two types of effects that aspirations can have on the welfare of both countries: effects caused by the aspirations, and effects that occur through the capital market. Furthermore, we find that these two effects on welfare do not necessarily work in the same direction.     

Public debt and demographic growth in an overlapping generations model

The comparative dynamics of changes in the rate of population growth are discussed in an overlapping generations economy where there is public debt. The focus is on the effects of such variations on capital accumulation, factor returns and welfare of individuals living in steady states.