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.     

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).     

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.     

Fixed price equilibria in an overlapping generations model with investment

We study fixed price temporary equilibria (with rationing) and sequences of temporary equilibria in a three commodities (goods, labor, bonds) overlapping generations model with endogenous investment. Young consumers, living two periods, work, consume, and buy bonds for financing next period's consumption. New firms, existing for two periods, make a production plan for the next period, taking into account expected rationing, assumed similar to present rationing. The plan determines the amount of goods to buy as capital, financed by bonds. Old firms produce, using labor and the previously bought capital. Different regimes exist and expectations can be self-fulfilling and self-destroying.We are grateful to the referees for helpful comments.     

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.     

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.     

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.     

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.     

Two-period cycles in a three-period overlapping generations model

We study the properties of two-period monetary cycles in simple pure exchange overlapping generations economies in which the households live for three periods. We demonstrate that these economies can support cycles under a much broader—and, arguably, more plausible—range of assumptions than the analogous two-period economies. We show that economies that fail the well-known Grandmont (Econometrica 53 (1985) 995) condition can have cycles, and that economies that satisfy the condition can fail to have cycles. In addition, we show that economies can have monetary cycles when they do not have conventional monetary steady states, and when aggregate demand for assets is not decreasing in the real return rate at a gross real rate of unity.     

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.     

Fiscal strategies,foreign indebtedness,and overlapping generations

Conclusions This paper offers a unifying dynamic system approach to real government debt and real capital formation in a world economy. The sustainability of permanently maintained primary fiscal deficits is investigated in an open economy. In particular if national governments compete in the issuance of debt at an international capital market sustainable debt profiles appear only as a theoretical (i. e., not empirically valid) curiosity. Within the more realistic regime of an undercapitalized world economy a nation can only run a permanently maintained primary surplus. Starting from a PMP surplus the paper also demonstrates the viability of temporary deficits implying an increase in taxation later to stabilize the fiscal debt. By reversing the argument this shows, the right way to reduce government debt in a non-traumatic manner is to run a higher temporary surplus via higher taxation. Using this extrasurplus to buy back fiscal debt the economy may reduce taxation later while enjoying vigorous capital accumulation towards a higher capital-labour ratio. Furthermore, the paper shows that ceteris paribus a relatively high social security load and a relatively high size of a balanced budget causes external indebtedness via consumption oriented current account deficits. It is left for further research to see what happens if government borrows for public investment instead of public consumption.My research was supported by Deutsche Forschungsgemeinschaft. While preparing the paper 1 had access to unpublished work by M. Carlberg and T. Ihori. Discussions with M. Carlberg, H. Großmann, J. Michaelis, and H. Schmid are gratefully acknowledged. The diagrams were mastered by C. Schwarz.     

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.     

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.     

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.     

Human capital and economic growth in an overlapping generations model

The paper describes an aggregative optimal growth model, the essential features of which are that individuals are mortal and obtain their labor skill through educational training. The process of human capital formation is described by an education function which relates the pass rate to the educational expenditure per student. Two alternative scenarios, private and public education regimes, are separately investigated. Under the decentralized education regime, risk-neutral individuals borrow to finance their education when young. Under the centralized education regime, the cost of education is financed by taxes imposed on the workers in the economy, and the central government maximizes a long-term social target function. The equilibria of both regimes are analyzed and various comparative static results derived. It is shown that educational investment in a decentralized equilibrium is higher than that in the centralized steady state. We also establish that there exists a time discount rate at which or above which the decentralized per capita consumption exceeds that of the centralized steady state whereas for time rates of discount sufficiently near the population growth rate, the above result will be reversed.     

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.     

The dynamics of capital accumulation in an overlapping generations model

This paper studies capital accumulation in a slightly altered, explicit OLG model. The fundamental difference with the standard model lies in the initial conditions. If a portion of the initial allocation of the capital stock is not assigned to retirees, the framework allowing for a genuine accumulation of capital is provided. Dynamic aspects of the resulting model are analyzed, including dynamics of the quotas of capital stock, shares of total output, partial influences of parameters, the connection between the depreciation rate and capital's contribution to production, and the relation of the latter to saddle-node bifurcations and the existence of real-valued equilibria. It is demonstrated that the model is able to describe the initial phase of accumulation.     

International trade and capital accumulation in an overlapping generations model with a public intermediate good

We investigate the effects of a public intermediate good on trade patterns, capital accumulation, and the gains from trade in a two‐country, three‐sector overlapping generations model. A public intermediate good affects not only the productivity of private production but capital accumulation; thus, the results differ from those obtained in previous studies. First, opening to trade may accelerate capital accumulation in the higher‐savings country. Additionally, the country producing a public intermediate good more (which is labor‐intensive) may be the importer of the investment good (which is the most capital‐intensive). Finally, the lower‐savings country may have lower steady‐state welfare under trade.     

Consumption tax and economic growth in an overlapping generations model with money holdings

This paper examines the effect of a consumption tax on economic growth using an overlapping generations (OLG) model with money holdings. We show that the neutrality of the consumption tax does not hold in the money-in-the-utility-function model, because a change in consumption taxation induces the substitution of money holdings for consumption, and the money is the net wealth within the OLG structure. An increase in the consumption tax rate lowers (raises) the growth rate under a low (high) monetary expansion rate. On the other hand, in the cash-in-advance model and the money-in-the-production-function model, the neutrality of consumption taxation holds even within the OLG structure, because in these models there is no substitution of consumption and money holdings.