Existence of a Pareto-optimal equilibrium in nearly-stationary overlapping-generations economies

Summary In overlapping-generations models of fiat money, the existence of a Pareto-optimal equilibrium — which defines an optimal quantity of money — is more general than well-known counter-examples suggest. Those examples, having no optimal equilibrium just because there are small variations in households' tastes and endowments across generations, are not typical. On the contrary: For an open-dense, full-measure subset of smooth stationary economies and an open-dense subset of continuous stationary economies, introducing small variations in tastes and endowments across generations preserves the existence of an optimal equilibrium. Put simply, optimal equilibria generically exist for nearly-stationary economies.I thank Scott Freeman, Katsuhiko Kawai, and two referees for proofreading this text; all lead to clarifications.     

Existence of steady – state equium in an overlapping-generations model with production

Summary This paper establishes an existence theorem of a non-trivial (positive capital stock) steady-state equilibrium in Diamond's (1965) overlapping-generations model with production by employing the steady-state consumption curve introduced in Ihori (1978). The assumptions on preferences and production technologies that ensure the existence of a nontrivial steadystate equilibrium are separated from each other, unlike in Galor and Ryder (1989). We also provide two simple examples which illustrate the importance of two conditions in the theorem.Detailed comments by Tomoichi Shinotsuka and the referees of the journal were quite helpful. We also thank Marcus Berliant, Mark Bus, John H. Boyd III, Ban Chuan Cheah, Rajat Deb, Jim Dolmas, Oded Galor, Greg Huffman, Toshihiro Ihori, Radhika Lahiri, Lionel McKenzie, Arundhati Sen, and the seminar participants at the Midwest Mathematical Economics Conference in Ann Abor and at University of Rochester. The second author gratefully acknowledges the financial supports from the European Community Human Capital Mobility Program.     

Consumption habits in an overlapping-generations model

This paper introduces consumption habits in the Blanchard (1985) overlapping-generations model. It shows that steady-state capital and consumption are higher if individuals have habits than otherwise. Moreover, “inward habits” lead to higher steady-state capital and consumption compared to “outward habits.”     

Existence of equilibrium in an OLG model with production and altruistic preferences

Summary. This note deals with the existence and uniqueness of a non-trivial steady-state equilibrium in an overlapping generations (OLG) model with productive capital and altruistic agents. We establish a necessary and sufficient condition for operative bequests which extends Abel (1987) and Weil (1987). Interestingly, we prove that the OLG model with production and altruistic agents always experiences a non-trivial steady-state equilibrium. Received: July 16, 1998; revised version: January 29, 1999     

Intergenerational natural-capital equality in an overlapping-generations model with logistic regeneration

Following Mourmouras [Scandinavian Journal of Economics 93 (1991): 585–591], in a Diamond [American Economic Review 55 (1965): 1126–1150] type overlapping-generations model with renewable natural resources a competitive path of manmade capital accumulation exists which meets the sustainability criterion of intergenerational natural-capital equ(al)ity (= sustainable growth). The alleged compatibility of decentralized optimization with natural-capital sustainability is appealing, but the rel-evance of this compatibility result is questionable: the growth factor of the renewable natural resource is assumed to be independent of the resource stock. Employing instead a nonlinear (logistic) regeneration function, this paper reconsiders Mourmouras' compatibility statement in another natural environment. It is shown that only under a certain complex relationship between the parameters of the utility, production, and natural-growth function does a nontrivial stationary state exist which is saddle-point stable. It exhibits by definition intergenerational natural-capital equality, but the non-linear setting precludes in general, natural-capital equality across generations on the growth path towards the stationary state.     

An overlapping-generations model with search

Search is embedded in an overlapping-generations model. The young participate in a centralized market, and then are matched in pairs in a decentralized market. The old only participate in the centralized market. If the buyer's bargaining power in pairwise trade is close to unity and if the old are risk averse, then the golden-rule rate of money transfer is positive. Such risk aversion, the pairwise meetings, and dependence of the young's saving on the rate of return are necessary for this result.     

Fertility and mortality changes in an overlapping-generations model with realistic demography

Many overlapping-generations models assume only working and retirement stages and are “not capable of representing the most basic feature of the human economic life cycle: that it begins and ends with periods of dependency, separated by a long intermediate period of consuming less than is produced” (Bommier and Lee, 2003). To examine the economic consequences of fertility and mortality changes in a common framework, we incorporate realistic demographic features into a continuous-time overlapping-generations model with childhood, adulthood and retirement stages. Using parameter values appropriate for industrial countries (such as the USA), we find that a fertility increase and a mortality decline, while both causing a rise in the population growth rate, have opposite effects on capital accumulation. We also consider simultaneous fertility and mortality changes, and find that the effect on capital accumulation of a mortality change dominates that of a fertility change.     

Heterogeneous expectations and capital intensity in an overlapping-generations model

In this paper we examine the macroeconomic effects of heterogeneous probability beliefs in the context of a modified Diamond-type overlapping-generations model. We derive the effect of an increase in the degree of heterogeneity on the steady-state savings rate, the capital intensity, and welfare.     

Sustainable government debt in a two-good,two-country overlapping generations model

The recent dramatic rise of government deficits in most advanced countries to counter the effects of the global financial crisis arouses renewed interest for one of the perennial topics of fiscal policy: the sustainability of government debt. This paper explores maximum sustainabile debt in a two-good, two-country overlapping generations (OLG) model and analyzes existence and dynamic stability of steady states as well as the transitional dynamics of private capital when government debt remains below the maximum sustainable level. We find that maximum government debt levels for both countries exist and are negatively related. Moreover, if sustainable government debt is unilaterally expanded, private capital is crowded out in both countries while the terms of trade of the debt-expanding country are unaffected if capital income shares are internationally equal.     

Existence of an equilibrium in first price auctions

Summary We study the first price auction game with an arbitrary number of bidders when the bidders' valuations are independent from each other. In technical words, we work within the independent private value model. We show that if the supports of the valuation probability distributions have the same minimum and if this minimum is not a mass point of any of these distributions, then a Nash equilibrium of the first price auction exists. We then modify the first price auction game by adding a closed interval of messages. Every bidder has to send a message with the bid he submits. These messages are used in the resolution of the ties. The winner of the auction is chosen randomly among the highest bidders with the highest value of the message among the highest bidders. In the general case, we prove the existence of a Nash equilibrium for this augmented first price auction.I wish to thank Mamoru Kaneko and a referee for their comments on an earlier draft.     

A voting model for the allocation of public goods: Existence of an equilibrium

It is well known that equilibria may not exist for majority voting over multidimensional policy spaces. This paper shows that certain institutional constraints can be imposed upon the voting process to ensure existence of a restricted equilibrium. A restricted equilibrium point must defeat only those points connected to it by one of an exogenously given set of linearly independent voting vectors. Using this procedure in a general equilibrium model to determine demands for public goods, existence of a general political equilibrium is proven. The equilibrium need not be Pareto optimal and may be manipulated by changing the vectors.     

Determinants of nonresident government debt ownership

We examine the determinants of nonresident government debt ownership, accounting for domestic and external factors and financial variables during the period 2000Q2–2014Q4, focussing on a small euro area open economy: Portugal. Our results show that better fiscal positions, higher systematic stress in Europe and higher shares of monetary and financial institutions (MFI) cross-border holdings of public debt, increase the share of nonresident held debt, and rising sovereign yields decrease that ratio.     

A positive theory of government debt

A government that cannot commit to future policy choices faces a trade-off that explains the level of debt. On the one hand, there is an incentive to increase debt and delay taxation, so as to reduce current distortions. On the other hand, inflating current prices lowers the real value of nominal debt and so there is a motive to reduce it now. The size of long-run debt will depend on the interaction of these two opposing incentives. The critical determinant is the willingness of households to substitute away from goods being taxed by inflation. Numerical simulations show that the model matches some qualitative and quantitative properties of U.S. policy variables, including the fact that wars are frequently financed with a mix of instruments. The theory interprets the unusual post-World War II inflation and fast liquidation of accumulated debt as being due to higher long-run debt and expenditure in the period leading up to the war.     

Existence and uniqueness of stochastic equilibrium in a simple macro model

This paper demonstrates that even the simplest rational expectations macro model may be plagued by nonexistent or multiple equilibria. The reason for these problems is the postulated existence of risk-averse behavior on the part of labor suppliers and purchasers of durable commodities. This risk-averse behavior introduces the price forecast variance into the behavioral parameters of the model, thus leading to a simultaneous nonlinear system.     

Non-connectedness of the set of equilibrium money prices: The overlapping-generations economy

Consider the overlapping-generations economy with nominal taxes and transfers. Under some conditions, the set of equilibrium money prices is a non-negative interval. It has not been known whether this set can consist of two or more disjoint intervals. Three examples are provided here in which the set of equilibrium money prices is a non-connected set. The examples are for a finite-horizon balanced economy, an infinite-horizon balanced economy, and an infinite-horizon non-balanced economy.     

Existence of a statistical equilibrium for an economy with endogenous offer sets

A statistical equilibrium consists of distributions over offer sets of agents that can be achieved in the greatest number of ways. Although it is known that a unique equilibrium exists when the offer sets are finite and exogenous, the general case has been an open question. This paper (1) generalizes the concept of statistical equilibrium to the case where offer sets are endogenous and not necessarily finite, (2) proves the existence of equilibrium, (3) discusses a computational algorithm to obtain the equilibrium, and (4) applies the theory to the labor market and analyzes the implication of the minimum wage policy.     

Political economy of taxation in an overlapping-generations economy

This paper analyzes the effects of intergenerational conflict on capital and labor income tax rates, transfers, and government spending in a model of multidimensional policy choice. The different nature of tax liabilities for the young and the old can explain why the old receive large gross lump-sum transfers through social security, while the young receive little or none. A natural link also emerges between the size of the government as a provider of public goods and the magnitude of transfers that the same government will implement.     

Limits to government debt sustainability in OECD countries

The recent euro area sovereign debt crisis has shown the importance of market reactions for the sustainability of debt in advanced economies. This paper calculates endogenous government debt limits given the markets assessment of the probability to default. The estimated primary balance reaction function to growing debt has the “fiscal fatigue” property (a loosening fiscal effort makes the primary balance insufficient to support rising debt) at high debt levels. The combination of this feature of the primary balance reaction function with the market interest rate reaction to growing debt determines the government debt limit beyond which debt cannot be rolled over. An application to OECD countries over the period 1985 – 2013 with a model-based risk-premium shows that current debt limits are high for most of the OECD thanks to particularly low risk-free interest rates. It also shows for some countries that current debt levels are not sustainable without a change in government behaviour. Most importantly, the framework illustrates the state contingent nature of debt limits and therefore the vulnerability of governments to a change in macroeconomic conditions and to market reactions. Last, computations with an estimated interest rate reaction to public debt illustrate that debt limits are lower in the euro area than in other countries because of a sharper market interest rate reaction to rising debt.     

Existence and uniqueness of steady-state equilibrium in a two-sector overlapping generations model

In his seminal paper Galor [A two-sector overlapping generations-model: a global characterization of the dynamical system, Econometrica 60 (1992) 1351-1386] establishes conditions for the existence of equilibrium in the two-sector overlapping generations (OLG) model. Although appealing theoretically, these conditions are implicit and not easy to apply. This paper develops new theorems on the existence and uniqueness of steady-state equilibrium in the two-sector OLG model. We provide explicit conditions on the utility and production functions for the existence and uniqueness of equilibrium, with which one only needs to check the derivatives of the production and utility functions and their interactions, without requiring solving for the savings function and its derivatives. We present detailed steps to check the existence and uniqueness of equilibrium and provide illustrative examples.