Price dynamics in overlapping generations environments

Summary This work examines the existence, uniqueness and computation of competitive equilibria in a class of overlapping generations environments. This set of environments represents a broad generalization of the overlapping generations model considered by Aliprantis and Plott [1]. Two types of results are presented in this paper. First, some general characteristics of perfect foresight competitive equilibrium price paths are developed for economies with finite or countably infinite time horizons and agents with finite lifetimes. The results establish the conditions leading to locally monotonic and locally stable equilibrium prices given arbitrarily many exogenous parameter shifts. Second, these results are strengthened when consideration is focused on a single parametric shift in a finite economy. Existence of a unique equilibrium price path is established. A simple set of rules are given to facilitate computation of this price path for any given shift.The authors wish to express their thanks to Donald Brown, Diego Moreno, Charles Plott, Vernon Smith, and Mark Walker for their comments and suggestions regarding this research.     

Indirect taxation and the welfare effects of altruism on the optimal fiscal policy

This paper analyzes the welfare effects of altruism on the optimal fiscal policy. The existence of positive bequests links present and future generations in the economy. We show that these altruistic links provide a new role for indirect taxation (consumption and estate taxes) with important welfare implications. We use three different altruistic approaches (warm-glow, dynastic, and family) to illustrate how the presence of bequests in the budget constraint of the donee gives the government the ability to use indirect taxation to mimic lump-sum taxes and to implement the first-best outcome in the long-run. This channel is not present in economies without altruism, such as the infinite-lived consumer economy or the overlapping generations economy, where long-run welfare is suboptimal and indirect taxation is irrelevant.     

Equilibrium existence in infinite horizon economies

In sequential economies with finite or infinite-lived real assets in positive net supply, we introduce constraints on the amount of borrowing in terms of the market value of physical endowments. We show that, when utility functions are either unbounded and separable in states of nature or separable in commodities, these borrowing constraints not only preclude Ponzi schemes but also induce endogenous Radner bounds on short-sales. Therefore, we obtain existence of equilibrium. Moreover, equilibrium also exists when both assets are numéraire and utility functions are quasilinear in the commodity used as numéraire.     

Approximate equilibria in markets with indivisible commodities

This paper presents results on the existence of approximate equilibria in large but finite exchange economies in which all the traders have non-convex consumption sets. As such, the paper gives a natural extension, to the finite economy, of Mas-Colell's results on existence with indivisible commodities and a continuum of agents. It also presents an approximate equilibrium theorem without any assumption of compactness or bounded non-convexity of preferences.     

Determinacy of competitive equilibria in economies with many commodities

This paper provides a framework for establishing the determinacy of equilibria in general equilibrium models with infinitely many commodities and a finite number of consumers and producers. This paper defines a notion of regular economy for such models and gives sufficient conditions on the excess savings equations characterizing equilibria under which regular economies have a finite number of equilibria, each of which is locally stable with respect to perturbations in exogenous parameters, and under which regular economies are generic. This paper also defines two notions of concavity, called uniform concavity and weighted uniform concavity, which generalize standard finite-dimensional notions of differential concavity to an infinite-dimensional setting by prohibiting goods from becoming perfect substitutes asymptotically. For the case of economies in which there are countably many commodities, such as discrete time models or markets with countably many assets, results in this paper show that equilibria are generically determinate as long as utility functions and production sets are uniformly concave or weighted uniformly concave. Received: November 7, 1996; revised version: March 13, 1998     

An expository note on individual risk without aggregate uncertainty

In economies where agents bear some risk, the analysis would often be facilitated by the assumption that the risks are i.i.d. and disappear in the aggregate. A formal appeal to the law of large numbers requires the consideration of a sequence of finite economies. In an economy with a continuum of agents there are countable families of sets for which it is impossible for a law of large numbers to be valid. With countably many agents and a finitely additive measure, independence is compatible with the law of large numbers.     

International Capital Movements In the Solow and Overlapping Generations Growth Models*

This paper examines capital movements in the overlapping generations and Solow models. For the overlapping generations model, a simple compensation scheme is developed to show how the gaining generation(s) can always compensate the losing generation(s) and still gain in the move from autarky to free capital mobility. Moreover, unlike the Solow model, the move to an open economy for the overlapping generations model has a tendency to reduce the assets held by the capital-exporting country.     

Observational equivalence of the overlapping generations and the discounted dynamic programming frameworks for one-sector growth

Two alternative frameworks for one-sector growth are considered: an overlapping generations model with two-period lived, strictly selfish agents and a discounted dynamic programming model with infinitely lived agents. It is shown that under certain assumptions the two models are observationally equivalent, i.e., generate identical timepaths for all aggregate variables. One of the key assumptions is that the steady-state real interest rate in the overlapping generations model be strictly greater than the growth rate. The result is proved for the deterministic case and extension to a stochastic case is indicated.     

Unawareness and bankruptcy: A general equilibrium model

Summary. We present a consistent pure-exchange general equilibrium model where agents may not be able to foresee all possible future contingencies. In this context, even with nominal assets and complete asset markets, an equilibrium may not exist without appropriate assumptions. Specific examples are provided. An existence result is proved under the main assumption that there are sufficiently many states that all the agents foresee. An intrinsic feature of the model is bankruptcy, which agents may involuntarily experience in the unforeseen states. Received: April 23, 1997; revised version: May 19, 1997     

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.     

Borrow and Adjust: Fiscal Policy and Sectoral Adjustment in an Open Economy*

Should the government run fiscal deficits in response to an adverse external shock that warrants transfer of resources from production of nontraded to traded goods? This article considers normative fiscal policy implications of sectoral adjustment costs in a two‐sector model with overlapping generations. Fiscal deficits benefit present generations by depleting foreign assets and slowing down the adjustment process. We show that despite no nominal rigidities, temporary fiscal deficits increase social welfare if adjustment costs prevent immediate sectoral reallocation of inputs. If there are no adjustment costs, the case for fiscal deficits vanishes.     

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     

An Elementary Approach to Approximate Equilibria with Infinitely Many Commodities

We prove the existence of approximate equilibria in a finite exchange economy with a countably infinite number of commodities and nonconvex preferences, when every trader has an excess demand set that is finitely spannable, i.e., that could be covered by a union of its convex subsets in finitely many steps. We show that the bound on the norm of the per capita aggregate excess demand is reciprocally related to the square root of the population. Extensions are also made to the case where countably many commodities are indivisible. The proofs are elementary. Journal of Economic Literature Classification Numbers: D50, C62, D52.     

Budget Deficits and Exchange-Rate Crises

This paper investigates currency crises in an optimizing general equilibrium model with overlapping generations. It is shown that a rise in government budget deficits financed by future taxes generates a decumulation of external assets, leading up to a speculative attack and forcing the monetary authorities to abandon the peg.     

Sufficient conditions for the existence of sunspot equilibria

This paper reports on conditions on agents' preferences and endowments sufficient to guarantee the existence of sunspot equilibria in a simple overlapping generations model of pure exchange. Sunspot equilibria are those in which uncertainty extrinsic to the economy operates through expectations to yield a fulfilled expectations competitive equilibrium in which the extrinsic randomness has real effects on prices and allocations. The paper also provides necessary and sufficient conditions for these equilibria to have agents trading in a fixed stock of valued fiat money. The condition derived can be interpreted as requiring that intertemporal income effects appropriately dominate substitution effects.     

‘Double dipping’: the combined effects of social security and civil service pensions on employee retirement

How do macro variables such as aggregate consumption, aggregate money demand, prices, and interest rates vary in response to government attempts to redistribute income across agents through selective tax-transfer policies? This question is investigated for an overlapping generations model consisting of heterogeneously endowed three-period lived agents. In the presumably most favorable case for invariance (identical log-linear utility functions), it is shown that positive interest rate macro equilibria are invariant with respect to redistributions in social security benefits if and only if all agents initially exhibit qualitatively identical liquidity preference behavior, i.e. positive money holding only in youth, only in middle-age, or never.     

GROWTH AND BUBBLES WITH CONSUMPTION EXTERNALITIES*

This paper explores the role of consumption externalities in an overlapping generations economy with capital accumulation. If consumers in each generation are concerned with other agents’ consumption behaviours, there exist intergenerational as well as intragenerational consumption externalities. It is the presence of intergenreational consumption externalities that may produce fundamental effects both on equilibrium dynamics and on steady‐state characterization of the economy. This paper demonstrates this fact in the context of a simple model of endogenously growing, overlapping‐generations economy with or without asset bubbles.     

General equilibrium, wariness and efficient bubbles

Wary consumers overlook gains but not losses in remote sets of dates or states. As preferences are upper but not lower Mackey semi-continuous, Bewley?s (1972) [4] result on existence of equilibrium whose prices are not necessarily countably additive holds. Wariness is related to lack of myopia and to ambiguity aversion (and, therefore, to Bewley?s (1986) [6] work on Knightian uncertainty). Wary infinite lived agents have weaker transversality conditions allowing them to be creditors at infinity and for bubbles to occur in positive net supply assets completing the markets. There are efficient allocations that can only be implemented with asset bubbles.     

Rational expectations in the overlapping generations model

This paper reports results on the character of the rational expectations equilibria of a stochastic overlapping generations model with heterogenous markets. The model considered is a stationary overlapping generations model in which the endowments of young agents are subject to i.i.d. random shocks. The main result shown is that if there are l > 1 commodities traded in every period, then for most preferences, the rational expectations equilibrium stochastic process of prices and allocations necessarily exhibits serial correlation. This is in marked contrast to the one commodity model in which there always exists an equilibrium which is measure isomorphic to the endowment process.     

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.