On the optimality of interest-bearing reserves in economies of overlapping generations

Summary Paying interest on required reserves is considered in an overlapping generations model in which the return to capital dominates the return to fiat money. As Smith (1991) showed, financing interest on reserves benefits the initial old at the expense of future generations. We show that the transfer of wealth associated with interest on reserves can be offset by an accommodating open market purchase, so that the payment of interest on reserves is a Pareto improvement. We also show that paying interest on reserves improves welfare even when financed by distorting taxes on capital.The authors thank Mike Cox, Greg Huffman, Evan Koenig, and Bruce Smith for helpful discussion. Any remaining errors are solely ours. This work originated while Freeman was a Research Associate at the Federal Reserve Bank of Dallas. The views expressed herein do not necessarily reflect those of the Federal Reserve Bank of Dallas or the Federal Reserve System.     

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.     

Short-memory equilibrium in stochastic overlapping generations economies

In stochastic OLG exchange economies, we show that short-memory equilibria—the natural extension from deterministic economies of steady states, low-order cycles, or finite state-space stationary sunspots equilibria—fail to exist generically in utilities. As a result, even with independent and identically distributed exogenous shocks there is serial correlation in endogenous economic variables in equilibrium. This arises even if utilities are time-separable, some goods inferior, and there are no technological lags. Hence, the origins of economic fluctuations can be traced only to the demographic structure of a heterogeneous agent, multiple-good economy.     

Dynamic inefficiency in an overlapping generations economy with production

Reichlin [Equilibrium cycles in an overlapping generations economy with production, J. Econ. Theory 40 (1986) 89-102] has shown in an OLG model with productive capital that whenever the steady state is locally indeterminate and undergoes a Hopf bifurcation, it is Pareto-optimal. While these results were established under the assumption of Leontief technology, the author has partially extended them to show that the Hopf bifurcation is robust with respect to the introduction of capital-labor substitution. In this note, we prove that the Pareto-optimality of the steady state does not extend to technologies with capital-labor substitution. When the steady state is a sink or undergoes a Hopf bifurcation, it is characterized by over-accumulation with respect to the Golden Rule—the interest rate is negative—hence not Pareto-optimal. Most importantly, it follows that stabilization policies targeting the steady state leave room for welfare losses associated with productive inefficiency, apart from the very special case of Leontief technology.     

Multiple equilibrium in the overlapping generations model revisited

Bliss [Bliss, C., 2008. Multiple equilibrium in the Diamond capital model. Economics Letters 100, 143-145] finds numerically that the Diamond OLG model can have uncountably many steady states. We use log preferences and show analytically that a continuum of steady states can still exist.     

Efficiency and prices in economies of overlapping generations

In a general economy of overlapping generations, I introduce a notion of uniform inefficiency, corresponding to the occurrence of a Pareto improvement with a small uniform destruction of resources [G. Debreu, The coefficient of resource utilization, Econometrica 19 (1951) 273-292]. I provide a necessary and sufficient condition for uniform inefficiency in terms of prices at a competitive equilibrium: an allocation is uniformly inefficient if and only if the relative price of the aggregate endowment in a given period into the aggregate endowment up to that period does not vanish over periods of trade, a sort of Modified Cass Criterion [D. Cass, On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization, J. Econ. Theory 4 (1972) 200-223]. Minimal assumptions on fundamentals are needed for such a complete characterization. Furthermore, proofs reduce to simple and short direct arguments. Finally, I verify that uniform inefficiency is preserved under perturbations, a property that might fail for the canonical notion of inefficiency. Remarkably, an allocation is uniformly inefficient if and only if a non-vanishing redistribution, like a social security mechanism, is welfare improving.     

Optimal growth and cycles in overlapping generations models

Summary This paper investigates the dynamical properties of optimal paths in one-sector overlapping generations models without assuming that the utility function of the representative agent is separable. When the utility function is separable, the optimal growth paths monotonically converges toward the modified golden rule steady state. In the non-separable case, we show that the optimal growth path may be oscillating and optimal two-period cycles may exist. Applying these results to the model with altruism, we show that the condition of operative bequest is fully compatible with endogeneous fluctuations provided that the discount factor is close enough to one. All our results are illustrated using Cobb-Douglas utility and production functions.We thank C. Blackorby, J. Blot, P. Cartigny and one anonymous referee for helpful comments and suggestions which generally improved the exposition of the paper. We would also like to thank the participants of the Population and demography session of the European Economic Association 10th Annual Congress (Prague, The Czech Republic, September 1–4, 1995).     

A characterization of inefficiency in stochastic overlapping generations economies

In this paper, we provide a characterization of interim inefficiency in stochastic economies of overlapping generations. With respect to the established body of results in the literature, we allow for sequentially incomplete markets and we remove the hypothesis of two-period horizons, by considering longer, though uniformly bounded, horizons for generations. The characterization exploits a suitably Modified Cass Criterion, based entirely on observable prices and independent of the length of the horizons of generations. For sequentially incomplete markets, we introduce a notion of unambiguous inefficiency, separating the inefficient intertemporal allocation of resources from incomplete risk-sharing. Unambiguous inefficiency reduces to inefficiency when markets are sequentially complete. Furthermore, our analysis shows that the hypothesis of two-period horizons is purely heuristic in establishing a criterion for inefficiency.     

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.     

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.     

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.     

The effects of the raising-the-official-pension-age policy in an overlapping generations economy

This paper studies how economic variables are affected by raising the official pension age. Although it is said that such a policy increases output, this paper shows that such a statement is not necessarily true. Moreover, the paper finds that the social security benefit can decrease, which implies that it might be impossible to sustain the same level of benefit only by such a policy.     

Seigniorage and Japanese fiscal sustainability: Simulation analysis using an overlapping generations model

This study examines two tax policies for achieving fiscal sustainability in Japan: (i) an increase in consumption tax and (ii) consumption tax hike combined with inflation. To evaluate these policies from both fiscal and welfare perspectives, I develop a multi-period overlapping generations model with money. The results reveal that, compared to the first policy, the second policy can substantially delay the timing of and curb the increase in consumption tax through seigniorage revenue. This suggests seigniorage could be a useful tool for the Japanese government in resolving its fiscal problems. In addition, in an aging Japan, the second policy can enhance future generations’ utility. Because inflation reduces money holdings and utility of the elderly, policies that cause inflation in the present but reduce it in the future improve the utility of future generations. From a social welfare viewpoint, such policies are desirable in a government that has foresight.     

Optimal growth and uncertainty: Learning

We introduce learning in a Brock-Mirman environment and study the effect of risk generated by the planner's econometric activity on optimal consumption and investment. Here, learning introduces two sources of risk about future payoffs: structural uncertainty and uncertainty due to the anticipation of learning. The latter renders control and learning nonseparable. We present two sets of results in a learning environment. First, conditions under which the introduction of learning increases or decreases optimal consumption are provided. The effect depends on the strengths and directions of the two sources of risk, which may pull in opposite directions. Second, the effects of the mean and riskiness of the distribution of the signal and initial beliefs on optimal consumption are studied.     

Specialization in a dynamic trade model: An overlapping generations case

Abstract

We explore a small open economy with overlapping generations to show that demographic structure is an important factor for the determination of a production pattern in the dynamic trade theory. In the representative agent model, Baxter (1992) shows that even if there are two commodities and two production factors, there is a Ricardian implication that opening up to trade leads to perfect specialization in a small open economy. In contrast, using the overlapping generations model, we find that the heterogeneity of the economic agents generally makes imperfect specialization occur. We also find that whether the stability condition holds or not is crucial for the determination of the long-run production pattern.     

Policy effects on transitional welfare in an overlapping generations model: A pay-as-you-go pension reconsidered

We study the welfare effects of a pay-as-you-go (PAYG) pension system in transition, as well as in the steady state, by showing how the total welfare effects are determined by a cumulative effect on capital. Theoretical studies have shown that the introduction of a PAYG pension system reduces steady-state welfare under dynamic efficiency. Nevertheless, such pension systems have been widely adopted in the real world. To explain this, we algebraically and graphically prove that the PAYG pension system could be Pareto-improving in transition under dynamic efficiency. Similarly, it is acknowledged that this pension system should be introduced under dynamic inefficiency because it improves steady-state welfare. However, we show that the PAYG pension system may be Pareto-deteriorating in transition. Our findings imply that governments adopt PAYG pension systems to achieve policy targets other than long-run welfare maximization.     

Robustness and ambiguity in continuous time

We use statistical detection theory in a continuous-time environment to provide a new perspective on calibrating a concern about robustness or an aversion to ambiguity. A decision maker repeatedly confronts uncertainty about state transition dynamics and a prior distribution over unobserved states or parameters. Two continuous-time formulations are counterparts of two discrete-time recursive specifications of Hansen and Sargent (2007) [16]. One formulation shares features of the smooth ambiguity model of Klibanoff et al. (2005) and (2009) [24] and [25]. Here our statistical detection calculations guide how to adjust contributions to entropy coming from hidden states as we take a continuous-time limit.     

Stationary solution to the overlapping generations model of fiat money: Experimental evidence

Overlapping generations model of fiat money yields an infinity of competitive equilibrium solutions, only one of which is stationary. Economies reported in this paper involved a sequence of overlapping generations of three or four individuals; each individual lived for two periods. In their young age individuals were endowed with chips that could be traded for fiat money wish the individuals of the old generation. In their old age, individuals could exchange their units o flat money for the consumption good. Results of the experiments exhibit some support for the stationary solution. The results are robust to two designs of exchange institutions (double oral auctior and supply schedule auction) and to two different endogenous ways of converting money into chips at the end of the game (average price prevailing during the last period the game is actually played and the average price forecast made during the last period the game is actually played).A preliminary version of this paper was presented at the meeting of the Economic Science Association and at the Federal Reserve Bank of Minneapolis. The authors are grateful for comments received from various participants at both presentations. Financial support was provided by the McKnight Foundation, the Honeywell Foundation, National Science Foundation (SES 89-12552), and Richard. M. and Margaret Cyert Family Funds.     

Utility representation of continuous preferences

Summary.  By generalising the Arrow-Hahn approach, we give new conditions under which a preference relation on a metric space can be represented by a continuous utility function. Received: December 11, 1995; revised version July 29, 1996