Residence-and source-based taxation of capital income in an overlapping generations model

By using an intertemporal equilibrium model with overlapping generations, this paper explores how residence-and source-based taxes on capital income affect the external current account in small open economies. These taxes influence the saving-investment balance not only through their incentive effects on rates of return but also through their impact on the intergenerational distribution of resources. This paper, in its examination of these effects — both intertemporal substitution and intergenerational distribution — identifies the net effect of the various impacts.The author would like to thank Dieter Bös and an anonymous referee for helpful comments on an earlier draft.     

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.     

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.     

The determinacy of equilibrium in economies of overlapping generations

We study the problem of uniqueness of equilibrium paths in the overlapping generations model. We show that, despite local calculation based on counting equations and unknowns, the equilibrium path may be unique. We do this by constucting an example of an economy of overlapping generations with just one equilibrium up to time shift, beside the steady states. Time is either discrete or continuous; in either case, it extend into the infinite future and, possibly, the infinite past. There is one, non-storable commodity at each date. The economy is stationary; intertemporal preferences are logarithmic; the endowments and discount factors of individuals need not depend continuously on time. With continuous time, equilibrium paths of prices are smooth; this, even for endowments and discount factors of individuals that do not depend continuously on time. With discrete time, as the number of periods in the life-span of individuals increases, equilibrium paths converge to the continuous time solutions. If time extends infinitely into the infinite past as well as into the infinite future, in continuous time, all non-stationary equilibrium paths of prices are time-shifts of a single path; in addition, there are two stationary solutions; in discrete time, there is a one dimensional family of non-stationary solutions, up to time-shift; however, the indeterminacy vanishes as the number of periods in the life span of individuals tends to infinity. If, alternatively, time has a finite starting point, in discrete time the degree of indeterminacy increases with the life-span of individuals, and, in continuous time, it is infinite; however, these are families of exponentially decreasing oscillations which, although they may exhibit pseudo-chaotic behaviour for a while, as time tends to infinity they all get damped, and asymptotic behaviour is that of the economy that originates in the infinite past. Stefano Lovo made interesting comments.     

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.     

The taxation of capital returns in overlapping generations models

This paper shows that in the Diamond (1965) overlapping generations economy with production and capital savings, there is a period-by-period balanced fiscal policy supporting a steady state allocation that Pareto-improves upon the laissez-faire competitive equilibrium steady state (whether dynamically inefficient or efficient) without resorting to intergenerational transfers. The policy consists of taxing linearly (or subsidizing, in the dynamically efficient case) the returns to capital, while balancing the budget period by period through a lump-sum transfer (or tax, respectively) in second period. This intervention grants every generation the highest steady state utility attainable through markets (i.e. remunerating factors by their marginal productivities and without transfers) which under laissez-faire is not a competitive equilibrium outcome. A transition from the competitive equilibrium steady state to this other steady state is also Pareto-improving when the former is dynamically inefficient. The result disentangles from redistributive considerations the impact of the taxation of capital returns on steady state welfare, and thus provides a rationale for the taxation of capital returns that is based on efficiency considerations and not on redistributive goals.     

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.     

A two-sector overlapping generations model with heterogeneous capital

Summary. This paper characterizes the existence and stability properties of steady state solutions as well as the nature of transition paths of a two-sector growth model with heterogeneous capital. It compares the properties of a Cobb-Douglas–Leontief economy with heterogeneous capital with the properties of the same economy with homogeneous capital. The model with heterogeneous capital reveals a set of characteristics different to those of the model with homogeneous capital. These include the saddle-path stability of the non-trivial steady state as well as the possibility of overshooting and in contrast to the homogeneous capital case, the possibility of damped oscillations along the transition path for realistic parameter values. Received: September 21, 2001; revised version: November 21, 2002 RID="*" ID="*" We thank Costas Azariadis, and Laurie Conway for helpful comments on a previous draft. The paper has substantially benefited from the feedback of an anonymous referee. Correspondence to: R. Wendner     

Efficiency in overlapping generations economies with longevity choices and fair annuities

When individuals can influence their life-expectancies and save in annuities, suboptimal savings result from the lack of incentives to choose the optimal longevity, even when annuity returns can be made contingent to longevity-related choices. Specifically, the golden rule steady state maximizing the representative agent utility cannot be attained as a competitive equilibrium under laissez-faire, even with actuarially fair annuities contingent to longevity-enhancing choices. In order to decentralize through markets the golden rule, longevity-enhancing expenditures need to be taxed if the steady state old-age consumption exceeds the annuitized capital return, and subsidized otherwise—the government budget being balanced through lump-sum transfers or taxes. Interestingly, with positive population growth the expected net contribution is negative when longevity-enhancing expenditures are taxed, and positive when subsidized.     

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.     

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.     

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.     

Human capital,externalities and growth in an overlapping generations model

We consider an overlapping generations model with endogenous labor supplies by young and old and a human capital accumulation process that relies on the interaction of these two types of labor. This interaction is not understood by the market hence we analyze fiscal policies designed to remedy this. We argue that taxes must be acceptable to people alive at the time of planning. This makes many proposed taxes unfeasible. Two distinct paths to growth emerge; one through increased savings and another through increased workforce participation. The long run rate of growth depends entirely on human capital but we find this to be of little relevance. Some simulation results are presented for two stylized economic blocks calibrated on the USA and the EURO-zone.     

Time consuming resource extraction in an overlapping generations economy with capital

For worldwide fisheries production, two major trends emerge for the next decades: a significantly larger role for aquaculture and reduced output due to climate change impacts. While the former leads to an increase in cost, the latter affects natural regeneration. To address both impacts, we investigate the relevance of resource extraction costs for a private property fishery in an intertemporal general equilibrium model with capital accumulation, commodity production and a labor market. We show how the extraction cost parameter—in addition to time preference, technology and natural regeneration—matters for the existence (and stability) of an economically feasible, nontrivial stationary state. Higher extraction costs increase the equilibrium resource stock, while a reduced regeneration rate (e.g. due to climate change) decreases the stock. Moreover, resource extraction overshoots its new equilibrium value after the cost shock while after a regeneration shock extraction levels adjust monotonically towards the new equilibrium.     

Stone–Geary preferences in overlapping generations economies under pure exchange: A note

We incorporate Stone–Geary preferences into an overlapping generations economy under pure exchange, and explore stability, indeterminacy, and cycles with positive levels of saving and nonnegative public debt. A stable nontrivial steady state exists for parameter values, for which there does not exist equilibrium in the model with purely logarithmic utility function. We also show the possibility of a period-doubling bifurcation (a two-cycle).     

Capital accumulation,income distribution and endogenous fertility in an overlapping generations general equilibrium model

A study is conducted in attempts to increase the understanding of the links between macroeconomic effects and causes of population growth in formulating policy. An overlapping generations general equilibrium model is employed aggregating household decisions about fertility, savings, and investment in the human capital of children with the objective of studying intertemporal relationships among population growth, income distribution, inter-generation social mobility, skill composition of the labor force, and household income. As a result of endogenous fertility, the equilibrium path attains steady state from the second generation. Income tax transfer, child taxation, and social security taxation policies are also examined in the paper. A structural explanation is given for the inverse household income-child quantity and negative child quality-quantity relationships seen in developing countries. In a Cobb-Douglas economy, these relationships hold in the short-run, potentially working over the long-run in other economies. Overall, the model shows that group interests may hinder emergence of perfect capital markets with private initiatives. Where developing countries are concerned, these results have strong implications for population policy. A policy mix of building good quality schools, or subsidizing rural education, introducing a formal social security program, and providing high-yield, risk-free investments, banking, and insurance services to the poor is recommended.     

Endogenous market incompleteness without market frictions: Dynamic suboptimality of competitive equilibrium in multiperiod overlapping generations economies

In this paper, we show that within the set of stochastic three-period-lived OLG economies with productive assets (such as land), markets are necessarily sequentially incomplete, and agents in the model do not share risk optimally. We start by characterizing perfect risk-sharing and find that it requires state-dependent consumption claims which depend only on the exogenous shock realizations. We show then that the recursive competitive equilibrium of any overlapping generations economy with weakly more than three generations is not strongly stationary. This then allows us to show directly that there are short-run Pareto improvements possible in terms of risk-sharing and hence, that the recursive competitive equilibrium is not Pareto optimal. We then show that a financial reform which eliminates the equity asset and replaces it with zero net supply insurance contracts (Arrow securities) will implement to Pareto optimal stochastic steady-state known to exist in the model. Finally, we also show via numerical simulations that a system of government taxes and transfers can lead to a Pareto improvement over the competitive equilibrium in the model.     

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.     

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.     

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.