The Under-Exploitation of Natural Resources: A Model with Overlapping Generations*

It is well known that competitive markets may fail to generate an optimal rate of extraction of a natural resource-stock. The barrier to optimality may be uncertainty about tenure, commonality of property rights in the resource, or uncertainty about the extent of the resource. In all these cases, suboptimality takes the form of over-extraction. We draw attention to an additional source of suboptimality. In an economy with overlapping generations, the resource-stock plays the double role of repository of savings and source of productive inputs. The decline in the supply of the resource-stock may eventually force its price so high that it ceases to perform its second function. Extraction comes to an end even though the resource has a positive marginal productivity in producing consumption goods. This is inefficient, hence suboptimal. This time, however, suboptimality takes the form of under-extraction.     

Fiscal Policy in an Overlapping Generations Model with Bequest-as-Consumption

This paper analyzes an overlapping generation (OLG) growth model wherein saving finances second period consumption and bequest‐as‐consumption. First, it looks at the market equilibrium and at the optimal solution; then it turns to the issue of decentralizing the optimal solution with various taxes and transfers. Depending on the available instruments, either a first‐best or a second‐best optimum can be achieved. Throughout the paper, the results are contrasted with those obtained in the standard OLG model without intergenerational transfers.     

A Stochastic Overlapping Generations Economy with Inheritance

An overlapping generations model of an exchange economy with two sources of uncertainty is considered. Individuals have a finite expected life span and uncertain annual income. Conditions concerning birth, death, inheritance and bequests are fully specified. Under such conditions, the existence of a stationary Markovian equilibrium is established in some generality, and several explicitly solvable examples are examined in detail. Received August 6, 2001; revised version received March 12, 2002 Published online: November 11, 2002     

An Overlapping Generations Model of Climate-Economy Interactions

A numerically calibrated overlapping generations model of climate change and the world econommy is examined in this paper. In the absence of intergenerational transfers, efficient rates of greenhouse gas emissions abatement rise from 16% in the present to 25% in the long run, while mean global temperature increases by 7.4°C relative to the preindustrial norm. A utilitarian optimum, which attaches equal weight to each generation's life-cycle utility, yields abatement rates that rise from 48% to 89%, with a long-run temperature increase of 3.4°C. A second-best utilitarian path, in which intergenerational transfers are by assumption institutionally infeasible, also supports stringent abatement measures.     

持续发展中代际财富转移简单模型

代际均衡发展是持续发展论的主要内容之一，其中代际财富转移和贴现率应用是其核心内容。本文探讨了一个代际财富转移的简单模型，并采用人们熟悉的柯布──道格拉斯函数形式表达。模型的敏感因素为利息率、工资和自然资源价格，并且是由代际间的跨代收入分配决定的。贴现率等于同期利息率，其水平是变动的。     

Determinacy of Equilibrium in an Overlapping Generations Model with Heterogeneous Agents

We study the determinacy of perfect foresight equilibrium near a steady state in an overlapping generations model with production and both altruistic and non-altruistic agents having distinct utility functions. The proportion of each type of consumer is exogenously given. Our main results show that when there are positive stationary bequests, some standard assumptions on preferences and technology rule out local indeterminacy for any positive value of the proportions. In the particular case of a separable utility function for altruistic agents, we prove that the determinacy property does not depend on the size of the “infinite lived” altruistic dynasties. Journal of Economic Literature Classification Numbers: C62, D91, O21, O41.     

Capital Accumulation in a Stochastic Overlapping Generations Model with Social Security

This paper analyzes the impact of pay-as-you-go financed social security on the stochastic process for the capital stock in a stochastic overlapping generations model. It is shown that the probability distribution of the capital stock in absence of social security dominates that in a pay-as-you-go system in the sense of stochastic dominance. Furthermore, the study demonstrates that the sufficient conditions ensuring the existence and uniqueness of stationary equilibria in a pay-as-you-go system are more restrictive than in the model without social security. Journal of Economic Literature Classification Numbers: C62, H55.     

Equity Between Overlapping Generations

This note is a demonstration that, in the presence of overlapping generations and under standard conditions for a social welfare ordering (Pareto optimality, transitivity, and independence), the only ordering consistent with utilitarianism for all people currently alive at any given point in time is one based on weighting all people equally, regardless of their date of birth. In particular, this implies that, under reasonable conditions, the pure rate of social time preference is zero.     

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.     

纯交换OLG经济中的习惯类型与经济的动态性质

在OLG的纯交换经济中,区分了内部习惯和外部习惯对经济动态性质的影响。我们发现内部习惯增加了年轻人的储蓄并可以把古典经济转变为萨谬尔森经济;外部习惯减少了年轻人的储蓄并可以把萨谬尔森经济转变为古典经济。不论是外部习惯还是内部习惯,都提高了在相对风险规避系数一定的情况下消费者忍受风险的能力,从而可能导致经济的周期运动。     

China's Growing Government Debt in a Computable Overlapping Generations Model

This paper simulates the effects of China's growing government debt in a computable equilibrium model of overlapping generations. Our model assumes that the government increases debt to finance its spending in the short run, and then increases taxes or cuts spending to keep the debt–GDP ratio constant. The spending‐driven government debt increases public capital and output in the short run, but decreases private investment, total capital stock, output, and net exports in the long run, and makes the future generations worse off. Among various means of debt control, a decrease in government spending seems to be the least harmful to private investment, capital stock, and output while an increase in capital taxation is most detrimental.     

Time Consistent Optimal Redistribution Policy in an Overlapping Generations Model

This paper analyzes optimal redistribution policy in a two‐period version of the overlapping generations model with heterogeneous individuals and asymmetric information between the government and the private sector. The government of the first period determines redistribution transfers for the first period but is not able to set the policy variables for the second period. With respect to savings the paper considers two scenarios: In the first scenario savings are observable and the government can set individual savings levels in addition to redistributive transfers. In the second scenario savings and capital incomes are not observable. In both cases the redistribution equilibrium is not second‐best efficient.     

Efficiency and Lack of Commitment in an Overlapping Generations Model with Endowment Shocks

This paper considers a pure exchange stochastic overlapping generations model in which, on each date, an economy faces an aggregate endowment shock. On each date, a young agent and an old agent simultaneously decide how much of their respective endowments to transfer to the other agent; however, a young agent cannot make promises about how much he or she will give when old. In this sense, an economy faces a limited commitment constraint. This paper characterizes an efficient intergenerational risk sharing allocation that satisfies a limited commitment constraint, and also studies the role of money and history in a stochastic overlapping generations economy.     

Learning and Equilibrium Selection in a Monetary Overlapping Generations Model with Sticky Prices

We study adaptive learning in a monetary overlapping generations model with sticky prices and monopolistic competition for the case where learning agents observe current endogenous variables. Observability of current variables is essential for informational consistency of the learning setup with the model setup but generates multiple temporary equilibria when prices are flexible and prevents a straightforward construction of the learning dynamics. Sticky prices overcome this problem by avoiding simultaneity between prices and price expectations. Adaptive learning then robustly selects the determinate (monetary) steady state independent from the degree of imperfect competition. The indeterminate (non-monetary) steady state and non-stationary equilibria are never stable. Stability in a deterministic version of the model may differ because perfect foresight equilibria can be the limit of restricted perceptions equilibria of the stochastic economy with vanishing noise and thereby inherit different stability properties. This discontinuity at the zero variance of shocks suggests one should analyse learning in stochastic models.     

The Transfer Problem and Intergenerational Allocation in an Overlapping Generations Model

We investigate the transfer problem between two countries in the steady state in a one-sector overlapping generations model and explain how transfers should be shared between the young and old generations of the donor country and allocated across the generations of the recipient country. Except at the golden rule of capital accumulation, the ratios of the burden and distribution of transfers between the young and old generations affect welfare. We obtain the following results. First, the sharing of the transfer burden in the donor country depends on the relative size of two effects, namely, a negative direct effect and a positive indirect effect. If the former exceeds the latter, it is preferable for the donor country to allocate all of the transfer burden to the old generation and vice versa. Second, from the viewpoint of welfare maximization, it is preferable for the recipient country to distribute all of the transfers to the young generation. In contrast to the existing literature, these results suggest that the setting whereby the young generation of the donor country defrays all transfer costs may not be justifiable from the viewpoint of donor welfare maximization.     

Donor Altruism and the Transfer Paradox in an Overlapping Generations Model

This paper examines the transfer problem between two countries when a donor exhibits altruistic utility toward a recipient in a one‐sector overlapping generations model. We demonstrate that if the donor has a larger marginal propensity to save than the recipient, the donor's altruism never contributes to donor enrichment irrespective of the degree of the donor's altruism. Donor enrichment occurs only if the donor has a smaller marginal propensity to save and a sufficiently high level of altruism. These findings imply that the altruism of a donor toward a recipient does not necessarily explain the motivation to voluntarily provide a transfer.     

Cooperation in an Overlapping Generations Experiment

Recent theoretical work shows that folk theorems can be developed for infinite overlapping generations games. Cooperation in such games can be sustained as a Nash equilibrium. But, of course, there are other equilibria. This paper investigates experimentally whether cooperation actually occurs in a simple overlapping generations game. Subjects both play the game and formulate strategies. Our main finding is that subjects fail to exploit the intertemporal structure of the game. Even when we provided subjects with a recommendation to play the grim trigger strategy, most of the subjects still employed safe history-independent strategies. Journal of Economic Literature Classification Numbers: C72, C92, D90.     

Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems

This paper analyses the sustainability of inter-generational transfers in Samuelson's consumption-loan model when agents are imperfectly informed about past events. We find that with mild informational constraints, transfers cannot be supported by pure-strategy equilibria. Mixed strategies allow transfers to be sustained even if agents have little information, so that a version of the Folk theorem holds. However, these equilibria are not robust. If each agent's utility function is subjected to a small random perturbation as in Harsanyi (1973), these mixed strategy equilibria unravel, and only the zero-transfer allocation survives as the unique rationalizable outcome. This result is an example of mixed strategy equilibrium of an extensive form game which cannot be purified.     

A Model of Trade Liberalization in Services*

This paper develops an intra‐industry service trade model taking into account important features of services. We find that service trade liberalization between identical economies is welfare enhancing when the pre‐trade domestic market liberalization is limited. This holds regardless of the degree of trade liberalization and of the mode of supply. However, if the pre‐trade environment is characterized by a free‐entry equilibrium, then service trade liberalization is not necessarily welfare improving. It is welfare enhancing if the trade liberalization is full and the mode of supply is cross‐border. The gain from trade in our model comes from the improvement in service quality—better matching between consumers’ ideal varieties and firms’ product specificity. The implications for the mode of supply in service trade are also explored.