Ramsey Rule Research Articles

Should we Discount the Far-Distant Future at ist Lowest Possible Rate?

AbstractIn this paper, we elaborate on an idea initially developed by Weitzman (1998) that justifies taking the lowest possible discount rate for far-distant future cash flows. His argument relies on the arbitrary assumption that when the future rate of return of capital (RRC) is uncertain, one should invest in any project with a positive expected net present value. We examine an economy with a risk-averse representative agent facing an uncertain evolution of the RRC. In this context, we characterize the socially efficient stochastic consumption path, which allows us in turn to use the Ramsey rule to characterize the term structure of socially efficient discount rates. We show that Weitzman’s claim is qualitatively correct if shocks on the RRC are persistent. On the contrary, in the absence of any serial correlation in the RRC, the term structure of discount rates should be flat.

Taxing Education in Ramsey’s Tradition

Assuming a two-period model with endogenous choices of labour, education, and saving, it is shown to be second-best efficient to deviate from Ramsey's Rule and to distort qualified labour less than nonqualified labour. The result holds for arbitrary utility and learning functions. Efficient incentives for education and saving are analysed under conditions of second and third best. It is argued that efficient tax policy should care more about incentives for education than for saving.

Expected Net Present Value, Expected Net Future Value, and the Ramsey Rule

Weitzman (1998) showed that when future interest rates are uncertain, using the expected net present value implies a term structure of discount rates that is decreasing to the smallest possible interest rate. On the contrary, using the expected net future value criterion implies an increasing term structure of discount rates up to the largest possible interest rate. We reconcile the two approaches by introducing risk aversion and risk-neutral probabilities. We show that if the aggregate consumption path is optimized, the two criteria are equivalent. Moreover, they are also equivalent to the Ramsey rule extended to uncertainty.

Should We Discount the Far-Distant Future at its Lowest Possible Rate?

In this paper, we elaborate on an idea initially developed by Weitzman (1998) that justifies taking the lowest possible discount rate for far-distant future cash flows. His argument relies on the arbitrary assumption that when the future rate of return of capital (RRC) is uncertain, one should invest in any project with a positive expected net present value. We examine an economy with a risk-averse representative agent facing an uncertain evolution of the RRC. In this context, we characterize the socially efficient stochastic consumption path, which allows us in turn to use the Ramsey rule to characterize the term structure of socially efficient discount rates. We show that Weitzman's claim is qualitatively correct if shocks on the RRC are persistent. On the contrary, in the absence of any serial correlation in the RRC, the term structure of discount rates should be flat.

Political competition and bilateral direct investments

This paper investigates a basic question about the international political economy—why is international trade not free? To answer this question, we modified Grossman and Helpman (1994) by considering that interest lobbies make political contributions to both the incumbent government and the political challenger in order to influence the incumbent government’s choice of trade policy. By examining the contribution schedules under a framework of bilateral direct investments, we find that the modified Ramsey rule still holds under our setting.

Endogenous contract structure and monetary policy

We analyze the co-determination of monetary policy and the labor contracts chosen by members of the public, who can either fix or index their nominal wages. Fixed nominal wages allow the central bank to offset productivity shocks, while the public fix nominal wages in response to the central bank offsetting shocks; so there is an equilibrium in which, realistically, nominal wages are fixed and shocks offset: a result which holds in single- as well as in multi-period games. In addition, there may be equilibria in which agents index their nominal wages, and the central bank optimally responds by stabilizing price. In contrast to conventional models, the Ramsey rule may be implemented in a finitely repeated game. The central bank does not deviate for fear that agents would change their labor contracts such that the central bank's least favored equilibrium will subsequently be played.

OPTIMAL TAXATION ON MIXED DIAMOND GOODS: IMPLICATIONS FOR PRIVATE CAR OWNERSHIP IN CHINA

Abstract. The ‘diamond effect’ exists when a consumer's utility depends on the exchange value, not just on the intrinsic consumption effects of the good. Yew‐Kwang Ng has discussed the optimal tax on a pure ‘diamond’ good. This paper extends Ng's model to cover mixed diamond goods. It uses three mathematical models to show that the optimal tax on a mixed diamond good with both intrinsic and diamond effects depends on the proportion of the diamond effect. The result may explain the violation of the Ramsey Rule in practice, and may be used to formulate private car taxes in China.

On the design of optimal grandfathering schemes for emission allowances

This paper derives optimal schemes for the free allocation of emission allowances in a dynamic context. We consider emissions- and output-based allocation rules which allow for updating of the basis of allocation over time and thereby do not rely on historical data only. We show that such dynamic schemes do not necessarily induce inefficient outcomes. In closed trading systems with an absolute cap on emissions, grandfathering schemes which allocate allowances proportionally to past emissions are first-best. However, in open trading systems where allowances can be traded with outsiders, first-best allocation schemes must not depend on firm-specific decisions while second-best schemes correspond to a Ramsey rule of optimal tax differentiation and are generally based on both past emission and output levels.

Instant Utility Approach to the Social Sciences

It is, of course, true of science that deeper theory opens new vistas, and economics may now justifiably advance to a more essential paradigm. The basis for this deeper theory is empirical (cardinal and measurable) instant utility (feeling state, Dolan [2002]) - the time derivative of utility (satisfaction). Immediate benefits could include: Reconciling sociology and economics (both could now agree that wants, desires, satisfactions, etc., are endogenous); Rigorous modeling of time and (periodic) human activity in microeconomics; Modeling macroeconomic equilibrium-states as a locus of dynamic states; And the substantive modeling of bounded rationality, including uncertainty and expected risk. Because socioeconomic theory could now be derived from deeper instant utility theory, the several branches may be unified in an overarching classification. As a demonstration, herein, Real Business Cycle Theory and Equilibrium Theory are connected or related by a sequence of definitional assumptions on the basis of instant-utility theory (the Gossen Equation). Then, after presenting the mathematical formulation of instant-utility theory, Ramsey's rule for saving is extended to account for autonomic and expected-risk discounting. Finally, the prospect for greater cooperation between sociology and economics is addressed. . . . It may be emphasized that much of the important and far-reaching progress in economics and social psychology over the past 100+ years is naturally accommodated by the instant-utility theory. This progress includes the rationality assumption, diminishing marginal rates of substitution, the theory of the firm in economics; and social-identity theory in social psychology. Furthermore, the historical bases for finite interest rates - time preference, better times ahead, shortness of life, increasing technological knowledge, diminishing vitality in later years, and risk - may be substantively formulated.

Commodity Taxation and Economic Growth

We construct a variety expansion growth model following Grossman and Helpman (1991) and incorporate various groups of goods into the model. Each group has its own elasticity of substitution. We seek to determine the goods on which the government should impose higher rates of commodity tax in order to raise a certain amount of tax revenue. We thus reconsider the Ramsey Rule (the Inverse Elasticity Rule) in a growing economy.

On the Design of Optimal Grandfathering Schemes for Emission Allowances

To meet its commitment under the Kyoto Protocol, the EU plans to implement an emissions trading system with grandfathering of allowances. Besides having distributional impacts, the choice of the grandfathering scheme may affect efficiency if firms anticipate how future allocations depend on upcoming decisions. In this paper, we determine central design rules for optimal grandfathering within a simple two-period model. We find that for (small) open trading systems, where allowance prices are exogenous, first-best second-period grandfathering schemes must not depend on firm-specific decisions in the first period. Second-best schemes correspond to a Ramsey rule of optimal tax differentiation and are generally based on both previous emissions and output. However, for closed emissions trading systems, i.e. endogeneous allowance prices, firstand second-best rules coincide and must not depend on previous output levels. They consist of an assignment proportional to the emissions in the first period plus a term which does not depend on firm-specific decisions in either of the two periods.

Optimum taxation and the allocation of time

A theory of optimal taxation is presented, building upon Becker's (1965) theory of the allocation of time. Optimal commodity taxation is governed by factor shares in household activities. Any market good which requires little household time, or even saves time, should carry a relatively low tax rate. This policy rule does not require the estimation of price elasticities and is therefore more applicable than traditional Ramsey rule taxation.

The Ramsey Rule Reconsidered

The Ramsey rule for optimal excise taxation suggests that goods should be taxed in inverse proportion to their elasticities of demand. This analysis shows that when the political process that determines tax rates is taken into account, the Ramsey rule may not be superior to a fiscal constitution that specifies that all goods are taxed at the same rate. The information necessary to set taxes in conformance with the Ramsey rule is not directly observable, which will lead to rent-seeking activities as interest groups try to influence the political determination of tax rates they face. Furthermore, incentives in the political process work against setting taxes according to the Ramsey rule. Building on Buchanan’s work on optimal taxation and the nature of the fiscal constitution, the Ramsey rule should be reconsidered as a guide to optimal excise tax policy.

Hidden Taxes and Representative Government: The Political Economy of the Ramsey Rule

A social planner finances a public good by taxing the consumption of two private goods. If leisure cannot be taxed, the tax burden is minimized by setting the tax rates on the two goods inversely proportional to their price elasticities of demand (Ramsey rule). The authors replace the social planner with an elected policy maker who cares not only about minimizing the tax burden but also about getting reelected. Electoral competition creates incentives for the incumbent to deviate from the Ramsey rule: He or she decreases the tax rate that is relatively visible and increases the tax rate that is relatively hidden.

Commodity Taxation and Social Welfare: The Generalized Ramsey Rule

Commodity taxes have three distinct roles: (1) revenue collection, (2) interpersonal redistribution, and (3) resource allocation. The paper presents an integrated treatment of these three concerns in a second-best general equilibrium framework, which leads to the “generalized Ramsey rule” for optimum taxation. We show how many standard results on optimum taxation and tax reform have a straightforward counterpart in this general framework. Using this framework, we also try to clarify the notion of “deadweight loss,” as well as the relation between alternative distributional assumptions and the structure of optimum taxes.

Direct Versus Indirect Taxation: The Design of the Tax Structure Revisited

This article studies the optimal direct/indirect tax mix problem when individuals differ in several unobservable characteristics (productivity and endowments). It presents general expressions for the optimal commodity tax rates and proves that contrary to Atkinson and Stiglitz's (1976) result, differential commodity taxation remains a useful instrument of tax policy even if preferences are separable between labor and produced goods. When cross substitution effects are zero, the expressions resemble traditional many households Ramsey rules. In a Cobb–Douglas illustration, where endowments differ only in good 1 (interpreted as “wealth”), the tax on good 2 provides an indirect way to tax the unobservable wealth.

The Permanent Income-Life Cycle Hypothesis in a Monetary Economy and the Neutrality of Money: A Continuous-Time Analysis

This paper addresses the viability of the permanent income– life cycle hypothesis in a monetary economy in which money enters the utility function of infinitely lived agents. Two forms of the hypothesis are distinguished: weak and strong. Deriving the Keynes–Ramsey rule of consumption under preferences of the Uzawa–Epstein recursive class and examining the optimal consumption–wealth relation, the paper studies the restrictions that these forms impose on the utility functional, identifies the necessary and sufficient conditions for the hypothesis to hold, and clarifies how such conditions are related to the neutrality of money. JEL Classification Numbers: D91, E21, E40, C61.

The effects of ageing and an environmental trust fund in an overlapping generations model on carbon emission reductions

Most currently employed Integrated Assessment Models for climate change are of a dynastic nature. They employ the Ramsey rule linking the interest rate, economic growth, and the rate of pure time preference. This paper argues that, although a dynastic framework might be convenient for economic analysis, it is restrictive and can be misleading. Overlapping Generations models, which do not employ the Ramsey rule, are more flexible and may give results different from those derived from dynastic models. With the Integrated Assessment Model ALICE 2.0, it is shown how various assumptions on demographic change and public institutions can affect the interest rate, thereby influencing the efficient greenhouse gas emission reductions. It is concluded that dynastic Integrated Assessment Models are in many respects inappropriate for providing policy makers with quantitative figures about the costs of carbon dioxide emissions and their desirable reduction levels.

Les démonstrations de la règle de Ramsey. Les mathématiques comme self-control

Nous proposons, dans cet article, de suivre pas à pas la démonstration originelle de la règle de Ramsey. Cette étude révèle paradoxalement une introduction prudente du calcul des variations, qui nous semble révélatrice tant des ambitions de Ramsey que de sa position atypique à Cambridge.

Productive Consumption and Growth in Developing Countries

Productive consumption enables the satisfaction of current needs and increases the productive potential of labor. The productive‐consumption hypothesis is of fundamental interest because it modifies the “harsh” intertemporal consumption tradeoff traditionally assumed. The incorporation of the productive‐ consumption hypothesis into a simple endogenous growth model reveals the following implications: (i) the possibility of a poverty‐trap; (ii) the rule of optimal consumption turns into a modified Keynes–Ramsey rule; (iii) the (effective) IES is based on, inter alia, the technological opportunities to enhance human capital due to productive consumption; (iv) a rising saving rate; and (v) transitional dynamics to an asymptotic balanced‐growth path.