Decreasing Impatience: A Criterion for Non‐stationary Time Preference and "Hyperbolic" Discounting

Despite recent interest in hyperbolic discounting, there has been little discussion of exactly what property of time preferences is instantiated by hyperbolic or quasi‐hyperbolic functional forms. The paper revives an earlier proposal in Prelec (1989) that the key property is Pratt–Arrow convexity of the log of the discount function, which corresponds to decreasing impatience(DI) at the level of preferences. DI provides a natural criterion for assessing the severity of departure from stationarity in that greater DI is equivalent to more choices of dominated options in two‐stage decision problems, as well as greater convexity of the log of the discount function. Inefficient choices may arise as intentional precommitments, or as unintended reversals of preference by “naïve” agents.     

The Hartwick Rule: Myths and Facts

We shed light on the Hartwick rule for capital accumulation and resource depletion by providing semantic clarifications and investigating the implications and relevance of this rule. We extend earlier results by establishing that the Hartwick rule does not indicate sustainability and does not require substitutability between man-made and naturalcapital. We use a new class of simple counterexamples (i) to obtain the novel finding that a negative value of net investments need not entail that utility is unsustainable, and (ii) to point out deficiencies in the literature.     

TURNPIKE PROPERTIES OF A MONEY‐IN‐THE‐UTILITY‐FUNCTION MODEL*

This study establishes the global stability of a long‐run stationary state in a money‐in‐the‐utility‐function model. The major finding is that the constant money supply rule results in a stable allocation and price system if consumers discount their future utilities sufficiently weakly. Nominal and real interest rates will be in the neighbourhood of the inverse of the consumers’ discount factor β^‐1.     

SOCIAL NORMS,LOCAL INTERACTION,AND NEIGHBORHOOD PLANNING*

This article examines optimal social linkage when each individual's repeated interaction with each of his neighbors creates spillovers. Each individual's discount factor is randomly determined. A planner chooses a local interaction network or neighborhood design before the discount factors are realized. Each individual then plays a repeated Prisoner's Dilemma game with his neighbors. A local trigger strategy equilibrium (LTSE) describes an equilibrium in which each individual conditions his cooperation on the cooperation of at least one “acceptable” group of neighbors. Our main results demonstrate a basic trade‐off in the design problem between suboptimal punishment and social conflict. Potentially suboptimal punishment arises in designs with local interactions since in this case monitoring is imperfect. Owing to the heterogeneity of discount factors, however, greater social conflict may arise in more connected networks. When individuals' discount factors are known to the planner, the optimal design exhibits a cooperative “core” and an uncooperative “fringe.”“Uncooperative” (impatient) types are connected to cooperative ones who tolerate their free riding so that social conflict is kept to a minimum. By contrast, when the planner knows only the ex ante distribution over individual discount factors, then in some cases the optimal design partitions individuals into maximally connected cliques (e.g., cul‐de‐sacs), whereas in other cases incomplete graphs with small overlap (e.g., grids) are possible.     

Sustainability,Optimality, and Development Policy

Considering sustainability a matter of intergenerational welfare equity, this paper examines whether an optimal development path can also be sustainable. It argues that the general “zero‐net‐aggregate‐investment” condition for an optimal development path to be sustainable in the sense of the maximin criterion of intergenerational justice is too demanding to be practical, especially in the context of developing countries. It further argues that while the maximin criterion of sustainability may be appealing to the rich advanced industrial countries, for the poor developing countries it implies equalization of poverty across generations, and as such is too costly a moral obligation to be acceptable. The paper suggests that a compromise development policy that follows the optimal growth approach but adopts certain measures to mitigate both the intergenerational and intragenerational welfare inequalities may be more appropriate for these countries. Some of the principal elements of such a policy are highlighted.     

From the Shadow Price of Capital to the Marginal Cost of Funds: In Search of the Implementation of a Principle

The “folk principle” for multi‐period project evaluation states that if all the costs and benefits of a project are expressed as withdrawals from and increments to private consumption at different time points, then the appropriate discount rate is the consumer's rate of interest. The shadow price of capital (SPC) approach intends to implement this principle, but faces serious practical difficulties. By taking a utility‐based perspective, this paper explains why the SPC approach cannot fully implement the folk principle even theoretically. Then, it derives, as a complete implementation of the folk principle, a multi‐period cost‐benefit rule that is based on the concept of the marginal cost of funds.     

An environmental-economic measure of sustainable development

A central issue in the study of sustainable development is the interplay of growth and sacrifice in a dynamic economy. This paper investigates the relationship among current consumption, sacrifice and sustainability improvement in a general context and in two canonical, stylized economies. We argue that the maximin value of utility measures what is sustainable and provides the limit to growth. Maximin value is interpreted as a dynamic environmental-economic carrying capacity and current utility as an environmental-economic footprint. The time derivative of maximin value is interpreted as net investment in sustainability improvement. It is called durable savings to distinguish it from genuine savings, usually computed with discounted-utilitarian prices.     

Fiscal Implications of Immigration—A Net Present Value Calculation

Focusing on the net fiscal effects, the gain from admitting immigrants is computed for a welfare state with large expenditures and a large tax burden (Sweden). Prices and behavior are held constant, which allows a detailed analysis of the effects of immigration. The present value of future tax revenues minus outlays is potentially large; USD 23,500 per young working‐age immigrant, but an average new immigrant represents a net government loss of USD 20,500. The dominant factors are employment rates and age. For young working‐age immigrants, the “break‐even” participation rate for which the gain would be zero is 60%, well below the empirical rate for this group.     

α‐SERIAL MECHANISMS FOR THE PROVISION OF AN EXCLUDABLE PUBLIC GOOD

We present a new class of “α‐serial mechanisms” for the provision of an excludable public good. Those mechanisms have a similar structure to the serial mechanism, but may let the non‐consumers pay a positive cost. They inherit desirable properties such as anonymity, envy‐freeness, Maskin monotonicity, and population monotonicity from the serial mechanism. We calculate the “maximal efficiency loss” and “maximal manipulation” of α‐serial mechanisms and point out a trade‐off between these two properties.     

On optimal steady states of n-sector growth models when utility is discounted

This paper contains results on local and global stability of n-sector growth models when utility is discounted mostly for small rates of discount. It is well known that when future utility is not discounted one can prove precise results about optimal steady states (OSS's) under fairly general assumptions. In particular, existence, uniqueness, and turnpike properties have been established by several authors. The counter examples presented by Kurz, Sutherland, and Weitzman, however, show that when utility is discounted, additional assumptions are required to obtain turnpike results. In general, it would be interesting to know how the submanifolds of stability change as δ changes. One hopes that certain conditions on the utility function would be sufficient to “classify” the submanifolds of stability and instability. Such a question is apparently very difficult to answer, but we think that the results obtained here will help in this task.The proof that the turnpike theorem holds for discount factors near one is divided in two parts. First, we prove that optimal paths “visit” neighborhoods of the modified OSS's. Then, we prove that local stability holds for such neighborhoods.In order to show this fact, we must prove that the local “stable manifold” varies continuously with the discount factor. This roundabout method is necessary since our problem is similar to proving uniform continuity with respect to a parameter of solutions of a differential equation in a noncompact interval of time.Other problems analyzed here include uniqueness and continuity of OSS's. We also discuss the relation between the saddle-point property and the local stability of infinite horizon optimal growth paths.     

Uncertainty and the Voluntary Provision of a Pure Public Good in a Two‐Moment Decision Model

In this paper, we explore the potential benefits of uncertainty that may arise in a two‐moment model of the voluntary provision of a pure public good. We find that an increase in a given contributor i’s risk associated with the aggregate contribution level of the other contributors (i.e., an increase in social uncertainty) induces that contributor to increase his own contribution level if and only if the uncertainty's incremental effect on the expected value of his net marginal utility is negative. Contributor i’s welfare likewise increases when a closely related condition is met, namely that the uncertainty's marginal effect on his expected marginal utility value of the public good exceeds its countervailing effect on the numeraire. Further, the corresponding aggregate contribution to the public good increases in the presence of free‐riding if and only if the incremental effect of contributor i’s contribution on the aggregate expected value of all other contributors’ net marginal utilities is small‐enough positive. We derive similar conditions for the case of private uncertainty, where the increase in contributor i’s risk is associated with his own marginal valuation of the public good. A simple example illustrates these conceptual results. Numerical analysis demonstrates that an increase in private uncertainty can have a nonmonotonic impact on contributor i’s welfare.     

Are Commodity Prices Driven by Fundamentals?

Physical scarcity is hardly sufficient to explain commodity price swings. However, despite of clues of commodity market inefficiency in the last decade, excess volatility in commodity markets emerges only under strong assumptions. When we allow for non‐stationarity in commodity prices and time variation in commodity‐specific risk premia, evidence of commodity market inefficiency becomes significantly weaker. Moreover, there is some evidence of commodity‐specific regime changes in commodity markets, with negligible or even positive correlation between efficiency and market liquidity.     

Trade,Growth, and Increasing Returns to Infrastructure: The Role of the Sophisticated Monopolist*

Equilibrium in international trade with increasing returns in infrastructure depends on whether the infrastructure provider is “naïve” or sophisticated. A monopolist produces infrastructure under decreasing cost using fixed equipment. Unlike similar work, we derive a unique closed‐economy equilibrium. In a small open economy, with “naïve” infrastructure provider(s), multiple equilibria obtain. The industrial export potential of the economy depends on unexhausted economies of scale, and equilibria are possible where manufactures are exported despite an autarky price higher than the world price. With a sophisticated infrastructure provider, even an open economy has a unique equilibrium, which, at least as long as economies of scale are unexhausted, also involves more industrialization than the “naïve” equilibria. Access to the unlimited world market is necessary for significant industrialization but is not sufficient: one may also require “Schumpeterian” entrepreneurs, monopolists with a panoramic vision of the economy and of their catalytic role in it.     

Public Expenditure and Revenue in Italy, 1862–1993

This study examines the long‐run equilibrium relationship between government expenditure and revenue in Italy from 1862 to 1993, using cointegration and causality techniques in the long as well as in the short‐run, through integrating the Error Correction Model (ECM) into the traditional Granger causality test. A Granger non‐causality test (due to Toda and Yamamoto) is also performed. Unit root tests have been applied in order to investigate the stationarity properties of the series. Moreover, three more homogeneous sub‐period (1862–1913; 1914–1946; 1947–1993) have been analysed. The nexus between public expenditure and revenue has been discussed also by Forecast Error Variance Decompositions (FEVDs). Empirical findings show that, for each sub‐period, the policy adopted reflects the prevailing paradigm of public finance. In fact, the ‘Tax‐and‐Spend' argument, received empirical support from the liberal period data. In contrast, the interwar years are in line with the ‘Spend‐and‐Tax' hypothesis. Finally, the “Fiscal Synchronization” hypothesis emerges in the republican ages.     

Nonstationarity and Stochastic Stability of Relative Income Clubs

The recent literature on “convergence” of cross‐country per capita incomes has been dominated by the two hypotheses of “global convergence” and “club‐convergence,” pertaining to limits of estimated income distribution dynamics. Utilizing a new measure of “stochastic stability,” we establish two stylized facts regarding short‐ and medium‐term distribution dynamics. The first is non‐stationarity of transition dynamics, in the sense of changing transition kernels, and the second is emergence, disappearance, and re‐emergence of a “stochastically stable” middle income group. This middle income group emerges as the gap between rich and poor clubs gets larger, and it changes the dynamics of transition to and from the rich and poor clubs, eventually narrowing the gap between the poor and rich as the middle club vanishes. Analyzing the stochastic stability of middle‐income groups is thus a first step toward understanding higher‐order dynamics of narrowing or widening of the gap between rich and poor countries.     

TESTING STRICT STATIONARITY WITH APPLICATIONS TO MACROECONOMIC TIME SERIES

We propose a model‐free test for strict stationarity. The idea is to estimate a nonparametric time‐varying characteristic function and compare it with the empirical characteristic function based on the whole sample. We also propose several derivative tests to check time‐invariant moments, weak stationarity, and pth order stationarity. Monte Carlo studies demonstrate excellent power of our tests. We apply our tests to various macroeconomic time series and find overwhelming evidence against strict and weak stationarity for both level and first‐differenced series. This suggests that the conventional time series econometric modeling strategies may have room to be improved by accommodating these time‐varying features.     

OPTIMAL GROWTH, GENUINE SAVINGS AND LONG-RUN DYNAMICS

Green accounting theories have shown that negative genuine savings at some point in time imply unsustainability. Consequently, recent studies advocate the use of the genuine savings measure for empirical testing: a negative index implies that sustainability be rejected. However, this criterion cannot ascertain sustainability, because positive current genuine savings do not rule out genuine dissaving in the future. This paper derives a one‐to‐one relationship between the sign of long‐run genuine savings and the limiting condition for sustained utility in the capital‐resource growth model, assuming technical progress and resource renewability. This result suggests to extend the genuine saving method to include a test of the limiting condition: if this condition is empirically rejected, positive current genuine savings are delivering a false message.     

A Note on α‐Gini Measures

This note provides a characterization of α‐Gini inequality measures. These measures generalize the standard Gini index by including one sensitivity parameter α, which captures different value judgments. The α‐Gini measures are shown to be weakly decomposable and unit consistent. Weak decomposition provides within‐group and between‐group inequalities. Unit consistency keeps unchanged the ranking of two income distributions when the income units vary. It is shown that the α‐Gini measures are relevant with either “leftist” or“rightist” views.     

PLATFORM PRICING IN MIXED TWO‐SIDED MARKETS

When a consumer can appear on both sides of a two‐sided market, such as a user who both buys and sells on eBay, the platform may want to bundle the services it provides to two sides. I develop a general model for such “mixed” two‐sided markets and show that a monopolist platform's incentive to bundle and its optimal pricing strategy are determined by simple formulas using familiar price elasticities of demand, which embody the bundling effect, and price‐cost margins adjusted for network externalities, which incorporate “two‐sidedness.” The optimal pricing rule in such markets generalizes the familiar Lerner formula.     

INCENTIVE ISSUES IN R&D CONSORTIA: INSIGHTS FROM APPLIED GAME THEORY

This article sketches how insights from applied game theory can be applied to Research and Development (R&D) consortia using a case study on an international plant breeding consortium. The insights jointly comprise a new “logic of collective action in R&D,” which is inspired by Olson’s Logic of Collective Action but goes beyond it. We analyze R&D consortia as institutions that respond to a variety of incentive problems which are obstacles to realizing the benefits of cooperation that arise due to the public goods nature of outputs, complementarities of inputs, and economies of scale and scope. Additionally, we sketch a “big‐picture” consortium game, which abstracts from specific incentive issues. (JEL B41, D02, H41, O31, O32)