Uncertainty,Learning and International Environmental Policy Coordination

In this paper we construct a simple model of global warming which captures a number of key features of the global warming problem: (i) environmental damages are related to the stock of greenhouse gases in the atmosphere; (ii) the global commons nature of the problem means that these are strategic interactions between the emissions policies of the governments of individual nation states; (iii) there is uncertainty about the extent of the future damages that will be incurred by each country from any given level of concentration of greenhouse gases but there is the possibility that at a future date better information about the true extent of environmental damages may become available; an important aspect of the problem is the extent to which damages in different countries may be correlated. In the first part of the paper we consider a simple model with two symmetric countries and show that the value of perfect information is an increasing function of the correlation between damages in the two countries in both the cooperative and non-cooperative equilibria. However, while the value of perfect information is always non-negative in the cooperative equilibrium, in the non-cooperative equilibrium there is a critical value of the correlation coefficient below which the value of perfect information will be negative. In the second part of the paper we construct an empirical model of global warming distinguishing between OECD and non-OECD countries and show that in the non-cooperative equilibrium the value of perfect information for OECD countries is negative when the correlation coefficient between environmental damages for OECD and non-OECD countries is negative. The implications of these results for international agreements are discussed.     

STOCK MARKET CRASH AND EXPECTATIONS OF AMERICAN HOUSEHOLDS

This paper utilizes data on subjective probabilities to study the impact of the stock market crash of 2008 on households' expectations about the returns on the stock market index. We use data from the Health and Retirement Study that was fielded in February 2008 through February 2009. The effect of the crash is identified from the date of the interview, which is shown to be exogenous to previous stock market expectations. We estimate the effect of the crash on the population average of expected returns, the population average of the uncertainty about returns (subjective standard deviation), and the cross-sectional heterogeneity in expected returns (disagreement). We show estimates from simple reduced-form regressions on probability answers as well as from a more structural model that focuses on the parameters of interest and separates survey noise from relevant heterogeneity. We find a temporary increase in the population average of expectations and uncertainty right after the crash. The effect on cross-sectional heterogeneity is more significant and longer lasting, which implies substantial long-term increase in disagreement. The increase in disagreement is larger among the stockholders, the more informed, and those with higher cognitive capacity, and disagreement co-moves with trading volume and volatility in the market.     

Imprecision as an account of violations of independence and betweenness

In an earlier paper we put forward a model of imprecise preferences which accounted for various forms of preference reversal. In this paper we show that the same model can also explain the best-known violations of expected utility theory's axioms of independence and betweenness. It appears that a simple model of imprecise preferences can account for a broader range of anomalies than many of the more elaborate alternative theories developed to date.     

A strategic analysis of global warming: Theory and some numbers

We model the global warming process as a dynamic commons game in which the players are countries, their actions at each date produce emissions of greenhouse gases, and the state variable is the current stock of greenhouse gases. The theoretical analysis is complemented by a calibration exercise. The first set of results establishes theoretically, and then with illustrative numbers, the over-emissions due to a “tragedy of the commons.” The power of simple sanctions to lower emissions and increase welfare is then examined as is the effect of cost asymmetry. Finally, a complete theoretical charactrization is provided for the best equilibrium, and it is shown that it has a very simple structure; it involves a constant emission rate through time.     

Optimal time paths with age-dependence: a theory of population policy

A mathematical model is established whereby optimal accumulation paths of population and the economy can be figured when the basic feature of population dynamics, age dependence, is taken into account. This model series links 2 previously separate disciplines and literatures - i.e., formal policy dealing with the dynamics of age and time. An integral-equation control theory is utilized. Recognition of age structure in analyzing fertility trends is important at both macro- and microeconomic levels. The present model was constructed by embedding an age-disaggregated population in a simple economic growth model where the fertility level and rate of savings can both be influenced by government policy. Such policy should balance the lifetime value of births and capital against the social costs necessary to create them. One the problem has been defined and a dynamic theory developed, optimum static theories can be establihsed where the variables are held constant over time.     

Dynamic stability and reform of political institutions

This paper examines endogenous institutional change in a class of dynamic political games. The political aggregation rules used at date t+1 are instrumental choices under rules at date t. Effectively, rules are “players” who can strategically delegate future policy-making authority to different rules. A political rule is stable if it selects itself. A reform occurs when an alternative rule is selected. The stability of a political rule is shown to depend on whether its choices are dynamically consistent. For instance, simple majority rules can be shown to be dynamically consistent in many common environments where wealth-weighted voting rules are not. The result extends to political rules that incorporate private activities such as extra-legal protests, threats, or private investment. The approach is one way of understanding various explanations of institutional change proposed in the literature. A parametric model of public goods provision gives an illustration.     

“十一五”期间银川市人口、资源、环境与经济协调发展的多目标规划模型

文章采用《银川市统计年鉴（2001～2007）》数据,建立银川市的人口、资源、环境和经济（PREE）的多目标模型。根据银川市的＂十一五＂发展规划确定了目标函数,应用模式搜索法对所建立的模型进行求解,并对计算结果进行分析,给出了相关政策建议。     

Dynamic stability and reform of political institutions

This paper examines endogenous institutional change in a class of dynamic political games. The political aggregation rules used at date t+1 are instrumental choices under rules at date t. Effectively, rules are “players” who can strategically delegate future policy-making authority to different rules. A political rule is stable if it selects itself. A reform occurs when an alternative rule is selected. The stability of a political rule is shown to depend on whether its choices are dynamically consistent. For instance, simple majority rules can be shown to be dynamically consistent in many common environments where wealth-weighted voting rules are not. The result extends to political rules that incorporate private activities such as extra-legal protests, threats, or private investment. The approach is one way of understanding various explanations of institutional change proposed in the literature. A parametric model of public goods provision gives an illustration.     

The projection dynamic and the geometry of population games

The projection dynamic is an evolutionary dynamic for population games. It is derived from a model of individual choice in which agents abandon their current strategies at rates inversely proportional to the strategies' current levels of use. The dynamic admits a simple geometric definition, its rest points coincide with the Nash equilibria of the underlying game, and it converges globally to Nash equilibrium in potential games and in stable games.     

The genuine savings criterion and the value of population

Summary. In any dynamic model of the economy with changing population, the latter should properly be one of the state variables of the system. It enters both in the maximand, at least under total utilitarianism, and into the production function in one way or another. If population growth is exponential and constant returns prevails, then a simple transformation to per capita variables can be used to eliminate one state variable, but this ceases to be true if growth is not exponential, as it obviously is not and cannot be. If the growth of population is exogenous, then introducing it into the system does not affect the optimal policy. However, if one asks whether the system is sustainable, in the sense of at least maintaining total welfare (integral of discounted utilities), then the criterion is that that the value of the rates of change of the state variables is non-negative, so that the shadow price of population becomes relevant. In this paper, we derive explicit formulas in a simple model, showing that the rate of growth of per capita capital is not the correct formula but must have another terms added to it. We also study the question under an alternative criterion of long-run average utilitarianism. Received: June 1, 2002; revised version: September 27, 2002 RID="*" ID="*"Research support was provided by the William and Flora Hewlett Foundation. An earlier version of this paper was presented at a celebration of Mordecai Kurz's 66th birthday at Stanford University, 1–3 August 2002. Correspondence to: K.J. Arrow     

二元经济理论与人口流动问题分析

二元经济理论框架下的核心问题是劳动力在两个部门之间的流动。刘易斯模型在分析剩余劳动力的存在、两部门交易条件的变化、输入地有效就业和传统部门在经济增长中的作用等问题时具有高度科学性和实用性。用区域生产总值（GRP）的概念,以向量内积的形式建立简单模型求证人口转移数量。实证揭示了人口流动的主方向是人均GRP较低的区域向较高区域的移动,但也存在反向移动。     

Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agent?s consumption is a time-invariant, strictly increasing function of a single state variable: the maximal level of the agent?s income realized to date. We characterize this function in terms of the agent?s outside option value function and the discounted amount of time in which the agent?s income process is expected to reach a new to-date maximum. Under constant relative risk aversion we solve the model in closed-form: optimal consumption of the agent equals a constant fraction of his maximal income realized to date. In the complete-markets implementation of the optimal contract, the Alvarez–Jermann solvency constraints take the form of a simple borrowing constraint familiar from the Bewley–Aiyagari incomplete-markets models.     

Information Efficiency in Betting Markets: a Survey

The concept of information efficiency is central to many studies of financial markets, and these studies have been well surveyed to date. A betting market is an example of a simple financial market, but one which offers researchers the added advantage that it is characterized by a well-defined termination point at which each asset (or bet) possesses a definite value. In consequence, it is much more convenient to use this particular context to formulate tests of information efficiency, and from these tests to draw useful conclusions. This paper surveys the rapidly growing literature which has to date addressed this issue of information efficiency in betting markets.     

Predicting UK Business Cycle Regimes

This paper uses logistic regression to construct a one‐quarter ahead prediction model for classical business cycle regimes in the UK. The binary dependent variable is obtained by applying simple mechanical rules to date turning points in quarterly real GDP data from 1963 to 1999. Using a range of real and financial leading indicators, several parsimonious one‐quarter‐ahead models are developed for the GDP regimes, with model selection based on the SIC criterion. A real M4 variable is consistently found to have predictive content. One model that performs well combines this with nominal UK and German short‐term interest rates. The role of the latter emphasises the open nature of the UK economy.     

Population growth and economic growth

This discussion of the issues relating to the problem posed by population explosion in the developing countries and economic growth in the contemporary world covers the following: predictions of economic and social trends; the Malthusian theory of population; the classical or stationary theory of population; the medical triage model; ecological disaster; the Global 2000 study; the limits to growth; critiques of the Limits to Growth model; nonrenewable resources; food and agriculture; population explosion and stabilization; space and ocean colonization; and the limits perspective. The Limits to Growth model, a general equilibrium anti-growth model, is the gloomiest economic model ever constructed. None of the doomsday models, the Malthusian theory, the classical stationary state, the neo-Malthusian medical triage model, the Global 2000 study, are so far reaching in their consequences. The course of events that followed the publication of the "Limits to Growth" in 1972 in the form of 2 oil shocks, food shock, pollution shock, and price shock seemed to bear out formally the gloomy predictions of the thesis with a remarkable speed. The 12 years of economic experience and the knowledge of resource trends postulate that even if the economic pressures visualized by the model are at work they are neither far reaching nor so drastic. Appropriate action can solve them. There are several limitations to the Limits to Growth model. The central theme of the model, which is overshoot and collapse, is unlikely to be the course of events. The model is too aggregative to be realistic. It exaggerates the ecological disaster arising out of the exponential growth of population and industry. The gross underestimation of renewable resources is a basic flaw of the model. The most critical weakness of the model is its gross underestimation of the historical trend of technological progress and the technological possiblities within industry and agriculture. The model does correctly emphasize the exponential growth of population as the source of several complications for economic growth and human welfare. Stabilization of population by reducing fertility is conducive for improving the quality of population and also advances the longterm management of the population growth and work force utilization. The perspective of longterm economic management involves populatio n planning, control of environmental pollution, conservation of scarce resources, exploration of resources, realization of technological possibilities in agriculture and industry and in farm and factory, and achievement of economic growth and its equitable distribution.     

Accounting for breakout in Britain: The industrial revolution through a Malthusian lens

This paper introduces a simple dynamic model to examine the breakout from a Malthusian economy to a modern growth regime. It identifies several factors that determine the fastest rate at which the population can grow without engendering declining living standards. We then apply the framework to Britain and find a dramatic increase in sustainable population growth at the time of the Industrial Revolution, well before the beginning of modern levels of income growth. The main contributions to the British breakout were technological improvements and structural change away from agricultural production, while coal, capital, and trade played a minor role. In addition to solidifying the link between the Industrial Revolution and rising living standards, this research reconciles the gradualist and limited Crafts–Harley view of the Industrial Revolution with a dramatic and rapid change in Britain’s macroeconomic character.     

Mixed feelings: Theories of and evidence on giving

This paper examines possible motives and institutional factors that impact giving. Specifically, I consider alternative theories parallel to dictator experiments that generate evidence on both allocation decisions and their effect on feelings. A number of new empirical findings as well as new interpretations for previously reported findings result. A novel test distinguishes warm glow from impure altruism and rules out the former as the sole motive for giving. Very generous donations to charities that aid the needy (with modal gifts of the entire dictator's stakes) cannot be attributed to familiarity with the charities. A charity that offers a matching grant increases its revenues by drawing donors and donations away from one that does not, although aggregate charitable donations do not rise. Additional results on emotions paint a picture of “mixed feelings:” generosity creates good feelings when the recipients are charities and bad feelings when they are fellow students. No group of dictators, however, feels better, on average, than a control group that is given no opportunity to donate. I propose a simple model that accounts for these results on allocation behavior and feelings by incorporating elements of two approaches, unconditional altruism and social preference theories, that to date have mostly evolved independently. A critical feature of this model is the social norm, and the results of the experiments corroborate the theory in the context of two norms of distributive justice that are important to real world giving: equity and need.     

The Evolution of Cooperation in Structured Populations

The present paper analyses the evolution of costly cooperation in a multi-group population. Building on insights first developed in modern biology the idea of viscous population equilibria is introduced (a population is said to be viscous when a (sub)population of players is spatially or genetically clustered). A simple model then analyses how the combined effect of viscosity within multiple subgroups and different levels of between-group segregation influences the evolution of cooperation. The results suggest that a key issue in the evolution of cooperation is the shifting balance between the need to protect cooperators and propagation of the tendency to cooperate.     

Malthus in cointegration space: evidence of a post-Malthusian pre-industrial England

This paper re-examines the interaction between population growth and income per capita in pre-industrial England. Our results suggest that, as early as two centuries preceding the Industrial Revolution, England had already escaped the Malthusian Epoch and entered a post-Malthusian regime, where income per capita continued to spur population growth but was no longer stagnant. Our formulation of a post-Malthusian hypothesis implies cointegration between vital rates (birth- and death rates) and income and builds explicitly on a simple model of Malthusian stagnation. We show that this hypothesis can be interpreted as an extension of the latter model where the negative Malthusian feedback effect from population on income, as implied by diminishing returns to labor, is offset by a positive Boserupian and/or Smithian scale effect of population on technology.