Overlapping Generations Model with Endogenous Labor Supply: General Formulation

This paper develops a one-sector overlapping generations model with endogenous labor supply and nonseparable preferences. It demonstrates that local indeterminacy arises easily under gross substitutability as soon as there exist multiple steady states. We show also that, depending on whether leisure and second-period consumption are gross substitutes, local indeterminacy holds for very different parameter configurations. If gross substitutability is satisfied, the existence of multiple equilibrium paths requires the share of capital in the total income to be strong enough with respect to the elasticity of capital-labor substitution. On the other hand, if gross substitutability is violated, local indeterminacy necessitates the share of capital in the total income to be weak enough with respect to the elasticity of capital-labor substitution. This paper is dedicated to the memory of Louis-André Gérard-Varet, Director of GREQAM from 1987 to 1999. We thank S. Catania, C. Deissenberg, J. P. Drugeon, L. A. Gérard-Varet, J. M. Grandmont, A. Kirman, T. Lloyd-Braga, P. Michel, P. Pintus,E.Thibault, B.Wigniolle, and two anonymous referees for helpful comments and suggestions. The paper benefited from comments received during a presentation at the Conference on Dynamic Equilibria, Expectations and Indeterminacies, Paris. France, 1999.     

Optimal portfolio‐consumption choice under stochastic inflation with nominal and indexed bonds

This research solves the intertemporal portfolio choice problems with and without interim consumption under stochastic inflation. We assume a one‐factor nominal interest rate and a one‐factor expected inflation rate, implying a two‐factor real interest rate in the economy. In contrast to other related research which adopts the one‐factor real interest rate model, the inflation‐indexed bond is not a redundant asset class even in a complete market. The infinitely risk‐averse investor would prefer to invest all her wealth in inflation‐indexed bonds maturing at the investment horizon. We also show that, with the two‐factor real interest rate model, the consumption‐wealth ratio is not determined by the real interest rate alone. The investor's consumption–wealth ratio is also affected by the nominal interest rate and expected inflation rate levels. The capital market is calibrated to U.S. stocks, bonds, and inflation data. The optimal weights show that aggressive investors hold more nominal bonds in order to earn the inflation risk premiums, while conservative investors concentrate on indexed bonds to hedge against the inflation risk. Copyright © 2011 John Wiley & Sons, Ltd.     

有政府债券的军事花费和经济增长(英文)

本文讨论了军事花费 ,资本积累和政府债券在一个随机内生的增长模型中 ,结果表明 :如果本国有一个低的消费替代弹性 ,则外国财富和军事花费的增长都会导致本国经济的增长 ;但是 ,如果本国有一个高的消费替代弹性时 ,外国军事花费的大的扰动也可导致本国经济的增长 .     

How do changes in risk and risk aversion affect self-protection with Selden/Kreps–Porteus preferences?

This paper examines the determinants of optimal effort in an intertemporal self-protection model. We separate attitude toward risk and attitude toward intertemporal substitution by adopting Selden/Kreps–Porteus preferences. We not only explore the sufficient conditions on risk preferences for guaranteeing the unambiguous effects of changes in risk on the optimal effort level but also show how a change in risk aversion alone affects the optimal effort level.     

On Equilibria when Agents Have Multiple Priors

We discuss the existence and the qualitative properties of equilibria when agents have multiple priors and there is only one good in each state of the world. We first prove a general existence result in infinite dimension economies. We then fully describe the equilibria in two special cases. We first consider the case of CEU maximizers that have same capacities. We next consider the case of no aggregate uncertainty. We prove that if agents have non-random initial endowments and are uncertainty averse and maximize the minimal expected utility according to a set of possible priors, then the existence of a common prior is equivalent to the existence of a unique equilibrium, the no-trade equilibrium. We lastly give a mild assumption for indeterminacy of equilibria and compute the dimension of indeterminacy.     

递规效用,污染和随机经济增长

本文在一个带有污染的随机内生增长模型中引入了递规效用.证明了在一定的宏观均衡条件下,主要经济指标的均衡值可唯一的决定于模型参数.并证明了许多模型参数对福利和经济增长的影响与跨时替代弹性而不是风险厌恶系数有关.     

Equilibria of a stationary economy with recursive preferences

We consider an intertemporal stationary economy in discrete time, where agents have recursive preferences. Using dynamic programming, we show that equilibrium consumption trajectories from a capital stock are interior Pareto optima and are characterized by a strictly positive parameter in ^n–1, the set of agents' initial weights. We then exhibit prices that support the Pareto optima and use the Negishi method to characterize the parameters corresponding to equilibria. Finally, we prove the existence of equilibria and show that the number of regular equilibria is odd.     

RECURSIVE UTILITY,PRODUCTIVE GOVERNMENT EXPENDITURE AND OPTIMAL FISCAL POLICY

This paper employs a stochastic endogenous growth model extended to the case of a recursive utility function which can disentangle intertemporal substitution from risk aversion to analyze productive government expenditure and optimal fiscal policy, particularly stresses the importance of factor income. First, the explicit solutions of the central planner＇s stochastic optimization problem are derived, the growth maximizing and welfare-maximizing government expenditure policies are obtained and their standing in conflict or coincidence depends upon intertemporal substitution. Second, the explicit solutions of the representative individual＇s stochastic optimization problem which permits to tax on capital income and labor income separately are derived ,and it is found that the effect of risk on growth crucially depends on the degree of risk aversion,the intertemporal elasticity of substitution and the capital income share. Finally, a flexible optimal tax policy which can be internally adjusted to a certain extent is derived, and it is found that the distribution of factor income plays an important role in designing the optimal tax policy.     

Existence of Equilibria in Economies with Externalities and Nonconvexities

We consider a general equilibrium model of an economy in which the production possibilities, the consumption sets and the preferences of the consumers are represented by set-valued mappings which depend on the environment to take into account the possibility of external effect. In order to encompass all kinds of nonconvexities, we do not put any convexity assumption either on the graph of the set-valued mapping which describes the technological possibilities or on the production set for a given environment. The firms are instructed to set their prices according to general pricing rules which may depend on the production plans of other producers and on consumption plans.We report an existence result of general equilibria. As in the model without external effects, the key hypotheses are bounded loss and survival assumptions. Nevertheless, we also assume that the set-valued mappings which describe the fundamentals of the economy are lower semi-continuous and have a closed graph.Our framework is sufficiently large to generalize previous works on the existence of competitive equilibria with externalities when the firms have convex production sets and on the existence of equilibria with general pricing rule without externality.     

Unbounded growth in the Neoclassical growth model with non-constant discounting

For a Neoclassical growth model, the literature highlights that exponential discounting is observationally equivalent to quasi-hyperbolic discounting, if the instantaneous discount rate decreases asymptotically towards a positive value. Conversely, in this paper a zero long-run value allows a solution without stagnation. We prove that a less than exponential but unbounded growth can be attained, even without technological progress. The growth rate of consumption decreases asymptotically towards zero, although so slowly that consumption grows unboundedly. The asymptotic convergence towards a non-hyperbolic steady-state which saving rate matches the intertemporal elasticity of substitution and the speed of convergence towards this equilibrium are analyzed.     

Coordinate Transformations and Derivation of Open-Loop Nash Equilibria

Leitmann (Ref. 1) introduced coordinate transformations to derive global optima of a class of dynamic optimization problems. We present applications of this method to derive open-loop Nash equilibria for finite-time horizon differential games. The method of coordinate transformations is especially useful in cases where the original game does not satisfy the global curvature conditions normally imposed in sufficient optimality conditions.     

Consumption-Investment Problem with Subsistence Consumption,Bankruptcy, and Random Market Coefficients

We consider a general continuous-time finite-horizon single-agent consumption and portfolio decision problem with subsistence consumption and value of bankruptcy. Our analysis allows for random market coefficients and general continuously differentiable concave utility functions. We study the time of bankruptcy as a problem of optimal stopping, and succeed in obtaining explicit formulas for the optimal consumption and wealth processes in terms of the optimal bankruptcy time. This paper extends the results of Karatzas, Lehoczky, and Shreve (Ref. 1) on the maximization of expected utility from consumption in a financial market with random coefficients by incorporating subsistence consumption and bankruptcy. It also addresses the random coefficients and finite-horizon version of the problem treated by Sethi, Taksar, and Presman (Ref. 2). The mathematical tools used in our analysis are optimal stopping, stochastic control, martingale theory, and Girsanov change of measure.     

THE POSSIBILITY OF CONTINUOUS GROWTH WITH EXHAUSTIBLE RESOURCES: UNKNOWINGLY AN AGREEMENT HAS BEEN REACHED,BUT IT MAY NOT BE CORRECT

ABSTRACT. It is the size of the elasticity of substitution that has been the central issue in the long debate over the possibility of continuous growth in the presence of exhaustible resources. This paper reviews the debate and comes to the surprising conclusion that, unnoticed by pessimists, the optimist position has gradually evolved so that it now approximates that of the pessimists. The paper also summarizes some preliminary work by the author that indicates that this common position may not be correct.     

奈特不确定下考虑红利和机制转换的最优消费投资

分析了在奈特不确定性环境下,股票的预期回报率服从Markov链的跨期消费和资产选择问题.首先,对由风险资产预期回报构成的不可观测状态下的隐Marbv状态转换模型做出了刻画,使人们对感性的“不可观测状态”的实际金融市场到其精确的数学模型表达有一个清晰的认识.其次,在连续时间风险模型下,假设具有递归多先验效用的投资者拥有一个不可观测的投资机会的先验集,借助Malliavin导数和随机积分方程求解投资者最优消费和投资策略的显式表达式.通过数值模拟分析时,发现不完备信息下的连续Bayes修正产生了能够削减跨期对冲需求的含糊对冲需求,含糊厌恶增大了最优投资组合策略中对冲需求的重要性.讨论了当市场上出现红利因素,上述最优投资组合结论将会发生何种变化,并对红利因素进行具体的量化,定量地研究不同大小的红利对最优投资组合的影响.最后,利用Monte Carlo Malliavin导数模拟计算法分别说明了考虑含糊情形下最优股票需求和跨期对冲需求的变化趋势,且考虑在股票是否考虑支付红利的情况下对投资的影响.     

The path player game

We give an explicit PDE characterization for the solution of the problemof maximizing the utility of both terminal wealth and intertemporal consumption undermodel uncertainty. The underlying market model consists of a risky asset, whosevolatility and long-term trend are driven by an external stochastic factor process. Therobust utility functional is defined in terms of a HARA utility function with risk aversionparameter 0 < α < 1 and a dynamically consistent coherent risk measure, whichallows for model uncertainty in the distributions of both the asset price dynamics andthe factor process. Ourmethod combines recent results by Wittmüß (Robust optimizationof consumption with random endowment, 2006) on the duality theory of robustoptimization of consumption with a stochastic control approach to the dual problemof determining a ‘worst-case martingale measure’.     

Advertising in a Differential Oligopoly Game

We illustrate a differential oligopoly game where firms compete à la Cournot in homogeneous goods in the market phase and invest in advertising activities aimed at increasing the consumers reservation price. Such investments produce external effects, characterizing the advertising activity as a public good. We derive the open-loop and closed-loop Nash equilibria, and show that the properties of the equilibria depend on the curvature of the market demand function. The comparative assessment of these equilibria shows that the firms advertising efforts are larger in the open-loop equilibrium than in the closed-loop equilibrium. We also show that a cartel involving all the firms, setting both output levels and advertising efforts, may produce a steady state where the social welfare level is higher than the social welfare levels associated with both open-loop and closed-loop noncooperative settings.     

考虑污染控制、技术进步和人力资本积累下的经济可持续增长

构建一个带有环境污染、污染控制、内生人力资本积累和内生技术进步的动态经济增长模型,并运用最优控制方法探讨经济最优增长路径.研究表明:人力资本积累效率、消费跨期替代弹性和时间贴现率决定着经济最优增长路径.消费跨期替代弹性、时间贴现率、人力资本积累效率、物质产品和技术研发部门的投入产出弹性、污染排放的产出和控制弹性会对稳态中的人均经济增长率、人均污染排放增长率产生影响.     

The spirit of capitalism,non-expected utility and asset pricing

0Intr0ducti0nAferEpsteinandZin(1989,199l)andWeil(1990),n0n-expectedutilitypreferences0ftenaPpwinassetpricingthe0ryinsteadofc0nventi0naltime-allitive,expectedutilityAnattrec-tivefeature0fthisgeneralisedspecificationisthatintertemp0ralsubStitutinnandriskaversioucanbepartiallydisentangled,incontr8ttothec0nventi0nalcaseofanadditiveandhomthgeneousVonNeumann-MorgellsternintertemPoralutilityfuncti0n,inwhichtheelasticityofsub8titutionandthec0efficielltofrelativeriskaversionarec0nstrainedtoberecipr0…     

Corrigendum to “A note on the Loewenstein–Prelec theory of intertemporal choice” [Math. Social Sci. 52 (1) (2006) 99–108]

In a critique of the Loewenstein and Prelec [Loewenstein G., Prelec D., 1992. Anomalies in intertemporal choice: Evidence and an interpretation. The Quarterly Journal of Economics 107, 573–597] theory of intertemporal choice, [al-Nowaihi, A., Dhami, S., 2006. A note on the Loewenstein–Prelec theory of intertemporal choice. Mathematical Social Sciences 52, 99–108] point out four errors. One of the alleged errors was that the elasticity of the value function in prospect theory is decreasing. But it is in fact increasing. We provide a correction and a formal proof. As a corollary, we show that the elasticity of the value function is bounded between zero and one. Nevertheless, all the remaining points in [al-Nowaihi, A., Dhami, S., 2006. A note on the Loewenstein–Prelec theory of intertemporal choice. Mathematical Social Sciences 52, 99–108] remain valid     

Sustainability,indeterminacy and oscillations in a growth model with environmental assets

We consider an economy where welfare of a continuum of (identical) agents depends on three goods: leisure, a free access renewable environmental asset and a produced good which can be consumed or saved to accumulate physical capital. We assume that aggregate consumption depletes the natural resource and that economic agents take as exogenously given the negative impact on the environmental asset by aggregate consumption. In this context, we show that indeterminacy and oscillating behavior may arise.