Stochastic optimal growth with nonconvexities

This paper studies optimal investment and dynamic behavior in stochastically growing economies. We assume neither convex technology nor bounded support of the productivity shocks. A number of basic results concerning the investment policy and the Ramsey–Euler equation are established. We also prove a fundamental dichotomy pertaining to optimal growth models perturbed by standard econometric shocks: either an economy is globally stable or it is globally collapsing to the origin.     

Stochastic optimal growth with risky labor supply

Production takes time, and labor supply and profit maximization decisions that relate to current production are typically made before all shocks affecting that production have been realized. In this paper we re-examine the problem of stochastic optimal growth with aggregate risk where the timing of the model conforms to this information structure. We provide a set of conditions under which the economy has a unique, nontrivial and stable stationary distribution. In addition, we verify key optimality properties in the presence of unbounded shocks and rewards, and provide the sample path laws necessary for consistent estimation and simulation.     

Stochastic optimal growth with a non-compact state space

This paper studies the stability of a stochastic optimal growth economy introduced by Brock and Mirman [Brock, W.A., Mirman, L., 1972. Optimal economic growth and uncertainty: the discounted case. Journal of Economic Theory 4, 479–513] by utilizing stochastic monotonicity in a dynamic system. The construction of two boundary distributions leads to a new method of studying systems with non-compact state space. The paper shows the existence of a unique invariant distribution. It also shows the equivalence between the stability and the uniqueness of the invariant distribution in this dynamic system.     

Implicitly additive utility and the nature of optimal economic growth

The solution of an optimization problem frequently depends only on the constraint set and on the indifference set through the optimum. This observation is spelled out and applied to the problem of optimal economic growth. The validity of the turnpike property of optimal growth plans is investigated when the intertemporal utility function is not additive, but has the property that each of its indifference sets is also an indifference set for some other utility function which is additive and has a constant rate of discount. A characterization is provided for such utility functions, which are called implicitly additive.     

Consumption paths under prospect utility in an optimal growth model

This paper studies the Cass-Koopmans-Ramsey model of optimal economic growth in the presence of loss aversion and habit formation. The representative agent's preferences for consumption can be gradually varied between the standard constant intertemporal elasticity of substitution (CIES) case and Kahneman and Tversky's prospect utility. We find that the transitional dynamics of optimal consumption paths differ distinctly from the standard model, in particular consumption smoothing is more pronounced. We also show that prospect utility can cause the economy to remain in a steady state with low consumption and low capital.     

The Solow–Swan model with a bounded population growth rate

The paper analyzes the dynamic of the Solow–Swan growth model when the labor growth rate is non-constant but variable and bounded over time. Per capita capital is seen to stabilize to the non-trivial steady state of the Solow–Swan model with a particular constant labor growth rate. The solution of the model is proved to be asymptotically stable. In case of a Cobb-Douglas production function and a generalized logistic population growth law, the solution is shown to have a closed-form expression via Hypergeometric functions.     

The generation gap and optimal economic growth

Among the problems confronting those who aspire to the development of a realistic and practicable optimal growth theory is that the human population is not homogeneous with respect to age. Those who are relatively young are apt to prefer a different pattern of capital accumulation from that preferred by those who are relatively old. This paper proposes a tentative solution to this particular problem. Essentially the proposal is that society should remain with what is an optimal private plan of an individual who is at the median age of the population at the beginning of the planning period, for one planning period, after which it revises the plan to switch to the optimal private plan of another individual (one planning period younger than the first) who is at the median age at the commencement of the new planning period. Thus the optimal social plan consists of a succession of one planning period implementations of the first periods of the optimal private plans of individuals who are at the median age at that time period. An example of the application of the method is given. An important sidelight of the paper is a critique of standard constant-rate exponential discounting in social planning of optimal capital accumulation, and the proposal that it be replaced by “mortality discounting.”     

Arbitrage and equilibrium in unbounded exchange economies with satiation

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner’s existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents’ preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades– that is, as long as agents’ preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation – a condition considerably weaker than local or global nonsatiation – that makes possible this transformation.     

Stochastic growth with social-status concern: The existence of a unique stable distribution

This paper extends Kurz’s (1968) growth model to a stochastic growth framework with social-status concern and unbounded production shocks. Using the stochastic monotonicity of a stochastic dynamic system and the methods adopted in Zhang (2007), the existence, uniqueness, and stability of invariant distribution are investigated. Different from the existence of multiple steady states under certainty, it is shown here that there exists a unique stable invariant distribution under uncertainty.     

A ‘funnel’ turnpike theorem for optimal growth problems with discounting

A turnpike theorem for the optimal control problem with discounting is given. The optimal trajectory is shown to lie in an exponentially bounded region of the optimal steady-state. This region, referred to as a funnel, is determined by the discount rate of the problem. The funnel theorem reduces to the classical turnpike theorem when the discount rate is zero.     

The simple analytics of optimal growth with illegal migrants: A clarification

This paper reexamines the welfare effects of illegal immigration studied by Hazari and Sgro [The simple analytics of optimal growth with illegal migrants. Journal of Economic Dynamics and Control 28(1) 141–151]. In contrast to their negative conclusion, we obtain ambiguous welfare prediction which is due to the presence of two opposing effects at work: a positive exploitation effect and a negative intertemporal effect. With Cobb–Douglas production technology, we show that per capita domestic consumption rises in the presence of illegal migration.     

Econometric analysis of structural systems with permanent and transitory shocks

This paper considers the implications of the permanent/transitory decomposition of shocks for identification of structural models in the general case where the model might contain more than one permanent structural shock. It provides a simple and intuitive generalization of the influential work of Blanchard and Quah [1989. The dynamic effects of aggregate demand and supply disturbances. The American Economic Review 79, 655–673], and shows that structural equations with known permanent shocks cannot contain error correction terms, thereby freeing up the latter to be used as instruments in estimating their parameters. The approach is illustrated by a re-examination of the identification schemes used by Wickens and Motto [2001. Estimating shocks and impulse response functions. Journal of Applied Econometrics 16, 371–387], Shapiro and Watson [1988. Sources of business cycle fluctuations. NBER Macroeconomics Annual 3, 111–148], King et al. [1991. Stochastic trends and economic fluctuations. American Economic Review 81, 819–840], Gali [1992. How well does the ISLM model fit postwar US data? Quarterly Journal of Economics 107, 709–735; 1999. Technology, employment, and the business cycle: Do technology shocks explain aggregate fluctuations? American Economic Review 89, 249–271] and Fisher [2006. The dynamic effects of neutral and investment-specific technology shocks. Journal of Political Economy 114, 413–451].     

A portfolio approach to endogenous growth: equilibrium and optimal policy

This paper develops a portfolio approach to modeling endogenous growth in continuous time that is especially suitable for addressing fiscal and financial issues in policy design. The analysis focuses on the equilibrium relationship between fiscal and financial policy, rates of return and wealth allocation. We analyze two models. The first is based on the Arrow-Romer model with increasing returns and an external effect of capital on labor productivity. The second draws on Barro's analysis of government spending and endogenous growth. In both models, we study the equilibrium allocation and discuss the optimal fiscal and financial policy.     

Uncertain horizon and stability: Analysis in an optimal growth model

In a one-sector optimal growth model with uncertainty about production optimal capital stocks converge in distribution to a stochastic modified golden rule [see, for example Brock and Mirman (1972, 1973)]. We show that such a result cannot be obtained, in general, if in addition to the random one-period shocks to production there is also a lasting shock to the production function at some random date in the future; however, the conditional optimal capital stocks ‘bunch together’ over time, i.e., a turnpike result for optimal programs is proved.     

Environmental externalities and regulation constrained cost productivity growth in the US electric utility industry

This paper examines whether having to comply with Phase 1 of Title IV of the 1990 Clean Air Act, and rate of return regulation, each impacted the rate of total factor productivity (TFP) growth when accounting for the production of good and bad outputs. Phase 1, effective from 1995 to 1999, requires electric utilities to reduce their emissions of sulfur dioxide and nitrogen oxide (bad outputs). Actions undertaken to reduce the emissions (using less sulfur content coal, installing equipment), may have led to higher production costs, and impacted the rate of TFP growth. Rate regulation may impact how the firm produces its selected output level, which could lead to higher cost over time, and biased estimates of TFP growth. Following the work of Ball et al. (Struct Change Econ Dyn 16(3): 374–394, 2005), who developed the standard Malmquist cost productivity (MCP) index, we develop a MCP index for a rate regulated firm (RMCP index) then use the standard and regulated indices to determine whether having to comply with Phase 1 impacted TFP growth. Empirical results indicate that (i) the RMCP index underestimated the rate at which TFP growth occurred, (ii) Phase 1 utilities on average experienced positive TFP growth from 1996 to 2000 (Phase 1 firms experienced higher TFP growth rates than the rates experienced by firms not subject to Phase 1), and operated more allocatively inefficient in complying with the Phase 1 restrictions. Complying with Phase 1 did not affect the rate at which technical change occurred or the rates of change in scale efficiency.     

Efficient sets with and without the expected utility hypothesis

Consider a feasible set, X, of c.d.f.'s. Assume that the set of decision makers, who must choose from X, includes non-expected utility decision makers who are risk averse in some weaker notions. We show that in this case the efficient set of X expands relative to the expected utility case. We characterize the efficient sets for each notion of risk aversion including the expected utility case. It is also shown that the limited-coverage insurance policies, which are not efficient under the expected utility hypothesis, belong to the efficient set when weakly risk-averse non- expected utility functionals are assumed to exist.     

Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces.     

质量随机的研发竞赛模型与最优奖励

假设研发质量具有随机性,建立了研发竞赛的非合作博弈模型,分别探讨了完全信息和不完全信息条件下竞赛参与人与竞赛发起者的最优策略。研究发现：竞赛参与人的研发投入水平在完全信息和不完全信息条件下都随自身研发效率的降低而降低;研发参与人的类型信息不完全程度越高,参与人的均衡研发投入越低;在每一种信息类型组合下都存在着最优奖励使得竞赛发起者的期望收益最大。     

一种具有模糊费用系数和随机需求的运输问题

对传统的运输问题进行了改进,研究了费用系数为模糊参数和需求为随机条件下的优化问题,构建了模糊随机运输问题的数学模型.通过引入机会约束规划对此模型进行确定性转化,使得决策成立的条件不小于某一给定的置信水平,再通过置信水平将机会约束规划转化为相应清晰的等价类.最后,通过数值算例,验证了模型的可行性,探讨了不同置信水平对最优解的影响.