Stochastic growth with correlated production shocks

This paper extends the stochastic growth model of Brock and Mirman [J. Econ. Theory4 (1972), 497–513] to allow the production shocks to be correlated over time. The resultant optimal savings and consumption policies depend not only upon the current level of output but also upon the most recent realization of the random shock. The properties of these policy functions are studied and it is shown that the Markov process on output, capital stock and consumption resulting from the application of these policies converges to a stationary distribution.     

Optimal stationary consumption with stochastic production and resources

Uncertainty about technology and resources is represented in terms of uncertainty about an (exogenous) environment whose successive states form a stationary stochastic process, with probabilities that are unaffected by economic decisions. The successive states of the economy depend both on the environment and on the decisions taken with regard to production and consumption. It is shown that, under conditions that are natural extensions of “neoclassical” conditions in the case of certainty, (1) Capital saturation is possible, i.e., an optimal stationary stochastic program exists, and (2) An optimal program can be sustained by a price system that takes the form of a stationary stochastic process of price vectors. In other words, an optimal stationary program can be sustained by a stochastic “equilibrium,” in which at each date the optimal production decisions maximize expected intertemporal profit, and the optimal aggregate consumption vector has minimum cost among all aggregate consumption vectors yielding no less (social) utility.     

The ramsey model revisited: The optimality of cyclical consumption and growth

This paper reconsiders the familiar Ramsey model of optimal saving. This model is modified with two respects: direct spillovers (positive or negative) of capital on utility and penalties for changes of consumption. It will be shown that these two modifications may substantially change the stability properties of an optimal programme if capital provides utility directly (in addition to indirectly through production). More precisely, complex strategies such as (stable) limit cycles or even unstable policies may be optimal. Adjustment costs must be sufficiently high in order to obtain stable limit cycles (or even exploding spirals). This is quite surprising because large adjustment costs are expected to smooth intertemporal strategies.     

Unique and multiple equilibria in a macroeconomic model with environmental quality: An analysis of local stability

This paper develops and analyzes an economic growth model which incorporates environmental quality into the production and utility functions. We solve our model for the balanced growth path and find that a unique low growth equilibrium is attained when environmental quality is given less weight in the utility function. Multiple equilibria exist if environment quality is given greater weight in the utility function. We also perform local stability analysis of our model. We conclude that an economy in which the environmental quality is given relatively less importance by the agents will be caught in low growth, high consumption poverty traps as is the case for many developing countries while other economies can potentially reach a relatively low consumption, high growth steady state if they place greater weight on environmental quality. Finally we look at how the gap between low and high growth equilibria shrinks when individuals place greater weight on environmental quality and how governmental policies can promote growth when societies give less weight to the environment.     

Sustained positive consumption in a model of stochastic growth: The role of risk aversion

In a stochastic economy, long run consumption and output may not be bounded away from zero even when productivity is arbitrarily high near zero and uncertainty is arbitrarily small. In the one-sector stochastic optimal growth model with i.i.d. production shocks, we characterize the nature of preferences that lead to this phenomenon for a stochastic Cobb–Douglas technology. For the general version of the model, we outline sufficient conditions under which the economy expands its capital stock near zero and long run consumption is bounded away from zero with certainty. Our conditions highlight the important role played by risk aversion for small consumption levels.     

A Case Against Zero Capital-Income Taxation

This paper develops a dynamic general equilibrium model to investigate the optimal level of capital income taxation in light of stochastic endogenous economic growth. Although endogenous human capital is incorporated into our model, we restrict our investigation to the issue of optimal physical capital income tax; and the labor supply is also endogenously determined. This paper proves that the optimal capital income tax should be zero provided exogenous government expenditure on production; however, capital income should be taxed if we consider endogenous government consumption.     

Sustainable development,the Hartwick rule and optimal growth

Defining sustainable development as non-declining utility, the consistency of this concept with the Hartwick rule and optimal growth is explored when resources are exhaustible. A simple proof that a generalized Hartwick rule is necessary and sufficient for constant consumption is derived. The existence of a maximal constant consumption path is shown to depend critically on the elasticity of substitution; if this is less than 1, consumption declines; if it is greater than 1 then consumption is not maximal; if it is equal to 1 (the Cobb-Douglas case) then existence is proved. Consumption can increase along an optimal path if the pure rate of time preference is 0; if it is non-zero then consumption declines.     

Public health infrastructure and growth: Ways to improve the inferior equilibrium under multiple equilibria

This paper develops an endogenous growth model in which public health infrastructure, specified as a stock, plays an important role in economic growth. A notable feature of the model is that it employs a non-separable utility function for consumption, leisure, and the level of public health. In addition, increasing the level of health infrastructure contributes to the production of goods through labor augmentation. With these settings, our model is found to have a unique equilibrium or multiple equilibria, depending on the magnitude of the intertemporal elasticity of substitution. For the case of multiple equilibria, we numerically study the ways to avoid the low-growth state in developing countries. From this, we identify two feasible policy implications. The results indicate that public health infrastructure has a vital role in the development policies of low-income countries. Lastly, we show that there are two possibilities in regard to the local dynamics of the model.     

Mean-Gini analysis of stochastic externalities: The case of groundwater contamination

The mean-Gini approach is used to analyze stochastic externalities generated by agricultural production. The model addresses the problem of groundwater pollution caused by excessive fertilizer application. Inherent in the mean-Gini approach to expected utility maximization is a two-fold value: the simplicity of the two-parameter mean-variance model and satisfaction of necessary and sufficient conditions for stochastic dominance. Price and quantity policy recommendations to control externalities are formulated based upon the relative assessment of uncertainty by the regulatory authority and the farmers. Using the Gini as a measure of risk allows for the quantification of control policy measures under differentiated risk aversion and multiple sources of pollution. The model shows that when producers underestimate uncertainty, quota policies restricting fertilizer are more efficient than tax policies in reducing groundwater contamination.Work on this paper was carried out when visiting the University of Maryland. Financial aid for the work was provided by the USDA ERS-NRED under a cooperative agreement between the Department of Agricultural and Resource Economics, University of Maryland, and the USDA — Economic Research Service — Natural Resource Economics Division, I am grateful to John Miranowski and Darrell Hueth for that support. I am indebted as well to Lana Shalit, who helped me revise the paper.     

QUEST III: An estimated open-economy DSGE model of the euro area with fiscal and monetary policy

This paper develops a DSGE model for an open economy and estimates it on euro area data using Bayesian estimation techniques. The model features nominal and real frictions, as well as financial frictions in the form of liquidity-constrained households. The model incorporates active monetary and fiscal policy rules (for government consumption, investment, transfers and wage taxes) and can be used to analyse the effectiveness of stabilisation policies. To capture the unit root character of macroeconomic time series we allow for a stochastic trend in TFP, but instead of filtering data prior to estimation, we estimate the model in growth rates and stationary nominal ratios.     

The effect on optimal consumption of increased uncertainty in labor income in the multiperiod case

We consider a multiperiod, additive utility, optimal consumption model with a riskless investment and a stochastic labor income. The main result is that for utility functions belonging to the set F, consumption decreases when we go from any sequence of distribution functions representing labor income to a more risky sequence. A concave utility function belongs to F if its first derivative exists everywhere and is convex.     

On the minimum degree of returns to scale in sunspot models of the business cycle

Bennett and Farmer (J. Econ. Theory 93 (2000) 118) claim that the degree of increasing returns to scale required for indeterminacy in a single sector growth model can be lowered by allowing for preferences that are non-separable in consumption and leisure. In this paper I show that the example they give violates concavity. In a more general setup, which does not impose specific functional forms on utility, I prove that there are no concave utility functions compatible with indeterminacy if the elasticity of scale is lower than the inverse of the labor share in production.     

Optimal development programs under uncertainty: The undiscounted case

One considers a many-commodity world where technology depends on an exogenous environment whose successive states form a stationary Markov process. A program is optimal if it overtakes any other program or has the maximum expected utility.It is shown there exists a best stationary program. One proves then there exists an optimal program, which converges asymptotically to the best stationary program, and is generated by a policy such that, at every date, a nonrandom production decision is chosen which depends only on the state of the world and of the economy at that time.     

Intellectual property rights and R&D subsidies: are they complementary policies?

IPR protection and R&D subsidy are simultaneously implemented in many economies. Are they complementary policies for improving the welfare of consumers? We address this question in a dynamic general equilibrium model with innovation-driven growth. Under concave utility, the answer is yes for two cases: (1) the economy does not begin from steady state and the elasticity of intertemporal substitution (EIS) is relatively large; (2) the economy begins from steady state with either a sufficiently small initial consumption and a relatively large EIS or a sufficiently big initial consumption and a relatively small EIS. Under linear utility, the answer is yes if the discounted lifetime utility is finite in equilibrium, no matter the economy begins from the steady state or not. As empirical evidence finds cross-country heterogeneity in EIS, they are not complementary for all economies. We also identify reasonable cases whereby they are substitute policies, so we show when it is not welfare-enhancing to simultaneously implement both policies.     

Non-parametric counterfactual analysis in dynamic general equilibrium

In this paper, we examine non-parametric restrictions on counterfactual analysis in a dynamic stochastic general equilibrium model. Under the assumption of time-separable expected utility and complete markets all equilibria in this model are stationary. The Arrow-Debreu prices uniquely reveal the probabilities and discount factor. The equilibrium correspondence, defined as the map from endowments to stationary (probability-free) state prices, is identical to the equilibrium correspondence in a standard Arrow-Debreu exchange economy with additively separable utility. We examine possible restriction on this correspondence and give necessary as well as sufficient conditions on profiles of individual endowments that ensure that associated equilibrium prices cannot be arbitrary. Although restrictions on possible price changes often exist, we show that results from a representative-agent economy usually do not carry over to a setting with heterogeneous agents.     

Optimal Thin Capitalisation Rule in a Simple Endogenous Growth Model with Tax Havens

In this paper we study the optimal thin capitalisation rules by developing a simple dynamic general‐equilibrium growth model incorporating tax havens. It is found that a stricter thin capitalisation rule will reduce the incentive to invest, and is therefore harmful to growth. This effect is ignored in previous static studies on the welfare analysis of tax havens. Accordingly, when taking the growth effect into consideration, reducing the utilisation of tax havens has ambiguous effects on social welfare. We also show that a looser thin capitalisation rule could be favourable for the policymakers if (i) the production technology is high; (ii) the existing income tax rate is high; (iii) the rate of time preference is low; or (iv) the weight factor of public consumption in utility is small.     

Money in the pure consumption loan model

The purpose of this paper is to show how modern techniques of Temporary competitive equilibrium analysis can be applied to models of the “pure consumption loan model” type. One considers Samuelson's simplest model where traders live two periods and where money is the only store of value. It is proved that a temporary equilibrium exists if price expectations are sufficiently independent of current prices. A stationary market equilibrium is shown to exist if there is a set of traders (i) whose total resources are greater when they are young than when they are old, (ii) who are indifferent between present and future consumption. It is proved that this existence theorem still holds if the economy is sufficiently “close” to an economy which has this property. A stationary market equilibrium is shown to be Pareto optimal if all traders hold positive cash balances. It may be inefficient if this condition is not satisfied, for some traders may then be willing to borrow, which they cannot do in this model.     

Altruism and Determinacy of Equilibria in Overlapping Generations Models with Externalities

This paper deals with an OLG model with production and a single commodity, in which agents are assumed altruistic and the aggregate production function contains external effects. I prove that, if the technology satisfies a minor assumption, which encompasses positive and negative externalities, some curvature conditions on the utility function ensure local determinacy of stationary and period 2 equilibria. I prove that non-separable, strictly concave preferences are a fundamental ingredient for the occurrence of indeterminate equilibria. Finally, considering the case of unbounded growth, I establish that for any utility and production functions a unique balanced growth path is globally determinate.
JEL Classification Numbers: C62, E32     

Non-convex aggregate technology and optimal economic growth

This paper examines a model of optimal growth where the aggregation of two separate well behaved and concave production technologies exhibits a basic non-convexity. First, we consider the case of strictly concave utility function: when the discount rate is either low enough or high enough, there will be one steady state toward which the convergence of the optimal path is monotone and asymptotic. When the discount rate is in some intermediate range, we will find sufficient conditions for having either one equilibrium or multiple equilibria steady state. Depending to whether the initial capital per capita is located with respect to a critical value, we show that the optimal paths monotonically converge to one single appropriate equilibrium steady state. Second, we consider the case of linear utility and provide sufficient conditions to have either unique or two steady states when the discount rate is in some intermediate range. In this range, we give conditions under which the above critical value might not exist, and the economy attains one steady state in finite time, then stays at the other steady state afterward. P. Michel passed away when this research was completed. This paper is dedicated to his memory as a friend and colleague. N. M. Hung and C. Le Van thank the referee for vey helpful remarks and criticisms. They are grateful to Takashi Kamihigashi for very fruitful discussions. They also thank J.-F. Leclerc for editing the final version of this paper.