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.     

Undiscounted optimal growth with consumable capital and labor-intensive consumption goods

This paper presents a complete characterization of the optimal policy in a two sector undiscounted growth model. The model is an extension of the Leontief two sector model, which analyzes the optimal allocation of capital and labor to a consumption good sector and an investment good sector. The paper extends this framework to include consumable capital. Thus, the planner has preferences over the consumption good and the consumable capital. Future welfare levels are treated equally as current ones. Geometric techniques are applied to characterize the optimal policy if the consumption good is labor-intensive. The results suggest that if the initial capital stock is above a threshold level, that depends upon the consumption of capital, every optimal program is monotonic, converges to the golden rule stock in a finite number of periods, and undergoes either unemployment or excess capacity of capital.     

On the existence of optimal processes in non-stationary environments

We consider an aggregative model of intertemporal allocation under uncertainty, in which the utility and production functions are allowed to be time dependent, the random shocks occurring in each period are entirely arbitrary, and the production functions are permitted to be non-concave. In this framework, we provide a theorem on the existence of infinite-horizon optimal processes. In the course of establishing this result, we obtain the existence of optimal policy functions and we show that they are monotone in the stock levels.This paper has benefitted from the comments of two referees of the journal. Research of the first author was supported by a National Science Foundation Grant.     

Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function

This paper studies a one-sector optimal growth model with linear utility in which the production function is only required to be increasing and upper semicontinuous. The model also allows for a general form of irreversible investment. We show that every optimal capital path is strictly monotone until it reaches a steady state; further, it either converges to zero, or reaches a positive steady state in finite time and possibly jumps among different steady states afterwards. We establish conditions for extinction (convergence to zero), survival (boundedness away from zero), and the existence of a critical capital stock below which extinction is possible and above which survival is ensured. These conditions generalize those known for the case of S-shaped production functions. We also show that as the discount factor approaches one, optimal paths converge to a small neighborhood of the capital stock that maximizes sustainable consumption.This paper is dedicated to Professor Mukul Majumdar on his 60th birthday. His research with various co-authors in the late 70s and the 80s pioneered innovative techniques for the analysis of nonconvex dynamic optimization models – both deterministic and stochastic. Roy considers himself particularly fortunate for having had the opportunity to learn economic theory and mathematical economics from Professor Majumdar. This paper has benefited from helpful comments and suggestions by an anonymous referee. Financial support from the 21st Century COE Program at GSE and RIEB, Kobe University, is gratefully acknowledged.     

Irreversible investment with regime shifts

Under the real options approach to investment under uncertainty, agents formulate optimal policies under the assumption that firms’ growth prospects do not vary over time. This paper proposes and solves a model of investment decisions in which the growth rate and volatility of the decision variable shift between different states at random times. A value-maximizing investment policy is derived such that in each regime the firm's investment policy is optimal and recognizes the possibility of a regime shift. Under this policy, investment is intermittent and increases with marginal q. Moreover, investment typically is very small but, in some states, the capital stock jumps. Implications for marginal q and the user cost of capital are also examined.     

On Cost Benefit Rules for Green Taxes

This paper concerns the welfare effects of a green tax reform in a dynamic general equilibrium model with preexisting taxes on labor income and capital income. In comparison with previous studies on green taxes in dynamic models, which have focused their main attention on long run effects of such reforms, I derive cost benefit rules for a change in the tax mix by using the properties of the value function in optimal control theory. This enables me to relate the welfare effect of a change in the tax mix to responses in employment, the capital stock, (flow) emissions and the stock of pollution along the whole general equilibrium path. Another contribution of the paper is to examine under what conditions an emission tax, which is set permanently below the marginal damage of pollution, is welfare superior to an emission tax path that fully internalizes the external effect.     

Investment in Human Capital in Team Members Who Are Involved in Collective Decision Making

This paper studies an investment policy which improves the ability of team members to decide correctly. We specify sufficient conditions on the learning function such that the best policy of investment in human capital is to invest first in the least competent person. Despite the fact that team members who are endowed with more human capital contribute more to the probability that the whole team would decide correctly, the liberal policy is still optimal under these conditions. Moreover, within the dichotomous model of collective decision‐making, we show that these conditions are not so stringent.     

On the impact of shock persistence on the dynamics of a recursive economy

The present note relies exclusively on numerical computation of a parametric version of a (stochastic) version of the one-sector neoclassical growth model to derive the qualitative properties of the optimal consumption/investment policy functions and of the resultant steady state, and to study the manner in which these properties are affected by an increase in the degree of shock persistence. In particular, we measure the effects of (differing degrees of) shock persistence on the means and variances of the resulting (stationary) distributions on output, consumption, and capital stock. Furthermore, we explore the effects of increasing degrees of shock persistence on the dynamic time path of the economy.     

A nonsmooth, nonconvex model of optimal growth

This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We develop various tools to overcome the technical difficulties posed by the generality of the model. We provide sufficient conditions for optimal paths to be bounded, to converge to zero, to be bounded away from zero, and to grow unboundedly. We also show that under certain conditions, if the discount factor is close to 1, any optimal path from a given initial capital stock converges to a small neighborhood of the golden rule capital stock, at which sustainable consumption is maximized. If it is maximized at infinity, then as the discount factor approaches 1, any optimal path either grows unboundedly or converges to an arbitrarily large capital stock.     

Monetary policy and multiple equilibria with constrained investment and externalities

This paper focuses on two mechanisms under which interest-rate feed-back rules induce local indeterminacy in a closed economy with capital accumulation: arbitrage activity and the pricing channel. It shows that constrained investment, in the sense that it requires liquidity or that adjustment to the stock of capital is costly, is enough to induce indeterminacy if monetary policy follows a strictly passive interest rate rule. Determinacy of equilibrium is ensured under an active monetary policy stance. These results change when production externalities are introduced into the model so as to mimic the pricing channel in New Keynesian models. In this case, a policy stance that ensures determinacy is either active or strictly passive. In view of the contradicting results for the passive stance and the similar results for the active stance it is recommended that central banks act according to the active stance.     

Exhaustible resources,technology choice and industrialization of developing countries

How should the world economy adapt to the increased demand for exhaustible resources from countries like China and India? To address that issue, this paper presents a dynamic model of the world economy with two technologies for production; a resource technology, which uses an exhaustible resource as an input and an alternative technology, which does not. I find that both the time path of resource extraction and the adoption of the alternative technology depend on the optimal allocation of capital across the technologies, and on the size of the capital stock in relation to the resource stock. In particular, if the capital stock is low, only the resource technology is used initially and the alternative technology is adopted with a delay. Next, I use the model to analyze the effects of industrialization of developing countries on the extraction of oil and technology choice for energy production. As a result of industrialization, the alternative technology for energy production is adopted earlier.     

Long horizon versus short horizon planning in dynamic optimization problems with incomplete information

Summary. This paper compares the implications of short and long horizon planning in dynamic optimization problems with the structure of a standard one-sector growth model if agents have incomplete knowledge about the production function. Agents know the output and rate of return at the current capital stock and use an estimation of the production function based on this knowledge to determine current consumption. For standard utility functions without wealth-effects both long and short planning horizons yield convergence to the steady state - however at a faster rate than optimal -, or fluctuations around the steady state, and in both cases, long horizon planning yields a policy which locally at the steady state is closer to the optimal one than short horizon planning. On the other hand, for preferences with wealth effects where the intertemporal optimal path exhibits fluctuations, long horizon planning destabilizes the path and short horizon planning can generate paths which are qualitatively closer to the optimal one and yield higher discounted utility.Received: 5 April 2001, Revised: 15 September 2003, JEL Classification Numbers: C61, D83, D90.Herbert Dawid: The author would like to thank Richard Day for numerous stimulating discussions which led to this article and an anonymous referee for helpful comments     

Optimal capital accumulation and durable goods production

Summary We have examined the optimal production of a consumer durable with the aid of a capital stock subject to deterioration. We assumed the durable was owned by the producer and its services rented; this is equivalent to assuming sale with perfect foresight and used good markets. If the firm has no more than modest initial endowments of productive capital and durable good, the deterioration of capital induces a hump-like profile of the stock of the durable product, with the top of the hump above the eventual steady state level. The rental price of the consumer durable, therefore, falls from its initial level to a low from which it ascends to its steady state value. This implication might be amenable to empirical testing.Among the possible extensions of this work might be an analysis of the relationship between market structure and the choice of durability along the lines of [7] with allowance for deterioration of the capital stock. Recent generalizations of the traditional model of capital accumulation to take into account obsolescence and maintenance, as in [19], [11] and [13], might also be applied to this model. Lastly, policy questions regarding the consequences of an investment credit tax addressed in [4] and [16] might also be investigated in the context of the model presented in this paper.     

The Optimal Timing of Adoption of a Green Technology

We study the optimal timing of adoption of a cleaner technology and its effects on the rate of growth of an economy in the context of an AK endogenous growth model. We show that the results depend upon the behavior of the marginal utility of environmental quality with respect to consumption. When it is increasing, we derive the capital level at the optimal timing of adoption. We show that this capital threshold is independent of the initial conditions on the stock of capital, implying that capital-poor countries tend to take longer to adopt. Also, country-specific characteristics, as the existence of high barriers to adoption, may lead to different capital thresholds for different countries. If the marginal utility of environmental quality decreases with consumption, a country should never delay adoption; the optimal policy is either to adopt immediately or, if adoption costs are “too high”, to never adopt. The policy implications of these results are discussed in the context of the international debate surrounding the environmental political agenda.      

Utility and production externalities, equilibrium efficiency and leisure specification

This paper analyzes the implications that the specification of the leisure activity has on the equilibrium efficiency in a two-sector endogenous growth model with human capital accumulation. We consider external effects of consumption and leisure in utility, and sector-specific externalities associated to physical and human capital in production. The optimal tax policy to correct for the distortions caused by the externalities is characterized under all the typical leisure specifications considered in the literature: home production, quality time and raw time. We show that the optimal policy depends markedly on the leisure specification.     

Consumption externalities with endogenous time preference

This paper shows that in a model with inelastic labor supply, consumption externalities have impacts on stationary consumption and capital. The key element in observing the effects of consumption externalities on stationary consumption and capital is the endogeneity of the time preference rate, which depends on future-oriented resources rather than on private consumption. We conclude that when individuals experience jealousy, they become more impatient, leading to a lower level of capital stock and a higher level of consumption relative to those of the social optimum, while when they experience admiration, these relationships are reversed. We examine an optimal tax policy that replicates the socially optimal path in the centrally planned economy. Finally, using numerical analysis we explore how this economy evolves through time.      

A characterization of piecemeal second best policy

This paper derives conditions under which prices may be set proportional to marginal cost in some sectors of the economy when fixed distortions exists in other sectors. Two simple neoclassical economies are considered - one with fixed producer prices and one with variable producer prices. In the former case, nacessary and sufficient conditions are derived for piecemeal policy in terms of properties of derivatives of the demand functions. These conditions are then interpreted in terms of separability properties of utility functions where we find that only weak separability is required. In the latter case, sufficient conditions are derived which involved both demand and supply derivatives. These are also interpreted in terms of separability properties of utility and production functions. The analysis differs from previous ones in that we use a dual formulation of the problem and obtain conditions in terms of demand and supply derivatives which are observable, and we explicitly take into consideration the budgetary constraint of the government. Because of the latter, the factor of proportionality in applying piecemeal policy is not necessarily unity. So, in general, complete laissez faire is not optimal.     

A role for preferred stock in the financing decision of a public utility

Summary We have shown that preferred stock has a unique role in the financing of public utility capital expenditures, particulary when returns allowed by regulatory commissions are perceived to be inadequate. From the firm's perspective there is no tax advantage for debt because the commission effectively passes the tax savings through the consumers. If allowed returns on common stock are inadequate and the firm has exhausted its perceived debt capacity, then preferred stock becomes the optimal financing instrument. The regulatory commissions compute the costs of debt and preferred stock so that companies can expect returns to cover payments on debt and preferred stock if the assets being financed are necessary and will be included in the rate base. During extremely bad years when revenues are much less than expected, the companies can delay or miss preferred stock dividends without running the risk of default. The data on new capital sources for the electric and gas utilities indicate that these companies made adjustments which are consistent with the implications of our model, but they did not follow the extreme policy of using only debt and preferred stock when market-to-book ratios for common stock were below one. Regulators have, on occasions, used capital structures for rate-making that differ from actual capital structures, and a utility might be penalized for using an extreme capital structure policy. The main emphasis of regulatory review of capital structure, however, has been on the debt component. One strategy would be to use a debt level that satisfies the regulatory commission and then adjust equity between preferred stock and common stock to maximize value for common stockholders.     

Optimal food price stabilisation policy

This paper proposes a framework for designing optimal food price stabilisation policies in a self-sufficient developing country. It uses a rational expectations storage model with risk-averse consumers and incomplete markets. Government stabilises food prices by carrying public stock and by applying a state-contingent subsidy/tax to production. The policy rules are designed to maximise intertemporal welfare. The optimal policy under commitment crowds out all private stockholding activity by removing the profit opportunity from speculation. The countercyclical subsidy/tax to production helps price stabilisation by subsidising production in periods of scarcity and by taxing it in periods of glut. It contributes little to welfare gains, most of which come from stabilisation achieved through public storage.