Endogenous growth with a limited fossil fuel extraction capacity

Campbell (1980) and following authors have discussed a limited resource extraction capacity as an augmentation of the well‐known Hotelling model. We integrate a limited extraction capacity and related investments in the endogenous growth model of Tsur and Zemel (2005) to study its effect on economic development. The capacity constraint gives rise to three effects. On the one hand, higher energy costs and the reallocation of production towards capacity investments decrease production available for consumption, research and/or capital investments (energy costs and reallocation effect). On the other hand, research investments may increase, which boosts available production (research effect). Depending on the capital endowment and the strength of the effects, long‐run consumption may be boosted or depressed. In particular, the capacity constraint may render everlasting consumption growth non‐optimal in a resource‐rich economy. Furthermore, we find that capacity investments may be postponed to later points in time if the capital endowment is high.     

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.      

Consumption externalities: a representative consumer model when agents are heterogeneous

We examine a growth model with consumption externalities where agents differ in their initial capital endowment and their reference group. We show under which conditions the aggregate equilibrium with heterogeneous agents replicates that obtained with a representative consumer, despite the fact that different individuals have different consumption levels. Next we consider the implications of the presence of consumption externalities for the long-run distributions of income and wealth. We find that, in a growing economy, “keeping up with the Joneses” results in less inequality than would prevail in an economy with no consumption externalities.     

Disutility of pollution and endogenous growth

Endogenous growth is generally built on a positive externality hypothesis which is the opposite of a negative externality caused by pollution. We study a linear technology with simple assumption: an aggregate capital stock which represents a learning by doing effect and a pollution flow proportional to production. In this framework, we analyse the precise effects on growth of the disutility of pollution and its interaction with the utility of consumption in an economy without abatement technology. The decentralized equilibrium always leads to unlimited growth, but optimal growth is often limited (the negative effect of pollution dominating the positive effect of learning by doing). In this case, the optimal policy which leads the decentralized economy to follow the optimal growth path is to tax capital; in contrast with the optimal subsidy policy in an economy without pollution. When an abatement technology is introduced, the optimal solution can lead the economy to unlimited growth, whatever the form of the utility function.     

International trade and directed search unemployment in general equilibrium

We develop an open economy general equilibrium model, with auction‐based directed search unemployment, to study the interactions of trade and unemployment. The theory ascribes all outcomes purely to the fundamentals of technology and endowment. If countries differ by endowment, trade makes both the unemployment rate and the rental in the capital‐(labour‐) abundant country rise (decline) but does not lead to equalization. If, alternatively, countries differ by technology, trade increases (decreases) the unemployment rate in the country whose technology is relatively superior (inferior) for producing the capital‐intensive good.     

Asset pricing with adaptive learning

We study the extent to which self-referential adaptive learning can explain stylized asset pricing facts in a general equilibrium framework. In particular, we analyze the effects of recursive least squares and constant gain algorithms in a production economy and a Lucas type endowment economy. We find that (a) recursive least squares learning has almost no effects on asset price behavior, since the algorithm converges relatively fast to rational expectations, (b) constant gain learning may contribute towards explaining the stock price and return volatility as well as the predictability of excess returns in the endowment economy but (c) in the production economy the effects of constant gain learning are mitigated by the persistence induced by capital accumulation. We conclude that in the context of these two commonly used models, standard linear self-referential learning does not resolve the asset pricing puzzles observed in the data.     

Skilled–unskilled wage inequality,product variety,public input and increasing returns: A static general equilibrium analysis

The paper develops a four sector small open economy model with two traded final good sectors, a public intermediate good producing sector and a nontraded good sector producing varieties of intermediate goods. There are three primary factors: capital, skilled labour and unskilled labour. Industrial sector producing a traded good uses capital, intermediate goods and skilled labour as inputs. Intermediate goods producing sector also uses capital and skilled labour. Public input producing sector and the agricultural sector producing the other traded good use capital and unskilled labour as inputs. It is shown that, if production technologies are the same for the agricultural sector and the public input producing sector and if the scale elasticity of output is very low, then an increase in capital stock (unskilled labour endowment) raises (lowers) the skilled–unskilled wage ratio. However, an increase in skilled labour endowment does not produce any unambiguous effect. On the other hand, an increase in the tax rate on industrial output and/or an increase in the price of the agricultural product, armed with the same set of assumptions, lowers the skilled–unskilled wage ratio.     

Monetary equilibrium in an overlapping generations model with productive capital

Summary We study perfect foresight competitive equilibrium in an overlapping generations model with productive capital and a fixed nominal stock of money. We obtain almost-complete characterizations of (a) the existence of a monetary equilibrium from an arbitrary initial capital stock, and (b) the existence of anefficient monetary equilibrium from an arbitrary initial capital stock. When the initial capital stock is no larger than the golden rule stock, the necessary and sufficient condition for both (a) and (b) is the dynamic inefficiency (in the sense of Malinvaud) of the autarkic (or nonmonetary) equilibrium from the same initial stock. However, this condition, though necessary, isnot sufficient for the existence of a monetary equilibrium when the initial stock exceeds the golden rule stock (and still more conditions are needed for anefficient monetary equilibrium to exist). We provide characterizations for these cases, and as corollaries obtain examples in which (a) the nonmonetary equilibrium is inefficient but no monetary equilibrium exists, and (b) monetary equilibria exist but no efficient monetary equilibrium does.We are grateful to a co-editor and an anonymous referee for comments that greatly improved the exposition in the paper.     

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.     

Inflation and capital accumulation in an OLG model with money in the production function

This article analyses the consequences of the money supply growth rate on capital intensity and economic growth in an overlapping-generations model with real balances entering the production function. Within this theoretical framework, anticipated inflation generates an ambiguous effect on capital–labour ratio, because two forces work simultaneously in opposite directions: one driving towards a pure Tobin effect (due to the OLG demographic structure of the economy) and the other pushing down the capital stock (due to the productive role of real balances). Despite the unclear effects exerted on capital intensity, higher monetary growth rates unambiguously reduce real money demand, consumption, total wealth and welfare.     

TECHNOLOGICAL CHANGE,HUMAN CAPITAL STRUCTURE,AND MULTIPLE GROWTH PATHS*

This paper presents a theoretical model to analyze the effects of technology change on growth rates of income and human capital in the uncertain environments of technology. The uncertainty comes from two sources: the possibility of a technology advance and the characteristics of new technologies. We set up an overlapping generations model in which young agents invest in both width and depth of human capital in order to adopt new technologies. The model develops explicitly the micro‐mechanism of the role of human capital in adopting new technologies as well as that of the process of human capital production in the uncertain environments. In our model, a higher level of width of human capital relative to the level of depth leads one country to a higher growth path. We also show that an economy can have different growth paths depending on the initial structure of human capital and the uncertainty about the nature of new technologies. In particular, new technologies with more uncertain characteristics may adversely affect human capital accumulation and income growth, leading the economy to a low growth trap.     

HISTORY‐DEPENDENT PATHS AND TRADE GAINS IN A SMALL OPEN ECONOMY WITH A PUBLIC INTERMEDIATE GOOD*

This study reexamines McMillan's (International Economic Review 19 (1978), 665–78) analysis of a dynamic small open economy with a public intermediate good. Concerning the trade patterns of the open economy, we find results that were overlooked in McMillan's analysis. Among others, if labor endowment is of intermediate size, there are two saddle‐point steady states, and the initial stock of the public good determines the long‐run trade pattern. We also add a gains‐from‐trade analysis to McMillan's model and demonstrate that if the economy has a comparative advantage in a good with productivity less sensitive to the public intermediate good, the economy may lose from trade at the steady state.     

Efficient contract enforcement

We study how the efficient choice of contract enforcement interacts with the efficient allocation of capital in a simple production economy. Contract enforcement makes trade possible but requires an aggregate investment of capital that is no longer available for production. In such an economy, more dispersion in ex-ante marginal products makes it optimal to invest more resources in enforcement. Furthermore, implementing the optimal allocation requires a specific distribution of the cost for enforcement across agents that is not monotonic and results in a redistribution of endowments. At the efficient solution, agents at the bottom of the endowment distribution benefit the most from investment in enforcement and these investments lead to a reduction in consumption and income inequality.     

Renewable resource and capital with a joy-of-giving resource bequest motive

In this article we ask whether a privately owned natural renewable resource can be conserved and managed efficiently when households have a joy-of-giving resource bequest motive. We model an overlapping generations economy in which firms have access to a CES production technology combining the natural resource, physical capital and labor. Our results shed light on the interplay between the resource bequest motive and the substitutability/complementarity relationship between capital and the natural resource in the determination of the equilibrium propensity to use the resource. The mere existence of the bequest motive does not guarantee that the resource will be conserved in the long run. When the resource is highly substitutable with capital, the equilibrium actually never exhausts the resource stock whatever the intensity of the bequest motive. When the resource is a poor substitute for capital, the equilibrium preserves the resource only if the taste for bequeathing is strong enough. Be the economy in over-accumulation or in under-accumulation of the natural resource, it always increases aggregate consumption to run the stock of capital at a level lower than the efficiency level.     

The optimal depletion of exhaustible resources: A complete characterization

We provide the closed form solution to the Dasgupta–Heal–Solow–Stiglitz (DHSS) model. The DHSS model is based on the seminal articles Dasgupta and Heal, 1974, Solow, 1974 and Stiglitz (1974) and describes an economy with two assets, man-made capital and a nonrenewable resource stock. We explicitly characterize, for such an economy, the dynamics along the optimal trajectory of all the variables in the model and from all possible initial values of the stocks. We use the analytical solution to prove several properties of the optimal consumption path. In particular, we show that the initial consumption under a utilitarian criterion starts below the maximin rate of consumption if and only the resource is abundant enough and that under a utilitarian criterion, it is not necessarily the present generation that benefits most from a windfall of resources.     

With exhaustible resources, can a developing country escape from the poverty trap?

This paper studies the optimal growth of a developing non-renewable natural resource producer. It extracts the resource, and produces a single consumption good with man-made capital. Moreover, it can sell the extracted resource abroad and use the revenues to buy an imported good, perfect substitute of the domestic consumption good. The domestic technology is convex-concave, so that the economy may be locked into a poverty trap. We show that the extent to which the country will escape from the poverty trap depends on the interactions between its technology and its impatience, the characteristics of the resource revenue function, the level of its initial capital stock, and the abundance of the natural resource.     

Transitional dynamics and the distribution of assets

Summary. We study the evolution of the distribution of assets in a discrete time, deterministic growth model with log-utility, a minimum consumption requirement, Cobb-Douglas technology, and agents differing in initial assets. We prove that the coefficient of variation in assets across agents decreases monotonically in a transition to the steady state from below, if (i) the consumption requirement is zero, or (ii) the consumption requirement is not too big and the initial capital stock is large enough. We also show how a positive consumption requirement or a small elasticity of substitution between capital and labor can generate non-monotonic paths for inequality.JEL Classification Numbers: D31, E21, O41.We would like to thank S. Chatterjee, M. Huggett, T. Keister, P. Krusell, M. Santos, S. Williamson, and an anonymous referee, for their valuable comments and suggestions. All remaining errors are ours. Urrutia aknowledges the support of Universidad Carlos III de Madrid, to which he was affiliated during early phases of this project.     

OPTIMAL TRANSITION DYNAMICS IN THE LEONTIEF TWO‐SECTOR GROWTH MODEL WITH DURABLE CAPITAL: THE CASE OF CAPITAL INTENSIVE CONSUMPTION GOODS*

We present results on undiscounted optimal policies in the Leontief two‐sector growth model with durable capital. Unlike the results with a labour intensive consumption goods sector, we show that a monotonic optimal programme is only one special case out of many richer possibilities of transition dynamics. Depending on the initial capital stock, and a key parameter ζ that could be interpreted as a marginal rate of transformation of capital between today and tomorrow, an optimal programme may converge to a period‐two cycle; and even when it converges to the golden rule stock, it can do so (damped) cyclically or with a “jump”.     

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.      

Equilibrium business cycles with idle resources and variable capacity utilization

Summary A real business cycle economy is studied in which some capital is idle each period and the fraction of capital left idle varies in response to technology shocks. Previous equilibrium business cycle models have the characteristic that the entire stock of capital is used for production in each period. Our objective is to determine whether incorporating idle resources, something regularly observed in actual economies, significantly affects the cyclical properties of the model and hence changes our views about the importance of technology shocks for aggregate fluctuations. In our analysis we do not assume an aggregate production function, but instead model production as taking place at individual plants that are subject to idiosyncratic technology shocks. Each period the plant manager must choose whether to operate the plant or to let the plant remain idle. We find that the cyclical properties of this model are surprisingly similar to those of a standard real business cycle economy. One difference is that the model displays variation in factor shares while the standard models does not.The authors acknowledge support from the National Science Foundation.