We solve a linear-quadratic model of a spatio-temporal economy using a polluting one-input technology. Space is continuous and heterogenous: locations differ in productivity, nature self-cleaning technology and environmental awareness. The unique link between locations is transboundary pollution which is modelled as a PDE diffusion equation. The spatio-temporal functional is quadratic in local consumption and linear in pollution. Using a dynamic programming method adapted to our infinite dimensional setting, we solve the associated optimal control problem in closed-form and identify the asymptotic (optimal) spatial distribution of pollution. We show that optimal emissions will decrease at given location if and only if local productivity is larger than a threshold which depends both on the local pollution absorption capacity and environmental awareness. Furthermore, we numerically explore the relationship between the spatial optimal distributions of production and (asymptotic) pollution in order to uncover possible (geographic) environmental Kuznets curve cases.
We review the most recent advances in distributed optimal control applied to Environmental Economics, covering in particular problems where the state dynamics are governed by partial differential equations (PDEs). This is a quite fresh application area of distributed optimal control, which has already suggested several new mathematical research lines due to the specificities of the Environmental Economics problems involved. We enhance the latter through a survey of the variety of themes and associated mathematical structures beared by this literature. We also provide a quick tour of the existing tools in the theory of distributed optimal control that have been applied so far in Environmental Economics.
The pure risk sharing mechanism implies that financial liberalization is growth enhancing for all countries as the world portfolio shifts from safe low-yield capital to riskier high-yield capital. This result is typically obtained under the assumption that the volatilities for risky assets prevailing under autarky are not altered after liberalization. We relax this assumption within a simple two-country model of intertemporal portfolio choices. By doing so, we put together the risk sharing effect and a well-defined instability effect. We identify the conditions under which liberalization may cause a drop in growth. These conditions combine the typical threshold conditions outlined in the literature, which concern the deep characteristics of the economies, and size conditions on the instability effect induced by liberalization.
This paper aims at clarifying the analytical conditions under which financial globalization originates welfare gains in a simple endogenous growth setting. We focus on an open-economy AK model in which the capital-deepening effect of financial globalization boosts growth in a in permanent but entails an entry cost in order to access international credit markets. We show that constrained borrowing triggers substantial welfare gains, even at small levels of international financial integration, provided that the autarkic growth rate is larger than the world interest rate. Such conditional welfare benefits boosted by stronger growth—long-run gain—arise in our preferred model without investment commitment and they range, relative to autarky, from about 2% in middle-income countries to about 13% in OECD-type countries under international financial integration. Sizeable benefits emerge despite the fact that consumption initially falls—short-run pain—which is, however, shown not to dwarf positive growth changes.
After years of high commodity prices, a new era of lower ones, especially for oil, seems likely to persist. This will be challenging for resource-rich countries, which must cope with the decline in income that accompanies the lower prices and the potential widening of internal and external imbalances. This column presents a new VOXEU eBook in which leading economists from academia and the public and private sector examine the shifting landscape in commodity markets and look at the exchange rate, monetary, and fiscal options policymakers have, as well as the role of finance, including sovereign wealth funds, and diversification.
Under uncertainty, mean growth of, say, wealth is often defined as the growth rate of average wealth, but it can alternatively be defined as the average growth rate of wealth. We argue that stochastic stability points to the latter notion of mean growth as the theoretically relevant one. Our discussion is cast within the class of continuous-time AK-type models subject to geometric Brownian motions. First, stability concepts related to stochastic linear homogeneous differential equations are introduced and applied to the canonical AK model. It is readily shown that exponential balanced-growth paths are not robust to uncertainty. In a second application, we evaluate the quantitative implications of adopting the stochastic-stability-related concept of mean growth for the comparative statics of global diversification in the seminal model due to Obstfeld (1994).
This paper revisits the optimal population size problem in a continuous time Ramsey setting with costly child rearing and both intergenerational and intertemporal altruism. The social welfare functions considered range from the Millian to the Benthamite. When population growth is endogenized, the associated optimal control problem involves an endogenous effective discount rate depending on past and current population growth rates, which makes preferences intertemporally dependent. We tackle this problem by using an appropriate maximum principle. Then we study the stationary solutions (balanced growth paths) and show the existence of two admissible solutions except in the Millian case. We prove that only one is optimal. Comparative statics and transitional dynamics are numerically derived in the general case.
This note introduces to the literature streams explored in the special section on international financial markets and banking systems crises. All topics tackled are related to the Great Recession. A brief overview of the research questions and related literatures is provided.
We provide with an optimal growth spatio-temporal setting with capital accumulation and diffusion across space in order to study the link between economic growth triggered by capital spatio-temporal dynamics and agglomeration across space. We choose the simplest production function generating growth endogenously, the AK technology but in sharp contrast to the related literature which considers homogeneous space, we derive optimal location outcomes for any given space distributions for technology (through the productivity parameter A) and population. Beside the mathematical tour de force, we ultimately show that agglomeration may show up in our optimal growth with linear technology, its exact shape depending on the interaction of two main effects, a population dilution effect versus a technology space discrepancy effect.