Boucekkine
Publications
Does drawing economic benefit from nature impinge on conservation? This has been a subject of controversy in the literature. The article presents a management method to overcome this possible dilemma, and reconcile conservation biology with economics. It is based on recent advances in the mathematical theory of dynamic systems under viability constraints. In the case of a onelocus twoallele plant coexisting with a onelocus twoallele parasite, the method provides a rule for deciding when and to what extent the resistant or the susceptible strain should be cultivated, in the uncertain timevarying presence of the parasite. This is useful for preventing the fixation of the susceptible allele  and thereby limiting the plant's vulnerability in the medium term, should the parasite reappear. The method thus provides an aid to decision for economic and ecologyfriendly profitability.
We solve a linearquadratic model of a spatiotemporal economy using a polluting oneinput technology. Space is continuous and heterogenous: locations differ in productivity, nature selfcleaning technology and environmental awareness. The unique link between locations is transboundary pollution which is modelled as a PDE diffusion equation. The spatiotemporal 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 closedform 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 lowyield capital to riskier highyield 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 twocountry model of intertemporal portfolio choices. By doing so, we put together the risk sharing effect and a welldefined 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.
We provide an optimal growth spatiotemporal setting with capital accumulation and diffusion across space to study the link between economic growth triggered by capital spatiotemporal dynamics and agglomeration across space. The technology is AK, K being broad capital. The social welfare function is Benthamite. In sharp contrast to the related literature, which considers homogeneous space, we derive optimal location outcomes for any given space distributions for technology and population. Both the transitional spatiotemporal dynamics and the asymptotic spatial distributions are computed in closed form. Concerning the latter, we find, among other results, that: (i) due to inequality aversion, the consumption per capital distribution is much flatter than the distribution of capital per capita; (ii) endogenous spillovers inherent in capital spatiotemporal dynamics occur as capital distribution is much less concentrated than the (prespecified) technological distribution; (iii) the distance to the center (or to the core) is an essential determinant of the shapes of the asymptotic distributions, that is relative location matters.
We consider an autocracy where the ruling elite control both the resource wealth and education policies. Education prompts economic growth and enriches the budget of the elite. However, education also increases the “awareness of citizens” – capturing their reluctance to accept a dictatorship and their labor market aspirations – and forces the elite to expand redistribution or handover the power. A power handover leads to a more democratic regime, where the elite retains (at least partially) its economic power. This tradeoff is the backbone of our Lipsetian theory of voluntary power handover. This theory provides new insights on the positive relationship between economic development, education, and democratization, and on the negative relationship between inequality and democratization. Finally, we revisit the resourcescurse hypothesis within our setting.
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 openeconomy AK model in which the capitaldeepening 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—longrun gain—arise in our preferred model without investment commitment and they range, relative to autarky, from about 2% in middleincome countries to about 13% in OECDtype countries under international financial integration. Sizeable benefits emerge despite the fact that consumption initially falls—shortrun 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 resourcerich 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.
In this paper, we consider an abstract optimal control problem with state constraint. The methodology relies on the employment of the classical dynamic programming tool considered in the infinite dimensional context. We are able to identify a closedform solution to the induced HamiltonJacobiBellman (HJB) equation in infinite dimension and to prove a verification theorem, also providing the optimal control in closed loop form. The abstract problem can be seen an abstract formulation of a PDE optimal control problem and is motivated by an economic application in the context of continuous spatiotemporal growth models with capital di usion, where a social planner chooses the optimal location of economic activity across space by maximization of an utilitarian social welfare function. From the economic point of view, we generalize previous works by considering a continuum of social welfare functions ranging from Benthamite to Millian functions. We prove that the Benthamite case is the unique case for which the optimal stationary detrended consumption spatial distribution is uniform. Interestingly enough, we also find that as the social welfare function gets closer to the Millian case, the optimal spatiotemporal dynamics amplify the typical neoclassical dilution population size effect, even in the longrun.
We study the joint determination of optimal investment and optimal depollution in a spatiotemporal framework where pollution is transboundary. Pollution is controlled at a global level. The regulator internalizes that: (i) production generates pollution, which is bad for the wellbeing of population, and that (ii) pollution flows across space driven by a diffusion process. We solve analytically for the optimal investment and depollution spatiotemporal paths and characterize the optimal longterm spatial distribution when relevant. We finally explore numerically the variety of optimal spatial distributions obtained using a core/periphery model where the core differs from the periphery either in terms of input productivity, depollution efficiency, environmental awareness or selfcleaning capacity of nature. We also compare the distributions with and without diffusion. Key aspects in the optimal policy of the regulator are the role of aversion to inequality, notably leading to smoothing consumption across locations, and the control of diffusive pollution adding another smoothing engine.
In this paper, we tackle a generic optimal regime switching problem where the decision making process is not the same from a regime to another. Precisely, we consider a simple model of optimal switching from competition to cooperation. To this end, we solve a two stage optimal control problem. In the first stage, two players engage in a dynamic game with a common state variable and one control for each player. We solve for openloop strategies with a linear state equation and linearquadratic payoffs. More importantly, the players may also consider the possibility to switch at finite time to a cooperative regime with the associated joint optimization of the sum of the individual payoffs. Using the oretical analysis and numerical exercises, we study the optimal switching strategy from competition to cooperation. We also discuss the reverse switching.