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 closed-form solution to the induced Hamilton-Jacobi-Bellman (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 long-run.
This paper analyzes the behavior of cross-country growth rates with respect to resource abundance and dependence. We reject the linear model that is commonly-used in growth regressions in favor of a multiple-regime alternative. Using a formal sample-splitting method, we find that countries exhibit different behaviors with respect to natural resources depending on their initial level of development. In high-income countries, natural resources play only a minor role in explaining the differences in national growth rates. On the contrary, in low-income countries abundance seems to be a blessing but dependence restricts growth.
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 long-term 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 self-cleaning 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 open-loop strategies with a linear state equation and linear-quadratic 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.
Disparities in physicians' geographical distribution lead to highly unequal access to healthcare, which may impact quality of care in both high and low-income countries. This paper uses a 2013-2014 nationally representative survey of French general practitioners (GPs) matched with corresponding administrative data to analyze the effects of practicing in an area with weaker medical density. To avoid the endogeneity issue on physicians' choice of the location, we enriched our variable of interest, practicing in a relatively underserved area, with considering changes in medical density between 2007 and 2013, thus isolating GPs who only recently experienced a density decline (identifying assumption). We find that GPs practicing in underserved areas do shorter consultations and tend to substitute time-consuming procedures with alternatives requiring fewer human resources, especially for pain management. Results are robust to considering only GPs newly exposed to low medical density. Findings suggest a significant impact of supply-side shortages on the mix of healthcare services used to treat patients, and point to a plausible increased use of painkillers, opioids in particular.
I develop a model of activism and polarization in the context of electoral competition. Two candidates simultaneously announce policy platforms and seek the support of ideologically inclined activists. Activists compete to influence electoral outcomes by expending costly support for their respective candidates. The presence of activists always moderates the platform choice of candidates, compared to the case of no activism. The central finding of the paper is that the relationship between partisanship of activists and polarization isambiguous. As activists become increasingly partisan, polarization of candidate platforms reduces or widens depending on the costs of activism. I present normative conditions under which the presence of activism and increased partisanship among activists are both welfare-improving for voters. Finally, introducing a public funding option for candidates increases polarization in the political process.
This paper discusses the theoretical choice of exchange rate regimes in Sub-Saharan African countries that are facing external vulnerabilities. To reduce instability, policymakers choose among promoting external competitiveness using a real anchor, lowering the burden of foreign debt using a nominal anchor or using a policy mix of both anchors. We observe that these countries tend to adopt mixed anchor policies. We solve a state space model to explain the determinants of and the strategy behind this policy. We find that the mixed targeting policy is a two-step strategy: First, monetary authorities choose the degree of nominal exchange rate flexibility according to the velocity of money, trade openness, foreign debt, degree of exchange rate pass-through and exchange rate target zone. Second, authorities seek to stabilize the real exchange rate depending on the degree of competition in the domestic goods market and the degree of foreign exchange intervention. We conclude with regime-switching estimations to provide empirical evidence of how these economic fundamentals influence exchange rate policy in Sub-Saharan Africa.
We consider an overlapping generations economy in which agents differ through their ability to procreate. Ex-ante infertile households may incur health expenditure to increase their chances of parenthood. This health heterogeneity generates welfare inequalities that deserve to be ruled out. We explore three different criteria of social evaluation in the long-run: the utilitarian approach, the ex-ante egalitarian criterion and the ex-post egalitarian one. We propose a set of economic instruments to decentralize each solution. To correct for the externalities and health inequalities, both a preventive (a taxation of capital) and a redistributive policy are required. We show that a more egalitarian allocation is associated with higher productive investment but reduced health expenditure and thus, lower population growth.
There is an urgent need to measure the impacts of COVID-19 among gay men and other men who have sex with men (MSM). We conducted a cross-sectional survey with a global sample of gay men and other MSM (n = 2732) from April 16, 2020 to May 4, 2020, through a social networking app. We characterized the economic, mental health, HIV prevention and HIV treatment impacts of COVID-19 and the COVID-19 response, and examined whether sub-groups of our study population are disproportionately impacted by COVID-19. Many gay men and other MSM not only reported economic and mental health consequences, but also interruptions to HIV prevention and testing, and HIV care and treatment services. These consequences were significantly greater among people living with HIV, racial/ethnic minorities, immigrants, sex workers, and socio-economically disadvantaged groups. These findings highlight the urgent need to mitigate the negative impacts of COVID-19 among gay men and other MSM.
City size distributions are not strictly Pareto, but upper tails are rather Pareto like (i.e. tails are regularly varying). We examine the properties of the tail exponent estimator obtained from ordinary least squares (OLS) rank size regressions (Zipf regressions for short), the most popular empirical strategy among urban economists. The estimator is then biased towards Zipf's law in the leading class of distributions. The Pareto quantile-quantile plot is shown to offer a simple diagnostic device to detect such distortions and should be used in conjunction with the regression residuals to select the anchor point of the OLS regression in a data-dependent manner. Applying these updated methods to some well-known data sets for the largest cities, Zipf's law is now rejected in several cases.