Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes

We study energy functionals obtained by adding a possibly discontinuous potential to an interaction term modeled upon a Gagliardo-type fractional seminorm. We prove that minimizers of such non-differentiable functionals are locally bounded, H\"older continuous, and that they satisfy a suitable Harnack inequality. Hence, we provide an extension of celebrated results of M. Giaquinta and E. Giusti to the nonlocal setting. To do this, we introduce a particular class of fractional Sobolev functions, reminiscent of that considered by E. De Giorgi in his seminal paper of 1957. The flexibility of these classes allows us to also establish regularity of solutions to rather general nonlinear integral equations.Comment: 59 page

“When You’re A Long, Long Way From Home”: The Establishment of Canadian-Only Social Clubs for CEF Soldiers in London, 1915–1919

This article examines the off–duty activities of Canadian Expeditionary Force (CEF) soldiers in Britain during the First World War. For many CEF soldiers abroad, Britain became their “home away from home,” with London serving as their main leave–time destination. Although thousands of CEF soldiers visited the English capital, Canadian federal and military authorities maintained a hands–off approach to the off–duty lives of the men. Fearing for the men’s well–being, Canadian philanthropist, Lady Julia Drummond, established the Canadian–only King George and Queen Mary Maple Leaf Club. Founded upon middle– and upper–class moral standards the Maple Leaf Club emphasizes the role of public patriotism at the time, while also highlighting a rising sense of Canadian nationalism and self–awareness at the time of simultaneous loyalty to the empire

Can Social Norms Affect the International Allocation of Innovation?

If economic agents coordinate on social norms more oriented towards the protection of national industries, an asymmetric international specialization in the research and development (R&D) arises even in a tariff free world with no a priori differences across countries in endowments, demography or technology. This paper exploits the indifference in the composition of R&D expenditure across sectors of the typical multi-sector Schumpeterian framework (forward-looking decisions, CRS R&D technology and free entry) to construct a theory of the international allocation of innovation and education based on sunspot equilibrium. A role for industrial policies as mere coordination devices emerges in an international Schumpeterian framework. The implications for the relationships between inequality and growth are examined.Schumpeterian Growth Theory, Inequality, International Trade, Social Norms, Indeterminacy, Sunspots.

Why the Rich Should Like R&D Less

It is well known that research and development (R&D) is an important engine for economic growth. Also, initial wealth inequality and subsequent economic growth are well known to be related. This paper links inequality and R&D-driven growth. It shows that in a class of economies where R&D is the main engine for growth, different wealth groups differ in their desire for aggregate innovative efforts: the higher the profit share of the individual's incomes the lower their ideal aggregate R&D and innovation. If rich shareholders were able to pursue their common interest and to discourage too much R&D compared, then a pro-labour government able to impose distortionary progressive taxation, by minimizing the difference between the rich and the poor can maximize growth. Such predicted negative relationship between desired R&D and dynastic wealth is robust to any subsidy rate lower than 100%R&D and Growth; Social Preferences for Innovation; Inequality, Redistribution and Growth.

Could Employment-Focused Policies Spearhead Economic Recovery in Europe?

In Development Viewpoint #66 we assessed the performance of two contrasting strategies for debt reduction in the US: a ‘fiscal-contraction’ versus a ‘fiscal-expansion’ approach. In this Policy Brief we apply a similar ‘fiscal-expansion’ approach to economic recovery in Europe, focusing here on the need, first and foremost, to foster rapid growth in employment. Employment generation should be a high priority for European policymakers, particularly because of secular declines in the size of the working-age population across the continent. Moreover, unemployment levels (especially among young workers) are unbearably high in many countries in the aftermath of the global financial crisis. So getting people back to work represents, indeed, one of the best strategies for debt reduction currently available. As in past exercises, we use the State of the World Economy global macroeconomic model to gauge the impact of such a strategy. In this case, we construct a model scenario that programs changes in macroeconomic policies that are designed to stimulate an employment-focused economic recovery in Europe (as well as in the US). We then compare this scenario’s results with those of a ‘baseline’ scenario (based on no change in policies). We are not interested in gauging short-term impacts alone so we extend our assessment through 2030. We present our results for blocs of countries (except for the UK and the US) because data in the model are aggregated in this fashion. We start with the policy lever that has the most immediate potential to stimulate Europe’s economies—i.e., an increase in government expenditures. We also assume that these expenditures will help promote private investment. For example, they could be public investments in infrastructure, skills training or new cutting-edge technology. In order to reinforce the desired increase in private investment, we also assume a modest stimulus to bank lending. Both public expenditures and private investment are marshalled to target an increase in employment, not economic growth alone. This target is based on the ratio of the number of employed to the number of people of working age. We calibrate the size of the stimulus in order to achieve a desirable, but also feasible, level of this ratio for each European bloc

Equilibrium Heterogeneous-Agent Models as Measurement Tools: some Monte Carlo Evidence

This paper discusses a series of Monte Carlo experiments designed to evaluate the empirical properties of heterogeneous-agent macroeconomic models in the presence of sampling variability. The calibration procedure leads to the welfare analysis being conducted with the wrong parameters. The ability of the calibrated model to correctly predict the long-run welfare changes induced by a set of policy experiments is assessed. The results show that, for the policy reforms with sizable welfare effects (i.e., more than 0.2%), the model always predict the right sign of the welfare effects. However, the welfare effects can be evaluated with the wrong sign, when they are small and when the sample size is fairly limited. Quantitatively, the maximum errors made in evaluating a policy change are very small for some reforms (in the order of 0.02 percentage points), but bigger for others (in the order of 0.6 p.p.). Finally, having access to better data, in terms of larger samples, does lead to substantial increases in the precision of the welfare effects estimates, though the rate of convergence can be slow.Ex-ante Policy Evaluation, Incomplete Markets, Heterogeneous Agents, Monte Carlo, Welfare

Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium

We consider a non-local phase transition equation set in a periodic medium and we construct solutions whose interface stays in a slab of prescribed direction and universal width. The solutions constructed also enjoy a local minimality property with respect to a suitable non-local energy functional

Incompressible Euler Equations and the Effect of Changes at a Distance

Because pressure is determined globally for the incompressible Euler equations, a localized change to the initial velocity will have an immediate effect throughout space. For solutions to be physically meaningful, one would expect such effects to decrease with distance from the localized change, giving the solutions a type of stability. Indeed, this is the case for solutions having spatial decay, as can be easily shown. We consider the more difficult case of solutions lacking spatial decay, and show that such stability still holds, albeit in a somewhat weaker form.Comment: Revised statement of Theorem 1 to include a missing definitio