In this paper we introduce a definition of approximate Pareto efficient solution as well as a necessary condition for such solutions in the multiobjective setting on Riemannian manifolds. We also propose an inexact proximal point method for nonsmooth multiobjective optimization in the Riemannian context by using the notion of approximate solution. The main convergence result ensures that each cluster point (if any) of any sequence generated by the method is a Pareto critical point. Furthermore, when the problem is convex on a Hadamard manifold, full convergence of the method for a weak Pareto efficient solution is obtained. As an application, we show how a Pareto critical point can be reached as a limit of traps in the context of the variational rationality approach of stay and change human dynamics.
Using a Markov-perfect equilibrium model, we show that the use of customer data to practice intertemporal price discrimination will improve monopoly profit if and only if information precision is higher than a certain threshold level. This U-shaped relationship lends support to a popular view that knowledge is good only if it is sufficiently refined. When information accuracy can only be achieved through costly investment, we find that investing in profiling is profitable only if this allows to reach a high enough level of information precision. Consumers expected surplus being a hump-shaped function of information accuracy, we show that consumers have an incentive to lobby for privacy protection legislation which raises the cost of monopoly's investment in information accuracy. However, this cost should not dissuade firms to collect some information on customers' tastes, as the absence of consumers' profiling is actually detrimental to consumers.
We present an inexact proximal point algorithm using quasi distances to solve a minimization problem in the Euclidean space. This algorithm is motivated by the proximal methods introduced by Attouch et al., section 4, (Math Program Ser A, 137: 91–129, 2013) and Solodov and Svaiter (Set Valued Anal 7:323–345, 1999). In contrast, in this paper we consider quasi distances, arbitrary (non necessary smooth) objective functions, scalar errors in each objective regularized approximation and vectorial errors on the residual of the regularized critical point, that is, we have an error on the optimality condition of the proximal subproblem at the new point. We obtain, under a coercivity assumption of the objective function, that all accumulation points of the sequence generated by the algorithm are critical points (minimizer points in the convex case) of the minimization problem. As an application we consider a human location problem: How to travel around the world and prepare the trip of a lifetime.
In this paper, we develop an overlapping generations model with endogenous fertility and calibrate it to the Swedish historical data in order to estimate the economic cost of the 1918–19 influenza pandemic. The model identifies survivors from younger cohorts as main benefactors of the windfall bequests following the influenza mortality shock. We also show that the general equilibrium effects of the pandemic reveal themselves over the wage channel rather than the interest rate, fertility or labor supply channels. Finally, we demonstrate that the influenza mortality shock becomes persistent, driving the aggregate variables to lower steady states which costs the economy 1.819% of the output loss over the next century.
We investigate whether and how an individual giving decision is affected in risky environments in which the recipient’s wealth is random. We demonstrate that, under risk neutrality, the donation of dictators with a purely ex post view of fairness should, in general, be affected by the riskiness of the recipient’s payoff, while dictators with a purely ex ante view should not be. Furthermore, we observe that some influential inequality aversion preferences functions yield opposite predictions when we consider ex post view of fairness. Hence, we report on dictator games laboratory experiments in which the recipient’s wealth is exposed to an actuarially neutral and additive background risk. Our experimental data show no statistically significant impact of the recipient’s risk exposure on dictators’ giving decisions. This result appears robust to both the experimental design (within subjects or between subjects) and the origin of the recipient’s risk exposure (chosen by the recipient or imposed on the recipient). Although we cannot sharply validate or invalidate alternative fairness theories, the whole pattern of our experimental data can be simply explained by assuming ex ante view of fairness and risk neutrality.
Top incomes are often related to Pareto distribution. To date, economists have mostly used Pareto Type I distribution to model the upper tail of income and wealth distribution. It is a parametric distribution, with interesting properties, that can be easily linked to economic theory. In this paper, we first show that modeling top incomes with Pareto Type I distribution can lead to biased estimation of inequality, even with millions of observations. Then, we show that the Generalized Pareto distribution and, even more, the Extended Pareto distribution, are much less sensitive to the choice of the threshold. Thus, they can provide more reliable results. We discuss different types of bias that could be encountered in empirical studies and, we provide some guidance for practice. To illustrate, two applications are investigated, on the distribution of income in South Africa in 2012 and on the distribution of wealth in the United States in 2013.
The objective of this paper is to emphasize the differences between a call and a warrant as well as the different valuation methods of warrants which have been introduced in the financial literature. For the sake of simplicity and applicability, we only consider a debt-free equity-financed firm. More recently a formal distinction between structural and reduced form pricing models has been introduced. This distinction is important whether one wishes to price a new warrant issue or outstanding warrants. If we are interested in pricing a new issue of warrants, e.g. in the context of a management incentive package, one has to rely on a structural model. However most of practitioners use the simple Black-Scholes formula. In this context, we analyze the accuracy of the approximation of the “true” price of a warrant by the Black-Scholes formula. We show that in the current low interest rate environment, the quality of the approximation deteriorates and the sensitivity of this approximation to the volatility estimate increases.
Although the Covid-19 crisis has shown how high-frequency data can help track the economy in real time, we investigate whether it can improve the nowcasting accuracy of world GDP growth. To this end, we build a large dataset of 718 monthly and 255 weekly series. Our approach builds on a Factor-Augmented MIxed DAta Sampling (FA-MIDAS), which we extend with a preselection of variables. We find that this preselection markedly enhances performances. This approach also outperforms a LASSO-MIDAS—another technique for dimension reduction in a mixed-frequency setting. Though we find that a FA-MIDAS with weekly data outperform other models relying on monthly or quarterly data, we also point to asymmetries. Models with weekly data have indeed performances similar to other models during “normal” times but can strongly outperform them during “crisis” episodes, above all the Covid-19 period. Finally, we build a nowcasting model for world GDP annual growth incorporating weekly data that give timely (one per week) and accurate forecasts (close to IMF and OECD projections but with 1- to 3-month lead). Policy-wise, this can provide an alternative benchmark for world GDP growth during crisis episodes when sudden swings in the economy make usual benchmark projections (IMF's or OECD's) quickly outdated.
We test the effectiveness of a social comparison nudge to enhance lockdown compliance during the Covid-19 pandemic, using a French representative sample (N=1154). Respondents were randomly assigned to a favourable/unfavourable informational feedback (daily road traffic mobility patterns, in Normandy - a region of France) on peer lockdown compliance. Our dependent variable was the intention to comply with a possible future lockdown. We controlled for risk, time, and social preferences and tested the effectiveness of the nudge. We found no evidence of the effectiveness of the social comparison nudge among the whole French population, but the nudge was effective when its recipient and the reference population shared the same geographical location (Normandy). Exploratory results on this subsample (N=52) suggest that this effectiveness could be driven by noncooperative individuals.
Canada exhibits no correlation between income and victimization, rich neighborhoods are less exposed to property crime, rich households are more victimized than their neighbors, and rich households and neighborhoods invest more in protection. We provide a theory consistent with these facts. Criminals within city choose a neighborhood and pay a search cost to compare potential victims, whereas households invest in self-protection. As criminals' return to search increases with neighborhood income, households in rich neighborhoods are likelier to enter a race to greater protection driving criminals toward poorer areas. A calibration reproduces the Canadian victimization and protection pattern by household/neighborhood income.