Miles et al. [1] recently produced an analysis of the costs and benefits of lockdown policies in the face of COVID-19, focussing on the case of the U.K. They argue that the March- June UK lockdown was more costly than the benefit of lives saved, if the latter are evaluated using the NICE threshold of {\pounds}30000 for a quality-adjusted life year (QALY). Looking forwards, they argue that the costs of a lockdown for 13 weeks from mid-June would be vastly greater than the benefits under any plausible QALY costing, even in a scenario in which easing lockdown led to a second infection wave that caused more than 7000 deaths a week by mid-September.

I note here two key problems that certainly significantly affect their estimates and cast doubt on their conclusions. Firstly, they cut off their calculations arbitrarily after 13 weeks, without costing the epidemic state at the end of the period. That is, they assume that we should be indifferent between mid-September states of 13 deaths a week and 7500 deaths a week, and corresponding infection rates. This seems indefensible unless one assumes that (a) there is only a small chance of any future vaccine and no future improvements in treatment or in non-medical interventions, (b) that COVID-19 will inevitably continue to propagate until herd immunity is reached. Even under these assumptions it is very questionable. Secondly, they ignore the costs of serious illness, possible long-term lowering of life quality, and possible lowering of life expectancy for COVID-19 survivors. These are uncertain, but clearly not negligible, and plausibly comparable to or larger than the costs in lives lost.

This paper presents the way in which can be determined the exchange rates that simultaneously balance the trade balances of all countries that trade with each other within a common market. A mathematical synthesis between the theory of comparative advantages of Ricardo and Mill and the New Theory on International Trade of Paul Krugman is also presented in this paper. This mathematical synthesis shows that these theories are complementary. Also presented in this paper is a proposal to organize a common market of the American hemisphere. This economic alliance would allow to establish a political alliance for the common defense of the entire American hemisphere. The formula we developed in this paper to determine the exchange rates of the countries solves the problem that Mexico, Canada, Europe, Japan and China currently experience with the United States in relation to the deficits and surpluses in the trade balance of the countries and their consequent impediment so that stable growth of international trade can be achieved.

Regional quarantine policies, in which a portion of a population surrounding infections are locked down, are an important tool to contain disease. However, jurisdictional governments - such as cities, counties, states, and countries - act with minimal coordination across borders. We show that a regional quarantine policy's effectiveness depends upon whether (i) the network of interactions satisfies a balanced-growth condition, (ii) infections have a short delay in detection, and (iii) the government has control over and knowledge of the necessary parts of the network (no leakage of behaviors). As these conditions generally fail to be satisfied, especially when interactions cross borders, we show that substantial improvements are possible if governments are proactive: triggering quarantines in reaction to neighbors' infection rates, in some cases even before infections are detected internally. We also show that even a few lax governments - those that wait for nontrivial internal infection rates before quarantining - impose substantial costs on the whole system. Our results illustrate the importance of understanding contagion across policy borders and offer a starting point in designing proactive policies for decentralized jurisdictions.

Topological data analysis has been acknowledged as one of the most successful mathematical data analytic methodologies in various fields including medicine, genetics, and image analysis. In this paper, we explore the potential of this methodology in finance by applying persistence landscape and dynamic time series analysis to analyze an extreme event in the stock market, known as Flash Crash. We will provide results of our empirical investigation to confirm the effectiveness of our new method not only for the characterization of this extreme event but also for its prediction purposes.

Global ballast water management regulations aiming to decrease aquatic species invasion require actions that can increase shipping costs. We employ an integrated shipping cost and global economic modeling approach to investigate the impacts of ballast water regulations on bilateral trade, national economies, and shipping patterns. Given the potential need for more stringent regulation at regional hotspots of species invasions, this work considers two ballast water treatment policy scenarios: implementation of current international regulations, and a possible stricter regional regulation that targets ships traveling to and from the United States while other vessels continue to face current standards. We find that ballast water management compliance costs under both scenarios lead to modest negative impacts on international trade and national economies overall. However, stricter regulations applied to U.S. ports are expected to have large negative impacts on bilateral trade of several specific commodities for a few countries. Trade diversion causes decreased U.S. imports of some products, leading to minor economic welfare losses.

Skill shortages are a drain on society. They hamper economic opportunities for individuals, slow growth for firms, and impede labor productivity in aggregate. Therefore, the ability to understand and predict skill shortages in advance is critical for policy-makers and educators to help alleviate their adverse effects. This research implements a high-performing Machine Learning approach to predict occupational skill shortages. In addition, we demonstrate methods to analyze the underlying skill demands of occupations in shortage and the most important features for predicting skill shortages. For this work, we compile a unique dataset of both Labor Demand and Labor Supply occupational data in Australia from 2012 to 2018. This includes data from 7.7 million job advertisements (ads) and 20 official labor force measures. We use these data as explanatory variables and leverage the XGBoost classifier to predict yearly skills shortage classifications for 132 standardized occupations. The models we construct achieve macro-F1 average performance scores of up to 83 per cent. Our results show that job ads data and employment statistics were the highest performing feature sets for predicting year-to-year skills shortage changes for occupations. We also find that features such as 'Hours Worked', years of 'Education', years of 'Experience', and median 'Salary' are highly important features for predicting occupational skill shortages. This research provides a robust data-driven approach for predicting and analyzing skill shortages, which can assist policy-makers, educators, and businesses to prepare for the future of work.

Many Stated Preference studies conducted in developing countries provide a low willingness to pay (WTP) for a wide range of goods and services. However, recent studies in these countries indicate that this may partly be a result of the choice of payment vehicle, not the preference for the good. Thus, low WTP may not indicate a low welfare effect for public projects in developing countries. We argue that in a setting where 1) there is imperfect substitutability between money and other measures of wealth (e.g. labor), and 2) institutions are perceived to be corrupt, including payment vehicles that are currently available to the individual and less pron to corruption may be needed to obtain valid welfare estimates. Otherwise, we risk underestimating the welfare benefit of projects. We demonstrate this through a rural household contingent valuation (CV) survey designed to elicit the value of access to reliable irrigation water in Ethiopia. Of the total average annual WTP for access to reliable irrigation service, cash contribution comprises only 24.41 %. The implication is that socially desirable projects might be rejected based on cost-benefit analysis as a result of welfare gain underestimation due to mismatch of payment vehicles choice in valuation study.

The paper introduces a simple way of recording and manipulating general stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no jumps are physically present). The calculus is fail-safe in that, under minimal assumptions, all informal calculations yield mathematically well-defined stochastic processes. The calculus is also intuitive as it allows the user to pretend all jumps are of compound Poisson type. The new calculus is very effective when it comes to computing drifts and expected values that possibly involve a change of measure. Such drift calculations yield, for example, partial integro-differential equations, Hamilton-Jacobi-Bellman equations, Feynman-Kac formulae, or exponential moments needed in numerous applications. We provide several illustrations of the new technique, among them a novel result on the Margrabe option to exchange one defaultable asset for another.

Today's consumer goods markets are rapidly evolving with significant growth in the number of information media as well as the number of competitive products. In this environment, obtaining a quantitative grasp of heterogeneous interactions of firms and customers, which have attracted interest of management scientists and economists, requires the analysis of extremely high-dimensional data. Existing approaches in quantitative research could not handle such data without any reliable prior knowledge nor strong assumptions. Alternatively, we propose a novel method called complex Hilbert principal component analysis (CHPCA) and construct a synchronization network using Hodge decomposition. CHPCA enables us to extract significant comovements with a time lead/delay in the data, and Hodge decomposition is useful for identifying the time-structure of correlations. We apply this method to the Japanese beer market data and reveal comovement of variables related to the consumer choice process across multiple products. Furthermore, we find remarkable customer heterogeneity by calculating the coordinates of each customer in the space derived from the results of CHPCA. Lastly, we discuss the policy and managerial implications, limitations, and further development of the proposed method.