Poisson brackets, quasi-states and symplectic integrators

This paper is a fusion of a survey and a research article. We focus on certain rigidity phenomena in function spaces associated to a symplectic manifold. Our starting point is a lower bound obtained in an earlier paper with Zapolsky for the uniform norm of the Poisson bracket of a pair of functions in terms of symplectic quasi-states. After a short review of the theory of symplectic quasi-states, we extend this bound to the case of iterated Poisson brackets. A new technical ingredient is the use of symplectic integrators. In addition, we discuss some applications to symplectic approximation theory and present a number of open problems.Comment: 23 page

China's Changing Outbound Foreign Direct Investment Profile: Drivers and Policy Implications

After decades of negligible outbound foreign direct investment (FDI), Chinese firms' outbound investment has reached significant levels in recent years, challenging international investment norms and affecting international relations. But China's outflows are poorly understood. Seen in context, China is a laggard in global investment, and the country faces numerous internal impediments to overcoming this disadvantaged position. Daniel H. Rosen and Thilo Hanemann review the data behind China's growing outbound investment, consider the commercial and political forces driving this growth, and analyze both foreign and domestic obstacles for Chinese overseas investors. While extensive media coverage has provoked worries that Chinese firms are buying up the world, China remains a relatively minor global investor compared with OECD countries. China's net FDI position remains negative, with $5 of FDI assets under foreign ownership in China for every$1 of Chinese direct investment assets abroad. But China's efforts to rebalance its economic growth and make the shift toward higher value-added economic activity will increasingly force Chinese firms to invest abroad. Government policy has evolved in recent years to encourage and support China's firms to look abroad. Investment regimes in host countries are one obstacle to Chinese outbound FDI, but China's firms are even more impeded by home-made problems, including the parochial executive leadership and a dearth of key management skills needed to operate successfully overseas. Rosen and Hanemann argue that the growing volume and changing nature of China's outbound investment have important implications for policymakers in host countries. Host country governments must clarify their policies and draw a clearer line between legitimate national security reviews and protectionist economic competitiveness impulses disguised as security concerns. The lack of data transparency contributes to the poor understanding of China's outbound investment, and these inadequacies must be corrected if China and investment incumbents are to work together optimally. In addition, given its disadvantaged FDI starting position China should be expected to pull considerable weight to preserve and promote an open international investment environment, including by maintaining openness at home. If China converges upward to OECD outbound investment levels rather than incumbent leaders trimming down to historic Chinese levels due to protectionism, then future flows coming from China can contribute positively to a range of international issues, from financial crisis recovery to mitigating climate change.

Deepening China-Taiwan Relations through the Economic Cooperation Framework Agreement

On June 13, 2010, representatives from China and Taiwan held a third round of talks in Beijing on an Economic Cooperation Framework Agreement (ECFA) that would liberalize important aspects of cross-Strait economic relations. It is clear from available details that ECFA will be an ambitious accord that fundamentally changes the game between Taiwan and China and hence affects the regional economy and even the transpacific tempo for the United States. Rosen and Wang's economic projections of the effects of a China-Taiwan ECFA point to significant benefits of cross-Strait economic reform, especially for Taiwan, which would increase its 2020 GDP by about 4.5 percent, or $21 billion, from the current trend line. The authors, however, also conclude that the regional economy around China and Taiwan is not standing still but is extraordinarily dynamic. Other agreements in the region will be negotiated (e.g., ASEAN+3), which will impose costs on Taiwan, if it does not do an ECFA, to the tune of almost -0.8 percent of GDP. So the net effect of ECFA for Taiwan would be some 5.3 percent improvement in GDP by 2020. For China, the net results of ECFA are positive, though far less so than for Taiwan in value terms and of course as a share of GDP. For the United States, the authors project a very modest positive result from ECFA (though statistically marginal) but a more negative impact as the scenarios incorporating further Asian integration (ASEAN + 3) unfold. If the US objective is to maximize Taiwan's economic prospects and hence its freedom of independent action, then ECFA is highly desirable, and Taiwan's involvement in further Asian deepening is to be supported. However, US economic interests per se erode as Asia draws tighter together without US inclusion. That is an econometric reality. More significant still is the geoeconomic, qualitative implication of even long-standing nemeses China and Taiwan drawing together in a free trade pact while the United States watches, unable to ratify already negotiated Asian trade agreements like the US-Korea free trade agreement. While modest in global economic effects, the geoeconomic implications of a China-Taiwan economic pact are significant enough to demand strategic attention from the United States and underscore the importance of securing US economic engagement of the first order in Asia.

Promises, Promises: The States' Experience With Income Tax Indexing

The paper discusses five early approaches to the price (and quantity) index number problem. The five approaches are: (1) the fixed basket approach; (ii) the statistical approach; (iii) the test or axiomatic approach; (iv) the Divisia approach and (v) the economic approach. The economic approach makes use of the assumption of optimizing behavior under constraint and the approach is discussed under four subtopics: (i) basic theoretical definitions; (ii) the theory of bounds; (iii) exact index numbers and (iv) econometric estimation of preferences. The paper also discusses several topics raised by Jack Triplett in a recent paper, including: (i) the merits of the test approach to index number theory, (ii) the chain principle and alternatives to it; (iii) the substitution bias and (iv) the new good bias. Although the paper is for the most part an extensive historical survey, there are a few new results in section 8 on multilateral alternatives to the chain principle. Also in section 6.3, it is shown that the Paasche, Laspeyres and all superlative indexes will satisfy the circularity test to the first order.

State Personal Income and Sales Taxes: 1977-1983

The two main workhorses of state tax systems are levies on sales and individual incomes. In this paper we develop and implement a coherent methodology for characterizing these systems. The measures thus generated are used to show how the various systems differ across states, and how they evolved over the seven year period 1977-1983. We consider the systems' revenue elasticities with respect to income, average and marginal tax rates at various income levels, and several other issues as well.

The Deductibility of State and Local Taxes: Impact Effects by State and Income Class

This paper provides careful estimates of the impact of removing the deductibility of state and local taxes by state andby income class. We show how deductibility affects marginal and average tax rates for both state and federal tax systems. One striking result is that combined federal income tax and state tax burdens would generally fall under the President's tax reform proposal, even for high income people in high tax states.

Tax Structure and Public Sector Growth

It has been hypothesized that a jurisdiction's tax structure exerts an independent effect upon the growth of its public sector. We test this hypothesis by examining the relationship between the growth of state general expenditure and the elasticity of tax revenues with respect to income. The work takes advantage of a very careful set of income elasticities for the personal income and sales tax systems for each state, for every year from 1978 to 1983. The main conclusion is that the data do not support the notion that the form of the tax structure exerts an independent effect on public sector growth.

Recent Developments in the Marriage Tax

The new tax law increases tax rates of high income individuals, and expands the earned income tax credit for low income individuals. We use a sample of actual tax returns to compute estimates of the 'marriage tax' - the change in couples joint tax upon marriage - under this new law. We predict that in 1994 52 percent of American couples will pay a marriage tax, with an average of about $1,244; 38 percent will receive a subsidy averaging about$1,399. These aggregate figures mask a considerable amount of dispersion in the population. Under the new law, the marriage tax for certain low-income families can exceed $3,000 annually; for certain very high income families it can exceed$10,000 annually.