Selective Categories and Linear Canonical Relations

A construction of Wehrheim and Woodward circumvents the problem that compositions of smooth canonical relations are not always smooth, building a category suitable for functorial quantization. To apply their construction to more examples, we introduce a notion of highly selective category, in which only certain morphisms and certain pairs of these morphisms are "good". We then apply this notion to the category $\mathbf{SLREL}$ of linear canonical relations and the result ${\rm WW}(\mathbf{SLREL})$ of our version of the WW construction, identifying the morphisms in the latter with pairs $(L,k)$ consisting of a linear canonical relation and a nonnegative integer. We put a topology on this category of indexed linear canonical relations for which composition is continuous, unlike the composition in $\mathbf{SLREL}$ itself. Subsequent papers will consider this category from the viewpoint of derived geometry and will concern quantum counterparts

Exporting deflation? Chinese exports and Japanese prices

Between 1992 and 2002, the Japanese Import Price Index (IPI) registered a decline of almost 9 percent and Japan entered a period of deflation. We show that much of the correlation between import prices and domestic prices was due to formula biases. Had the IPI been computed using a pure Laspeyres index like the CPI, the IPI would have hardly moved at all. A Laspeyres version of the IPI would have risen 1 percentage point per year faster than the official index. Second we show that Chinese prices did not behave differently from the prices of other importers. Although Chinese prices are substantially lower than the prices of other exporters, they do not exhibit a differential trend. However, we estimate that the typical price per unit quality of a Chinese exporter fell by half between 1992 and 2005. Thus the explosive growth in Chinese exports is attributable to growth in the quality of Chinese exports and the increase in new products being exported by China.

Defining Price Stability in Japan: A View from America

Japanese monetary and fiscal policy uses the consumer price index (CPI) as a metric for price stability. Despite a major effort to improve the index, the Japanese methodology of calculating the CPI seems to have a large number of deficiencies. Little attention is paid in Japan to substitution biases and quality upgrading. This implies that important methodological differences have emerged between the United States and Japan since the former started to correct for these biases in 1999. We estimate that using the new corrected U.S. methodology, Japanfs deflation averaged 1.2 percent per year since 1999. This is more than twice the deflation suggested by Japanese national statistics. Ignoring these methodological differences is misleading, because it would suggest that U.S. real per capita consumption growth has been growing at a rate that is almost 2 percentage points higher than that of Japan between 1999 and 2006. When a common methodology is used, Japanfs growth has been much closer to that of the United States over this period. Moreover, we estimate that the bias of the Japanese CPI relative to a true cost-of- living index is around 2 percent per year. This overstatement in the Japanese CPI in combination with Japanfs low inflation rate is likely to cost the government more than \69 trillion?or 14 percent of GDP?over the next 10 years in increased Social Security transfers and debt service. For monetary policy, the overstatement of inflation suggests that if the BOJ adopts a formal inflation target without changing the current CPI methodology, a lower band of less than 1.8 percent would not achieve its goal of price stability.Inflation; Consumer price index bias; Monetary policy

GLOBALIZATION AND THE GAINS FROM VARIETY

Since the seminal work of Krugman (1979), product variety has played a central role in models of trade and growth. In spite of the general use of love-of-variety models, there has been no systematic study of how the import of new varieties has contributed to national welfare gains in the United States. In this paper we show that the unmeasured growth in product variety from US imports has been an important source of gains from trade over the last three decades (1972-2001). Using extremely disaggregated data, we show that the number of imported product varieties has increased by a factor of four. We also estimate the elasticities of substitution for each available category at the same level of aggregation, and describe their behavior across time and SITC-5 industries. Using these estimates we develop an exact price index and find that the upward bias in the conventional import price index is approximately 1.2 percent per year. The magnitude of this bias suggests that the welfare gains from variety growth in imports alone are 2.8 percent of GDPGains from trade, Love-of-variety models, US Trade, Elasticities of Substitution.

The bottleneck degree of algebraic varieties

A bottleneck of a smooth algebraic variety $X \subset \mathbb{C}^n$ is a pair of distinct points $(x,y) \in X$ such that the Euclidean normal spaces at $x$ and $y$ contain the line spanned by $x$ and $y$. The narrowness of bottlenecks is a fundamental complexity measure in the algebraic geometry of data. In this paper we study the number of bottlenecks of affine and projective varieties, which we call the bottleneck degree. The bottleneck degree is a measure of the complexity of computing all bottlenecks of an algebraic variety, using for example numerical homotopy methods. We show that the bottleneck degree is a function of classical invariants such as Chern classes and polar classes. We give the formula explicitly in low dimension and provide an algorithm to compute it in the general case.Comment: Major revision. New introduction. Added some new illustrative lemmas and figures. Added pseudocode for the algorithm to compute bottleneck degree. Fixed some typo

Product Creation and Destruction: Evidence and Price Implications

This paper describes the extent and cyclicality of product creation and destruction in a large sector of the U.S. economy and quantifies its implications for the measurement of consumer prices. We find four times more entry and exit in product markets than is typically found in labor markets because most product turnover happens within the boundaries of the firm. Net product creation is strongly pro-cyclical, but contrary to the behavior of labor flows, it is primarily driven by creation rather than destruction. High rates of innovation are also accompanied by substantial price volatility of products. These facts suggest that the CPI deviates from a true cost-of-living index in three important dimensions. The quality bias that arises as new goods replace outdated ones causes the CPI to overstate inflation by 0.8 percent per year; the cyclicality of the bias implies that business cycles are more volatile than indicated by official statistics; and finally, sampling error is sufficiently large that over the last 10 years policymakers could not statistically distinguish whether quarterly inflation was accelerating or decelerating 65 percent of the time.

Defining Price Stability in Japan: A View from America

Japanese monetary and fiscal policy uses the consumer price index as a metric for price stability. Despite a major effort to improve the index, the Japanese methodology of calculating the CPI seems to have a large number of deficiencies. Little attention is paid in Japan to substitution biases and quality upgrading. This implies that important methodological differences have emerged between the U.S. and Japan since the U.S. started to correct for these biases in 1999. We estimate that using the new corrected U.S. methodology, Japan's deflation averaged 1.2 percent per year since 1999. This is more than twice the deflation suggested by Japanese national statistics. Ignoring these methodological differences misleading suggests that American real per capita consumption growth has been growing at a rate that is almost 2 percentage points higher than that of Japan between 1999 and 2006. When a common methodology is used Japan's growth has been much closer to that of the U.S. over this period. Moreover, we estimate that the bias of the Japanese CPI relative to a true cost-of-living index is around 2 percent per year. This overstatement in the Japanese CPI in combination with Japan's low inflation rate is likely to cost the government over 69 trillion yen -- or 14 percent of GDP -- over the next 10 years in increased social security expenses and debt service. For monetary policy, the overstatement of inflation suggests that if the BOJ adopts a formal inflation target without changing the current CPI methodology a lower band of less than 2 percent would not achieve its goal of price stability.

Globalization and the Gains from Variety

Since the seminal work of Krugman (1979), product variety has played a central role in models of trade and growth. In spite of the general use of love-of-variety models, there has been no systematic study of how the import of new varieties has contributed to national welfare gains in the United States. In this paper we show that the unmeasured growth in product variety from US imports has been an important source of gains from trade over the last three decades (1972-2001). Using extremely disaggregated data, we show that the number of imported product varieties has increased by a factor of four. We also estimate the elasticities of substitution for each available category at the same level of aggregation, and describe their behavior across time and SITC-5 industries. Using these estimates we develop an exact price index and find that the upward bias in the conventional import price index is approximately 1.2 percent per year. The magnitude of this bias suggests that the welfare gains from variety growth in imports alone are 2.8 percent of GDP.

What Role for Empirics in International Trade?

In the field of international trade, data analysis has traditionally had quite modest influence relative to that of pure theory. At one time, this might have been rationalized by the paucity of empirics in the field or its weak theoretical foundations. In recent years empirical research has begun to provide an increasingly detailed view of the determinants of trade relations. Yet the field as a whole has been slow to incorporate these findings in its fundamental worldview. In this paper, we outline and extend what we view as key robust findings from the empirical literature that should be part of every international economists working knowledge.

Technological Superiority and the Losses from Migration

Two facts motivate this study. (1) The United States is the world's most productive economy. (2) The US is the destination for a broad range of net factor inflows: unskilled labor, skilled labor, and capital. Indeed, these two facts may be strongly related: All factors seek to enter the US because of the US technological superiority. The literature on international factor flows rarely links these two phenomena, instead considering one-at-a-time analyses that stress issues of relative factor abundance. This is unfortunate, since the welfare calculations differ markedly. In a simple Ricardian framework, a country that experiences immigration of factors motivated by technological differences always loses from this migration relative to a free trade baseline, while the other country gains. We provide simple calculations suggesting that the magnitude of the losses for US natives may be quite large $72 billion dollars per year or 0.8 percent of GDP.