Relative Entropy in Biological Systems

In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe the dynamics of a population or probability distribution. Under suitable assumptions, the distribution will approach an equilibrium with the passage of time. Relative entropy - that is, the Kullback--Leibler divergence, or various generalizations of this - provides a quantitative measure of how far from equilibrium the system is. We explain various theorems that give conditions under which relative entropy is nonincreasing. In biochemical applications these results can be seen as versions of the Second Law of Thermodynamics, stating that free energy can never increase with the passage of time. In ecological applications, they make precise the notion that a population gains information from its environment as it approaches equilibrium.Comment: 20 page

Pass-through estimates and the choice of an exchange rate index

We examine exchange rate pass-through into U.S. import prices in 29 manufacturing industries using eight exchange rate indexes. These indexes vary by the number currencies included; whether the weight on each currency is based on total trade with the United States or solely imports; and, whether the weights vary by industry. Our results indicate that pass-through is generally incomplete but varies across industries. Moreover, pass-through is sensitive to the exchange rate index. Using bootstrapped J tests we show that major currency indexes perform better than their broad currency counterparts. When using a major currency index, industry-specific exchange rate indexes are preferred to aggregate indexes.Foreign exchange rates

Constructing and using national and regional TWEXs: the case for chaining

The breakdown of the Bretton Woods system of fixed exchange rates spurred the development of trade-weighted exchange rates(TWEXs). These indexes measure changes in the average foreign exchange value of a currency over time. The construction of a TWEX index requires numerous decisions. Producers of TWEXs are revisiting many of their construction decisions because, with the advent of the single currency in Europe, all TWEXs will have to be modified. In addition, countries adopting the single currency may find it useful to develop their own TWEXs, similar to those that exist for regions within the United States. All commonly-used TWEXs are based on either a Laspeyres or Paasche price index. In the present paper we argue that producers of TWEXs should consider using the chain approach for the construction of their indexes because of an issue that affects TWEXs based on either Laspeyres or Paasche price indexes - the choice of base period. We illustrate this problem and show how it leads to different measures of exchange rate changes. A chain index, which links together the exchange rates and trade weights from year-to-year, eliminates the needs for a base period.Foreign exchange

Comparing manufacturing export growth across states: what accounts for the differences?

The expansion of United States manufacturing exports has spread unevenly across states. Cletus C. Coughlin and Patricia S. Pollard use shift-share analysis to account for the difference between a state’s manufacturing export growth and national manufacturing export growth between 1988 and 1998. Three effects are examined. The industry mix effect indicates that a state should have experienced export growth above the national average if its exports were relatively more concentrated in industries whose exports expanded faster than the national average. The destination effect indicates that a state should have experienced export growth above the national average if its exports were concentrated in foreign markets whose purchases from the United States expanded faster than the national increase in exports. The competitive effect is what remains after accounting for these two effects. Coughlin and Pollard find that the competitive effect, which in previous research was related to increases in human capital per worker, is the key determinant of a state’s relative export performance. Furthermore, the industry mix and destination effects, which are of similar importance, are generally dominated by the competitive effect in accounting for a state’s relative export performance.Manufactures ; Exports ; Regional economics

A question of measurement: is the dollar rising or falling?

Trade-weighted exchange rate indexes that measure changes in the average foreign exchange value of the U. S. dollar produce different answers to how much the dollar has changed and, in some cases, even whether the value of the dollar has risen or fallen. After discussing the differences in constructing these indexes, Cletus C. Coughlin and Patricia S. Pollard examine some factors that might account for the contrasting views of changes in the dollar. Their analysis uses two indexes-one produced by the staff of the Board of Governors and the other by the Federal Reserve Bank of Dallas. These indexes differ in three aspects: the method used to calculate the trade weights, the base period for the trade weights, and the foreign currencies included. Their comparison reveals that the difference between the two indexes is driven primarily by the choice of the currencies.Foreign exchange ; Foreign exchange rates ; Money

Size matters: asymmetric exchange rate pass-through at the industry level

Changes in costs faced by firms have direct implications for their price-cost margins. Knowing how prices respond to such cost changes is crucial for understanding how individual markets function and, in turn, for understanding the macroeconomy. We analyze exchange rate pass-through into U.S. import prices for 30 industries to address two questions related to this issue. First, does the direction of a change in the exchange rate affect pass-through? Second, does the size of a change in the exchange rate matter for pass-through? We find that firms in over half the industries studied respond asymmetrically to appreciations and depreciations, but the direction of asymmetry varies. Likewise, most firms respond asymmetrically to large and small changes in the exchange rate with pass-through positively related to the size of the change. When taking into account both direction and size effects we find that the size effect dominates.Foreign exchange rates

To chain or not to chain trade-weighted exchange rate indexes

With the advent of chain calculations for the U.S. national income and product accounts, it seems reasonable to contemplate using the chain approach for other indexes, such as trade-weighted exchange rates (TWEXs). A fundamental criticism of measuring the growth of gross domestic product by a fixed-base-year method is that the estimates are highly sensitive, especially when the economy?s structure is changing dramatically, to the arbitrary choice of the base year. Such a criticism can be levied against TWEXs. In fact, even TWEXs constructed using a Paasche index rather than a Laspeyres index have problems related to base periods. We examine theoretically and empirically the use ofa chain TWEX in relation to two well-known TWEX indexes: the Federal Reserve Bank of Atlanta index, which uses a Laspeyres index, and the Federal Reserve Bank of Dallas index, which uses a Paasche index. The choice of base year alters the behavior ofthe dollar in these two indexes. We contrast this result with the behavior of the dollar in comparable chain TWEXs, where the base year sensitivity is absent. Our results indicate that developers of TWEXs, as well as those revising TWEXs, should consider a chain approach. Furthermore, users need to be aware of the sensitivity of TWEXs to changes in either the base period for trade weights or the reference base period for exchange ratesForeign exchange rates ; Dollar, American