Exact moment calculations for genetic models with migration, mutation, and drift

Using properties of moment stationarity we develop exact expressions for the mean and covariance of allele frequencies at a single locus for a set of populations subject to drift, mutation, and migration. Some general results can be obtained even for arbitrary mutation and migration matrices, for example: (1) Under quite general conditions, the mean vector depends only on mutation rates, not on migration rates or the number of populations. (2) Allele frequencies covary among all pairs of populations connected by migration. As a result, the drift, mutation, migration process is not ergodic when any finite number of populations is exchanging genes. in addition, we provide closed form expressions for the mean and covariance of allele frequencies in Wright's finite-island model of migration under several simple models of mutation, and we show that the correlation in allele frequencies among populations can be very large for realistic rates of mutation unless an enormous number of populations are exchanging genes. As a result, the traditional diffusion approximation provides a poor approximation of the stationary distribution of allele frequencies among populations. Finally, we discuss some implications of our results for measures of population structure based on Wright's F-statistics.

An 'Ideal' Decomposition of Industry Dynamics: An Application to the Nationwide and State Level U.S. Banking Industry

This paper considers the aggregate performance of the banking industry, applying a modified and extended dynamic decomposition of bank return on equity. The aggregate performance of any industry depends on the underlying microeconomic dynamics within that industry . adjustments within banks, reallocations between banks, entry of new banks, and exit of existing banks. Bailey, Hulten, and Campbell (1992) and Haltiwanger (1997) develop dynamic decompositions of industry performance. We extend those analyses to derive an ideal decomposition that includes their decomposition as one component. We also extend the decomposition, consider geography, and implement decomposition on a state-by-state basis, linking that geographic decomposition back to the national level. We then consider how deregulation of geographic restrictions on bank activity affects the components of the state-level dynamic decomposition, controlling for competition and the state of the economy within each state and employing fixed- and random-effects estimation for a panel database across the fifty states and the District of Columbia from 1976 to 2000.

Understanding Molecular Orbitals; Sigma Orbitals

Various plots of sigma molecular orbitals in diatomic molecules are discussed.

The Great Moderation and the Relationship between Output Growth and Its Volatility

This study examines the effect of the Great Moderation on the relationship between U.S. output growth and its volatility over the period 1947 to 2006. First, we consider the possible effects of structural change in the volatility process. In so doing, we employ GARCH-M and ARCH-M specifications of the process describing output growth rate and its volatility with and without a one-time structural break in volatility. Second, our data analyses and empirical results suggest no significant relationship between the output growth rate and its volatility, favoring the traditional wisdom of dichotomy in macroeconomics. Moreover, the evidence shows that the time-varying variance falls sharply or even disappears once we incorporate a one-time structural break in the unconditional variance of output starting 1982 or 1984. That is, the integrated GARCH effect proves spurious. Finally, a joint test of a trend change and a one-time shift in the volatility process finds that the one-time shift dominates.