Stopping the Panzers: The Untold Story of D-Day (Book Review) by Marc Milner

Review of Stopping the Panzers: The Untold Story of D-Day by Marc Milne

The Myth of the Good War: America in the Second World War Revised Edition (Book Review) by Jacques R. Pauwels

Review of The Myth of the Good War: America in the Second World War Revised Edition by Jacques R. Pauwel

Decomposing and Analyzing Korea’s Declining GDP Growth: Some Cautions and Suggestions

Chin Hee Hahn and Sukha Shin (2007) have developed new decompositions of Korean economic growth from 1990 to 2004. They find that Korea’s declining GDP growth has been accompanied by a sharp decline in capital deepening and an increase in total factor productivity. By contrast, Jorgenson and Vu’s (2007) decompositions of Korea’s GDP growth find that total factor productivity decreased over this period. This paper compares the two decompositions; evaluates Hahn and Shin’s hypothesis that competition from Chinese imports may be driving the decline in GDP growth; and briefly presents four other candidates (decline in Korean savings, business cycle effects, weak IT investment, and regulatory and wealth redistribution initiatives) that could be partially responsible for the slowdown in Korean GDP growth.GDP, TFP, China, Korea, capital, labor, decomposition, productivity.

The Singular Values of the GOE

As a unifying framework for examining several properties that nominally involve eigenvalues, we present a particular structure of the singular values of the Gaussian orthogonal ensemble (GOE): the even-location singular values are distributed as the positive eigenvalues of a Gaussian ensemble with chiral unitary symmetry (anti-GUE), while the odd-location singular values, conditioned on the even-location ones, can be algebraically transformed into a set of independent $\chi$-distributed random variables. We discuss three applications of this structure: first, there is a pair of bidiagonal square matrices, whose singular values are jointly distributed as the even- and odd-location ones of the GOE; second, the magnitude of the determinant of the GOE is distributed as a product of simple independent random variables; third, on symmetric intervals, the gap probabilities of the GOE can be expressed in terms of the Laguerre unitary ensemble (LUE). We work specifically with matrices of finite order, but by passing to a large matrix limit, we also obtain new insight into asymptotic properties such as the central limit theorem of the determinant or the gap probabilities in the bulk-scaling limit. The analysis in this paper avoids much of the technical machinery (e.g. Pfaffians, skew-orthogonal polynomials, martingales, Meijer $G$-function, etc.) that was previously used to analyze some of the applications.Comment: Introduction extended, typos corrected, reference added. 31 pages, 1 figur

The Singular Values of the GUE (Less is More)

Some properties that nominally involve the eigenvalues of Gaussian Unitary Ensemble (GUE) can instead be phrased in terms of singular values. By discarding the signs of the eigenvalues, we gain access to a surprising decomposition: the singular values of the GUE are distributed as the union of the singular values of two independent ensembles of Laguerre type. This independence is remarkable given the well known phenomenon of eigenvalue repulsion. The structure of this decomposition reveals that several existing observations about large $n$ limits of the GUE are in fact manifestations of phenomena that are already present for finite random matrices. We relate the semicircle law to the quarter-circle law by connecting Hermite polynomials to generalized Laguerre polynomials with parameter $\pm$1/2. Similarly, we write the absolute value of the determinant of the $n\times{}n$ GUE as a product n independent random variables to gain new insight into its asymptotic log-normality. The decomposition also provides a description of the distribution of the smallest singular value of the GUE, which in turn permits the study of the leading order behavior of the condition number of GUE matrices. The study is motivated by questions involving the enumeration of orientable maps, and is related to questions involving powers of complex Ginibre matrices. The inescapable conclusion of this work is that the singular values of the GUE play an unpredictably important role that had gone unnoticed for decades even though, in hindsight, so many clues had been around.Comment: v2 - Updated proof of Corollory 2 to make it self contained. Added references to related work on GOE. Corrected minor typos. 31 pages, 26 pdf figures (use of Adobe reader recommended

On the Golden Rule of capital accumulation under endogenous longevity

This note derives the Golden Rule of capital accumulation in a Chakraborty-type economy, i.e. a two-period OLG economy where longevity is endogenous. It is shown that the capital per worker maximizing steady-state consumption per head is inferior to the Golden Rule capital level prevailing under exogenous longevity. We characterize also the lifetime Golden Rule, that is, the capital per worker maximizing steady-state expected lifetime consumption per head, and show that this tends to exceed the standard Golden Rule capital level.Golden Rule, longevity, OLG models

Adult longevity and economic take-off: from Malthus to Ben-Porath

We propose four arguments favoring the idea that medical effectiveness, adult longevity and height started to increase in Europe before the industrial revolution. This may have prompted households to increase their investment in human skills as a response to longer lives and initiated the transition from stagnation to growth.life expectancy, height, industrial revolution, human capital, adult mortality.

Underemployment and capital irreversivility in a unionized overlaping generations economy

In a unionized OLG model, it is shown that steady-state underutilization of labour and equipment can be due to the combination of the two following elements: (i) Irreversibility of capital, technology and skill decisions, (ii) Firm specific shocks on productivity. The presence of unions is neither sufficient nor necessary for having unemployment. The result of Devereux and Lockwood (1991) that union power affect positively the capital stock in general equilibrium does not always hold under capital irreversibility