Wealth inequality in the United States and Great Britain

In this paper we describe the household wealth distribution in the US and UK, and compare both wealth inequality and the form in which wealth is held. Unconditionally, there are large differences in financial wealth between the two countries at the top fifth of the wealth distribution. And even after controlling for age and income differences between the two countries, we show that the median US household accumulates more financial wealth than their UK counterpart. We explore a number of alternative reasons for these differences and reject some explanations as implausible. These include differential receipt of financial inheritances or desired bequests, and differential average rates of return to corporate equity or housing. While less certain, we also argue that the differences that are concentrated among the older well-to-do are not likely due to differences in income or employment risks, savings for college expenses, or changes in permanent income. Some of the observed differences are due to what we refer to as "initial conditions", in particular previously high rates of corporate equity ownership in the US and housing ownership among young British households. But since these differences existed even in the early 1980s, initial conditions only provide a partial explanation. One further possibility may be that due to forced and voluntary annuitization of retirement incomes, older British households face considerably less longevity risk. Looking more widely, however, we find wealth held in different forms across the two countries, in particular in housing, which to some extent offsets the differences we observe in financial wealth patterns. We therefore point out that it is important that comparative studies compare genuine economic phenomena (such as the ability to smooth consumption) rather than particular economic measurements (such as the level of wealth in any one particular form). We also argue that it is crucial that comparative exercises of this form acknowledge the importance of institutional differences across countries, and in this particular comparison the role of housing markets, annuity markets and stock markets appear crucial and all merit further more detailed research. On balance, we are encouraged by the degree to which a detailed investigation can point to potential explanations of observed wealth differences between the two countries, and such an investigation will also lead to a deeper understanding of the household wealth accumulation process more generally.

Realistic Ionizing Fluxes for Young Stellar Populations from 0.05 to twice solar metallicity

We present a new grid of ionizing fluxes for O and Wolf-Rayet stars for use with evolutionary synthesis codes and single star H II region analyses. A total of 230 expanding, non-LTE, line-blanketed model atmospheres have been calculated for five metallicities (0.05, 0.2, 0.4, 1 and 2 solar) using the WM-basic code of Pauldrach et al. (2001) and the CMFGEN code of Hillier & Miller (1998). The stellar wind parameters are scaled with metallicity for both O and W-R stars. We incorporate the new models into Starburst99 (Leitherer et al. 1999) and compare the ionizing outputs with Schaerer & Vacca (1998) and Leitherer et al. (1999). The changes in the output ionizing fluxes are dramatic, particularly below 228 A. We also find lower fluxes in the He I continuum for Z > 0.4 solar and ages < 7 Myr because of the increased line blanketing. We test the accuracy of the new models by constructing photoionization models. We show that for the dwarf O star grid, He I 5876/H beta decreases between Z = 1 and twice solar in a similar manner to observations (e.g. Bresolin et al. 1999) due to the increased effect of line blanketing. We therefore suggest that a lowering of the upper mass limit at high abundances is not required to explain the observations. For the case of an instantaneous burst, we plot the softness parameter "eta prime" against the abundance indicator R_23. The new models are coincident with the data of Bresolin et al. (1999), particularly during the W-R phase, unlike previous models which over-predict the hardness of the ionizing radiation.Comment: 21 pages, 15 postscript colour figures, includes mn2e.cls. To be published in MNRAS. Revised version containing modifications to Tables 1-

Probabilistic lower bounds on maximal determinants of binary matrices

Let ${\mathcal D}(n)$ be the maximal determinant for $n \times n$ $\{\pm 1\}$-matrices, and $\mathcal R(n) = {\mathcal D}(n)/n^{n/2}$ be the ratio of ${\mathcal D}(n)$ to the Hadamard upper bound. Using the probabilistic method, we prove new lower bounds on ${\mathcal D}(n)$ and $\mathcal R(n)$ in terms of $d = n-h$, where $h$ is the order of a Hadamard matrix and $h$ is maximal subject to $h \le n$. For example, $\mathcal R(n) > (\pi e/2)^{-d/2}$ if $1 \le d \le 3$, and $\mathcal R(n) > (\pi e/2)^{-d/2}(1 - d^2(\pi/(2h))^{1/2})$ if $d > 3$. By a recent result of Livinskyi, $d^2/h^{1/2} \to 0$ as $n \to \infty$, so the second bound is close to $(\pi e/2)^{-d/2}$ for large $n$. Previous lower bounds tended to zero as $n \to \infty$ with $d$ fixed, except in the cases $d \in \{0,1\}$. For $d \ge 2$, our bounds are better for all sufficiently large $n$. If the Hadamard conjecture is true, then $d \le 3$, so the first bound above shows that $\mathcal R(n)$ is bounded below by a positive constant $(\pi e/2)^{-3/2} > 0.1133$.Comment: 17 pages, 2 tables, 24 references. Shorter version of arXiv:1402.6817v4. Typos corrected in v2 and v3, new Lemma 7 in v4, updated references in v5, added Remark 2.8 and a reference in v6, updated references in v