Partial stochastic dominance for the multivariate Gaussian distribution

Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the partial stochastic dominance result that the cumulative distribution function of the maximum of a multivariate normal random vector, with positive intraclass correlation coefficient, intersects the cumulative distribution function of a standard normal random variable at most once. This result can be applied to the Bayesian design of a clinical trial in which several experimental treatments are compared to a single control.Comment: 7 page

A representation of the natural numbers by means of cycle-numbers, with consequences in number theory

In this paper we give rules for creating a number triangle T in a manner analogous to that for producing Pascal's arithmetic triangle; but all of its elements belong to {0, 1}, and cycling of its rows is involved in the creation. The method of construction of any one row of T from its preceding rows will be defined, and that, together with starting and boundary conditions, will suffice to define the whole triangle, by sequential continuation. We shall use this triangle in order to define the so-called cycle-numbers, which can be mapped to the natural numbers. T will be called the 'cyclenumber triangle'. First we shall give some theorems about relationships between the cyclenumbers and the natural numbers, and discuss the cycling of patterns within the triangle's rows and diagonals. We then begin a study of figures (i.e. (0,1)- patterns, found on lines, triangles and squares, etc.) within T. In particular, we shall seek relationships which tell us something about the prime numbers. For our later studies, we turn the triangle onto its side and work with a doubly-infinite matrix C. We shall find that a great deal of cycling of figures occurs within T and C, and we exploit this fact whenever we can. The phenomenon of cycling patterns leads us to muse upon a 'music of the integers', indeed a 'symphony of the integers', being played out on the cycle-number triangle or on C. Like Pythagoras and his 'music of the spheres', we may well be the only persons capable of hearing it!

Convergence and Diversity in International and Comparative Industrial Relations

[Excerpt] In this essay, we reexamine a critical paradox in international and comparative industrial relations, a paradox that already decades ago demonstrated its ability to intrigue scholarly curiosity (Galenson, 1952,1963; Kerr et al, 1960). As we see it, convergence along a number of important dimensions, such as labor law and organizational and bargaining structure, is occurring simultaneously with widespread cross-national and local divergence, or diversity, in industrial relations practices and outcomes. Along with economic and political interdependence and with intensifications of market competition, convergence and diversity both appear to be product of an increasing spread of markets and ideas sometimes referred to as globalization. In employing this term, we intend to make the point that the conduct of global business is no longer confined to the sort of international trading and related activities that have been carried on for centuries already. In the modern era, the production and exchange of both goods and services occur increasingly on a global scale (Reich, 1991). At this level, as capital mobility expands and trade agreements proliferate (NAFTA, CATT, the single European market), national governments find it increasingly difficult to regulate markets. This globalization of markets, we suggest, is the dominant force driving change (whether toward convergence or diversity) in the contemporary period. Our observations are especially applicable to the advanced industrial countries of the Organization for Economic Cooperation and Development (OECD), the primary focus of this paper, although the trends identified here probably also hold to some extent for newly industrialized countries and less developed societies as well

‘The Greatest Bubble in History’: Stock Prices during the British Railway Mania

Although the British Railway Mania has been described as one of the greatest bubbles in history, it has been largely neglected by academics. This paper attempts to redress this neglect by creating a daily stock price index for the 1843-50 period and by assessing the contribution of the many newly-created railways to the bubble-like pattern in stock prices. The paper then examines whether this bubble-like pattern was due to an increase in the stochastic discount factor arising from an increase in the probability of large-scale adoption of railway technology. We find little evidence to support this hypothesis.bubbles, financial crises, Railway Mania

Cohort Crowding: How Resources Affect Collegiate Attainment

Analyses of college attainment typically focus on factors affecting enrollment demand, including the financial attractiveness of a college education and the availability of financial aid, while implicitly assuming that resources available per student on the supply side of the market are elastically supplied. The higher education market in the United States is dominated by public and non-profit production, and colleges and universities receive considerable subsidies from state, federal, and private sources. Because consumers pay only a fraction of the cost of production, changes in demand are unlikely to be accommodated fully by colleges and universities without commensurate increases in non-tuition revenue. For this reason, public investment in higher education plays a crucial role in determining the degrees produced and the supply of college-educated workers to the labor market. Using data covering the last half of the twentieth century, we find strong evidence that large cohorts within states have relatively low undergraduate degree attainment, reflecting less than perfect elasticity of supply in the higher education market. That large cohorts receive lower public subsidies per student in higher education explains this result, indicating that resources have large effects on degree production. Our results suggest that reduced resources per student following from rising cohort size and lower state expenditures are likely to have significant negative effects on the supply of college-educated workers entering the labor market.

The trading of unlimited liability bank shares: the Bagehot Hypothesis

From the mid-1820s, banks became the first business sector in Great Britain and Ireland to be granted the right to form freely on an unlimited liability joint stock basis. Walter Bagehot, the renowned contemporary banking expert, warned that shares in such banks would ultimately be owned by widows, orphans and other impecunious individuals. An alternative hypothesis is that the governing bodies of these banks constrained by special legal restrictions on share trading acted effectively to prevent such shares being transferred to the less wealthy members of society. We test both conjectures using the archives of an Irish joint stock bank. The results do not support Bagehot's hypothesis, but instead indicate that shares continued to be owned by wealthy individuals.unlimited liability, corporate governance, joint stock companies, banking

Closing the Gap or Widening the Divide: The Effects of the G.I. Bill and World War II on the Educational Outcomes of Black Americans

The effects of the G.I. Bill on collegiate attainment may have differed for black and white Americans owing to differential returns to education and differences in opportunities at colleges and universities, with men in the South facing explicitly segregated colleges. The empirical evidence suggests that World War II and the availability of G.I. benefits had a substantial and positive impact on the educational attainment of white men and black men born outside the South. However, for those black veterans likely to be limited to the South in their educational choices, the G.I. Bill had little effect on collegiate outcomes, resulting in the exacerbation of the educational differences between black and white men from southern states.