Remarks on the convergence of pseudospectra

We establish the convergence of pseudospectra in Hausdorff distance for closed operators acting in different Hilbert spaces and converging in the generalised norm resolvent sense. As an assumption, we exclude the case that the limiting operator has constant resolvent norm on an open set. We extend the class of operators for which it is known that the latter cannot happen by showing that if the resolvent norm is constant on an open set, then this constant is the global minimum. We present a number of examples exhibiting various resolvent norm behaviours and illustrating the applicability of this characterisation compared to known results.

Disparate Wages in a Globalized World

This study uses wage data from the UBS Prices and Earnings survey to highlight Disparate Wages in a Globalized World from di↵erent perspectives. This wage data is characterised by remarkable consistency over the last 40 years, as well as unusual global comparability. In the first chapter we analyse the convergence hypothesis for purchasing power adjusted wages across the world for 1970 to 2009. The results provide solid evidence for the hypotheses of absolute and conditional convergence in real wages, with the key driver being faster overall growing wage levels in lower wage countries compared to higher wage countries. At the same time, the highest skilled professions have experienced the highest wage growth, while low skilled workers’ wages have lagged, thus no convergence in this sense is found between skill groups. In the second chapter we examine deviations in international wages from Factor Price Equalisation theory (FPE). Following an approach analogous to Engel (1993) we find that deviations from FPE are more likely driven by the higher variability of wages between countries than by the variability of di↵erent wages within countries. With regard to the traditional analysis of the real exchange rate and the Balassa-Samuelson assumptions our analysis points to a larger impact on the real exchange rate likely stemming from the movements in the real exchange rate of tradables, and only to a lesser extent from the lack of equalisation of wages within countries. In the third chapter our results show that India’s economic and trade liberalisation, starting in the early 1990s, had very di↵erential impacts on skill premia, both over time and over skill levels. The most striking result is the large increase in wage inequality of high-skilled versus low-skilled professions. Both the synthetic control group method and the di↵erence-in-di↵erences (DID) approach suggest that a significant part of this increase in wage inequality can be attributed to India’s liberalisation.

Quick divergence but slow convergence during ecotype formation in lake and stream stickleback pairs of variable age

When genetic constraints restrict phenotypic evolution, diversification can be predicted to evolve along so-called lines of least resistance. To address the importance of such constraints and their resolution, studies of parallel phenotypic divergence that differ in their age are valuable. Here, we investigate the parapatric evolution of six lake and stream threespine stickleback systems from Iceland and Switzerland, ranging in age from a few decades to several millennia. Using phenotypic data, we test for parallelism in ecotypic divergence between parapatric lake and stream populations and compare the observed patterns to an ancestral-like marine population. We find strong and consistent phenotypic divergence, both among lake and stream populations and between our freshwater populations and the marine population. Interestingly, ecotypic divergence in low-dimensional phenotype space (i.e. single traits) is rapid and seems to be often completed within 100 years. Yet, the dimensionality of ecotypic divergence was highest in our oldest systems and only there parallel evolution of unrelated ecotypes was strong enough to overwrite phylogenetic contingency. Moreover, the dimensionality of divergence in different systems varies between trait complexes, suggesting different constraints and evolutionary pathways to their resolution among freshwater systems.

Topology of the ambient boundary and the convergence of causal curves

We discuss the topological nature of the boundary spacetime, the conformal infinity of the ambient cosmological metric. Due to the existence of a homothetic group, the bounding spacetime must be equipped not with the usual Euclidean metric topology but with the Zeeman fine topology. This then places severe constraints to the convergence of a sequence of causal curves and the extraction of a limit curve, and also to our ability to formulate conditions for singularity formation.

The Improving Relative Status of Black Men

Using data from the Current Population Survey, we examine recent trends in the relative economic status of black men. Our findings point to gains in the relative wages of black men (compared to whites) during the 1990s, especially among younger workers. In 1989, the average black male worker (experienced or not) earned about 69 percent as much per week as the average white male worker. In 2001, the average younger black worker was earning about 86% percent as much as an equally experienced white male; black males at all experience levels earned 72 percent as much as the average white in 2001. Greater occupational diversity and a reduction in unobserved skill differences and/or labor market discrimination explain much of the trend. For both younger and older workers, general wage inequality tempered the rate of wage convergence between blacks and whites during the 1990s, although the effects were less pronounced than during the 1980s.

Economics and Ideology: Causal Evidence of the Impact of Economic Conditions on Support for Redistribution and Other Ballot Proposals

There is a large literature demonstrating that positive economic conditions increase support for incumbent candidates, but little understanding of how economic conditions affect preferences for parties and for particulars of their platforms. We ask how exogenous shifts to the value of residents. human capital affect voting behavior in California neighborhoods. As predicted by economic theory, we find that positive economic shocks decrease support for redistributive policies. More notably, we find that conservative voting on a wide variety of ballot propositions--from crime to gambling to campaign finance--is increasing in economic well being.