A Goodwillie-type Theorem for Milnor K-Theory

Goodwillie's rational isomorphism between relative algebraic K-theory and relative cyclic homology, together with the lambda decomposition of cyclic homology, illustrates the close relationships among algebraic K-theory, cyclic homology, and differential forms. In this paper, I prove a Goodwillie-type theorem for relative Milnor $K$-theory, working over a very general class of commutative rings, defined via the stability criterion of Van der Kallen. Early results of Van der Kallen and Bloch are special cases. The result likely generalizes in terms of de Rahm-Witt complexes, by weakening some invertibility assumptions, but the class of rings considered is already more than sufficiently general for the intended applications. The main motivation for this paper arises from applications to the infinitesimal theory of Chow groups, first pointed out by Bloch in the 1970's, and prominent in recent work of Green and Griffiths. Related results and geometric applications are discussed in the final section.Comment: 34 page

Singular Chern Classes of Schubert Varieties via Small Resolution

We discuss a method for calculating the Chern-Schwartz-MacPherson (CSM) class of a Schubert variety in the Grassmannian using small resolutions introduced by Zelevinsky. As a consequence, we show how to compute the Chern-Mather class and local Euler obstructions using small resolutions instead of the Nash blowup. The algorithm obtained for CSM classes also allows us to prove new cases of a positivity conjecture of Aluffi and Mihalcea.Comment: Addressed referee's comments, Section 6.2 contains new material; 35 pages, 3 figures, and 2 table

The Anatomy of Start-Stop Growth

This paper investigates the remarkable extremes of growth experiences within countries and examines the changes that occur when growth starts and stops. We find three main results. First, all but the very richest countries experience both growth miracles and failures over substantial periods. Second, growth accounting reveals that physical capital accumulation plays a negligible role in growth take-offs and a larger but still modest role in growth collapses. The implied role of productivity in these shifts is also directly reflected in employment reallocations and changes in trade. Third, growth accelerations and collapses are asymmetric phenomena. Collapses typically feature reduced manufacturing and investment amidst increasing price instability, whereas growth takeoffs are primarily associated with large and steady expansions in international trade. This asymmetry suggests that the roads into and out of rapid growth expansions may not be the same. The results stand in contrast to much growth theory and conventional wisdom: despite much talk of poverty traps, even very poor countries regularly grow rapidly, and the role of aggregate investment in growth accelerations is negligible.

Hit or Miss? The Effect of Assassinations on Institutions and War

Assassinations are a persistent feature of the political landscape. Using a new data set of assassination attempts on all world leaders from 1875 to 2004, we exploit inherent randomness in the success or failure of assassination attempts to identify assassination's effects. We find that, on average, successful assassinations of autocrats produce sustained moves toward democracy. We also find that assassinations affect the intensity of small-scale conflicts. The results document a contemporary source of institutional change, inform theories of conflict, and show that small sources of randomness can have a pronounced effect on history.

The burden of knowledge and the ‘death of the Renaissance man’: Is innovation getting harder?

This paper investigates, theoretically and empirically, a possibly fundamental aspect of technological progress. If knowledge accumulates as technology progresses, then successive generations of innovators may face an increasing educational burden. Innovators can compensate in their education by seeking narrower expertise, but narrowing expertise will reduce their individual capacities, with implications for the organization of innovative activity - a greater reliance on teamwork - and negative implications for growth. I develop a formal model of this “knowledge burden mechanism” and derive six testable predictions for innovators. Over time, educational attainment will rise while increased specialization and teamwork follow from a sufficiently rapid increase in the burden of knowledge. In cross-section, the model predicts that specialization and teamwork will be greater in deeper areas of knowledge while, surprisingly, educational attainment will not vary across fields. I test these six predictions using a micro-data set of individual inventors and find evidence consistent with each prediction. The model thus provides a parsimonious explanation for a range of empirical patterns of inventive activity. Upward trends in academic collaboration and lengthening doctorates, which have been noted in other research, can also be explained by the model, as can much-debated trends relating productivity growth and patent output to aggregate inventive effort. The knowledge burden mechanism suggests that the nature of innovation is changing, with negative implications for long-run economic growth.

The Burden of Knowledge and the 'Death of the Renaissance Man': Is Innovation Getting Harder?

This paper investigates, theoretically and empirically, a possibly fundamental aspect of technological progress. If knowledge accumulates as technology progresses, then successive generations of innovators may face an increasing educational burden. Innovators can compensate in their education by seeking narrower expertise, but narrowing expertise will reduce their individual capacities, with implications for the organization of innovative activity - a greater reliance on teamwork - and negative implications for growth. I develop a formal model of this "knowledge burden mechanism" and derive six testable predictions for innovators. Over time, educational attainment will rise while increased specialization and teamwork follow from a sufficiently rapid increase in the burden of knowledge. In cross-section, the model predicts that specialization and teamwork will be greater in deeper areas of knowledge while, surprisingly, educational attainment will not vary across fields. I test these six predictions using a micro-data set of individual inventors and find evidence consistent with each prediction. The model thus provides a parsimonious explanation for a range of empirical patterns of inventive activity. Upward trends in academic collaboration and lengthening doctorates, which have been noted in other research, can also be explained by the model, as can much-debated trends relating productivity growth and patent output to aggregate inventive effort. The knowledge burden mechanism suggests that the nature of innovation is changing, with negative implications for long-run economic growth.

Above-Threshold Poles in Model-Independent Form Factor Parametrizations

The model-independent parametrization for exclusive hadronic form factors commonly used for semileptonic decays is generalized to allow for the inclusion of above-threshold resonant poles of known mass and width. We discuss the interpretation of such poles, particularly with respect to the analytic structure of the relevant two-point Green's function in which they reside. Their presence has a remarkably small effect on the parametrization, as we show explicitly for the case of $D \to \pi e^+ \nu_e$.Comment: 8 pages, no figures, REVTeX. Version accepted by Phys. Rev. D. References and clarifying remarks adde