Large deviations of continuous regular conditional probabilities

We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a sequence of probability measures on the product space that satisfies a large deviation principle, we present necessary and sufficient conditions for the conditional probabilities under these measures to satisfy a large deviation principle. The arguments of these conditional probabilities are assumed to converge. A way to view regular conditional probabilities as a special case of product regular conditional probabilities is presented. This is used to derive conditions for large deviations of regular conditional probabilities. In addition, we derive a Sanov-type theorem for large deviations of the empirical distribution of the first coordinate conditioned on fixing the empirical distribution of the second coordinate

Integrals for functions with values in a partially ordered vector space

We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure space leads to the classical space of integrable functions

Bochner integrals in ordered vector spaces

We present a natural way to cover an Archimedean directed ordered vector space $E$ by Banach spaces and extend the notion of Bochner integrability to functions with values in $E$. The resulting set of integrable functions is an Archimedean directed ordered vector space and the integral is an order preserving map

Are computers going to solve urban problems? On ICTs and social inclusion

In this paper, it is argued that large cities can benefit from higher levels of ICT (information and communication technology) adoption among the population. An analytical framework is developed, that enables the analysis, assessment and comparison of urban ICT adoption stimulation policies. In the empirical part, the frame is applied to four types of ICT adoption policies that are pursued in different European cities: The Hague, Eindhoven, Helsinki, and Manchester. It is concluded that adoption policies can be justified for a number of reasons, and may contribute to urban development in several respects. However, in many cases, policies lack effectiveness, because crucial factors that determine ICT adoption are not taken into account. Also, in too many cases, public policies interfere with market initiatives. On the basis of the case studies, the conclusion is drawn that the most effective policies are not only problem driven but also opportunity-based and integrative. That includes infrastructure provision, content development and resource building among low-adoptive groups.

On-the-job search, sticky prices, and persistence

Models of the monetary transmission mechanism often generate empirically implausible business fluctuations. This paper analyzes the role of on-the-job search in the propagation of monetary shocks in a sticky price model with labor market search frictions. Such frictions induce long-term employment relationships, such that the real marginal cost is determined by real wages and the cost of an employment relationship. On-the-job search opens up an extra channel of employment growth that dampens the response of these two components. Because real marginal cost rigidity induces small price adjustments, on-the-job search gives rise to a strong propagation of monetary shocks that increases output persistence.

Why have the dynamics of labor productivity changed?

The strength of the nascent economic recovery--and of the labor market--will depend importantly on labor productivity. By itself, faster productivity growth contributes to faster output growth. At the same time, stronger productivity gains allow firms to increase output without adding workers. Some analysts believe that faster productivity growth contributed to the “jobless recoveries” after the 1990-91 and 2001 recessions. ; In recent years, the U.S. economy has undergone a change in the behavior of productivity over the business cycle. Until the mid-1980s, productivity growth rose and fell with output growth. But since then the relationship between these two variables has weakened, and they have even moved in different directions. ; Fluctuations in productivity depend on two factors: the mix of shocks that drive the business cycle and the transmission of those shocks to output and labor market activity. Thus, two hypotheses stand out as plausible explanations for the change in the cyclical behavior of productivity. First, a decline in the importance of supply shocks for the business cycle may have changed the relationship of productivity and output over the business cycle. Second, structural changes in the labor market may have altered the transmission of shocks to the labor market and production. Specifically, a different labor market environment may have prompted firms to modify the way they meet their labor needs in response to shocks to the economy. ; Van Zandweghe examines the shift in the behavior of labor productivity over the business cycle and assesses the supply shock and structural change explanations for the shift. He finds that the importance of supply shocks in the business cycle has been stable over time. However, the behavior of productivity over the business cycle has shifted in response to both supply and demand shocks. Together, these results imply the shift in the business cycle behavior of productivity is most likely the result of structural changes in the labor market.

Quantitative Results on Diophantine Equations in Many Variables

We consider a system of integer polynomials of the same degree with non-singular local zeros and in many variables. Generalising the work of Birch (1962) we find quantitative asymptotics (in terms of the maximum of the absolute value of the coefficients of these polynomials) for the number of integer zeros of this system within a growing box. Using a quantitative version of the Nullstellensatz, we obtain a quantitative strong approximation result, i.e. an upper bound on the smallest integer zero provided the system of polynomials is non-singular.Comment: Accepted for publication in Acta Arithmetica. Added a few pages so that familiarity with Birch's work is no longer assumed; 24 page