Multiscale Systems, Homogenization, and Rough Paths:VAR75 2016: Probability and Analysis in Interacting Physical Systems

In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. We survey the origins of this theory and then revisit and improve the analysis of Kelly-Melbourne [Ann. Probab. Volume 44, Number 1 (2016), 479-520], taking into account recent progress in $p$-variation and c\`adl\`ag rough path theory.Comment: 27 pages. Minor corrections. To appear in Proceedings of the Conference in Honor of the 75th Birthday of S.R.S. Varadha

Vacancy durations and entry wages: evidence from linked vacancy-employer-employee data

This paper explores the relationship between the duration of a vacancy and the starting wage of a new job, using unusually informative data comprising detailed information on vacancies, the establishments posting the vacancies, and the workers eventually filling the vacancies. We find that vacancy durations are negatively correlated with the starting wage and that this negative association is particularly strong with the establishment component of the starting wage. We also confirm previous findings that growing establishments fill their vacancies faster. To understand the relationship between establishment growth, vacancy filling and entry wages, we calibrate a model with directed search and ex-ante heterogeneous workers and firms. We find a strong tension between matching the sharp increase in vacancy filling for growing firms and the response of vacancy filling to firm-level wages. We discuss the implications of this finding as well as potential resolutions

Vacancy durations and entry wages: evidence from linked vacancy-employer-employee data

This article explores the relationship between the duration of a vacancy and the starting wage of a new job, using linked data on vacancies, the posting establishments, and the workers eventually filling the vacancies. The unique combination of large-scale, administrative worker, establishment, and vacancy data is critical for separating establishment- and job-level determinants of vacancy duration from worker-level heterogeneity. Conditional on observables, we find that vacancy duration is negatively correlated with the starting wage and its establishment component, with precisely estimated elasticities of −0.07 and −0.21, respectively. While the negative relationship is qualitatively consistent with search-theoretic models where firms use the wage as a recruiting device, these elasticities are small, suggesting that firms’ wage policies can account only for a small fraction of the variation in vacancy filling across establishments