The Clean Air Act Amendments and Firm Investment in Pollution Abatement Equipment

The command-and-control approach to environmental regulation requires that firms install prescribed technologies to meet specified goals. However, environmental regulations change frequently; in addition, the enforcement agency cannot perfectly monitor firm compliance. We examine the impact of uncertainties surrounding the enactment and the enforcement of the Clean Air Act Amendments of 1990 on firm investment in air pollution abatement equipment. We find that our measures of the likelihood of CAAA passage clearly affect a firm's investment in pollution equipment. Enforcement actions also affect a firm's investment, but these effects are weaker and are statistically significant only after enactment

On the Hausdorff dimension of ultrametric subsets in R^n

For every e>0, any subset of R^n with Hausdorff dimension larger than (1-e)n must have ultrametric distortion larger than 1/(4e).Comment: 4 pages, improved layou

A node-capacitated Okamura-Seymour theorem

The classical Okamura-Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face of a planar graph, there exists a feasible concurrent flow if and only if the cut conditions are satisfied. Simple examples show that a similar theorem is impossible in the node-capacitated setting. Nevertheless, we prove that an approximate flow/cut theorem does hold: For some universal c > 0, if the node cut conditions are satisfied, then one can simultaneously route a c-fraction of all the demands. This answers an open question of Chekuri and Kawarabayashi. More generally, we show that this holds in the setting of multi-commodity polymatroid networks introduced by Chekuri, et. al. Our approach employs a new type of random metric embedding in order to round the convex programs corresponding to these more general flow problems.Comment: 30 pages, 5 figure