Productivity growth in electric energy retail in Colombia. A bootstrapped malmquist indices approach

This paper offers a productivity growth estimate for electric energy commercialization firms in Colombia, using a non-parametric Malmquist bootstrap methodology. The estimation and methodology serve two main purposes. First, in Colombia Commercialization firms are subject to a price-cap regulation scheme, a non-common arrangement in the international experience for this part of the industry. Therefore the paper’s result suggest an estimate of the productivity factor to be used by the regulator, not only in Colombia but in other countries where commercialization is a growing part of the industry (renewable energy, for instance). Second, because of poor data collection from regulators and firms themselves, regulation based on a single estimation of productivity seems inappropriate and error-prone. The nonparametric Malmquist bootstrap estimation allows an assessment of the result in contrast to a single one estimation. This would open an opportunity for the regulator to adopt a narrower and more accurate productivity estimation or override an implausible result and impose a productivity factor in the price-cap to foster the development of the industry.

Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.