To cointegrate or not to cointegrate? That's a topological question

We show that for any multivariate I( 1) process which does not cointegrate, it is possible to find another process sufficient1y elose to it where cointegration applies. Closeness is defined in terms of the spectral density matrices of the respective processes in differences, i.e., a metric which takes into account only the information in the (centred) second moments. The result may explain why in practice cointegration is found a bit "too often". Examples developing this point and simulations giving an insight on the metric used are also presented.

Affiliation, equilibrium existence and the revenue ranking of auctions

We consider private value auctions where bidders’ types are dependent, a case usually treated by assuming affiliation. We show that affiliation is a restrictive assumption in three senses: topological, measure-theoretic and statistical (affiliation is a very restrictive characterization of positive dependence). We also show that affiliation’s main implications do not generalize for alternative definitions of positive dependence. From this, we propose new approaches to the problems of pure strategy equilibrium existence in first-price auctions (PSEE) and the characterization of the revenue ranking of auctions. For equilibrium existence, we slightly restrict the set of distributions considered, without loss of economic generality, and offer a complete characterization of PSEE. For revenue ranking, we obtain a characterization of the expected revenue differences between second and first price auctions with general dependence of types.