Some results concerning off-training-set and IID error for the Gibbs and the Bayes optimal generalizers

In this paper we analyse the average behaviour of the Bayes-optimal and Gibbs learning algorithms. We do this both for off-training-set error and conventional IID (independent identically distributed) error (for which test sets overlap with training sets). For the IID case we provide a major extension to one of the better known results. We also show that expected IID test set error is a non-increasing function of training set size for either algorithm. On the other hand, as we show, the expected off-training-set error for both learning algorithms can increase with training set size, for non-uniform sampling distributions. We characterize the relationship the sampling distribution must have with the prior for such an increase. We show in particular that for uniform sampling distributions and either algorithm, the expected off-training-set error is a non-increasing function of training set size. For uniform sampling distributions, we also characterize the priors for which the expected error of the Bayes-optimal algorithm stays constant. In addition we show that for the Bayes-optimal algorithm, expected off-training-set error can increase with training set size when the target function is fixed, but if and only if the expected error averaged over all targets decreases with training set size. Our results hold for arbitrary noise and arbitrary loss functions.     

DEBT BAILOUTS AND CONSTITUTIONS

A demand‐based theory of subnational debt bailouts is presented. It is shown that demand for bailouts among politicians with regional constituencies is affected by revenue sharing arrangements as a bailout implies a shift of taxation toward the federal tier. Automatic revenue sharing may lead to the formation of pro‐bailout coalitions formed by indebted states and states that are net recipients of the revenue sharing arrangement. The model shows that the state debt bailouts approved by the Brazilian Senate prior to the enactment of the Fiscal Responsibility Act were consistent with politicians who maximize the proceeds accruing to their constituencies. (JEL H70, D70)     

Mobility hub or hollow? Cross‐border travelling in the Mediterranean, 1995–2016

The Mediterranean is often portrayed as a hub of human mobility. In this article, we test this widespread view by exploring the structure of travel flows in the region over the last two decades (1995–2016). We find that mobility is much higher and increasing more strongly along the northern than along the southern shore, thus creating a growing mobility divide. South–north and north–south movements are even scarcer and stagnate or even decline over time. With a Gini coefficient of .87, mobility flows are distributed extremely unequally across country pairs in the Mediterranean. Community detection algorithms reconfirm that mobility predominantly takes place in disparate clusters around the Mediterranean, not across it. These findings imply that a ‘neo‐Braudelian’ view of the Mediterranean as a mobility hub is less justified than a ‘Rio Grande’ perspective that conceives of the Mediterranean as a mobility hollow. Multivariate regression models for network data suggest that geographical distance and, to a lesser extent, political visa regulations, explain the unequal mobility structure better than differences in economic well‐being.