Laws of large numbers for non-additive probabilities

We apply the concept of exchangeable random variables to the case of non-additive robability distributions exhibiting ncertainty aversion, and in the lass generated bya convex core convex non-additive probabilities, ith a convex core). We are able to rove two versions of the law of arge numbers (de Finetti's heorems). By making use of two efinitions. of independence we rove two versions of the strong law f large numbers. It turns out that e cannot assure the convergence of he sample averages to a constant. e then modal the case there is a true" probability distribution ehind the successive realizations of the uncertain random variable. In this case convergence occurs. This result is important because it renders true the intuition that it is possible "to learn" the "true" additive distribution behind an uncertain event if one repeatedly observes it (a sufficiently large number of times). We also provide a conjecture regarding the "Iearning" (or updating) process above, and prove a partia I result for the case of Dempster-Shafer updating rule and binomial trials.

Non-durable consumption and real-estate prices in Brazil: panel-data analysis at the state level

Housing is an important component of wealth for a typical household in many countries. The objective of this paper is to investigate the effect of real-estate price variation on welfare, trying to close a gap between the welfare literature in Brazil and that in the U.S., the U.K., and other developed countries. Our first motivation relates to the fact that real estate is probably more important here than elsewhere as a proportion of wealth, which potentially makes the impact of a price change bigger here. Our second motivation relates to the fact that real-estate prices boomed in Brazil in the last five years. Prime real estate in Rio de Janeiro and São Paulo have tripled in value in that period, and a smaller but generalized increase has been observed throughout the country. Third, we have also seen a recent consumption boom in Brazil in the last five years. Indeed, the recent rise of some of the poor to middle-income status is well documented not only for Brazil but for other emerging countries as well. Regarding consumption and real-estate prices in Brazil, one cannot imply causality from correlation, but one can do causal inference with an appropriate structural model and proper inference, or with a proper inference in a reduced-form setup. Our last motivation is related to the complete absence of studies of this kind in Brazil, which makes ours a pioneering study. We assemble a panel-data set for the determinants of non-durable consumption growth by Brazilian states, merging the techniques and ideas in Campbell and Cocco (2007) and in Case, Quigley and Shiller (2005). With appropriate controls, and panel-data methods, we investigate whether house-price variation has a positive effect on non-durable consumption. The results show a non-negligible significant impact of the change in the price of real estate on welfare consumption), although smaller then what Campbell and Cocco have found. Our findings support the view that the channel through which house prices affect consumption is a financial one.