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-monotone insurance contracts and their empirical consequences

The goal of this paper is to show the possibility of a non-monotone relation between coverage ans risk which has been considered in the literature of insurance models since the work of Rothschild and Stiglitz (1976). We present an insurance model where the insured agents have heterogeneity in risk aversion and in lenience (a prevention cost parameter). Risk aversion is described by a continuous parameter which is correlated with lenience and for the sake of simplicity, we assume perfect correlation. In the case of positive correlation, the more risk averse agent has higher cosr of prevention leading to a higher demand for coverage. Equivalently, the single crossing property (SCP) is valid and iplies a positive correlation between overage and risk in equilibrium. On the other hand, if the correlation between risk aversion and lenience is negative, not only may the SCP be broken, but also the monotonocity of contracts, i.e., the prediction that high (low) risk averse types choose full (partial) insurance. In both cases riskiness is monotonic in risk aversion, but in the last case there are some coverage levels associated with two different risks (low and high), which implies that the ex-ante (with respect to the risk aversion distribution) correlation between coverage and riskiness may have every sign (even though the ex-post correlation is always positive). Moreover, using another instrument (a proxy for riskiness), we give a testable implication to desentangle single crossing ans non single croosing under an ex-post zero correlation result: the monotonicity of coverage as a function os riskiness. Since by controlling for risk aversion (no asymmetric information), coverage is monotone function of riskiness, this also fives a test for asymmetric information. Finally, we relate this theoretical results to empirical tests in the recent literature, specially the Dionne, Gouruéroux and Vanasse (2001) work. In particular, they found an empirical evidence that seems to be compatible with asymmetric information and non single crossing in our framework. More generally, we build a hidden information model showing how omitted variables (asymmetric information) can bias the sign of the correlation of equilibrium variables conditioning on all observable variables. We show that this may be the case when the omitted variables have a non-monotonic relation with the observable ones. Moreover, because this non-dimensional does not capture this deature. Hence, our main results is to point out the importance of the SPC in testing predictions of the hidden information models.

Distribution strategies for the base of the pyramid: an exploratory study in Brazil

Access has been one of the main difficulties companies have faced in emerging markets (PRAHALAD, 2005). The capillarity of the market, the existence of small, not professionalized and sometimes informal retailers, the lack of infrastructure and high transportation costs are some of the distribution challenges companies face in poorer regions. The literature concerning the Base of the Pyramid (BoP) is still recent and only after the seminal article by Prahalad and Hart (2002), it evolved into many different management perspectives. However, there is a lack of researches concerning distribution strategies to the BoP. Therefore, the main objective of this research is to identify, in the perception of executives working in the market, the conditions associated to a satisfactory distribution for the BoP market in Brazil and to build a substantive theory that helps to shed light to the understanding of the distribution phenomenon adopted by consumer goods companies to reach the BoP market in Brazil. In order to accomplish the objectives of this thesis, a grounded theory methodology (Glaser; Strauss, 1967; Corbin; Strauss, 2008) was used. This approach helped to identify the channel strategies used by local and global companies in the market. Many techniques for data collection were applied. The most important one was in-depth interviews with 26 executives from 24 different consumer goods companies in Brazil. Among the companies there were small, medium and large enterprises; which were also grouped as manufacturers, distributors and retailers. Furthermore, secondary data were examined to identify business strategies to reach BoP and map global distribution initiatives. A database from a consumer panel was also used to analyze what and where BoP consumers purchase non-durable goods. It was verified that small and traditional retailing is a very strong format in BoP markets and in the Northern/Northeastern regions. Cash & Carry is a format that is growing a lot. On the other hand, hypermarkets are not very used by low income population. The results suggest that three major categories are associated to a satisfactory distribution: (a) willingness, which means the effort, knowledge and enthusiasm a firm has to operate at BoP markets; (b) well-done execution, which is related to designing correctly the marketing channel and operating efficiently in an environment full of obstacles, such as lack of infrastructure, capillarity, lack of safety, regional differences and informality, and (c) relationship, which was perceived to be friendlier and essential at BoP markets, since it is very difficult for manufacturers to reach the entire market alone. It is more likely to have a satisfactory distribution when manufacturers establish strong relationships in the marketing channel. Besides, small retailers have a perception of isolation and expect a higher level of relationship. These major categories explain also the competitive advantage that local companies have in relation to MNCs and large companies. Despite of the limitations of an exploratory study, it is expected that this thesis will contribute to the BoP knowledge as well as to the identification of the peculiarities of distribution in BoP markets.

Money distribution with intermediation

This pap er analyzes the distribution of money holdings in a commo dity money search-based mo del with intermediation. Intro ducing heterogeneity of costs to the Kiyotaki e Wright ( 1989 ) mo del, Cavalcanti e Puzzello ( 2010) gives rise to a non-degenerated distribution of money. We extend further this mo del intro ducing intermediation in the trading pro cess. We show that the distribution of money matters for savings decisions. This gives rises to a xed p oint problem for the saving function that di cults nding the optimal solution. Through some examples, we show that this friction shrinks the distribution of money. In contrast to the Cavalcanti e Puzzello ( 2010 ) mo del, the optimal solution may not present the entire surplus going to the consumer. At the end of the pap er, we present a strong result, for a su cient large numb er of intermediaries the distribution of money is degenerated.

Non-monotone insurence contracts and their empirical consequences

The goal of t.his paper is to show the possibility of a non-monot.one relation between coverage and risk which has been considered in the literature of insurance models since the work of Rothschild and Stiglitz (1976). We present an insurance model where the insured agents have heterogeneity in risk aversion and in lenience (a prevention cost parameter). Risk aversion is described by a continuou.'l parameter which is correlated with lenience and, for the sake of simplicity, we assume perfect correlation. In the case of positive correlation, the more risk averse agent has higher cost of prevention leading to a higher demand for coverage. Equivalently, the single crossing property (SCP) is valid and implies a positive correlation between coverage and risk in equilibrium. On the other hand, if the correlation between risk aversion and lenience is negative, not only may the sep be broken, but also the monotonicity of contracts, i.e., the prediction that high (Iow) risk averse types choose full (partial) insurance. In both cases riskiness is monotonic in risk aversion, but in the last case t,here are some coverage leveIs associated with two different risks (low and high), which implies that the ex-ante (with respect to the risk aversion distribution) correlation bet,ween coverage and riskiness may have every sign (even though the ex-post correlation is always positive). Moreover, using another instrument (a proxy for riskiness), we give a testable implication to disentangle single crossing and non single crossing under an ex-post zero correlation result: the monotonicity of coverage as a function of riskiness. Since by controlling for risk aversion (no asymmetric informat, ion), coverage is a monotone function of riskiness, this also gives a test for asymmetric information. Finally, we relate this theoretical results to empirica! tests in the recent literature, specially the Dionne, Gouriéroux and Vanasse (2001) work. In particular, they found an empirical evidence that seems to be compatible with asymmetric information and non single crossing in our framework. More generally, we build a hidden information model showing how omitted variabIes (asymmetric information) can bias the sign of the correlation of equilibrium variabIes conditioning on ali observabIe variabIes. We show that this may be t,he case when the omitted variabIes have a non-monotonic reIation with t,he observable ones. Moreover, because this non-monotonic reIat,ion is deepIy reIated with the failure of the SCP in one-dimensional screening problems, the existing lit.erature on asymmetric information does not capture t,his feature. Hence, our main result is to point Out the importance of t,he SCP in testing predictions of the hidden information models.

Regulation and wage adjustment patterns : non parametric evidence from longitudinal data

This paper gives a first step toward a methodology to quantify the influences of regulation on short-run earnings dynamics. It also provides evidence on the patterns of wage adjustment adopted during the recent high inflationary experience in Brazil.The large variety of official wage indexation rules adopted in Brazil during the recent years combined with the availability of monthly surveys on labor markets makes the Brazilian case a good laboratory to test how regulation affects earnings dynamics. In particular, the combination of large sample sizes with the possibility of following the same worker through short periods of time allows to estimate the cross-sectional distribution of longitudinal statistics based on observed earnings (e.g., monthly and annual rates of change).The empirical strategy adopted here is to compare the distributions of longitudinal statistics extracted from actual earnings data with simulations generated from minimum adjustment requirements imposed by the Brazilian Wage Law. The analysis provides statistics on how binding were wage regulation schemes. The visual analysis of the distribution of wage adjustments proves useful to highlight stylized facts that may guide future empirical work.