Introducing higher moments in the CAPM: some basic ideas

We show how to include in the CAPM moments of any order, extending the mean-variance or mean-variance-skewness versions available until now. Then, we present a simple way to modify the formulae, in order to avoid the appearance of utility parameters. The results can be easily applied to practical portfolio design, with econometric inference and testing based on generalised method of moments procedures. An empirical application to the Brazilian stock market is discussed.

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have data-dependent penalties for a lack of parsimony, as well as the traditional ones. We suggest a new procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties. In order to compute the fit of each model, we propose an iterative procedure to compute the maximum likelihood estimates of parameters of a VAR model with short-run and long-run restrictions. Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arise from the joint determination of lag-length and rank, relative to the commonly used procedure of selecting the lag-length only and then testing for cointegration.

Competitive equilibria in infinite-horizon collateralized economies with default penalties

Araújo, Páscoa and Torres-Martinez (2002) have shown that, without imposing either debt constraints or transversality conditions, Ponzi schemes are ruled out in infinite horizon economies with default when collateral is the only mechanism that partially secures loans. Páscoa and Seghir (2008) subsequently show that Ponzi schemes may reappear if, additionally to the seizure of the collateral, there are sufficiently harsh default penalties assessed (directly in terms of utility) against the defaulters. They also claim that if default penalties are moderate then Ponzi schemes are ruled out and existence of a competitive equilibrium is ensured. The objective of this paper is two fold. First, contrary to what is claimed by Páscoa and Seghir (2008), we show that moderate default penalties do not always prevent agents to run a Ponzi scheme. Second, we provide an alternative condition on default penalties that is sufficient to rule out Ponzi schemes and ensure the existence of a competitive equilibrium.

A generalization of judds method of out-steady-state comparisons in perfect foresight models

We show that Judd (1982)’s method can be applied to any finite system, contrary to what he claimed in 1987. An example shows how to employ the technic to study monetary models in presence of capital accumulation.

A contractive method for computing the stationary solution of the euler equation

A contractive method for computing stationary solutions of intertemporal equilibrium models is provide. The method is is implemented using a contraction mapping derived from the first-order conditions. The deterministic dynamic programming problem is used to illustrate the method. Some numerical examples are performed.

Decision rules and information provision: monitoring versus manipulation

The paper focuses on the organization of institutions designed to resolve disputes between two parties, when some information is not veriable and decision makers may have vested preferences. It shows that the choice of how much discretional power to grant to the decision maker and who provides the information are intrinsically related. Direct involvement of the interested parties in the supply of information enhances monitoring over the decision maker, although at the cost of higher manipulation. Thus, it is desirable when the decision maker is granted high discretion. On the contrary, when the decision maker has limited discretional power, information provision is better assigned to an agent with no direct stake. The analysis helps to rationalize some organizational arrangements that are commonly observed in the context of judicial and antitrust decision-making.

Endogenous collateral: arbitrage and equilibrium without bounded short sales

We study the implications of the absence of arbitrage in an two period economy where default is allowed and assets are secured by collateral choosen by the borrowers. We show that non arbitrage sale prices of assets are submartingales, whereas non arbitrage purchase prices of the derivatives (secured by the pool of collaterals) are supermartingales. We use these non arbitrage conditions to establish existence of equilibrium, without imposing bounds on short sales. The nonconvexity of the budget set is overcome by considering a continuum of agents. Our results are particularly relevant for the collateralized mortgage obligations(CMO) markets.

Testing the optimality of aggregate consumption decisions: is there rule-of-thumb behavior?

Consumption is an important macroeconomic aggregate, being about 70% of GNP. Finding sub-optimal behavior in consumption decisions casts a serious doubt on whether optimizing behavior is applicable on an economy-wide scale, which, in turn, challenge whether it is applicable at all. This paper has several contributions to the literature on consumption optimality. First, we provide a new result on the basic rule-of-thumb regression, showing that it is observational equivalent to the one obtained in a well known optimizing real-business-cycle model. Second, for rule-of-thumb tests based on the Asset-Pricing Equation, we show that the omission of the higher-order term in the log-linear approximation yields inconsistent estimates when lagged observables are used as instruments. However, these are exactly the instruments that have been traditionally used in this literature. Third, we show that nonlinear estimation of a system of N Asset-Pricing Equations can be done efficiently even if the number of asset returns (N) is high vis-a-vis the number of time-series observations (T). We argue that efficiency can be restored by aggregating returns into a single measure that fully captures intertemporal substitution. Indeed, we show that there is no reason why return aggregation cannot be performed in the nonlinear setting of the Pricing Equation, since the latter is a linear function of individual returns. This forms the basis of a new test of rule-of-thumb behavior, which can be viewed as testing for the importance of rule-of-thumb consumers when the optimizing agent holds an equally-weighted portfolio or a weighted portfolio of traded assets. Using our setup, we find no signs of either rule-of-thumb behavior for U.S. consumers or of habit-formation in consumption decisions in econometric tests. Indeed, we show that the simple representative agent model with a CRRA utility is able to explain the time series data on consumption and aggregate returns. There, the intertemporal discount factor is significant and ranges from 0.956 to 0.969 while the relative risk-aversion coefficient is precisely estimated ranging from 0.829 to 1.126. There is no evidence of rejection in over-identifying-restriction tests.

Testing production functions used in empirical growth studies

We estimate and test two alternative functional forms representing the aggregate production function for a panel of countries: the extended neoclassical growth model, and a mincerian formulation of schooling-returns to skills. Estimation is performed using instrumentalvariable techniques, and both functional forms are confronted using a Box-Cox test, since human capital inputs enter in levels in the mincerian specification and in logs in the extended neoclassical growth model. Our evidence rejects the extended neoclassical growth model in favor of the mincerian specification, with an estimated capital share of about 42%, a marginal return to education of about 7.5% per year, and an estimated productivity growth of about 1.4% per year. Differences in productivity cannot be disregarded as an explanation of why output per worker varies so much across countries: a variance decomposition exercise shows that productivity alone explains 54% of the variation in output per worker across countries.

Optimal auction with a general distribution: virtual valuation without densities

We characterize the optimal auction in an independent private values framework for a completely general distribution of valuations. We do this introducing a new concept: the generalized virtual valuation. To show the wider applicability of this concept we present two examples showing how to extend the classical models of Mussa and Rosen and Baron and Myerson for arbitrary distributions

Finding a maximum skewness portfolio - A general solution to three-moments portfolio choice

Considering the three first moments and allowing short sales, the efficient portfolios set for n risky assets and a riskless one is found, supposing that agents like odd moments and dislike even ones. Analytical formulas for the solution surface are obtained and important geometric properties provide insights on its shape in the three dimensional space defined by the moments. A special duality result is needed and proved. The methodology is general, comprising situations in which, for instance, the investor trades a negative skewness for a higher expected return. Computation of the optimum portfolio weights is feasible in most cases.

A note on learning chaotic sunspot equilibrium

In this paper we prove convergence to chaotic sunspot equilibrium through two learning rules used in the bounded rationality literature. The rst one shows the convergence of the actual dynamics generated by simple adaptive learning rules to a probability distribution that is close to the stationary measure of the sunspot equilibrium; since this stationary measure is absolutely continuous it results in a robust convergence to the stochastic equilibrium. The second one is based on the E-stability criterion for testing stability of rational expectations equilibrium, we show that the conditional probability distribution de ned by the sunspot equilibrium is expectational stable under a reasonable updating rule of this parameter. We also report some numerical simulations of the processes proposed.

A demanda de importações de etanol pela Suécia e pela União Europeia

Como consequência da crescente preocupação, especialmente dos países desenvolvidos, em relação à dependência do petróleo e às mudanças climáticas, a participação dos biocombustíveis na matriz energética global está se tornando cada vez mais relevante. No Brasil, o mercado interno foi o determinante para o desenvolvimento da indústria sucroalcooleira nos últimos anos, mas sabe-se que a continuação desta tendência no médio prazo dependerá da demanda internacional pelo etanol brasileiro. De forma a compreender o potencial importador de etanol da União Europeia e, em particular, da Suécia, propôs-se, nesta dissertação, analisar os determinantes de suas importações. O presente trabalho descreveu a evolução do mercado de etanol no bloco, focando-se nos incentivos e políticas adotadas na Suécia, país-membro que está mais avançado na substituição da gasolina pelo etanol. Utilizando-se de dados de 2006 a 2009 e assumindo que as importações de etanol são resultantes de um excesso de demanda doméstica pelo biocombustível, analisaram-se as relações econômicas entre as variáveis. Observou-se que as variáveis associadas à demanda daquele bloco são, de forma geral, mais importantes na explicação do quantum importado do combustível do que as variáveis associadas à oferta regional. O impacto do aumento em 1% do preço da gasolina é de decréscimo de aproximadamente 1,8% nas importações de etanol. Quando o preço deste se eleva 1% na União Europeia, reduz em 1,4% as importações. Já em sentido oposto se movimentam as importações quando ocorre alteração na renda (PIB) e no preço do trigo, o principal insumo. Acréscimo de 1% na renda e no preço do trigo geram, respectivamente, 10,1% e 1,4% de crescimento nas importações de etanol. Assim, as principais oportunidades de exportação de etanol brasileiro para o bloco podem se dar por possíveis frustrações da safra de cereais e pelo crescimento da renda europeia. Já a tendência de ascensão do preço do petróleo pode ter impacto negativo na demanda de etanol, caso não haja compensação através de políticas mais agressivas de uso de biocombustíveis. As importações suecas comportam-se de maneira semelhante às do bloco quando ocorrem choques. Um porcento de elevação no preço da gasolina sueca reduz em 2,71% as importações de etanol e, estas crescem 4,4% quando do acréscimo de 1% do PIB do país. Importante é o impacto nas importações da frota preparada para E85: 1% de elevação nesta frota gera acréscimo de 8% no volume importado. Desta forma, a extinção recente de alguns incentivos para a compra de veículos movidos a E85 pode significar estabilidade da necessidade de importações de etanol relacionada a esta variável, passando então a renda a ter um papel mais importante no crescimento das importações. Já o coeficiente do preço do E85 apresentou-se estatisticamente não diferente de zero, podendo este resultado ser consequência de uma possível diferença do perfil dos proprietários de carros movidos a E85, relativamente ao dos proprietários de carros movidos exclusivamente à gasolina, dando margem a uma política de preços mais remuneradora para os produtores de etanol, sendo estes suecos ou brasileiros, com baixo impacto sobre a demanda.

The forward- and the equity-premium puzzles: two symptoms of the same illness?

Using information on US domestic financial data only, we build a stochastic discount factor—SDF— and check whether it accounts for foreign markets stylized facts that escape consumption based models. By interpreting our SDF as the projection of a pricing kernel from a fully specified model in the space of returns, our results indicate that a model that accounts for the behavior of domestic assets goes a long way toward accounting for the behavior of foreign assets prices. We address predictability issues associated with the forward premium puzzle by: i) using instruments that are known to forecast excess returns in the moments restrictions associated with Euler equations, and; ii) by pricing Lustig and Verdelhan (2007)’s foreign currency portfolios. Our results indicate that the relevant state variables that explain foreign-currency market asset prices are also the driving forces behind U.S. domestic assets behavior.