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Estimating the Stochastic Discount Factor without a Utility Function

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  • Fabio Araujo
  • Joao Victor Issler

Abstract

In this paper we take seriously the consequences of the Pricing Equation in constructing a novel consistent estimator of the stochastic discount factor (SDF) using panel data. Under general conditions it depends exclusively on appropriate averages of asset returns, and its computation is a direct exercise, as long as one has enough observations to fit our asymptotic results. We identify the logarithm of the SDF using the fact that it is the serial correlation "common feature" in every asset return of the economy. Our estimator does not depend on any parametric function representing preferences, or on consumption data. This property allows its use in testing different preference specifications commonly employed in finance and in macroeconomics, as well as investigating the existence of several puzzles involving intertemporal substitution, such as the equity-premium puzzle. It is also straightforward to construct an estimator of the risk-free rate based on our SDF estimator. When applied to quarterly data of U.S.$ real returns from 1972:1 through 2002:4, our estimator of the SDF is close to unity most of the time and yields an equivalent average annual real discount rate of 2.46%. When we examined the appropriateness of different functional forms to represent preferences, we concluded that standard preference representations used in the literature on intertemporal substitution cannot be rejected by the data. Moreover, estimates of the relative risk-aversion coefficient are close to what can be expected a priori -- between 1 and 2, statistically significant, and not different than unity in testing. A direct test of the equity-premium puzzle using our SDF estimator cannot reject the null that the discounted equity premium in the U.S. has mean zero. However, when consumption-based SDF estimates are employed in the same test, the null is rejected. Further empirical investigation shows that our SDF estimator has a large negative correlation with the equity premium, whereas that of consumption-based estimates are usually too small in absolute value, generating the equity-premium puzzle

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 202.

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Date of creation: 11 Nov 2005
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Handle: RePEc:sce:scecf5:202

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Keywords: common features; stochastic discount factor;

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  1. Bonomo, Marco Antônio Cesar & Terra, Maria Cristina T., 2005. "Special Interests and Political Business Cycles," Economics Working Papers (Ensaios Economicos da EPGE) 597, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  2. Athanasopoulos, George & de Carvalho Guillén, Osmani Teixeira & Issler, João Victor & Vahid, Farshid, 2011. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Journal of Econometrics, Elsevier, vol. 164(1), pages 116-129, September.
  3. Andrei G. Simonassi, 2006. "Estimando A Taxa De Retorno Livre De Risco No Brasil," Anais do XXXIV Encontro Nacional de Economia [Proceedings of the 34th Brazilian Economics Meeting] 180, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
  4. Barbosa, Fernando de Holanda, 2005. "The Contagion Effect of Public Debt on Monetary Policy: The Brazilian Experience," Economics Working Papers (Ensaios Economicos da EPGE) 591, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  5. Araújo, Fabio & Issler, João Victor & Fernandes, Marcelo, 2005. "Estimating the Stochastic Discount Factor without a Utility Function," Economics Working Papers (Ensaios Economicos da EPGE) 583, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  6. Carlos Enrique Carrasco Gutierrez & Wagner Piazza Gaglianone, 2008. "Evaluating Asset Pricing Models in a Fama-French Framework," Working Papers Series 175, Central Bank of Brazil, Research Department.
  7. Gomes, Fábio Augusto Reis & Issler, João Victor, 2009. "Testing the Optimality of Aggregate Consumption Decisions: Is there Rule-of-Thumb Behavior?," Economics Working Papers (Ensaios Economicos da EPGE) 682, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).

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