IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Estimating the Stochastic Discount Factor without a Utility Function

  • Fabio Araujo
  • Joao Victor Issler

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

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://repec.org/sce2005/up.6443.1107044922.pdf
Download Restriction: no

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

as
in new window

Length:
Date of creation: 11 Nov 2005
Date of revision:
Handle: RePEc:sce:scecf5:202
Contact details of provider: Web page: http://comp-econ.org/
Email:


More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. 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).
  2. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  4. Vahid, Farshid & Engle, Robert F., 1997. "Codependent cycles," Journal of Econometrics, Elsevier, vol. 80(2), pages 199-221, October.
  5. Andrei G. Simonassi & Luiz Renato Lima, 2005. "Dinâmica Não-Linear E Sustentabilidade Da Dívida Pública Brasileira," Anais do XXXIII Encontro Nacional de Economia [Proceedings of the 33th Brazilian Economics Meeting] 051, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
  6. Hansen, Lars Peter & Singleton, Kenneth J, 1983. "Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 249-65, April.
  7. repec:fth:harver:1435 is not listed on IDEAS
  8. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  9. Richard Blundell & Martin Browning & Costas Meghir, 1994. "Consumer Demand and the Life-Cycle Allocation of Household Expenditures," Review of Economic Studies, Oxford University Press, vol. 61(1), pages 57-80.
  10. John Y. Campbell & N. Gregory Mankiw, 1989. "Consumption, Income and Interest Rates: Reinterpreting the Time Series Evidence," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 185-246 National Bureau of Economic Research, Inc.
  11. Engle, Robert F & Ito, Takatoshi & Lin, Wen-Ling, 1990. "Meteor Showers or Heat Waves? Heteroskedastic Intra-daily Volatility in the Foreign Exchange Market," Econometrica, Econometric Society, vol. 58(3), pages 525-42, May.
  12. Vahid, F. & Issler, J.V., 2001. "The Importance Of Common Cyclical Features in VAR Analysis: A Monte-Carlo Study," Monash Econometrics and Business Statistics Working Papers 2/01, Monash University, Department of Econometrics and Business Statistics.
  13. Terra, Maria Cristina T. & Gonzaga, Gustavo Maurício & Menezes Filho, Naércio Aquino, 2002. "Trade liberalization and the evolution of skill earnings differentials in Brazil," Economics Working Papers (Ensaios Economicos da EPGE) 457, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  14. Sydney Ludvigson & Xiaohong Chen, 2004. "Land of Addicts? An Empirical Investigation of Habit-Based Asset Pricing Models," 2004 Meeting Papers 692, Society for Economic Dynamics.
  15. Issler, João Victor & Vahid, Farshid, 2001. "The missing link: using the NBER recessions indicator to construct coincident and leading indices of economic activity," Economics Working Papers (Ensaios Economicos da EPGE) 429, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  16. Issler, Joao Victor & Vahid, Farshid, 2001. "Common cycles and the importance of transitory shocks to macroeconomic aggregates," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 449-475, June.
  17. Engle, Robert F. & Issler, Joao Victor, 1995. "Estimating common sectoral cycles," Journal of Monetary Economics, Elsevier, vol. 35(1), pages 83-113, February.
  18. Campbell, John Y, 1987. "Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis," Econometrica, Econometric Society, vol. 55(6), pages 1249-73, November.
  19. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-62, April.
  20. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  21. Joshua Rosenberg & Robert F. Engle, 2000. "Empirical Pricing Kernels," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-014, New York University, Leonard N. Stern School of Business-.
  22. Aloisio Araujo & Luciano I. de Castro Filho, 2004. "Pure Strategy Equilibria of Multidimensional and Non-Monotonic Auctions," Econometric Society 2004 Latin American Meetings 300, Econometric Society.
  23. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
  24. Yacine Aït-Sahalia & Andrew W. Lo, . "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," CRSP working papers 332, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  25. Maria Cristina T. Terra & Ana Lucia Vahia de Abreu, 2004. "Purchasing Power Parity: the Choice of Price Index," Econometric Society 2004 Latin American Meetings 247, Econometric Society.
  26. A. Abel, 2010. "Asset prices under habit formation and catching up with the Jones," Levine's Working Paper Archive 1395, David K. Levine.
  27. Marjorie Flavin, 1993. "The Excess Smoothness of Consumption: Identification and Interpretation," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 651-666.
  28. Amemiya, Takeshi, 1971. "The Estimation of the Variances in a Variance-Components Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 12(1), pages 1-13, February.
  29. Orazio P. Attanasio & Guglielmo Weber, 1994. "Is Consumption Growth Consistent with Intertemporal Optimization? Evidence from the Consumer Expenditure Survey," NBER Working Papers 4795, National Bureau of Economic Research, Inc.
  30. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
  31. Hansen, Lars Peter & Richard, Scott F, 1987. "The Role of Conditioning Information in Deducing Testable," Econometrica, Econometric Society, vol. 55(3), pages 587-613, May.
  32. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-87, December.
  33. Runkle, David E., 1991. "Liquidity constraints and the permanent-income hypothesis : Evidence from panel data," Journal of Monetary Economics, Elsevier, vol. 27(1), pages 73-98, February.
  34. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  35. Rubens Penha Cysne, 2007. "Public debt indexation and denomination, the case of Brazil: a comment," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(4), pages 417-425.
  36. David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
  37. John Campbell & Angus Deaton, 1989. "Why is Consumption So Smooth?," Review of Economic Studies, Oxford University Press, vol. 56(3), pages 357-373.
  38. Attanasio, Orazio P & Browning, Martin, 1995. "Consumption over the Life Cycle and over the Business Cycle," American Economic Review, American Economic Association, vol. 85(5), pages 1118-37, December.
  39. Chapman, D.A., 1996. "Approximating the Asset Pricing Kernel," Papers 96-02, Rochester, Business - Financial Research and Policy Studies.
  40. Boivin, Jean & Ng, Serena, 2006. "Are more data always better for factor analysis?," Journal of Econometrics, Elsevier, vol. 132(1), pages 169-194, May.
  41. Alain Hecq & Franz Palm & Jean-Pierre Urbain, 2001. "Testing for Common Cyclical Features in Var Models with Cointegration," CESifo Working Paper Series 451, CESifo Group Munich.
  42. Monteiro, P. K., 2004. "First-Price auction symmetric equlibria with a general distribution," Economics Working Papers (Ensaios Economicos da EPGE) 568, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  43. Sallum, Elvia Mureb & Barbosa, Fernando de Holanda & Cunha, Alexandre Barros da, 2005. "Competitive equilibrium hyperinflation under rational expectations," Economics Working Papers (Ensaios Economicos da EPGE) 578, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  44. Cysne, Rubens Penha, 2004. "On the statistical estimation of diffusion processes - a partial survey," Economics Working Papers (Ensaios Economicos da EPGE) 570, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  45. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-60, Oct.-Dec..
  46. Cysne, Rubens Penha, 2005. "Equity-premium puzzle: evidence from Brazilian data," Economics Working Papers (Ensaios Economicos da EPGE) 586, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  47. Casey B. Mulligan, 2002. "Capital, Interest, and Aggregate Intertemporal Substitution," NBER Working Papers 9373, National Bureau of Economic Research, Inc.
  48. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
  49. Bai, Jushan & Ng, Serena, 2006. "Evaluating latent and observed factors in macroeconomics and finance," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 507-537.
  50. Anderson, Heather M. & Victor Issler, Joao & Vahid, Farshid, 2006. "Common features," Journal of Econometrics, Elsevier, vol. 132(1), pages 1-5, May.
  51. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
  52. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
  53. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  54. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
  55. Robert F. Engle & Sharon Kozicki, 1990. "Testing For Common Features," NBER Technical Working Papers 0091, National Bureau of Economic Research, Inc.
  56. Issler, João Victor & Vahid, Farshid, 2002. "The missing link: using the NBER recession indicator to construct coincident and leading indices economic activity," Economics Working Papers (Ensaios Economicos da EPGE) 450, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  57. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  58. Martin Lettau & Sydney Ludvigson, 1999. "Resurrecting the (C)CAPM: a cross-sectional test when risk premia are time-varying," Staff Reports 93, Federal Reserve Bank of New York.
  59. Brown, David P & Gibbons, Michael R, 1985. " A Simple Econometric Approach for Utility-based Asset Pricing Models," Journal of Finance, American Finance Association, vol. 40(2), pages 359-81, June.
  60. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
  61. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  62. Cysne, Rubens Penha, 2004. "Is there a price puzzle in Brazil? An application of Bias-Corrected Bootstrap," Economics Working Papers (Ensaios Economicos da EPGE) 577, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  63. Cysne, Rubens Penha, 2005. "What happens after the central bank of Brazil increases the target interbank rate by 1%?," Economics Working Papers (Ensaios Economicos da EPGE) 584, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  64. Fama, Eugene F & French, Kenneth R, 1992. " The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-65, June.
  65. Casey B. Mulligan, 2004. "Robust Aggregate Implications of Stochastic Discount Factor Volatility," NBER Working Papers 10210, National Bureau of Economic Research, Inc.
  66. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  67. Barbosa, Fernando de Holanda, 2005. "A paridade do poder de compra: existe um quebra-cabeça?," Economics Working Papers (Ensaios Economicos da EPGE) 582, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  68. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-86, April.
  69. Pedro Cavalcanti Ferreira & Samuel de Abreu Pessôa & Fernando A. Veloso, 2005. "On The Tyranny of Numbers: East Asian Miracles in World Perspective," IBMEC RJ Economics Discussion Papers 2005-10, Economics Research Group, IBMEC Business School - Rio de Janeiro.
  70. Cysne, Rubens Penha, 2004. "Solving the non-convexity problem in some shopping-time and human-capital models," Economics Working Papers (Ensaios Economicos da EPGE) 567, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  71. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-95, October.
  72. Flavin, Marjorie A, 1981. "The Adjustment of Consumption to Changing Expectations about Future Income," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 974-1009, October.
  73. Flôres Junior, Renato Galvão, 2004. "Os desafios da integração legal," Economics Working Papers (Ensaios Economicos da EPGE) 573, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:sce:scecf5:202. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.