IDEAS home Printed from https://ideas.repec.org/p/fip/fednrp/9712.html
   My bibliography  Save this paper

Approximation bias in linearized Euler equations

Author

Listed:
  • Sydney Ludvigson
  • Christina H. Paxson

Abstract

This paper concerns pitfalls associated with the use of approximations to dynamic Euler equations. Two applications of the approximations are notable. First, tests for precautionary saving motives typically involve regressing consumption growth on uncertainty in expected consumption growth. The parameter estimates are used to measure the strength of precautionary motives, which is also related to the coefficient of relative risk aversion. Another application estimates the sensitivity of consumption growth to the expected real interest rate, with the coefficient on the latter equal to the intertemporal elasticity of substitution in consumption, often the inverse of the coefficient of relative risk aversion. The two literatures yield very different estimates of how prudent or risk averse consumers are or, alternatively, how willing they are to substitute consumption over time. We investigate one possible reason for these apparently contradictory results: both methods of estimation rely on linear approximations of Euler equations. We demonstrate that biases associated with these approximations can be substantial, and that the direction of the biases is consistent with the divergent estimates found in the literature.

Suggested Citation

  • Sydney Ludvigson & Christina H. Paxson, 1997. "Approximation bias in linearized Euler equations," Research Paper 9712, Federal Reserve Bank of New York.
  • Handle: RePEc:fip:fednrp:9712
    as

    Download full text from publisher

    File URL: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/research_papers/9712.html
    Download Restriction: no

    File URL: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/research_papers/9712.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Pischke, Jorn-Steffen, 1995. "Individual Income, Incomplete Information, and Aggregate Consumption," Econometrica, Econometric Society, vol. 63(4), pages 805-840, July.
    2. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    3. Zeldes, Stephen P, 1989. "Consumption and Liquidity Constraints: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 97(2), pages 305-346, April.
    4. John Campbell & Angus Deaton, 1989. "Why is Consumption So Smooth?," Review of Economic Studies, Oxford University Press, vol. 56(3), pages 357-373.
    5. repec:fth:jonhop:390 is not listed on IDEAS
    6. Tony S. Wirjanto, 1995. "Aggregate Consumption Behaviour and Liquidity Constraints: The Canadian Evidence," Canadian Journal of Economics, Canadian Economics Association, vol. 28(4b), pages 1135-1152, November.
    7. 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 263-286, April.
    8. Kuehlwein, Michael, 1991. "A test for the presence of precautionary saving," Economics Letters, Elsevier, vol. 37(4), pages 471-475, December.
    9. Guiso, Luigi & Jappelli, Tullio & Terlizzese, Daniele, 1992. "Earnings uncertainty and precautionary saving," Journal of Monetary Economics, Elsevier, vol. 30(2), pages 307-337, November.
    10. Attanasio, Orazio P, et al, 1999. "Humps and Bumps in Lifetime Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 22-35, January.
    11. Merrigan, Philip & Normandin, Michel, 1996. "Precautionary Saving Motives: An Assessment from UK Time Series of Cross-Sections," Economic Journal, Royal Economic Society, vol. 106(438), pages 1193-1208, September.
    12. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-1248, September.
    13. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
    14. David I. Laibson & Andrea Repetto & Jeremy Tobacman, 1998. "Self-Control and Saving for Retirement," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 29(1), pages 91-196.
    15. Carroll Christopher Dixon, 2001. "Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health to the Second-Order Approximation)," The B.E. Journal of Macroeconomics, De Gruyter, vol. 1(1), pages 1-38, April.
    16. Carroll, Christopher D & Kimball, Miles S, 1996. "On the Concavity of the Consumption Function," Econometrica, Econometric Society, vol. 64(4), pages 981-992, July.
    17. Stephen P. Zeldes, 1989. "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," The Quarterly Journal of Economics, Oxford University Press, vol. 104(2), pages 275-298.
    18. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    19. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
    20. Christopher D. Carroll, 1994. "How does Future Income Affect Current Consumption?," The Quarterly Journal of Economics, Oxford University Press, vol. 109(1), pages 111-147.
    21. Orazio P. Attanasio & Guglielmo Weber, 1993. "Consumption Growth, the Interest Rate and Aggregation," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 631-649.
    22. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    23. Sydney Ludvigson, 1999. "Consumption And Credit: A Model Of Time-Varying Liquidity Constraints," The Review of Economics and Statistics, MIT Press, vol. 81(3), pages 434-447, August.
    24. MaCurdy, Thomas E., 1982. "The use of time series processes to model the error structure of earnings in a longitudinal data analysis," Journal of Econometrics, Elsevier, vol. 18(1), pages 83-114, January.
    25. Deaton, Angus, 1992. "Understanding Consumption," OUP Catalogue, Oxford University Press, number 9780198288244.
    26. 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.
    27. Christopher D. Carroll, 1991. "Buffer stock saving and the permanent income hypothesis," Working Paper Series / Economic Activity Section 114, Board of Governors of the Federal Reserve System (U.S.).
    28. Hall, Robert E, 1988. "Intertemporal Substitution in Consumption," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 339-357, April.
    29. Skinner, Jonathan, 1988. "Risky income, life cycle consumption, and precautionary savings," Journal of Monetary Economics, Elsevier, vol. 22(2), pages 237-255, September.
    30. Abowd, John M & Card, David, 1989. "On the Covariance Structure of Earnings and Hours Changes," Econometrica, Econometric Society, vol. 57(2), pages 411-445, March.
    31. repec:fth:harver:1435 is not listed on IDEAS
    32. Karen E. Dynan, 1993. "How prudent are consumers?," Working Paper Series / Economic Activity Section 135, Board of Governors of the Federal Reserve System (U.S.).
    33. Lusardi, Annamaria, 1996. "Permanent Income, Current Income, and Consumption: Evidence from Two Panel Data Sets," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 81-90, January.
    34. Dynan, Karen E, 1993. "How Prudent Are Consumers?," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1104-1113, December.
    35. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
    Full references (including those not matched with items on IDEAS)

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fednrp:9712. 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: (Amy Farber). General contact details of provider: http://edirc.repec.org/data/frbnyus.html .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.