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

Approximation Bias in Linearized Euler Equations

Listed author(s):
  • Sydney Ludvigson
  • Christina H. Paxson

A wide range of empirical applications rely on linear approximations to dynamic Euler equations. Among the most notable of these is the large and growing literature on precautionary saving that examines how consumption growth and saving behavior are affected by uncertainty and prudence. Linear approximations to Euler equations imply a linear relationship between expected consumption growth and uncertainty in consumption growth, with a slope coefficient that is a function of the coefficient of relative prudence. This literature has produced puzzling results: Estimates of the coefficient of relative prudence (and the coefficient of relative risk aversion) from regressions of consumption growth on uncertainty in consumption growth imply estimates of prudence and risk aversion that are unrealistically low. Using numerical solutions to a fairly standard intertemporal optimization problem, our results show that the actual relationship between expected consumption growth and uncertainty in consumption growth differs substantially from the relationship implied by a linear approximation. We also present Monte Carlo evidence that shows that the instrumental variables methods commonly used to estimate the parameters correct some, but not all, of the approximation bias.

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://www.nber.org/papers/t0236.pdf
Download Restriction: no

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0236.

as
in new window

Length:
Date of creation: Mar 1999
Publication status: published as Ludvigson, Sydney and Christina H. Paxson. "Approximation Bias In Linearized Euler Equations," Review of Economics and Statistics, 2001, v83(2,May), 242-256.
Handle: RePEc:nbr:nberte:0236
Contact details of provider: Postal:
National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.

Phone: 617-868-3900
Web page: http://www.nber.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. Pishke, J.S., 1992. "Individual Income, Incomplete Information and Aggregate Consumption," Papers 9238, Tilburg - Center for Economic Research.
  2. Miles S. Kimball, 1989. "Precautionary Saving in the Small and in the Large," NBER Working Papers 2848, National Bureau of Economic Research, Inc.
  3. Stephen P. Zeldes, "undated". "Consumption and Liquidity Constraints: An Empirical Investigation," Rodney L. White Center for Financial Research Working Papers 16-88, Wharton School Rodney L. White Center for Financial Research.
  4. repec:fth:jonhop:390 is not listed on IDEAS
  5. John Campbell & Angus Deaton, 1989. "Why is Consumption So Smooth?," Review of Economic Studies, Oxford University Press, vol. 56(3), pages 357-373.
  6. 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.
  7. 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.
  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," CEPR Discussion Papers 699, C.E.P.R. Discussion Papers.
  10. Orazio P. Attanasio & James Banks & Costas Meghir & Guglielmo Weber, 1995. "Humps and Bumps in Lifetime Consumption," NBER Working Papers 5350, National Bureau of Economic Research, Inc.
  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. 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.
  13. Angus Deaton, 1989. "Saving and Liquidity Constraints," NBER Working Papers 3196, National Bureau of Economic Research, Inc.
  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. Christopher D. Carroll, 1997. "Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health to the Second-Order Approximation)," NBER Working Papers 6298, National Bureau of Economic Research, Inc.
  16. Christopher D. Carroll & Miles S. Kimball, 1995. "On the Concavity of the Consumption Function," Macroeconomics 9503003, EconWPA.
  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, 1993. "Intertemporal Asset Pricing Without Consumption Data," Scholarly Articles 3221491, Harvard University Department of Economics.
  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, 1996. "Consumption and credit: a model of time-varying liquidity constraints," Research Paper 9624, Federal Reserve Bank of New York.
  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 Working Papers 2924, 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. Robert E. Hall, 1981. "Intertemporal Substitution in Consumption," NBER Working Papers 0720, National Bureau of Economic Research, Inc.
  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. John M. Abowd & David Card, 1986. "On the Covariance Structure of Earnings and Hours Changes," NBER Working Papers 1832, National Bureau of Economic Research, Inc.
  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)

This item is featured on the following reading lists or Wikipedia pages:

  1. Quantitative Macroeconomics and Real Business Cycles (QM&RBC)

When requesting a correction, please mention this item's handle: RePEc:nbr:nberte:0236. 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: ()

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.