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Is the elasticity of intertemporal substitution constant?

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  • Thomas Crossley

    ()
    (Institute for Fiscal Studies and University of Cambridge)

  • Hamish Low

    ()
    (Institute for Fiscal Studies and Trinity College, Cambridge)

Abstract

This paper shows that a power utility specification of preferences over total expenditure (ie. CRRA preferences) implies that intratemporal demands are in the PIGL/PIGLOG class. This class generates (at most) rank two demand systems and we can test the validity of power utility on cross-section data. Further, if we maintain the assumption of power utility, and within period preferences are not homothetic, then the intertemporal preference parameter is identified by the curvature of Engel curves. Under the power utility assumption, neither Euler equation estimation nor structural consumption function estimation is necessary to identify the power parameter. In our empirical work, we use demand data to estimate the power utility parameter and to test the assumption of the power utility representation. We find estimates of the power parameter larger than obtained from Euler equation estimation, but we reject the power specification of within period utility.

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Bibliographic Info

Paper provided by Institute for Fiscal Studies in its series IFS Working Papers with number W05/25.

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Length: 24 pp.
Date of creation: Nov 2005
Date of revision:
Handle: RePEc:ifs:ifsewp:05/25

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Keywords: Elasticity of intertemporal substitution; Euler equation estimation; demand systems;

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  1. Lewbel, Arthur, 1996. "Demand Estimation with Expenditure Measurement Errors on the Left and Right Hand Side," The Review of Economics and Statistics, MIT Press, vol. 78(4), pages 718-25, November.
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  5. Martin Browning & Thomas F. Crossley, 2000. "Luxuries Are Easier to Postpone: A Proof," Journal of Political Economy, University of Chicago Press, vol. 108(5), pages 1022-1026, October.
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  8. Atkeson, Andrew & Ogaki, Masao, 1996. "Wealth-varying intertemporal elasticities of substitution: Evidence from panel and aggregate data," Journal of Monetary Economics, Elsevier, vol. 38(3), pages 507-534, December.
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  11. Arthur Lewbel, 2003. "A rational rank four demand system," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(2), pages 127-135.
  12. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June.
  13. Orazio Attanasio & Hamish Low, 2002. "Estimating Euler equations," IFS Working Papers W02/06, Institute for Fiscal Studies.
  14. Muellbauer, John, 1976. "Community Preferences and the Representative Consumer," Econometrica, Econometric Society, vol. 44(5), pages 979-99, September.
  15. Pollak, Robert A, 1971. "Additive Utility Functions and Linear Engel Curves," Review of Economic Studies, Wiley Blackwell, vol. 38(116), pages 401-14, October.
  16. Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
  17. MacKinnon, James G, 1992. "Model Specification Tests and Artificial Regressions," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 102-46, March.
  18. Attanasio, Orazio P & Weber, Guglielmo, 1995. "Is Consumption Growth Consistent with Intertemporal Optimization? Evidence from the Consumer Expenditure Survey," Journal of Political Economy, University of Chicago Press, vol. 103(6), pages 1121-57, December.
  19. Lwebel Arthur & Perraudin William, 1995. "A Theorem on Portfolio Separation with General Preferences," Journal of Economic Theory, Elsevier, vol. 65(2), pages 624-626, April.
  20. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
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Citations

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Cited by:
  1. Moore, Michael J. & Roche, Maurice J., 2010. "Solving exchange rate puzzles with neither sticky prices nor trade costs," Journal of International Money and Finance, Elsevier, vol. 29(6), pages 1151-1170, October.
  2. Natalia, Khorunzhina & Wayne Roy, Gayle, 2011. "Heterogenous intertemporal elasticity of substitution and relative risk aversion: estimation of optimal consumption choice with habit formation and measurement errors," MPRA Paper 34329, University Library of Munich, Germany.
  3. Mumtaz, Haroon & Surico, Paolo, 2011. "Estimating the Aggregate Consumption Euler Equation with State-Dependent Parameters," CEPR Discussion Papers 8233, C.E.P.R. Discussion Papers.
  4. Timo Boppart, 2011. "Structural change and the Kaldor facts in a growth model with relative price effects and non-Gorman preferences," ECON - Working Papers 002, Department of Economics - University of Zurich.
  5. H. Kim & Keith McLaren & K. Wong, 2013. "Empirical demand systems incorporating intertemporal consumption dynamics," Empirical Economics, Springer, vol. 45(1), pages 349-370, August.

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