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Demand Systems with Nonstationary Prices

  • Arthur Lewbel

    (Boston College)

  • Serena Ng

    (University of Michigan)

Relative prices are nonstationary and standard root-T inference is invalid for demand systems. But demand systems are nonlinear functions of relative prices, and standard methods for dealing with nonstationarity in linear models cannot be used. Demand system residuals are also frequently found to be highly persistent, further complicating estimation and inference. We propose a variant of the translog demand system, the NTLOG, and an associated estimator that can be applied in the presence of nonstationary prices with possibly nonstationary errors. The errors in the NTLOG can be interpreted as random utility parameters. The estimates have classical root-T limiting distributions. We also propose an explanation for the observed nonstationarity of aggregate demand errors, based on aggregation of consumers with heterogeneous preferences in a slowly changing population. Estimates using U.S. data are provided. © 2005 President and Fellows of Harvard College and the Massachusetts Institute of Technology.

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Article provided by MIT Press in its journal Review of Economics and Statistics.

Volume (Year): 87 (2005)
Issue (Month): 3 (August)
Pages: 479-494

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Handle: RePEc:tpr:restat:v:87:y:2005:i:3:p:479-494
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  1. Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-29, July.
  2. Lewbel, Arthur, 1987. "Fractional demand systems," Journal of Econometrics, Elsevier, vol. 36(3), pages 311-337, November.
  3. Ng, S., 1995. "Testing for Homogeneity in Demand Systems when the Regressors Are Non-Stationary," Cahiers de recherche 9516, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. Blundell, Richard & Pashardes, Panos & Weber, Guglielmo, 1993. "What Do We Learn About Consumer Demand Patterns from Micro Data?," American Economic Review, American Economic Association, vol. 83(3), pages 570-97, June.
  5. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
  6. 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.
  7. W. Erwin Diewert & T.J. Wales, 1989. "Flexible Functional Forms and Global Curvature Conditions," NBER Technical Working Papers 0040, National Bureau of Economic Research, Inc.
  8. Arthur Lewbel & Serena Ng, 2005. "Demand Systems with Nonstationary Prices," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 479-494, August.
  9. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  10. Moschini, GianCarlo, 1999. "Imposing Local Curvature Conditions in Flexible Demand System," Staff General Research Papers 1745, Iowa State University, Department of Economics.
  11. Barten, A. P., 1969. "Maximum likelihood estimation of a complete system of demand equations," European Economic Review, Elsevier, vol. 1(1), pages 7-73.
  12. Pollak, Robert A & Wales, Terence J, 1980. "Comparison of the Quadratic Expenditure System and Translog Demand Systems with Alternative Specifications of Demographic Effects," Econometrica, Econometric Society, vol. 48(3), pages 595-612, April.
  13. Lewbel, Arthur, 1996. "Aggregation without Separability: A Generalized Composite Commodity Theorem," American Economic Review, American Economic Association, vol. 86(3), pages 524-43, June.
  14. Perron, P. & Ng, S., 1994. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Cahiers de recherche 9427, Universite de Montreal, Departement de sciences economiques.
  15. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-30, May.
  16. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June.
  17. McElroy, Marjorie B, 1987. "Additive General Error Models for Production, Cost, and Derived Demand or Share Systems," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 737-57, August.
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