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Testing and imposing Slutsky symmetry in nonparametric demand systems

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  • Haag, Berthold R.
  • Hoderlein, Stefan
  • Pendakur, Krishna

Abstract

Maximization of utility implies that consumer demand systems have a Slutsky matrix which is everywhere symmetric. However, previous non- and semi-parametric approaches to the estimation of consumer demand systems do not give estimators that are restricted to satisfy this condition, nor do they offer powerful tests of this restriction. We use nonparametric modeling to test and impose Slutsky symmetry in a system of expenditure share equations over prices and expenditure. In this context, Slutsky symmetry is a set of nonlinear cross-equation restrictions on levels and derivatives of consumer demand equations. The key insight is that due to the differing convergence rates of levels and derivatives and due to the fact that the symmetry restrictions are linear in derivatives, both the test and the symmetry restricted estimator behave asymptotically as if these restrictions were (locally) linear. We establish large and finite sample properties of our methods, and show that our test has advantages over the only other comparable test. All methods we propose are implemented with Canadian micro-data. We find that our nonparametric analysis yields statistically significantly and qualitatively different results from traditional parametric estimators and tests.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 153 (2009)
Issue (Month): 1 (November)
Pages: 33-50

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Handle: RePEc:eee:econom:v:153:y:2009:i:1:p:33-50

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Demand system Slutsky symmetry Rationality Nonparametric regression Nonparametric testing;

References

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  14. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
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  16. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
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Citations

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Cited by:
  1. Anyck Dauphin & Abdel‐Rahmen El Lahga & Bernard Fortin & Guy Lacroix, 2011. "Are Children Decision‐Makers within the Household?," Economic Journal, Royal Economic Society, vol. 121(553), pages 871-903, 06.
  2. Hoderlein, Stefan, 2011. "How many consumers are rational?," Journal of Econometrics, Elsevier, vol. 164(2), pages 294-309, October.
  3. Holger Dette & Stefan Hoderlein & Natalie Neumeyer, 2011. "Testing multivariate economic restrictions using quantiles: the example of Slutsky negative semidefiniteness," CeMMAP working papers CWP14/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Joel Horowitz, 2013. "Ill-posed inverse problems in economics," CeMMAP working papers CWP37/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Pendakur, Krishna & Scholz, Michael & Sperlich, Stefan, 2010. "Semiparametric indirect utility and consumer demand," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2763-2775, November.
  6. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2011. "Bounding quantile demand functions using revealed preference inequalities," CeMMAP working papers CWP21/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Krishna Pendakur & Stefan Sperlich, 2010. "Semiparametric estimation of consumer demand systems in real expenditure," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(3), pages 420-457.
  8. Hoderlein, Stefan & Mihaleva, Sonya, 2008. "Increasing the price variation in a repeated cross section," Journal of Econometrics, Elsevier, vol. 147(2), pages 316-325, December.
  9. Fabrizio Balli, 2012. "Are Traditional Equivalence Scales Still Useful? A Review and A Possible Answer," Department of Economics University of Siena 656, Department of Economics, University of Siena.

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