Testing and imposing Slutsky symmetry in nonparametric demand systems
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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- Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
- Herman J. Bierens & Werner Ploberger, 1997.
"Asymptotic Theory of Integrated Conditional Moment Tests,"
Econometric Society, vol. 65(5), pages 1129-1152, September.
- Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
- Gallant, A. Ronald & Souza, Geraldo, 1991. "On the asymptotic normality of Fourier flexible form estimates," Journal of Econometrics, Elsevier, vol. 50(3), pages 329-353, December.
- Hoderlein, Stefan, 2011. "How many consumers are rational?," Journal of Econometrics, Elsevier, vol. 164(2), pages 294-309, October.
- Stefan Hoderlein, 2009. "How Many Consumers are Rational?," Boston College Working Papers in Economics 748, Boston College Department of Economics.
- Stefan Hoderlein, 2009. "How many consumers are rational?," CeMMAP working papers CWP32/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- 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.
- Wolfgang HÄRDLE & A. TSYBAKOV, 1995. "Local Polynomial Estimators of the Volatility Function in Nonparametric Autoregression," SFB 373 Discussion Papers 1995,42, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
- Arthur Lewbel & Krishna Pendakur, 2009. "Tricks with Hicks: The EASI Demand System," American Economic Review, American Economic Association, vol. 99(3), pages 827-863, June.
- Arthur Lewbel & Krishna Pendakur, 2006. "Tricks With Hicks: The EASI Demand System," Boston College Working Papers in Economics 651, Boston College Department of Economics, revised 26 Nov 2008.
- Lewbel, Arthur, 1995. "Consistent nonparametric hypothesis tests with an application to Slutsky symmetry," Journal of Econometrics, Elsevier, vol. 67(2), pages 379-401, June.
- Richard Blundell & Alan Duncan & Krishna Pendakur, 1998. "Semiparametric estimation and consumer demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 435-461.
- Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
- Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
- Blundell, Richard & Robin, Jean Marc, 1999. "Estimation in Large and Disaggregated Demand Systems: An Estimator for Conditionally Linear Systems," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 209-232, May-June.
- R, Blundell & Jean-Marc Robin, 1997. "Estimation in Large and Dissagregated Demand Systems : An Estimator for Conditionally Linear Systems," Working Papers 97-08, Centre de Recherche en Economie et Statistique.
- Richard Blundell & Jean-Marc Robin, 1999. "Estimation in large and disaggregated demand systems: an estimator for conditionally linear systems," Post-Print hal-00359353, HAL.
- Tripathi, Gautam & Kim, Woocheol, 2003. "Nonparametric Estimation Of Homogeneous Functions," Econometric Theory, Cambridge University Press, vol. 19(04), pages 640-663, August.
- Tripathi, Gautam & Kim, Woocheol, 2000. "Nonparametric estimation of homogeneous function," SFB 373 Discussion Papers 2000,85, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- 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.
- Gozalo, Pedro L., 1997. "Nonparametric bootstrap analysis with applications to demographic effects in demand functions," Journal of Econometrics, Elsevier, vol. 81(2), pages 357-393, December.
- Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-829, July.
- Ait-Sahalia, Yacine & Bickel, Peter J. & Stoker, Thomas M., 2001. "Goodness-of-fit tests for kernel regression with an application to option implied volatilities," Journal of Econometrics, Elsevier, vol. 105(2), pages 363-412, December.
- Epstein, Larry G. & Yatchew, Adonis J., 1985. "Non-parametric hypothesis testing procedures and applications to demand analysis," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 149-169. Full references (including those not matched with items on IDEAS)