Testing multivariate economic restrictions using quantiles: the example of Slutsky negative semidefiniteness
AbstractThis paper is concerned with testing rationality restrictions using quantile regression methods. Specifically, we consider negative semidefiniteness of the Slutsky matrix, arguably the core restriction implied by utility maximization. We consider a heterogeneous population characterized by a system of nonseparable structural equations with infinite dimensional unobservable. To analyze the economic restriction, we employ quantile regression methods because they allow us to utilize the entire distribution of the data. Difficulties arise because the restriction involves several equations, while the quantile is a univariate concept. We establish that we may test the economic restriction by considering quantiles of linear combinations of the dependent variable. For this hypothesis we develop a new empirical process based test that applies kernel quantile estimators, and derive its large sample behavior. We investigate the performance of the test in a simulation study. Finally, we apply all concepts to Canadian individual data, and show that rationality is an acceptable description of actual individual behavior.
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Bibliographic InfoPaper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP14/11.
Date of creation: May 2011
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Other versions of this item:
- Holger Dette & Stefan Hoderlein & Natalie Neumeyer, 2013. "Testing Multivariate Economic Restrictions Using Quantiles: The Example of Slutsky Negative Semidefiniteness," Boston College Working Papers in Economics 836, Boston College Department of Economics.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
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- Wolak, Frank A, 1991. "The Local Nature of Hypothesis Tests Involving Inequality Constraints in Nonlinear Models," Econometrica, Econometric Society, vol. 59(4), pages 981-95, July.
- 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.
- 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?," CeMMAP working papers CWP32/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Stefan Hoderlein, 2009. "How Many Consumers are Rational?," Boston College Working Papers in Economics 748, Boston College Department of Economics.
- Rosa L. Matzkin, 2003.
"Nonparametric Estimation of Nonadditive Random Functions,"
Econometric Society, vol. 71(5), pages 1339-1375, 09.
- Rosa L. Matzkin, 1999. "Nonparametric Estimation of Nonadditive Random Functions," Working Papers 38, Universidad de San Andres, Departamento de Economia, revised Sep 2001.
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521608275.
- Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008.
"Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth,"
Working Papers ECARES
2008_042, ULB -- Universite Libre de Bruxelles.
- Marc Hallin & Davy Paindaveine & Miroslav Šiman, 2010. "Multivariate quantiles and multiple-output regression quantiles: From L1 optimization to halfspace depth," ULB Institutional Repository 2013/127979, ULB -- Universite Libre de Bruxelles.
- Pendakur, K., 1999.
"Taking Prices Seriously in the Measurement of Inequality,"
dp99-7, Department of Economics, Simon Fraser University.
- Pendakur, Krishna, 2002. "Taking prices seriously in the measurement of inequality," Journal of Public Economics, Elsevier, vol. 86(1), pages 47-69, October.
- Holger Dette & Jens Wagener & Stanislav Volgushev, 2011. "Comparing Conditional Quantile Curves," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 63-88, 03.
- Sun, Y., 2003.
"A Consistent Nonparametric Equality Test of Conditional Quantile Functions,"
2003-10, University of Guelph, Department of Economics and Finance.
- Sun, Yiguo, 2006. "A Consistent Nonparametric Equality Test Of Conditional Quantile Functions," Econometric Theory, Cambridge University Press, vol. 22(04), pages 614-632, August.
- Kihlstrom, Richard E & Mas-Colell, Andreu & Sonnenschein, Hugo, 1976. "The Demand Theory of the Weak Axiom of Revealed Preference," Econometrica, Econometric Society, vol. 44(5), pages 971-78, September.
- Stoker, Thomas M, 1989. "Tests of Additive Derivative Constraints," Review of Economic Studies, Wiley Blackwell, vol. 56(4), pages 535-52, October.
- Haag, Berthold R. & Hoderlein, Stefan & Pendakur, Krishna, 2009. "Testing and imposing Slutsky symmetry in nonparametric demand systems," Journal of Econometrics, Elsevier, vol. 153(1), pages 33-50, November.
- Wolfgang Härdle & Werner Hildenbrand & Michael Jerison, 1989.
"Empirical Evidence on the Law of Demand,"
Discussion Paper Serie A
264a, University of Bonn, Germany.
- HARDLE, Wolfgang & HILDENBRAND, Werner & JERISON, Michael, . "Empirical evidence on the law of demand," CORE Discussion Papers RP -968, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Haerdle,W. Hildenbrand,W. Jerison,M., 1988. "Empirical evidence on the law of demand," Discussion Paper Serie A 193, University of Bonn, Germany.
- Stefan Sperlich, 2009. "A note on non-parametric estimation with predicted variables," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 382-395, 07.
- Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
- Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, 07.
- Robert Serfling, 2002. "Quantile functions for multivariate analysis: approaches and applications," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 214-232.
- Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June.
- Jerry Hausman & Whitney Newey, 2013. "Individual heterogeneity and average welfare," CeMMAP working papers CWP34/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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