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A Bootstrap Test for Positive Definiteness of Income Effect Matrices


  • Härdle, Wolfgang
  • Hart, Jeffrey D.


Positive definiteness of income effect matrices provides a sufficient condition for the law of demand to hold. Given cross section household expenditure data, empirical evidence for the law of demand can be obtained by estimating such matrices. Härdle, Hildenbrand, and Jerison used the bootstrap method to simulate the distribution of the smallest eigenvalue of random matrices and to test their positive definiteness. Here, theoretical aspects of this bootstrap test of positive definiteness are considered. The asymptotic distribution of the smallest eigenvalue null, of the matrix estimate is obtained. This theory applies generally to symmetric, asymptotically normal random matrices. A bootstrap approximation to the distribution of null is shown to converge in probability to the asymptotic distribution of null. The bootstrap test is illustrated using British family expenditure survey data.

Suggested Citation

  • Härdle, Wolfgang & Hart, Jeffrey D., 1992. "A Bootstrap Test for Positive Definiteness of Income Effect Matrices," Econometric Theory, Cambridge University Press, vol. 8(02), pages 276-292, June.
  • Handle: RePEc:cup:etheor:v:8:y:1992:i:02:p:276-292_01

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    References listed on IDEAS

    1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    2. Kiefer, Nicholas M & Neumann, George R, 1979. "An Empirical Job-Search Model, with a Test of the Constant Reservation-Wage Hypothesis," Journal of Political Economy, University of Chicago Press, vol. 87(1), pages 89-107, February.
    3. Greene, William H., 1980. "Maximum likelihood estimation of econometric frontier functions," Journal of Econometrics, Elsevier, vol. 13(1), pages 27-56, May.
    4. Heckman, James J. & Singer, Burton, 1984. "Econometric duration analysis," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 63-132.
    5. Pakes, Ariel S, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," Econometrica, Econometric Society, vol. 54(4), pages 755-784, July.
    6. Lancaster, Tony & Chesher, Andrew, 1983. "An Econometric Analysis of Reservation Wages," Econometrica, Econometric Society, vol. 51(6), pages 1661-1676, November.
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    Cited by:

    1. Joachim Freyberger & Joel L. Horowitz, 2013. "Identification and shape restrictions in nonparametric instrumental variables estimation," CeMMAP working papers CWP31/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Hardle, W. & Park, B. U., 1995. "Testing increasing dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 641-653, June.
    3. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
    4. Manisha Chakrabarty & Anke Schmalenbach, 2002. "The Representative Agent Hypothesis: An Empirical Test," Bonn Econ Discussion Papers bgse26_2002, University of Bonn, Germany.
    5. Werner Hildenbrand & Alois Kneip, 2002. "Aggregation under structural stability: the change in consumption of a heterogeneous population," Bonn Econ Discussion Papers bgse4_2002, University of Bonn, Germany.
    6. Koebel, Bertrand M. & Falk, Martin & Laisney, François, 2000. "Imposing and testing curvature conditions on a Box-Cox function," ZEW Discussion Papers 00-70, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    7. Freyberger, Joachim & Horowitz, Joel L., 2015. "Identification and shape restrictions in nonparametric instrumental variables estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 41-53.

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