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Hypothesis testing of multiple inequalities: the method of constraint chaining

  • Le-Yu Chen


    (Institute for Fiscal Studies and Academia Sinica)

  • Jerzy Szroeter

    (Institute for Fiscal Studies)

Econometric inequality hypotheses arise in diverse ways. Examples include concavity restrictions on technological and behavioural functions, monotonicity and dominance relations, one-sided constraints on conditional moments in GMM estimation, bounds on parameters which are only partially identified, and orderings of predictive performance measures for competing models. In this paper we set forth four key properties which tests of multiple inequality constraints should ideally satisfy. These are (1) (asymptotic) exactness, (2) (asymptotic)similarity on the boundary, (3) absence of nuisance parameters from the asymptotic null distribution of the test statistic, (4) low computational complexity and boostrapping cost. We observe that the predominant tests currently used in econometrics do not appear to enjoy all these properties simultaneously. We therefore ask the question : Does there exist any nontrivial test which, as a mathematical fact, satisfies the first three properties and, by any reasonable measure, satisfies the fourth ? Remarkably the answer is affirmative. The paper demonstrates this constructively. We introduce a method of test construction called chaining which begins by writing multiple inequalities as a single equality using zero-one indicator functions. We then smooth the indicator functions. The approximate equality thus obtained is the basis of a well-behaved test. This test may be considered as the baseline of a wider class of tests. A full asymptotic theory is provided for the baseline. Simulation results show that the finite-sample performance of the test matches the theory quite well.

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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP13/09.

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Date of creation: Jun 2009
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Handle: RePEc:ifs:cemmap:13/09
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  1. Peter Hansen, 2003. "Asymptotic Tests of Composite Hypotheses," Working Papers 2003-09, Brown University, Department of Economics.
  2. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
  3. Fisher, Gordon & Willson, Douglas & Xu, Kuan, 1998. "An empirical analysis of term premiums using significance tests for stochastic dominance," Economics Letters, Elsevier, vol. 60(2), pages 195-203, August.
  4. Andrews, Donald W. K., 1998. "Hypothesis testing with a restricted parameter space," Journal of Econometrics, Elsevier, vol. 84(1), pages 155-199, May.
  5. Wolak, Frank A., 1989. "Testing inequality constraints in linear econometric models," Journal of Econometrics, Elsevier, vol. 41(2), pages 205-235, June.
  6. Donald W. K. Andrews & Panle Jia Barwick, 2012. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Econometrica, Econometric Society, vol. 80(6), pages 2805-2826, November.
  7. Davidson, Russell & Duclos, Jean-Yves, 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Cahiers de recherche 9805, Université Laval - Département d'économique.
  8. King, Maxwell L. & Smith, Murray D., 1986. "Joint one-sided tests of linear regression coefficients," Journal of Econometrics, Elsevier, vol. 32(3), pages 367-383, August.
  9. Savin, N E, 1980. "The Bonferroni and the Scheffe Multiple Comparison Procedures," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 255-73, January.
  10. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  11. Guggenberger, Patrik & Hahn, Jinyong & Kim, Kyooil, 2008. "Specification testing under moment inequalities," Economics Letters, Elsevier, vol. 99(2), pages 375-378, May.
  12. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  13. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
  14. Oliver Linton & Kyungchul Song & Yoon-Jae Whang, 2008. "Bootstrap tests of stochastic dominance with asymptotic similarity on the boundary," CeMMAP working papers CWP08/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  15. Savin, N.E., 1984. "Multiple hypothesis testing," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 14, pages 827-879 Elsevier.
  16. Hazilla, Michael & Kopp, Raymond J., 1986. "Testing for separable functional structure using temporary equilibrium models," Journal of Econometrics, Elsevier, vol. 33(1-2), pages 119-141.
  17. Adam Rosen, 2006. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," CeMMAP working papers CWP25/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  18. Ricardo Reis, 2004. "Inattentive Consumers," Working Papers 135, Princeton University, Woodrow Wilson School of Public and International Affairs, Discussion Papers in Economics..
  19. Horowitz, Joel L., 2002. "Bootstrap critical values for tests based on the smoothed maximum score estimator," Journal of Econometrics, Elsevier, vol. 111(2), pages 141-167, December.
  20. Koebel, Bertrand & Falk, Martin & Laisney, Francois, 2003. "Imposing and Testing Curvature Conditions on a Box-Cox Cost Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 319-35, April.
  21. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
  22. Richardson, Matthew & Richardson, Paul & Smith, Tom, 1992. "The monotonicity of the term premium *1: Another look," Journal of Financial Economics, Elsevier, vol. 31(1), pages 97-105.
  23. Matthew Richardson & Paul Richardson & Tom Smith, . "The Monotonicity of the Term Premium: Another Look (Reprint 026)," Rodney L. White Center for Financial Research Working Papers 3-92, Wharton School Rodney L. White Center for Financial Research.
  24. Andrews, Donald W K, 2002. "Generalized Method of Moments Estimation When a Parameter Is on a Boundary," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 530-44, October.
  25. Kodde, David A & Palm, Franz C, 1986. "Wald Criteria for Jointly Testing Equality and Inequality Restriction s," Econometrica, Econometric Society, vol. 54(5), pages 1243-48, September.
  26. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228 Elsevier.
  27. McAdams, David, 2008. "Partial identification and testable restrictions in multi-unit auctions," Journal of Econometrics, Elsevier, vol. 146(1), pages 74-85, September.
  28. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1932, October.
  29. Gael M. Martin & Andrew Reidy & Jill Wright, 2009. "Does the option market produce superior forecasts of noise-corrected volatility measures?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 77-104.
  30. McManus, Douglas A., 1991. "Who Invented Local Power Analysis?," Econometric Theory, Cambridge University Press, vol. 7(02), pages 265-268, June.
  31. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January.
  32. Kodde, David A & Palm, Franz C, 1987. "A Parametric Test of the Negativity of the Substitution Matrix," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 2(3), pages 227-35, July.
  33. Frank A. Wolak, 2007. "Quantifying the supply-side benefits from forward contracting in wholesale electricity markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(7), pages 1179-1209.
  34. Fleming, Jeff & Kirby, Chris & Ostdiek, Barbara, 2006. "Bootstrap tests of multiple inequality restrictions on variance ratios," Economics Letters, Elsevier, vol. 91(3), pages 343-348, June.
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