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Hypothesis testing of multiple inequalities: the method of constraint chaining

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  • Le-Yu Chen

    (Institute for Fiscal Studies and Academia Sinica)

  • Jerzy Szroeter

Abstract

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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Bibliographic Info

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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Cited by:
  1. Donald W.K. Andrews, 2011. "Similar-on-the-Boundary Tests for Moment Inequalities Exist, But Have Poor Power," Cowles Foundation Discussion Papers 1815, Cowles Foundation for Research in Economics, Yale University.
  2. Huber, Martin & Mellace, Giovanni, 2011. "Testing instrument validity in sample selection models," Economics Working Paper Series 1145, University of St. Gallen, School of Economics and Political Science.
  3. Huber, Martin, 2012. "Statistical verification of a natural "natural experiment": Tests and sensitivity checks for the sibling sex ratio instrument," Economics Working Paper Series 1219, University of St. Gallen, School of Economics and Political Science.
  4. Chen, Le-Yu & Szroeter, Jerzy, 2014. "Testing multiple inequality hypotheses: A smoothed indicator approach," Journal of Econometrics, Elsevier, vol. 178(P3), pages 678-693.
  5. Huber, Martin & Mellace, Giovanni, 2011. "Testing instrument validity for LATE identification based on inequality moment constraints," Economics Working Paper Series 1143, University of St. Gallen, School of Economics and Political Science.

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