EconStor >
Institute for Fiscal Studies (IFS), London >
cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS) >

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10419/64780
  
Title:Hypothesis testing of multiple inequalities: The method of constraint chaining PDF Logo
Authors:Chen, Le-Yu
Szroeter, Jerzy
Issue Date:2009
Series/Report no.:cemmap working paper CWP13/09
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.
Subjects:tests
multiple inequality constraints
exactness
similarity on the boundary
smoothing
chaining methods
JEL:C1
C4
Persistent Identifier of the first edition:doi:10.1920/wp.cem.2009.1309
Document Type:Working Paper
Appears in Collections:cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS)

Files in This Item:
File Description SizeFormat
602161819.pdf548.1 kBAdobe PDF
No. of Downloads: Counter Stats
Download bibliographical data as: BibTeX
Share on:http://hdl.handle.net/10419/64780

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.