Identification robust confidence set methods for inference on parameter ratios with application to discrete choice models
AbstractWe study the problem of building confidence sets for ratios of parameters, from an identification robust perspective. In particular, we address the simultaneous confidence set estimation of a finite number of ratios. Results apply to a wide class of models suitable for estimation by consistent asymptotically normal procedures. Conventional methods (e.g.Â the delta method) derived by excluding the parameter discontinuity regions entailed by the ratio functions and which typically yield bounded confidence limits, break down even if the sample size is largeÂ (Dufour, 1997). One solution to this problem, which we take in this paper, is to use variants ofÂ Fieller's (1940, 1954) method. By inverting a joint test that does not require identifying the ratios, Fieller-based confidence regions are formed for the full set of ratios. Simultaneous confidence sets for individual ratios are then derived by applying projection techniques, which allow for possibly unbounded outcomes. In this paper, we provide simple explicit closed-form analytical solutions for projection-based simultaneous confidence sets, in the case of linear transformations of ratios. Our solution further provides a formal proof for the expressions in Zerbe etÂ al. (1982) pertaining to individual ratios. We apply the geometry of quadrics as introduced by (Dufour and Taamouti, 2005) and (Dufour and Taamouti, 2007), in a different although related context. The confidence sets so obtained are exact if the inverted test statistic admits a tractable exact distribution, for instance in the normal linear regression context. The proposed procedures are applied and assessed via illustrative Monte Carlo and empirical examples, with a focus on discrete choice models estimated by exact or simulation-based maximum likelihood. Our results underscore the superiority of Fieller-based methods.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 157 (2010)
Issue (Month): 2 (August)
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Web page: http://www.elsevier.com/locate/jeconom
Confidence set Generalized Fieller's theorem Delta method Weak identification Parameter transformation Discrete choice Maximum simulated likelihood;
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