Identification robust confidence set methods for inference on parameter ratios with application to discrete choice models

Denis Bolduc (), Lynda Khalaf and Clement Yelou

Journal of Econometrics, 2010, vol. 157, issue 2, 317-327

Abstract: We 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. 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 large (Dufour, 1997). One solution to this problem, which we take in this paper, is to use variants of 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 et 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.

Keywords: Confidence; set; Generalized; Fieller's; theorem; Delta; method; Weak; identification; Parameter; transformation; Discrete; choice; Maximum; simulated; likelihood (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (22)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304-4076(10)00028-X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:157:y:2010:i:2:p:317-327

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().