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

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  • Bolduc, Denis
  • Khalaf, Lynda
  • Yélou, Clément

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.

Suggested Citation

  • Bolduc, Denis & Khalaf, Lynda & Yélou, Clément, 2010. "Identification robust confidence set methods for inference on parameter ratios with application to discrete choice models," Journal of Econometrics, Elsevier, vol. 157(2), pages 317-327, August.
  • Handle: RePEc:eee:econom:v:157:y:2010:i:2:p:317-327
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    References listed on IDEAS

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    Cited by:

    1. Reed, W. Robert & Zhu, Min, 2017. "On estimating long-run effects in models with lagged dependent variables," Economic Modelling, Elsevier, vol. 64(C), pages 302-311.
    2. Christian Murray & Juan Urquiza, 2017. "Do Estimated Taylor Rules Suffer from Weak Identification?," Working Papers 2017-274-09, Department of Economics, University of Houston.
    3. Luger, Richard, 2012. "Finite-sample bootstrap inference in GARCH models with heavy-tailed innovations," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3198-3211.
    4. Jean-Thomas Bernard & Michael Gavin & Lynda Khalaf & Marcel Voia, 2011. "The Environmental Kuznets Curve: Tipping Points, Uncertainty and Weak Identification," Cahiers de recherche CREATE 2011-4, CREATE.
    5. Jean-Thomas Bernard & Michael Gavin & Lynda Khalaf & Marcel Voia, 2015. "Environmental Kuznets Curve: Tipping Points, Uncertainty and Weak Identification," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 60(2), pages 285-315, February.
    6. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2014. "Exact confidence sets and goodness-of-fit methods for stable distributions," Journal of Econometrics, Elsevier, vol. 181(1), pages 3-14.
    7. John Dagsvik & Tom Kornstad & Terje Skjerpen, 2013. "Labor force participation and the discouraged worker effect," Empirical Economics, Springer, vol. 45(1), pages 401-433, August.
    8. Ferris, J. Stephen & Voia, Marcel C., 2015. "The effect of federal government size on private economic performance in Canada: 1870–2011," Economic Modelling, Elsevier, vol. 49(C), pages 172-185.
    9. Jean-Thomas Bernard & Ba Chu & Lynda Khalaf & Marcel-Cristian Voia, 2017. "Non-standard Confidence Sets for Ratios and Tipping Points with Applications to Dynamic Panel Data," Carleton Economic Papers 17-05, Carleton University, Department of Economics.
    10. Daziano, Ricardo A. & Achtnicht, Martin, 2014. "Accounting for uncertainty in willingness to pay for environmental benefits," Energy Economics, Elsevier, vol. 44(C), pages 166-177.
    11. Gatta, Valerio & Marcucci, Edoardo & Scaccia, Luisa, 2015. "On finite sample performance of confidence intervals methods for willingness to pay measures," Transportation Research Part A: Policy and Practice, Elsevier, vol. 82(C), pages 169-192.
    12. Khalaf, Lynda & Urga, Giovanni, 2014. "Identification robust inference in cointegrating regressions," Journal of Econometrics, Elsevier, vol. 182(2), pages 385-396.
    13. Daziano, Ricardo A., 2013. "Conditional-logit Bayes estimators for consumer valuation of electric vehicle driving range," Resource and Energy Economics, Elsevier, vol. 35(3), pages 429-450.

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