Identification Robust Confidence Sets Methods for Inference on Parameter Ratios and their Application to Estimating Value-of-Time
AbstractThe problem of constructing confidence set estimates for parameter ratios arises in a variety of econometrics contexts; these include value-of-time estimation in transportation research and inference on elasticities given several model specifications. Even when the model under consideration is identifiable, parameter ratios involve a possibly discontinuous parameter transformation that becomes ill-behaved as the denominator parameter approaches zero. More precisely, the parameter ratio is not identified over the whole parameter space: it is locally almost unidentified or (equivalently) weakly identified over a subset of the parameter space. It is well known that such situations can strongly affect the distributions of estimators and test statistics, leading to the failure of standard asymptotic approximations, as shown by Dufour. Here, we provide explicit solutions for projection-based simultaneous confidence sets for ratios of parameters when the joint confidence set is obtained through a generalized Fieller approach. A simulation study for a ratio of slope parameters in a simple binary probit model shows that the coverage rate of the Fieller's confidence interval is immune to weak identification whereas the confidence interval based on the delta-method performs poorly, even when the sample size is large. The procedures are examined in illustrative empirical models, with a focus on choice models
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 48.
Date of creation: 11 Nov 2005
Date of revision:
confidence interval; generalized Fieller's theorem; delta-method; weak identification; ratio of parameters.;
Find related papers by JEL classification:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
- R40 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - General
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- DUFOUR, Jean-Marie & TAAMOUTI, Mohamed, 2003.
"Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments,"
Cahiers de recherche
2003-10, Universite de Montreal, Departement de sciences economiques.
- Jean-Marie Dufour & Mohamed Taamouti, 2005. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Econometrica, Econometric Society, vol. 73(4), pages 1351-1365, 07.
- DUFOUR, Jean-Marie & TAAMOUTI, Mohamed, 2003. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Cahiers de recherche 08-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Jean-Marie Dufour & Mohamed Taamouti, 2003. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," CIRANO Working Papers 2003s-39, CIRANO.
- Davidson, R. & Mackinnon, J.G., 1996.
"The Size Distorsion of Bootstrap Tests,"
96a15, Universite Aix-Marseille III.
- James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
- Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
- Daniel McFadden, 1987.
"A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration,"
464, Massachusetts Institute of Technology (MIT), Department of Economics.
- McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
- DUFOUR, Jean-Marie, 2003.
"Identification, Weak Instruments and Statistical Inference in Econometrics,"
Cahiers de recherche
2003-12, Universite de Montreal, Departement de sciences economiques.
- Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
- Jean-Marie Dufour, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," CIRANO Working Papers 2003s-49, CIRANO.
- Bolduc, Denis, 1992. "Generalized autoregressive errors in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 26(2), pages 155-170, April.
- Davidson, Russell & MacKinnon, James G, 1999.
"Bootstrap Testing in Nonlinear Models,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 487-508, May.
- DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 10-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Bolduc, Denis, 1999. "A practical technique to estimate multinomial probit models in transportation," Transportation Research Part B: Methodological, Elsevier, vol. 33(1), pages 63-79, February.
- Dufour, J.-M., 1986.
"Nonlinear hypotheses, inequality restrictions and non-nested hypotheses: Exact simultaneous tests in linear regressions,"
CORE Discussion Papers
1986016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, vol. 57(2), pages 335-55, March.
- De Vany, Arthur, 1974. "The Revealed Value of Time in Air Travel," The Review of Economics and Statistics, MIT Press, vol. 56(1), pages 77-82, February.
- James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
- ABDELKHALEK, Touhami & DUFOUR, Jean-Marie, 1997.
"Statistical Inference for Computable General Equilibrium Models with Application to a Model of the Moroccan Economy,"
Cahiers de recherche
9713, Universite de Montreal, Departement de sciences economiques.
- Touhami Abdelkhalek & Jean-Marie Dufour, 1998. "Statistical Inference For Computable General Equilibrium Models, With Application To A Model Of The Moroccan Economy," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 520-534, November.
- James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc.
- Bates, John J, 1987. "Measuring Travel Time Values with a Discrete Choice Model: A Note," Economic Journal, Royal Economic Society, vol. 97(386), pages 493-98, June.
- Russell Davidson & James G. MacKinnon, 2001.
"Bootstrap Tests: How Many Bootstraps?,"
1036, Queen's University, Department of Economics.
- Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
- Bolduc, D., 1990. "Autoregressive Alternatives in the Multinomial Probit Model," Papers 9013, Laval - Recherche en Energie.
- Ben-Akiva, M. & Bolduc, D. & Bradley, M., 1993. "Estimation of Travel Choice Models with Randomly Distributed Values of Time," Papers 9303, Laval - Recherche en Energie.
- Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum).
If references are entirely missing, you can add them using this form.