Conditional inference for possibly unidentified structural equations
AbstractThe possibility that a structural equation may not be identified casts doubt on the measures of estimator precision that are normally used. We argue that the observed identifiability test statistic is directly relevant to the precision with which the structural parameters can be estimated, and hence argue that inference in such models should be conditioned on the observed value of that statistic (or statistics). We examine in detail the effects of conditioning on the properties of the ordinary least squares (OLS) and two-stage least squares (TSLS) estimators for the coefficients of the endogenous variables in a single structural equation. We show that: (a) conditioning has very little impact on the properties of the OLS estimator, but a substantial impact on those of the TSLS estimator; (b) the conditional variance of the TSLS estimator can be very much larger than its unconditional variance (when the identifiability statistic is small), or very much smaller (when the identifiability statistic is large); and (c) conditional mean-square-error comparisons of the two estimators favour the OLS estimator when the sample evidence only weakly supports the identifiablity hypothesis, can favour TSLS slightly when that evidence is moderately favourable, but there is nothing to choose between the two estimators when the data strongly supports the identification hypothesis
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 Economics Division, School of Social Sciences, University of Southampton in its series Discussion Paper Series In Economics And Econometrics with number 9906.
Date of creation: 01 Jan 1999
Date of revision:
Other versions of this item:
- Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(05), pages 707-743, October.
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.:
- Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
- D.S. Poskitt & C.L. Skeels, 2002. "Assessing Instrumental Variable Relevance:An Alternative Measure and Some Exact Finite Sample Theory," Department of Economics - Working Papers Series 862, The University of Melbourne.
- Frank Kleibergen & Eric Zivot, 2003.
"Bayesian and Classical Approaches to Instrumental Variable Regression,"
UWEC-2002-21-P, University of Washington, Department of Economics.
- Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
- Frank Kleibergen & Eric Zivot, 1998. "Bayesian and Classical Approaches to Instrumental Variable Regression," Discussion Papers in Economics at the University of Washington 0063, Department of Economics at the University of Washington.
- Frank Kleibergen & Eric Zivot, 1998. "Bayesian and Classical Approaches to Instrumental Variables Regression," Econometrics 9812002, EconWPA.
- Kleibergen, F.R. & Zivot, E., 1998. "Bayesian and classical approaches to instrumental variable regression," Econometric Institute Research Papers EI 9835, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Frank Kleibergen & Eric Zivot, 1998. "Bayesian and Classical Approaches to Instrumental Variable Regression," Working Papers 0063, University of Washington, Department of Economics.
- Adrian Pagan, 2007. "Weak Instruments: A Guide to the Literature," NCER Working Paper Series 13, National Centre for Econometric Research.
- Poskitt, D.S. & Skeels, C.L., 2008.
"Conceptual frameworks and experimental design in simultaneous equations,"
Elsevier, vol. 100(1), pages 138-142, July.
- C.L. Skeels, 2007. "Conceptual Frameworks and Experimental Design in Simultaneous Equations," Department of Economics - Working Papers Series 1020, The University of Melbourne.
- Phillips, Peter C.B., 2003.
"Vision And Influence In Econometrics: John Denis Sargan,"
Cambridge University Press, vol. 19(03), pages 495-511, June.
- Peter C.B. Phillips, 2003. "Vision and Influence in Econometrics: John Denis Sargan," Cowles Foundation Discussion Papers 1393, Cowles Foundation for Research in Economics, Yale University.
- Grant Hillier & Giovanni Forchini, 2004. "Ill-posed Problems and Instruments' Weakness," Econometric Society 2004 Australasian Meetings 357, Econometric Society.
- Forchini, G., 2006.
"On The Bimodality Of The Exact Distribution Of The Tsls Estimator,"
Cambridge University Press, vol. 22(05), pages 932-946, October.
- Giovanni Forchini, 2005. "On the Bimodality of the Exact Distribution of the TSLS Estimator," Monash Econometrics and Business Statistics Working Papers 14/05, Monash University, Department of Econometrics and Business Statistics.
- Chao, John & Swanson, Norman R., 2007.
"Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction,"
Journal of Econometrics,
Elsevier, vol. 137(2), pages 515-555, April.
- John Chao & Norman Swanson, 2003. "Alternative Approximations of the Bias and MSE of the IV Estimator Under Weak Identification With an Application to Bias Correction," Departmental Working Papers 200315, Rutgers University, Department of Economics.
- John C. Chao & Norman Rasmus Swanson, 2004. "Alternative Approximations of the Bias and MSE of the IV Estimator Under Weak Identification with an Application to Bias Correction," Yale School of Management Working Papers ysm375, Yale School of Management.
- John Chao & Norman R. Swanson, 2003. "Alternative Approximations of the Bias and MSE of the IV Estimator under Weak Identification with an Application to Bias Correction," Cowles Foundation Discussion Papers 1418, Cowles Foundation for Research in Economics, Yale University.
- Russell Davidson & James G. MacKinnon, 2011. "Confidence Sets Based on Inverting Anderson-Rubin Tests," Working Papers 1257, Queen's University, Department of Economics.
- Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.
- Peter C. B. Phillips, 2003.
"Laws and Limits of Econometrics,"
Royal Economic Society, vol. 113(486), pages C26-C52, March.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Thorn).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.