Conditional inference for possibly unidentified structural equations


Forchini, G. and Hillier, G.H. (1999) Conditional inference for possibly unidentified structural equations. Southampton, UK, University of Southampton (Discussion Papers in Economics and Econometrics 9906).

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Description/Abstract

The 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

Item Type: Monograph (Discussion Paper)
Related URLs:
Subjects: H Social Sciences > HB Economic Theory
H Social Sciences > HA Statistics
Divisions: University Structure - Pre August 2011 > School of Social Sciences > Economics
ePrint ID: 33141
Date Deposited: 14 Jun 2007
Last Modified: 27 Mar 2014 18:20
URI: http://eprints.soton.ac.uk/id/eprint/33141

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