On the Inconsistency of Instrumental Variables Estimators for the Coefficients of Certain Dummy Variables
AbstractIn this paper we consider the asymptotic properties of the Instrumental Variables (IV) estimator of the parameters in a linear regression model with some random regressors, and other regressors that are dummy variables. The latter have the special property that the number of non-zero values is fixed, and does not increase with the sample size. We prove that the IV estimator of the coefficient vector for the dummy variables is inconsistent, while that for the other regressors is weakly consistent under standard assumptions. However, the usual estimator for the asymptotic covariance matrix of the I.V. estimator for all of the coefficients retains its usual consistency. The t-test statistics for the dummy variable coefficients are still asymptotically standard normal, despite the inconsistency of the associated IV coefficient estimator. These results extend the earlier results of Hendry and Santos (2005), which relate to a fixed-regressor model, in which the dummy variables are non-zero for just a single observation, and OLS estimation is used.
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Bibliographic InfoPaper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 1106.
Length: 16 pages
Date of creation: 04 May 2011
Date of revision:
Note: ISSN 1485-6441
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Postal: PO Box 1700, STN CSC, Victoria, BC, Canada, V8W 2Y2
Web page: http://web.uvic.ca/econ
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Dummy variables; indicator variables; instrumental variables; inconsistent estimator;
Find related papers by JEL classification:
- C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
- C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
- C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
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