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On the Inconsistency of Instrumental Variables Estimators for the Coefficients of Certain Dummy Variables

In 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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File URL: http://www.uvic.ca/socialsciences/economics/assets/docs/econometrics/ewp1106.pdf
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Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 1106.

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Length: 16 pages
Date of creation: 04 May 2011
Handle: RePEc:vic:vicewp:1106
Note: ISSN 1485-6441
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  1. Giles, David E. A., 1984. "Instrumental variables regressions involving seasonal data," Economics Letters, Elsevier, vol. 14(4), pages 339-343.
  2. Michael C. Lovell, 1963. "Seasonal Adjustment of Economic Time Series and Multiple Regression," Cowles Foundation Discussion Papers 151, Cowles Foundation for Research in Economics, Yale University.
  3. David F. Hendry & Carlos Santos, 2005. "Regression Models with Data-based Indicator Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(5), pages 571-595, October.
  4. Salkever, David S., 1976. "The use of dummy variables to compute predictions, prediction errors, and confidence intervals," Journal of Econometrics, Elsevier, vol. 4(4), pages 393-397, November.
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