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The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One

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  • Nelson, Charles R
  • Startz, Richard

Abstract

Instrumental variables estimation is used when there is reason to suspect feedback from a dependent variable to the explanatory variable, but the results will tend to be highly misleading if the instrument is a poor one. In this case, the distribution of the estimated coefficient is concentrated around a value that is related to the amount of feedback rather than to the true coefficient. When the true coefficient is zero, the instrumental variables coefficient will nevertheless appear to be highly significant, and this effect increases with the amount of feedback. Thus, it is in the cases where least squares is a poor estimator that instrumental variables with a poor instrument will be even worse. Some guidelines for practice are suggested. Copyright 1990 by the University of Chicago.

Suggested Citation

  • Nelson, Charles R & Startz, Richard, 1990. "The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One," The Journal of Business, University of Chicago Press, vol. 63(1), pages 125-140, January.
  • Handle: RePEc:ucp:jnlbus:v:63:y:1990:i:1:p:s125-40
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    1. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-987, December.
    2. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-976, July.
    3. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
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