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On the Geometry of the Instrumental Variable Estimator

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  • Halvor Mehlum

Abstract

I derive the exact distribution of the exact determined instrumental variable estimator using a geometric approach. The approach provides a decomposition of the exact estimator. The results show that by geometric reasoning one may efficiently derive the distribution of the estimation error. The often striking non‐normal shape of the instrumental variable estimator, in the case of weak instruments and small samples, follows intuitively by the geometry of the problem. The method allows for intuitive interpretations of how the shape of the distribution is determined by instrument quality and endogeneity. The approach can also be used when deriving the exact distribution of any ratio of stochastic variables.

Suggested Citation

  • Halvor Mehlum, 2009. "On the Geometry of the Instrumental Variable Estimator," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(3), pages 427-435, June.
  • Handle: RePEc:bla:obuest:v:71:y:2009:i:3:p:427-435
    DOI: 10.1111/j.1468-0084.2009.00552.x
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    References listed on IDEAS

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    1. 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.
    2. Maddala, G S & Jeong, Jinook, 1992. "On the Exact Small Sample Distribution of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 60(1), pages 181-183, January.
    3. Woglom, Geoffrey, 2001. "More Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 69(5), pages 1381-1389, September.
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