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When performing IV regression, it is often taken as a sign of unbiasedness if the IV estimates are similar to the OLS estimates of the same model. My question is: If the estimates are very different, what possible explanations are there for the difference?

Say for example, with a strong instrument, that one finds that the IV estimates of some coefficient are 10 times larger than the OLS estimates. Is this most likely a sign of severe bias in the OLS estimates? Or is it just as likely that the exclusion restriction is not satisfied, and so the IV estimator is possibly even more biased than OLS?

I understand that this is an open question, but if anyone could just give me the basic range of possible explanations, and perhaps point me towards some literature on interpreting IV results when they are significantly different from OLS, that would be much appreciated?

Best regards,

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Let me take an example based on the estimation of returns to education, which has been a well-studied problem. The usual result is that researchers find the 2SLS estimate to be larger than the OLS estimate by approximately 25%-50%, e.g. Card (1999, 2001).

Three reasons :

  1. An omitted variable that could be negatively correlated with the amount of education. This omitted variable would lead to an downward bias in the OLS estimate of the schooling coefficient.
  2. Errors in variables that arise because years of schooling are a noisy measure of education that leads to higher earnings. This measurement error in education biases the OLS estimate of the treatment effect toward zero. OLS estimates are thus too small. Since the IV estimate is unaffected by the measurement error, they tend to be larger than the OLS estimates.
  3. It's possible that the IV estimate to be larger than the OLS estimate because IV is estimating the local average treatment effect (ATE). OLS is estimating the ATE over the entire population. By contrast, IV is estimating the local ATE: the instrument shifts the behavior of a subgroup of individuals for whom the returns to education are larger than average. In other words, the IV estimate is the effect of increasing education only for the population whose choice of the treatment was affected by the instrument, while the OLS estimate describes the average difference in earnings for those whose education differs by one year. Then IV estimates will be larger than OLS estimates because of heterogeneity in the studied population.

References

  • Card, D. (1999), The causal effect of education on earnings. In: Ashenfelter, O. C., and D. Card (eds). Handbook of Labor Economics Vol. 3A. Amsterdam: Elsevier, 1801–1863.
  • Card, D. (2001), Estimating the Return to Schooling, Econometrica, 1127-1152.
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