IV gives higher point estimate than OLS, but less significant: is OLS downwards biased?

[Xavier Pedros]

I have a regression where my OLS point estimate is statistically significant at the 1% level. The IV regression second stage gives a higher point estimate, but statistically significant at the 5% level.

Specifically:

OLS coefficient: 0.194*** (.026)
IV 2nd stage coefficient: 0.524** (.210)

The F Stat for my instrument is 19

Can I conclude that my OLS estimate is downwards biased?

For context: OLS standard errors are robust (", robust" option of reg command on Stata), and IV standard errors should be robust too (", robust" option of ivreg2 command on Stata). In the related literature of the model that I estimate, OLS estimates are typically downwards biased - and there is a theory for that. I am just wondering if the change in the statistical significance is something that matters, to be able to conclude that OLS is downwards biased in my results too.

[Joro Kolev]

OLS is biased towards 0 under classical measurement error.

You do not say what you are instrumenting with what, and what is the type of endogeneity you are suspecting.

[Xavier Pedros]

OLS is biased towards 0 under classical measurement error.

You do not say what you are instrumenting with what, and what is the type of endogeneity you are suspecting.

Thanks Joro. I am looking at the relationship between immigration and vote to anti-immigration parties, with municipality-level data. OLS estimates are very generally thought to be downwards biased because immigrants self-select themselves in more left-wing locations.

My question is. I see the point estimate increases in IV, relative the point estimate in OLS. Yet, the IV estimate is significant at the 5% level, while OLS is statistically significant at the 1% level. Can I then conclude that OLS is downwards biased, as in most of related literature?

Specifically:

OLS coefficient: 0.194*** (.026)
IV 2nd stage coefficient: 0.524** (.210)

The F Stat for my instrument is 19

[Joro Kolev]

I think yes, you can conclude that.

First it is normal for IV estimates to have much larger errors than OLS.

Second, you already seem to have a story why OLS is downward biased.

So is it not obvious?

[Fei Wang]

You may formally test for the difference between the OLS and IV estimates by specifying the endog option in ivreg2. Moreover, please be cautious that your explanation is one possibility and it's also possible that the OLS and IV estimates are not comparable at all due to the LATE nature of the IV estimators.

[Xavier Pedros]

Thanks everyone

[Jeff Wooldridge]

And remember that everything hinges on having an exogenous instrument — which can’t be tested in your setting.