Instrumental Variable and reverse causality

[Solomon Lin]

Hi,

From what I understand, the two conditions for an instrument to be appropriate is:
1) The covariance between the instrument and the error term in the structural model is zero
2) The covariance between the endogenous variable and the instrument is non-zero

What happens if it is the case that the instrument and the endogenous variable are correlated BUT the instrument is the variable that impacts the endogenous variable (i.e. there is reverse causality). Can the instrument still be used?

[Eric de Souza]

I don't see the difference between 2) and the next paragraph, unless you mean endogenous regressor in 2), and dependent variable in the next para.

[Solomon Lin]

Hi,

My question is what if the instrument and the endogenous variable are correlated but it is because the instrument impacts the endogenous variable (reverse causality)? Is the instrument still appropriate?

[Eric de Souza]

You have just repeated what you wrote in #1. An instrument has to be correlated with the endogenous regressor. Otherwise, it would not be an instrument.

[Solomon Lin]

You have just repeated what you wrote in #1. An instrument has to be correlated with the endogenous regressor. Otherwise, it would not be an instrument.

Hi Eric,

Thanks for all your replies. To provide an example. Say I was running a regression of Wages on Alcohol Consumption and I suspect that there is endogeneity from simultaneity bias.

If Weight is not correlated with the error term in the structural model and it is correlated with Alcohol Consumption, it should be a suitable instrument.

But I suspect that increased alcohol consumption increases an individual's weight while an individual's weight does not influence their alcohol consumption. In this case, is weight still a valid IV?