Is correlation between instrumental variables a problem (e.g. in 2SLS)?

[Rosemary Li]

Hi Experts,

Happy New Year!

I am studying endogeneity and understand that instruments must be relevant and exogenous. However, so far, I did not see any literature mentioning correlations among instruments themselves. I suppose instruments for the same endogenous variable will be highly correlated. I have this concern because, when we use OLS for example, multicollinearity is problematic. I am not sure how scholars deal with multicollinearity in Two State Least Squares (2sls) for example.

Assuming I use two instruments for the same endogenous variable, will the high correlation between the two instrumental variables (for the same endogenous variables) be a problem?

If I have two endogenous variables and use one instrument for each, will the high correlation between these two instruments (for two different endogenous variables) be a problem? Of course, correlation between instruments of different endogenous variables is not necessarily high. But, in my case, it happens to be high.

Thank you for commenting in the coming year!


Best,
Rosemary

[Phil Bromiley]

The issue for the instrument is the ability to predict the endogenous variable while not correlating with the error term in the structural equation (a condition similar to being exogenous). The exogenous variables can be highly correlated - high correlations among regressors largely increases the standard error on parameter estimates.

[Rosemary Li]

Thank you for commenting Phil. I understand your points. You first pointed out instrumental relevance and instrumental exogeneity. These are the two requirements for any instrument to be valid. Then you explained the consequence of multicollinearity. For sure, regressors can be highly correlated, as long as they are not perfectly correlated. But, because of the consequence you mentioned, usually we try to avoid/address multicollinearity. The consensus is reached in the context of OLS for example.

In the context of 2SLS or Heckman, I think we still need to avoid/address multicollinearity like we do in OLS (for independent variables of interest and other control variables). Feel free to correct me if my understanding is not correct.

However, my question is about multicollinearity issue among instruments in the first equation of 2SLS or Heckman. I know in 2SLS all control variables and exogenous independent variables of interest in second equation are called included instruments in first equation. Here, by instruments, I mean excluded instruments. In Heckman, they are called 'exclusion restrictions'. I hope I had made my question clear now. Thanks again for spending your valuable time on my post

Please keep commenting, experts Thanks.

[Jesse Wursten]

The exogenous variables he refers to are what you call instruments/exclusion restrictions. To largely reiterate Phil's point, correlation among instruments is not a problem per se. However, the more correlated they are, the less powerful they become as the extra information provided by the second instrument decreases. The two instruments combined still contain more information than any of the individual instruments on its own, unless they are perfectly correlated.

[Rosemary Li]

Thank you Jesse, for your informative answer and for letting me know that I misunderstood Phil's "exogenous variables".

[Rosemary Li]

Dear Phil,

Thanks to Jesse's comment, I see now that I misunderstood your comment earlier.

As I reflect, it shows how past experiences may bias current decision making. Because, unfortunately, your answer shares a similarity with patterns of comments I experienced, where questions were misinterpreted. So, unconsciously, I thought your comment belonged to the category.

It is going to be hard for human beings , but next time I will try to not let past experiences affect current communications.

Thank you again, for your earlier post. And my apology that I neglected its greatness.


Best,
Rosemary