Is my instrument too noisy?

[Xavier Pedros]

Hi,

I have an instrumental variable, that I want to use with IV 2SLS, to predict my endogenous variable.

The scatter plot of my instrument against my endogenous variable looks like this. Using Stata's binscatter, I can absorb control variables and fixed effects, and the resulting binscatter plot looks like this.

The First Stage of IV 2SLS is statistically significant (0.357***, using robust standard errors), and the F Stat is above the 10 critical threshold.

My question is: is my instrument too noisy? I see many outliers, and I am not sure about whether the fact that I get a positive and significant First Stage, and F Stats above 10, is a statistical artefact.

Thanks!

[Fei Wang]

Xavier, "being noisy" is not a well-defined concept. An instrument should be 1) exogenous and 2) relevant, and you were talking about the second condition. Use weakivtest (from SSC) to test if the IV is sufficiently relevant in the first stage, and 10 is just a rough rule of thumb and cannot be applied formally.

[Xavier Pedros]

Xavier, "being noisy" is not a well-defined concept. An instrument should be 1) exogenous and 2) relevant, and you were talking about the second condition. Use weakivtest (from SSC) to test if the IV is sufficiently relevant in the first stage, and 10 is just a rough rule of thumb and cannot be applied formally.

Many thanks Fei. The instrument indeed appears to be sufficiently relevant, as per the package that you propose. I guess I am just wondering if the data distribution in my scatter plot makes it unappropriate for OLS, to provide an unbiased and efficient estimator, or even for these relevance tests to be robust.

[Fei Wang]

Many thanks Fei. The instrument indeed appears to be sufficiently relevant, as per the package that you propose. I guess I am just wondering if the data distribution in my scatter plot makes it unappropriate for OLS, to provide an unbiased and efficient estimator, or even for these relevance tests to be robust.

Xavier, I don't think you need to worry about the consistency of the IV estimators as long as the instrument is exogenous and relevant. But you may want to double-check whether the data distribution is true or a result of data errors -- No need to worry if the data are correctly recorded.

[Xavier Pedros]

Xavier, I don't think you need to worry about the consistency of the IV estimators as long as the instrument is exogenous and relevant. But you may want to double-check whether the data distribution is true or a result of data errors -- No need to worry if the data are correctly recorded.

That makes sense. Thanks Fei.