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I have an instrument, 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.

enter image description here

Using Stata's binscatter, I can absorb control variables and fixed effects, and the resulting binscatter plot looks like this. In the X axis, all data points are distributed across 100 equal bins, and the chart reports the mean value for each bin, for values in the X and Y axes (after controlling for control variables and fixed effects).

enter image description here

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 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!

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  • $\begingroup$ Have you taken the log of endogenous variable 2? What do the variables mean? $\endgroup$ Aug 30, 2022 at 21:53

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This is something you should probably approach from the standpoint of theory, not empirical/statistical work. You have to ask yourself, “How big do I think the effect of x on y is? What values are actually likely, before seeing the data?”

Once you have that answer, you can calculate using a prior predictive simulation—Statistical Rethinking has a great section on this.

But if you think the effect of x on y (which determines the effect of x on z) is small a priori, then seeing a large measured effect shouldn’t convince you; large estimates can indicate lots of noise.

As for outliers, I’d suggest doing a QQ plot to quickly check if the residuals really are normally distributed. I really only see 1 outlier, in the middle-right. I’d recommend manually checking if something is wrong with that point (e.g. a data entry mistake or an inaccurate value). If there’s nothing wrong with it, I’d just leave it be.

(Also, robust standard errors are evil! They’re severely downward-biased; I jokingly call them robust to everything, including the data. If you think heteroscedasticity is present, use a model that accounts for it, although from the plot it looks fine.)

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