Is my instrumental variable too noisy? 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.

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).

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!

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.)
