If we're back to discussing Chetty, Friedman and Rockoff again, I'll get something off my chest. I've not seen much discussion of how higher test scores translate to better long term outcomes. What's the model exactly, and in particular, how does this work per subject area?
From the perspective of ELA, and reading tests in particular, this is pretty mysterious. I mean, learning more is good! More vocabulary, better reading skills, insofar as they exist, are good, but it is hard to break it down beyond the most general handwaving.
In math, it is much more plausible and straightforward, because math is used as a gatekeeper course and presented as a linear progression. If one good teacher can bump a handful of kids up a level in math -- particularly if the school is tracked by math, as would have been common in the timeframe for Chetty's study -- that will change their opportunities, peer group, etc. in a fairly straightforward way. If you bump up a group in math, you don't need to maintain a higher rate of learning indefinitely, just one accelerated year and then you can continue at the same pace as your peers.
Or, one bad year has similar knock on effects.
Also, whether or not your math curriculum or assessment is "authentic," a standardized math test is going to be a fairly valid predictor of how you're going to do on other math tests, at least compared to, say, a reading test's assessment of how you do on all types of reading and ELA assessments in class.
I'm not going to dig back into it now, but I think at the time I looked for separate data for math and reading and did not find it.
On a personal level, it is not hard for me to believe that if I'd had a single "top 5%" math teacher in high school, I might not be making 1% more a year, I might be making two or three times what I make now. Over a lifetime, that'd be like two or three million, which would more than cover Chetty's predictions for a whole class. It is a lot harder to imagine a great English teacher would have made me rich.
Economists are math people, so they tend to think that math education is the standard paradigm for education in general. It isn't. It is the outlier. If you build your model of education around the subject of mathematics, you have no chance of getting it right.