Several comments on this paper. First, it's nice to see someone taking the units of measurement issue seriously. But I still see many issues, especially when y >= 0 and we have better alternatives.
1. A search is required over units of measurement.
#metricstotheface
1. A search is required over units of measurement.
#metricstotheface
https://twitter.com/ArneHenningsen/status/1397073857358483457
How do a compute a legitimate standard error of, say, an elasticity? I've estimated theta but then I ignore the fact that I estimated it? That's not allowed.
2. As with many transformation models, the premise is there exists a transformation g(.) such that g(y) = xb + u.
2. As with many transformation models, the premise is there exists a transformation g(.) such that g(y) = xb + u.
u is assumed to be indep of x, at a minimum. Often the distrib is restricted. In 1989 in an IER paper I argued this was a real problem with Box-Cox approaches b/c u >= -xb. If I model E(y|x) directly I need none of that. It's what Poisson regression does.
3. I'm puzzled by the application to Lalonde, which is an experiment with y >= 0. The experimental estimate of the semi-elasticity is .394 (se = .164); we can take this as the target. On the plus side, you conclude it's likely between .31 and .38 (but no stnd error).
In about 2 minutes I had the Poisson estimate that controls for 1975 earnings: .384 (se = .162). I don't much care about the elasticity wrt 1975 earnings, but I get .056 using arcsinh(re75).
So I can use Poisson to essentially recover the experimental value and obtain a valid se in 2 minutes, or I can go through a complicated data mining exercise that doesn't produce a valid standard error -- and implicitly imposes strong assumptions. Why should I do this?
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