# The Predictive Power of Quitters

Part of the implication of the earlier post is that if the relationship between the quit rate and the unemployment rate is so strong, then the quit rate should be a very good predictor of the unemployment rate. It's a bit hard to see how good exactly, though, without actually running the regression.

So that's what I've done. Note that this post is entirely technical.

The graph I showed before was clearly nonlinear. So I used a log-linear regression model. It worked. The unemployment rate is well estimated by the quit rate (r^{2} = 0.93). Let* u *be the rate of unemployment and *q *be the quit rate. *a *and *b *are OLS regression coefficients, and *e* is the error term.

log *u* = *a *+ *bq* + *e*I get an

*a*of 3.3691 and a

*b*of -0.8287. I've plotted the unemployment rate, the quit-rate estimate of it, and a 95-percent confidence interval --which, as a note, is tricky to construct because the relationship is nonlinear.

Here's the graph:

You really don't see very many relationships that precise and accurate in econometrics or macroeconomics.

Via Matthew Boesler of Business Insider, I've also learned that the San Francisco Fed does something similar to estimate the natural rate of unemployment. You'll notice in the quits graph that it's the strongest predictor out of the four they graph -- and it implies that, no, the natural rate of unemployment hasn't risen since the recession. But it hasn't fallen, either, which is the implication of the view that the unemployment rate underestimates how loose labor markets are.