I've been doing some tweets about the qualitative behavior of the unemployment rate U(t). One thing that's important is that the derivative of U(t) (slope) is also a qualitative behavior of a time series.

So I made a gallery of things U(t) does *not* do.

First let's look at what U(t) *does* do. That is to say, what is there evidence for in the past time series behavior of the unemployment rate.

It does this:

There is no evidence that it ever does this:

There is no evidence it ever does this:

There is also no evidence it ever does this:

Nor is there any evidence that it ever does this:

This means if you ever see the black line in the data, and your model shows the red curve as a projection it is not qualitatively consistent with the historical data.

The blue curve is a consistent projection. You might not know the amplitude, but you know a shock is coming.

If the data goes a bit further and shows the unemployment rate rising, then the red curve is not consistent with past data. The unemployment rate will not level out, and your model is wrong. You are inventing something not in evidence.

Finally, if you then see the data turn around, it won't level out at an unemployment rate U > 0 like this red curve.

I mean it could! However it means your model is making something up that has never happened in the data — at least not without the U rising in another shock.

It's entirely possible that the unemployment rate could follow these paths in the future. Who knows? There's just no evidence in the currently available data matching the qualitative behavior of any of these red paths.

And if there is no evidence for these qualitative behaviors in the past data but your model still has them, the reason your model has them — **whatever it is** — has no empirical basis.

Your model is wrong — and you can't glean anything from it until you excise the problem.

(BTW this basically means any "natural rate" u* model is wrong.)