John Handley challenged me to take on the 1930s, 40s, and 50s with the dynamic equilibrium model. While the Great Depression is fairly uncertain (because the model operates on the log of the unemployment rate, returning to the linear scale makes the bands exponentially larger for higher unemployment rates), the overall model works well:
In the interest of making the optimization run in a reasonable time, I split the data for the 30s and the 50s, keeping the 40s in common between them. Here's the fit for the 30s and 40s (illustrating that exponential increase in the width of the error bands):
Per the original thread, it is hard to see any effects of the New Deal (possibly it arrested the increase of the unemployment rate, similar to the possible effect of the various actions in 2008-9). Overall, the best thing to say is we don't know.
The remaining time period from the 40s through the 60s (to overlap with the original model) has smaller confidence intervals:
In both of these graphs we do however see a potential effect of the draft: WWII and Korea. There are two fairly large positive shocks centered in 1942.6 and 1950.5.
Another feature of the data from the 50s and 60s (also apparent in the 70s and 80s, but gradually disappears over time) is a reproducible "overshooting" effect (which I highlighted in green, scribbling on the graph):