Frank Steindl reports:
depression, both output and prices fell, as was their usual behavior in
depressions. The bottom of the depression was May 1938, one year after it
began. Thereafter, output began growing quite robustly, rising 58 percent by
August 1940. Prices, however, continued to fall, for over two years. Figure 8
shows the depression and revival experience from May 1937 through August 1940,
the month in which prices last fell. The two shaded areas are the year-long
depression and the price "spike" in September 1939. Of interest is that the shock
of the war that spurred the price jump did not induce expectations of further
price rises. Prices continued to fall for another year, through August 1940.
Here are some graphs (see Figure 8) and more. Steindl concludes:
The economic phenomenon that was driving the recovery was probably increasing
In his view that also explains why it was a "jobless recovery" in the 1938-1940 period, namely that the demand for labor did not need to rise so much. It also has been argued that the technological innovations of the Great Depression were labor-saving ones and that 1930s unemployment cannot be understood apart from this fact.
I do not mean to present these opinions as definitive (by the way here is more by Steindl); I hope to read more in the area and report back to you. Most generally, I would like to stress how poorly we understand the economics of the 1930s and 40s.