To prove it, he shows this graph, adding "The economy had another recession in 1938, which was a result of a policy mistake again, but the mistake was quickly reversed with a fiscal injection of $5 billion. And the economy continued its recovery."
"Franklin D. Roosevelt became president of the United States in March 1933. Promptly he introduced four key policy initiatives: (1) suspend the Gold Standard, which allowed the Fed to expand money supply; (2) restore confidence in the financial sector through a process of restructuring and sanitizing commercial banks; (3) implement a fiscal stimulus package; (4) introduce new regulation. As a result of these measures, the growth rate of the economy was 10.8% in 1934, 8.9% in 1935, 13% in 1936, and 5% in 1937! Overall the US economy expanded by 44% during his first term. The US economy is supposed to grow at about 3% per year and not 3 or 4 times this rate. During the first term of Roosevelt, the US real GDP had returned to its pre-Depression level."
This seems like an interesting hypothesis, but I think we need more data to know for sure. His graph ends in 1940, before the US joined the war, so we don't get to see what effect that had. So I took some data from BEA, and made these to charts showing GDP from 1929-1950. This should show us the effects of FDR's programs, as well as the war, and what happened after. The first chart is this data in nominal terms, and the second is in real dollars. I colored 1933 red, which is the year FDR became president, and I shaded the war years.
We can see that GDP rose quickly after New Deal programs, accelerated into the war years, then dropped slightly after the war. However, if we factor out inflation, as in the second chart, we see the post-war economy had a major drop for two years.
Let's look at similar data in a much busier chart. This shows percent changes in GDP between 1930 and 1950. 1933 is colored white, and the war years are shaded. The negative growth part of the graph is shaded as well. The two lines show real and nominal changes.This shows that growth slowed throughout the war years, and went negative in the immediate post-war years. Growth was high, except for 1938, following the rise of FDR. The peak of the growth rate was in 1942.
If you are wondering which of these graphs is comparable to Mihov's, it isn't any of them. His chart is the integral of the real line in the previous chart. (Stop and think about that.) To see what would happen if we extended his methodology out further, we have here RGDP (indexed to 1929), 1929-1950. (In other words, the sums of the percentage changes.) 1933 is in red, and the years the US was at war are shaded. Here we see that the rate of change was basically constant from 1937 to the peak of the war. After the war, it fell and took five-ish years to get back. But the Depression seems more effected by Roosevelt-era programs than the war.
Here's the same graph, extended to 1960, to see where this fits into the growth rates of the post-war economy. President changes are marked in red.
Finally, I extended the graph to the present, did a linear regression, and shaded all years in which the US was involved in a major armed conflict. (There is some debate about when the US joined the Vietnam War, but I think 1959, the year the first US soldier was killed, is the latest you could reasonably argue.) This shows something very interesting. Mihov writes, "During the first term of Roosevelt, the US real GDP had returned to its pre-Depression level." He's saying that in 1936, the economy was above where is was in 1929. (You can see this in his graph.) This doesn't say a whole lot, as without the Depression, the GDP should have been higher in 1936. If we look at the trend line, however, we see that it crosses the data in 1941, meaning that in that year, it returned to where it would have been had there been no Depression. This, I think, more conclusively shows that war spending was not a crucial factor in ended the Great Depression. The war years had above-trend GDP growth, and then it fell and settled by end of 1950s. Eyeballing the shaded areas (especially the years associated with World War II, the Korean War, and the Vietnam War), it seems war years have some above-trend growth, but it settles to trend afterward. Case closed.
(Of course, the case is never closed in economics, but this is only because it isn't a real science.)
(Any graph can be clicked for a larger version.)