Did World War II end the Great Depression?

Joseph Cullen and Price Fishback write:

We examine whether local economies that were the centers of federal spending on military mobilization experienced more rapid growth in consumer economic activity than other areas.  We have combined information from a wide variety of sources into a data set that allows us to estimate a reduced-form relationship between retail sales per capita growth (1939-1948, 1939-1954, 1939-1958) and federal war spending per capita from 1940 through 1945.  The results show that the World War II spending had virtually no effect on the growth rates in consumption that we examined.  This contrasts with Fishback, Horrace, and Kantor's (2005) findings of about half a dollar increase in retail sales associated with a dollar of New Deal public works and relief spending.  Several factors contributed to this relative lack of impact. World War II spending often required a conversion of plants designed for civilian good production into military factories and back again over the 9 year period.  Substantially higher federal tax rates that were paid by the majority of households imposed much stronger fiscal drags on the benefits of the spending.  Finally, less of the military spending was earmarked for wages and use of locally produced inputs, which reduced the direct stimulus to the local economy.

Here is the paper, here are non-gated versions.  My understanding has long been that wartime orders from Europe, by 1940, provided the decisive turning point for the American economy.  So if WWII did end America's Great Depression, it was not through the traditional mechanism of massive domestic fiscal stimulus.

Addendum: Here is James Hamilton on the Great Depression.  And Brad DeLong replies to critics, but if we are going to count as monetary policy we must recognize 1937-8 as a disaster which cut off a recovery.  And Paul Krugman chips in, see the comment by Robert Waldmann, I am myself skeptical that a liquidity trap was in place.

Second addendum: The authors have another good paper on crime and social spending during the New Deal.