Did he say can't or won't? Both Bernanke in his 1999 paper on Japan and Krugman in his 1998 paper on the liquidity trap both agree that monetary policy can be used to escape the liquidity trap.
Indeed they did write that. And Bernanke now says that the Fed can't/won't do much more, and Krugman now bangs the table for more spending.
It's easy to say when applying the standards to others, i.e. Japan. However, when one is in the morass, ideas can change.
Second, the context is that WWII finally got us out of the Depression and we stayed out. It doesn't matter if the spending was not efficient. What matters is what happened after the spending stopped. If this were the equivalent of borrowing a trillion dollars to do nothing but dig ditches with TFP=0, then the economy should have collapsed afterwards. But that did not happen.
It didn't happen because aggregate demand had been permanently increased. If you think government spending did it, you've gotta believe a model with multiple equilibria where a "push" from the government can permanently change monetary velocity. Or you can say that NGDP was increased by the fact that the war debt was monetized. I personally think the latter makes more sense.
First, given your knowledge of the topic at hand, I'm assuming your handle isn't a coincidence.
However, though its been 15 years since I sat down in front of econometric software and hence my mathematical skills have disappeared down black hole, after spending my career in the capital markets, I've come to the conclusion that the assumptions in economic modeling in a Gaussian framework do not accurately reflect human behavior, at least all of the time. I think such a framework can be a useful approximation under normal conditions, but in times of stress and unusual circumstances, I believe the models can fly out the window. Thus, in times of duress or war, human behavior changes, and the models break down.
But even if we accept such a framework, its not that monetary velocity has to rise to a permanently higher plateau. Instead, it has to be brought up to where it was before if it has collapsed, as it did during the Depression. Money in circulation to deposits soared during the Depression, as irrational bank runs caused people to hoard money and take it out of the financial system. You can see it here.
As to your last sentence, I agree to some extent. The government pegging long-term rates at 2.5%, which monetized the debt, was significant. (Hello future!) The answer is, of course, complex, and not dependent upon any one thing. After a generation of depression and war, for example, there was tremendous pent up consumer demand that was unleashed in the 1950s and 1960s. Also, the conceptualization and development of suburbs influenced the patterns of economic growth. Government programs such as the GI bill - which were passed in an attempt to avoid a collapse like after WWI - also had an affect. But I also think government war spending was very significant.
Since I assume you are well versed - and certainly much better versed than I - on the DSGE framework, you'll understand the concept of agent-based modeling. I'm not sure if it can be modeled properly when the tails get fat, but I look at the world in terms of agents, with government being an agent through which economic activity flows. The arguments of guys like Lucas, Cochrane, Roll, etc., are that the government is an inefficient allocator of capital and income. In general, I would agree.
Generally, the government is an inefficient allocator of capital. However, to assume that it is
always an inefficient allocator of capital assumes that individuals are hyper-rationalists, constantly maximizing infinite utility curves under all circumstances. I do not believe this is correct. Peoples' motivations are not always driven by the maximization of individual utilities (unless one assumes that utility also includes the desire to maximize the utilities of others, which may be a fair point). At times, individuals will sacrifice their own well-being for the good of the whole, which should be patently obvious in a discussion about war, given that people are willing to sacrifice their lives for the country. If people are willing to die for their country, why is it unreasonable to assume that people will also subsume their own desires and work as hard for the nation as they do for themselves? If this is true, then in war time, people may be as productive working for the collective, i.e. the nation, as they are for themselves, which may not be true during peacetime. And if this is true, then the assumptions behind traditional econometric modeling break down. Ergo, government war spending in a time of duress can have an independent positive affect on the economy that can be sustained when the economy reverts back to a more normal framework, even when the government spending is withdrawn, especially when excess capacity is expunged from the economy.