I am no fan of New Deal socialism. However, FDR didn’t take office until March 4, 1933. After that, the highest tax rate went up, but those other measures of economic health improved, even before 12/7/41. I’m not trying to give the Brain Trust credit (evidently neither did Morgenthau). But at least the economic cycle during the first two FDR administrations was on a more favorable path than between October 1929 and FDR’s inauguration.
Those numbers are fiction. Government was engaged in massive price fixing during the entire New Deal and WWII period. GDP is compiled by aggregating quantities sold and prices, but the prices weren't real market prices. They were bureaucrat dictated prices.
Also, incredibly, the GDP calculation counts government spending as production when it is obviously consumption. Back the public sector portion of GDP out twice (once because it shouldn't have been added and once more because it should have been subtracted) to get a better picture of what the economy was doing. (Though even this won't make the GDP numbers from the FDR period reliable.)
Understand, Britain had devalued the pound by 35% went it went off gold. The entire empire followed - a quarter of the world's economy at the time. Central europe had gone down even farther even earlier and reneged on all its debts. The US stayed on gold through 1933 and continued to operate the gold standard, mechanically, long after practically everyone else had ceased to operate according to its informal rules. (Only the French and Belgians, and a few of the Scandanavian states, remained as a "gold bloc", and that caused rigorous deflation there, too).
This means the currency was extremely overvalued. And gold therefore left the country because it could buy more abroad than within the US. Under the mechanical rules of the gold standard system, the Fed deliberately reduced the US money supply in direct proportion as gold left the country. This is why the money supply collapsed by a third between 1930 and 1933. (It had scarcely fallen in the first year after the crash BTW).
Driving down the money supply by a third and maintaining a hugely overvalued currency in the middle of the biggest economic slump ever recorded, was incredibly stupid. It was at the time, however, regarded as the tough minded virtuous classical economics thing to do.
The first thing FDR did in office, practically, was devalue the dollar from $20.67 to $35 to the ounce. This exceeded even the pound's fall since the start of the depression, and it halted the gold outflow. It also halted the collapse in trade, and led to a recovery in the stock market (which rose in dollars even just to stay even in world currency terms). The halt of the gold outflow stopped the collapse of the money supply, and that stopped the endlessly cascading bank failures.
It also effectively meant that wages were finally cut. Hoover has browbeaten industry to maintain wages, thinking it helped keep up final demand, and unions had enthusiastically seconded the motion. The price level had fallen by a third. The result was those who still had jobs were being paid a much higher real wage in 1933 than they had been in 1929 - all of it completely unaffordable to business, and dumped on the unemployed. Well, finally devaluing cut wages in world price terms, to something like a feasible level.
Those were the effective immediate actions. The relief stuff probably helped at the margin, but modestly, because it was pretty small scale. Much of the rest of the public works spending didn't help or hurt appreciably.
None of that caused any strong recovery, not one strong enough to reduce the high unemployment appreciably, but it sufficed to halt the continuing plunge into the abyss, which had been a monetary-driven positive feedback process driving the economy toward zero. Basically, the gold standard flat broke, internationally not just domestically, and only leaving it stopped the immediate slide.
The real recovery to full employment was caused by WW II, and began even before full belligerency status, on the back of war orders being filled for British and French war efforts, along with FDRs naval rearmament program, around 1940. This involved foreign governments and the US government spending money they did not first take in taxation, running up their debts or down their existing portfolio holings in the US, and spurred serious investment in new industrial plant and equipment in the US.
When actual belligerency hit, US government spending exploded and took up every bit of slack the economy had and then some. Very large deficit spending is stimulative in the short run, there is no question about it whatever. Some classical economics and Austrian types don't like to hear but, but tough toenails it is the fact. It can result in price rises later, and by 1953 (post Korea) the US price level was roughly twice what it was at the depression lows. But that was deferred by price controls and rationing and material-allocation schemes until 1946-7, and still took a while to happen.
(Incidentally, exactly the same thing happened in WW I, significantly faster - and in the US civil war - and in the Napoleonic wars for the British, etc - it is an utterly normal side effect of war finance).
None of which means the New Deal was smart economic policy. FDR wasn't an economic thinker at all; he was confused when Keynes tried to explain anything to him; he deferred to Morgenthau who was an idiot on the subject and persuaded him to emphasize budget balancing in 1937, crashing the economy again, etc. FDR hit on the right monetary fix, or a close enough version, empirically. He simply tried things and dropped them when the stopped working or if they didn't seem to. (He got the ideas from Fischer among others, who was a crude inflationist - but sensibly dropped that side of it as too risky).
Which was better than Hoover managed because Hoover thought he understood it all and was behaving perfectly. Not a hard standard to beat, incidentally.
You don't hear this told straight by Austrians and other economic libertarian-conservative thinkers because they hate the attack on gold involved. But modern monetarists know that the gold standard as operated by the early 1930s Fed was criminally stupid monetary policy. This is inconvenient, to say the least, for those who think the great problem with the Fed is that it isn't a gold standard...
Whatever might be said for the ability of a commodity money standard to maintain price stability in the long run if all leading states in the world are operating according to its rules, and in normal economic circumstances - being the last one on earth still playing by it after everyone else has dropped it for "beggar thy neighbor" - leaves one, unsurprisingly, reduced to being a beggar.
FDR stopped that, to his lasting credit. He certainly messed up much that followed, but devaluation and stopping the collapse of the money supply, was the right thing to do in 1933.