FDR... The New Deal... Government spending on infrastructure and investing in the country... it's what Obama is starting to do.
This is the first and only real experiment we have had in U.S. history that gives us actual empirical proof of what works and what doesn't.
By the way, in 1937, FDR cut spending and cut taxes. In 1938 he saw the effect and rolled back his tax cuts and increased spending again... Do you see what happened?
Thanks to http://open.salon.com/blog/caveat_canem_croceum for the charts!

Source: BEA(2)
Real GDP declined by 25% in three years. ("Real" in economic jargon is used as an adjective to denote the elimination of the effects of inflation or deflation so that statistics are comparable over time.)
Under FDR's stewardship, the economy turned around almost immediately due to active Federal intervention and Real GDP grew at 7% per year compounded from 1933 through 1939.

Source: Census Bureau(3)
Per Capita Income Growth:
All the talk about growth in GDP or aggregate output (jargon, means the same thing) would be for nought if personal disposable income (i.e. after taxes) did not increase concomitantly.
Following a decline of 30% during the Hoover years, real per capita income in the US increased by 50% in the first seven years of the New Deal. By 1937 it had surpassed the highest it had been during the Hoover administration -- at its inauguration!
- By 1936, in just three years, GDP had surpassed the 1929 level where Hoover began his assault upon it.
- By 1937, per capita income, which had been also been Hoovered, surpassed 1929 levels.
- The economy continued to grow at this pace through 1939, despite a small hiccup in 1938 (when stimulus had been mistakenly reduced; but FDR was smart enough to recognize this and get back on course).
- WW II HAD NOTHING TO DO WITH ANY OF THIS. The recovery had been ongoing for six years when the war started in late 1939. ( GDP growth in the US accelerated to 11% per year during 1939-45(2), but only loonies living in undisclosed locations believe in wars as prescription for economic recovery.)
So what was that about the New Deal not working?

Source: Census Bureau(4), Darby(6)
Few would know that the only contemporaneous numbers in the series are the decennial ones i.e. 1930 and 1940 when the censuses occurred(4). The interpolating years are the result of brilliant econometric analyses done in the mid 1940s by Stanley Lebergott(5) at the Bureau of Labor Research. But it has a problem which has been known for some time: the series leaves out of the employment rolls an average of almost 2 million workers a year employed by the WPA during the peak years of the New Deal(6).
This was not by accident. Officials regarded these workers as the equivalent of welfare recipients(5), even though they could earn upto $1200 per year, almost twice the national per capita income at the time.
Michael Darby(6), another distinguished economist, was the first to correct the record in a 1976 article. His work is reproduced in Chart III above (purple line) to show the "adjusted" employment figures including WPA workers. In this view, unemployment fell rapidly from 25% to 10% and thence to 7% by the start of WW II. It should also be noted that the civilian labor force comprised "persons 14 years old and over"(4) in those days.
So, unemployment fell rapidly, with a concomitant increase in per capita income, from the very inception of the New Deal.
So what was that about the New Deal not working?

Source: OMB(7)
How this growth was achieved:
Gross Domestic Product, the aggregate measure of the size of a national economy, has just four terms.
GDP = Consumption + Investment + Government Spending + Trade
When consumers are beset by massive unemployment and investors, be they bankers or businesses, do not have the wherewithal or the stones to invest -- does the picture sound faintly familiar? -- there are not too many options left in terms of reenergizing the economic engine.
The New Dealers saw this and dealt with it immediately, as shown in Chart IV. From 1933 to 1939 Federal spending was doubled from $4.5 billion to $9.1 billion, in current or "then" dollars. And the economy responded by expanding almost 50% during that period in terms of Real GDP (more than 70% growth in current dollars).
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