The graph below shows two different series for unemployment in the 1930s in the USA: the official BLS level by Lebergott; and a data series constructed famously by Michael Darby.
Figure 1: US unemployment rate, 1929 – 40: Darby and Lebergott estimates
Source: Robert Margot (1993).
Darby includes workers in the emergency government labour force as employed – the most important being the Civil Works Administration (CWA) and the Works Progress Administration (WPA). Once these workfare programs are accounted for, the level of U.S. unemployment fell from 22.9% in 1932 to 9.1% in 1937, a reduction of 13.8%.
For 1934-1941, the corrected unemployment levels are reduced by two to three-and-a half million people and the unemployment rates by 4 to 7 percentage points after 1933.
Not surprisingly, Darby titled his 1976 Journal of Political Economy article Three-and-a-Half Million U.S. Employees Have Been Mislaid: Or, an Explanation of Unemployment, 1934-1941. The corrected data by Darby shows stronger movement toward the natural unemployment rate after 1933.
From about 1935, the unemployment rate in the Great Depression in the USA is not much different from what it is in Europe in recent decades under Eurosclerosis.
In the 1930s in the USA, many unemployed were employed by the Civil Works Administration and the Works Progress administration. In contemporary Europe, the unemployed are simply paid not to work under their welfare state arrangements.
Utopia, you are standing in it! 
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