What do the data show about multipliers? Because it is not easy to separate movements in government purchases from overall business fluctuations, the best evidence comes from large changes in military purchases that are driven by shifts in war and peace. A particularly good experiment is the massive expansion of U.S. defense expenditures during World War II. The usual Keynesian view is that the World War II fiscal expansion provided the stimulus that finally got us out of the Great Depression. Thus, I think that most macroeconomists would regard this case as a fair one for seeing whether a large multiplier ever exists.
I have estimated that World War II raised U.S. defense expenditures by $540 billion (1996 dollars) per year at the peak in 1943-44, amounting to 44% of real GDP. I also estimated that the war raised real GDP by $430 billion per year in 1943-44. Thus, the multiplier was 0.8 (430/540). The other way to put this is that the war lowered components of GDP aside from military purchases. The main declines were in private investment, nonmilitary parts of government purchases, and net exports — personal consumer expenditure changed little. Wartime production siphoned off resources from other economic uses — there was a dampener, rather than a multiplier.
I think this is running together two separate issues. One is “whether a large multiplier ever exists” and one is whether such multipliers suffer from diminishing returns. World War II spending was enormous relative to GDP. Wartime spending on that kind of scale goes way beyond the conversations we’re having right now about fiscal stimulus—the equivalent today would be something like a $5.2 trillion package rather than the $800 billion or so we’re talking about. And to get spending up to that level the government had to resort to quasi-forced savings (“war bonds”), rationing, etc.—deliberate efforts to direct production away from where demand was highest and toward the national objective of military production. The 0.8 multiplier is probably the result of diminishing returns. The question is whether you got a decent multiplier out of the first 5-10 percent of GDP you spend on stimulus. It shouldn’t surprise us if it turns out that defense spending eventually got somewhat higher than would be economically optimal in the middle of the largest war in history.