How big is the multiplier?

Is the stimulus act (ARRA) having a noticeable effect on the U.S. economy? Greg Mankiw says not really, citing Volker Wieland's analysis on VoxEU:

Proponents of discretionary fiscal stimulus hope for a Keynesian multiplier effect... A government-induced increase in total spending then raises income and boosts private consumption, which in turn raises total spending further... President Obama’s advisers Christina Romer and Jared Bernstein estimate that 1% of government spending would generate a 1.6% increase in GDP. They give much weight to the type of traditional macro models used by some forecasting firms. As a result, they believe the ARRA stimulus is good for 3% to 4% additional growth by end of 2010. A robustness analysis with New-Keynesian models conducted by Cogan, Cwik, Taylor, and Wieland (2009) indicates only about one-sixth of this effect. Our analysis suggests government spending quickly crowds out private consumption and investment, because forward-looking households and firms will consider eventual increases in future taxes, government debt, and interest rates...

Our findings confirm the earlier analysis with models of the US economy. Once you allow for a significant role of forward-looking behaviour by households and firms, there is no multiplier. The expectation of future tax increases, or rising government debt and future interest rate increases leads to a reduction in private consumption and investment spending. This holds in particular for the three New Keynesian models developed by economists at the ECB, the IMF and the EU Commission (see Smets and Wouters 2003, Laxton and Pesenti 2003, and Ratto, Roeger and in’t Veld 2009). These models include extensive Keynesian features such as price and wage rigidities, but also employ up-to-date microeconomic foundations. The model of EU Commission researchers is especially interesting because it is recently estimated and one-third of its households do not care about the future and follow a traditional Keynesian consumption function.

It's important to understand that Wieland is not citing empirical evidence for the size of the multiplier. Rather, he is running simulations of various theoretical models in the New Keynesian tradition (that is, they are general equilibrium, rational expectations models with a real business cycle "core" extended to include rigidities in wages and prices) and reporting the range of multipliers he finds. The results are entirely driven by the theoretical assumptions on which these models are based, chief among which is the assumption that when consumers see the debt the government incurs when it raises spending or cuts taxes, they calculate their expected future tax liability and reduce their consumption proportionately. If you believe that's how consumers behave, then you will put some stock in Wieland et al.'s estimates of the multiplier. If you think consumers are not that foresighted, then you'll believe Romer, Bernstein et al.'s estimates.

Somewhere in my files I have a paper Robert Lucas wrote in the early 1970s mocking Keynesian economists for the kind of sloppy reasoning I suspect is going on with Wieland and Mankiw. Lucas claimed that predictable changes in the money supply would have no effect on the economy. Keynesians responded, that's nonsense, all our models say it would have an effect. Lucas came back at them with, what kind of idiot interprets results from theoretical models assuming his worldview to be the truth as empirical evidence in favor of his worldview?