The CBO has just updated their estimate of the impact that the stimulus package enacted in the US in early 2009, the American Recovery and Reinvestment Act ("ARRA"). I've summarized the conclusion in the chart below. The blue line shows actual real GDP (incorporating today's updated figures from the BEA for 2011:Q1), while the red line shows what would have happened in the absence of the ARRA.
(Note that to construct this chart I used the average between the CBO's high and low estimates of the impact of the ARRA.)
The impact was significant, and at its peak in 2010 the ARRA was responsible for creating between 1.3 and 3.3 million additional jobs for unemployed Americans.
To generate this estimate, the CBO relied primarily on "versions of the commercial forecasting models of two economic consulting firms, Macroeconomic Advisors and Global Insight, and on the FRB-US model used at the Federal Reserve Board." In other words, the CBO is using the type of macroeconomic models that businesses rely on to understand the macro economy, which means that the models have effectively been "market-tested".
A technical note about multipliers: the CBO's estimate embodied various different multipliers for different components of the ARRA. Those multipliers were drawn from the results of published, peer-reviewed empirical research, and ranged from a low of +0.2 for one-time tax cuts for upper-income people, to a high of +2.5 for direct purchases of goods and services by the federal government (or transfers to state governments to do the same). If we add up all of the additional output that will have been created in the US between 2009 and 2011 thanks to the ARRA (in other words, the area between the two lines in the chart), we get a total of about $750 billion in additional production in the US. Since that's approximately equal to the amount of money that the ARRA will have cost the federal government for those years, we find that the ARRA had an average multiplier of about +1.0.