Basic Math for the Math Challenged
Since Richard Posner has decided to exhibit his math skills again, I thought it useful to work through some math to see how one can obtain back-of-the-envelope estimates for the stimulus package. I'll use Mr. Posner's numbers to illustrate.
Stipulate that $89 billion in stimulus funds were expended (this is Economy.com's estimate), in combined tax rebates, transfers to support state spending on goods and services and transfers, and direct Federal spending. This is higher than the $60 billion cited by the IMF (page 6), but lower than the $100 billion cited by Dr. Romer in her study (where she used IRS information on tax cuts; as Donald Marron has pointed out, Recovery.gov reports only expenditures on goods/services and transfers).
Assume 40% of the $89 billion was transfered to the states, of which most supports spending on goods and services.
Note that the GDP deflator is about 10% higher now than in 2005.
Calculate real government spending on goods and services by end-2009Q2:
(89 × 0.40)/1.10 = 32.4 Ch.2005$
Divide this stimulus by 2009Q2 GDP, not at annual rates. 2009Q2 GDP is about 3223 billion Ch.2005$.
32.4/3223 = 0.01
The resulting percentage increment to GDP assuming the multiplier for spending on goods and services is 1.0 is 0.01.
Annualize the implied increment to 2009Q2 GDP:
(1.01)4 = 1.04
In other words, the $89 billion results in 4 percentage points increase in growth, assuming zero spending out of tax cuts. Assume 0.5 multiplier for spending on goods and services (kinda wierdly low, but plausible when discussing impact multipliers), and one still gets 2 percentage points increase in growth.