## Wednesday, November 12, 2008

### Krugman's Stimulus Math: \$600 Billion

Interesting post from Paul Krugman about how large an upcoming U.S. stimulus package should be. Lets see if I can't make his already easy to understand post even clearer for those that prefer a visual format:

First, Paul determines the likely employment gap (the difference between the natural rate of unemployment and the likely unemployment we will see when this cycle bottoms). Using 5% as the natural rate of unemployment and an 8.5% unemployment rate (a Goldman Sachs estimate... I personally think it will be higher), we get a 3.5% employment gap. According to Okun's Law:

For every 1% excess of the natural unemployment rate, a 2%reduction in GDP is predicted. The difference between actual and potential GDP is called the GDP (or output) gap.

So if we take 3.5% and multiply by 2, we come up with a 7% output gap in GDP. To close this gap, we need a stimulus package that adds this 7% back to the economy. Considering the poor result of the first stimulus package, Paul assigns a multiplier of 2 to any package (the stimulus isn't spent once, it is spent multiple times as it works its ways through our consumer economy). With this 2x multiplier, the stimulus package should be 7% / 2 = 3.5%, which he rounds up to 4% be on the safe side or ~\$600 Billion.

How big could a package get? Looking at only two variables, unemployment and the multiplier, we can see how the size of a package moves in response to any change. Moving the unemployment out to 9.5% (massive, but not altogether impossible) and the multiplier down to 1 (if unemployment is 9.5%, will people really be spending their checks?), the "required" package more than doubles to \$1.4 Trillion or about 10% of our GDP. Still significantly lower than China's (as a percent of GDP) which was almost 20% of their GDP.