As the debate over the nature and size of a stimulus package wends its way through the Congress (0), (1), (2), I thought it would be useful to bring numbers into the debate, especially as we are considering fiscal stimulus in a time when the Bush Administration has constrained, by dint of previous profligacy, our options. In particular, I want to return to the issue of multipliers, discussed in nearly a year ago. Here, I want to provide a little more specificity, regarding the impact depending upon the type of outlays.

From the testimony of Economy.com's Mark Zandi back in July (thanks to Chad Stone for the pointer):

Remember, what is a multiplier? It's:

?Y/?Z

where Y and Z are measured in real dollars. Note that in principle, one can re-write the multiplier in terms of percentage point change of income relative to baseline income for a given percentage point change of the Z-to-Y baseline ratio.

What is apparent is that some tax cuts, or really rebates, can have a substantial effect. But in most cases, tax policies will have a relatively minor impact on aggregate demand, relative to increases in spending on goods and services. That's because the first round of injection of the dollar into the economy via tax reductions or transfer increases initially augments disposable income, and then, by indirectly increasing consumption, increases GDP over time. In other words, for an increase in transfers, the impact of one dollar increase in outlays by the government is:

(c(1-t)) + (c(1-t)) ² + (c(1-t)) ³ + .... = c(1-t)/(1-c(1-t))

Whereas for spending on goods and services:

1 + (c(1-t)) + (c(1-t)) ² + (c(1-t)) ³ + ....