# Math is Math: There Was No "Second Stimulus"

One of the best rules in mathematics is that, to determine the value of all the variables, you need only as many distinct equations as you have variables. (previous sentence edited for clarity.) So let’s combine a couple of recent articles (h/t Mark Thoma for the first, Digby for the second.)

Richard Florida finds three studies of State Government Spending Multipliers. The three studies find multipliers of 1.5, 1.7, and 2.12. Let’s be nice (in context) and use the lower one. StateMultiplier = 1.5

David Dayden notes that budget cuts in just two (large) states can be matched against the Fed’s “stimulus” monies. Let’s see how much, putting the best face possible on the data (i.e., taking the most optimistic projections). CADeficit (ignoring “reserve”): \$26.4B (12.5 + 12 + 1.9). ILDeficit: \$19B (13 + 6).

That gives us a CA-ILEconomyCost of (26.4 + 19)*1.5 = US\$68.1B

The Federal Stimulus is \$55-60B. Again, let’s be optimists and say \$60B. The required multiplier is then:

FedMultiplier * FedStim = CA-ILEconomyCost

FedMultiplier * \$60B = \$68.1B

FedMultiplier = 1.135

That’s the minimum multiplier needed just to counter those two states. Add in Texas (whose shortfall appears to be on par with California’s, and is larger than Illinois)and you’re at 1.77.

Only 47 states to go.

The maximum multiplier needed just to solve the CA-IL gap is 1.71. Add in TX and you’re at 2.63 with 47 states to go.

The Right-Leaning Econ Bloggers (e.g., Tyler Cowen and Greg Mankiw; I apologize to the former for linking him to the latter) argued in 2008-2009 that Federal Stimulus has a multiplier of 1.3 or less.*

1.3 would put the economy at neutral if the multiplier is 1.7 (median estimate) and most but not all of the CA ambiguities break the wrong way.

And that’s just eliminating the effect of those two states. Add in TX and the multiplier goes to 2.64—rather close to Christina Romer’s 3.0 that was attacked continually by Mankiw et al.

Repeat after me: There was No “Second Stimulus.” If the economy is going to go into full recovery—i.e., can I have jobs with that?—it will have to be from Private Sector Investment, which has been (let’s be nice) on the sidelines so far,* and really doesn’t appear to be warming up to replace TARP.

*Strangely, this was not argued by them as an argument that the initial “stimulus” was too small for the even-then-obvious shortfalls in C and I; I can’t believe they thought MX was going to cover the difference, but that’s a side discussion, perhaps.

*We can quibble over whether that was and remains the correct decision. As has often been noted here, a lack of demand is not exactly an incentive to expand, unless you think that will be changing soon. A true recovery should have convinced firms that a change is gonna come.