Multiplier Math: Is U.S. Protectionism on the Way?

We detailed in a prior post how large a stimulus package would need to be based on certain assumptions in unemployment and the multiplier (a summary chart of that discussion is as follows):



As can be seen above, if unemployment were to rise above current 8.5% estimates, the multiplier becomes increasingly important in determining an appropriate size for a stimulus package. Thus, an important question is how large will the multiplier be?

Fortunately, Dani Rodrick's recent post dives into the math behind the multiplier and he isn't fond of what it tells him.

First, the multiplier:



In other words, the three ways to increase the multiplier is to:

• Increase the rate of consumption (hence the public works projects, rather than rebate checks which went right to savings first pass)
• Decrease the tax rate (for this reason, I expect the Obama administration to put tax hikes on hold)
• Decrease imports (thus, more production within the U.S. is needed to satisfy any given level of demand)
  

Dani seems to believe the third (i.e. decreasing imports) would be rather easy. In an example he calculates a multiplier of 1.8 based on MPC of .8, MTR of .2, and MPI of .2, which is increased more than 50% in his example through the raising of import tariffs:

It is pretty easy to increase the multiplier; just raise import tariffs by enough so that the marginal propensity to import out of income is reduced substantially (to zero if you want the multiplier to go all the way to 2.8). Yes, yes, import protection is inefficient and not a very neighborly thing to do--but should we really care if the alternative is significantly lower growth and higher unemployment? More to the point, will Obama and his advisers care?

With unemployment at 10%, a difference in the marginal propensity of imports can mean the difference of hundreds of billions of dollars in stimulus. In other words:

unless we come up with a solution to the credit constraints in the developing world, we are going to either endanger the effectiveness of Keynesian policies in the U.S. and other advanced nations, or risk a sharp increase in protectionism. Not a pleasant choice.