# The Optimal Size of the Deficit

As a follow up to my (admittedly simplistic) post yesterday optimal tax collections, I noticed that there is one interesting bit of information in the spreadsheet, still untouched, that would make a nice post by itself.

So how does growth (in real GDP per capita) look for deficits of different size? Letting A equal deficits > 4% of GDP, B equal deficits between 2% and 4% of GDP, C equal deficits between 2% and 0% of GDP, and D be surpluses, and using data going back to 1950:

__________A_______B______C_______D
t to t+1___2.81%___1.89%___2.81%___0.46%
t to t+2___2.75%___1.98%___2.34%___1.18%
t to t+3___2.49%___1.91%___2.34%___1.46%
t to t+4___2.17%___1.96%___2.26%___1.77%
t to t+5___2.11%___2.00%___2.28%___1.74%
t to t+6___1.86%___2.12%___2.20%___1.84%
t to t+7___1.89%___2.11%___2.20%___1.90%
t to t+8___1.92%___2.13%___2.11%___2.28%

As an example of how to read the table, the annualized growth rate, over a seven year period beginning in a year when deficits lie between 0 and 2% of GDP is 2.20%.

What does this show? Well, over the short run, say, one to three years, the largest growth rates are associated with a large deficit. Two explanations I see for this:

1. The responsible reason: Governments are Keynesian, spending a lot when times are bad, and cut back on spending when times are good (to pay off the debt raised when times are good)
2. The irresponsible reason: In the short term, a deficit is free money. After a few years, though, it has to be paid back. The larger the deficit, the more principal and interest have to be paid back.

I would think option 1 can be dismissed out of hand by anyone with the self-awareness of a stick of gum. Few administrations have made much of an effort to pay off debt when times are good.

Over the longer haul (8 years), it seems that running a small deficit or perhaps even a surplus (see year 8!) is correlated with the highest growth. I would imagine this is especially true if growth can exceed the deficit, and interest rates are low.

Data
Deficit and surplus from OMB Table 1.3
Real GDP per capita from BEA NIPA Table 7.1.

Note that because tax and deficit data is for fiscal year, I used real GDP per capita for the third quarter of the calendar year.

As always, if you want my spreadsheet, drop me a line.