Ultra Amateurish Thoughts on “Optimal Fiscal Policy in a Liquidity Trap (Ultra-Wonkish)”

Paul Krugman argued that optimal fiscal policy in a liquidity trap targets unemployment equal to the non accelerating inflation rate of unemployment (NAIRU). He uses a model with Ricardian equivalence. This means that the public debt does not affect consumption.

When he wrote his post, I said I thought his conclusion depended on this assumption. My thought was that deficit spending which keeps unemployment equal to the NAIRU will imply high public debt after the economy is out of the liquidity trap. In the real world, such public debt creates the illusion of wealth which causes higher consumption than people would choose if they were deluded. This is a cost of high public debt. I guessed that it meant that one should accept higher than NAIRU unemployment.

Formally it is possible to achieve NAIRU unemployment without deficit spending. Increased public spending financed by increased taxes stimulates the economy. In Krugman’s model with Ricardian equivalence a balanced budget spending increase stimulates just as much as deficit financed public spending. In the real world somewhat less for dollar of public spending, but the NAIRU can still be achieved. Of course in the real world it is very hard to raise taxes.

So my argument becomes “assuming you can’t raise taxes and can only adjust public spending, is it optimal to set the unemployment rate equal to the NAIRU?”
I have a new answer. First assume that there is public spending which can be rescheduled without any inefficiency. That is it doesn’t matter at all if we do it now or do it later. In theory some spending on building infrastructure or on maintenance of infrastructure could be like this.

With that strong assumption, the optimal unemployment rate during a liquidity trap is the NAIRU even if Ricardian equivalence doesn’t hold.
The reason is that the duration of the liquidity trap is endogenous. OK a liquidity trap occurs when the nominal interest rate which gives unemployment at the NAIR is negative. Imagine an exogenous shock which will cause a liquidity trap lasting for say 2 years. Krugman says raise public spending during those 2 years so the unemployment rate is NAI. The spend normally. This is fine if taxes can be raised or if the resulting debt is sustainable and there is Ricardian equivalence.
Assuming taxes are fixed such a policy would require spending cuts after 2 years.
That does not imply unemployment higher than the NAIRU after 2 years. Lets say in the third year, the optimal interest rate would be 1% for normal public spending. Cutting spending so that the NAIRU interest rate is 0% is consistent with NAI unemployment. The period of zero interest rates can be extended until the extra debt built up during the 2 years of low demand is paid off.

It is not necessary to accept unemployment over the NAUIRU in order to deal with deficits even if tax increases are absolutely impossible.

It is necessary to time public spending for purely macroeconomic reasons, so this conclusion depends on the assumption that changing the spending schedule is costless.