Tuesday, December 12, 2006

Answer from Ed Prescott

Yesterday, I said in a post here that I was confused about Ed Prescott's conclusion in his latest op-ed that "the optimal amount of public debt that maximizes the welfare of new generations of entrants into the workforce is two times gross national income, or GDP." Ed very graciously emails an explanation. Here it is:


Kathryn Birkeland and I come to our conclusions using a calibrated OLG model. Crucial is the length of the retirement period and the population growth rate. Bob Fogel is confidently predicting longer retirement periods because of a projected decreases in morbidity. He convinced us. Our expected length of lives is low if anything.

The U.S. economy has been growing at 3% and the average return on capital has been 4% (See McGrattan and Prescott, AER Papers and Proceedings, May 2003). Birkeland and I have people beginning to work at 21 and continuing to work until they are 65, which is higher than the median retirement age in the United States. Model people die when they are 85. Productivity grows at 2%, population grows at 1%, and people discount at rate 1%. Consequently all ages at a point in time consume the same amount and the households face a 4% real interest rate.

We know there is no competitive equilibrium for the Diamond (1965) economy unless government debt is (or alternatively the size of taxes and transfers are) such that the interest rate is above the economy’s growth rate. It is true that with land that does not depreciate and provides a service, there always is an equilibrium and it is efficient. But even land requires some maintenance and land is taxed. We restricted attention to policies for which an equilibrium exists and the equilibrium interest rate is 1% above the sum of population growth rate and productivity growth (labor augmenting) rate.

The important point of our analysis is that it is welfare improving to have government debt rather than taxing the labor income of the workers and making transfers to the retirees where both policies are such that the real interest rate is 4%. The latter policy has much lower government debt though the present value of government promises is large. Making these liabilities explicit and shifting to a saving for retirement system improves the welfare of all except retirees, whose welfare is unchanged. The resulting large increase in government debt is not a burden on our grandchildren. The tax and transfer system to finance retirement consumption is a burden because workers value leisure.


P.S. We did not argue that the U.S. economy is dynamically inefficient, so our results do not contradict the finding in Abel, et al.

I have not processed all this sufficiently to say that I fully understand it, but this note certainly goes a long way toward clarifying Ed's thinking for me. I greatly appreciate his taking the time to write.

Update: On reflection, I am inclined to interpret Ed as saying he is worried that, absent government debt (or social security), the economy would oversave and end up dynamically inefficient, a situation characterized by a real interest rate less than the growth rate and a capital stock greater than Phelps's Golden Rule level. This outcome is a theoretical possibility, but I am skeptical that it is in fact the case for the U.S. economy.

I don't know of a link to the research paper Ed mentions, but if I find one, I will post it.

Update 2: Click here.