This is a post about macroeconomic theory. It is technical and I honestly don’t know how much is already in the literature. The aim is to address an important policy question — is public debt a burden on future generations.

It is possible in theory that the answer is no and that higher public debt causes permanently higher consumption and welfare. In such a case, it is clear that the low debt market outcome is inefficient, so this is called dynamic inefficiency. The standard result from simple models is that an economy is dynamically inefficient if r

This formula isn’t very useful in the real world, because there isn’t one real interest rate — rather there is a low real interest rate on safe assets and higher rates on risky assets. The standard interpretation of “r” is that it refers to the ratio of total capital income to total capital. A lot of this r is not called interest at all since the claim on the income is equity not any kind of loan or bond.

The question of interest is whether increased public debt can cause increased welfare when the safe real interest rate (r1) is lower than g but the average return on capital (r2) is greater than g. I think the answer is yes, so I think it is plausible that, in the real world, greater public debt will cause permanently higher welfare.

I stress that I am not talking about any benefits of government spending which can be financed by the debt — the result would hold if the bonds are just given (that is the deficit is due to tax cuts) and the result is that people who weren’t alive at the time of the tax cut would benefit. Also it is assumed that wages and prices are flexible and markets clear (there is no unemployment) so the benefits of public debt have nothing to do with Keynesian stimulus.

This post was supposed to link to a pdf with models and proofs, but I can’t force myself to write the pdf without publicly promising it will exist. I will sketch the argument and 3 models after the jump.