Sunday, July 06, 2008

I attempt to translate this post into English.

The post analyses a variety of super standard neoclassical models in which the government is not allowed to tax wealth or consumption and must decide between a distortionary tax on capital income (which can't be over 100% as part of the not tax on wealth rule) and just not doing stuff. It confirms the general result that the optimal tax rate goes to zero as t goes to infinity. I think this mathematical result has some effect on the writings of economists who have some effect on tax policy. However, they tend to assume that t has gone to infinity already.

I prove that the result can be characterised further. In the models I consider, for the special case of logarithmic utility, it is that it is optimal to tax capital income with a rate of 100% so long as there is any reason to tax at all. Then stop (as noted in the literature) so the government should tax as much as it can so long as it has any reason to tax. For a more plausible utility function, the same result holds so long as the government can't precommit to a tax policy which it will want to change later. If the utlity function is CES and remotely similar to empirical estiamtes and the government can precommit it should tax even more -- that is tax at the maximum rate possible so long as there is any reason to tax then tax more even when it has no remaining reason to tax (and woulnd't if it couldn't precommit).

Huh ? Whah ? What's going on ? I try to explain in English. Two words will do.

Public endowement.

That is negative public debt. The optimal policy involves tax revenues which are, at early times, far above spending and a huge public endowment. This is how it can be otimal to make the tax on capital income zero at later times even if some government spending is very desireable (or absolutely necessary) and there is no other way to tax. It also means that the best way to deal with distortions due to taxation of capital income is with more taxation of capital income.

A tax on capital income discourages saving. One would wish to have a higher savings rate. We know how to make a low savings rate. We have discovered that deficit spending does this wonderfully well. IN the model the way to have high savings is to do the opposite -- have a budget surplus, public saving, build an endowment. This works in the model with perfectly rational infinitely lived savers, because the revenue is given to the poor or spent on public consumption and never returns to the taxpayers.

Basically, the result is that, if one wishes to promote savings, in the model, it is definitely always better to cut the deficit than to reduce taxes on capital income. This works for the model which is taken seriously when only its implications for what will be to be done as t goes to infinity are considered.

Now the idea of a public endowment is very strange and no one talks about its effect on savings. However, the idea is implicit in the now standard result that the tax on capital income should go to zero. It is not made explicit, because the analysis focuses on an Eurler equation (temporal first order condition) and not on the level of public debt or the totally non-existant constraint that the public debt must be positive (which is not assumed and has no role in any of the analysis anywhere in the literature).

The fact that people translate "taxes on capital income should be zero once the government has built up a huge enough endowment that the interest on that endowment will pay for whatever it wants to do" as "taxes on capital income should be zero starting now with an endowment of negative trillions" is really no more absurd than "let's assume t has gone to infinity," since nothing could be more absurd.

1 comment:

Kaleberg said...

The endowment idea is not new. Basically, governments are allowed to carry assets on their books that can not be monetized by any other party, for example, the strength of the nation's children's bones. You can't carry the value of your children's bones on your asset sheet, at least not with a direct cash value. Your children can't carry them on their books, though they can use their good bones to carry their books. So here we have an asset, one that has an acquisition cost, a depreciation, and so on, but no mechanism for accounting it. At least, there is no private mechanism.

When slavery was allowed, slaves were considered as assets, valued based on the expected market value of their labor. That's why they used Irish immigrants to build canals in Louisiana instead of slaves. No one wanted to place their book assets at such high levels of risk from disease. (My source is secondary - Lebergott). When the slaves were freed, African American well being went off the books. Obviously, we as accountants can do better than this.