Waldmann: Optimal Capital Income Taxation It Is

Robert Waldmann (2008), "Optimal Capital Income Taxation It Is" http://www.economia.uniroma2.it/nuovo/facolta/docenti/curriculum/Robert%20JamesWaldmann.pdf

It is well known that, in standard growth models, the optimal tax on capital income goes to zero asymptotically. Even some serious economists (cough Glenn Hubbard cough) seem to have decided this means that capital income taxes should be eliminated right now. However, asymptotically we'll all be dead. One can tell more if one looks at the simplest cases of standard growth models: an aK model with optimizing consumers who have logarithmic utility or a Cass-Koopmans model with Cobb-Douglas production and logarithmic utility (OK that was wonky but it's about assumptions so I have to be honest).

Consider such an economy in which the distribution of wealth is unequal at time 0. A utilitarian state would want to redistributed income. The first best way to do this is with a lump sum transfer. Let's rule that out by setting an upper limit on the tax on wealth (or an upper limit on the tax on capital income). What is the best policy?

The best policy would be to tax capital income at the maximum allowed by the assumption and use the revenues to reduce inequality until perfect equality is achieved. After perfect equality is achieved, there is no more reason to tax and taxes are zero. Thus, as noted above, the optimal tax goes to zero in the long run. The reason is that it is optimal to tax as much as is allowed by assumption so long as there is any reason at all to tax. Then stop.

A simple-minded application of the model to policy would suggest that we should tax as much as we can until everyone is perfectly equal. Now the model is not the world and this would be a terrible policy. However, the argument for roughly the opposite policy is based on the same silly model plus totally turning its implications upside down by pretending that time has already gone to infinity.

The assumption of logarithmic utility is not at all innocent. It makes a huge difference. A more general assumption (which is standard in the literature) is constant elasticity of substitution utility. In this case the optimal policy depends on the intertemporal elasticity of substitution of consumption and on whether the state can pre-commit to a policy that it would like to change later if it could.

If the state can't precommit, the implications are just like those for logarithmic utility described above: tax as much as possible so long as there is any reason to tax at all, then stop when everyone is perfectly equal.

With precommitment, if the intertemporal elasticity of substitution is less than one (as are all empirical estimates of said elasticity) the result is to tax even more, that is to tax as much as possible until the initially rich are as poor as the initially poor, then tax them some more.

These conclusions follow from analysis using standard techniques of the simplest case of the standard model. I think that they are not noted in the literature. I conclude, as always, that to the economics profession mathematical analysis of stylized models is taken seriously exactly so long as the conclusions fit the prejudices of economists. Thus when an economist says "Mathematical analysis which you wouldn't understand of my model shows that X is a bad policy" you should hear "I don't like X."