Obamův a McCainův daňový plán a motivace Grega Mankiwa

Grega Mankiw na svém blogu porovnává, jak ho motivují k práci daňové plány, které navrhují John McCain a Barack Obama. Obamův daňový plán přitom z porovnání vychází dost zle. Mankiw sice provádí jen zjednodušený výpočet, díky složenému úročení jsou ale rozdíly tak dramatické, že nějaká zaokrouhlení mohou rozdíly těžko smazat.

Naše diskuse na Facebooku upozorňuje na některá Mankiwova důležitá opomenutí.
Alan Moreira píše, že při vyšší míře zdanění kapitálu dojde k poklesu objemu kapitálu v ekonomice, nový kapitálový výnos po zdanění ale bude stejný jako ten původní (perfektní elasticita kapitálu v dlouhém období). Rozdíly, které jsou u Mankiwa způsobené zejména rozdílnou mírou zdanění kapitálu, se tak z velké míry smažou.

Guys..MAnkiw exercise is misleading. Not because the reasons that Ben gave. But simply because it taking gross returns as given, while any standard model tell us that savings are perfectly elastic in the long run ( and that is exactly why it is not a good idea to tax capital). So the Net returns on capital has to be the close to similar under both tax plans. The only difference is that under Mccain there is more capital accumulation and in a world of fixed labor supply and homogenous labor would yield higher wages. But regarding the exercise that he does the only differences are the income and the estate tax. And since the estate tax is not that hard to evade, looks like that all that matter is the difference between income taxes. I am not saying that Obama's plan is a good idea. I am just saying that regarding the exercise that Mankiw is doing, if we compare steady state there is almost no difference between them. (6.2 Mccain and 4.8, using as estate tax the tax rate effectively paid conditional on paying estate taxes, that is way less than 45%)

Alan má pravdu a je s podivem, že Greg Mankiw tyto efekty zcela ignoroval. Na druhou stranu ale musím dodat, že je důležité brát v úvahu také dynamiku přechodu z jednoho steady statu do druhého. Potom se sice rozdíly v dopadech mezi Obalovým a McCainovým plánem oproti Mankiwově verzi sníží, stále však budou dost velké.

What Alan omits is the transitional dynamics. Let us assume steady state today, no changes in labor taxes, inelastic labor, Cobb Douglas production, no growth. Let us also assume that we believe in the standard growth model. This is just a theoretical exercise. A quick off-the-hand calculation reveals that a change in the capital/dividend and corporate tax rate from McCain's 36.35% (compound) to 48% (compound) under Obama will: 1. decrease the steady state K/L by 26.4% (= (0.52/0.6375)^(1/(1-1/3))) 2. decrease the steady state wage rate by 9.7% (the above number ^ (1/3)) (I hope I haven't made any numerical mistakes) It is true that the return on capital at the new steady state will be higher. To make our life easier, let us assume that this higher return is compensated by the lower wages that the children will have to accept.

A drop in the capital level by 26.4% is dramatic. So how long can such an adjustment take? 35 years? That depends on the intertemporal elasticity of substitution. Since we don't know what is the right value, let us talk purely empirically. If the adjustment was linear in percentage terms, then we would need a decrease of 0.75% per year. Taking K/Y ratio to be about 3, we are talking a 2.25% decrease in investment rate calculated as I/Y, over 35 years.

Is 2.25% of GDP a lot? When you look at investment data, you can see that the investment rate in the U.S. moves cyclically in the 17-23% range, with very few outliers. So a decrease of 2.25% of GDP puts the investment sector from the steady state into a situation that (in the investment sector) corresponds to a pretty solid recession.

This calculation is not supposed to make any welfare conclusions. It is supposed to show how long the transition could take. Given this, could we expect a faster convergence? Hardly.

Conclusion - it would take pretty long to reach the new steady state. So I think it that if we believe in the model, about half of the effects from capital taxes would still be there (just averaging linear approximations along the linear adjustment path, don't beat me on that). And that's still quite a lot.

Disclaimer: 1. This is not supposed to slander Alan's argument. On the contrary - he is one of the few that brought this up, and I agree with him that Mankiw's calculations are very misleading in this respect. My attempt is just to make more precise the arguments that Alan very correctly initiated.

2. I myself actually don't believe Mankiw's argument for a completely different reason, and that is a politico-economic one. Nobody can expect that Obama's prospective changes will last for 35 years. On the contrary - it may very well that Obama's higher capital taxation will move us in the other direction, and make us lower capital taxes in the future even more than we would do without this experiment.

3. I don't want to run into arguments about the details of the U.S. tax code, which I don't understand well enough to be able to argue about it. Take this as a theoretical exercise.