The Lure of Capital Taxation

The taxation of capital income – corporate profits, capital gains, interest, dividends, etc. – has always been attractive to both politicians and to economists.

Politicians are drawn to capital taxation because it presents an opportunity to raise a substantial amount of income but at the same time is politically popular in a way that labor income taxation or the elimination of the home mortgage interest deduction isn’t.

Economists are drawn to capital income taxation not because it is a good idea – many (most?) economists oppose taxing capital income – but because it presents a number of academically interesting features that are worthy of study. In particular, capital income taxation presents several tricky dynamic considerations that many other forms of taxation do not.

Suppose the United States government sharply increases taxes on business income – say by increasing the corporate profit tax rate. What are the short-run and long-run consequences of such a policy?

In the immediate wake of the higher tax, standard theory would predict that basically nothing would happen to production or employment (?). This probably strikes many of you as puzzling. If I tax business income shouldn’t I discourage the creation of this income? According to standard economic analysis, such a tax should not. The reason is that real business capital – the equipment, machines, factories, etc. – are inelastically supplied in the short run. The factories are all still here. The grills, ovens and sinks still work as do the espresso machines. The excavators still run … All of the capital that was functioning before the tax is functioning after the tax. Moreover, businesses cannot escape capital taxes by laying off workers – the firm’s wage bill is already tax deductible. As a result, the firm should behave the same in the face of the capital tax hike. The immediate effects of the capital tax increase are simply a reduction in the after-tax capital income for owners, investors and savers.  Put differently, it is the capitalists bear all of the burdens on the tax increase.

As time passes however, the burden of the tax hike shifts to workers rather than capital owners. While the tax increase doesn’t influence the supply of capital in the short run, according to the standard model, it discourages the capital accumulation over time. In particular, it should discourage capital accumulation – and thus reduce the capital stock – to the point at which the after tax real rate of return is in its long run equilibrium. In the standard model this is usually the exact same rate of return that the economy began with. At the same time, the reduction in capital also reduces the demand for labor and so wages fall.  So, in the long run, the consequences of an increase in capital taxation are the opposite of the short run.  In the long-run, the workers bear all of the tax burden and the capitalists bear none of it.

The fact that the economic incidence of a tax increase is different from the statutory incidence is one of the classic insights of public finance economics. The dynamic effects of a change in capital taxes is a particularly stark example of such a distinction. The difference between the short run and long run effects of the tax changes comes from the differences between the short-run and the long-run supply of capital.  In the short run, the capital stock “is what it is.” Over time however, capital can be accumulated or decumulated – that is, the long-run supply is relatively elastic. This simply insight alone strongly suggests that the optimal taxation of capital income should be higher in the short run that in the long run.

The tension between long run and short run optimal taxes also presents a problem for policy makers.  While they will constantly be tempted to tax capital, they will also want to commit to lower taxes in the future.

Among the most famous results in modern public finance is the Chamley-Judd theorem (see C. Chamley 1986 and K. Judd 1985). This result says that if tax rates are chosen optimally then, if the economy attains a steady state, the tax rate on capital income should be zero (!). Many economists (myself included) have interpreted this result as a formal articulation of the intuitions above.

Recently, there may have been an important development in the literature on optimal capital taxation. Ivan Werning and Ludwig Straub (MIT) have circulated a paper in which they argue that the Chamley-Judd result is of more limited importance that is commonly believed.  They argue that under certain circumstances optimal tax paths do not lead to a steady state the way we normally think of it and in these cases, the tax on capital income can be positive. In other cases, while the Chamley-Judd result technically holds, the steady state is attained only after an extended period of time (centuries in their examples) and is thus of limited relevance.

I am not going to go into the details of the Straub and Werning paper in a blog post. The short version of the explanation is that the suppositions required for the Chamley-Judd result are more stringent than one would imagine. For the textbook Chamley-Judd result to hold, the economy must approach an interior steady state with finite Lagrange multipliers for the various constraints in the model.  In many of the solutions in the new paper, the economy converges to a rest point with zero capital (and is thus not interior).  In other solutions, the Lagrange multipliers do not converge.

In fairness, the counter-examples Straub and Werning provide are all in the family of isoelastic preferences which sometimes have weird features in certain settings.  It is not clear to me whether the authors’ findings will necessarily extend to more malleable preference specifications but what is clear is that researchers will have to look much closer at the meaning of one of the most prominent results in modern public finance theory.

More to come I’m sure …

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