Yesterday, I was reading Gorry, Hassett, Hubbard, and Mathur (2015) in this week's NBER release. Their paper is about how taxes affect the structure of executive compensation (e.g., between cash, stock grants, and stock options). This motivated me to try to think carefully about the extent to which tax avoidance is socially costly.
The classical answer, most notably introduced by Feldstein (1999), is "yes." Specifically, Feldstein (1999) argued that the response of taxable income to tax changes --- melding in tax avoidance just as well as real labor responses --- is a sufficient statistic for welfare calculations.
The basic, textbook story is the following. Suppose agents choose total income y and avoidance activities A (which reduce taxable income); they face a local linear tax rate t. They pay (y-A)t + I(t) in taxes, where I(t) is virtual income (virtual income is the intercept of the local budget constraint extended to the y axis --- in the case of a flat tax, it's zero). They have increasing utility over consumption c, which equals y(1-t)+tA+I(t) and decreasing utility over A and y. Furthermore, suppose the utility function is continuously differentiable. Facing the tax rate t, they maximize with respect to A and y.
With this set-up, suppose that the government is considering small increase in the tax rate Δt, which will increase revenue (per taxpayer, say) by ΔR. Let's define ΔM as the "static" or "mechanical" increase in revenue, which comes from applying the new tax rate to the existing y and A (i.e., disallowing behavioral responses). Then, as an identity, we have ΔR = ΔM + ΔB, where ΔB represents the change in revenue due to taxpayers' reoptimization. Typically, we think of ΔB as being negative for a tax increase; i.e., ΔM>ΔR.
The upshot will be that the marginal dead weight loss (DWL) is (-ΔB). To see this, suppose that the government is considering two proposals. The first is to increase revenue by ΔR by increasing tax rates by Δt, as mentioned above. The second is to increase revenue by ΔM via a lump sum, nondistortive tax.
Under the first proposal, the government loses (-ΔB) relative to the second proposal. And, critically, the taxpayers are indifferent between the two proposals. Thus, the distortionary nature of the taxation has reduced total welfare by (-ΔB), multiplied by however we want to weight a dollar in the hands of the government (which I'll normalize to one).
Why are taxpayers indifferent? This relies heavily on the envelope theorem. Let V(t) be the indirect utility function; i.e., V(t) = maxy,Au(y(1-t)+tA+I(t),A,y). By the envelope theorem, the total derivative of V(t) is equal to the partial derivative of u(.,.,.) with respect to t, evaluated at the optimal choice of y and A. Because individuals are, and remain, near the optimal choice of y and A, their reoptimization decisions have no first-order effects on utility. If this reoptimization comes from increasing A, then the benefit of the tax reduction offsets the marginal difficulty of increasing A.
So, when we increase distortionary taxes by Δt--raising ΔR of revenue---we get ΔV=V'(t)Δt=uc*(-(y-A)+I'(t))Δt; this is just equal to the (opposite of the) marginal utility of consumption times the increase in mechanical tax revenue: (y-A)Δt - I'(t)Δt = ΔM. If, instead, we were to simply confiscate ΔM via a lump-sum tax, the utility loss would be the same (to first order). Therefore, agents are indifferent between raising ΔR via distortionary taxes and ΔM via lump-sum taxes, and (-ΔB) is the DWL.
But, what if the tax reform were designed in such a way that taxpayers could costlessly avoid the tax increase? In the absurd extreme case, imagine that the top tax rate increases on paper from 39.6% to 45%, but taxpayers can check a box to have the 39.6% rate continue to apply to them. In this case ΔM is large --- equal to 5.4% times all income above the bottom of the highest bracket. And because avoidance is costless, ΔB = -ΔM! The arguments before would say that this tax change has created a huge DWL. But that's nonsense; nothing has happened in reality.
What's going on here is that the utility function is no longer continuously differentiable in A, so the envelope theorem no longer applies. This means that the taxpayer would clearly not be indifferent between a ΔM lump-sum tax (ΔM is large and positive!) and a "distortionary" tax raising ΔR = 0. The logic breaks down. In reality, the DWL is zero because the tax reform was meaningless.
This brings me back to Gorry, et al. In their Appendix A, they claim that the (-ΔB) associated with deferred compensation represents the DWL. In their context, this (-ΔB) comes solely from the ability to shift taxation of income from high-tax periods to low-tax periods. This type of avoidance might be akin to the "checking a box for a lower tax rate"--- basically costless. So the intepretation of (-ΔB) as the DWL probably overstates the distortionary nature of taxation. On the other hand, if this avoidance activity entails real costs in a nice, continuously differentiable way (e.g., by exposing an executive to incrementally more risk), then Gorry, et al.'s analysis is probably more appropriate. I'll have to think more carefully about this in their context to say anything more conclusive.