Do income effects matter for tax policy?

In a previous post, I explained that for determining the deadweight loss from taxing labor income, one should consider the substitution effect of taxes on labor supply but ignore the income effect. Several commenters questioned how far this conclusion extends. In particular, if we are interested in the impact of taxes on hours worked and national income, shouldn't we consider both the substitution effect and the income effect? And if these two effects are offsetting, as much evidence suggests, shouldn't we conclude that the impact of labor taxes on these macroeconomic variables is minimal?

The answer is, it depends. To be more specific, it depends on how the government spends the tax revenue it raises. Let's consider three cases:

Case 1. The tax revenue is spent on a feckless war overseas (or on some other program that does not affect private consumption). Then the labor tax to fund the war does indeed have offsetting income and substitution effects. This seems to be the case that people naturally assume. For many purposes, however, it is not the right one.

Case 2. The tax revenue is rebated lump-sum to households in the form of transfer payments (Social Security) or through publicly-financed consumption (health care). In this case, the income effect of higher taxes is offset by the opposite income effect of the rebated revenue. The only effect left is the substitution effect. The magnitude of the subsitution effect is measured by the compensated elasticity of labor supply.

Case 3. The tax revenue is rebated progressively in the form of transfer payments (welfare) or publicly-financed consumption (food stamps) for low-income households. The benefit gets phased-out as a person's income rises. Once again, there is no overall income effect, because the government's tax and transfer scheme does not directly reduce the resources of the private sector. But the substitution effect is now enhanced because the effective tax rate on income includes the phase-out of the low-income benefit. Naturally, one would get the largest effect on hours worked and national income in this case.

FYI, in my paper with Weinzierl on dynamic scoring, we assumed Case 2. As a result, tax cuts were partially self-financing in that model, even though the assumed utility function implied a vertical long-run labor supply curve (for productivity-driven wage growth) because of offsetting income and substitution effects. This seemed a reasonable compromise for theoretical work, but it is an empirical question which of these three cases is most relevant in practice.