samlet årgang - Økonomisk Institut - Københavns Universitet

LABOR SUPPLY BEHAVIOR AND THE DESIGN OF TAX AND TRANSFER POLICY 331
that the welfare loss is given by the revenue loss created by changed behavior, is not
related to the specific model adopted here but holds in general for tax policy analysis.
For empirical applications, it is useful to rewrite the above result. Let denote the
elasticity of hours worked with respect to the net-of-tax wage rate. 7 Then the change in
the deadweight loss in proportion to the aggregate wage income may be written as
DWL m
– · · m (3)
wh 1 –m
This expression is a classic Harberger-type formula for the marginal deadweight
burden of taxation. 8 It shows that the marginal welfare cost depends on the initial level
of the marginal tax rate, the increase in the marginal tax rate, and the hours-of-work
elasticity. Notice that the marginal loss is equal to zero when the marginal tax rate is
zero. That is, initially the welfare cost of raising tax revenue is zero. As the tax rate is
increased, the marginal welfare cost of taxation also increases at a given labor supply
elasticity. In other words, it becomes more and more costly to raise additional government
revenue as the tax rate goes up. In fact, welfare effects can be substantial even for
very small labor supply elasticities provided that initial marginal tax rates are high.
Finally, since the empirical evidence does not give any indication of large, significant
differences in hours-of-work responses across individuals (conditional on labor force
participation), we may conclude that the largest efficiency gains of tax rate reductions
are to be found where marginal tax rates are relatively high.
3.2 The excess burden of taxation with extensive labor supply responses
The modeling of tax distortions along the extensive margin is a bit more complicated.
As noted in Section 2, an appropriate theory requires some type of non-convexity
in order to account for the observed discreteness in labor supply behavior. 9
In addition, the theory has to incorporate heterogeneity across individuals. With no
heterogeneity in preferences or productivity, either everybody participates or nobody
participates in the labor market. In reality, some fraction of those in their working age
7. To be precise, is the compensated hours-of-work elasticity. As described in footnote 3, income effects
are irrelevant for the measurement of the excess burden of taxation.
8. The result is more general than it appears. Specifically, the result is not restricted to a proportional tax
scheme although this is the case for Figure 3a, b and for expression (1). The relationship in (3) holds for any
tax system as long as the marginal tax rate is locally constant. The result also holds for other definitions of
the deadweight loss. Here, we have derived expression (3) from a simple Marshalian definition but the
result may also be derived from deadweight loss measures based on compensating variation, equivalent
variation, or compensating surplus.
9. A general framework for analyzing welfare effects with discrete choice is provided by Small and Rosen
(1981).