A dubious and horizontal transformation is given in Figure 27, where the assumption of ‘fixed bracket lengths’ has been assumed rather than ‘fixed bracket positions’. When we now substract a fixed sum from the line through the origin, the original function cannot be retrieved, and the higher incomes pay more tax. It now seems as if the tax credit is ‘fairer’. However, the true cause is that taxes have been raised by shifting the bracket positions.
Figure 27. Horizontal translation
The Dutch Government “Tax Plan for the 21st Century” used this misleading horizontal translation to argue that tax credits would be more just than plain old exemption. See Colignatus & Hulst (2003:32) for the misleading statements.
Useful approaches are:
1. Introduce a new separate ‘tax group’ that only holds for workers below the current minimum wage. Let this group have a high exemption at the new minimum wage and a normal marginal rate of 50%. Clearly, there could be jump in taxes at the current minimum wage. However, the high exemption can be said to apply to all citizens - and many simply don’t qualify since they do not fall in the new group. (The latter is only unfortunate for them, if they prefer a high exemption above their current high income.)
2. One might opt for a 100% marginal rate from subsistence (the new minimum wage) up to the current minimum wage. In this case there is no tax jump. High exemption again applies to all citizens, but its effect is undone by an intermediate high marginal rate region. Whether this is considered to be a bad situation, depends upon the analysis of marginal tax rates: see below.
3. Introduce a nonlinear trajectory from subsistence to some place in the current regime. Since reduction of wage costs generates employment, the state saves on benefit payments, and some revenue can be used to reduce taxes also above the current minimum wage. This reduction can be done in a nonlinear way that allows for a fluent change, without jumps and without new tax groups. Figure 28 gives an example of such nonlinear trajectory, where the function Tax[.] has been estimated to fit the 1997 Dutch tax code (inclusive of premiums) but with a nonlinear repair towards subsistence. The special point is that this estimated Tax[.] has a negative curvature parameter. The 1988 income distribution has been used to approximate tax revenues. The currency here still is Dutch guilders.