· There is the combination of nonlinear tax and lognormal productivity, which causes an upswing of the CWIRU in the early phase of stagflation.
· This holds for a wide class of tax functions, even some very nonlinear ones.
· Where the term ‘income tax’ is used, it also applies to VAT and insurance for old age, disability and the like, as long as part of these are considered to be part of subsistence and thus should be included in exemption.
· This theorem and proof are for a structural form, and inspire the theorem and proof for the reduced form that we discuss later.
Raising exemption
Our analysis points to the suggestion of ‘waiving taxes for the lowly productive’, which can be translated as ‘raising exemption’. Interestingly, this latter translation appears to provoke some terminological confusions.
The notion of ‘raising exemption’ is often taken to imply that all other brackets shift along with exemption. This causes a huge loss of tax revenue. E.g. Gelauff (1992), who uses the official general equilibrium model of the Central Planning Bureau to compute the economic impact of raising exemption, adopts this expensive approach. (His scenario also includes the Dutch concoction of the ‘transfer of exemption’ by partners, so that his implementation is even more expensive.)
However, there are some alternative implementations. Their common feature is that taxes above the current minimum wage are essentially unchanged.
The issue can be clarified by the following two graphs. In Figure 26, the function with an exemption (bold line) can be compared to a function without an exemption (thin line) but with a tax credit (bold line again). The tax credit is given as c = r1 x where r1 is the rate of the first bracket (taking that as defined by the tax credit). The two systems are mathematically identical, when seen as a vertical translation while keeping the bracket positions fixed.