There is one area where the DMR cannot easily be overlooked. This is the area of policy simulation, where tax adjustment cannot be neglected. For sure, empirical analyses and government projections indeed deal with tax parameter changes. For example the well-known Reagan tax cuts were put into the forecasts at that time. However, we should wonder now whether the methods have been right. The analysis above focusses our attention on the impact on individual behaviour, where we regard the marginal calculation by agents themselves.
Let us regard policy simulations using common practical economic models. Let us for example regard the effects of a rise of government investments as financed by taxes, for a sustained period of 8 years (two presidential terms). To do a simulation properly, the tax function used must reflect government policy, which includes indexation. For example, exemption and other brackets are adjusted for last year inflation while the statutory marginal rates remain the same. The different investment paths result in different paths for the taxes. This is not just a model result, but also the agents in the economy would encouter different regimes. Thus the model generates different dynamic marginal rates, while the agents are assumed to react only to the same (static) rates. The situation gets even complexer when the alternative policy includes a different indexation scheme, such as indexation of taxes on national income. All this means, then, that we are justified in doubting the validity of current modeling practices. Modelers should start wondering about this kind of dynamic consistency (not to be confused with the ‘dynamic consistency of policy’ as another topic in economic literature on ‘credibility’).
It might even be, then, that the best way to understand the dynamic marginal rate is to see it as a solution to this kind of dynamic inconsistency.
Balanced growth
Under balanced growth, taxes will grow as fast as incomes, with a constant tax share TAX / Y, assuming proper indexation of the tax parameters. A result will be that the dynamic marginal equals the average tax rate, for all individuals. Book III already mentioned the key relationship here, in property (13.3e).
We use Tax[.] for an illustration. Here a solution for a balanced growth path is that parameters x and c are indexed on y. With the index for y as i = P ryi ( i > 0), we find for the (individual) average tax burden that the index drops from both numerator and denominator:
T[ i y; r, i x, i c] / (i y) = r (i y - i x) / (i c + i y) = T[y; r, x, c] / y
(Less relevant, (29.1) remains the same too.)
The situation of a constant dynamic marginal rate is depicted in Figure 30.
Figure 30: A balanced growth shift
A-2A: constant frequency, A-C: the same average tax