Chapter 3: Optimal income taxation over the business cycle101
3.7 The optimal distribution of the tax burden over the business
3.7.1 The case with three income taxes
In this section we analyse how optimal income taxes and the key macro- economic variables behave following a temporary standard deviation shock to total factor productivity, productivity of capital equipment and govern- ment spending. Figure 3.1 presents the impulse responses (IRs) from an output-enhancing shock.85 This allows us to evaluate how the government optimally distributes the tax burden in the short- and medium-run in re- sponse to output-enhancing exogenous shocks.
85Note that Figure 3.1 plots the percent deviations from the steady state for every variable.
Figure3.1:Impulseresponsesofoptimalpolicy(Benchmarkcase)
A positive shock to total factor productivity will lead to higher immediate income tax rate for the hand-to-mouth agents ( h). The increase of the income tax of the hand-to-mouth agents is only present in the short-run because the government wants to smooth out their consumption. In addition, in the short-run the income taxes of the other two types of agents decrease, as the government can reduce these taxes and maintain the same level of tax revenue, given the rise in tax bases. The income tax of the unskilled agents exhibits the highest reduction compared to the skilled income tax. As a result, the progressivity of the income taxes is mixed after a TFP shock, since the income tax of the low income agents increases, whereas the income tax of the middle income agents decreases more compared to that of the high income agents.
In the medium-run we can see that the income tax of skilled agents in- creases above its steady state. As the economy returns to the steady state, it is optimal for the government to generate the tax revenue required by increasing faster the tax rate for the largest income source, so that it can maintain a low tax rate for unskilled and hand-to-mouth for a longer time.
Figure 3.1 also shows that the increase in equipment capital and decrease in relative skill supply induced by the changes in TFP and income taxation increase the skill premium. As a result, the skill premium is procyclical.
The impulse responses of the optimal income taxes are di¤erent under a positive shock to the productivity of capital equipment. In particular, this shock creates an increase in wage inequality, re‡ecting the rise in the productivity of skilled labour via capital-skill complementarity, to which the government responds, by increasing the tax for skilled workers and decreasing the tax for unskilled workers.86 Hence, in this case, the government …nds it optimal, given the exogenous productivity gains for skilled households, to redistribute the tax burden in favour of the unskilled households. As a result,
86However, the stock of capital equipment decreases following the positive shock to its productivity. That happens because of the important income gains of skilled workers as a result of the increase in the returns to capital equipment. This e¤ect causes a reduction of the investment in capital equipment, leading to an increase in consumption. Lindquist (2004) gets a similar reaction of equipment capital although in a model without optimal taxation.
income taxation becomes more progressive.
After an output-enhancing temporary reduction to government spending all taxes can fall, since the government needs to generate less tax revenue.
However, driven by the incentive to support the households who are most constrained in the asset market, the reduction is bigger for the income tax of the hand-to-mouth agents, followed by that of the unskilled agents. There- fore, a temporary spending cut is followed by an increase in the progressivity of income taxes. The reductions in the income tax rates lead to a propor- tionately larger increase for the supply of unskilled labour, relative to skilled, which in turn increases the skill premium.
3.7.2 The case with di¤erent …scal policy menu
In this section we present the reaction of the optimal income taxes and the key macroeconomic variables following a temporary standard deviation shock to total factor productivity, productivity of capital equipment and government spending. Note that, as we presented in the previous section, the shock to government spending is an output-enhancing shock (negative shock to government spending). Figure 3.2 presents the impulse responses under each shock.87
Comparing the responses of the model with the consumption tax and the model without, we can see that there are no qualitative di¤erences in the reaction of the optimal income taxes after a temporary shock to the economy.
Regarding the reaction of the optimal consumption tax, we can see that under a TFP shock it increases in the short-run so as for the government to smooth out shocks to consumption. In the medium-run the optimal consumption tax decreases and falls below its steady state and then it converges slowly to its long run value. Under a capital equipment productivity shock the consumption tax has a similar reaction with the TFP shock but with a smaller magnitude. Finally, under an output-enhancing government spending shock the optimal consumption tax decreases in the short-run below its long-run value, as the rest of the income taxes.
87Note that again Figure 3.2 plots the percent deviations from the steady state for every variable.
Figure3.2:Impulseresponsesofoptimalpolicywiththeinclusionoftheconsumptiontax