Chapter 3: Optimal income taxation over the business cycle101
3.6 Optimal taxation over the business cycle
3.6.2 Properties of optimal taxes over the business cycle
Table 3.6 presents the optimal properties of the tax system under shocks to all stochastic processes. As it can be seen by the steady state income taxes, optimal tax policy is progressive and, in fact, relatively more progressive compared with the data averages. In particular, s > 60 100, u < 20 60,
h < 0 20.79 This is noteworthy since the progressivity of the tax system as captured by the three tax rates considered here has indeed increased since the mid-1960s (see e.g. the data in Piketty and Saez (2007)).80 Therefore, the assumed imperfections and inequalities in our model justify progressive income taxation.
78The business cycle statistics are calculated in this case as in the exogenous policy case. Thus, we perform 1000 simulations under shocks to the exogenous processes, each simulation is 296 periods long and then we drop the initial 200 periods. Afterwards, we get the business cycle statistics for each simulation and we calculate the averages across the simulations.
79Note that we observe the largest di¤erence between the optimal income tax and the data in the case of the hand-to-mouth households. In practice, though, subsidies that are targeted to a speci…c group of agents alleviate part of the tax burden for that group, leading to a more realistic distribution of the tax burden in our model that is closer to reality. However, we do not discuss further about the targeted subsidies since for the optimal taxation case we do not include any lump-sum transfers.
80Using the dataset of Piketty and Saez (2007) we …nd that for the period 1966-2001 the income tax of the high income earners has increase 5 percentage points, whereas the income tax of the middle income group agents has decreased 4 percentage points and for the low income groups agents has decreased 5 percentage points, similar to our results.
Table 3.6: Optimal tax policy
s u h
Steady state 0.285 0.143 -0.041
Autocorrelations 0.754 0.832 0.891
Correlations withY -0.461 -0.732 -0.110 Standard deviation 0.012 0.070 0.173
These results in Table 3.6 further suggest that the volatility and co- movement of optimal taxes with output di¤er signi…cantly with each other and with the data reported in Table 3.2. As discussed above, the policy problem we consider implies that the tax rates need to be generally more volatile and more counter-cyclical, compared with the data. However, Table 3.6 also reveals important di¤erences between the tax rates. These result from the trade-o¤ that the government faces when deciding how to distrib- ute the distortions re‡ected by the higher volatility and counter-cyclicality of the three tax rates over the business cycle. On one hand, such distortions have a larger impact on hand-to-mouth households, since they are less able to smooth shocks. There is thus an incentive to minimise the impact of pol- icy for this type of household. On the other hand, tax-induced distortions to skilled households have the strongest propagation e¤ects in the economy, given the complementarity of skilled hours with equipment capital. There- fore, there is also an incentive to minimise distortions to the choices of skilled households, since this acts to amplify external shocks
Delving deeper into the cyclical properties of each income tax rate under optimal …scal policy we can see that the volatilities are higher than those ob- served in the data. This is expected given the balanced budget restriction we imposed together with the restricted set of …scal instruments. Note that the volatilities observed in the data are similar across the three income tax rates with the income tax for the high income earners having the highest volatility and the income tax for the lowest income earners the lowest volatility. How- ever, under the optimal taxation the volatilities of the three income taxes have signi…cant di¤erences. In this case the income tax of the lowest income
group is the most volatile and the income tax of the highest income group is the smoothest.81
A smoother income tax creates fewer distortions in the household’s op- timisation problem. Since income taxes are the only choices for the policy- maker in this framework, implying that smoothing is not possible for all tax rates, the government …nds it optimal to keep the tax rate which distorts incentives the most, the smoothest. Given the higher complementarities of skilled hours with equipment capital, implying that tax-induced ‡uctuations in skill supply propagate more in the economy via the equipment capital channel, the government …nds it optimal to keep the tax to skilled house- holds the least volatile. In contrast, since hand-to-mouth households do not own capital stock, their choices a¤ect the endogenous propagation mecha- nism in the economy the least, so that their taxes are optimally the most volatile.
Regarding the cyclicality of the tax rates over the business cycle, we found in the data (Table 3.2) that taxes are positively correlated with out- put. Speci…cally, the data indicate that the correlation of the income taxes with output are: 0.587 for skilled income tax; 0.654 for unskilled income tax; and 0.198 for hand-to-mouth income tax. As expected, the results in Table 3.6 con…rm that the correlations become negative when the tax instru- ments are the only optimally chosen instruments in the government’s budget constraint. However, the results also indicate that the optimal correlations of the tax rates are symmetrically opposite to the data correlations. For example, the strongest pro-cyclical tax in the data becomes optimally the strongest counter-cyclical, while the least cyclical in the data becomes the least counter-cyclical. Hence, the requirement of the government to make the tax system generally counter-cyclical, is not translated into a proportional reduction of the correlation coe¢ cients of all tax rates.82
81The results we obtain regarding the magnitude and range in volatilities of the three income tax rates are within the range of the optimal volatilities for tax instruments con- sidered in the model with search frictions and government debt in Arseneau and Chugh (2012) and the neoclassical model with a balanced budget restriction in Stockman (2001).
82The literature has not examined the behaviour of di¤erent income taxes under opti- mal …scal policy, like in our chapter. However, it has been shown that market frictions are important for de…ning the optimal cyclicality of the tax rates. For example, under
Counter-cyclical taxes intensify ‡uctuations in income, as they amplify the e¤ects of exogenous productivity shocks. Therefore, a government that needs to make use of counter-cyclical taxes over the business cycle, does so with a view to minimise the distortions that they cause. In this setup, it is optimal to minimise such policy distortions to the income of the hand-to- mouth households, by making their tax rate to be the least counter-cyclical.
This is because these agents are the most exposed to economic ‡uctuations.
Comparing skilled and unskilled households, it is optimal to least distort the choices of skilled, given the higher complementarities of skilled hours with equipment capital. As a result, the unskilled workers face the most counter- cyclical income tax.
Finally, the persistence of the income taxes (autocorrelation) is optimally chosen to be similar across the three taxes. Compared with the data, the persistence of the income taxes is slightly lower under optimal …scal policy, especially the skilled income tax.