1.7.1 Steady-state
The results from the exogenous and Ramsey policy in the long-run are given in Tables 1.5 and 1.6. Comparing the two policies it can be seen that under optimal …scal policy the capital income tax rate is reduced. Also, the skilled labour income tax rate has increased to balance the budget constraint and the unskilled labour income tax rate remained relatively stable.17 Therefore, under the current setup of the model, with capital-skill complementarity and capital market imperfection, the optimal capital income tax rate will be positive and equal to 6%. This result contradicts the early studies of Judd (1985) and Chamley (1986) that suggested a zero optimal tax rate on capital income. But as it will become clear in the next session, the positive optimal tax rate on capital income is present under current setup due to the capital market imperfections, as in Judd (1997) and Guo and Lansing (1999).
The systematic assessment of how optimal …scal policy is a¤ected when the economy exhibits capital market imperfection, in the form of di¤erent cost of capital holdings, and capital-skill complementarity, is worth noting in this chapter and contributes the related literature. Therefore, in the next section we examine how the long-run optimal …scal policy changes when there is
16Appendix A shows the derivation of equation (16).
17Note that this result is a¤ected from the assumed calibration. For instance, if unskilled labour is less substitutable with capital then their wage tax rate will be higher than the exogenous case, but still very close to the exogenous case.
no capital market imperfection and/or no capital-skill complementarity and compare these results with the literature.
It is also important to note that the assumed skill heterogeneity leads to optimally progressive labour income tax system. As Conesa et al. (2009) suggest, skill heterogeneity leads to higher progressivity of the labour income tax rate. But also, under the current setup of the model, the government can a¤ect optimally the after-tax skill premium and as a consequence labour income inequality. Thus, the government takes into account the e¤ect of its policies on the returns to skill and income inequality and then forms the optimal progressive labour income tax rate.
The capital-skill complementarity assumption creates an additional chan- nel through which the optimal …scal policy can redistribute income and in- crease overall welfare. For instance, in the case that the returns to skill are endogenously determined and agents with higher labour return hold more capital, an increase in the tax rate of capital income will also result in a reduction of capital accumulation. The decrease of capital stock levels will result in an increase of the returns to unskilled agents and also skill premium will decline as a consequence. As a result, under this setup, optimal …scal policy is more e¤ective in terms of income redistribution.
In addition, skilled agents will keep working less than the unskilled agents but this gap will increase and both will work less in comparison to the ex- ogenous case due to the increase in capital holdings for both agents.
Under optimal …scal policy, skilled agents will choose similar amount of consumption as in the exogenous case and their capital holdings will increase.
On the other hand, the unskilled agents will increase both their consumption and capital holdings. In particular, skilled agents hold the 66.7% of capital as it was expected from the imposed calibration. Thus the capital income distribution will remain the same as it was in the exogenous case.
Moreover, the after-tax skill premium will decrease under optimal …scal policy. This result occurs because the e¤ect from the higher progressivity of the labour income taxes is larger than the e¤ect of the higher pre-tax wage rates. Since the capital income distribution remains constant, due to the exogenously determined cost of capital holdings, the change in the after-tax
wage rates will be the main determinant of income inequality.
Therefore, now that the progressivity of labour income tax rates is endoge- nously determined the government will choose to impose a more progressive labour tax system to reduce income inequality.
Table 1.5: Steady-state results of exogenous and optimal …scal policy
Param. De…nitions Exogen. Opt. Policy
Ksts cap. structures skilled agents hold 0.54 1.00 Keqs cap. equipment skilled agents hold 0.85 1.55 Kstu cap str. holdings of unskilled agents 0.27 0.50 Kequ cap. eq. holdings of unskilled agents 0.43 0.68 hs working time by skilled workers 0.28 0.25 hu working time by unskilled workers 0.29 0.28
Cs consumption of skilled agents 0.23 0.24
Cu consumption of unskilled agents 0.18 0.21
Y output 0.42 0.48
_
Gc government spending 0.14 0.14
r tax rate of returns on capital 0.44 0.06
w
s wage tax rate of skilled agents 0.30 0.52
w
u wage tax rate of unskilled agents 0.20 0.19 rst pre-tax returns on capital structures 0.11 0.07 req pre-tax returns on capital equipment 0.18 0.11 ws pre-tax wage rate of skilled agents 0.96 1.41 wu pre-tax wage rate of unskilled agents 0.68 0.78
ws=wu skill premium 1.41 1.81
(1 ws)ws
(1 wu)wu after-tax skill premium 1.23 1.06 Therefore, the reduction of the capital income tax rate causes an increase in the total stock of capital through an increase in investment. The increase in the stock of capital will have a positive e¤ect on output. Moreover, since it has been assumed that skilled agents are more complementary with capital equipment than the unskilled agents, the increase in the stock of capital equipment will cause an increase in the demand for skilled labour. This in turn will cause an increase in the pre-tax wage rate for skilled agents and as a result there will be greater disparity between the skilled and unskilled agents’pre-tax wage rates. This is the reason for obtaining a higher pre-tax skill premium under the optimal …scal policy case study than the exogenous
Table 1.6: Great ratios and welfare under exogenous and optimal …scal policy
Param. De…nitions Exogen. Opt. policy
Ksts=Y Ksts over output 0.78 1.24
Keqs=Y Keqs over output 1.22 1.68
Kstu=Y Kstu over output 0.26 0.41
Kequ=Y Kequ over output 0.41 0.56
Cs=Y cons. of skilled ag. over output 0.33 0.30 Cu=Y cons. of unskilled ag. over output 0.17 0.18
_
Gc=Y government spending over output 0.34 0.30 Ists=Y investment onKsts over Y 0.03 0.04 Ieqs=Y investment onKeqs over Y 0.09 0.12 Istu=Y investment onKstu over Y 0.01 0.02 Iequ=Y investment onKequ over Y 0.03 0.04 W aggregate lifetime welfare -90.01 -85.73 Ws s.s. welfare of skilled agent -86.88 -83.60 Wu s.s. welfare of unskilled agent -94.71 -88.93
a - - 13.34%
s - - 10.69%
u - - 16.90%
…scal policy case study.