Chapter 3 Consumption Tax, Seigniorage Tax, and Tax Switch Policy in a
3.6 Concluding Remarks and Future Extensions
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increases. This implies that relative to the case where mt ct (the corresponding government constraint is gyt (c)ct), a decrease in c by an unit must be associated with a relatively lower money growth rate due to a larger tax base. Since the effect of seigniorage tax is weakened, the growth effect of consumption tax dominates. Thus, tax switch from consumption taxation to seigniorage taxation has a favorable effect on economic growth.
3.6 Concluding Remarks and Future Extensions
The paper develops a monetary endogenous growth model with endogenous labor-leisure choice and cash-in-advanced constraint which is only imposed on consumption to investigate the effects of alternative tax policies (the growth rate of money supply, consumption tax rate, and tax switch) under different usages of the tax revenue. With the framework, first, we find that the different usages of the tax revenue do result in a transformation in the effects of the growth rate of money supply and consumption tax respectively. Second, we show that the Friedman rule which claims the zero nominal interest rate is no longer optimal but a deflation is still necessary for social optimum if there exists the production externality of capital and the consumption tax. Finally, we re-examine the effects of a switch from consumption taxation to inflation taxation to finance a given stream of government expenditure, namely tax switch, to complement the unclear discussion in Ho et al. (2007). It has been found that the tax switch causes an increase in the steady-state growth rate through the increase in labor supply. Moreover, in contrast with the inconsistent results between MIUF and CIA approaches derived in Ho et al. (2007), this result suggests that the qualitative equivalence between MIUF and CIA approaches is still valid.
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Finally, by referring to the similar effects of consumption tax and the money growth rate in our framework, it might be an interesting future research to evaluate the welfare consequences of the two tax policies with a numerical assessment.
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In the Appendix, we prove the uniqueness and existence of the steady-state equilibrium when 1 and 0.
A.1 Case 1:
When 1, the endogenous adjustment of lump-sum transfer Rt, clearly has no direct effect on equations (15d) and (15e). From this perspective, Rt can be recursively determined by (15c). By substituting equation (15d) with xt 0 into equation (15e) with
0
zt , the steady-state equilibrium can be derived by the resulting equation and equation (15d) with xt 0 as follows: steady-state equilibrium exists and is unique.
Furthermore, let and 1 be the two characteristic roots of the dynamic system. 2
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and 2 0. As documented in the literature of dynamic rational expectation models, including Buiter (1984) and Turnovsky (2000b), the dynamic system has unique perfect-foresight equilibrium if the number of unstable roots equals to the number of jump variables. The dynamic system stated in equation (17) has two jump variables xt and zt, thus a unique stable path leading to the determinate steady-state equilibrium is ensured.
A.2 Case 0:
Contrast with Case A.1, we have to substitute equation (15c) into equations (15d) and (15e). Next, by substituting equation (15d) with xt 0 into equation (15e) with zt 0, the steady-state equilibrium can be derived by the resulting equation and equation (15d) with
0
The uniqueness and existence of steady-state equilibrium claim that xt 0 and zz loci have to intersect at a single point in the (xt,zt) space. As a consequence, we show that
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the 0xt locus intersects the zt-coordinate at [(1 ) ] 0 1
1
A when lt 0
(xt 0). Under the restriction of non-negative working hours (lt 1), along the xt 0 locus, zt has a lower bound
1
min 1
zt when lt 1, and the slope approaches 0 at the point. Together with the zz locus, Figure 2 indicates that the steady-state equilibrium exists and is unique.
In addition, let and 1 be the two characteristic roots of the dynamic system 2 expressed by equation (17) with 0, we then have: (1 )
ˆ ) ˆ 1 ˆ{(
2 2
1
z x x
0 } ˆ)]
( 1
[ l x 1lx
A
and (1 ) [1 (ˆ)] } 0
ˆ {1 ) ˆ 1
ˆ( 1
2
1 A l x lx
x z
z
, thus
10
and 2 0. The number of unstable roots equals to the number of jump variables in equation (17), thus there exits a unique stable path leading to the steady-state equilibrium.
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with 0zt , the steady state relationships are expressed by the resulting equation and equations (24a) with xt 0 as follows: uniqueness and existence of steady-state equilibrium. From equations (B1) and (B2), we show that the xt 0 locus and the zz locus intersect the zt -coordinate at equilibrium exists and is unique.Furthermore, let and 1 be the two characteristic roots of the dynamic system 2
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expressed by equation (25), we then have:
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Figures
Figure 1. The Existence and Uniqueness of the Steady-State Equilibrium when 1 ]
) 1 )[(
1
( c A
zz
0 xt
xt
zt
0
) 1 ( c
Figure 2. The Existence and Uniqueness of the Steady-State Equilibrium when 0 ]
) 1 1 [(
1
A
zz
0 xt
xt
zt
0
1
1
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] ) 1 )[(
1
( c g A zz
0 xt
xt
zt
0
1 ) ( 1
c
A g
Figure 3. The Existence and Uniqueness of the Steady-State Equilibrium when Tax Switch
) 1 ( c
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Chapter 4
Conclusions
To keep up with the rapid globalization of the world economy, governments have made efforts in the tax reform policies for the sake of enhancing competitiveness of nations, stimulating capital accumulation, and improving efficiency. Owens (2006) indicates that, driven by the need to provide a more competitive fiscal environment, the tax reform such as a shift in the tax structure from taxes on income and profits towards taxes on consumption is an on-going process in almost all OECD countries. Owing to the topic have been highly concerned in the developed and developing countries, we have developed two different endogenous growth frameworks—real model and monetary model to discuss the related issues to enrich the understandings in this field.
In Chapter 2, we have developed a simple Romer (1986)-type endogenous growth model with endogenous fertility choice and explore the role of endogenous fertility choice in terms of influencing the effects of tax reform on economic growth and social welfare. It has been found that the effects of tax reform on the steady-state fertility rate, the balanced growth rate, and social welfare are ambiguous. Specifically, the effect of tax reform on the steady-state fertility rate depends on the relative extent between the marginal utility of fertility and the average child-rearing cost-labor time ratio. Based on this ambiguity, we have pointed out that tax reform can serve to decrease, rather than increase, economic growth and social welfare. This result not only contrasts with the existing literature, but also provides a new insight into the policy implications.
In Chapter 3, a monetary endogenous growth model with endogenous labor-leisure
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choice and cash-in-advance constraint which is only imposed on consumption is established to investigate the effects of alternative tax policies (seigniorage tax, consumption tax, and tax switch) under different methods of adjustment to maintain the balanced government budget.
With the framework, we find that the different methods to maintain the balanced government budget do result in a transformation in the results of the growth rate of money supply and consumption tax respectively. In the normative analysis, we show that the Friedman rule which claims the zero nominal interest rate is no longer optimal but a deflation is still necessary for social optimum if there exists the production externality of capital and the consumption tax. Finally, we re-examine the effects of a switch from consumption taxation to inflation taxation to finance a given amount of government expenditure, namely tax switch, to complement the unclear discussion in Ho et al. (2007). It has been found that the tax switch causes an increase in the steady-state growth rate through the increase in labor supply.
Moreover, contrast to the inconsistent results between MIUF and CIA approaches derived in Ho et al. (2007), this result suggests that the qualitative equivalence between MIUF and CIA approaches is still valid.
‧
國立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
References
Ho, W. H., Zeng, J. and Zhang, J., 2007, “Inflation Taxation and Welfare with Externalities and Leisure,” Journal of Money, Credit, and Banking 39, 105-131.
Owens, J., 2006, “Fundamental Tax Reform: an International Perspective,” National Tax Journal 69, 131-164.
Romer, P. M., 1986, “Increasing Returns and Long-Run Growth,” Journal of Political Economy 94, 1002-1037.