Chapter 2 The Long-Run Growth and Welfare Effects of Tax Reform with
2.8 Future Extensions
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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.
2.8 Future Extensions
Since the present framework is quite simple, we summary some future extensions in this section. One obvious extension is to discuss the reform in the family-caring or child-caring policies which can influence the fertility decision directly, such as specific cash transfers or subsidies, loans on preferential terms, or tax deductions to families with children. Since low fertility is a common phenomenon in developing and developed countries, governments has made many efforts to deal with it. It might be an interesting topic to investigate that how the family-caring or child-caring policy reform affects the fertility choice, and thus the economic growth and social welfare.
Based on the complicated structure of the welfare function shown in equation (21), we do not directly solve the second-best optimal tax reform policy in that section. Thus, the first-best optimal tax reform policy can be another extension in which a more clear-cut result might be derived. Furthermore, we can also extend our framework to investigate the role of the usage of the tax revenues collected by a government under a given method of budget financing.
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In this appendix we provide the detailed procedures in deriving the sign of in equation (21) in the text. As shown in equation (21), is rewritten as follows:
Since the balanced growth condition (13) implies that xˆ and the balanced government budget constraint (7) implies that (I)A(1nˆ)1 xˆ 0 , we have
We manipulate the items in the brackets as follows:
As xˆ is true from the balanced growth condition and the balanced government budget constraint (7) implies that (I)A(1nˆ)1 xˆ 0, we find that the sign of the brackets is positive and hence item (ii) is positive. Together with (i) and (ii), we conclude that the sign of in equation (21) of the text is positive.
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Figures and Tables
xt
xˆ xt
xt
Figure 2. Phase Diagram 0
NN
0 xt
nt
1
I)A (
xt
(1 I)]A 1
[
0
Figure 1. The Existence of the Steady-State Growth Equilibrium.
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Benchmark Values
A 1
0.4
0.03
0.22
I 0.15
ˆ c 0.0865
1.53
46.1
Table 1. The Values of Parameters in the Benchmark
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Figure 3-a. The Fertility Effect: Sensitivity to Figure 3-b. The Growth Effect: Sensitivity to
Figure 3-c. The Welfare Effect: Sensitivity to
Figure 4-a. The Fertility Effect: Sensitivity to
Figure 4-b. The Growth Effect: Sensitivity to
Figure 4-c. The Welfare Effect: Sensitivity to
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References
Abel, A. B. and Blanchard, O. J., 1983, “An Intertemporal Model of Saving and Investment,”
Econometrica 51, 675-692.
Auerbach, A. J., Kotlikoff, L. J. and Skinner, J., 1983, “The Efficiency Gains from Dynamic Tax Reform,” International Economic Review 24, 81-100.
Barro, R. J. and Sala-i-Martin, X., 2004, Economic Growth, 2nd Ed., Cambridge, MA: MIT Press.
Batina, R. G., 1987, “The Consumption Tax in the Presence of Altruistic Cash and Human Capital Bequests with Endogenous Fertility Decisions,” Journal of Public Economics 34, 329-354.
Buiter, W. H., 1984, “Saddlepoint Problems in Continuous Time Rational Expectations Models: A General Method and Some Macroeconomic Examples,” Econometrica 52, 665-680.
Chamley, C., 1985, “Efficient Tax Reform in a Dynamic Model of General Equilibrium,”
Quarterly Journal of Economics 100, 335-356.
Chatterjee, S. and Turnovsky, S. J., 2007, “Foreign Aid and Economic Growth: The Role of Flexible Labor Supply,” Journal of Development Economics 84, 507-533.
Christiano, L. J. 1988, “Why Does Inventory Investment Fluctuate So Much?” Journal of Monetary Economics 21, 247-280.
Eckstein, Z. and Wolpin, K. I., 1985, “Endogenous Fertility and Optimal Population Size,”
Journal of Public Economics 27, 93-106.
Eckstein, Z., Stern, S. and Wolpin, K. I., 1988, “Fertility Choice, Land, and the Malthusian Hypothesis,” International Economic Review 29, 353-361.
Ermisch, J., 1986, “Impacts of Policy Actions on the Family and Household,” Journal of Pubic Policy 6, 297-318.
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Grant, J. et al., 2004, “Low Fertility and Population Ageing: Causes, Consequences, and Policy Options,” Santa Monica: RAND.
Kobayashi, Y., 1996, “Endogenous Fertility and the Consumption Tax,” Japanese Economic Review 47, 313-321.
Lucas, R. E. Jr., 1988, “On the Mechanics of Economic Development,” Journal of Monetary Economics 22, 3-42.
Lucas, R. E. Jr., 1990, “Supply-Side Economics: An Analytical Review,” Oxford Economic Papers 42, 293-316.
Palivos, T., 1995, “Endogenous Fertility, Multiple Growth Paths, and Economic Convergence,” Journal of Economic Dynamics and Control 19, 1489-1510.
Palivos, T. and Yip, C. K., 1993, “Optimal Population Size and Endogenous Growth,”
Economics Letters 41, 107-110.
Pecorino, P., 1993, “Tax Structure and Growth in a Model with Human Capital,” Journal of Public Economics 52, 251-271.
Pecorino, P., 1994, “The Growth Rate Effects of Tax Reform,” Oxford Economic Papers 26, 492-502.
Razin, A. and Ben-Zion, U., 1975, “An Intergenerational Model of Population Growth,”
American Economic Review 65, 923-933.
Romer, P. M., 1986, “Increasing Returns and Long-Run Growth,” Journal of Political Economy 94, 1002-1037.
Sleebos, J. E., 2003, “Low Fertility Rates in OECD countries: Facts and Policy Responses,”
OECD Social, Employment, and Migration Working Papers 15.
Summers, L. H., 1981, “Capital Taxation and Accumulation in a Life Cycle Growth Model,”
American Economic Review 71, 533-544.
Turnovsky, S. J., 2000a, “Fiscal Policy, Elastic Labor Supply, and Endogenous Growth,”
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Journal of Monetary Economics 45, 185-210.
Turnovsky, S. J., 2000b, Methods of Macroeconomic Dynamics, 2nd Ed., Cambridge, MA:
MIT Press.
Wang, P., Yip, C. K. and Scotese, C. A., 1994, “Fertility Choice and Economic Growth:
Theory and Evidence,” Review of Economics and Statistics 76, 255-266.
Wen, J. and Love, D. R. F., 1998, “Evaluating Tax Reforms in a Monetary Economy,”
Journal of Macroeconomics 20, 487-508.
Yip, C. K. and Zhang, J., 1996, “Population Growth and Economic Growth: A Reconsideration,” Economics Letters 52, 319-324.
Yip, C. K. and Zhang, J., 1997, “A Simple Endogenous Growth Model with Endogenous Fertility: Indeterminacy and Uniqueness,” Journal of Population Economics 10, 97-110.
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Chapter 3
Consumption Tax, Seigniorage Tax, and Tax Switch Policy in a Cash-in-Advance Economy of Endogenous Growth
3.1 Introduction
Taxations, such as capital and labor income taxes, are regarded as essential tools for government policies, but their distortionary effects always make them more undesirable.
Therefore, a taxation which can maintain the operation of government, avoid the distortions, and even stimulate the economic growth is broadly and intensively discussed in macroeconomics and public finance.
In the past decades, consumption taxation is proposed to be an alternative to substitute for the existing income taxation to finance government expenditure, since it may eliminate the bias against investment and savings inherent in the income tax system, encouraging capital accumulation (or enhancing economic growth), and improving social welfare [see, for example, Auerbach, Kotlikoff, and Skinner (1983), Chamley (1985), Pecorino (1993), (1994), and Turnovsky (2000a)]. Summers (1981), Abel and Blanchard (1983), Auerbach and Kotlikoff (1987), and Itaya (1991) show that consumption tax can affect neither the capital stock nor consumption in the steady state if the tax revenue collected is rebated to households as a lump-sum transfer in the neoclassical growth model without labor-leisure choice. By developing endogenous growth models, Rebelo (1991) and Milesi-Ferreti and Roubini (1998) conclude that this so-called neutrality of consumption tax is also valid in the growth-rate sense. Recently, by going beyond these studies, Itaya (1998) and Kaneko and Matsuzaki (2009) extend a real economy model to a monetary economy model and re-examine the
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effects of consumption tax in various monetary economy. Under a neoclassical growth model, Itaya (1998) shows that the neutrality of consumption tax is valid in the money-in-utility-function (MIUF), money-in-production-function (MIPF), cash-in-advance (CIA), and transactions cost models, while it does not hold in a shopping time model.
Under an overlapping generation model, Kaneko and Matsuzaki (2009) points out that the neutrality of consumption tax does not hold in the MIUF model, while it is valid in CIA and MIPF models. One common characteristic is that they assume inelastic labor supply which confines some scopes to analyze the effects of consumption tax.
In addition to consumption tax, in a monetary economy, the growth rate of money supply provides another alternative for government to collect its revenue, i.e. seigniorage tax.
The research on the effect of the growth rate of money supply can be traced to as early as the studies of Mundell (1963) and Tobin (1965). Both of them argue that a higher money growth rate stimulates capital accumulation. The beneficial effect of the growth rate of money supply is dubbed “the Mundell-Tobin effect.” However, Sidrauski (1967) develops an intertemporal optimizing model with MIUF and shows that the long-run capital stock can be independent of the growth rate of monetary growth, i.e. the superneutrality of money. By following this line of research, Stockman (1981) incorporates the CIA constraint into neoclassical growth model and proves that (i) the superneutrality of money is valid if money balance is only required prior to carry out consumption; (ii) however, the reversed Mundell-Tobin effect emerges, if both consumption and investment are restricted by CIA constraint.
Thereafter, there is a large body of studies focus on this issue in variety of endogenous growth models. There is a general result: similar to Stockman (1981), money is neutral to economic growth if only consumption is subject to a CIA constraint (cf., Marquis and Reffett, 1991). Specifically, Mino (1997) employs the two-sector model proposed by King et al.
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(1988) and finds that the reversed Mundell-Tobin effect exists when labor supply is endogenous.1 Under the one sector AK model with the stochastic money supply rule, Dotsey and Sarte (2000) point out a negative relationship between the output growth rate and the average inflation rate, implying that economic growth decrease with an expansionary monetary policy. In contrast, Chang et al. (2000) shed light on the motive of status-seeking to support the Mundell-Tobin effect.
In this paper, we develop a monetary endogenous growth model with endogenous labor supply and a CIA constraint which is only imposed on consumption. Our analysis focuses on consumption tax, seigniorage tax, and a tax switch between them for three reasons. First, although Phelps (1973), Braun (1994), and Palivos and Yip (1995) have compared an income tax with seigniorage tax, the two alternative taxations which may be better than traditional income taxation have attracted relatively little attention in the literature. Second, Ho et al.
(2007) develop a MIUF growth model to examine how consumption tax, seigniorage tax and their tax switch affect resource allocation and social welfare. Nevertheless, the corresponding effects in a CIA growth model are not clear. The extended investigation is important, particularly when our results turn out to be rather different from theirs. Third and most importantly, we will show that in an endogenous growth model of CIA, the usage of the tax revenues collected by a government plays a crucial role in terms of governing the effects of consumption tax, seigniorage tax, and tax switch. The relevant studies cited above enabled a common feature, namely lump-sum transfer has to adjust endogenously to balance the government budget. However, in the present paper we will point out that consumption tax, seigniorage tax, and tax switch end up with very different macro
1 Mino (1997) finds that money has no effect on the long-term growth rate if there is no labor-leisure choice of the households.
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consequences, if government expenditure is used to balance its budget constraint.2 The empirical evidence reveals that in many countries, particularly within the developing world, the government often uses government spending to balance its budget, thereby generating procyclical fiscal policies [see, for example, Gavin and Roberto (1997) and Talvi and Végh (2005)]. Likewise, in Japan, Singapore, and Irish, the government also adjusts the government expenditure, such as the salary of public staff, to maintain the balanced budget.
In effect, endogenously-adjusted public spending is a common balanced-budget rule in the real business cycle literature [see, for example, Greenwood and Huffman (1991), Cooley and Hansen (1992), and Galí (1994)].
Our findings can be summarized as follows. First, an increase in the growth rate of money supply gives rise to a “reversed Mundell-Tobin effect” on the balanced-growth rate, if the tax revenues are used to provide rebates to all agents in a lump-sum manner. However, due to the resources withdrawal effect stemming from government expenditure, a
“Mundell-Tobin effect” emerges if the tax revenues are used to finance government expenditure. The results not only contrast with the traditional wisdom whereby money is superneutrality when only consumption is subjected to the CIA constraint [Marquis and Reffett (1991), Mino (1997), and Chen and Guo (2008)], but also provide a theoretical explanation to the empirically mixed relationship between the growth rate of money supply and economic growth. Some empirical studies, such as Gomme (1993), De Gregorio (1993), Barro (1995), and Gylfason and Herbertsson (2001), find that there exists a negative relationship between the growth rate of money supply and economic growth, others, such as Bullard and Keating (1995), show that both of them exhibit a positive relationship. Second,
2 For the sake of comparison and to make our result more striking, we follow Pelloni and Waldmann (2000) and assume that in our model the government expenditure is wasteful, being not purposely used in utility-enhancing and infrastructure.
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in contrastive with Itaya (1998) and Kaneko and Matsuzaki (2009), the neutrality of consumption tax is not valid if the tax revenue collected is rebated to agents as lump-sum transfer. Nevertheless, consumption tax is neutral to economic growth if the tax revenue collected is contributed to the government expenditure. Third, by shedding light on the optimal monetary policy, we show that the so-called Friedman rule (which claims a 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, our extended analysis complements the study of Ho et al. (2007). Under a MIUF model, Ho et al. (2007) found that the switch from consumption taxation to inflation taxation reduces leisure and accelerates the economic growth. However, such a tax switch has no effect on the economy if the CIA constraint is only imposed on consumption. In other words, their results are inconsistent with the qualitative equivalence between MIUF and CIA approaches.3 In contrast, our analysis point out that tax switch from consumption taxation to inflation taxation can also enhance economic growth and, as a result, the qualitative equivalence between MIUF and CIA approaches is still valid, provided that the CIA constraint is subject to the consumption gross of the consumption tax, such as Auerbach and Obstfeld (2004, 2005).
The reminder of this Chapter is organized as follows. In section 2, we construct the optimizing behavior of the representative household-producer and government in the monetary endogenous growth framework. Meanwhile, under different methods of government budget adjustment, the steady-state equilibrium and the dynamic properties are also derived. Section 3 examines the steady-state effects of alternative tax policies under different methods of government budget adjustment. Section 4 then addresses the optimal
3 Wang and Yip (1992) establish a qualitative equivalence between MIUF and CIA approaches on the inflation-growth relationship, when CIA constraint is only imposed on consumption.
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monetary policy. The effect of tax switch is examined in Section 5. Finally, Section 6 concludes the main findings and provides future extensions of our analysis.
3.2 The Analytical Framework
There is a monetary economy which consists of a continuum of representative, infinitely-lived household-producer and a government. The role of money is introduced by a cash-in-advance constraint which is subject to consumption. Thus, our analysis focuses on Lucas’s (1980) economy.
3.2.1 Government
The government collects tax revenues from consumption tax (at the tax rate c) and seigniorage tax (with the money growth rate ) and uses them to either provide rebates to all agents in a lump-sum manner (lump-sum transfers are denoted as R ) or finance t government expenditure (denoted as G ). In order to make our point more striking, the t government’s expenditure is assumed to be wasteful; i.e., it is not valued by private agents.
As we will see later, the distinct usage of the tax revenues will end up with very different macro consequences of taxation. To shed light on the difference, we specify the following generalized government budget constraint:
t t
t t
cc m R (1 )G
, (1) where c is consumption, t
t t
t p
m M is real money balance (M is nominal money stock t
and p is price level).t 4 The term is a policy parameter. If 1, the adjustment of lump-sum transfers is responsible to maintain the balanced government budget, which is in line with that specified by Marquis and Reffett (1991), Wang and Yip (1992), and Mino (1997). Under such a situation, the government controls the tax rate ( or c) as an
4 To emphasize the effect under the two methods of government budget adjustment, we exclude the case of 1
0 .
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instrument and let the lump-sum transfer R adjust endogenously to maintain the balanced t government budget. If 0, the government expenditure G endogenously adjust in t order to satisfy the balanced government budget while government controls the tax rate.
Schmitt-Grohé and Uribe (1997), Pelloni and Waldmann (2000) and Guo and Harrison (2004) have the same specification.
In addition, the law of motion of real money balances is given by:
t t
t
m
m . (2)
3.2.2 Household-Producer
The economy is inhabited by a single, infinitely-lived representative household-producer who optimizes decisions on the basis of perfect foresight regarding the future. Each household-producer is endowed with a unit of time which is allocated to leisure (l ) and t labor supply (1 ). Thus, the individual’s object is to maximize the discounted sum of lt future instantaneous utilities as follows:
t
W
0 (lnct lt111)etdt, (3)where is a non-negative parameter representing the elasticity of marginal utility of leisure, and (0,1) is a constant rate of time preference.
At each instant of time, the household-producer is bounded by three types of constraints.
First, a flow constraint links money accumulation to any difference between its gross income (total output and lump-sum transfer in the case where 1) and its gross expenditure (consumption, investment, consumption tax, and inflation tax). Accordingly, the household’s budget constraint can be expressed as follows:
t t t t t c t
t y c i m R
m (1 ) , (4) where, y is total output, t i is investment, t
t t
t p
p
is the inflation rate (an overdot
‧
denotes the time derivative). The total output, y , is produced by the technology of Romer t (1986)-type specification whereby an increase in a firm’s capital stock leads to a parallel increase in its stock of knowledge. The external effect refers to the spillovers of knowledge that operate at the average level of the overall economy. That is
yt Akt[(1lt)kt], with A0, 0 1, 10 , (5) where k is the average economy-wide level of capital stock and t 0 refers to the extent
of production externality from k . To allow for the sustained growth in the economy, we t further impose 1.
Second, capital accumulation and investment are related by the following constraint:
t
t i
k . (6) Third, by following Auerbach and Obstfeld (2004, 2005), we assume the following cash-in-advance constraint in which money balance is required prior to implement consumption expenditure gross of consumption tax:
t c
t c
m (1 ) . (7) Given the initial money and capital holdings m0 0 and k0 0, the optimization problem for the representative household-producer is to maximize equation (3) subject to equations (4), (6), and (7). Defining t and q as the co-state variables associated with t equations (4) and (6), and t as the multiplier associated with equation (7) respectively, the current-value Hamiltonian can be expressed as:
].
The first-order conditions necessary for this optimization problem are:
)
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together with equations (4)-(7) and two transversality conditions lim 0
q . Equation (8a) equates the marginal utility of consumption to the tax-adjusted shadow value of wealth. Equation (8b) equates the marginal utility of leisure to the value of marginal productivity of labor. Equation (8c) implies the equality between the return and the cost of investment. Equations (8d) and (8e) are the intertemporal arbitrage conditions which equate the return on consumption to the returns of capital and money accumulation, respectively.
From equations (8c), (8d), and (8e), it is easy to obtain:
Equation (9) is a non-arbitrage condition between real money holding and capital stock and equation (10) is the Euler condition governing the optimal choice between consumption and assets accumulation (real money holding or capital stock). Moreover, by substituting equations (7) and (8a) into equation (9) yields the inflation rate as follows:
t
3.2.3 Competitive Dynamic Equilibrium
3.2.3 Competitive Dynamic Equilibrium