growth effect of taxes - eco

*E-mail: [email protected]

Journal of Economic Dynamics and Control23 (1998) 125—158

Growth effect of taxes in an endogenous growth model:to what extent do taxes affect economic growth?

Se-Jik Kim*Research Department, International Monetary Fund, Washington, DC 20431, USA

Received 7 October 1997

Abstract

This paper presents an endogenous growth model comprising of financial, human andphysical capital and incorporating major features of a general tax system. Technologyand preference parameter values in the model are chosen to fit the actual growthexperiences of the United States and a rapidly growing East Asian NIC. Using thecalibrated model, I assess the role of differences in taxes and other variables in explainingthe difference in growth rates. The main findings are: (i) the difference in tax systemsacross countries explains a significant proportion (around 30%) of the difference ingrowth rates; (ii) the difference in preferences explains at most 4%; and (iii) differences inlabor income tax, debt-equity ratio and inflation can be important in explaining thegrowth difference. Further, I evaluate the contribution of the monetary factor to thegrowth rate gap, and the growth effect of US tax reforms, e.g., revenue-neutral changes inrelative tax structure. ( 1998 Elsevier Science B.V. All rights reserved.

JEL classification: H20; H30; O41; O50

Keywords: Taxes; Financial assets; Endogenous growth; Calibration

1. Introduction

This paper addresses two questions related to the effects of taxes on long-runeconomic growth. First, to what extent do differences in tax systems, preferencesand technology across countries explain the difference in their long-run growthrates? Second, how much can a tax reform increase a country’s growth rate? Can

0165-1889/98/$ — see front matter ( 1998 Elsevier Science B.V. All rights reserved.PII S 0 1 6 5 - 1 8 8 9 ( 9 7 ) 0 0 1 1 1 - 5

1 In the case of Korea, e.g., Bahl et al. (1986) write: “Korean tax policy was much oriented tosupporting rapid economic growth” and “Korean fiscal planners, it would appear, discovered thesupply side about ten years before their American counterparts.”

a tax reform dramatically increase the US growth rate to match the levelachieved by some rapidly growing East-Asian countries? To answer thesequestions, this paper constructs an endogenous growth model consisting offinancial, human and physical capital. Using this type of model offers theadvantage of accommodating major features of a general tax system, allowingone to evaluate the effects of various tax measures on the long-run growth rate.In particular, the per capita income growth rate turns out to be affected by suchgovernment tax instruments as capital gains tax, corporate income tax, invest-ment tax credit, labor tax, education subsidies, value-added tax and inflation.

The idea that government tax policy can affect economic growth has longbeen conjectured by both economists and policy-makers. In particular, theexperience of three decades of rapid growth has led many people in the so-calledNICs (Newly Industrialized Countries) to believe that government tax policymust have been the decisive factor in those countries’ rapid growth.1 However,ever since Solow (1956), existing economic growth theory has not been support-ive of the government’s ability to influence economic growth. In the dominantSolow model, in which exogenous technical progress is the main determinant ofthe long-run per-capita income growth rate, tax policy can affect long-runincome levels but not long-run growth rates.

More recent endogenous growth models, however, re-opened the theoreticalpossibility that government tax policy can affect long-run growth rates. Amongthem are Lucas (1990), Jones and Manuelli (1990), Rebelo (1991), King andRebelo (1990), Yuen (1991) and Kim (1992). By introducing human capital or byspecifying a particular production function, these models allow physical andhuman capital accumulation to persist along the balanced growth path. Themodels’ endogenously determined growth rate depends on the net rate of returnfrom investment, which, in turn, depends on the tax rates. Consequently, taxrates can influence the growth rate.

The model developed in this paper shares a common feature with the recentendogenous growth models in asserting that a simultaneous accumulation ofhuman and physical capital leads to positive and constant marginal products ofcapital; this guarantees sustained endogenous growth. However, my modeldiffers from others in incorporating the accumulation of such financial assets asbonds and equities. This feature enables an accommodation of the major fea-tures of a complicated actual tax system. First, capital taxation is imposed notonly at the corporate level, but also at the personal level in the form of taxes onfinancial assets. Second, there is a difference in tax treatment (e.g., deductibility)

126 S.-J. Kim / Journal of Economic Dynamics and Control 23 (1998) 125–158

2The advantage of this type of model over traditional models in public finance is substantial.Public finance literature is replete with results on the effect of various tax rates on capitalaccumulation or on the effective tax rate. But this literature, in line with the Solow model, has dealtwith the effects of taxes on other economic variables, taking as given a country’s long-run growthrate, and has neglected the effects on the growth rate itself. In contrast, the model of this paper allowsfor the evaluation of the effects of the various individual tax variables on the long-run growth rate.

between debt and equity so that the debt-equity ratio affects the tax system.Third, without indexation, inflation impacts taxes imposed on nominal rates ofreturn on financial assets. Finally, investment tax credits, education subsidies,tax treatment of depreciation allowances and value-added tax have majorimpacts on the tax system. Thus, the model establishes links between thelong-run per capita income growth rate and various tax variables includinginflation.2

The main application of this model is to explain for the wide diversity inlong-run growth rates across countries. For the last three decades, the long-runper capita income growth rates of some countries like the NICs have farexceeded those of other countries. From 1965 to 1987, the per capita incomegrowth rate of the so-called ‘Asian Tigers’ such as Hong Kong, Singapore, SouthKorea and Taiwan reached over 6%, while that of the United States lagged at1.5%, according to the Economic Development Report of 1989. Explanationsfor the wide diversity in long-run growth rates across countries are now centralto economic growth literature. Recent endogenous growth models suggesta difference in tax systems as an explanation. However, very little is knownabout the extent to which differences in tax systems account for the difference inthe actual growth rates across countries. The main thrust of this paper is to fillthis gap in the literature by moving beyond stating purely theoretical supposi-tions to providing a quantitative assessment of the role of differences in taxsystems, preferences and technology in explaining the diversity.

For the purpose of explaining this diversity, the actual growth experiences ofthe United States and of Korea, a rapidly growing East Asian country, are usedto determine taste and technology parameters. Using estimates of the tax,preference and technology parameters, the contributions of the differences in taxstructures, preferences and technology to the difference in growth rates areevaluated. From this calibrated model, differences in the tax systems account forapproximately 30%, a significant proportion of the difference in the growthrates. The difference in preferences, by contrast, explains at most 4% under thestandard assumption on preference parameters. These results suggest that theremaining 70% can be ascribed to differences in technology.

In addition, I conduct a further decomposition of the growth rate difference toidentify which tax variables are more important in explaining the difference ingrowth rates. Among the individual tax instruments, labor income tax appears

S.-J. Kim / Journal of Economic Dynamics and Control 23 (1998) 125—158 127

3Rebelo and Stokey (1995) also compare an earlier version of this paper, Kim (1992), with Lucas(1990), King and Rebelo (1990) and Jones et al. (1993) to assess the potential growth effect of taxreform.

to be at least as important as taxes on capital income in accounting for thegrowth rate diversity. I also find that the difference in debt-equity ratio, inflationand tax rates on financial assets can be also important in explaining the growthrate difference. Further, I find that the growth effect of each tax variable dependscritically on the tax system itself. For example, in a tax system with a highdebt-equity ratio, inflation has a substantial positive effect on the growth rate,while in a tax system with a low debt ratio, the effect is almost negligible.

I also present a variation of the basic model incorporating the cash-in-advance constraint to evaluate the role of monetary factors. I find that theincorporation of monetary factors does not significantly alter the contributionof the tax factor to the growth rate gap. In addition, by introducing thedifference in monetary systems, the contribution of technology or residuals canbe reduced from 70% to 65%.

The basic model is also used to evaluate the impact of US tax reforms on thegrowth rate. The calibrated model predicts that the hypothetical elimination ofall taxes in the US raises the growth rate by 0.85 percentage points. The resultsuggests that this tax reform alone cannot dramatically raise the US growth rateto the level enjoyed by some rapidly growing East Asian NICs, but the effect isstill sizable. My estimation on the growth effect of US tax reforms differsmarkedly from some other studies employing endogenous growth models.A comparison with alternative studies on the magnitude of the growth effectsuggests that the marginal product of capital suggested by the parameter valuesused in this paper is consistent with the actual one, while the parameters chosenby others lead to marginal products that are too high.3

This paper also assesses the growth effect of a revenue-neutral change in therelative tax structure and in the combinations of individual taxes in the UnitedStates. Eliminating all the taxes at once might be the best policy. However,realistically speaking, governments are not free to remove all taxes; their taxpolicies are restricted by budget constraints. Thus when the possibility ofexploiting a shift in the general tax level (tax/GNP ratio) is restricted, a rev-enue-neutral change in the relative tax structure is the only alternative. I findthat a revenue-neutral change in the relative tax structure has a substantialpotential growth effect, amounting to above 30% of the growth effect inducedby a change in the overall tax level (tax/GNP ratio).

The remainder of this paper is organized as follows. In Section 2, I propose anendogenous growth model. Section 3 employs the model to evaluate the contri-bution of the differences in tax systems, technology and preferences to the


difference in growth rates across countries. In Sections 4 and 5, contributions ofdifferences in individual tax rates and monetary systems are assessed. Section 6evaluates the magnitude of the growth effect of tax reforms in the United States.Section 7 is the conclusion.

2. An endogenous growth model with financial, physical and human capital

In this section, I present an endogenous growth model comprising offinancial, physical and human capital. The model economy consists of a largenumber of identical households. It is assumed that a representative householdmaximizes the following intertemporal utility function:

=+t/0

btu(ct) ,

where ctis consumption and b is the subjective discount factor. Further, it is

assumed that the momentary utility function takes the constant elasticity form:

u(ct)"c1~p

t/1!p.

A distinguishing feature of this model is that the household faces a choicebetween investments in education, stocks and bonds. The household’s income isderived from these three different investments and from a government transfer.Thus, the household faces a budget constraint of the form:

ct#(b

t`1!b

t)#q

t`1(E

t`1!E

t)#(1!/)i

)t

4r"tbt#d

tqtEt#w

thtlt#¹

t

![hwthtlt#m

"(r"t#n)b

t#m

ndtqtEt#m

#(Dq/q)

tqtEt],

where bt`1

is the demand for bonds, qt`1

is the price of equities in terms ofoutput, E

t`1is the number of equities demanded, / is the education subsidy

rate, i)t

is the educational investment, r"t

is the real interest rate on bonds, dtis

the dividend yield ("dividend at t/qtEt), w

tis the real wage rate, h

tis the level of

labor skill or human capital, ltis the supply of labor, ¹

tis the transfer payment,

h is the labor income tax rate, m"

is the interest tax rate on bonds, n is theinflation rate, m

/is the dividend tax rate, m

#is the capital gains tax rate and

(Dq/q)tis the capital gain yield ("(q

t`1!q

t)/q

t#n).

The left side of the budget constraint represents expenditures, i.e., consump-tion, purchases of bonds, purchases of equities and investment in human capital.The right side represents net income, which is the sum of incomes from bonds,stocks, effective labor, and government transfer payments less the sum of laborincome tax and individual capital income taxes.


4m%"m

/j/#m

#(1!j

/) where j

/is the ratio of dividend return to equity return (i.e.,

dt"(r

%t#n)j

/and (Dq/q)

t"(r

%t#n)(1!j

/)).

5 If we introduce uncertainty into the model, equity could offer a much higher net rate of returnsthan debt does. Appendix B presents a stochastic growth model which can generate the growth rateand the equity premium that are consistent with the actual data.

6Following Brock and Turnovsky (1981), I derived the firm’s value and the appropriate cost ofcapital from the firm’s constraints in a discrete time case.

Furthermore, a relationship between educational investment and the skilllevel of labor is formulated. It is assumed that human capital accumulation isa linear function of human capital expenditures as follows:

ht`1

!ht"B i

)t!d

)ht,

where B represents how efficiently human capital is produced and d)

is thedepreciation rate of human capital. However, since the concern here is with percapita income growth rate, without loss of generality, labor is normalized aslt"1.The consumer chooses consumption, educational investment and debt and

equity holdings to maximize utility, taking prices as given. The first-orderconditions for consumer maximization are (if the consumer invests a positiveamount on each asset):

u@(ct)"u@(c

t`1)b[1!d

)#(1!h)w

t`1B/(1!/)], (1)

u@(ct)"u@(c

t`1)b[1#(1!m

")(r

"t`1#n)!n], (2)

u@(ct)"u@(c

t`1)b[1#(1!m

%)(r

%t`1#n)!n], (3)

where m%is the average tax rate on equity return4 and r

%t`1is the real rate of

return on equity. These conditions reveal that if the household invests in humancapital, bonds and equities, the net real rates of return from these three invest-ments should be the same.5

In addition, on the firm side, a constant returns to scale production functionof physical capital and effective labor is assumed. Then, the marginal product ofcapital is expressed as a function of the human—physical capital ratio (h/k). Thus,along the balanced growth path, where h/k is constant, the marginal product ofcapital remains positive at the level consistent with a positive growth rate, whichgenerates endogenous growth. Further, it is assumed that a firm seeks tomaximize its firm value, i.e., the present value of its net cash flows. The firm’svalue can be expressed as follows:6

»0"

=+t/0

(1!q)[(1!u) f (kt, h

tlt)!w

thtlt]!(1!Z!Z

$)(k

t`1!k

t#dk

t)

<ts/0

(1#o4)

,


7Z$

depends on the tax depreciation method. In the case of declining-balance depreciation,Z

$":q de~(d`o`n)tdt. With straight-line depreciation, Z

$":q(1/¸)e~(o`n)tdt. Here d is the tax

depreciation rate and ¸ is the tax lifetime.

8For simplicity, this paper utilizes a fixed debt—financing ratio. However, the model can beextended to allow for a variable debt ratio. Kim (1992) presents a variant of the model withheterogenous agents facing different tax brackets, which allows for an equilibrium where both bondand equity financing coexist while the firm chooses the debt ratio as in Miller (1977).

where q is the corporate income tax rate, u is the value-added tax rate, ktis the

capital stock, htltis the effective labor, Z is the tax savings from investment tax

credit, Z$is the tax savings from tax depreciation allowances,7 d is the economic

depreciation rate of physical capital, and otis the cost of capital.

The firm chooses optimal capital stock and effective labor to maximize thefirm value, taking prices as given. The firm’s first-order condition for optimalcapital stock is

(1!q) (1!u) fk(k

t, l

tht)"(1!Z!Z

$) (o

t#d). (4)

This tells us that the net marginal return from investment must be equal to thenet marginal cost of investment. The first-order condition for optimal laboremployment is

(1!u) fn(k

t, l

tht)"w

t. (5)

Here we allow the firm to finance investments through debt and equity. Thus thecost of capital is a weighted sum of the cost of bond and equity. If the firmfinances investment through debt, the firm has to pay nominal interest (r

"#n);

however, the firm then gets a corporate tax deduction of q(r"#n). Thus, the net

cost of debt is (r"#n)(1!q). In the case of equity financing, where no tax

deduction is allowed, the net cost of equity financing is just (r%#n). If the firm

uses debt at the weight of j",8 the total real cost of capital is written as follows:

ot"[(r

"t#n)(1!q)j

"#(r

%t#n)(1!j

")]!n. (6)

Therefore, the behavior of the firm can be characterized by Eqs. (4)—(6).Finally, we introduce government which collects taxes from the private sector.

The government budget constraint is as follows:

Gt#¹

t#/i

)t"hw

thtlt#m

"(r"t#n)b

t#m

/dtqtE

t#m

#(Dq/q)

tqtEt

#u f (kt, h

tlt)#q[(1!u) f (k

t, h

tlt)!w

thtlt!(r

"t#n)b

t]!(Z#Z

$)it,

where Gtis government consumption and i

tis investments in physical capital.

Then the resource constraint of the economy can be written as

ct#i

t#i

)t#G

t"y

t. (7)

In this economy, a competitive equilibrium is determined as follows. Theconsumer’s maximization problem yields a set of demand functions for


9This model has interesting dynamic properties. Competitive equilibrium conditions at timet determine g

tand (h/k)

tas functions of only tax variables at time t. If we assume the government

imposes tax rates constant over time, it implies a constant g and (h/k). This suggests that a balancedgrowth where consumption, output and capital grow at the same rate is a result of a constant taxpolicy.

consumption, bonds and equities, and a supply function of human capital.Likewise, the firm’s optimization behavior yields demand functions for physicaland human capital and supply functions for bond, equity and output in terms oftax and price parameters. The government’s tax revenue net of subsidies andtransfers is equal to government consumption. The equilibrium growth rate andrate of returns are then obtained from the market clearing conditions.

Implementing the market clearing conditions, we can focus on the case whereoutput, consumption, physical and human capital grow at the same rate g.9 Forthe constant relative risk aversion utility, the balanced-growth-path equationsystem is then summarized as

(1#g)p"b[1!dh#(1!t

h) f

h(1, h/k)B], (8)

(1#g)p"b[1!t$d#(t

$!1)n#(1!t

k) f

k(1, h/k)], (9)

c/y#(d#g) (k/y)#((dh#g)/B) (h/y)#(G/y)"1, (10)

where

th"1!(1!h) (1!u)/(1!/),

tk"1!C

j"

(1!m")#

(1!j")

(1!q)(1!m%)D

~1 (1!u)

(1!Z!Z$),

t$"C

(1!q)j"

(1!m")#

(1!j")

(1!m%)D

~1.

We can interpret thas the marginal effective labor income tax rate and t

kas the

marginal effective capital tax rate to represent the complicated tax system. Theseeffective tax rates can take negative values if the rates of subsidies on investment(i.e., education subsidies and ITC) are greater than tax rates on income fromcapital and labor. And t

$reflects the capital tax structure and determines the

sign of the effect of inflation on the growth rate. If t$is equal to one, inflation has

no effect on the growth rate. However, if it is greater than one, inflation hasa positive impact on the growth rate. The sign and magnitude of t

$depends on

the structure of such capital taxes as corporate tax, capital gains tax, interest taxand debt ratio. In sum, individual tax variables affect the growth rate throughth, t

kand t

$. Furthermore, differences in tax systems across countries are

summarized as differences in these three tax variables.


10 In this model without nonconvexities, the steady state is unique and stable. In particular,transition takes only one period during which the levels of capital adjust to the new balanced growthpath. For example, if the initial ratio of the endowment of physical and human capital differs fromthe steady state ratio at time t, the individuals adjust their capital at time t. Then, after t#1, theeconomy will stay on the new balanced growth path where consumption and capital grow at thesame steady state rate (see Kim (1992) for the elaboration of transitional dynamics of this model).This is in contrast with the models of endogenous growth with externalities or increasing returns toscale, which can generate multiple steady states or equilibria (e.g., Azariadis and Drazen, 1990,Becker et al., 1990 and Benhabib and Perli, 1994). Obviously, however, an incorporation ofnonconvexities into my model could produce multiple steady state or equilibria depending on theparameter values.

Also, Eqs. (8) and (9) determine two endogenous variables (g, h/k) indepen-dently of Eq. (10) which is only used to determine c/y for a given G/y. Fig. 1illustrates how the growth rate and the h/k ratio are determined. The steadystate growth rate and h/k ratio are determined by the intersection of the twocurves for Eqs. (8) and (9). Under the standard assumptions of diminishingmarginal products and a constant Z

$, f

h(1, h/k) is a decreasing function of h/k,

and fk(1, h/k) is an increasing function of h/k. Consequently, the curve for Eq. (8)

is decreasing in h/k, and the curve for Eq. (9) is increasing in h/k. It follows thatthe steady state solution of the endogenous variables including growth rate isunique.10 Along this path, h/k is constant, so the marginal product of capital isa positive constant. Accordingly, in this model, a positive sustained growth canbe achieved. And the resulting endogenous growth rate is a function of the tax,preference and technology parameters. Hence, differences in the tax variableslead to differences in per capita income growth rates. Furthermore, changes inindividual tax parameters affect the long-run growth rate. For example, a reduc-tion in the capital gains tax rate reduces t

k, causing a shift of the physical capital

curve, Eq. (9), upwards, thereby raising the growth rate.

3. The contribution of differences in taxes, technology and preferences

The model developed in Section 2 suggests that the difference in growth ratesbetween any two countries can be attributed to differences in taxes, tastes andtechnology. In this section, I assess how quantitatively important the differencesin each of these parameters are to explaining the difference in the growth ratesacross countries. To address this issue of decomposing growth differences,I choose two countries, one of which is the United States and the other SouthKorea, a rapidly growing Asian NIC.

To provide a benchmark for preference and technology parameters in thisanalysis, I begin by calibrating this model to find the values of the parameters inquestion which are consistent with the actual growth experiences of the two


Fig. 1. The determination of the growth rate.

countries. Within the calibrated model, what fraction of the growth ratedifference can be accounted for by differences in tax systems, technology andtaste, respectively, is determined. Then, a sensitivity analysis follows.

3.1. Benchmark estimates of tax parameters

The focus of the quantitative analysis will be on the United States and SouthKorea. The choice of these two countries is advantageous for several reasons.Both countries have shown stable growth without displaying any noticeabledeclining trends for the past three decades, which could justify an assumption ofa balanced-growth and other model specifications such as linear human capitalaccumulation function. The United States could represent average growthcountries in terms of per capita GNP growth rate at the annual rate of 1.5%,while Korea one of the top with 6.4% from 1965 to 1987. Another morepractical advantage is the existence of information on various tax rates utilized


11Recently, several studies constructed the same type of data on tax rates as used in this paper tocalculate estimates of the marginal capital income tax rate: King and Fullerton (1984) for fourcountries (the US, the UK, West Germany and Sweden); Makin and Shoven (1987) for Japan; andKim (1990) for Korea.

Table 1Summary of benchmark values of tax parameters (%)

United States Korea

Value-added tax rate (u) 0.0 4.2Corporate income tax rate (q) 49.5 46.2Capital gains tax rate (m

#)! 5.3 0.0

Tax rate on interest (m") 23.0 5.4

Tax rate on dividend (m/) 35.6 17.0

Investment tax credit (Z) 3.9 2.7Inflation rate (n) 5.8 14.4Debt ratio (j

") 33.8 60.0

Labor tax rate (h) 36.0 9.0Subsidy rate on human capital (/) 23.0 20.0Effective capital tax rate (t

k) 34 21

Effective labor tax rate (th) 17 !9

Inflation effect parameter (t$)" 1.06 1.31

!The value for capital gains tax rate is an effective rate."The unit of t

$is not a percentage but a numeral.

in the model of Section 2, which are currently available only for a small numberof countries.11

The key question addressed here is what fraction of the difference between thetwo countries’ long run growth rates ("0.049) can be explained by differencesin tax systems, technology and tastes. To address this issue, information onvarious tax rates of the countries is first required. Table 1 summarizes thebenchmark estimates for the tax parameters of the two countries. Many of theestimates for the US capital taxes are drawn from King and Fullerton (1984).The estimates for Korea are drawn from Kim (1990). Since these data wereoriginally disaggregated, I take a weighted sum of these disaggregated data withsuch weights as capital stock shares to obtain aggregated values. Note that thevarious tax rates in the table refer to marginal tax rates. The reason for focusingon marginal tax rates rather than on average tax rates is that the tax rates whichaffect the allocative margins are marginal rates. Among the parameter estimates,the estimate of the subsidy rate on human capital investment requires a morecomplete description. Following Kendrick (1976), I assume that human capitalinvestment consists of education expenditures, health expenditures andchild-rearing costs. Then the subsidy rate can be calculated by dividing the


government expenditures on education and health by the sum of governmentand private expenditures on education, health and children.

An examination of the tax systems of the two countries reveals that there areno significant differences in capital tax rates at the corporate level, investmenttax credit and education subsidy rates. In addition, Korea has a value-addedtax, while the US does not. However, the US labor tax and personal capital taxrates are much higher than those of Korea. Furthermore, the US debt-financingratio and inflation rate are much lower. These differences in individual taxesaccount for the difference in the effective tax rates. A comparison of the effectivetax rates indicates that the effective tax rates for both labor and capital in Koreaare much lower than those of the US, which suggests that the Korean tax systemis more investment-stimulating than that of the United States. Then the questionis how important such differences in effective tax rates are to explaining thedifferences in capital accumulation and growth rates.

3.2. Model calibration

In addition to tax estimates, growth comparison analysis also requires in-formation on technology and preference parameters of the countries. Among thetechnology parameters, we can choose the units of human capital so that theefficiency parameter of the production function is set equal to one (i.e., A"1).For the production function, the C.E.S. form is assumed. In particular, asa benchmark for the elasticity of the technical substitution, I consider the casewhere p

1"1 (Cobb—Douglas case), as employed by most of the recent taxation

studies. The distribution parameter in the C.E.S. production function, a, is equalto the capital income share in the Cobb—Douglas case, as available directly fromthe data. In 1980, capital income shares (which include tax and depreciation) ofGNP were approximately 34% and 49% for the United States and Korea,respectively. Thus I set a

64"0.34, and a

,0"0.49. For the human capital

depreciation parameter, I use d)"0.01 based on the estimate of Mincer (1974).

Based on King and Fullerton (1984) and Kim (1990), I use d64"0.057 and

d,0"0.048 for the physical capital depreciation parameter. Then, three para-

meters remain to be considered: the human capital efficiency parameter, B, andtwo preference parameters, p and b. However, we do not have enough informa-tion to directly estimate these parameters.

To obtain the most plausible values for the parameters, I calibrate the modelto fit US and Korean experiences. The logic of calibration is as follows. Asshown in Section 2, the balanced growth path of the model is characterized byEqs. (8) and (9). This equation system consists of two endogenous variables (g, h/k)and three different types of exogenous variables: (1) preference parameters (p, b),(2) technology parameters (B, a, d, d

h), and (3) tax parameters (t

k, t

h, t

$). Thus, if

we have information on the values of three different types of exogenous vari-ables, inputting the values into the model will provide the values of two


endogenous variables (g, h/k). The problem here is that we do not have enoughinformation on some technology and preference parameters. But we insteadhave some information on the endogenous variables of the model. The idea ofcalibration is to place a reasonable restriction of requiring that the values of theendogenous variables generated by the model match the actual counterparts.The restriction enables us to solve the model for the unknown preference andtechnology parameters in reverse from the information on the endogenousvariables (g, h/k).

To determine the values of the parameters in question, I use the US andKorea’s values of growth rate (g

64and g

,0) and marginal product of capital (f

k,64,

fh,64

, fk,,0

and fh,,0

) as well as estimates of tax parameters for the two countries.To calculate the marginal product of physical capital, I utilize the equation,which holds for any C.R.S. production function: f

k"w

#(y/k) where w

#is the

capital income share and (y/k) is the output—capital ratio. To compute theoutput—capital ratio, I use the following relation:

investment/output"[(kt`1

!kt)#dk

t]/y

t

"(g#d)(k/y).

Using the actual data for the investment—output ratio, the depreciation rate, d,the growth rate, g, and the capital income share, I obtain the following estimatesof the marginal products of capital for the two countries: f

k(k, h)

64"0.129 and

fk(k, h)

,0"0.217. Then the fact that both the marginal products of physical and

human capital are function of (h/k), can be used to calculate the marginalproducts of human capital.

I now input the estimates of the tax rates, the growth rates and the marginalproducts of capital of the two countries into the following system of equations:

(1#g64)p64"b

64[1!d

h,64#(1!t

h,64) f

h,64B

64], (8@)

(1#g,0

)p,0"b,0

[1!dh,,0

#(1!th,,0

) fh,,0

B,0

], (8A)

(1#g64)p64"b

64[1!t

$,64d64#(t

$,64!1)n

64#(1!t

k,64) f

k,64], (9@)

(1#g,0

)p,0"b,0

[1!t$,,0

d,0#(t

$,,0!1)n

,0#(1!t

k,,0) f

k,,0]. (9A)

Despite an equation system which consists of four equations with six un-knowns (p

64, p

,0, b

64, b

,0, B

64, B

,0), this system of equations can be solved for the

technology parameter, B, of each country. Since Eqs. (8) and (9) imply that

B"[d)!t

$d#(t

$!1)n#(1!t

,) f

,(1, h/k)]/(1!t

h) f

h(1, h/k),

the information on th, t

k, t

$, n, f

k, f

h, d

hand d for each country determines the

technology parameter, B, for the country independently of b and p. The solu-tions are

B64"0.054, B

,0"0.122.


Fig. 2. The b—p locus.

12 In this paper, I assume each country’s B is constant over time so that the difference in thetechnology parameter remains constant without any declining trend. This seems to be a reasonableapproximation at least for the last three decades on which this paper focuses, in view of the fact thatthere did not appear any significant changes in growth rates, tax rates and marginal product ofcapital of the two countries during that period. For example, 10 year average growth rate of percapita income in Korea, which was around 6.4% in 1960s, remained stable largely within a range of6—7% also in the subsequent two decades. In addition, three decades seem to be a sufficiently longrun to justify a long-run analysis. Obviously, my assumption to approximate the last three decadesdoes not imply that the huge difference in the growth rate between the East Asian NICs and othercountries will persist even for the next one or two hundred years.

This result is significant since the human capital efficiency parameter in Korea ismore than double that of the US.12 This suggests that the difference in techno-logy might be a critical factor in the difference in growth rates.

As shown in Fig. 2, the above system of equations decides a locus of (p, b) foreach country. A unique combination of (p, b), however, can be determined under


Table 2The growth rate (%) generated by the model (p"1.94 and b"0.991)

U.S. tax system Korean tax system Growth rate difference

a"0.34, B"0.054 1.5 2.6 1.1a"0.49, B"0.122 4.5 6.4 1.9

some assumptions about the relation between the preferences of the two coun-tries. Some people believe that human nature or preferences are similar regard-less of nationality so that differential growth experiences cannot be explained bydifferent national preferences. As a benchmark case, therefore, I adopt theassumption that preferences are common across countries. Under this assump-tion, the system of Eqs. (8@), (8A), (9@) and (9A) reduces to four equations with fourunknowns. Thus the system can be solved for a unique combination of commonvalues for p and b. The values are p"1.94 and b"0.991.

3.3. The contribution of differences in tax systems and technology

Within the calibrated model, the evaluation of the contribution of the differ-ences in tax systems to the difference in growth rates is straightforward. Table 2presents the results. In the case of US technology (i.e., a"0.34, B"0.054), theUS and Korean tax systems generate 1.5% and 2.6% growth rates, respectively,which indicates a growth rate difference of 0.011 (20% of the actual growth ratedifference). In the case of Korean technology, the two systems generate 4.5%and 6.4%, respectively, which implies a growth rate difference of 0.019 (40% ofthe actual growth rate difference). Thus, on average, the difference in growth rateattributable to the total tax system amounts to 0.015 ("(0.011#0.019)/2). Thisleads to the conclusion that differences in the tax systems account for approxim-ately 30%, a significant proportion of the actual growth rate difference("0.049).

The result also implies that the remaining 70% must be due to differences intechnology since identical preferences are assumed. Note that the term ‘techno-logy’ here must be interpreted as residuals, or something unexplained, afterconsidering the effect of preferences and tax parameters. Thus the contributionof differences in technology reflects the effect of differences not only in puretechnology, but also in some institutional factors or non-tax government policyor some other yet unexplained factors.

3.4. The contribution of differences in preferences

A tempting and often suggested explanation for differential growth ratesacross countries is the difference in preferences. Proponents of this idea argue


13This calculation is based on the standard assumption that b41. This standard assumption issupported by some empirical literature. For example, Hansen and Singleton (1982) suggest that theestimates of b exceed 0.99, but are less than unity. On the other hand, Kocherlakota (1990) suggeststhat competitive equilibria with positive interest rates only require b(1#g)(1, so that b mayexceed one in a growing economy. If I allow for b'1, increases in b would reduce the contributionof the difference in taxes to the growth difference and increase the contribution of the difference inpreferences. For instance, when b is 1.02 for Korea and 1.01 for the US, the p is determined at 2.41for Korea and 3.21 for the US. Then the difference in growth rates as caused by a difference in taxsystems is on average 0.011 (or 22% of the actual growth difference). Therefore we can interpret thedifference in preferences to contribute 0.004 (or 8% of the actual growth difference).

that a faster growth in the East-Asian countries stems largely from highersavings and investment spurred by an innate national frugality. In the context ofthe endogenous growth model where the preference difference is represented asthe difference in the subjective discount factor, b, and the elasticity of substitu-tion parameter, p, a hypothesis can be formulated with the assumption thatKorea’s b is greater than that of the United States and that Korea’s p is less thanthat of the United States. The range for the preference parameters of the twonations is further restricted by information on the actual growth experiences andthe balanced growth equations. Under the hypothesis and the standard assump-tion that the subjective discount factor, b, cannot exceed one, the calibratedmodel consistent with the growth experiences indicates that the difference inp cannot exceed 0.4. The maximum difference in p is achieved when b for the twocountries is at its maximum of 1, and the corresponding US and Korea’s p is 2.5and 2.1, respectively. The difference in b also cannot exceed 0.007.

Within the plausible range for the combination of b and p for the two countries,the contribution of the difference in taxes to the growth difference can becalculated. Table 3 reports the results. When the US value for b and p are 1 and2.5, and Korea’s values are 1 and 2.1, the difference in growth rates as caused bya difference in tax systems is on average 0.013 (or 27% of actual growth differ-ence). This indicates that as the preference difference in p increases from zero to0.4, keeping technology parameters constant, the contribution of the difference innon-tax parameters (i.e., preference and technology) increases from 0.034 to 0.036.Thus we can interpret the difference in preferences to contribute 0.002, which is4% of the actual growth difference. For other combinations of b and p, thecontributions of the preference difference are less than the level achieved when thedifference in p is 0.4. These findings suggest that the difference in preferencesexplains, at most, 4% of the growth difference, while the difference in taxesaccounts for 27% even when we assume differences in preferences.13

3.5. Sensitivity analysis

This subsection tests the sensitivity of the result obtained in the previoussubsections. First, I check the sensitivity against the assumption of different


Table 3Decomposition of growth difference

p64—p

,0Contribution ofdifference in taxes

Contribution ofdifference in tastes

Contribution ofdifference intechnology

0 (1.94!1.94) 1.5% 0% 3.4%0.4 (2.5!2.1) 1.3% 0.2% 3.4%

Table 4The growth rate (%) generated by the model (p"2 and b"0.98)

U.S. tax system Korean tax system Difference

a"0.34 B"0.073 1.5 2.7 1.2B"0.187 4.5 6.4 1.9

a"0.49 B"0.046 1.5 2.9 1.4B"0.142 4.4 6.4 2.0

technology and preference parameters across countries. Then I also test thesensitivity to the calibrated choice of technology and preference parameters.

To check the sensitivity against the assumption of different technology andpreference parameters, I assume technology and preference parameters areidentical across countries. Under this assumption, the only difference acrosscountries lies in the tax systems and, thus, the difference in growth rates can besaid to stem only from differences in tax systems. For this hypothetical experi-ment, I adopt some benchmark values of preference and technology parametersbased on previous studies. For the preference parameters, I use p"2 for thecoefficient of risk aversion as in Lucas (1990) and b"0.98 for the subjectivediscount rate. For the human capital depreciation rate and the elasticity of thetechnical substitution parameter, d

)"0.01 and p

1"1 are chosen. For the

distribution parameter, a, I assign a range between 0.34 of the US and 0.49 ofKorea. Thus one parameter remains to be considered: the human capitalefficiency parameter, B. I assign to this unknown parameter some plausiblerange so that the model can generate growth rates that are higher than theactual US growth rate of 1.5%, but lower than Korea’s growth rate of 6.4%.

Table 4 reports the estimated contribution of the difference in tax systems inthis benchmark case. The table shows that the range of a between 0.34 and 0.49and of B between 0.046 and 0.187 produces a range from 25% ("1.2/4.9) to41% ("2.0/4.9) for the contribution of the difference in tax structures. Notethat this difference in growth rates is only attributable to the difference in tax


14This Lucas’ argument is based on a deterministic model. In a stochastic setting, however, theinterest rate is not necessarily increasing in r. For a lognormal distribution of consumption growthrate, Kandel and Stambaugh (1991) derive the riskless interest rate as r"!ln b#pk!0.5p2 var.A similar expression is also derived in my stochastic growth model in Appendix B. Assuminga lognormal distribution of productivity shock, a first-order condition for the consumer can beexpressed as r"[1/(bE[(c

t`1/c

t)~p])!(1!n)]/(1!m

")!n"[(1#g)p/(b exp[!pk#0.5p2 var])

!(1!n)]/(1!m")!n. If we set n"m

""g"0 and take a linear approximation for a logarithmic

function, the above expression for the riskless interest rate is reduced to the one in Kandel andStambaugh.

structures. Thus the result does not support the hypothesis of identicaltechnology and preferences which suggests that the entire growth rate differenceshould be accounted for by the difference in tax systems. More significant isthe fact that even in this hypothetical experiment the estimate of the contribu-tion of the tax system is similar to that in the calibrated model, which isapproximately 30%. This suggests that the estimate of the contribution oftax differences is robust to changes in the assumptions on preferences andtechnology.

Further, I conduct an assessment of the sensitivity of our results to changes inthe parameter values. The benchmark values taken for some parameters includ-ing p

1, b and p may be biased to some degree, which requires testing if results are

affected significantly by changes in parameter values. From the sensitivityexperiment, however, I find that the estimates of the contribution of the taxsystem are insensitive to changes in such parameters as the substitution elastic-ity parameter, the subjective discount factor and the human capital depreciationparameter. For the elasticity of technical substitution, for example, I choosep1"0.6 as in Lucas (1990). In this case, the estimated contribution of the tax

structure difference is almost the same as in the case of p1"1.

In the absence of uncertainty, one parameter critical to the determination ofthe contribution of the difference in tax systems is the coefficient of risk aversion.In the case of p"4, for instance, the range of the contribution of tax differencesdecreases to around 15%. In the case of p"1, the range increases to around55%. However, we might set p"2 as an upper bound for the value of theparameter based on Lucas (1990) which states that from the viewpoint ofcross-country interest differentials, p"4, and even p"2, seems too high.14 Inthe deterministic model with p(2, the difference in tax systems explains, onaverage, more than 30 percent of the actual growth rate difference.

4. The contribution of differences in individual taxes

In the previous section, I calibrate the model and assess what fraction of thegrowth rate difference can be accounted for by differences in tax systems,


15 In this experiment, tax revenue changes are endogenous, and each tax change induces a differ-ent magnitude of tax revenues. For example, an exchange of a corporate tax rate of the US from49.5% to 46.2% has much smaller revenue effect than that of a value-added tax rate from zero to4.2%. Section 6 presents the result of another type of experiment where a change in a particular taxis compensated by a change in another non-lump-sum tax.

16Appendix A presents a modification of the model of Section 2 which incorporates time input asan argument in human capital function: h

t`1!h

t"Bva

t(i)t/h

t)bh

t!d

hht. According to the calib-

ration exercises, the importance of labor taxes in explaining the growth rate gap appears robust tosuch a modification. When a"b"0.5, e.g., a substitution of the current Korean labor tax rate forthe US tax rate raises the growth rate gap to 1.14% ("6.4%!5.26%), which is almost the same as1.23% ("6.4%!5.17%) obtained in the basic model for Table 5. Further, as the elasticityparameters (a, b) get larger, the contribution of labor taxes could be even bigger. If a"b"0.7,a substitution of the current Korean labor tax rate for the US rate raises the growth rate gap to 1.5%("6.4%!4.9%).

technology and taste, respectively. In this section, I conduct a further decompo-sition of the growth rate difference. In particular, the contribution of thedifferences in the entire tax system is further broken down into contributions ofdifferences in individual tax rates. In this way, we can identify which taxvariables are more important in explaining the difference in the growth ratesacross countries. This is one advantage of our model incorporating variousfeatures of a general tax system.

The contribution of the difference in each tax variable is assessed as follows.Using the calibrated model, I measure the changes in a country’s growth ratewhen another country’s tax rate is substituted for the current rate. In thisexperiment, I assume that a change in a particular tax variable is offset bya change in a lump-sum tax or transfer, keeping the other tax variablesconstant.15 This experiment allows me to assess a partial effect of individualtaxes. Table 5 lists the results of this experiment for the various tax variables.For example, an exchange of the current capital gains tax rate for the othercountry’s tax rate raises the growth rate by 0.05% ("1.55%!1.50%) in thecase of the US and reduces the rate by 0.14% ("6.40%!6.26%) in the case ofKorea. This indicates that the difference in capital gains tax rates on averageaccounts for 2% of the actual growth rate difference.

From this experiment, individual tax variables which are more important inexplaining the growth difference can be identified. Noteworthy is the fact thatthe difference in labor tax rates accounts for a large portion of the growth ratedifference. The fraction of the growth rate difference explained by the labor taxdifference is 0.99% ("[(2.25%!1.50%)#(6.40%!5.17%)]/2), which is 20%of the actual growth rate difference. In contrast to most previous research whichemphasized the importance of the capital tax system, this result suggests thatlabor taxes are at least as important as capital income taxes in accounting forthe growth rate difference between the two countries.16 In addition, according tothe table, differences in debt-equity ratio, inflation and tax rates on financial


Table 5The growth effects of difference in individual taxes

US tax system Korean tax system

(1) Corporate profit tax rateUS ("0.495) 1.50 6.38Korea ("0.462) 1.52 6.40

(2) Interest and dividend tax rateUS ("0.230, 0.356) 1.50 5.62Korea ("0.054, 0.170) 1.57 6.40

(3) Capital gains tax rateUS ("0.053) 1.50 6.26Korea ("0) 1.55 6.40

(4) Investment tax creditUS ("0.039) 1.50 6.46Korea ("0.027) 1.48 6.40

(5) Value-added tax rateUS ("0) 1.50 6.72Korea ("0.042) 1.38 6.40

(6) Inflation rateUS ("0.058) 1.50 6.00Korea ("0.144) 1.51 6.40

(7) Debt and equity ratioUS ("0.34, 0.66) 1.50 5.69Korea ("0.60, 0.40) 1.60 6.40

(8) Labor tax rateUS ("0.36) 1.50 5.17Korea ("0.09) 2.25 6.40

(9) Human capital subsidy rateUS ("0.23) 1.50 6.55Korea ("0.20) 1.43 6.40

Note: The unit of growth rates is percentage.

assets are also identified as important in explaining the growth rate differencebetween the two countries.

Another important finding is that a change in individual tax rates may havea large impact on the growth rate of a country, but a very small impact ina country with a different structure. In particular, inflationary effects are of


17Kormendi and Mcguire (1985) regress the long-run average growth rate on the long-runinflation rate using data of 47 countries. From the standpoint of my model, where the effect ofinflation on the growth rate depends on the tax system, a more appropriate regression is one whichcontrols tax variables.

18 In my model, the mechanisms through which inflation affects the capital tax system are thesame as those in Feldstein and Summers (1979) and King and Fullerton (1984). But in contrast totheir focus on the effective tax rate, I deal with the effect of inflation on the growth rate.

19Table 5 reports the growth effect of inflation when keeping the debt ratio constant. We couldalso compute the growth effect of inflation when allowing for changes in the debt ratio. In the lattercase, if the debt ratio in Korea decreases by 10% in response to a reduction in inflation rate to 5.8%,the growth rate would be reduced from 6.4% to 5.9% as opposed to 6.0% in the former case. Thisimplies that with flexible debt ratio, the inflation effect in Korea will be even larger.

interest.17 Under the current US tax structure, inflation has a negligible effect onthe growth rate. In the case of the Korean tax system, however, an increase inthe inflation rate causes a considerable rise in the growth rate.18 The reason forthis is clear. Without indexation, taxes are imposed on nominal income, not onreal income. Thus inflation impacts the tax system. There are two main channelsthrough which this can be accomplished. First, the nominal interest paymentscan be deducted from corporate income tax. As the inflation rate rises, thecorporate tax deduction increases, causing corporate income tax to decrease.This is a positive inflation effect. Second, as the inflation rate rises, personal taxon asset returns increases. The second channel produces negative inflationeffects. Therefore, the overall effect of inflation on the tax system and on thegrowth rate depends upon the relative strength of the two effects. In Korea,where the debt-financing ratio is high and the tax rates on financial assets arelow, the first effect is much larger than the second. As a result, the overall effectof inflation in Korea is to reduce capital taxes and consequently to increase thegrowth rate.19

Finally, given the interactions among taxes, sum of the partial effect of thedifference in individual taxes is not equal to the total effect of the difference inoverall tax structure reported in Table 2. The latter is greater than the former inthe US, while it is the other way around in Korea. This implies that as theoverall tax structure gets closer to the Korean tax system, the growth effects ofindividual taxes also tend to increase.

5. The contribution of monetary factors

In this section, I extend the model of Section 2 to incorporate the cash-in-advance constraint. This modification allows me to evaluate how the mainresults obtained in the previous sections (e.g., the contribution of the tax factorto the growth rate gap) are affected by the incorporation of monetary factors.


20One may view the model in the previous section as implicitly assuming the time-invariance ofinflation, for which monetary growth adjusts passively to output growth.

5.1. Model with money

It is an age-long conjecture that the government’s monetary policy may havea significant impact on long-run economic growth. A simple variation of myprevious model suggests a growth model that is suitable for analyzing the effectof monetary policy on inflation and economic growth. In the model of Section 2,without indexation, inflation can affect the long-run growth rate. Thus, byintroducing money into the model, I can easily establish a link between monet-ary policy and economic growth.

The following is an example of the model with money that incorporates thecash-in-advance constraint. The consumer’s optimization problem here is thesame as before, except that it introduces money into budget constraint andcash-in-advance constraint. The budget constraint here is

ct#(b

t`1!b

t)#q

t`1(E

t`1!E

t)#(1!/)i

)t#M

t/p

t

4r"tbt#d

tqtEt#w

thtlt#¹

t![hw

thtlt#m

"(r"t#n)b

t

#m/dtqtEt#m

#(Dq/q)

tqtE

t]#(M

t~1#H

t)/P

t,

where Mtand H

trepresent the demand for money and the increase in money

stock per person at time t, respectively. In addition, the cash-in-advance con-straint is given by

ztPtct4(M

t~1#H

t),

where ztis the fraction of final goods the agent purchases using money.

Then the balanced-path equation system is given by Eqs. (8)—(10) (as in theprevious model) and Eq. (11)

g#n"m, (11)

where m ("DMt/M

t!Dz

t/z

t) is the growth rate of money per person adjusted

for changes in zt.

The above system of equations can be solved for the growth rate andinflation rate as a function of preference, technology, taxes and monetaryvariable, m. Hence, in this model, the inflation rate is endogenously deter-mined, unlike the previous model where inflation is given exogenously.20In addition, a change in the monetary rule will affect both the inflation andgrowth rate.


Table 6The rate of growth and inflation (%) generated by the model

US tax system Korean tax system Growth rate difference

a"0.34, B"0.054 g"1.5 g"2.3 Dg"0.8m"0.073 n"5.8 n"5.0

a"0.49, B"0.122 g"4.5 g"6.4 Dg"1.9m"0.208 n"16.3 n"14.4

21One can also easily calculate the rate of change in zt

(i.e., Dzt/z

t) from the definition of

m ("DMt/M

t!Dz

t/z

t) and actual money growth rates. Using the M2 growth rate for 1965—1987,

I assign Dzt/z

t"0.094 for Korea and Dz

t/z

t"0.021 for the US.

22 It is also interesting to compare the growth effects of the corporate tax in the model ofexogenous inflation and of endogenous inflation, because inflation affects income growth mainly viathe corporate tax. I find that the contribution of the corporate tax on the growth difference is onlyslightly affected by the introduction of endogenous inflation. For example, in the case of Korea, anincrease in the corporate tax from the current 46.2% to 56.2% would reduce the growth rate fromthe current 6.40% to 6.324% in the case of endogenous inflation, and to 6.318% in the case ofexogenous inflation.

5.2. The contribution of monetary and tax systems

Using the modified model, I explore whether the result on the contribution ofthe tax factor to the growth rate gap is robust to the incorporation of monetaryfactors. Table 6 reports the contribution of tax systems after controlling monet-ary factors. This experiment requires information on m, which can be easilyobtained using Eq. (11) and the actual values for g and n. The estimates of themonetary variable, m, for the countries are: m

64"0.073 ("0.015#0.058) and

m,0"0.208 ("0.064#0.144).21 Using the estimates for m, the growth rate gap

attributable to the tax system is calculated to be 0.0135 ("(0.008#0.019)/2) or28% of the actual growth rate difference ("0.049). One implication of thisresult is that, even with the incorporation of monetary factors, the contributionof the tax factor to the growth rate gap is almost same as before.22

I also evaluate the contribution of the combined difference in monetary andtax systems to the difference in the growth rate. This exercise can provide us witha further breakdown of the difference in technology or residuals which amountsto 70% in the model without money. Table 7 presents the results. Assuming UStechnology levels (i.e., a"0.34, B"0.054), the Korean monetary and taxsystems together would generate 2.8% growth rates, which indicates a growthrate difference of 0.013. Assuming Korean technology, the US system would


Table 7The rate of growth and inflation (%) generated by the model

US monetary andtax system

Korean monetaryand tax system

Growth rate difference

a"0.34, B"0.054 g"1.5 g"2.8 Dg"1.3n"5.8 n"18.0

a"0.49, B"0.122 g"4.3 g"6.4 Dg"2.1n"3.0 n"14.4

generate 4.3%, which implies a growth rate difference of 0.021. Thus, the growthrate gap attributable to the combined difference in monetary and tax systemamounts to 0.017 ("(0.013#0.021)/2) or 35% of the actual growth ratedifference. This finding suggests that, by introducing the difference in monetarysystems, the contribution of technology or residuals can be reduced to 65%from 70%.

6. The magnitude of the growth effect of taxes in the US

In this section, I explore the magnitude of the growth effect of taxes in theUnited States. A key question is whether tax reform can improve the US growthrate dramatically to match those of some rapidly growing East Asian countries.Using a formula for the growth effect, I calculate how large are the growtheffects of tax changes in the United States. Then I calculate the magnitude of thegrowth effect of revenue-neutral changes in the relative tax structure and thecombination of individual taxes in the United States.

6.1. Formula and calculation of the growth effect in the US

I start by deriving a formula for the magnitude of the growth effects bydifferentiating a system of equations characterizing a balanced growth path inthe model of Section 2. Under the assumption of the Cobb—Douglas Productionfunction, the total differentiation of Eqs. (8) and (9), can express the growth ratechange (dg) as follows:

dg"!M[(1!tk)/(1!t

h)]a(1!a)dt

h#[(1!t

h)/(1!t

k)]1~aa dt

kNQ,

(12)

where

Q"

B1~a(1!a)1~aaa[p(1#g)p~1/b]

.


23Q is affected by the level of growth rate through [p(1#g)p~1/b]. However, the value of Q isalmost constant for a wide range of growth rates: 0.038!0.039 for g"0—3%. Thus I take 0.0385 asthe value for Q regardless of the growth rate.

24Growth-enhancing tax reforms do not have to be welfare-improving. Hence it could be the casethat such increases in the US growth rate may reduce the welfare, e.g., if the current tax system forthe US is optimal for the country. More discussions on the effect of tax reforms on welfare in thistype of model are in Kim (1992).

25For the purpose of comparison, I assume a general technology including the technologies ofJMR, KR and this paper as special ones. The production function of physical capital isy"A

1F(h,k); the production function of human capital is y"A

2F(h,k); and the human capital

The above formula suggests that the growth rate change, (dg), depends on tasteand technology parameters mainly through Q and on the tax system through theterms inside the bracket. The technology and preference parameter valueschosen in the calibrated model in Section 3 indicate that, in the United States,Q is 0.0385.23 Then the formula for dg in the United States can be written as:

dg"!0.0385M[(1!tk)/(1!t

h)]a(1!a)dt

h#[(1!t

h)/(1!t

k)]1~aa dt

kN.

Using this formula, I calculate the growth effect of a hypothetical eliminationof all US taxes, which is equivalent to changing the US effective tax rates fromthe current values (t

h"0.17 and t

k"0.34) to zeros. I find that the complete

elimination of taxes raises the US growth rate by 0.85 percentage points. Thisresult suggests that a tax reform has a sizable growth effect, but that zeroeffective tax rates are not enough to raise the US growth rate to the levels ofrapidly growing East-Asian countries. This is consistent with the result ofSection 3 which suggests that the US adoption of the tax system of a rapidlygrowing economy alone is not enough to raise the growth rate to over 6%.24

This sizable but moderate estimate of growth effect contrasts sharply witha recent taxation study by Jones et al. (1993) and King and Rebelo (1990). Thesestudies use much of the same but simpler class of models where human capitalaccumulation depends on education expenditures. Surprisingly, however, themagnitude of the growth effects (dg/dt) in the benchmark cases of Jones et al.(JMR) and King and Rebelo (KR) are four to five times larger than that of thispaper. In these models with a large growth effect, US tax reform has thepotential to raise the growth rate dramatically to the level achieved by the NICs.

Examinations of the formula for growth effect and the chosen parametervalues provide an explanation for the difference in magnitudes among thestudies. The estimate of this paper for Q is much lower than those of JMR andKR, making my growth effect lower than those of the other two authors. If weunify the value of the elasticity of the substitution parameter which differswidely, the main difference between the authors, among the parameters compris-ing Q, comes from differences in the assumed values of technology parameter B.The estimate of B in this paper is around 1

4of the value in JMR and 1

3of KR.25


(foot note 25 continued)investment technology is h

t`1!h

t"Bi

ht. The values used for (A

1, A

2, B) in these studies are as

follows: (0.374, 0.374, 1) in JMR, (1, 0.182, 0.822) in KR and (1, 1, 0.054) here. If we unify the units bynormalizing A

1"1 and A

2"1, then the values for B are 0.21 in JMR, 0.15 in KR, and 0.054 in this

paper.

26Further discussions on comparisons among JMR, KR and an earlier version of this paper are inRebelo and Stokey (1995) and in Kim (1992). One important reason for higher marginal product ofcapitals and larger growth effect in JMR and KR is that they assume a depreciation rate of 10% forphysical and human capital. Rebelo and Stokey (1995) point out that the depreciation rates assumedin JMR and KR are too high, compared to realistic estimates which are close to the numberssuggested in this paper.

The determination of which of the three values for the technology parameteris the most appropriate is critical to deciding a realistic estimate of the growtheffect of taxes in the United States. One critical test is to check which marginalproduct of physical capital implied by B in the three studies most closelymatches the actual value. In JMR, the values of the marginal product range from17.8% to 20.5% for a range of p"1.01—2.0. KR assumes MPK to be 16.5%.However, these values for the marginal product of physical capital in JMR andKR seem too high to be consistent with US data, in view of the existing studies.For example, according to Feldstein and Summers (1977), the gross rate ofreturn on capital was calculated to be 11% on average for the period of1948—1976 in the United States. In contrast to JMR and KR, this paper’s valueof MPK closely matches the actual value suggested by the existing literature.The reason is that this paper derives the marginal product to be 12.9% usingactual data on K/y ratio and income share. These considerations suggest thatthis paper’s estimate for the growth effect is more realistic.26

6.2. Government budget and the growth effect of the relative tax structure

Another important calculation assesses the growth effect of a change in therelative tax structure given government budget constraints. Eliminating all taxeswill increase the growth rate, but such a drastic step is restricted by governmentbudget constraints. Thus we might assume a positive government spending orG/y ratio along the growth path. If a change in the overall tax level (G/y ratio) isnot feasible, a remaining feasible policy for growth stimulation is a change in therelative tax structure. Then, a crucial question is whether or not the relative taxstructure change has a quantitatively important growth effect.

Due to the differences in the feasibility of tax changes, I distinguish the effectof the overall tax level from the effect of a relative tax structure. Eq. (12) showsthat while the growth change, (dg), depends on the overall change in the taxlevel, it also critically hinges on the relative tax structure through(1!t

k)/(1!t

h). To isolate the effect of the general tax level, I assume identical


tax rates th"t

k, and d(G/y)"dt

h"dt

k. Then the terms inside the bracket on

the right side of Eq. (12) can be simplified as d(G/y). If I take the value forG/y"0.23 as implicit in the calibrated model in Section 3, the US elimination ofoverall taxes would increase the country’s growth rate by 0.89 percentage points(DdgD"0.0385]0.23"0.0089).

The magnitude of the growth effect due to changes in the relative tax rates canalso be calculated. For this purpose, I isolate the effect of the relative taxstructure, which can be calculated by assuming d(G/y)"0. Then since budgetconstraints yield dt

k"!dt

h(1!a)/a, the terms inside the bracket can be

written as M[(1!tk)/(1!t

h)]a![(1!t

h)/(1!t

k)]1~aN(1!a)dt

h.

Furthermore, I calculate the maximum value of the above term within theranges of t

hand t

k, which are t

h3[0, 0.34], t

k3[0, 0.68] for G/y ".23. Then, the

maximum growth effect calculated is approximately 0.28 percentage points.A comparison of the two values calculated above (0.89% and 0.28%) indicates

that the maximum growth change due to a change in the relative tax structure isequivalent to 31% of the growth change induced by the total elimination oftaxes. Note that this calculation of the growth effect of the relative tax structureis only for non-negative effective tax rates, and that effective tax rates can benegative when the rates of investment subsidies are sufficiently high. In the caseof negative effective tax rates, the growth effect due to the relative tax structurecan be even greater than 0.28 percentage points. This result suggests thata change in the relative tax structure impacts economic growth substantiallywithout affecting the overall tax level.

6.3. Growth effect of the combination of individual taxes

Another practical policy issue is a calculation of the growth effect of a changein the combination of individual taxes as restricted by both government budgetconstraints and differences in the feasibility of tax changes. It is well known that,if a reduction of income taxes by a compensating change in lump-sum taxes (orconsumption taxes) is feasible, this kind of tax reform would be growth-enhancing (see Turnovsky, 1996). I here calculate the growth effect of a change inthe combination of individual taxes when the changes in lump-sum taxes are notfeasible. To address this issue, I first calculate growth rate changes induced bychanges in individual taxes having the same revenue effect (i.e., same change ina tax revenue-output ratio). Suppose that the government is able to reduce thetax revenue as a fraction of GNP by DR and that the tax revenue decrease isachieved by a change in only one tax variable. Then the decrease in the taxvariable will increase the growth rate. If we denote the effect of the tax revenuechange on t

ias (Dt

i/DR) and the effect of t

ion g as (Dg/Dt

i), then the growth rate

change resulting from a change in the ith tax, (Dgi) will be

Dgi"(Dg/Dt

i) (Dt

i/DR)DR. (13)


Table 8The growth effects of changes in individual taxes with the same revenue effect (DR"0.1) in the US

Current New Newti

ti

DDti/DRD g DDg/Dt

iD Dg

i

(1) Corporate tax 49.5 44.8 4.7 1.5354 0.00753 0.0354(2) Interest tax 23.0 10.2 12.8 1.5359 0.00280 0.0359(3) Dividend tax 35.6 !21.6 57.2 1.5359 0.00063 0.0359(4) Capital gains tax 5.3 1.3 4.0 1.5359 0.00898 0.0359(5) Labor tax 36.0 34.7 1.3 1.5395 0.03038 0.0395(6) Value-added tax 0.0 !1.4 1.4 1.5416 0.02971 0.0416(7) ITC 3.9 8.3 4.4 1.5550 0.01250 0.0550(8) Education subsidy 23.0 25.6 2.6 1.5679 0.02612 0.0679

Note: The unit of growth and tax rates is percentage.

The growth effectiveness (Dgi) can be calculated for all tax variables. The last

column of Table 8 reports the growth effectiveness of various taxes inducinga change in the revenue-output ratio by 0.01 in the current US tax system.

The comparison of a pair of Dgiprovides information on which tax is more

effective in affecting the growth rate with the same revenue effects in eachcountry. Growth-enhancing changes can be induced by simultaneously loweringthe tax rate of higher effectiveness and raising the tax rate of lesser effectiveness.For example, a combination of an increase in ITC and corporate income tax inthe US will increase the growth rate, since investment tax credit is more effectivein stimulating growth than corporate income tax. The reason is that, withoutaffecting the tax revenue/output ratio, the government can reduce the tax ratewith higher growth effectiveness with an offsetting increase in the tax rate withlower growth effectiveness. Then the growth gain caused by the decrease in thetax rate with higher effectiveness exceeds the growth loss from the increase in thetax rate with lower effectiveness, which results in a positive net increase in thegrowth rate. The ranking of the growth effectiveness of various taxes can bedifferent across countries, because the growth effect of individual taxes criticallydepends on the tax structure, as illustrated in Section 4. For example, a corpo-rate tax has the lowest effectiveness in the US, as shown in Table 8. However,the calibrated model indicates that it has higher effectiveness than an interest taxand a value-added tax in Korea with high debt-equity ratio.

The magnitude of the growth effect of a change in the combination of twodifferent types of taxes in the US can be easily calculated from the table. Forinstance, a change in the combination of an increase in ITC and corporateincome tax, equivalent to 0.01 change in G/y ratio, respectively, would havea growth effect of 0.0196% ("0.0550%!0.0354%), without affecting thegeneral tax level (G/y ratio). A calculation shows that 0.01 change in overall tax


level would increase the country’s growth rate by 0.0385%. This indicates that ina revenue-neutral way, a rise in ITC accompanied by an increase in corporatetax has roughly an 50% ("0.0196/0.0385) growth effect of the reduction in theoverall tax level. In sum, a change in the combination of individual taxes hasa substantial growth effect without burdening the government budget.

7. Conclusions

This paper presented an endogenous growth model that considered house-hold decisions between investments in financial assets and human capital, andincorporated major features of a general tax system. The model established linksbetween the long-run per capita income growth rate and various tax variablesincluding the inflation rate.

This growth model allowed for the assessment of the extent to which differ-ences in tax systems, preferences and technology account for the difference in theactual growth rates across countries. Using estimates of tax variables obtainedfrom actual data, I estimated technology and preference parameters consistentwith the actual growth experiences of the United States and an East Asian NIC.Within the calibrated model, I found that the difference in tax systems accountsfor a significant proportion (around 30%) of the difference in growth rates. Thedifference in preferences, by contrast, explains at most 4% under the standardassumption on preference parameters. In addition, the effects of individual taxinstruments on the difference in growth rates were quantitatively assessed.Labor income tax appeared to be at least as important as taxes on capitalincome in explaining the growth difference.

I also evaluated the role of monetary factors in explaining the growth rategap. An incorporation of money into the model can reduce the contribution oftechnology or residuals from 70% to 65%. The effect of US tax reforms on itsgrowth rate was also evaluated. Within the calibrated model, the hypotheticalelimination of all taxes in the US raises the growth rate by 0.85%, suggestingthat the growth effect of taxes is substantial. I also found that revenue-neutralchanges in relative tax structure and a combination of individual taxes havesizable potential growth effects. In this way, the model in this paper providedboth qualitative and quantitative answers to many practical tax policy andgrowth issues. In particular, the introduction of essential features of a generaltax system and an appropriate choice of parameter values increased the accu-racy of the quantitative analysis.

For a better understanding of economic growth, the exploration of thedifference in technology is much needed. The result on the contribution ofdifferences in tax systems suggests that cross-country differences in technology(or residuals) account for roughly 70% of the growth difference. This paper hasexamined the extent to which an incorporation of monetary factors help to


explain the residuals. However, this paper alone cannot fully address whatproduces such a difference in technology or residuals. Thus, recent growthmodels investigating various causes for differences in technology should providea useful complement to this paper.

Acknowledgements

This paper is based on chaps. 2 and 6 of my dissertation at the University ofChicago. I am very grateful to Robert Lucas and Nancy Stokey, who haveguided me with many insightful suggestions. I also thank Andrew Atkeson,Casey Mulligan, In-Koo Cho, Robert Chrinko, John Cochrane, Lars Hansen,Robert Townsend, Michael Woodford and two anonymous referees for helpfulcomments and the Ssangyong Economic Research Institute for financial sup-port.

Appendix A. Model with general human capital function

This appendix presents a variation of the model of Section 2, which incorpor-ates a more general human capital function so that I can deal with theinteraction of education time and education expenditures.

A general human capital production function, which allows human capitalaccumulation to be affected both by the time of education v

t(or (1!l

t) where

ltis the fraction of time spent on work) and by education expenditures i

ht, is

given by:

ht`1

!ht"G(v

t, (i

ht/h

t))h

t!d

hht.

Assuming that the function G (vt, (i

ht/h

t)) takes the Cobb—Douglas form, then the

above equation for human capital accumulation becomes

ht`1

!ht"Bva

t(iht/h

t)bh

t!d

hht. (A.1)

If a"0 and b"1, the equation is reduced to the function in Section 2. If a'0and b"0, it is the same as the function in Lucas (1990). I here assume a'0 andb'1, so that the model is a synthesis of Lucas (1990) and the model ofSection 2.

Using the human capital function (A.1), I can formulate the consumer behav-ior and the resulting economic dynamics. The balanced-growth-path equationsystem, which is derived from the first-order conditions of the consumer and thefirm and the equilibrium condition, is given by

(1#g)p"b[1!dh#(1!t

h) f

h(1, h/k)Bva(1!v)b(i

h/h)b~1], (A.2)

(1#g)p"b[1!t$d#(t

$!1)n#(1!t

k)fk(1, h/k)], (A.3)


27Turnovsky (1993) presents a stochastic growth model with money and taxes to address theissues of the tradeoff between capital accumulation and inflation and the welfare-maximizinginterest rate target in a stochastic environment.

(1#g)p"bBava~1(1!v)(ih/h)b, (A.4)

g"Bva(ih/h)b!d

h. (A.5)

The above system of equations consists of four equations in four endogenousvariables (g, h/k, v and i

h/h). Hence the above equations can be solved for the

growth rate and the other endogenous variables as a function of preference,technology and tax parameters.

Appendix B. Model with uncertainty

In this appendix, I present another variation of my previous model, whichintroduces uncertainty. This variant of the basic model allows us to deal with theequity premium and other uncertainty-related issues.27 I assume that the repre-sentative household maximizes the expected utility

Et

=+t/0

btu(ct),

where Etis the expectation given information at time t.

For simplicity, we assume that bonds are risk-free assets. Then the first-orderconditions for consumer maximization are given by

bEt[(c

t`1/c

t)~p(1!d

h#(1!h)w

t`1B/(1!/))]"1, (B.1)

bEt[(c

t`1/c

t)~p][1#(1!m

") (r

"t`1#n)!n]"1, (B.2)

bEt[(c

t`1/c

t)~p(1#(1!m

%) (r

%t`1#n)!n)]"1. (B.3)

The first-order conditions indicate that the accumulation of each type of capitalis affected by uncertainty. In this stochastic growth model, the net real return ondebt and equity are not equal any longer. Uncertainty can generate the wedgebetween E

t(r%t`1

) and r"t`1

.On the firm side, a constant returns to scale production function of physical

capital and effective labor is assumed:

yt"A

tf (k

t, h

tlt)"A

tkat(h

tlt)1~a,

where At

represents a stochastic process for technology level. In addition,a risk-neutral firm chooses optimal capital stock and effective labor to maximize


the firm value after the productivity shock (At) is revealed. The firm’s first-order

condition for optimal capital stock and labor is

(1!q) (1!u)Atfk(k

t, l

tht)"(1!Z!Z

d) (o

t#d). (B.4)

(1!u)Atfn(k

t, l

tht)"w

t. (B.5)

For the stochastic process of technology, we assume that xt`1

"At`1

/Atfollows

an i.i.d. process. In addition, for simplicity, we assume that E(xt`1

)"1. Then theexpected income growth rate is expressed as

E(yt`1

/yt)"E[(A

t`1/A

t) (1#g

t`1)]"(1#g

t`1),

where gt`1

is the growth rate of human and physical capital along the growthpath where human and physical capital grow at the same rate. Further,along the balanced growth path where all the variables grow at the same rate,we have

E[(ct`1

/ct)~p]"E[(y

t`1/y

t)~p]"E[(x

t`1)~p](1#g

t`1)~p

"¸(1#gt`1

)~p,

E[(ct`1

/ct)~px

t`1]"E[(x

t`1)1~p](1#g

t`1)~p"M(1#g

t`1)~p,

where ¸"E[(xt`1

)~p] and M"E[(xt`1

)1~p].Then, we can derive a relationship between the equity premium and the

growth rate as follows. From the first-order condition (B.2), we have

r"t`1

"[1/(bE[(ct`1

/ct)~p])!(1!n)]/(1!m

")!n

"[(1#gt`1

)p/(b¸)!(1!n)]/(1!m")!n. (B.6)

In addition, we have

E(r%t`1

)"E[xt`1

](1!q)(1!u)Atfk(k

t, l

tht)/(1!Z!Z

$)(1!j

")

#(n!d)/(1!j")!(r

"t#n)(1!q)j

"/(1!j

")!n.

Then the equity premium (ep) is given by

ep"E(r%t`1

)!r"t`1

"(1!q)(1!u)Atfk(k

t, l

tht)/(1!Z!Z

$)(1!j

")

#(n!d)/(1!j")!((1!q)j

"/(1!j

")#1)

][((1#g)p/b¸)!(1!n)]/(1!m"). (B.7)

Using the first-order conditions and market clearing conditions, we can alsoderive the following conditions:

(1#gt`1

)p"b[¸(1!dh)#M(1!t

h)A

tfh(1, h/k)B], (B.8)

(1#gt`1

)p"b[¸(1!t$d#(t

$!1)n)#M(1!t

k)A

tfk(1, h/k)]. (B.9)


Then the equation system of this economy is summarized by Eqs. (B.7)—(B.9).Given a stochastic process (L and M) and other parameters, the three equationsdetermine three endogenous variables (g, h/k and ep). In this model, therefore, thegrowth rate and the equity premium are affected by the tax, preference, techno-logy parameters and stochastic process of productivity shocks. In addition,equity can offer a substantially higher average rate of return than debt does.

The extended model can be used to calculate the effect of tax reforms on theequity premium and the growth rate. For this calculation, we assume that theunderlying stochastic process has a property that ¸("E[(x

t`1)~p]) and

M ("E[(xt`1

)1~p]) are invariant. Then we can calibrate the model to deter-mine the parameters including ¸, M and B, using the actual data on the growthrate and the equity premium. For example, in the US case, we can use g"1.5%and ep"2.6% based on the estimate of average equity premium reportedfor 1959—1979 in Mehra and Prescott (1985). Then ¸, M and B are determinedat ¸"1.03, M"0.69 and B"0.033. Within the calibrated model, the evalu-ation of the effect of tax reform is straightforward. For example, an exchangeof the US current tax system with the Korean tax system would increase theUS growth rate from 1.5% to 2.2% and the equity premium from 2.6%to 3.8%.

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