OPTIMAL TARIFFS, OPTIMAL TAXES, ∗ AND ECONOMIC DEVELOPMENT Michael B. Loewy Department of Economics University of South Florida BSN3403 Tampa, FL 33620-5500 (813) 974-6532 fax: (813) 974-6510 e-mail: [email protected] May 2002

ABSTRACT Cross section and time series data show that nations substitute income taxes for tariffs as they develop. This paper confronts this observation within the context of a two-country open-economy endogenous growth model in which public expenditure is financed by an optimal tariff and income tax the second of which is subject to an administrative cost. Assuming, as Slemrod and Yitzhaki (1996) suggest, that the administrative cost per good collected is declining with the tax rate, the model predicts that an open economy will optimally substitute the income tax for the tariff as its level of output rises along the transition. In the steady state, the optimal tariff equals zero and the tax rate equals the government’s share of output. The model is calibrated and its transition is shown to yield time paths for the shares of total government revenue derived from the tariff and the income tax that are consistent with the data.

Key Words: Optimal Tariffs, Optimal Taxes, Growth JEL Classification: E62, F43, H21

∗

I thank participants at the 2002 Midwest Macroeconomics Conference for their comments. The usual disclaimer applies.

1.

Introduction

A generally accepted feature of economic development is that reliance on trade taxes declines while reliance on various forms of indirect taxation rises. Indeed, researchers have found both cross section and time series evidence supporting this relationship.1 Figures 1 and 2 provide examples of the former type of evidence. Figure 1 plots tariff revenue as a percentage of government revenue against gross national income per capita (in $1999) relative to that of the U.S. for a sample of 70 countries. For the same 70 countries, Figure 2 plots income, payroll, and goods and services tax revenue as a percentage of government revenue against the same measure of relative income. Figure 1: Tariff Revenue as a Percentage of Government Revenue

Figure 2: Income, Payroll, and G&S Tax Revenue as a Percentage of Government Revenue

80

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Percent

Percent

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10

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35

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GNI Per Capita Relative to US (%)

45

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GNI Per Capita Relative to US (%)

One explanation that is typically offered for developing countries’ greater reliance on tariffs is that in such economies the marginal administrative cost of income taxes is “high” compared to that of tariffs.2 Yet, because tariffs limit trade, many open-economy endogenous growth models predict that such economies can increase both their levels of income and their rates of growth by reducing their tariffs. Of course, by reducing their tariffs, developing economies must necessarily raise some other tax, typically

1

Examples of studies providing cross-section evidence include Mourmouras (1991), Burgess and Stern (1993), and Easterly and Rebelo (1993). Examples providing time-series evidence include Gardner and Kimborough (1989), Easterly and Rebelo (1993), Polley (2000), and Tanzi and Zee (2000). 2 This argument has been made in one form or another by Corden (1974), Gardner and Kimbrough (1989, 1992), Mourmouras (1991), Burgess and Stern (1993), Bearse, Glomm, and Janeba (2000), Polley (2000), and Tanzi and Zee (2000), among others.

2 an income tax, one that carries with it an administrative cost that is absent when tariffs are used. However, as Slemrod and Yitzhaki (1996) have noted, the average cost of operating most income tax systems declines as the tax rate rises. This suggests that as an economy develops, it may be optimal to substitute an income tax for a tariff. If so, and if the negative growth effects of an income tax are weaker than are those of a tariff, then these open-economy growth models imply that such an economy will ultimately see its steady-state rate of growth increase. That high-tariff/low-income countries often have low rates of growth while low-tariff/high-income countries often have high(er) rates of growth suggests that this may well be the case. The goal of this paper is to model explicitly the relationship between tariffs, income taxes, and development just described.

Thus, the paper seeks to formalize the administration-cost-of-taxation

argument for the inverse relationship between economic development and the reliance on tariffs, an argument which heretofore in the literature has typically been made only in passing. To this end, the paper offers a simple two-country, open-economy growth model in which tariff and income tax revenues are used to finance both government expenditures and the administrative cost of the income tax. The government is assumed to optimally choose both the tariff and income tax rate at each point in time. Since the average administrative cost of the income tax declines as both the tax rate and output rise, at low levels of income the government finds it optimal to rely on tariffs as a revenue source much more so than it does when the level of income is higher. In the limit, the tariff goes to zero  free trade obtains  while the income tax rate approaches government expenditure’s share of income. Despite the general absence of formal theorizing mentioned above, one notable example where it does occur is Polley (2000). In contrast to the approach taken here, Polley considers a static model and assumes that administrative costs take the form of an auditing cost. Such costs arise because private agents’ revenues are unobservable to the government in the absence of an audit. When the cost of auditing the income of producers is sufficiently greater than the cost of auditing the revenue of importers, Polley shows that the optimal tax system includes a both a positive tariff and a positive income tax rate.

3 Moreover, should producer income be sufficiently large or the marginal cost of auditing producer income be sufficiently small, the optimal tariff is shown to equal zero. While these results can be viewed as explaining the inverse relationship between tariff revenue and economic development, because Polley’s model is static and so only provides a link from income to optimal tariffs and taxes, perhaps they are only suggestive of it. Since the model developed in this paper is dynamic, it not only captures the link found in Polley’s paper, but also addresses the reverse linkage from optimal tariffs and tax rates back to income. In this sense, the present paper is not only a model of optimal tariffs and taxes, but one of economic development as well. The remainder of the paper is as follows. Section 2 lays out the open-economy endogenous growth model and the administrative cost function. Section 3 solves the household and the government’s problems and Section 4 describes the economy’s dynamics including its steady state. In Section 5, the model is calibrated to data contained in the World Development Indicators 2001 and the resultant time path for shares of government revenue derived from the tariff and the income tax are shown to capture features of the data seen in Figures 1 and 2. Section 6 summarizes and offers some concluding remarks.

2.

The Model

I consider a two-country, open-economy version of a discrete-time neoclassical growth model in which knowledge is a factor of production. Following Dollar et.al (1988), Rivera-Batiz and Romer (1991a, b), Grossman and Helpman (1991, 1995), and others, trade is assumed to serve as a conduit for knowledge flows. In the presence of international trade, these knowledge flows in turn serve as the source of growth of per capita output. To the extent that tariffs and income taxes can and do impact trade, the government’s optimal choice of these tax instruments determines not just the economy’s level of per capita income, but its rate of growth as well. Were trade to be absent, the model reduces to a neoclassical growth model in which the rate of technical progress corresponds to the now exogenous rate of knowledge accumulation.

4 In order to focus on the role of optimal tariffs and taxes on knowledge accumulation and hence on their impact on economic growth, in what follows physical capital is normalized to unity. In addition to this benefit, the normalization of physical capital also permits an analysis of both transitional dynamics and the steady state. By including physical capital, the former quickly becomes intractable although the latter is still possible.3 Given that the main line of investigation of this paper is on how the optimal choices of the tariff and income tax rate change as income rises, an ability to study transitional dynamics is key. Consider then a two-country world. In what follows, it is useful to think of one country as being “poor,” Country 1 say, and the other, Country 2, as being “rich.” For each country i = 1, 2, let good i be the distinct output of country i. Let the population in country i at time t be Li,t with Li,0 = 1. Population is taken to increase at the possibly distinct rates of ni. Assume further, for convenience, that the population and the labor force are the same in each country. The utility of agents in country i, Ui, is given by ∞

U i = Li ,0 ∑ β t (1 + ni )t α i1 ln ci1,t + α i 2 ln ci 2,t 

(1)

t =0

where cij,t is the real per capita consumption of good i in country j at time t, α i1 + α i 2 = 1 , and β is the common discount rate and is assumed to satisfy β(1 + ni) < 1 for i = 1, 2. Good i is produced using labor, physical capital (which recall is normalized to one), and knowledge. Assuming that the production function is constant returns to scale in physical capital and labor, write this relationship in per capita terms as yi ,t = H iε,ti

(2)

where yi,t and Hi,t are per capita output and the aggregate stock of knowledge in country i at time t, and εi > 0. As this specification makes clear, the rate of knowledge accumulation determines the rate of economic growth.

3

Ben-David and Loewy (1998) utilize the same normalization of capital and do so for the same reasons as here.

5 The government in country i raises revenue through a combination of a tariff on the imported good and an income tax. Letting τ ij ,t be country i’s tariff on good j at time t and σi,t be country i’s labor income tax rate at time t, it follows that country i’s time t budget constraint in per capita terms is given by cii ,t +

p j ,t (1 + τ ij ,t ) pi ,t

cij ,t = (1 − σ i ,t ) AH iε,ti

(3)

where pi ,t is the price of good i in terms of good 1, the numémaire good. In contrast to the approach found in many trade models, it is assumed here that government revenue is not returned to agents lump-sum. Instead, this revenue is used to finance both government expenditure and the administrative cost of operating the income tax.

With regard to government

expenditure, it is taken to be a fixed share, γi, of time t output. Turning to administrative costs, Yitzhaki (1979), Polinsky and Shavell (1982), Kaplow (1990), Mayshar (1991), and Slemrod and Yitzhaki (1996) suggest that such costs are likely to be an increasing function of the tax base and/or the tax rate. Additionally, Slemrod and Yitzhaki (1996) argue that a higher tax rate reduces the administrative cost per good collected. For present purposes, I assume that because tariffs can be applied “at the port,” they do not entail any administrative costs. Thus, only the income tax bears this cost.4 One specification that focuses on only the income tax and satisfies the criteria mentioned above is

particular, the administrative cost per good collected,

yiψ,t−1 1 + σ i ,t

σ i ,t ψ yi ,t where 0 < ψ < 1. In 1 + σ i ,t

, declines (for a given level of income) as

the tax rate increases.5 Combining the tariff and income tax revenue terms from the per capita budget constraint, eq. (3), with the expenditure and administrative costs terms described above, it follows that the time t per capita government budget constraint for country i is given by

4

Mourmouras (1991) makes a similar assumption. Along the same lines, Polley (2000) assumes that the marginal monitoring cost for imports is significantly less than that for domestically produced goods. 5 Although they speak in terms of tax evasion or corruption rather than administrative costs, the resultant effective marginal income tax rate described by Bearse, Glomm, and Janeba (2000) has properties similar to those seen here.

6

τ ij ,t p j ,t cij ,t pi ,t

+ σ i ,t yi ,t = γ i yi ,t +

σ i ,t ψ 6 yi ,t . 1 + σ i ,t

(4)

Growth in country i is derived from the accumulation of knowledge. Lucas (1988) suggests that knowledge accumulation in country i is constant returns to scale in country i’s level of knowledge. This idea is extended here inasmuch as I assume that knowledge accumulation in country i is constant returns to scale in the level of knowledge of both countries. However, the extent to which country j’s stock of knowledge is able to contribute to the growth of knowledge in country i depends upon (i) the extent to which country i can access country j’s knowledge stock and (ii) the extent to which country i can absorb and utilize the accessible part of country j’s knowledge. Following Grossman and Helpman (1991), the time t share of country j’s knowledge that is accessible to country i, what I denote as vij,t, is assumed to be an increasing function of the volume of trade between countries i and j. Specifically, vij ,t is taken to be the ratio of country i’s total trade with country j (bilateral imports plus bilateral exports) to country i’s aggregate output. Thus, vij ,t =

Li ,t

p j ,t pi ,t

cij ,t + L j ,t c ji ,t Li ,t yi ,t

.

(5)

Turning next to the question of applicability, let aij ,t , 0 ≤ aij ,t ≤ 1, be the time t share of country j’s accessible knowledge stock that country i is in fact able to utilize as part of its own knowledge stock.7 Following Ben-David and Loewy (2001), I assume that aij ,t depends upon the similarity of Hi,t and Hj,t. By “similarity” I mean that the more nearly equal are Hi,t and Hj,t, the more comparable (in terms of their levels of technology) are the two countries’ knowledge stocks (as opposed to being nearly identical sets of knowledge). Specifically, the more similar are the two countries’ knowledge stocks, the better position each is in to obtain knowledge spillovers from the other. 6

To see why this should be, suppose that Hi,t

Both eqs. (3) and (4) assume that the government does not issue debt. While this is clearly an oversimplification, data contained in Table 4.11 of the World Development Indicators 2001 show that in 1998 the world average for overall government budget deficit as a percentage of GDP was 1.5% while the world average for debt and interest payments as a percentage of GDP was 3.12%. By comparison, the 1998 world average for total government expenditure as a percentage of GDP was 27.9%. Thus, the assumption of budget balance, and hence of no government debt, is not unreasonable. 7 In a certain sense, aij,t captures Abramovitz’s (1986) concept of “social capability,” the ability of a country to utilize existing technologies.

7 greatly exceeds Hj,t. In such a case, presumably there is little in country j’s knowledge stock that is germane to country i. Conversely, if Hj,t greatly exceeds Hi,t, then the level of development in country i is sufficiently low that it will not possess the capability to utilize knowledge spillovers from country j. While this discussion implies that aij,t is maximized (at one) when Hi,t = Hj,t, it leaves open the question of whether aij,t exceeds or is less than aji,t when the two knowledge stocks differ. As one can reasonably argue that this inequality can run either way, I follow Ben-David and Loewy (2001) and set aij,t = aji,t always. Given this assumption, aij,t is defined as follows:

aij ,t

 H j ,t = A H  i ,t

  H µ   j ,t     H i ,t   =  −µ   H j ,t     H i ,t 

if 0
0 ,

 τ −2  1 ≥ λ1,t 1 − 12,t α12 − y1,ψt−1 (1 + σ 1,t )  ; = if σ 1,t > 0, 1 − σ 1,t  1 + τ12,t 

8

(9)

(10)

For similar set-ups see Heller and Shell (1974), Mayshar (1991), Dubravko (1992), Polley (2000), and especially Yitzhaki (1979).

9 where λ1,t is the Lagrange multiplier associated with the time t government budget constraint. Assuming, as will be the case in the calibration, that eqs. (9) and (10) both hold at equality, they can then be used to eliminate λ1,t. Therefore, an interior solution to the government’s problem must satisfy  τ12,t −2  α12 − y1,ψt−1 (1 + σ 1,t )  . 1 = (1 + τ12,t ) 1 −  1 + τ 12,t 

(11)

Combining eq. (11) with the government budget constraint, eq. (8), determines the optimal values of τ12,t * * and σ1,t, τ12, t and σ 1, t . As y1,t increases over time through the accumulation of knowledge, the optimal

* choices of σ 1,t* and τ12,t change in a manner consistent with the fact that the administrative cost of the

income tax per good collected falls not just as the tax rate rises (as Slemrod and Yitzhaki [1996] argue), but as Country 1’s income rises as well. Therefore, as its income increases, Country 1’s optimal tariff rate falls and its optimal income tax rate rises. To close the description of behavior at time t, it suffices to solve for the market clearing price, p2,t. Defining the private agent and government problems for Country 2 in a like fashion to those of Country 1 and assuming as Osang and Pereira (1996) as others do that trade is balanced, L1,t pt c12,t = L2,t c21,t , it follows that p2,t =

* α12 (1 − σ 1,* t ) L1,t y1,t (1 + τ12, t)

* α 21 (1 − σ 2,* t ) L2,t y2,t (1 + τ 21, t)

.

(12)

With p2,t being a function of the optimal tariffs and tax rates (which are themselves functions of the current stocks of knowledge), it follows that the optimal tariffs and tax rates affect the time t equilibrium quantities of imports and exports. Therefore, eqs. (5) and (7) imply that the stocks of knowledge for time t+1 are themselves determined. Specifically, H H1,t +1 = A  2,t  H1,t

*  2φα12 (1 − σ 1,t ) ⋅ H 2,t + (1 + φ − δ ) H1,t ,  ⋅ * 1 + τ12, t 

H H 2,t +1 = A  1,t  H 2,t

*  2φα 21 (1 − σ 2,t ) ⋅ ⋅ H1,t + (1 + φ − δ ) H 2,t .  * + τ 1 t 21, 

(13)

(14)

10 4.

Steady-State Analysis

Before illustrating the model’s transitional dynamics by means of a calibration, I first consider the model’s steady-state behavior. By definition, a steady state is such that both tariff rates and both income tax rates must equal constants and output in each country must grow at a constant rate. From eq. (11) it

(

)




follows that as t → ∞, 1 + τ ij* ,t − τ ij* ,tα ij − 1 + τ ij* ,t yi ,t

ψ −1

(1 + σ ) 

* i ,t

−2

= 1 where the hat signifies the steady 

state. Since output is rising at a constant rate, the only solution to this expression is τ ij*,t = 0 . Therefore, the steady state exhibits free trade.9 Turning to the limiting version of the government budget constraint, 

σ i*,t



eq. (4), dividing both sides by yi,t and letting t → ∞ implies that σ i*,t = γ i +



1 + σ i*,t



yi ,t

ψ −1

. The only



solution to this expression is σ i*,t = γ i so that in the steady state the optimal income tax rate equals the share of government expenditure in output. Next, consider the steady-state rate of growth of knowledge and therefore of output in each country. From eqs. (13) and (14), steady-state growth is governed by the system   H   1+φ −δ A  2,t  ⋅ 2φα12 (1 − γ 1 ) H   H1,t +1     H1,t   1,t   =  .   H 2,t +1    H1,t    H 2,t   ⋅ 2φα 21 (1 − γ 2 ) 1+φ −δ  A    H 2,t   









(15)







As shown in Ben-David and Loewy (1998), the steady-state growth rate of knowledge equals the



maximum eigenvalue of eq. (15) minus one while the steady-state ratio of knowledge stocks, H1,t H 2,t , corresponds to the ratio of elements of the associated eigenvector. After a bit of algebra, the steady-state rate of growth of knowledge, ρ H , can be shown to equal

9

Results in Polley (2000) are suggestive of a similar result.

11  H1,t φ −δ + H  2,t


µ

 .5  ⋅ 2φ α12α 21 (1 − γ 1 )(1 − γ 2 )  

(16)




where it is assumed without loss of generality that H1,t H 2,t is less than one.10 From eqs. (2) and (16), the steady-state rate of growth of per capita output in country i is seen to

(

equal to ρ yi = 1 + ρ H 



)

εi

− 1 . Consequently, if both countries possess the same income elasticities of

knowledge, their levels of per capita output in the steady state will grow at the same rate. It need not be the case that these levels be equal, however. In general they will differ as long as α12 ≠ α 21 and/or

γ1 ≠ γ 2 . 



the

eigenvector

associated

with

implies

that

v   α (1 − γ 1 )  =  12  =  12  . This in turn implies that if there is a common value of ε, then steadyv   α 21 (1 − γ 2 )   21  .5



H1,t

1 + ρH 

Specifically, .5



H 2,t



state relative income satisfies

y1,t

y2,t

.5ε

 α (1 − γ 1 )  =  12  . Consequently, the country with the smaller share of  α 21 (1 − γ 2 ) 

government expenditure in output and/or the larger share of imports in after-tax income will achieve the higher level of steady-state income. Be that as it may, in the calibration that follows, per capita income will converge in the steady state since the on-going rise in y1,t y2,t along the transition will ultimately imply that α12 = α 21 and γ 1 = γ 2 .

5.

Calibration

To illustrate the behavior of the model along the transition to and in the steady state, I consider a simulation in which the behavior of the model’s parameters are, whenever possible, drawn from data in the World Development Indicators 2001. For the purposes of the calibration, I use the following four income groups as defined by the World Bank: Low Income; Lower Middle Income; Upper Middle

ρ H unchanged.

10

If not, then the ratio of knowledge stocks must be taken to the −µ power. This, of course, leaves the value of

12 Income; and High Income. The ranges of 2000 Gross National Income per capita that define these groups, their average income levels, and the number of countries per group appear in Table 1. Table 1: World Bank Income Groups Low Income Lower Middle Income Upper Middle Income High Income Income Range ≤ $755 ≥ $9266 $756 − $2995 $2996 − $9265 Average Income $420 $1140 $4620 $27,510 Number of Countries 63 54 38 52

In the simulation, I let Country 1 be the “poor” economy and Country 2 be the “rich” economy. To this end, I classify Country 2 as High Income and allow the classification of Country 1 to vary as its income relative to Country 2 rises along the transition. Since all the data used to calibrate the model are from 1999 (except shares of government revenue which are for 1998), I use figures found in Table 1.1 of the WDI 2001 to set the initial incomes of both countries. Specifically, the initial income of Country 1, y1,0, is assumed to equal the average income level of the Low Income group in 1999, $420, while the initial income of Country 2, y2,0, is assumed to equal the average income level of the High Income group in 1999, $26,440. With income group classifications only available in 2000-dollar figures, I use these to determine when Country 1 switches income groups. Specifically, when Country 1’s per capita income rises to 2.7% of Country 2 ($756/$27510), it is reclassified as Lower Middle Income.

Similarly, Country 1 is

reclassified as Upper Middle Income when its income is 10.9% ($2996/$27,510) of Country 2 and then as High Income when its income reaches 33.7% ($9266/$27,510) of Country 2. Turning to the composition of demand in each of the four income groups, here I use data contained in Table 4.9 of the World Development Indicators 2001 to calibrate values for α12, α21, γ1, and

γ2. Since the model assumes that private consumption takes the form of domestically produced goods, cii, and imported goods, cij, that there exists government consumption, and that investment (both private and public) is absent, the WDI data must be adjusted to account for these features.

13 Before making these adjustments, Table 2 provides the needed data drawn from WDI 2001 Table 4.9 for 1999. In the Table, G/Y, I/Y, and M/Y represent the shares of output allocated to government consumption, investment, and imports.11 Table 2: WDI Data on Structure of Demand (% of GDP)

G/Y I/Y M/Y

Low Income Lower Middle Income Upper Middle Income High Income 0.11 0.14 0.15 0.16 0.22 0.26 0.22 0.22 0.26 0.28 0.25 0.21

To calibrate each αij I calculate αii and then subtract that value from one. The steps to derive αii are as follows. First, determine the share of GDP going to the consumption of domestically produced goods, CD/Y. As the WDI provides data on the shares of GDP allocated to government consumption, investment, and imports, this entails subtracting these shares from one: CD / Y = 1 − G / Y − I / Y − M / Y . Second, adjust this value for the absence of investment in the model by dividing by the share of output that is not invested, 1 − I / Y . The resulting value, (1 − G / Y − I / Y − M / Y ) (1 − I / Y ) , is the empirical counterpart to cii / yi = α ii (1 − γ i ) . Last, calculate 1 − γ i as 1 − (G / Y ) (1 − I / Y ) and divide. After some algebra, the resulting expression implies that

α ij = 1 −

CD Y CD Y

+

M Y

.

(17)

Table 3 provides the computed values for αii, αij, and γi for each of the four World Bank Income Groups. Reported values for the High Income group will be used to parameterize Country 2 while those for the Low Income group will be used to initially parameterize Country 1 with the remaining three sets of values to be used as Country 1 grows along the transition path.

11

As one would expect, the data in row 1 of Table 2 are consistent with “Wagner’s Law,” namely that G/Y increases with per capita income. Among the many sources where this behavior is documented is Easterly and Rebelo (1993) who find evidence for it in both their time series and cross-section data sets. See, for example, their Figure 2.

14 Table 3: Calibrated Spending Parameters

αii αij γi

Low Income Lower Middle Income Upper Middle Income High Income 0.533 0.634 0.662 0.612 0.388 0.467 0.338 0.366 0.141 0.189 0.2 0.205

To complete the specification of the model, it remains to assign values to ε , φ , δ , ψ and µ as well as determine the economy’s initial values, H1,0 and H2,0 To determine the first three parameters, I assume that the initial rate of growth of per capita output in Country 2 equals 1.6% which is the average value of same for the High Income group between 1990 and 1999. Hence, (1 + φ − δ ) = 1.016 . Next, I utilize the ε

result that the model implies income convergence in the long run since eventually Country 1 enters the High Income group. I set this common steady-state rate of per capita income growth equal to 2.2%, the average rate of per capita growth of the United States during the 1990s.12 From eq. (16) we then have that ε

1 + φ − δ + 2φα 21 (1 − γ 2 ) = 1.022


where convergence implies that H1,t = H 2,t . As these two restrictions cannot determine independently all three parameters in question, I set ε = 0.3, its value in Ben-David and Loewy (1998, 2001), and then solve for the remaining two. The resulting values are found to be φ = 0.0389 and δ = 0.0155. Note further that given the value of ε, the initial values of the two knowledge stocks are found by inverting eq. (2) and substituting in the initial values of per capita income. To calibrate ψ, I require that at t = 0 the model match the 1998 share of tariff revenue in total government revenue of the World Bank’s South Asia group. I use the South Asia group rather than the Low Income group since (i) there does not exist any government revenue data for the Low Income group (see WDI 2001 Table 4.13) and (ii) the 1999 per capita incomes of the two groups are roughly equal, $440 vs. $420. Within the model, this ratio corresponds to

12

The data used to calculate these two rates of growth are found in Tables 4.1 and 2.1 of the World Development Indicators 2001.

15

θ1,0 =

* * * τ 12,0 α12 (1 − σ 1,0 ) (1 + τ12,0 )

* * * * σ 1,0 + τ12,0 α12 (1 − σ 1,0 ) (1 + τ12,0 )

.

(18)

WDI 2001 Table 4.13 provides 1998 data on the shares of total government revenue derived from five types of taxes plus nontax revenue.13 To obtain an empirical counterpart to θ1,0, suppose, as was argued above, that total government revenue equals total government spending. Next, since nontax revenue does not derive from sources that can be reasonably construed as types of “income taxes,” the estimate of θ1,0 must be adjusted to account for this. Hence, the empirical counterpart to eq. (18) is the ratio of taxes on international trade to the sum of taxes on income, profits, and capital gains plus social security taxes plus taxes on goods and services plus taxes on international trade plus other taxes. From WDI 2001 Table 4.13 it follows that θ1,0 = 0.257 .14 Given this value and the initial values for α12, γ1, and * * y1,0, eqs. (10), (4), and (18) can be solved for τ12,0 , σ 1,0 , and ψ . Doing so yields ψ = 0.59.

It remains to calibrate µ. To do so, I assume that the initial growth rate of Country 1 is 5%. This value represents a reasonable estimate of the growth experiences of countries that have liberalized trade during the past half-century. Substituting for A (⋅) in eq. (13), setting t = 0, and dividing both sides by 1/ ε y1,0 = H1,0 implies that µ solves the following:

(1.05)

1/ ε

* 2φα12 (1 − σ 1,0 )  y1,0 =  * 1 + τ 12,0  y2,0

  

( µ −1) / ε

+1+φ −δ .

(19)

Substituting for the other parameters and the initial income levels implies that µ = 0.8816. Therefore, the share of accessible Country 2 knowledge that Country 1 can utilize increases quite slowly. Table 4 summarizes the remainder of the calibration exercise.

13

The five types of taxes are (i) taxes on income, profits, and capital gains; (ii) social security taxes; (iii) taxes on goods and services; (iv) taxes on international trade; and (v) other taxes. 14 Burgess and Stern (1993, Table 5) provide 1989 data on tax revenue by type as a percentage of total taxes for a group of developing countries. Likewise, Tanzi and Zee (2000, Table 2) provide 1995-7 data on tax revenue by type as a percentage of GDP for a different group of developing countries. Making comparable calculations of θ1,0 using these two data sets implies estimates of 0.264 (Burgess and Stern) and 0.206 (Tanzi and Zee). Given the differences in group composition and time periods covered across these two estimates as well as the one I report using WDI data, it appears that these various estimates of θ1,0 are quite consistent with one another.

16 Table 4: Remaining Calibrated Parameters

φ δ ε ψ µ 0.0389 0.0155 0.3 0.59 0.8816

Figure 3 shows the behavior of the optimal tariff and income tax rates along the transition to the steady state. Figure 4 shows the rates of growth for both countries while Figures 5 and 6 plot for Country 1 the share of tariff revenue and income tax revenue in government expenditure versus per capita income relative to that of Country 2. Given the initial values of per capita income for the two countries, y1,0 = 420 * * * = 0.125, σ 1,0 = 0.111, τ 21,0 = 0.016, and and y2.0 = 26440, and the calibration of ψ, it follows that τ12,0

* σ 2,0 = 0.203 . Note that consistent with the discussion in Section 4, Country 2’s high initial level of per

capita income implies that its optimal tariff and income tax rate are nearly equal to their steady-state values of 0 and 0.205. Hence, as Figure 3 suggests, Country 2 raises almost all of its government revenue through the income tax. On the other hand, Country 1 initially raises roughly 25% of its revenue through the tariff and the latter declines (although not monotonically) as Country 1 develops. Figure 3: Tariff and Income Tax Rates

Figure 4: Rates of Growth

0.25

6

0.2

5

0.15

4

0.1

3

0.05

2

0

1 0

20

40

60

80

100

120

140

160

180

Period Tau_12

Sigma_1

200

0

20

40

60

80

100

120

140

Period Tau_21

Sigma_2

Country 1

Country 2

160

180

200

17

Figure 6: Income Tax Revenue as Share of Government Expenditure

Figure 5: Tariff Revenue as Share of Government Expenditure 100 30 95

25

90

Percent

Percent

20

15

85

10

80

5

75

0

70

1.59

5.07

11.74

19.84

30.74

y_1 as a Percentage of y_2

43.77

1.59

5.07

11.74

19.84

30.74

43.77

y_1 as a Percentage of y_2

As shown in Figure 4, Country 1 initially grows at 5% while Country 2 grows at 1.6%. Naturally, this enables Country 1’s income to rise relative to Country 2. By period 18, this ratio exceeds 2.7% so that Country 1 enters the Lower Middle Income group. In so doing, its share of after-tax income spent on imported goods rises sharply as does its share of output going to the public sector. Given the rise in government spending, both the tariff rate and the income tax rate increase with τ12 rising from 8.6% to 9% and σ1 jumping from 12.1% to 16.5% (see Figure 3). Although both of these increases are growth reducing, the rise in imports is strongly growth enhancing and so Country 1’s rate of growth increases on net rising from 4.45% to 4.81%. Despite the rise in Country 1’s relative income, this value continues to be sufficiently small that knowledge spillovers from Country 1 to Country 2 are negligible. Hence, Country 2 continues to grow at the autarky rate of 1.6% (see Figure 4). As Figure 5 illustrates, Country 1’s greater reliance on the income tax implies that its share of government revenue derived from tariffs,

θ1,t, drops from 18.3% to 16.3%. Country 1 remains in the Lower Middle Income group until period 75 at which time its relative income surpasses 10.9% and it enters the Upper Middle Income group. Although the size of Country 1’s public sector once again rises, its income level is now sufficiently high that its optimal tariff rate drops from 3.3% to 2.6%. As expected, this necessitates an increase in the income tax rate from 18% to 19.6%

18 (see Figure 3). Since the Upper Middle Income group devotes a smaller share of after-tax income to imports than does the Lower Middle Income group, Figure 4 shows Country 1’s rate of growth dropping from 3.57% to 3.11%. Once again, given the relatively slow rate at which accessible knowledge spills over from one country to another, Country 2 continues growing at roughly 1.6%. Finally, the rise in Country 1’s tax rate coupled with the drop in its tariff rate reduces θ1,t from 6.4% to 3.7% (see Figure 5). Country 1’s declining rate of growth coupled with the slow rate of knowledge spillovers implies that it is not until period 170 that Country 1 enters the High Income group. At this point, it is identical to Country 2 save for its income level and hence its optimal tariff and tax rate. Since this switch once again entails a decline in α12 coupled with a (slight) increase in γ1, Figure 3 shows that Country 1 again experiences a slight downward jump in its tariff rate, from 0.89% to 0.83%, along with a slight upward jump in its income tax rate, from 19.9% to 20.4%. Both of these values are nearly indistinguishable from those of Country 2.

Since Country 1’s import sector now falls, Figure 4 shows that its rate of growth

drops from 2.59% to 2.51%. There is also a slight decline in the share of government revenue derived from the tariff, from 1.3% to 1.1%. Were the simulation to continue beyond period 200, we would observe Country 1’s relative income continuing to rise albeit slowly. Eventually however, as this ratio increases, eq. (6) implies that both countries will begin to experience ever greater knowledge spillovers. In particular, these spillovers ultimately cause Country 2’s rate of growth to increase. In the limit, incomes and growth rates converge










and, as shown in Section 4, σ 1,* t = σ 2,* t = γ 2 = 0.205 , τ1,* t = τ 2,* t = 0 , and H1,t H 2,t = 1 . From eq. (16) it follows that the steady-state rate of growth of knowledge in each country equals 7.5%. This in turn implies that the steady-state rate of growth of output equals 2.2%. Since this value exceeds the autarky rate of 1.6%, it follows that both countries benefit from Country 1 opening up to trade. Empirically, the keys results of the calibration are shown in Figures 5 and 6. The first figure shows that the model is consistent with the data plotted in Figure 1, namely that countries reduce their reliance on tariffs as they develop. In particular, the hyperbolic trend line in Figure 1 is quantitatively

19 quite similar to what is found in Figure 5. The same similarity holds for Figures 2 and 6.15, 16 Given these two sets of figures, the model provides theoretical justification not just for the long-held argument that the high administrative costs associated with income taxes can explain the relatively high reliance on tariffs found among the poorer nations of the world, but also to the beneficial growth effects that emanate from trade liberalization.

6.

Conclusion

Both cross section and time series data suggest that as their level of income rises, nations find it optimal to substitute income taxes for tariffs. A common explanation for this behavior is that revenue sources such as income taxes are subject to administrative costs that for low-income countries are prohibitively high at the margin. To the extent that the administrative cost of the income tax per good collected declines with increases in both the income tax rate and per capita income, then developing nations ought to find it optimal to substitute an income tax for tariffs as their level of income rises. Furthermore, to the extent that this optimal substitution of an income tax for a tariff is growth enhancing, poorer nations who open up their economy’s to trade will begin to grow faster and thereby strengthen these growth benefits by hastening the rate at which they do in fact reduce their reliance on tariffs. To these ends, the paper considers a two-country endogenous growth model in which growth is driven by knowledge accumulation that in turn depends upon the tariff rate and income tax rate of both countries. These two sets of rates are taken to be the solutions to a pair of optimal taxation problems where each government must raise sufficient revenue to cover both its expenditures and the administrative costs of the income tax. In addition to considering the model’s steady state, a calibration of the model using data contained in the World Development Indicators 2001 is used to analyze the model’s 15

That the trend line in Figure 2 is quantitatively less than what appears in Figure 6 reflects the absence of other taxes and nontax revenue in Figure 2. In particular, the latter is quite large for many low-income countries with an average value of 19% for the World Bank’s South Asia group (see WDI 2001 Table 4.13). 16 Formally speaking, Figures 1 and 2 plot cross-section data while Figures 5 and 6 effectively plot time series data. However, as Mourmouras (1991), Easterly and Rebelo (1993), and Polley (2000) report, both types of data yield the same substitution of income taxes for tariffs as per capita income rises.

20 transitional dynamics. The calibration produces a time path for the share of government revenues derived from the tariff that closely matches what is found in the data. An interesting extension of this model would be to include physical capital as a non-trivial input in production. Among other things, this would provide private agents with an intertemporal decision not present in this model and so allow the model to match another aspect of the data, investment’s share of output. Such an extension comes at some cost however since the government’s problem now becomes intertemporal as well and so such brings with it issues of time consistency.

21 References

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