Who Bears the Burden of a Tax on Carbon by xfo14057


									          Who Bears the Burden of a Tax on Carbon Emissions in Japan?

                                     Don Fullerton

                                      Garth Heutel

                               Department of Economics

                             University of Texas at Austin

                                  Austin, TX, 78712

                                     February 2005

This paper is very preliminary and is not for quotation, but comments and suggestions are

welcome. We are grateful for financial assistance from Japan’s Economic and Social

Research Institute (ESRI).
       Much debate surrounds the proposed introduction in Japan of an "environmental

tax" on carbon emissions. A great deal of this debate centers on the question of who will

ultimately have to pay the costs of the tax and who will reap the benefits. While

estimates indicate that the average family will have to pay about 3000 Japanese Yen per

year due to the tax, some families will bear disproportionately high burdens. A careful

analysis of the proposed policy must contain a discussion of the incidence of the tax.

While the tax may be successful at its primary goal, to help Japan meet its obligations

under the Kyoto Protocols, it may carry some unintended and unwanted distributional

side effects. If the tax is too regressive, it may not be the most preferred policy choice to

reach the desired reduction in carbon emissions. Indeed, one of the four long-term

objectives of Japan’s Basic Environmental Plan is to ensure that all parties are

participants to environmental policy and share the burden fairly.

       Many papers, using both analytical models and numerical approximations, have

examined the incidence of various taxes. The paper that we choose to use as our starting

point is the quintessential analytical model of the incidence of a tax, the Harberger model

(Harberger 1962). This paper provides a simple two-sector, two-input general

equilibrium model that can be solved through linear algebra for evaluating how a tax on

one factor in one sector will affect the prices of both factors in both sectors. By

generating expressions for the change in the prices of labor and capital, it can be seen

how owners of those two factors will be burdened by the tax as it passes through the

economy via general equilibrium effects. The Harberger model is simple, which can be

both an advantage and a liability. It is easy to see how certain parameters, like factor

intensities and substitution elasticities, affect the results. However, a large number of
simplifying assumptions are employed, and these caveats may render any numerical

estimates unusable.

       In this paper, we solve for the incidence of the proposed Japanese environment

tax by applying an extension of the Harberger model. This extension has previously been

used to analyze a broad range of environmental taxes (Fullerton and Heutel 2004a) and

policies (Fullerton and Heutel 2004b) in the United States. We generate explicit

analytical expressions for the changes in the wage rate and the capital rental rate due to

the tax. Through these expressions, it can be seen how economic parameters will affect

who bears the burden of the tax. Then, we use the model to generate numerical estimates

of the size of these price changes. By utilizing a range of reasonable parameter values,

we can see how sensitive these estimates are to the assumptions in the model.

       Through our simple extension of the Harberger model to include pollution, we

develop a model that can be used to analyze the distributional effects of an environmental

tax. We then apply that model to a specific policy initiative. Many studies have modeled

and studied environmental taxation, but the main focus is usually on its efficiency, e.g.,

solving for the optimal pollution tax or determining how pollution taxes affect labor

supply. Fewer studies have considered the distributional effects of taxes, and most of

those that have do so using a numerical model rather than an analytical one. Robison

(1985) solves for the effect of policy on output prices, West and Williams (2002)

empirically estimate the distribution of burdens of a gasoline tax, and Metcalf (1999)

studies how the return of tax revenue affects the regressivity of a tax. Unlike those

papers, though, our paper contains a simple and interpretable analytical component. The

effects that can be quantified in a more detailed numerical analysis are here presented to

provide the intuition behind them.

        Our main analytical results concern how factor intensities and substitution

elasticities affect the incidence of the tax. Intuitively, we expect that if the taxed sector

(the “dirty” sector) is capital-intensive, then a pollution tax should hurt capital more than

labor. We find that this outcome is likely, but we give a condition under which it does

not hold. Likewise, intuition suggests that the factor which is a better substitute for

pollution will be hurt less than the other factor, but we find a condition under which this

intuition fails as well. Applying reasonable parameter values to the model, we find that

the burden of the environment tax in Japan is very likely to fall more on capital than on

labor. This is due to the fact that the heaviest emitting are capital-intensive, and it is in

spite of the fact that capital is likely to be a better substitute for emissions than labor.

        The next section briefly discusses the history of Japanese environmental policy

and the environment tax. In section two, we present the model and summarize some

analytical results. Section three provides numerical estimates of the distributional

impacts of the environment tax, and section four concludes.

I. Japanese Environmental Policy and the Environment Tax

        Founded to address ecological and environmental issues, the Japanese Ministry of

the Environment (MOE) was founded in 1971. The centerpiece of environmental

legislation in Japan in the Basic Environment Law, passed in 1993. Before this law was

passed, most Japanese environmental policies were based on two laws: the Basic Law for

Environmental Pollution (1967) and the Nature Conservation Law (1972). The Basic

Environment Law outlined the direction for Japanese environmental policy. Essential to

the Law is Article 15, the Basic Environment Plan (BEP), established on December 16,


           The BEP sets long-term objectives of Japan’s environmental policy. Forecasting

through the middle of the 21st century, it establishes objectives, sets out expectations for

local governments, corporations, citizens and private organizations, and specifies the role

of each party in meeting the goals. The BEP sets four long-term objectives: Sound

Material Cycle, Harmonious Coexistence, Participation, and International Activities. The

third of these long-term objectives, Participation, demonstrates the importance of

distributional issues to policy makers in Japan. In describing the purpose behind the

objective, the BEP reads: “Each sector of society, each party, must assume its fair share

of burden, according to the environmental load they generate, the benefits they enjoy and

the capability they have to contribute to environmental conservation. In so doing, it is

indispensable that all parties recognize they generate environmental load, either directly

or indirectly, through daily business activities or everyday living.”1 This wording, in the

introduction to a section describing one of the four main pillars of Japan’s major

environmental policy, explicitly states that distributional concerns are of utmost

importance. Demanding that each sector pay a “fair” share of the burden of

environmental policy is a resounding call for research such as the tax incidence analysis

presented here. Though we make no claim as to what allocation of the burden is “fair,”

we take an important first step towards that objective by solving for how the burden is

borne by different parties, including capital owners, laborers, and different types of

    Basic Environment Plan, Part III, Chapter 3, Basic Direction (Introduction)

        While the BEP remains the central piece of domestic environmental legislation,

another main policy focus is the Kyoto Protocol, the international agreement to reduce

global emissions of greenhouse gases. As the host country of the forum in which the

agreement was drafted, the Third Session of the Conference of the Parties to the United

Nations Framework Convention on Climate Change (COP3), in December 1997, the

MOE holds a desire to take the lead among countries in ensuring its implementation. A

main element of the Kyoto Protocol is the nation by nation goals in carbon emissions

reductions. Japan is required to reduce its carbon emissions 6% from its 1990 levels

between 2008 and 2012. However, emissions grew 17% from 1990 to 2001, meaning

that a reduction of 20% from 2001 levels is necessary to meet the Kyoto goal. While

Japan has demonstrated and declared commitment to the Kyoto Protocol, it remains a

major emitter. As of 2001, Japan was the world’s fourth largest energy consumer,

accounting for 5.4% of the world’s total, and 4.8% of the world’s energy-related carbon

emissions. Its pre-capita energy consumption, though, is lower than most G7 nations and

is about one-half that of the United States.2

        Emissions standards have long been a part of Japanese environmental policy and

were last amended in 1998. While SO2 emissions have steadily decreased since the

1960s, NOX levels have been stagnant. The effect of stricter environmental regulation is

being offset by the increased number of vehicle-miles being driven. In an effort to

strengthen regulation enough to meet the Kyoto standards, the Japanese government has

announced that it will levy a tax on carbon emissions, dubbed the “environment tax,”

starting in January 2006. The rate is to be 2400 Yen per one ton of carbon emissions.

 From US Energy Information Administration, available online at:

The Japanese people will have to pay a higher tax on gasoline, light oil, home oil,

electricity and gas. It is estimated that the average family will pay 3000 Yen annually,

yielding government revenue of 490 billion Yen. The majority of this revenue, 340

billion yen, is earmarked for use in emissions reducing programs, and the rest for

reducing the burden on businesses of paying social insurance.

        The implementation of the tax will not come without controversy. Many people

are complaining about the portion of revenue being used on the state’s pension system.

Much opposition also comes from business groups. At a September 17, 2004 news

conference, Akio Mimura, chairman of the Japan Iron and Steel Federation, warned that

the tax will force steelmakers to move their plants abroad, estimating that the steel

industry will have to pay an additional 150 billion yen per year. The Petroleum

Association of Japan accused the government of dumping its responsibility onto industry,

and Nippon Keidanren (Japanese Business Federation) advocates for voluntary

agreements to reduce greenhouse gas emissions.3 Japan’s Industry Minister and Finance

Minister have both been reluctant to support the measure, and Hiromitsu Ishi, chairman

of the government’s Tax Commission, has questioned whether or not the tax will even be

implemented. While the MOE supports the environment tax, claiming that it will reduce

carbon emissions by 4%, the Economy, Trade, and Industry Ministry opposes the tax. A

more lukewarm reaction was provided by an official at the Finance Ministry, who

suggested renaming it rather than rescinding it: “If the aim is to reduce greenhouse gases,

it shouldn’t be called a tax. It should be called a surcharge, for example.”4 The

  Welch and Hibiki (2003) point out that Japan offers the longest experiment on voluntary policy in the
world, Voluntary Pollution Prevention Agreements.
  Information on the environment tax is taken from articles in Japan Today, Asahi Shimbun and Yomiuri
Shimbun, available at: http://www.japantoday.com/e/?content=shukan&id=255,

responses to the tax listed above underscore the importance placed on distributional

issues in the BEP. Even if ensuring that all parties assume a “fair share of the burden” of

policy were not mandated by law, it appears that coming close to that may be necessary

to get the measure passed in political reality.

        While no study of the Japanese environment tax appears in the economics

literature,5 some analysis of Japanese environmental policies is available. Kochi et. al.

(2001) perform a cost-benefit analysis on Japan’s SO2 emissions control policy. They

conclude that the benefit-cost ratio has decreased from 5.39 (in 1968-1973) to 1.18

(1974-1983) to 0.41 (1984-1993), indicating that the policy has become less efficient

over time. As the policy was mainly one of command and control (CAC) regulations, the

authors interpret this finding as a tacit endorsement of using economical incentives such

as taxes. Popp (2004) examines the innovation and diffusion of pollution control

technologies across nations, focusing on Japan, Germany, and the United States. He

finds evidence that, in Japan, a tightening of environmental regulations led to increased

domestic innovation of abatement technologies. A number of case studies examine

specific Japanese policies or environmental problems. Welch and Hibiki (2003) analyze

the voluntary agreements of a Japanese city, Kita Kyushu. Hayami et. al. (2003) examine

international cooperation for clean development mechanisms (CDMs), particularly the

relationship between China and Japan for developing bio-coal briquette (biobriquette) to

replace coal. Yoshida et. al. (2003) study the itai-itai disease case, an infamous example

of cadmium poisoning at the Kamioka mine.

http://www.climateark.org/articles/reader.asp?linkid=35422, and
  Cansier and Krumm (1997) summarize a number of other environmental taxes in various nations,
including the SO2 tax in Japan introduced in 1974. Carbon taxes from other countries are discussed, and
the authors conclude that inefficiencies arise since not all CO2 units are taxed at the same rate.

II. Model

        The model presented here is identical to the one found in Fullerton and Heutel

(2004a). As in the original Harberger (1962) model of the incidence of the corporate

income tax, this economy consists of two sectors producing two different goods, X (the

“clean” good) and Y (the “dirty” good). The clean sector uses only capital and labor in

production while the dirty sector uses capital, labor, and pollution:

                                         X = X(KX, LX)

                                        Y = Y(KY, LY, Z)

In these two production functions, Ki and Li represent the capital and labor,

respectively, utilized by sector i. Pollution is denoted by Z and is modeled as an input

to production rather than as a joint byproduct. The production function could be

rewritten as the latter, so that both output and pollution appear on the left-hand side. We

keep pollution as an input to allow more freedom in producers’ ability to substitute

among capital, labor, and pollution.

        We assume that capital and labor are both fully employed, in fixed total quantity,

and perfectly mobile between sectors. That is,

                                         K X + KY = K

                                         L X + LY = L ,

where K and L are the fixed total amounts of capital and labor in the economy. We

totally differentiate the capital constraint to get:

                                     ˆ          ˆ
                                     K X λ KX + K Y λ KY = 0 ,                           (1)

where λ KX ≡          is the share of capital in the economy that is employed in sector X,

                                             ˆ     dK X
and λKY is defined analogously. The variable K X ≡                     represents the proportional

change in capital employed by the clean sector, and likewise for K Y . Applying the same

technique to the labor constraint yields:

                                        ˆ          ˆ
                                        L X λ LX + LY λ LY = 0 ,                                 (2)

with all variables defined analogously. Pollution is used only by the dirty sector and is

not in fixed supply, so no analogous pollution constraint equation is in the model.

       Firms in the both sectors face the same input prices for both capital and labor, r

and w, respectively. In the clean sector, the decision between those inputs can be

described by σX, the elasticity of substitution in production between capital and labor.

We define this parameter to be positive, and so that the following equation holds:

                                       ˆ     ˆ
                                       K X − LX = σ X (w − r ) .
                                                       ˆ ˆ                                       (3)

       ˆ     ˆ
Again, w and r are defined as proportional changes in the input prices. In the dirty

sector, the choice of inputs is more complicated since they choose among three inputs

rather than only two. While firms face no private price for pollution, they do have to pay

a specific tax on their emissions, τZ. We follow Mieszkowski (1972) in modeling this

choice of inputs. Details of this method are available in Fullerton and Heutel (2004a).

Two equations are needed to describe the dirty sector’s input choices; these are:

                    ˆ     ˆ
                    K Y − Z = (a KK − a ZK )r + (a KL − a ZL ) w + (a KZ − a ZZ )τˆZ ,
                                            ˆ                  ˆ                                 (4)

                    ˆ    ˆ
                    LY − Z = (a LK − a ZK )r + (a LL − a ZL ) w + (a LZ − a ZZ )τˆZ .
                                           ˆ                  ˆ                                  (5)

The aij variables represent input demand elasticities of input i with respect to the price

of input j. It is shown that these elasticities are equal to the Allen elasticities of

substitution, eij, times the share of factor j in total costs, θYj (Allen 1938).

         By assuming constant returns to scale production technologies and perfect

competition in both sectors, we get two zero profit conditions. We differentiate these,

along with the production functions themselves, and substitute in firms’ first order profit

maximizing conditions, to yield:

                                   ˆ         ˆ ˆ                ˆ ˆ
                             p X + X = θ XK (r + K X ) + θ XL ( w + L X )
                             ˆ                                                                    (6)

                           ˆ         ˆ ˆ                ˆ ˆ                     ˆ
                      pY + Y = θ YK (r + K Y ) + θ YL ( w + LY ) + θ YZ ( p Z + Z )
                      ˆ                                                   ˆ                       (7)

                                       ˆ        ˆ          ˆ
                                       X = θ XK K X + θ XL L X                                    (8)

                                     ˆ       ˆ          ˆ         ˆ
                                    Y = θ YK K Y + θ YL LY + θ YZ Z                               (9)

The theta variables represent an input’s factor share in that sector, so for example

         rK Y
θ YK ≡        . Finally, consumer utility can be modeled by an elasticity of substitution in
         pY Y

consumption σu. The relationship between output prices pX and pY and the quantity of

each final good demanded is

                                      ˆ ˆ
                                      X − Y = σ u ( pY − p X ) .
                                                    ˆ    ˆ                                       (10)

         The ten equations (1) through (10) represent all of the endogenous changes to

prices and quantities, in log-linearized terms, in the economy due to an exogenous change

in the pollution tax τZ. The system of equations has eleven unknowns, so it cannot be

solved without choice of a numeraire.6 We set p X = 0 , so that good X is numeraire,

 In Harberger (1962) the wage rate was chosen as numeraire. The same could be done here, or a number
of other choices for numeraire exist.

and all price changes are relative to this price. Since we will be primarily concerned with

the relative burden of the tax, this choice of numeraire will not inhibit our understanding

of the results.

        The solutions are expressed in terms of changes in prices, which are relative to the

numeraire. The main conclusions to be drawn from this are on which factor bears a

disproportionate burden of the tax.. For example, if we find that the wage rate falls and

the capital rental rate rises, this means that laborers bear a fraction of the tax which is

higher than their share in national income. It does not mean that capital owners are better

off; though the return on capital relative to the numeraire rises, in real terms this return

may still fall. Throughout the paper, we express our incidence results in nominal terms.

Our choice of numeraire implies that the change in the wage and the change in the rental

rate will always be of opposite sign (relative to the numeraire).7

        The general solutions to this system for the changes in the wage, the capital rental

rate, the price of the dirty good and the amount of pollution emitted are available in

Fullerton and Heutel (2004a). We omit them here due to their length and the difficulty in

interpretation. Instead, as in that previous paper, we focus on special cases to isolate

effects. In the first special case, we assume equal factor intensities. That is, we set LY/LX

= KY/KX. Under this condition we can isolate the effect of substitution elasticities.8 The

solutions for the endogenous price changes are:

                                              pY = θ YZτˆZ

  To see why, subtract equation (8) from equation (6), and set the change in the numeraire price equal to
  As Mieszkowski (1967) observes of the original Harberger (1962) model, no output effect exists when the
two sectors have equal factor intensities.

                                                  θ XK γ (a LZ − a KZ )τˆZ

                                                    θ XLγ (a KZ − aLZ )τˆZ

                                                                                   LY  K
where D1 ≡ σ X − θ XL γ (a KK − a LK ) − θ XK γ (a LL − a KL ) and γ ≡                = Y . The uses-
                                                                                   LX  KX

side incidence, which is given by the expression for pY , is unambiguous: the price of

the dirty good rises relative to the price of the clean good. Hence, consumers who spend

more than average on the dirty good bear a disproportionately high burden. On the

sources side, the sign of the changes in the factor prices is determined by the sign of aLZ

– aKZ. The sign of this term indicates whether capital or labor is a better substitute for

pollution. Suppose for now that D1 > 0. If aLZ > aKZ, then the wage rate increases and

the rental rate decreases after an increase in the pollution tax. The inequality aLZ > aKZ

means that when the price of pollution increases, the quantity demanded of labor

increases more than the quantity demanded of capital (see equations (4) and (5)). In other

words, labor is a better substitute for pollution than is capital.9 This results matches


           However, this result is reversed when D1 < 0. It can be shown that this

inequality holds under the following condition:

                                               − σ X + θ XL γa KK + θ XK γa LL
                                      e KL <                                   .
                                                  γ (θ XLθ YK + θ XK θ YL )

The right hand side of this inequality is negative definite. Therefore, D1 can be negative

only if eKL is negative. That is the definition of capital and labor being complementary

    Alternatively, the Allen elasticity eLZ > eKZ.

inputs. In fact, for D1 to be negative, it is not sufficient that capital and labor are

complements, they must be highly complementary, so that eKL is not just negative but

satisfies the inequality above. In this case, the factor that is a better substitute for

pollution is actually worse off after an increase in the pollution tax.

        The explanation for this surprising result is as follows. Suppose that capital and

labor are sufficiently complementary, and suppose that capital is a better substitute for

pollution. When the pollution tax is increased, firms in the dirty sector will demand more

capital and more labor, but their increase in demand for capital will be greater than their

increase in demand for labor. But since labor is a complement to capital, the increased

use of capital will increase their demand for labor. If this second effect dominates the

primary effect, then the amount of labor demanded will increase greater than the amount

of capital demanded. The price of labor in general equilibrium will rise relative the the

price of capital. Therefore, capital is hurt more than labor, even though it is a better

substitute for pollution.

        The second special case that we focus on eliminates any substitution effects and

focuses only on output effects, of effects caused by differential factor intensity. We drop

the assumption of equal factor intensity, but instead we assume that all of the Allen

elasticities of substitution for the dirty sector are equal to zero. This implies that aij = 0

for all i,j, or that firms in the dirty sector must use all three inputs in the same proportion,

regardless of any change in relative prices. Under this assumption, the solutions for the

effect of a change in the pollution tax on prices are:

                                             − Cσ X θ YZ
                                      pY =
                                      ˆ                  τˆZ

                                             (γ L − γ K )θ XK θ YZ σ u
                                        ˆ                              τˆZ

                                             (γ K − γ L )θ XLθ YZ σ u
                                        ˆ                             τˆZ

                                                                   KY        L
Here D2 = (γK – γL)σu(θXKθYL – θXLθYK) – CσX, γ K ≡                   , γ L ≡ Y , and C is a
                                                                   KX        LX

positive constant that is a function of model parameters.10 It can be shown that D2 must

be negative. On the uses side we reach the same result; the price of the dirty good

increases. On the sources side, which input bears a higher burden is determined by the

sign of γK – γL. The sign of this term indicates factor intensity; if it is positive then the

dirty sector is capital intensive. Then, according to the equations above, an increase in

the pollution tax will hurt capital disproportionately more than labor. The intuition is as

follows. An increase in the price for pollution would normally cause the dirty sector to

substitute into other inputs, but here that is impossible. All that the dirty sector can do is

to reduce demand for all inputs by the same proportion. If the dirty sector uses relatively

more capital than the clean sector, then their decreased demand for capital will weigh

more in general equilibrium than their decreased demand for labor, and the price of

capital will go down. This is a pure output effect since any possibility of substitution has

been assumed away.

III. Numerical Analyis

           Before attaching numbers to the parameters and using them to quantify the results

described above, we identify a number of weaknesses of the model. The assumptions

     C = θXKλKY/λKX + θXLλLY/λLX + 1.

that Harberger and we employ make the model much more tractable and interpretable,

but they come at a price. For example, allowing full employment and perfect mobility of

capital and labor is a more suitable assumption to make when considering a closed

economy or a large economy, where external macroeconomic variables have no impact

internally. This may be a good assumption for studying the corporate income tax in the

United States, but is unlikely to be appropriate for studying Japan’s economy, which is

smaller and entangled internationally. If capital is perfectly mobile internationally, and if

Japan is small, then a fixed world price for capital will hold, and capital will bear none of

the burden of the tax. Similarly, the no-profit condition implied by the assumption of

perfect competition may not be appropriate for polluting industries in Japan. If market

power is wielded by these industries, then key equations in this model will yield incorrect

results. However, as mentioned earlier, the model is an important first step towards a

more thorough analysis of the distributional impacts of the environment tax.


           To calibrate this model to the Japanese economy, we must first choose what

industries fall under the “dirty” category and what fall under the “clean” category.

According to the model, only dirty industries emit pollution, though more generally it can

be interpreted as only dirty industries must pay for the pollution they emit. That is, the

clean sector may still emit pollution, but if they have no price to pay for it, then their

production decisions on capital and labor input will still be accurately modeled by a two-

input production function. While the environment tax applies to most carbon emissions

from all industries11, we choose as the dirty sector the electricity, gas, and heat supply

industry and the chemical products industry. In the United States, these industries
     Some exceptions exist, like coal for power generation is exempted.

account for a significant portion of the total economy-wide carbon emissions. For this

reason, we choose these industries as our dirty sector. Since they emit the most carbon,

they will face the largest direct impact from the tax.

         Data on the employment of labor and capital sector-by-sector in Japan are

available for 1995 and 2000 from the Statistics Bureau of the Ministry of Internal Affairs

and Communication.12 These data include total labor compensation by each sector and

total “operating surplus,” which we use for capital employment. However, this value

represents corporate profits, and it may be sensitive to economic fluctuations and

imperfectly represent the true value of capital stock. To smooth this error, we use the

data from both 1995 and 2000, as well as the mean values of both years. Summary

statistics from these data appear in Table 1. A previous policy simulation using this

model applied to the U.S. economy sets the dirty sector equal to about 10% of the entire

economy;13 here the dirty sector represents only about 4% of the economy. The dirty

sector is relatively capital-intensive, consistent with previous simulations.14 From this

information, we can calibrate the factor intensity parameters θij and λij in the following

way. Normalize all initial input prices to one. Also suppose that the fraction of revenue

of the dirty industry that goes towards pollution taxes is 20%.15 Then, we use the

definitions of the factor intensity parameters to calculate their values. For example,

         rK X      rK X         KX
θ XK =        =            =          . These parameters are also presented in Table 1.
         p X X rK X + wL X   K X + LX

   See http://www.stat.go.jp/english/data/io/.
   Fullerton and Heutel (2004a). The dirty sector in that simulation consists of electric and gas utilities and
chemical industries.
   See Antweiler et. al. (2001, p. 879).
   As in previous studies, this parameter is somewhat arbitrarily set. It could be estimated from emissions
permit markets or by estimating shadow prices on emissions.

                                             Table 1.
                              Factor Intensity from Japanese Data
                                   (in million Yen, nominal)
                                   1995                  2000                             Average
          KY                     5293819               4711449                           5002634
          KX                    94412412              91812285                           93112349
          LY                     5255123               4974701                           5114912
          LX                    267905379             270614447                         269259913
                                  Factor Intensity Parameters
          λKY                           0.0530942                   0.0488113                  0.0509875
          λKX                           0.9469058                   0.9511887                  0.9490125
          λLY                           0.0192382                   0.0180511                  0.0186421
          λLX                           0.9807618                   0.9819489                  0.9813579
          θXK                            0.260579                   0.2533265                  0.2569522
          θXL                            0.739421                   0.7466735                  0.7430478
          θYK                           0.4014673                   0.3891287                  0.3955611
          θYL                           0.3985327                   0.4108713                  0.4044389

        We assign a value of unity to both σX, the elasticity of substitution in production

in the clean sector, and σu, the elasticity of substitution in consumption. Both of these

values are consistent with previous estimations and simulations.16 The last piece of

information needed for the numerical results is the set of values of the input demand

elasticities for the dirty sector, the aij parameters. While nine of these parameters appear

in the model, we know that, due to their relationship to the Allen elasticities, they are

fully determined by the factor share parameters and the six Allen elasticities.

Furthermore, we know that for any factor i, aiL + aiK + aiZ = 0 . These three equations

reduce the number of degrees of freedom to three. Therefore, all of the input demand

elasticities are determined by the three cross-price Allen elasticities eKL, eKZ, and eLZ.

Unfortunately, as far as we know these parameters have never been estimated, where the

  See Claro (2003) and Babiker et. al. (2003) for σX and Fullerton and Metcalf (2001) for σu. While these
parameters are estimated from or used in simulations of the U.S. economy, there is little reason to believe
them to be significantly different for the Japanese economy.

three inputs are capital, labor, and pollution. The closest analogy is the corresponding

elasticities where the inputs are capital, labor, and energy. DeMooij and Bovenberg

(1998) use values for these parameters that have been estimated in previous papers. The

values they use, which we apply for our base case, are eKL = 0.5, eKZ = 0.5, and eLZ =

0.3. In this base case, then, capital is a better substitute for pollution than is labor.

        The estimates of the Allen elasticities cited above suffer from two

misspecifications. First, as already mentioned, the third input is energy, not pollution. If

these two inputs were utilized with a fixed ratio, so that every unit of energy used

resulted in the same amount of emissions, then these elasticities would be identical. In

actuality producers have some freedom to alter their ratio of energy inputs to carbon

emissions. They may use different types of energy inputs, for instance cleaner burning

coal, or treat emissions before they are released, for instance using scrubbers. These

parameters provide the best available measures of the elasticities that we really want.

The second misspecification of the Allen elasticities is that they were estimated using

data from Western European countries, not Japan. While this clearly makes these

estimates imprecise, is there any reason to expect them to be biased? Labor markets are

more tightly regulated in Europe than in Japan, so firms in Europe may be less able to

substitute in to or out of labor when prices change, even with identical technologies to

Japan’s. In fact, this may partly account for the lower elasticity of labor with respect to

pollution than capital. In our simulations, we allow these elasticities to vary, to

accommodate the fact that they may be biased and provide only rough estimates of the

true values in Japan.


         Table 2 presents our numerical sensitivity analysis of the incidence results. The

policy experiment is modeled as a ten percent increase in the pollution tax.17 We

estimate the change in the wage and rental rate, relative to the price of the clean good, for

the three sets of factor intensity parameters and for a series of values for the Allen cross-

price elasticities. We hold constant the elasticities eKL and eKZ and allow the elasticity

eLZ to vary about its calibrated value of 0.3.

                                            Table 2.
                                       Numerical Analysis
                            Results of a 10% Pollution Tax Increase
                                              1995 factor intensities
       eLZ                   wˆ                ˆ
                                               r                  ˆ
                                                                  pY                             ˆ
        0                      0.0039%               -0.0110%               1.9971%               -3.9644%
       0.3                     0.0069%               -0.0197%               1.9949%               -5.1672%
       0.6                     0.0100%               -0.0284%               1.9926%               -6.3692%
                                                    2000 factor intensities
       eLZ                     ˆ
                               w                     ˆ
                                                     r                  ˆ
                                                                        pY                       ˆ
        0                      0.0033%               -0.0097%               1.9976%               -3.9058%
       0.3                     0.0061%               -0.0179%               1.9955%               -5.1453%
       0.6                     0.0089%               -0.0261%               1.9935%               -6.3841%
                                                  Average factor intensities
       eLZ                     ˆ
                               w                    ˆ
                                                    r                  ˆ
                                                                       pY                        ˆ
        0                      0.0036%               -0.0104%               1.9973%               -3.9364%
       0.3                     0.0065%               -0.0188%               1.9952%               -5.1567%
       0.6                     0.0094%               -0.0273%               1.9930%               -6.3764%

                                                        ˆ     ˆ
         Before turning to the incidence results in the w and r columns, consider the

two other columns. The results for pY , the proportional change in the price of the dirty

good, is about two percent in each calibration. This reflects the ten percent tax increase

on a factor which is 20 percent of a sector’s expenses (10% × 20% = 2%). In other words,
  This figure is somewhat arbitrary. The solution is linear in the tax increase, so any larger tax increase
will result in proportionally larger changes in all endogenous values. For example, a 20% tax increase
would double all of the values in table 2. However, the log-linearization method employed is appropriate
only for considering small changes in the tax rate.

the dirty sector is passing on the additional cost of production to consumers. On the uses

side, then, the incidence result is clear: consumers of the dirty industries’ goods are hurt

more than other consumers. The final column in the table, Z , presents the effect on

emissions from the tax. This value varies by quite a bit, and it is larger as eLZ is larger.

Because a larger value of this elasticity implies easier substitution for the dirty sector,

firms substitute out of pollution more, and hence emissions decrease. From the variation

in that elasticity from 0 to 0.6, a ten percent tax increase decreases pollution by anywhere

from four to seven percent. The Allen elasticity values are important not only for

incidence results, but also for gauging the policy’s impact on environmental quality.

        The main results involve the changes to the wage and rental rate brought about

by the environment tax. Under all nine scenarios, the wage increases and the rental rate

decreases, relative to the numeraire. According to this model, then, capital bears a larger

share of the burden of the tax. The variation in these tables only alters how much larger a

share capital bears. This reflects the dominance of the dirty sector’s capital intensity.

Whether or not labor is a better substitute for pollution than is capital, labor is better off

since it is used less intensively in the dirty sector. Labor is a better substitute than capital

only in the cases where eLZ = 0.6, since eKZ = 0.5 throughout. Even when the elasticity

of substitution between labor and pollution is zero (an increase in the price of pollution

does not increase demand for labor at all, and vice versa) labor is still better off.

        The variance in the substitution elasticity does matter in regards to the magnitude

of the burden of the tax that falls on each factor. As that elasticity increases, the increase

in the wage gets even higher, and the drop in the rental rate gets even lower. This

demonstrates the above-mentioned impact of factor substitutability on the incidence

results. As labor becomes a better substitute for pollution, firms can more easily

substitute away from pollution and into labor, and they do so. The dirty sector therefore

demands more labor as eLZ increases, and in general equilibrium its price increases to

meet this increased demand. Since in these simulations the substitution elasticity

between capital and pollution is fixed, the same effect does not show up in Table 2.

                                  ˆ     ˆ
       Finally, the values in the w and r columns are quite small; neither factor’s

price changes by more than three-hundredths of one percent. This is not to say that the

tax will be entirely meaningless. While these magnitudes suggest that the environment

tax will have only a negligible effect on the relative prices of capital and labor, some of

the simplifying assumptions may account for this fact. For example, we defined the dirty

sectors to only constitute about four percent of the entire economy. Pollution accounts

for twenty percent of their expenditure, and the tax rate is increasing by ten percent,

suggesting an impact on the order of one tenth of one percent (4% × 20% × 10% =

0.08%). In actuality, the environment tax will have an effect on nearly all sectors of the

economy, to different degrees. We chose only the two industries which are the highest

emitters and hence should face the largest burden. A more complex model could

incorporate more than two sectors. However, our simple model clearly demonstrates how

factor intensities and substitution elasticities impact the tax’s incidence. While the

magnitudes of the results may be inaccurate, we have provided support to the claim that

the environment tax will fall more harshly on capital than on labor.

IV. Conclusion

           We use a two-sector general equilibrium analytical model in the style of

Harberger to analyze the impact of the proposed Japanese “environment tax” on carbon

emissions. The analytical model shows that if the polluting sector is capital intensive, the

tax tends to fall more heavily on capital, and if capital is a better substitute for pollution

than is labor, the tax tends to fall more heavily on labor. In the case of the Japanese

economy, both of those conditions seem likely to hold. The effect from factor intensity

dominates, and in this model the environment tax hurts capital more than labor.

           As has been mentioned earlier, the model employed here is very simple. This is

advantageous for the intuitive analytical results that is provides, but it is disadvantageous

to the extent that it omits a number of features that may alter the result. Extending the

model to more than two sectors, and possibly creating a computable general equilibrium

(CGE) model may improve upon the results presented in Table 2. Like the original

Harberger (1962) model, this model can be significantly extended without abandoning

the two-sector framework. Extensions to the Harberger model have considered market

power, imperfect factor mobility between sectors, and open economies.18 For example, if

capital is perfectly mobile internationally, then the rental rate is fixed at that international

level, so the tax must be borne wholly by labor. Our model, while omitting many of

these features, is a first step towards analyzing the incidence of environmental taxation.

           Japanese business leaders as well as some Ministry officials have criticized the

environment tax, claiming it will hurt business profits. The evidence here may support

that view. The central piece of Japanese environmental legislation calls for all factors to

bear a “fair” share of the burden of environmental policy. Our results are not to be

interpreted as claiming that capital will be forced to bear an “unfair” share of the tax. It
     See McLure (1975) for a summary of these extensions.

may be the case that the “fair” burden on capital is indeed for it to be made relatively

worse off than labor; that judgment is not within the scope of this research. It is, however,

up to policy makers at some level to determine what these fair levels are, and this

research into tax incidence is necessary to making an informed decision.


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