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Green Tax Reforms and Computational Economics: A Do-it-yourself Approach Christoph Böhringer1, Wolfgang Wiegard2, Collin Starkweather3, Anna Ruocco4 1

Centre for European Economic Research (ZEW), Mannheim, Germany (E-mail: [email protected]) Department of Economics, University of Regensburg, Regensburg, Germany 3 Department of Economics, University of Colorado, Boulder, USA 4 Presso Centro Studi della Confindustria, Rome, Italy 2

Abstract The double or even triple dividend hypothesis of green tax reforms has been a major issue of dispute in both the scientific community and the political arena during the last decade. Theoretical analysis has provided a number of important qualitative insights to the debate but lacks of actual policy relevance due to very restrictive assumptions. Applied research that takes the step from stylized analytical to complex numerical models usually comes as a blackbox to non-expert modelers. This paper aims at bridging the gap between stylized theoretical work and numerical analysis. We develop a flexible, interactive simulation model which is accessible under Users can specify their own green tax reforms and evaluate the induced economic and environmental effects. Based on illustrative simulations, we demonstrate the usefulness of our do-it-yourself approach for a better understanding of the double (triple) dividend hypothesis. Keywords:

Green Tax Reforms, Computable General Equilibrium Models, Optimal Taxation, Teaching of Economics

JEL Code:

A23, C64, H21

Acknowledgements: We are grateful to Tim Hoffmann for valuable technical assistance and Andreas Pfeiff for editorial support. We would also like to thank an anonymous referee for valuable comments.



Green tax reforms continue to rank high on the political agenda of many OECD countries and have figured prominently in economic research during the last decade. As green taxes raise revenues which can be used to reduce existing tax distortions, they can present an opportunity to earn a double (or even triple) dividend (Pearce 1991 or Repetto 1992). They not only improve the environment - the first dividend. They may also contribute to a reduction of the overall excess burden of the tax system - the second dividend - and may help to alleviate the unemployment problem - the third dividend. The potential effects of green tax reforms have been investigated in a large number of theoretical and applied papers (for surveys see Goulder 1995 and Bovenberg 1999). The theoretical literature casts doubts on the existence of a second or third dividend from environmental taxation. Based on simple analytical general equilibrium models, it is shown that the costs of introducing green taxes are in general higher than the benefits from the revenue-neutral cut of existing taxes on income or final demand (Bovenberg and van der Ploeg 1993a/b, Bovenberg and de Mooij 1994a/b). Although, theoretical analysis provides important qualitative insights, its contribution to actual policy analysis remains limited. The reason is that theoretical models are highly stylized to keep analytical tractability. As soon as certain real-world complexities are taken into account, e.g. a more detailed production structure, analytical solutions are no longer available and numerical solutions methods are required. In this context, a second class of papers uses computable general equilibrium (CGE) models to evaluate the possibilities of multiple dividends of green tax reforms (see Majocchi 1996 for a survey). These models incorporate lots of details and come up with precise numbers on the economic and environmental effects of introducing or changing green taxes. The computational approach to the analysis of green tax reforms, however, has also shortcomings of its own. In general, scientific publications neither include a complete listing of the algebraic model underlying the numerical simulation nor of the data used to calibrate model parameters. Even if the model algebra and the data were fully laid out, replication of results requires specialized programming skills. As a consequence, CGE analyses often come as a black box to non-expert readers. Our paper aims at bridging the gap between stylized theoretical work and the numerical approach to economic policy analysis. We present a simple do-it-yourself CGE simulation model which allows for an interactive analysis of the economic and environmental effects induced by green tax reforms. The reader can access our interactive model under the web address On this site, we provide instructions on how to specify green tax reforms through a user-friendly interface (see Appendix I for a non-technical tutorial and Appendix II for a programmer's guide to the web-based model interface GAMS-X). Our simulation model then calculates the corresponding equilibria and quantifies the effects that the specified tax reforms have on the excess burden of the tax system, employment, energy 2

consumption, and other key variables. The user-friendly interface allows for a systematic sensitivity analysis of circumstances under which a second and/or third dividend might occur. Without requiring programming expert knowledge, our model is well suited for graduate students and professionals to develop and strengthen their economic intuition on key economic mechanisms involved in the impact analysis of green tax reforms. In addition, it provides a good starting point for those readers that want to pick up on computational economics for doing applied policy analysis. Our small-scale model – written in the easily comprehensible GAMS programming language (see for more information) – can be downloaded in the source code from the Internet. After a quick introduction to the basics of GAMS (see our quick tutorial provided at, it is then straightforward to extend our model to concrete needs such as additional production sectors, several household types, more tax details, etc. The remainder of this paper is organized as follows. Section II briefly lays out the policy background to green tax reforms. Sections III and IV serve to explain the theoretical model and its numerical specification. Section V presents some comparative-static results regarding the economic and environmental impacts of green tax reforms. Section VI concludes.



The debate on green tax reforms has addressed the question of whether the trade-off between environmental benefits and gross economic costs of environmental taxes (i.e. the costs disregarding environmental benefits) prevails in economies where distortionary taxes finance public spending. Unlike policy instruments such as regulations and non-auctioned tradable emission permits, green taxes raise public revenues which can be used to reduce existing tax distortions. Revenue recycling may provide prospects for a double or even triple dividend from green tax reforms. The first dividend refers to an improvement in environmental quality. The second dividend is associated with an a reduction in the overall excess burden of the tax system by using additional tax revenues for a revenue-neutral cut of existing distortionary taxes. The reasoning behind the second dividend is straightforward: Financing of public expenditure by distortionary taxes imposes an efficiency loss on the economy, i.e. the marginal cost of public funds (MCF) will be greater than one for each unit raised (Pigou 1947). Environmentally related taxation also carries a tax burden and it is the interaction between this burden and other distortionary taxes in the economy that determines whether or not a second dividend can be realized. If - at the margin - the excess burden of the environmental tax is smaller than that of the replaced (decreased) existing tax, public financing becomes more efficient and welfare 3

gains will occur. Rules of thumbs to exploit initial inefficiencies in the course of a green tax reform include (i) the burden of the environmental tax should fall on factors whose initial taxation is associated with a relatively low marginal excess burden, (ii) additional revenues should be recycled to cut down taxes with a high marginal excess burden, and (iii) the tax base of the environmental tax should be large and subject to low demand and supply elasticities. The third dividend relates to the possibility that green tax reforms could generate employment gains through cuts in labor costs. In practice, most governments that have introduced environmentally related taxes have reduced distortionary labor taxes, particularly employers' social security contributions (OECD 2001). If the double (triple) dividend hypothesis holds, this implies a "no-regret" strategy for policy makers: Even for negligible environmental benefits, a swap of environmental taxes for other taxes is desirable as overall economic welfare (in non-environmental efficiency terms) is increased. The theoretical literature remains rather skeptical on the double (triple) dividend hypothesis (Goulder 1995 and Bovenberg 1999). Based on simple analytical general equilibrium models it is shown that swapping environmental taxes for broad-based income or value-added taxes makes the mechanism for financing public expenditures less efficient. Environmental taxes not only induce distortions on markets for dirty intermediate or final goods but cause additional distortions similar to those of the replaced taxes. Due to a narrow tax base and the application to intermediate goods (see Diamond and Mirrlees 1971 on the production efficiency theorem), the costs of environmental taxes are in general higher than the benefits from a revenue-neutral cut of existing broad-based taxes on income or final consumption. However, the theoretical models are typically far tool special and restrictive to allow for any generalized conclusions. Applied studies based on numerical models accommodate a more comprehensive representation of initial tax distortions and additional market distortions such as wage rigidities. The incorporation of real-world complexities may significantly increase the prospects for a double dividend. In fact, the evidence from simulation studies is mixed reflecting country-specific differences in the representation of complex real-world market distortions as well as uncertainties regarding core elasticities (Majocchi 1996). The major shortcoming to published numerical analyses is a wide-spread lack in transparency and reproducibility. As a rule, and often due to space constraints in scientific journals, there is neither a complete listing of the theoretical model underlying the numerical simulation nor of the data used to calibrate model parameters. Even if the data and model code were fully available, readers would find it difficult to test their economic intuition on the results without expert programming knowledge. Against this background, our paper accommodates a non-technical access to applied policy analysis. We develop and numerically specify a simple general equilibrium model which is used to assess the impacts of green tax reforms. Our illustrative simulations deal with three key questions associated with the levying and recycling of green taxes: What is the 4

environmental effectiveness? Is there a second or a third dividend, i. e. does the green tax reform contribute to reduce excess burdens of the tax system and does it alleviate unemployment? We perform sensitivity analysis of results with respect to changes in the tax reform design and alternative macroeconomic hypothesis. The reader can then take advantage of the user-friendly model interface and study a huge number of additional tax reform measures to deepen its economic understanding.


The Theoretical Model

An appropriate analysis of the effects induced by green tax reforms requires the careful specification of several key model elements: different energy tax rates in the private and production sectors must be jointly represented with other initial tax distortions; the phenomenon of unemployment needs to be endogenously explained; finally, alternative possibilities of the use of the energy tax revenue have to be taken into consideration and incorporated within the model.

1. Household Sector In our model, E H denotes the use of energy in the household sector and EY the use of energy for the production of the household's non-energy consumption good YH . For simplification, we assume a representative household which demands – besides energy E H – the non-energy consumption good YH , leisure l and a free public good G. The utility associated with the consumption of these goods is captured by the function u (YH , EH , l , G ) , where all first partial derivatives are positive.

Environmental damages associated with emissions from overall consumption of energy ( E H + EY ) are represented by means of the v( E H + EY ) with v' < 0 . For simplicity, we assume a linear relationship between energy use and emissions. Furthermore, utility from consumption and dis-utility from environmental damages are assumed to be separable. Additive linking of the functions u(⋅) and v(⋅) then results in the utility U of the representative household: (1)

U = u (YH , EH , l , G ) + v ( EH + EY ) .

Taking the budget constraint (2)

pY YH + pE EH + w (1 − τ w ) l = w (1 − τ w ) T + r (1 − τ KR ) K + B


into account, the household chooses the quantities YH , E H and l in order to maximize its utility U. The consumer prices for the goods YH and E H are denoted by pY and pE, w is the wage rate, τw denotes the labor income tax rate, τ KR is the tax rate on capital income (where the superscript index R indicates capital taxation according to the “residence principle”) and r indicates the interest rate. T and K are given exogenously in our static model and denote the endowment with time and capital, respectively. ( T – F) = LS is then the labor supply. The household receives additional income B from transfers which are explained below. We assume that consumers neglect the contribution of their individual energy consumption to the overall energy consumption ( E H + EY ) since the representative household is considered as an aggregate of many identical households. Together with the additivity property of the utility function, this assumption ensures that the overall energy consumption of the economy leaves the household decisions unaffected. The solution to the household’s optimization problem generates demand functions for YH and E H as well as leisure demand l (i. e. also the labor supply function), each depending on consumer prices and household income from capital endowment r (1 − τ KR )K and transfers B: (3 a – c)



YH = YH pY , pE , w (1 − τ w ) , r (1 − τ KR ) K , B ;

EH = EH ( ⋅) ;

l = l (⋅) .

The provision of the public good is kept constant (see equation 15) and, therefore, need not be included as an argument of the demand function.

2. Production Sector We distinguish three sectors on the production side of the economy. The consumer goods industry produces the non-energy consumption good with inputs capital (KY), labor (LY) and energy (EY), subject to the following linear-homogenous production function: (4)

Y = f Y ( KY , LY , EY ).

Linear-homogenous production functions also apply for domestic energy production E and the production of the public good: (5)

E = f E ( K E , LE )


G = f G ( KG , LG ).

Within our model, we allow for the taxation of all factors. The tax rate on the use of energy in the consumer goods sector is represented by τ EY ; labor and capital may get taxed at sectorally uniform rates τ L and τ KS , where the index “S” stands for “source principle” of capital taxation. Under perfect competition on all goods markets, the economic rent is zero and the zero-profit condition for each of the three production sectors is: 6


qY Y = w(1 + τ L ) LY + r (1 + τ KS ) KY + q E (1 + τ EY ) E Y


q E E = w(1 + τ L ) LE + r (1 + τ KS ) K E


qG G = w(1 + τ L ) LG + r (1 + τ KS ) KG .

Here, qY, qE and qG denote the producer prices. Cost-minimization generates the following factor demand functions:


(10 a - c)

LY = LY w(1 + τ L ), r (1 + τ KS ), q E (1 + τ EY ), Y

(11 a - b)

LE = LE w(1 + τ L ), r (1 + τ KS ), E

(12 a - b)

LG = LG w(1 + τ L ), r (1 + τ KS ), G


KY = KY ( ⋅) ;



K E = K E (⋅) ,



KG = KG (⋅) .

EY = E Y ( ⋅) ,

The relationships between producer and consumer prices for energy and the non-energy consumption good are given by: (13 a - b)

pY = (1 + τ C ) qY ;



pE = (1 + τ C ) 1 + τ EH q E

where τ C represents a uniform consumption tax rate and τ EH the tax on energy consumption by private households. The tax base of the consumption tax, thus, includes the energy tax.


Public Sector

In a static model, current expenditure and tax revenues of the public sector have to be equal. The budget equation is: (14)

qG G + B =


τ C éë qY YH + qE (1 + τ EH ) EH ùû + τ w w T − l


+ τ L w(LY + LE + LG ) + τ KS r (K Y + K E + K G ) + τ KR rK + τ EH q E E H + τ EY q E EY . The left-hand side of this equation shows the expenditure for the provision of public goods and the transfers to households. The terms on the right-hand side correspond to the government revenues from the general consumption tax, the labor income tax, payroll taxes, the capital income tax (according to the source or the residence principle), as well as from the tax on the energy consumption of private households and on the use of energy for the


production of consumer goods. Finally, for simplicity we assume that the public good is provided at a constant quantity: (15)

G = G.

4. Market Equilibrium Conditions The formulation of the market equilibrium conditions depends on the foreign closure of the model (closed economy versus small open economy) and the specification of the labor market (full employment versus unemployment). Below, the associated four different variants will be discussed. Our paper puts emphasis on the basic understanding of economic mechanisms. By comparing the four different model variants, the dependence of results on the models’ structural assumptions becomes clear. Table 1 summarizes the key settings for the model variants. Table 1:

Classification of model variants Full Employment (FE)

Unemployment (UE)

Closed Economy (CE)



Small Open Economy (SOE)



In the following sections, we will discuss the market equilibrium conditions for the different model specifications.

a) CE-FE The market equilibrium for the closed economy with full employment is determined by the following set of equations: (16)

Y = YH


E = E H + EY 8


K = KY + K E + KG


( L ≡) T − l = L S


+ LE + LG ( ≡ L )

In equation (19) LS denotes the labor supply and L the aggregate labor demand. According to Walras’ Law, we can drop one of the market equilibrium conditions and fix one price as a numeraire. We ignore the capital market equilibrium condition (18) and set the interest rate r equal to 1.

b) SOE-FE For the small open economy, we assume that capital is mobile across domestic borders and that energy can be traded internationally while the consumer goods X can not. With respect to taxation of energy consumption, the destination principle applies. Equations (17) and (18) must then be replaced by the following balance of payments condition: (20)

q E ( E − E H − EY ) + r ( K − KY − K E − KG ) = 0.

The first term on the left-hand side concerns the trade balance and the second term summarizes the capital income flows between the domestic economy and abroad, which are reported in the balance of services. In equilibrium, the trade deficit (trade surplus) must equal the inflow (outflow) of capital income. Full employment is still characterized by equation (19). In the small open economy, the prices of traded goods and factors, i.e. qE and r, are exogenously determined on the world markets. Note that equation (20) is automatically fulfilled as a consequence of Walras’ Law.

c) CE-UE and SOE-UE One stated policy objective of green tax reforms is the reduction of unemployment. In both of our unemployment model variants (indicated by the suffix “-UE”), we will investigate the impact of the green tax reform on the level of unemployment. We introduce unemployment through the specification of a “wage curve”, which postulates a negative relationship between the real wage rate and the rate of unemployment:

w = g(ur ) P

with g ′ < 0 ,


where P denotes a consumer goods price index (21)

P = P ( pY , pE )

and ur ( ≡ (LS − L ) / LS ) is the unemployment rate. This type of wage curve can be derived from trade union wage models, as well as from efficiency wage models (see e. g. Hutton and Ruocco 1999). Figure 1 illustrates the wage curve in the traditional labor market diagram (rather than in the ur − w / P − space). The real wage rate w/P is measured on the vertical axis and the labor supplied and demanded are measured on the horizontal axis. Figure 1:

Wage curve and unemployment

real wage wage curve

labor unemployment

Full employment occurs with the real wage rate of (w/P)0 at the intersection of the (inverse) labor demand function L and the labor supply function LS. The wage curve now replaces the labor supply curve. Consequently, the equilibrium wage rate (w/P)1 lies above the market 1 1 clearing wage rate. This causes unemployment at an amount of (LS ) − (L ) . 10

Taking taxes and unemployment benefits into account, the wage curve can be specified stating a negative relationship between the unemployment rate ur and the net wage rate: wρ = g (ur , B ) P 1−τ w . where: ρ ≡ 1+τ L

with g ′ < 0 ,

The expression (1 − ρ ) then indicates the tax wedge between the employers’ gross wage costs and the employees’ net wages.

Instead of equation (19), the following equilibrium condition for the labor market then applies in the model variants with unemployment: (22)

L = LS (1 − ur ) .

With unemployment, we interpret the transfers to the private household sector which enter their budget equation as unemployment benefits. Following Koskela and Schöb (1999), the employment effects of a green tax reform depend crucially on the form of these transfer payments. Here we assume that the unemployment benefit payments Br are constant in real terms and are not taxed. The relationship between nominal and real unemployment benefits is given by: (23)

B = PBr LS ur .

With these assumptions, we obtain a simple specification of the wage curve as a log-linear function (Hutton and Ruocco, 1999, p. 273): (24)

æ wö logç ÷ = γ 0 + γ 1 log(ur ) − log ρ è Pø

where γ0 is a positive scale parameter and γ1 < 0 indicates the elasticity of the real wage with respect to the unemployment rate. Real unemployment benefits are included in the parameter γ0. If the household gets rationed on the labor market, the budget restriction changes in so far as the actual net wage income is determined by w(1 − τ w )L and no longer by w (1 − τ w ) T − l . Determination of welfare effects is also based on enforced (rather than voluntary) leisure consumption. The details of welfare measurement for rationed goods can be found in Johansson (1987, chapter 5). In our model variants with full employment, we also assume transfers in real terms. These, however, are constant and do not vary with the rate of unemployment. Equation (23) simply becomes:





B = PBr .

For the sake of transparency, let us summarize at the end of this section which variants of the model are specified through which equations, and which variables are to be determined endogenously. All variants of the model have 18 equations and 18 endogenous variables in common. These are equations (3a-c), (4), (5), (6), (10a-c), (11a-b), (12a-b), (13a-b), (14), (15), (21), and variables YH, EH, l, Y, E, G, LY, KY, EY, LE, KE, LG, KG, pY, pE, pG, P as well as the endogenous equal-yield tax rate, for example τw. Table 2 provides an overview of the additional equations and variables that are model-specific. Table 2:

Model-specific equations and variables






(16), (17), (19), (25)

(16), (17), (22), (23), (24)

qY, qE, w, B

qY, qE, w, ur, B

(19), (25)

(22), (23), (24)

w, B

w, ur, B

Numerical Model Specifications

Analytically, the economic and environmental implications of a green tax reform can be studied in a comparative-static framework. For example, one could derive the total differentials of the market equilibrium conditions and solve this system of equations for the relative changes in the variables of interest. This is the normal procedure employed in the theoretical literature (see e.g. Bovenberg and de Mooij 1994a/b or Schneider 1997). Although our model is a radical simplification of the real economy, it is still so complicated that an analytical solution would not deliver any results for a sound economic interpretation. Simulation analyses on a numerical basis provide an alternative. For this type of analysis, we must first specify the concrete functional forms for the utility function and the cost functions, 12

and fix the values of the model parameters as well as of the exogenous variables. A specific data set then corresponds to a specific benchmark equilibrium. Within the policy simulations single parameters or exogenous variables are changed and a new (counterfactual) equilibrium is computed. Comparison of the counterfactual and the benchmark equilibrium then provides information on the policy-induced changes of economic variables such as employment, production, consumption, relative prices, etc. We assume that the same benchmark equilibrium underlies all of our four model variants. In principle, one could construct such a benchmark equilibrium from the national accounts and other statistics (such as input-output tables) for a selected benchmark year. In this paper, we are not interested in the techniques of harmonizing observed data from different sources to yield a consistent benchmark data set. Our main objective is to strengthen the economic intuition on key mechanisms associated with the implementation of green tax reforms. For this purpose, it is sufficient to employ stylized data as provided by Table 3. By definition, the benchmark equilibrium must correspond to the numerical solution for each model variant. Based on the benchmark data, we determine parameters of functional forms for each variant, so that the quantities and prices of the benchmark equilibrium are replicated with these parameters as the numerical solution of the respective model variant. In the literature, this procedure is called calibration (see e.g. Mansur and Whalley, 1984). Typically, the number of all model parameters is larger than the number of model equations, and we will have to fix the remaining "free" parameters (e. g. elasticities of substitution across inputs in production). Table 3 describes our benchmark equilibrium in terms of a social accounting matrix (King 1985). The upper section presents the benchmark prices and tax rates, the lower section reports the benchmark quantities, labor income tax revenues and transfers. For the sake of transparency, we have indicated the equation references (see section III) for the market equilibrium conditions associated with the rows (market clearance) and columns (zero profit for production sectors, income balance for household and government). In general, data consistency of a social accounting matrix requires that the sums of each of the rows and columns equal zero. Note that the benchmark equilibrium given in Table 3 is the same for all four variants of the model developed in section III. This means that there is no trade at the benchmark for the small open economy. Exports and imports of capital and goods will then only be induced when tax reform measures are undertaken. In the model variant with unemployment, the value at the intersection of the "L"-row and the "Household"-column indicates rationed labor supply (see equation (24)).


Table 3:

Prices and quantities in the benchmark equilibrium Prices qY = qE = r = w = 1.0

Tax Rates τ C = τ L = τ = τ = τ EH = τ EY = 0; τ w = 0.333 R K


Social Accounting Matrix



– 25





– 15




Eq.-No. CE-FE












– 27






– 16














The utility and production functions have yet to be specified. In principle, there is the choice among various functional form. In the standard literature, the functional forms employed belong to the type of constant-elasticity-of-substitution (CES) functions. Such functions have certain mathematical properties (regularity) that ease the numerical analysis considerably, but are still flexible enough to allow for the appropriate representation of economic behavior. Table 4 summarizes our concrete choices of CES functions. Utility is given as a CES composite which combines leisure with an aggregate consumption good. At the bottom level, we aggregate the consumption of the goods X and EH to an aggregate consumption good C, which is then combined with leisure demand F at the top 14

level. The resulting utility function is weakly separable in goods YH and EH, and leisure l. Both “utility branches” are represented by CES functions. The parameters πC and πU correspond to the substitution elasticities between YH and EH, and between C and F, respectively; in illustrative terms, these elasticities indicate the curvature of the indifference curve in the YH -EH space as well as in the C-l-space. The parameters βC and βl are called share parameters. Because the provision of the public good is assumed to be constant, it can be omitted from the utility function u(⋅) without loss of relevant information. The equation for the consumer price index follows from the underlying CES utility function over YH and EH. Also, we employ CES-functions to characterize production. In the production of the nonenergy consumption good, capital and labor are combined at the bottom level to yield valueadded Q (KY, LY), whereas at the top level value-added Q and intermediate energy EY are combined to yield output Y. The substitution elasticities are represented here with σ, and the share parameters with α, where the indices in subscript refer to the production sector. The concrete form of the environmental damage function has no empirical foundation and is simply specified in such a way that the implied marginal damage function (-v´) is linear and exhibits a positive gradient. Finally, we provide the wage curve which has already been stated in equation (24). In addition to the functional forms, the above mentioned “free” parameters, as well as the values for the exogenous variables of the model, must be carefully determined. On the one hand, the CES functions turn into a Cobb-Douglas specification for certain parameter values (this applies to πC = 1 or σ = 1, for example), which will alter the concrete algebraic formulation. On the other hand, certain parameter combinations may not lead to solutions at all, or deliver solutions which do not make sense from an economic point of view. The values for parameters or exogenous variables, specified in the last row and column of Table 4, were selected so that the benchmark equilibrium in Table 3 exhibits economically meaningful characteristics. One example would be that the labor supply elasticity with respect to the real wage rate takes on a plausible value. Another example for the reasonable choice of values would be that the economy in the benchmark equilibrium is on the rising branch of the Laffer-curve. Note that the “free” parameter values for all four model variants are identical, but the remaining parameters for each model variant are calibrated so that the numerical solution of the model replicates the benchmark equilibrium shown in Table 3.


Table 4:

Functional forms and values for the free parameters

Functional Form Utility Function u ( C (YH , EH ) , l )



1/ π C

C = é βY1/Hπ C YH + 1 − β YH êë where Ω C = (π C − 1) / π C ΩC

1/ π u

u = é β C1/ π u C Ωu + (1 − β C ) ë where Ωu = (π u − 1) / π u

Consumer goods price index P ( pY , pE )

Production function E = f E ( K E , LE ) G = f G ( K G , LG )


EHΩC ù úû

1/ Ωu

l Ωu ù û


1/ σ E


1/ σ G

where θ E = (σ E − 1) / σ E G = α G1 / σ G K Gθ G + (1 − α G )

where θ G = (σ G − 1) / σ G



1/θ E

σ E = 0.8



σ G = 0.98


1/ θG



Y = α Y1 / σ Y QθY + (1 − α Y )




1/ σ Q

where θ Q = (σ Q − 1)/ σ Q 1/ σ Y

1/ θQ

Environmental damage γ v = A − E2 function v ( E ) 2

Exogenous variable

π u = 0.884 (calibrated)


K Y Q + (1 − α Q )

1/ σ Q

where θ Y = (σ Y − 1) / σ Y

wθ = g (ur ) P

π C = 11 .



E = α 1E/ σ E K Eθ E + (1 − α E )


Wage curve

1/ ΩC

P = éë βYH pY1−π C + 1 − β YH p1E−π C ùû 1−π C

Q = αQ

Y = f Y (Q( K , L), EY )

Parameter Values

æ wö logç ÷ = γ 0 + γ 1 log(ur ) − log θ è Pø

σ Q = 0.68 1 / θY

σ Y = 0.7 A = 10, γ = 01 .

γ 1 = 0.5

K = 16; G = 8; T = 47.5 (calibrated - full employment case)

T = 52.5 (calibrated - unemployment case with initial ur = 0.1)



Simulation Results and Economic Interpretation

1. First, Second and Third Dividend of a Green Tax Reform In this section, we will discuss our simulation results. Given the simple generic structure of the model and its parameterization with stylized data, the meaning of the exact numerical values should not be overemphasized. Our primary goal is to draw qualitative conclusions based on the numerical results. We will see that some findings are rather surprising. This is precisely the advantage of our simulation model: through comparative-static exercises we gain insights that could hardly be derived by analytical manipulations, no matter how tricky they might be. We restrict the presentation and interpretation of results to certain tax reforms for the model variants CE-FE and CE-UE (closed economy with full employment and closed economy with unemployment). The other model variants - SOE-FE and SOE-UE - could be analyzed parallel to this. It is also possible to investigate further tax reform packages for each of these model variants. We will leave this up to the interested reader as do-it-yourself exercise with the interactive model. It should be the primary goal of a green tax reform to achieve positive environmental effects, e.g. via the reduction of harmful emissions from fossil fuel combustion. The induced change in environmental quality is referred to as the first dividend (D1) of a green tax reform. In addition to that, many protagonists of green tax reform hope for a “better”. i.e. more efficient tax system due to the swap of green taxes for existing distorting taxes. The literature denotes this as second dividend (D2) or gross welfare gains neglecting environmental benefits. Finally, employment gains might be achieved if the tax revenue is used to reduce the tax burden on labor. In the case of positive employment effects, a green tax would then yield a third dividend (D3). Based on our simulation model, one can identify under which conditions one or more of these dividends will occur. Measurement of the dividends is easiest with respect to the employment effects. In this context, we simply calculate the third dividend as the percentage points change in the employment rate. For example, a reduction of the unemployment rate from 10 per cent in the benchmark equilibrium ( ur = 0.1) to 8 per cent ( ur = 0.08) due to a green tax reform, would deliver the value “-2.000” for D3 (unemployment is reduced by 2 percentage points). Similarly, a value of “1.500” for D3 would imply an increase in unemployment by 1.5 percentage points. The second dividend captures changes in the costs of raising public revenues. In the public finance literature, these costs are referred to as the so-called excess burden measuring the efficiency properties of the existing tax system. With revenue-neutral tax reforms the change 17

in the excess burden of the tax system corresponds to the induced income change (in units of the numéraire good) for the representative consumer. The second dividend is positive if it improves the income situation. The concrete measurement of the first dividend is problematic. Energy taxation should reduce energy consumption and, thus, harmful emissions. For simplicity, we have assumed a constant relationship between pollutants and energy consumption. The first dividend could then be defined as the percentage change of the overall energy consumption of domestic households and production. This setting reflects the prevailing public focus in the policy debate on concrete emission reduction targets. We will speak of D1(P) when having this interpretation of the first dividend in mind, where P stands for a percentage reduction in quantity. A value of “-10.000” would indicate a 10 percent reduction of the domestic energy consumption. The reduction of harmful emissions, which is closely connected to the reduction of energy consumption, is not an end in itself. After all, there is an optimal environmental pollution and further reductions of harmful emissions would result in a decrease of overall welfare. What really matters, then, are the concrete welfare effects of a change in harmful emissions. Due to the lack of exact empirical information on damage functions and the valuation of environmental damages, welfare effects can hardly be determined empirically. We have assumed a simple - and admittedly somewhat arbitrary - environmental damage function v( E H + EY ) to indicate that welfare effects - and not quantity effects - matter. The first dividend, measured by the welfare effects of the environmental policy, is characterized by the notation D1(W), where W is the abbreviation for welfare. Note that D1(W) and D1(P) are connected via a monotonic transformation. The change in aggregate welfare ∆U j of the representative household can be calculated as the sum of D2 and D1:


0 0 æ u j − u0 æ v j − v0 0 u ö 0 v ö ∆U = ç INC INC ÷+ç ÷. u0 U 0 ø è v0 U0 ø è"" " """! """ """ ! D2 D1 j

The index j represents the counterfactual equilibrium after the tax reform, and the index 0 indicates the benchmark equilibrium. U 0 is the benchmark utility which equals the sum of utility u 0 from full consumption and the associated environmental damage v 0 . INC 0 is the benchmark income:




INC 0 = w0 (1 − τ w0 ) T + r 0 1 − τ KR K + B 0 . 0

D2 denotes the change in gross economic efficiency disregarding environmental quality and refers to the traditional public finance aspect of tax reforms. For the model variants with 18

unemployment, we quantify employment impacts as the change D3 in the unemployment rate. The separate accounting of changes in gross efficiency (D1), environmental quality (D2) and employment (D3) allows to determine whether D1, D2 and D3 evolve in the same direction or whether they constitute conflicting targets.


Model simulations

Our simulation model is accessible under, where the interested reader will find a detailed instruction as well. Before we investigate the implications of green tax reforms, the reader should be aware of some fundamental restrictions with respect to numerical policy analysis. One never knows if the concrete results are correct. It must be assumed, of course, that the numerical solution algorithm works properly, but a wrong model - i.e. wrongly specified with respect to the underlying economics - may have been solved. A small programming error (that can easily creep in) is enough to cause such a dilemma. One may relax this problem, however, in the following way: as an initial consistency check, those policy measures should be simulated first, where the qualitative results are already known based on rigorous theoretical analysis. If the simulation model produces different results, one must assume that it is mis-specified. Otherwise, one can proceed with the analysis of reform packages, where results are open in theory. Yet, one can still not be sure that the numerical solutions are “correct”. Therefore it is very important that all numerical results are convincingly explained in economic terms. a)

Consistency Tests

In this section, we check the consistency of our model by means of tax reform scenarios whose effects are theoretically unambiguous. Best for this purpose are the model variants with full employment (CE-FE, SOE-FE) since the economic intuition is straightforward. Our first test entails a tax reform where the labor income tax is supplemented with a payroll tax in a revenue-neutral way. The simulation results reveal that the equilibrium values for all quantitative variables remain unchanged. From the theory of tax incidence we know that it is irrelevant for the equilibrium values who actually pays the tax. What matters is who bears the tax burden. As long as the tax wedge θ on the labor market remains unchanged, it makes no difference if the tax is levied on households or producers. Secondly, we replace the initial labor income tax by a tax on the domestic capital stock (i.e. the associated capital income) or - alternatively - by a uniform consumption tax. From a theoretical point of view, the results are obvious. The taxation of labor income induces distortions on the labor market. These can be completely avoided by switching to the taxation of domestic capital income. As the domestic capital endowment is fixed in our static model, a 19

capital income tax works as a lump-sum tax; in other words, capital income taxes are firstbest when we only consider the welfare component D2. Since the distortions on the labor market are reduced, employment, disposable income, consumption and overall production rise. As a consequence, the production of energy also rises resulting in an increase of pollutants, i.e. a positive D1(P), and a decrease of environmental quality, i.e. a negative D1(W). Furthermore, the theory of optimal taxation suggests that a general consumption tax is second-best in the case of homothetic and weakly separable utility functions. With respect to D2, the general consumption tax is superior to a labor income tax, because the burden of the general consumption tax does not only fall on labor, but also on capital. A general consumption tax, hence, corresponds to a labor income tax combined with a lump-sum tax. The distortions on the job market decline, employment rises and so does energy production. The latter induces a negative D1(W) as compared to the benchmark equilibrium, but the decrease in environmental quality is smaller than it would be for the case of an exclusive capital income tax which achieves the maximum in economic performance. Finally, we impose an exogenous reduction target for overall energy consumption. Such a setting reflects the policy framework in many industrialized countries with respect to national and international climate mitigation programs. In this case, the percentage change D1(P) in pollutants is exogenously given and so is the associated welfare effect D1(W). Given the availability of the various tax instruments, what would then be the optimal structure of taxes to maximize D2? From a theoretical point of view, the result is clear if energy taxes complement first-best taxes or lump-sum transfers that finance the public good or can be used to refund energy taxes to private households. In that case, energy consumption of the private and production sector should be taxed with equal rates (Pigouvian tax). Uniform energy tax rates for the implementation of emission reduction targets are even then unambiguously optimal in D2 terms if the budget account is balanced by a second-best general consumption tax. b)

Green Tax Reform in the Case of Full Employment: Energy Taxes versus Income Taxes

The economic effects of revenue-neutral tax reforms are not very surprising if, in return to the introduction of energy taxes, pre-existing first-best or second-best taxes are reduced. Positive environmental effects are counterbalanced by the negative impacts on the excess burdens of the tax system and on unemployment. The question of the impact of a green tax reform on gross welfare (neglecting environmental benefits) and employment does not become exciting until third best worlds are taken into consideration. Labor income taxes are third-best taxes in our model. With regard to the induced excess burden, they are clearly inferior compared to first-best taxes on the given capital stock or second-best general consumption taxes.


In this section, we are going to present and explain effects of green tax reforms that include the imposition of energy taxes combined with revenue-neutral cuts of pre-existing labor taxes. Such a scenario is in line with the design of green tax reforms in various OECD countries (OECD 2001). The primary objective of energy taxation should be the cutback in harmful emissions associated with energy consumption. In our simulations with the model variant of a closed economy and full employment, we distinguish two cases. One in which we impose energy taxes and let the model endogenously determine the induced reduction in energy consumption (see left-hand side of Table 5). And a second one where we exogenously impose the required energy (emission) reduction target and let the model endogenously calculate the level of energy taxes that are required to achieve that reduction target (see right-hand side of Table 5). As to the latter, we investigate two emissions reduction targets of 5 and 15 per cent that can be achieved either through uniform or through differentiated energy tax rates for the household and the production sector. In order to do so, we fix the ratio of the energy tax rate equal to 1 (equal tax rates), to 0.5 and to 1.5. A value of 0.5 (1.5) means that the energy tax rate in the production sector is half (1.5 times) of that in the household sector. The energy tax rates and the labor income tax rate which balances the public budget result endogenously. We start interpretation of results for the case of fixed energy tax rates. We can see that all three of our selected tax rate combinations exhibit a double dividend. Total energy consumption is reduced by about 5 per cent. At the same time, the excess burden of the tax system is reduced. The second dividend is highest for a tax rate combination of τ EY = 19 and τ EH = 13 . A wider spread of the tax rate in favor of the household sector or - inversely - tax discrimination in favor of the production sector decreases D2 (which can easily verified by the reader using the interface). We need to explain why (low) energy tax rates generate a double dividend, and why the energy consumption of the production sector should be taxed more heavily than that of the private sector. Both results are surprising at first glance. Having studied the production efficiency theorem by Diamond and Mirrlees (1971), one would expect that distorting taxes in production should be abstained from altogether. However, this result applies to a second-best tax system only - a condition that is not satisfied in the scenarios described in Table 5. In our third-best system of a labor income tax, efficiency gains can occur due to an intentionally induced distortion in the production sector.


– 0.00916

– 0.00895

MWC (τ EH )

MWC (τ w )



– 0.00870



MWC (τ EY )

– 5.808



; τ EH ) =

– 0.00897

– 0.00897

– 0.00898



– 5.435


– 0.00901

– 0.00882

– 0.00917



– 4.911


MWC (τ w )

MWC (τ EH )

MWC (τ EY )


– 0.00901

– 0.00893

– 0.00898




/ τ EH ) =

τ EH



D1(P) = 5

τ EY


Endogenous Variable

– 0.00827

– 0.01083

– 0.00802

– 0.195




Uniform versus differentiated energy taxes: environmental effects and excess burden (variant: GV-VB)


Table 5:




/ τ EH ) =

– 0.136


– 0.00822

– 0.01014

– 0.00882

D1(P) = 15

– 0.00818


– 0.00947

– 0.155





This leaves us to explain the amount and the direction of the differentiation of the tax rates. In order to do so, we employ the marginal cost concept of public funds (MCF); see Schöb (1994) or Snow and Warren (1996). Based on the newly calculated equilibrium, i.e. the equilibrium after implementation of the green tax reform, we raise the public expenditures for goods by a marginal unit and finance the latter with the alternative tax instruments available in the respective model set-up. The marginal costs of public funds then specify the costs for the overall economy, which are associated with additional public expenditures for goods by one unit. Accordingly, a value of (-1.05) means that 1 additional dollar tax revenue causes overall economic costs of 1.05 dollars. The costs of 0.05 dollar, which accrue on top of the 1 dollar revenue effect, correspond to the marginal welfare cost MWC of public funds, i.e. MCF - 1 = MWC. The rates of available tax instruments should be chosen in such a way that for each tax MCF or respectively MWC are the same. This means that the rates for taxes with low (high) MWCs should be raised (lowered). Our simulation program computes the MWCs numerically. The last three rows of Table 5 show the respective values. Under public finance aspects, the energy tax rate combination of (19;13) is optimal because the MWCs just coincide. Turning to the impacts of exogenous emission reduction targets, we see that a moderate reduction target of 5 per cent (with respect to the overall energy use) generates a double dividend if the energy tax rates are suitably differentiated. With stricter reduction targets, such as 15 per cent, this is no longer the case. The resulting energy tax rates are so high that the excess burden of the whole tax system increases (negative D2). Indeed, in that case, uniform energy tax rates would be better than differentiated ones. The economic explanation is that with stricter reduction targets, the environmental objective dominates the public finance objective of minimizing the excess burden. More ambitious environmental targets are, thus, best achieved by uniform energy tax rates. The MWCs are given in Table 5 but do not provide any further information with respect to the differentiation of the tax rates. The reason is that these indicators merely reflect the public finance marginal excess burden of the tax system but not the trade-off with the environmental objective. c)

A Green Tax Reform with Unemployment

Apart from the reduction of harmful emissions, protagonists of green tax reforms often claim that revenue-neutral cuts in labor costs can alleviate the problem of unemployment. Table 6 describes the results of some simulation runs in a closed economy with unemployment (CEUE) where the revenues of additional energy taxes are used for cuts in the labor income tax. The results indicate that a green tax reform may be able to create three dividends simultaneously: firstly, energy consumption is curtailed and, therefore, harmful emissions are reduced as well; secondly, the efficiency of the tax system is improved due to a reduction of the excess burden and finally, positive employment effects can be achieved, i.e. unemployment is reduced. 23

– 0.01095

– 0.01091

– 0.01186

MWC (τ EH )

MWC (τ w )

– 0.902


MWC (τ EY )


– 4.815


(τ Y E


– 0.01114

– 0.01113

– 0.01116

– 1.359


– 8.488


; τ EH ) =




– 1.624



τ EH




τ EY

Endogenous Variable

/ τ EH ) =







– 1.788

D1(P) = 15

Effects of energy taxes on environment, excess burden and employment (variant: GV-UB)



Table 6:

– 1,874







Table 6 shows that - for the same degree of tax differentiation - energy tax rates should be higher in the case of unemployment as opposed to the case with full employment. If the productive use of energy is taxed at 19 per cent and the energy use of private households at 13 per cent, the MWCs of labor income taxes are higher than those of the energy taxes. Consequently, it is appropriate to raise the energy tax rates and to reduce the labor income tax. With reference to D2, the optimal energy tax rate combination is 35 per cent on productive energy use and 23 per cent on final energy consumption. In this case, unemployment declines by 1.36 percentage points while overall energy consumption is reduced by 8.5 per cent. The second part of Table 6 shows that an energy reduction target of 15 per cent is compatible with public finance as well as employment objectives. While the reduction in the excess burden of the tax system would suggest uniform energy tax rates, the employment objective would make the case for a higher tax on the productive use of energy. The higher energy tax revenues, which are induced by the latter, allows for a stronger decrease of the tax wedge on the labor market. The reason for the positive employment effects is that the tax burden on labor is partially passed on to other factors, i.e. earners of other incomes. Since unemployment transfers are assumed constant in real terms, the green tax reform shifts the tax burden partly onto capital causing a reduction of the real interest rate. These results cannot be generalized without restrictions. For very ambitious reduction targets, the excess burden of the tax system increases substantially and unemployment rises since the distortionary effects of high energy taxes dominate the beneficial revenue-recycling effect. It can be also shown that a green tax reform does not provide a second or third dividend for moderate energy reduction targets if energy taxes complement an initial general consumption tax. Obviously, the second-best setting of an initial consumption tax reduces the prospects for a multiple dividend from environmental taxation as compared to a third-best labor income tax

VI. Conclusion We have presented a simple CGE model to study the effects of green tax reforms on environmental quality, the excess burden of the tax system and the level of unemployment. Our main objective has been to lower the barriers to numerical analysis of the double (triple) dividend issue in environmental taxation. Without any programming skills, the reader can use our interactive model to explore the determinants of multiple dividends from green tax reforms. Learning-by-doing involves the specification of green tax reforms, the ex-ante economic reasoning on the potential effects, and the ex-post cross-check with the results provided by the computer simulations. The illustrative examples of explanations included for 25

selected policy scenarios have provided some orientation. In this way, the reader can gain valuable insights that would hardly be available through stylized theoretical analysis. In more general terms, we also hope that our approach stimulates students or professionals to enter the field of applied (computable) general equilibrium analysis. Having gained some experience in the CGE analysis of tax reforms at the non-technical level, the interested reader may be better prepared and motivated to extend our generic model framework to its own needs for policy analysis.

References Bovenberg, A.L. and F. van der Ploeg (1993a): Direct Crowding Out, Optimal Taxation, and Pollution Abatement. Economic Letters 43, 83-93. Bovenberg, A.L. and F. van der Ploeg (1993b): Environmental Policy, Public Goods, and the Marginal Cost of Public Funds. Economic Journal 104, 444-454. Bovenberg, A. L. and R. A. de Mooij (1994a): Environmental Levies and Distortionary Taxation. American Economic Review 84, 1085-1089. Bovenberg, A. L. and R. A. de Mooij (1994b): Environmental Taxes and Labor-Market Distortions. European Journal of Political Economy 10 (4), 655-684. Bovenberg, A.L. (1999): Green tax reforms and the double dividend: An updated reader's guide. International Tax and Public Finance 6, 421- 424. Bovenberg, A.L. and L. H. Goulder (1996): Optimal Environmental Taxation in the Presence of Other Taxes: General Equilibrium Analyses. American Economic Review 86 (4), 985-1000. Bovenberg, A.L. and L. H. Goulder (1997): Costs of Environmentally Motivated Taxes in the Presence of Other Taxes: General Equilibrium Analyses. National Tax Journal 50 (1), 59-87. Diamond, P. A. and J. A. Mirrlees (1971): On Optimal Taxation and Public Production. I: Production Efficiency. American Economic Review 51, 8-27; II: Tax Rules, 261-278. Goulder, L. H. (1992): Carbon Tax Design and U.S. Industry Performance Environmental Taxation and the Double Dividend: A Readers’ Guide. In: Poterba, J. M. (ed.): Tax Policy and the Economy, Cambridge, Mass., Vol. 6, 59-104. Goulder, L. H. (1994): Energy Taxes: Traditional Efficiency Effects and Environmental Implications. In: Poterba, J. M. (ed.): Tax Policy and the Economy, Cambridge, Mass., Vol. 8, 105-158. Goulder, L. H. (1995): Environmental Taxation and the Double Dividend: A Readers’ Guide. International Tax and Public Finance 2, 157-183. Hutton, J. and A. Ruocco (1999): Tax Reform and Employment in Europe. International Tax and Public Finance 6, 263-288. Johansson, P.-O. (1987): The Economic Theory and Measurement of Environmental Benefits. Cambridge etc.


King, B. (1985): What is a SAM? In: Pyatt, G. and J. I. Round (eds.), Social Accounting Matrices: A Basis for Planning. Washington D. C.: The World Bank. Koskela, E. and R. Schöb (1999): Alleviating Unemployment: The Case for Green Tax Reforms. European Economic Review. 43, 1723 - 1746. Majocchi, A. (1996): Green Fiscal Reform and Employment: A Survey. Environmental and Resource Economics 8, 375-397. Mansur, A. and J. Whalley (1984): Numerical Specification of Applied General Equilibrium Models: Estimation, Calibration, and Data. In: Scarf, H. E. and J. B. Shoven (eds.), Applied General Equilibrium Analysis, Cambridge etc., 69-127. Oates, W. E. (1995): Green taxes: can we protect the environment and improve the tax system at the same time?. Southern Economic Journal 61 (4), 915-922. OECD (2001): Environmentally Related Taxes in OECD countries - Issues and Strategies, OECD Publications, Paris. Pearce, D.W. (1991): The Role of Carbon Taxes in Adjusting to Global Warming. Economic Journal 101, 938-948. Pigou, A.C. (1947): Economic Progress in a Stable Environment. Economica 14, 180-188. Repetto, R. et al. (1992): Green Fees: How a Tax Shift Can Work for the Environment and the Economy. Washington D.C.: World Resources Institute. Schneider, K. (1997): Involuntary Unemployment and Environmental Policy: The Double Dividend Hypothesis. Scandinavian Journal of Economics 99, 45-59. Snow, A. and R.S.. Warren (1996): The Marginal Welfare Cost of Public Funds: Theory and Estimates. Journal of Public Economics 61, 289 - 305. Schöb, R (1994): On Marginal Cost and Marginal Benefit of Public Funds. Public Finance 49, 87 106.


Appendix I: Short Tutorial on the “Do-it-yourself” Simulation Model A B C D

User Login Casebook Definition Scenario Definition and Evaluation Summary

A User Login After entering, click on „Login to Interface“. This will bring you to the disclaimer. If you agree to the conditions, click on „Continue“, if you disagree, click „Exit“.

You can now access the actual login mask. Type in a user name and a password. Then click on the „New User“ button. Your new account will be created. Should you already have an account, then simply click the „Log in“ button. You can make changes to your existing account by clicking the „Edit Account Information“ button. „Reset“ erases any information you have previously entered.


Please confirm your password. Optionally, you may want to enter your e-mail address and your affiliation. Pressing „Submit“ will enter your data, whereas „Reset“ will erase any previous input. Now choose „Energy Taxes and Employment“ to access our interactive model on green tax reforms.

B Casebook Definition You can set up folders in the „Casebook Index“ to organize your simulation runs (scenarios). The first scenarios discussed in the paper referred to a closed economy without unemployment (CE-FE); we will therefore name our first Casebook accordingly. Enter the name as it is shown below. If you want, you can type an elaborate description of the casebook in the field „Description“. Then click on „Create“ to set up the casebook. Note that you have a casebook already, named „Default“, which includes the default case of the model, i.e. the initial benchmark equilibrium.


After the casebook has been created, it appears as new entry in the „Casebooks“ list. You can open a casebook by clicking on it.

C Scenario Definition and Evaluation C.1 Case TL 10

We will now compute our first scenario („item\case“) which performs a simple consistency check of the model. As a concrete example, we impose a payroll tax rate TL of 10 percent (while using the labor income tax rate TW as equal-yield recycling instrument). Do not forget to identify your scenario with a unique name. As you can see, we haven chosen here „TL 10“ as scenario identifier.


To enter the payroll tax rate, click the associated pull-down menu, move the cursor to the desired value („10“ in our case) and click. Since the default value for the equal-yield tax instrument is already TW, no further modification to the default set-up is necessary.

We can now start the computation of the new scenario by clicking on „Create“.


The model is solved on the model's host machine which may take some seconds. By clicking the button “Check on Solving Cases” the screen will be updated as soon as the model solution is available. Your solved scenario „TL 10“ will be listed under „Solved Cases“ and the associated results will then be automatically appear in the „Outputs“ section at the bottom of the window.


As expected, the imposition of the payroll tax should not alter any prices or quantities. The tax wedge between the net wage and gross wage is now composed of the payroll tax and the labour income tax but remains the same in total. If you click on the case button „TL 10“ in the „item\case“ row you obtain an extensive results report including the pre- and aftertax reform level of tax revenues across tax instruments.


One can compare the results of scenarios in the current folder with scenario outcomes from other folders. In our case, we will compare the „TL 10“ scenario with the „Default“ case.

To do so, we import the „Default“ case by clicking on the pull-down menu associated with the button „Import“ at the top of the screen. We then select the „Default“ case. Note that you can import any other case that has been previously saved in one of your casebooks. If you click on „Import“, the case will be actually added to the scenarios already displayed. In our concrete case, scenarios „TL 10“ and „Default“ only differ with respect to the „TL“ (blue marks).


As to the results section, we see that the labour income tax decreases from 33,33% to 26,66% upon introduction of a payroll tax of 10% (keeping the labor tax wedge constant).

C.2 Case D1(P)5

The second scenario also refers to the model variant of a closed economy with full employment. We therefore stick to the (CE-FE)-Casebook. Now, we want to impose an exogenous energy (emission) reduction target of 5 % and let the computer calculate the required energy taxes on the production and household sectors after specifying some energy tax differentiation ratio. We will call this new case „D1(P)5”. To run scenarios with exogenous reduction targets, you need not only to specify the explicit reduction objective. You must also activate the setting for „Exogenous energy reduction objective” by selecting „yes” in the associated pull-down menu.


We furthermore select the„Energy reduction target” of „5” in the corresponding box. As we want to impose a uniform energy tax across households and industry we select „1” for „Energy tax differentiation” which imposes a tax differentiation ratio of unity.

The remainder of calculating our scenario should be familiar – we click on „Create” and, after some seconds, on „Check on Solving Cases” to obtain the solution.


Unlike our first example, this scenario yields substantial changes in economic indicators which must be checked against the reader's economic intuition.

D Summary

In this short tutorial, we have laid out how you can log into the user-interface for our do-ityourself model. You should be able to set up new casebooks, view existing cases/scenarios and define new cases. Finally, we have described how the new cases are solved and results can be displayed/loaded and compared across scenarios. At each stage, of the do-it-yourself exercise you can use the buttons at the top of the screen to navigate through all the functionality provided by the interface.


Appendix II: GAMS-X Architectural Overview The web-based model interface, GAMS-X, consists of an open source application and modeling toolkit available at The GAMS-X framework is composed of a set of GAMS include files, HTML, Perl modules, JavaScript, Perl scripts and/or executable binaries, and shell scripts. Perl was chosen for its wide application as both a web language and "glue" language, with powerful parsing tools that allow it to provide a bridge between disparate document and language formats, and for its cross-platform compatibility. Figure 2:

Installing a model

The GAMS-X architecture conforms loosely to the Model-View-Controller (MVC) design pattern to encapsulate data processing, internal controls, and GUI rendering tasks. The view component consists of a toolkit which can produce a local (native) GUI, built against the cross-platform Perl/Tk bindings, or a remote web interface through the GAMS::CGI class library. Primitive templating of the web interface is possible through a slug-replacement mechanism. The controller treats GAMS as a black box. When modellers decide to put their model online, they define the set of inputs, outputs, and plots through a call to a GAMS include file; e.g., $LIBINCLUDE X INPUT BET 0.95 "Discount factor" 0.90 0.925 0.975 $LIBINCLUDE X INPUT FTA_USC NO "FTA includes USA and Canada" YES $LIBINCLUDE X INPUT BET 0.95 "Discount Factor" MAX 0.975 MIN 0.95 $LIBINCLUDE X OUTPUT CONSUM TL $LIBINCLUDE X PLOT C.L T TL


During model installation (see Figure 2 for the generic menu), which is done through the local Tk UI, an initial solve generates a configuration file that is parsed by the GAMS-X model component and used to populate a flat file with configuration information specified in an internal configuration format. Figure 3:

Scenario activity diagram

A user may select inputs and view output and plots through a native Tk GUI or a web interface

User selects inputs

[new scenario]

System call to GAMS [scenario previously solved]

[optimal solution found]

[error or infeasibility]

Parse solution file

Flag scenario as error

Display outputs and plots

Display GAMS listing

After a GAMS model is installed, users may submit inputs for a scenario through either a web page or a native GUI (see Figure 3). If a scenario has been solved previously (possibly by another user), the solution is incorporated into the user's casebook. (A casebook is simply a set of scenarios which is given a name by a user). Otherwise, GAMS is executed through a system call replacing the model value slugs replaced with the user-specified scenario values. If the model solves normally (i.e., if GAMS produces a zero exit value), a solution file is produced which is then parsed by the model component and stored in a flat file in an internal format and all necessary plots are generated. Otherwise, an error flag is associated with the scenario and the user has the option of viewing the GAMS listing file in order to identify the error.