This paper shows that the dividing lines between the three possible outcome of a revenue-neutral ecological tax reform – double dividend, employment failure, environmental failure – can be ordered in terms of the slope of the wage curve and the slope of the Laffer curve in an efficiency wage model. A comparison of the efficiency wage model with bargaining models shows that the relation between the three outcomes and the slope of the Laffer curve is not the same but rather the opposite in the two models.environmental economics ;

Ziesemer,Thomas

English

Research Papers in Economics

 
 
MERIT-Infonomics Research Memorandum series 
 
 
 
 
 
 
 
 
 
 
 
  
  Green Tax Reform and the Laffer 
curve in labour market models:  
  A brief note  
   
Thomas Ziesemer 
 
        2003-012 (revised version of 2002-014) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
MERIT – Maastricht Economic Research 
Institute on Innovation and Technology 
 
PO Box 616 
6200 MD Maastricht 
The Netherlands 
T: +31 43 3883875 
F: +31 43 3884905 
 
 
http://meritbbs.unimaas.nl 
e-mail:secr-merit@merit.unimaas.nl 
 
 
International Institute of Infonomics 
 
 
c/o Maastricht University 
PO Box 616 
6200 MD Maastricht 
The Netherlands 
T: +31 43 388 3875 
F: +31 45 388 4905 
 
http://www.infonomics.nl 
e-mail: secr@infonomics.nl   1
Green Tax Reform and the Laffer curve in labour market models: A brief note 
 
Thomas Ziesemer, Department of Economics, Maastricht University, P.O. Box 616, NL 
6200 MD Maastricht. E-mail: T.Ziesemer@algec.unimaas.nl.
1 
 
Abstract. This paper shows that the dividing lines between the three possible outcome of 
a revenue-neutral ecological tax reform – double dividend, employment failure, 
environmental failure – can be ordered in terms of the slope of the wage curve and the 
slope of the Laffer curve in an efficiency wage model. A comparison of the efficiency 
wage model with bargaining models shows that the relation between the three outcomes 
and the slope of the Laffer curve is not the same but rather the opposite in the two 
models.   
 
Keywords: Taxation, government revenue, ecological tax reform, Laffer curve, 
environment, energy, unemployment, wage curve, bargaining.    
  
I.  Introduction 
 
Revenue neutral ecological tax reforms aim at an improvement of the natural environment and a 
reduction of unemployment through raising energy emission taxes and reduction of labour taxes. 
Most of the debate about these reforms has concentrated on the question whether or not the 
unemployment objective can be reached. In a recent paper Bayιndιr-Upmann and Raith (2003) 
                                                 
1 I am grateful for useful comments to Dieter Imboden, Hans Nutzinger, and to Kerstin Schneider also for 
providing the graphs, which I have modified only slightly. Responsibility is entirely mine. This paper has 
not been submitted elsewhere in identical or similar form, nor will it be during the first three months after its 
submission to the Publisher.   2
have derived the exact conditions for employment failure environmental failure and a double 
dividend for three cases of a bargaining model based on a Bovenberg and van der Ploeg (1996). 
   In this paper we derive the exact conditions for the double dividend and the two possibilities of 
failure for an efficiency-wage model by Schneider (1997) and compare them to the results of the 
bargaining model. Schneider (1997) did show that the success of a green tax reform depends 
crucially on a small slope of the wage curve of an efficiency wage model in which production 
occurs using a second factor E, energy or emissions. Scholz (1998) revealed that there is a second 
necessary condition that the marginal revenue of the wage income tax is negative.  
   In this note we show in Section 2 that (i) these two conditions are not independent, but rather 
depend both on the slope of the wage curve; and (ii) if Schneider’s condition of a sufficiently flat 
wage curve is fulfilled, marginal revenue of wage income taxes must be negative. By implication, 
both the green tax reform and the sign of the marginal revenue of wage income taxes depend on 
the slope of the wage curve which allows to distinguish three cases of a tax reform: a) a double 
dividend for a very small slope of the wage curve (Schneider’s case); b) failure of unemployment 
reduction (Scholz’ case) for a very steep wage curve; c) failure of emission reduction for an 
intermediate case of a wage curve slope. In Section 3 we compare these results to those of the 
bargaining model obtained by Bayιndιr-Upmann and Raith (2003). In particular, we show that in 
the efficiency-wage model (bargaining models) employment failure occurs when the Laffer curve 
is upward (downward) sloping and environmental failure occurs when the Laffer curve is 
downward sloping.   
 
II.  Old and new results from the efficiency wage model  
 
Scholz (1998) considers the reduced form of Schneider’s model (see definition of symbols at the 
end of the paper) and derives three essential results:   3
 
 
DET G T u / ˆ / ˆ β =  
 
 
) / (
/ ˆ / ˆ L E DET
s
p u θ θ
σ
=  
 
                
α
σ
DET
s
p E
/ ˆ / ˆ =  
 
 
Here DET = {βu (1-τ) θL -εθE - ετθL}/s is the determinant of the reduced form of the model; α = 
τε -(1-τ)βu. With all parameters but DET and α defined in a way that they are positive, Scholz 
shows that Schneider’s results not only require α > 0 but also DET < 0. The latter condition 
implies that the marginal revenue of wage income taxes, the first of the three results, must be 
negative.  
  We show now, that the sign of DET also depends on the slope of the wage curve in a way 
that α > 0 implies DET < 0, but not vice versa, capturing the result in proposition 1. 
 
Proposition 1: The cases of a double dividend and those of the failure in regard to employment 
and emissions can be formulated in terms of the slope of the wage curve.    
 
Proof. From the definitions of DET and α given above one can see that   
   4
 
DET >(<) 0 exactly if 
τ
ετ θ εθ
β
−
+
< >
1
/
) (
L E
u and  
 
α>(<)0, exactly if 
τ
τε
β
−
> <
1
) ( u .  
 
From the right-hand sides of the inequalities one can see that the fraction of the inequality 
derived from DET is larger than the fraction of the inequality derived from α because in the first 
of these a term is added to ετ in the numerator. Therefore we can distinguish three cases: 
 
1. 
τ
τε
τ
ετ θ εθ
β
−
>
−
+
>
1 1
/ L E
u , implies DET > 0, α<0,  . 0 ˆ / ˆ , 0 ˆ , 0 ˆ > > < G T u E  (Employment 
failure under a steep wage curve) 
 
An increase of the energy or emissions tax reduces energy use and emissions, but increases 
unemployment. Marginal revenue of wage income taxes is positive.   
 
2. 
τ
τε
β
τ
ετ θ εθ
−
> >
−
+
1 1
/
u
L E , implies DET < 0, α<0,  . 0 ˆ / ˆ , 0 ˆ , 0 ˆ < < > G T u E  (Emission failure 
under a moderately sloped wage curve) 
 
The energy or emissions tax increases employment but also energy use. Marginal revenue of 
wage income taxes is negative. If this latter result is believed to be unrealistic then environmental 
failure is also unrealistic.  
   5
3.  u
L E β
τ
τε
τ
ετ θ εθ
>
−
>
−
+
1 1
/
, implies DET < 0, α > 0,  . 0 ˆ / ˆ , 0 ˆ , 0 ˆ < < < G T u E (Double dividend 
under a flat wage curve)•  
 
In the case of a flat wage curve unemployment and emissions are both reduced and a double 
dividend can be reaped. These results can be summarized as follows. 
 
Proposition2: A sufficiently flat wage curve implies negative marginal revenue of wage income 
taxes (slope of the Laffer curve) and the conditions for a double dividend are not independent of 
each other. 
 
Corollary 2.1: Schneider￿s condition α > 0 implies the one revealed by Scholz, DET < 0, i.e., a 
negative marginal revenue of wage income taxes, but not vice versa.    
 
By implication, Schneider’s case is not weakened but rather we have the empirical question how 
flat the wage curves are. Authors providing support for a double dividend view tend to use 
horizontal labour supply or wage curve (besides Schneider 1997, see Nielsen et al. 1995 and 
Koskela et al. 2001). Otherwise the success of a green tax reform depends on having a labour cost 
reduction that does not benefit the unemployed or black market workers (Bovenberg and van der 
Ploeg 1998, Koskela and Schöb 1999). As in most countries institutional arrangements are such 
that the unemployed would also benefit from a labour tax reduction (see Koskela and Schöb 
1999), either institutional change is required or this latter way does not work and the slope issue 
of the Schneider paper remains crucial. 
 
As the sign of the marginal revenue of wage income taxes is identical to that of the slope of 
Laffer-curve we get the following:   6
 
Corollary 2.2:  The cases of a double dividend and emission failure are obtained on the 
decreasing part of the Laffer curve, whereas the case of employment failure is obtained on the 
increasing part of the Laffer curve.   
 
III.  Comparison with bargaining models 
 
Bayιndιr-Upmann and Raith (2003) show in a bargaining model that there are three critical 
labour-tax rates, which allow to classify, on the one hand, the range of validity of the double 
dividend and the two possibilities of failure and, on the other hand, the slope of the Laffer curve. 
We summarize their results according to their Table 1: 
 
{{
}
sin sin
00 1 1 2 0, ,
increa g decrea g
Laffer Laffer
curve curve
L
double higher low er
dividend emissions employment
tt t t t t →< < <
64748
123  
  
In the bargaining model, employment failure occurs when the Laffer curve is decreasing, whereas 
it did so in the efficiency-wage model when the Laffer curve is increasing. In the bargaining 
model environmental failure occurs when the Laffer curve is increasing, whereas it did so in the 
effciency-wage model when the Laffer curve is decreasing. A double dividend can be reached in 
the bargaining models when the labour tax is low and in the efficiency-wage model when it is 
high. This can be summarized as follows. 
   7
Proposition 3: Going from lower to higher labour taxes the three ranges in the bargaining model 
are: (i)Double dividend; (ii) Emission failure;(iii) Employment failure. In the efficiency wage 
model the sequence is the other way around. 
 
Corollary 3.1: If an economy is in the neighbourhood of the peak of the Laffer curve it will suffer 
from one type of failure in each of the models; which type it is depends on the model. If an 
economy is at slightly lower tax rates than the peak of the Laffer curve, the efficiency wage 
model predicts employment failure whereas the bargaining models predict environmental failure. 
By implication, slightly below the peak of the Laffer curve the bargaining models are much more 
optimistic in regard to the employment effects than the efficiency wage mode.  
  
As there is no clear-cut evidence as to which of the labour market models is more realistic and on 
which side of the Laffer curve countries are it is hard to draw any conclusion concerning the 
question which case of which model is realistic. Therefore we can only proceed with some 
tentative empirical considerations regarding the efficiency wage model, which indicate that there 
is also not even a clear-cut result if one assumes that the efficiency wage model is relevant.  
 
IV.  Some ‘back –on-the-envelop’ empirics for the efficiency wage model 
 
If a politician wants to know whether or not unemployment and emissions will increase or 
decrease after the introduction of an eco-tax (s)he needs to know the value of Beta relative to the 
other terms. This will be very difficult for two reasons.  
First, the wage curve replaces the textbook labour-supply curve in the model, which is 
structurally very similar. Labour supply curves are normally expected to be very steep. 
Bovenberg (1995) reports that an increase of wages by 1% increases labour supply by 0.02%. 
This is an almost vertical function, which comes very close to an exogenous labour supply.  If the   8
wage curve replaces the labour-supply function, the question is whether or not empirical results 
can differ very much from those of a labour supply function. The structural equations, which have 
to be estimated for different models are always very similar to each other (see Pissarides 1998). 
This view would support the assumption of a very high value of Beta, which in turn would 
support the view that an eco-tax increases unemployment. On the other hand, this latter result of 
an increase in unemployment could be an optimum because it buys an improvement of the 
environment  (see Schneider 1997, section IV). One may doubt however, that voters and 
politicians have the individual welfare or utility function, which drives this policy result, because 
results based on questionnaires show a huge priority for employment (see Böhringer und Vogt 
2001). In sum, it is not surprising, that scientific support for a green tax reform has been based on 
models with fixed wages and the implied horizontal labour supply curve (see Nielsen et al. 1995 
and Koskela et al. 2001).
2  
 
FIGURE 1 AND 2 OVER HERE  
 
Second, the term α =  ε β ) / 1 1 ( / T T u − + −  must be positive. τ ≡ 1-1/T is the percentage tax 
rate on gross wages and 1/T is the percentage that remains after taxes. Graafland and Huizinga 
(1999) estimate an equation similar to a wage curve – derived from a bargaining model - and 
obtain a semi-elasticity (- ∂w/w/∂u) between 1.5 for the second half of the 1970s and 3.0 for the 
beginning of the 1990s. In order to make these values comparable with Beta, the semi-elasticity 
can be multiplied with the European unemployment rates of the corresponding time periods: the 
first number with the unemployment rate of about u=5% and the second with u=10%. This yields 
values for Beta of 0.075 and 0.3. The higher the unemployment rate is, the higher the elasticity. 
This method clearly differs from a constant elasticity approach. Each figure drawn below shows 
                                                 
2 Other support has been based on bargaining models in which the revenues of a green tax reform are used 
to improve the situation of working people compared to those not working.   9
two surfaces. The flat one is the benchmark-value of Beta as derived from the Graafland-
Huizinga semi-elasticities, assuming for illustrative purposes that they are more generally valid 
than just for the Netherlands. The bended curve shows values for the right-hand side of the 
inequality condition for double dividend,  β β ≡ − − < ) 1 /( ) 1 ( u T u u  , called ‘beta’ on the vertical 
axis of the graph, which are calculated for alternative values of the unemployment rate u and the 
tax factor t=1/T, which is the percentage of the gross wage, which the employee gets. The lower 
this percentage and the higher the rate of unemployment the larger is the right-hand side of the 
inequality. In the case of the higher elasticity βu = 0.3, the after-tax percentage, which the 
employee gets has to be fairly low (below 40%) for all unemployment rates below 15% in order 
to get a double dividend. In the case of the lower elasticity βu=0.075, however, a large right-hand 
side is much more easy to get. Therefore one cannot derive a clear-cut answer to the question 
whether or not the wage curve is flat enough to guarantee a double dividend or predict increasing 
emissions or unemployment.    
 
V.  Conclusion 
 
We have shown that the condition of a flat wage curve as revealed by Schneider (1997) and the 
condition of negative marginal revenue of wage income taxes are not independent of each other. 
But rather a sufficiently steep (flat) wage curve implies positive (negative) marginal revenue of 
wage income taxes. The dismissal of negative marginal revenue of wage income taxes is 
premature unless one can prove that wage curves are not sufficiently flat. So far flat and steep 
curves are used in the literature. Our back-on-the-envelop calculations do not allow excluding any 
of the cases. In more general terms we have shown the exact conditions for a double dividend and 
the two possible ways of failure. Intuitively, a double dividend can be obtained at a flat wage 
curve. Employment failure will result from a steep wage curve and environmental failure from an   10
intermediate steepness of the wage curve, where wages, employment, income, consumption and 
production increase strongly and drive up emissions. A comparison with results for the bargaining 
model reveals that these regimes are associated with certain levels of labour tax rates but 
inversely so in the efficiency wage model.   
 
References 
 
Bayιndιr-Upmann and Raith (2003), ‘Should high-tax countries pursue revenue-neutral 
ecological tax reforms?’. European Economic Review 47, 41-60.   
 
Böhringer, C. und C. Vogt (2001), ‚Internationaler Klimaschutz – nicht mehr als symbolische 
Politik?’. ZEW Discussion Paper No. 01-06. 
 
Bovenberg, A.L. (1995), ‘Environmental Taxation and Employment’. De Economist.143 (2), 
111-140. 
 
Bovenberg and van der Ploeg (1996), ‘Optimal taxation, public goods and environmental policy 
with unvoluntary unemployment’. Journal of Public Economics 55, 349-390. 
 
Bovenberg, A.L. und Frederick van der Ploeg (1998), ’Tax Reform, Structural Unemployment 
and the Environment’. Scandinavian Journal of Economics 100 (3), 593-610. 
 
Graafland, J.J. and F.H. Huizinga (1999), ‘Taxes and Benefits in a Non-Linear Wage Equation’, 
De Economist 147 (1), 39-54. 
   11
Koskela, E. und R. Schöb (1999), ‘Alleviating unemployment: The case for green tax reforms’. 
European Economic Review 43, 1723-1746. 
 
_____________________, H.W. Sinn (2001), ‘Green Tax Reform and Competitiveness’. German 
Economic Review 2 (1), February 2001, 19-30.  
 
Nielsen, S.B., L.H. Pedersen, P.B. Sørensen (1995), ‘Environmental Policy, Pollution, 
Unemployment, and Endogenous Growth’. International Tax and Public Finance 2 (2), 185-205.  
 
Pissarides , C.  (1998), ‘The impact of employment tax cuts on unemployment and wages; The 
role of unemployment benefits and tax structure’. European Economic Review 42, 155-183. 
 
Schneider, K. (1997), ‘Involuntary Unemployment and Environmental Policy: The Double 
Dividend Hypothesis’. Scandinavian Journal of Economics 99 (1), 45-49. 
 
Scholz, C.M. (1998), ‘Involuntary Unemployment and Environmental Policy: The Double 
Dividend Hypothesis: A Comment’. Scandinavian Journal of Economics 100 (3), 663-664. 
 
 
 
 
 
 
 
   12
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 1 
High values of the unemployment rate, u, and low values of the after-
tax factor, t, allow for a double dividend if the wage curve has an 
elasticity of 0.075  
0
0.05
0.1
0.15
u
0
0.2
0.4
0.6
0.8
1
t
0
1
2
beta  13
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 2 
Only very high values of the unemployment rate, u, 
and very low values of the after-tax factor, t, allow 
for a double dividend if the wage curve has an 
elasticity of 0.3 
0
0.05
0.1
0.15
u
0
0.2
0.4
0.6
0.8
1
t
0
2
4
beta  14
 
 
 
 
 
List of symbols 
^  indicates a growth rate 
 
E energy  input 
 
G government  expenditure 
 
L labour  input 
 
p  price of energy emissions in terms of output 
 
s  government expenditure as share of output 
 
T tax  factor;  τ ≡ 1-1/T is the percentage tax rate on gross wages and  
 
t = 1/T  is the percentage of the gross wage that remains after taxes   
 
u   percentage rate of unemployment 
 
βu  slope of the wage curve (positively defined) 
 
ε ≡ u/(1-u) 
 
σ   elasticity of substitution between emissions and labour 
 
θi  cost share of factor i. 

Green Tax Reform and the Laffer curve in labour market models: A brief note

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