Does Income Tax Actually Discourage Work:
Model and Evidence from OECD Countries
Kakuho Furukawa
University College London
Abstract
It is commonly argued that income tax is a disincentive for people to work because it takes
money away and social benefits are also a disincentive because it gives free money.
However this paper suggests that income tax and social benefits together can in fact
encourage people to work more if (i) people look at their consumption level rather than
absolute income, and income tax alone can encourage people to work more if (ii) people’s
health is negatively linked to income inequality or (iii) people look at their relative income
rather than absolute income. Examining data from the OECD countries and other countries
this paper finds empirical support for the second case.
1. Introduction
Income tax is often regarded as a major disincentive for work imposed by a government.
In theory, when income tax rises, people’s income decreases and therefore people work
more to maintain the living standard, known as income effect, but at the same time they
substitute away from work to leisure because the opportunity cost of work is now lower,
known as substitution effect. Hence, theoretically, the direction of the overall change is
ambiguous. Nevertheless it is generally assumed empirically that income tax overall
decreases work effort.
However, this approach implicitly assumes that people’s work is rewarded by their
absolute incomes. But this may not be the case. This paper presents three models that
consider other factors that may affect people’s work decision. The first model looks at
consumption. The second model considers the case where people’s productivity is affected
by the society’s income equality and the third model takes the idea from comparison
income effect, which argues that people’s satisfaction is determined by relative income
rather than absolute income. The second and the third models take into account past
papers’ results. In all cases the models suggest that redistribution or income tax alone can
improve the overall work effort in a society when the initial income inequality is high. The
three models are entirely original.
This paper also provides empirical tests with two data sets from the OECD countries and
other countries in general. Taking a long term economic growth rate as a measure of
people’s work effort, this paper finds strong empirical support for the second model. I will
first present in Section 2 the thought experiment that led me to investigate the
relationship between income tax and work effort. Section 3 will therefore review past
papers about the impact of income tax on work effort. Section 4 will present the models
with reference to the past papers on which the models are based. Section 5 will examine
the hypotheses for the first and the second models. Section 6 will discuss and conclude the
results.
2. Thought experiment: what happens when inequality widens?
I would first like to present the thought experiment that led me to write on the
relationship between income tax and economic growth. I was initially motivated to write
about the following question: does inequality incentivize people to work harder? This
question is of a great relevance today in the face of widening inequality. The answer, of
course, depends on the underlying mechanism of the inequality. This has been largely
debated in a vast literature. One common explanation is the skilled-biased technological
change. It states that the rapid development in information technology has increased the
demand for skilled labour and hence the income distribution is skewed toward skilled
labour. Another popular explanation is globalization. It hypothesises that low skilled
workers in developed countries are losing against workers in developing countries who
work for much lower wages. Although these hypotheses sound intuitively plausible, they
are not without problems. Empirically they only partially explain the widening inequality
(See Card et al. (2002) and Daron (2000) for skill-biased technological change and
Feenstra et al. (1996) for globalization argument). Another hypothesis, although less
commonly accepted, is the so-called superstar hypothesis (Rosen 1981). It argues that
workers’ compensation increasingly depends on relative performance rather than
absolute performance. For example, a CEO’s pay depends not just on how much he can
improve the employees’ productivity (absolute performance), but also on how much he
can outcompete rival firms in the market (relative performance). It is on this idea that I
proceeded my though experiment.
The fact that a worker’s pay is determined by his relative performance implies his wage is
not proportional to his productivity. If we denote his productivity by F, his wage is rather
proportional to Fα where α>1. This means a worker with a higher productivity can earn an
increasingly higher wage because he is more likely to win the competition with other
workers. I use α as a measure of inequality. My question is then: does a larger α lead to a
greater effort by workers? After all, the larger the value of α is the richer his reward is by
being more productive. To see this, I first assume that workers are initially endowed with
different potential abilities A which is normally distributed with mean 0 and variance σ2.
On top of his ability he can decide to make an effort λ. Then his productivity, or individual
contribution to the economic output, is F(A+ λ) where F is an increasing function. Then, as
I assumed earlier, his wage is B*Fα where B is a constant. Now making effort has a
disutility C(λ). Therefore he chooses his level of effort so as to maximize his total utility
B*F(A+λ)α- C(λ). This is the basic framework of my thought experiment. In order to solve
this I specify each function as follows:
Note that C(0)=0 and C(λ)<0 if λ<0, that is, there is a positive utility in shirking. Now the
worker chooses the level of λ to maximize the total utility
Note that we must have k>α>1 or otherwise workers make infinite amount of effort to
enjoy infinitely large wage. The value of B can be determined by the following argument.
The total economic output is calculated by adding up the individual productivities.
(2.1)
where f(A) is the probability distribution of the ability. On the other hand the total wage
paid to all the workers in the economy is
(2.2)
Evidently the total wage cannot exceed GDP because it is only one factor of GDP in the
income approach. Hence we have
Taking c as given, we can calculate GDP by equating the two integrals (2.1) and (2.2). The
result is
(2.3)
This function has a straightforward bell-shape. See Appendix A for some sample graphs.
One can see that in the limits α=0 and α=k GDP is zero. Indeed it can be analytically shown
that this is always the case when σ>0. Note that when σ=0, GDP is strictly increasing with
α. Hence the assumption of heterogeneity of workers’ abilities is crucial in bell-shape
nature of GDP. The two limiting cases are intuitive. When α=0, everyone gets the same
wage regardless of his productivity. Hence he has an incentive not to work at all. As a
result, the total output of the economy ends up zero. In the second case when α
approaches k, only a few people at the very top gets significant wages. This means the
other workers find it worthless to make an effort since they do not get enough
compensations in wage. These disincentivized workers push down the total economic
output, which in turn pushes down the wages of those in the top since the total wage sum
cannot exceed GDP. As a result in the limit of α=k, GDP of the economy becomes zero.
Hence, the implication of the model is that there is a level of inequality that maximizes
GDP.
What happens now if the government introduces a redistribution plan? Suppose that the
redistribution scheme is such that
(2.4)
where WAT is the wage after redistribution, is a constant and WBT is the wage before
redistribution. is determined by the government’s budget constraint
When τ=0 there is no redistribution and when τ=1 there is perfect redistribution. This
form of redistribution follows Benabou(1996). Workers now care about the after-tax
utility. Hence they decide the level of effort they make to maximize
The calculation goes in exactly the same way as before. The resultant GDP is
Hence α is now replaced by α(1-τ) in (2.3). This means that when α is too large a positive τ
will increase GDP whereas when α is below that GDP-maximizing value, a positive τ will
decrease GDP. This makes sense given the bell-shape nature of GDP against α.
So far, we have seen that if workers decide on the amount of effort they make based on the
trade off between effort and wage, and if the abilities of the workers are not homogeneous,
then too much inequality as a form of productivity-wage gap leads to a reduced total
output and therefore redistribution as a means of closing the gap can help increase the
output. This model is interesting by itself but there are problems. After all, inequality may
not exist because of productivity-wage gap to begin with. Even if it does, it would be very
hard to testify the model empirically. Firstly it would be difficult to measure α. Secondly,
where the measured α is placed on the bell curve depends on many other variables such as
σ and k, which are also hard to quantify. Therefore simple cross-country or time-series
comparisons will not yield the expected bell curve graph.
The above model depends on the specific cause of inequality and the specific form of
redistribution. Faced with these difficulties, I next asked myself if I could relax the
assumptions and make a more general statement. It turned out that this is indeed possible
under some other assumptions regarding workers’ incentives and productivities if I look
at the relationship between redistribution and workers’ incentives rather than between
inequality and workers’ incentives. Before presenting the models in Section 4, I will now
go through literature review.
3. Literature Review
There have been numerous studies on the relationship between redistribution and
workers’ incentives. Redistribution is often measured by the size of tax since the large part
of government redistribution takes the form of tax. Workers’ incentives are tricky to
quantify but economic growth and labour supply are often taken as proxies.
Many studies specifically look at the impact of income tax (Padovano et al., 2001;
Holocombe 2004) while others look at various tax forms such as corporate tax and tax on
goods and services (Kneller et al., 1998, 2011; Barro et al., 2011; IMF, 2010) on economic
growth. Overall agreement is that tax, whether it is income tax or corporate tax, reduces
economic growth both for rich countries such as OECDs and other countries in general.
Some studies that attempt to investigate how tax affects economic growth differently in
democratic and non-democratic countries (Perotti, 1996) find the impacts indeed different.
Fölster et al. (2001) argues that the correlation persists even when they consider other
factors that may also affect economic growth.
The impact of income tax on labour supply has been also studied by many researchers.
The studies vary from those that look at male labour supply (Ashenfelter and Heckman,
1974; Bourguignon and Magnac, 1990; Kaiser et al. 1992) to those that look at married
single female labour supply (Arellano and Meghir, 1992; Blomquist and HanssonBrusewitz, 1990; Blundell et al., 1998). Most studies use hours worked, weekly or annually,
as a measure of labour supply. Although the estimated wage elasticities vary, the general
consensus is that hour worked is not responsive to income tax for full-time male workers.
Meanwhile labour supply by part-time workers and participation rate for female show
negative responsiveness to a tax increase, although the degree of such response is again
unsettled. Meghir and Phillips (2010) provides a good review. However, Manski (2012)
points out that the results depend too much on the specifications of labour supply
functions. Since workers can provide more labour supply not only by working longer but
also by being more productive within the hours worked, these studies suggest that hours
worked may not be a good measure of labour supply.
Finally, the relationship between inequality and economic growth is also a hotly debated
issue in economics. Many studies find the relationship significantly negative. Benabou
(1996) and Aghion et al. (1999) suggest constrained credit markets as a reason for the link
between inequality and economic growth. They argue that when the credit markets are
constrained redistribution can have a growth-enhancing effect. If the credit markets are
more likely to be constrained in more unequal societies, this means that redistribution will
have more positive impacts in those societies. Another channel through which
redistribution and inequality affect GDP growth is sociopoliticl instability. Many papers
have found positive correlation between inequality and socio-political instability and
negative correlations between instability and GDP growth (Alesina et al. 1996; KeeferKnack 1995; Perotti 1992, 1994). However, the extent to which these hypotheses hold for
the already rich OECD countries is not clear.
Overall, to my knowledge, the impacts of tax and inequality and tax on economic growth
are studied separately and no study has taken into account income inequality as a factor
that changes the impacts of tax.
4. Theory
4.1 Effective Wage Model
The first model assumes that the reward for people’s work is their consumption level
rather than absolute income. When a government collects income tax it also provides
certain goods such as medical care and education free or subsidized.
Consider an economy in which there are two consumption goods, denoted by c1 and c2,
and an agent’s utility of consumption is given by
Suppose that the agent earns an income of W. Hence his budget constraint is
where p1 and p2 are the prices of c1 and c2 respectively.
Now assume that there is a government which imposes a tax rate τW, depending on the
income W, and redistributes the money to subsidize the consumption of c1 so that its price
is now (1-s)p1. An agent’s budget constraint becomes
Let us illustrate this situation in a diagram. In Diagram 1 the budget constraint before tax
is given by BC1. The agent’s optimal consumption is given by the bundle A, where the
budget constraint is tangent to the indifference curve U=U1. Now assume the government
imposes an income tax and subsidizes the good c1. As a result the budget constrain after
tax is flatter and shifts inwards. Hence the budget constraint is now BC2. The agent’s
optimal consumption is given by the bundle B and utility by U2.
C2
U2
W/p2
U1
W(1-τW)/p2
B
A
BC2
BC1
W/p1
W(1-τW)/(1-s)p1
C1
Diagrams 1
We can draw a parallel line to BC1 tangent to U2. This represents what I define as the
effective wage, which is the wage the worker would have to earn in the absence of
redistribution in order to achieve the same level of utility as when there is redistribution.
In this diagram the effective wage is higher than the wage before tax. In order to
understand the implication of this simple example, consider the indirect utility function
V(W, p1, p2). The effective wage, We, can be defined as the wage that satisfies
(4.1.1)
where WAT is a after tax wage (1-τW)W. This suggests that we write We as
When there is no tax or redistribution, We equals W. Hence
Now the indirect utility V is increasing with the wage and decreasing with the prices. This
means that
Hence, when s>0, G(s)>1. Therefore, differentiating We with respect to labour supply l, one
obtains
Hence, if G(s) is larger enough than 1 and the tax rate τW is small enough, the above
equation implies the possibility
(4.1.2)
In words, the marginal return to labour in effective wage is greater than that in actual wage
before tax. Note that if τW is large enough the sign of the inequality is reversed.
Let us illustrate the argument with an example. Suppose an agent’s utility is given by
His indirect utility is then given by
Suppose the government introduces a redistribution plan. The agent’s indirect utility
becomes
Hence his effective wage is
This shows that
Now assume an agent in labour market decides how he will respond to a redistribution
plan. He can specifically choose the level of labour supply. The return of labour is the
effective wage. The effective wage, rather than the actual wage, is what matters for agents
because the effective wage unambiguously represents the level of utility. There is,
however, also a cost because supplying labour involves sacrificing leisure time. Denote the
labour supply by l, the effective wage by We(l) and the cost by C(l). An agent chooses l that
maximizes
The first order condition is
Now assume that
is an increasing function of l. Then if (4.1.2)holds,
Therefore this agent will supply more labour than when there is no redistribution. Of course,
(4.1.2) is not true for all agents. For agents who face a high income tax rate the inequality
sign is reversed and hence he will supply less labour. Note that in this formulation I did
not take into account income effect. This helps to simplify the model. It is not without
empirical support since some studies suggest that substitution effect indeed overwhelms
income effect(Meghir and Phillips; 2010).
This mechanism can be shown on diagram. In Diagram 2 the x-axis is labour supplied by
agents. The y-axis shows the marginal effective wage and cost of additional labour supply.
Since
is increasing with λ the marginal cost curve is upward sloping. An agent
supplies labour at the point where the marginal cost (show by MC1 and MC2) and
marginal effective wage (shown by MEW1) of labour meet. Now assume there is
redistribution by the government. By virtue of the earlier result, I assume the marginal
effective wage rotates clockwise (MEW2). As a result the agent with MC1 increases his
labour supply and the agent with MC2 decreases his. It should be reminded that the agent
with MC1 has a lower income compared to the other given the fact that he can supply less
labour at the same cost.
MC1
MC2
MEW1
MEW2
Labour Supply
Diagrams 2
Hence, redistribution can have impact in either direction on labour supply depending on
the position of an agent’s labour cost curve. The question now is; what is the overall
impact in the whole economy?
Before answering the question, let us consider how a government is restricted in
designing a redistribution plan. If the government knows people’s indirect utility function,
for any given We and s it can calculate WAT using (4.1.1). The government is bounded by
the budget constraint
where W is the wage before tax and the integral is over all the agents in the economy. If
WAT so calculated does not satisfy the budget constraint, the government can reduce We by
a constant until the budget constraint is met. Since this does not change
, people’s
incentives do not change. Of course a government can only do so until anyone’s income is
negative, but in reality the above budget constraint may not always have to hold since a
government also has other sources of revenues such as tax on goods and services. Hence
in theory a government could design a redistribution plan that has any incentive effects on
people.
In order to show how people respond to a redistribution plan overall, look at Diagram 3.
On the x-axis to the right is a scale on which people are placed. Further right you go people
are able to supply labour at lower costs. The y-axis is labour supply. The x-axis to the left
shows the marginal effective wage and marginal cost of labour. Therefore the left part of
the diagram is basically a rotated Diagram 2. Here the marginal costs of the agents at x=0,
x=0.5 and x=1 are shown. The resultant labour supply is mapped on to the right part of the
diagram. By connecting the projected points, one obtains the upward sloping curve S,
which shows the labour supply of all the agents. Therefore, the area under the curve S and
the x-axis represents the overall labour supply in the economy.
x=1
ℓ
S
x=0.5
Labour
Supply
x=0
/
x
0
0.5
1
Diagrams 3
Now suppose that the government introduces a redistribution plan. This rotates the
marginal effective wage curve. As a result the labour supply curve shifts and the total
labour supply changes. This change is described in Diagram 4. It happens that in this
particular case the total labour supply does not seem to have changed.
x=1
ℓ
S’
x=0.5
x=0
/
x
0
0.5
1
Diagrams 4
Consider now the case in Diagram 5. Here at the original marginal effective wage curve the
total labour supply is convex. This shows that people at the high end of the economy
supply increasingly more labours, hence the income inequality is high. Diagram 6 shows
what happens when the government introduces the same redistribution plan as in
Diagram 5. One can see that in this case the total labour supply increases as people
respond to the redistribution plan. Hence we reach the proposition of the model:
Proposition. Redistribution plan has more positive impacts, or less negative
impacts, on total labour supply in societies with higher income inequality.
x=1
ℓ
S
x=0.5
x=0
/
x
0
0.5
Diagrams 5
1
x=1
ℓ
x=0.5
x=0
x
/
0
1
0.5
Diagrams 6
4.2 Social health model
The second model looks at income tax’s role in reducing income inequality. Income
inequality is known to be correlated with various social variables such as health, criminal
rates and educational performance (Wilkinson and Pickett, 2005; Kondo et al. 2009). In
general the more unequal the society is, the less healthy, more violent and less educated
the population is. Several studies did try to examine the causal relationship. Moving to
Opportunity for Fair Housing, for instance, was a randomized social experiment in the US
in the 1990s (Shroder et al. 2012), which gave randomly chosen families living in high
poverty vouchers to move in lower poverty areas. Researchers found that families who
moved to lower poverty areas had lower rates of obesity and depression and positive
impacts on behaviour was also found. This randomized controlled experiment suggests
that the environment of neighbourhood does impact people’s health status and behaviour
(Orr et al., 2003; Sanbonmatsu et al. 2011).
Even though the causal impact of income inequality on people’s behaviour remains elusive,
this paper assumes that less income inequality does cause people’s health to improve.
In the model, an improvement in health reduces people’s marginal cost of labour.
x=1
ℓ
S
S’
x=0.5
x=0
/
x
0
Diagrams 7
0.5
1
Diagram 7 describes this shift. Here we do not consider government’s subsidies. Therefore
effective wage is the same as the actual wage and marginal effective wage only rotates
clockwise without shifting as a result of progressive income tax. At the same time, the
marginal cost of labour curves shift upwards as a result of improved health due to the
reduced income inequality. In this diagram the total labour supply does not seem to have
changed much.
x=1
ℓ
x=0.5
x=0
/
x
0
0.5
1
Diagrams 8
Diagram 8 describes the same tax schedule with the same impact on health improvement
but here the income inequality is higher. One can see in this case that the total labour
supply has increased. Therefore, assuming that the same income tax schedule has the
same impact on health improvement and hence reduction in marginal cost of labour,
income tax is likely to have a positive impact on societies where income inequality is large.
In fact, this synergy is likely to be greater in reality because in a more unequal society the
same income tax plan will reduce inequality more significantly and reduce labour cost
more significantly. Hence in this model we reach the same proposition as before:
redistribution plan has more positive impacts, or less negative impacts, on total labour
supply in societies with higher income inequality.
4.3 Comparison income effect model
There is voluminous evidence that people’s happiness and behaviours depend on their
relative income to a “reference” income rather than the absolute incomes. Brady et al.
(1947) find that people’s saving behaviour does not depend on the absolute income but on
relative income. Clark at el. (1996) and Ferrer-i-Carbonell (2005) study household data in
Britain and Germany and conclude that an increase in absolute income relative to the
reference income leads to an increase in happiness.
This model assumes that the reference income is the average wage after tax income in the
society. Hence the effective wage that matters in this case is WAT/S, where S is the average
after tax wage.
Assume that a worker who provides l units of labour supply gains w l as his wage. His after
tax wage is (w l)1-τ, which is a progressive tax when 0<τ<1 and w l>1. Also assume that the
cost of providing l units of labour is
where k is a constant and A is the ability of the worker. Hence people with high abilities
can provide the same amount of labour units for lower costs. Now a worker decides his
labour supply so as to maximize his utility,
Thus his labour supply is
(4.3.1)
Therefore the total labour supply in this economy is
where f(A) is the distribution function of ability. Assume that the total output of the
economy is given by
where K denotes the capital. If the labour market is competitive the wage per labour unit
is the marginal productivity of labour,
It can be also seen that
These conditions determine the total labour supply. If ability is normally distributed with
the mean μ and the standard deviation σ and truncated at μ-a and μ+a, one obtains
where
and
Although this result is rather complicated and seems hard to draw general conclusions, we
can still analyze how tax rate, τ, affects the labour supply. The labour supply function
breaks into two parts; the one that contains Z and Z’ and the rest. Z and Z’ are increasing
with τ while the other is decreasing. Therefore we can guess that τ can have positive
impact on labour supply when Z and Z’ responds sensitively to τ, that is, when σ is large.
On the other hand, by virtues of (4.3.1) the after tax wage
is log normally
distributed with the logarithm standard deviation σk(1-τ)/(k-(1-τ). Hence a large σ will
make the income inequality large. Therefore one reaches a general proposition
Proposition. Progressive income tax leads to an increased labour supply when
the income inequality in the economy is large.
See Appendix D for the graphs when σ is large and small. For certain sets of values σ=1
produces a bell-shape curve, which shows that an initial increase in τ increases GDP,
whereas for σ=0.5 GDP is strictly decreasing with τ.
Therefore, in all the three models I reach the same proposition through different channels.
The next question is: do they have empirical supports?
5. Empirical Test
5.1 Data
In this section I examine regressions to test model 1 and 2.
This paper uses a long-term GDP per capita growth rate as a measure for labour supply.
This is because between economic growth and labour supply, labour supply is less
responsive to income tax and labour supply measured by hours worked may not be a good
measure of workers’ efforts, as we have seen in the literature review. Specifically I look at
a 10-year average GDP per capita growth between 2002 and 2011. Although it is evidently
subject to numerous other factors, GDP per capita growth is positively related with labour
supply and it seems a convenient measure to capture people’s efforts in work either by
working longer or being more productive within the given hours.
The size of redistribution is measured by several variables. One of them is tax on income,
profit and capital gain of individuals as percentage of GDP(simply denoted as income tax
henceforth). This paper simply takes the average tax rate inclusive of social security
contributions as a measure of income tax, though in a detailed study it might be desirable
to use different marginal tax rates at different levels of earning. The social security
contributions may have a different incentive effect from income tax given their specific
purposes, but this paper does not separate them because the models do not differentiate a
form of payment to the government. Another measure of redistribution is public social
expenditure as percentage of GDP. This paper uses different measures of redistribution to
see if they produce different results.
Finally the measure of income inequality is gini coefficient before tax and transfers.
The datasets are taken from OECD Factbook and each variable is averaged over 10 years
between 2002 and 2011. The reason for this is that some data, especially gini coefficient,
are not available every year and therefore it is appropriate to take average of available
data over some time span. It also serves to eliminate short term fluctuations. There are 22
countries in the sample. See Appendix B for the countries used.
5.2 Specification
In order to test the proposition, my specification of regression is
GDP growth=β0+ β1*gini+ (β2+β3*gini)*redistribution+ β4*others
The coefficient of redistribution depends on gini coefficient. The model predicts that the
sign of β3 is positive, so that a higher inequality causes redistribution to have a more
positive effect. Others are other variables that can also affect GDP per capita growth. They
are included in order to test the robustness of the regression.
First let us examine the regressions using three different measures of redistribution;
income tax, public social expenditure and income tax and public social expenditure
combined, all as percentage of GDP. As another variable I include gross capital formation
as percentage of GDP. I also examine regressions without the interaction term. The result
is presented below:
Table 1 OLS regression for GDP per capita growth on various measures of redistribution (OECD countries)
Dependent Variable: GDP per capita growth
Measures of Redistribution
Public Social
Expenditure
Income Tax
inv
gini
Redistribut
ion
Gini*Redis
tribution
Constant
Income tax and public
social expenditure
combined
-0.01
-0.01
(0.06)
(0.07)
-2.22
-0.18
(2.25)
(1.87)
-0.01
(0.07)
-2.14
(2.33)
-0.01
(0.06)
-15.83**
(5.90)
-0.01
(0.06)
-2.09
(2.41)
-0.01
(0.06)
-1.57
(2.86)
0.00
(0.03)
-0.61*
(0.31)
-0.01
(0.02)
0.00
(0.03)
-0.00
(0.01)
0.03
(0.03)
-
1.41*
(0.73)
7.93***
(2.73)
-
-
2.19
(1.73)
-0.02
(0.05)
1.94
(2.19)
2.13
(1.93)
-0.14
(0.13)
1.62
(1.81)
22
0.04
22
0.04
22
0.03
22
0.09
1.98
(2.12)
Observatio
ns
22
22
R-squared
0.03
0.17
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
The table shows that only income tax as a measure of the size of redistribution produces
significant results when the interaction term is included. Note that the coefficient of the
interaction is positive, as the model predicted. It suggests that if gini coefficient is greater
than 0.43 income tax is expected to have a positive association with GDP growth. In the
sample countries, this is the level of Sweden before tax income tax.
This result is at odds with model 1. Model 1 does not work with income tax only. What
really encourages people to work more is the presence of subsidy. Therefore the result
does not support the first model.
An obvious question that arises is the existence of endogeniety in the regression. For
instance in countries where income inequality is low, a high GDP growth may encourage
governments to give back to the people by lowering income tax since there is relatively
less need for redistribution. On the other hand in countries where income inequality is
high, governments may be better able to raise income tax to increase social expenditure if
GDP growth is high. Hence GDP growth causes income tax to change contingent on
inequality rather than the other round. Even though this logic sounds sensible, there is
little reason to assume that only income tax is subject to such changes. Therefore, to test
the argument, I examine the same regression with different tax sources. The result is
presented in Table 2.
Table 2 OLS regression for GDP per capita growth on various taxes (OECD countries)
Dependent Variable: GDP per capita growth
Tax Measures
Tax on income, profit
and capital gain of
corporations
inv
-0.01
(0.06)
gini
-7.36
(6.53)
tax
-0.80
(0.95)
Gini*tax
1.80
(2.24)
Constant
4.42
(2.80)
Observations
22
R-squared
0.06
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Tax on goods and
services
Total tax
-0.01
(0.06)
-1.62
(5.63)
0.02
(0.25)
-0.07
(0.58)
2.04
(3.06)
22
0.04
-0.01
(0.06)
-2.88
(15.36)
-0.01
(0.22)
0.02
(0.48)
2.65
(7.18)
22
0.04
Table 2 shows that such result does not hold for other sources of tax revenues. Although
this does not entirely reject the presence of endogeneity, it does cast doubt on the
argument. Perotti (1992), studying the relation between inequality and economic growth,
also questions the endogeniety of fiscal policy on the basis of income distribution. Other
studies reach similar conclusions (Keefer-Knack, 1995; Lindert, 1996).
The next issue is how robust the correlation between GDP growth and income tax is. To
test this, I include other variables that in previous literature has been found to be
positively correlated with GDP growth. This approach follows Ross and Renelt (1992).
They suggest including other possible variables to the original regression and if the
coefficient of interest remains significant and consistent in value, we say the result is
robust. I choose as the other variables the share of export in GDP, R&D expenditure as a
share of GDP, labour participation rate and public social expenditure.
Table 3 OLS regression for GDP per capita growth on income tax while including other variables (OECD countries)
Dependent Variable: GDP per capita growth
Other variables
GDP per
capita
inv
Export
-0.00
-0.00
(0.06)
(0.06)
gini
-15.21**
-15.71**
(6.17)
(6.12)
tax
-0.60*
-0.61*
(0.32)
(0.32)
tax*gini
1.38*
1.41*
(0.75)
(0.75)
Other
0.00
0.00
(0.00)
(0.00)
Constant
7.34**
7.73**
(3.09)
(2.91)
Observations
22
22
R-squared
0.18
0.18
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
R&D
0.03
(0.05)
-11.90**
(5.58)
-0.57**
(0.25)
1.30**
(0.60)
0.41**
(0.16)
4.57
(2.94)
22
0.48
Labour
Participation
Rate
0.01
(0.06)
-14.22**
(6.39)
-0.66**
(0.28)
1.54**
(0.66)
0.02
(0.02)
5.37
(4.18)
22
0.24
Public Social
Expenditure
-0.01
(0.05)
-15.62**
(6.16)
-0.61*
(0.31)
1.41*
(0.73)
-0.01
(0.02)
8.06***
(2.61)
22
0.18
Hence the regression is indeed robust at least at 10% significant level to inclusion of other
variables and the coefficients are reasonably consistent around 1.4~1.5.
Therefore the validity of the proposition is strongly supported by data.
5.3 Testing Model 2
Now I test Model 2 as a possible channel for such correlation. To do this, this paper
postulates that the impact of reduced income inequality on health is only significant when
the average health in a society is relatively low. This is because health is evidently affected
by many other factors and as health improves, direct factors, such as medical technology
and diet nutrition, become more important than indirect factors such as income inequality.
To see if this is true, I divide the sample countries into two groups with a health measure
below and above the median. If the assumption is true there should be a negative
correlation between income inequality and the health measure for the below median
group but not for the above median group.
For health measures I use life expectancy at birth and Human Development Index (HDI).
HDI is an index that measures an overall well-being of society by taking into account
various factors such as education attainment and literacy rate. Life expectancy data is
taken from the World Bank Data and HDI from UN Development Programme Report.
Table 4 Correlation between inequality and health measures (OECD countries)
Measure of Health
Life expectancy
HDI
Above
Below
Above
Below
Median
Median Median Median
gini
3.41
-7.46
-0.02
-0.52**
(7.11)
(5.62)
(0.18)
(0.20)
Constant
79.89*** 81.27*** 0.92*** 1.03***
(2.06)
(1.72)
(0.06)
(0.05)
Observations 11
11
11
11
R-squared
0.02
0.24
0.00
0.61
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Hence the assumption seems true when HDI is used as a measure of health. Although the
assumption does not seem to work for life expectancy, this is likely to be due to the
existence of an outlier. See Appendix C for the graphs. Indeed if we omit Denmark from the
sample above median, a significant result is obtained.
Hence the regressions confirm that the impact of income inequality on health is
insignificant once the health level reaches a certain point. This means that for those
countries the marginal cost of labour does not shift appreciably after income tax reduces
inequality. The basic assumption of the model is thus violated and the previous
regressions should be insignificant. The regressions below confirm the prediction for life
expectancy. For HDI most coefficients are significant but only the interaction term fails to
be significant.
Table 5 OLS regression for GDP per capita growth on income tax among groups with different health level (OECD
countries)
Dependent Variable: GDP per capita growth
Measure of Health
Life Expectancy
Above Median
Below Median
inv
0.06
-0.01
(0.10)
(0.07)
gini
3.62
-19.21**
(15.53)
(6.52)
tax
0.41
-0.86**
(0.81)
(0.30)
tax*gini
-0.73
1.98**
(1.81)
(0.73)
Constant
-3.12
9.67***
(7.62)
(2.43)
Observations
11
11
R-squared
0.31
0.66
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
HDI
Above Median
0.01
(0.08)
4.23
(30.93)
0.26
(1.62)
-0.38
(3.59)
-1.96
(14.09)
11
0.29
Below Median
-0.06
(0.03)
-24.97**
(7.72)
-0.73*
(0.38)
1.58
(0.91)
13.80***
(3.30)
11
0.37
These regressions, however, evidently suffer from the small sample size. I therefore
extend the dataset to World Bank. The World Bank does not offer gini coefficients before
tax and transfer but only after tax. It also only offers total tax revenue as percentage of
GDP rather than income tax on individuals. This paper assumes that they are good proxies
to the desired variables. First I test whether the interaction between gini coefficients and
tax revenue is also significant for this sample.
Table 6 OLS regression for GDP per capita growth on income tax while including other vairables (World Bank
countries)
Dependent Variable: GDP per capita growth
Other Variables:
inv
gini
tax
tax*gini
Other
None
GDP per capita
Export
0.12***
(0.03)
-17.19***
(4.70)
-0.37***
(0.13)
0.65**
(0.25)
0.13***
(0.03)
-14.39***
(4.46)
-0.28**
(0.12)
0.47*
(0.24)
-0.00***
(0.00)
8.06***
(2.25)
86
0.33
0.12***
(0.04)
-17.85***
(4.78)
-0.40***
(0.14)
0.70***
(0.26)
0.01
(0.01)
9.62***
(2.34)
86
0.30
Government
Expenditure
0.13***
(0.04)
-19.20***
(4.65)
-0.54***
(0.16)
0.88***
(0.27)
0.05
(0.03)
9.99***
(2.32)
82
0.33
Constant
9.48***
(2.36)
Observations
86
R-squared
0.29
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Hence the hypothesis holds that the interaction between gini coefficients and income tax is
significant and positive.
Let us again test whether income inequality negatively affects life expectancy.
Table 7 Correlation between inequality and health measures (World Bank countries)
Dependent Variable: Life expectancy
Below
All
Median
gini
-22.29**
-41.43***
(10.37)
(12.61)
Constant
75.83***
76.84***
(4.00)
(5.02)
Above
Median
-3.5
(3.85)
74.84***
(1.63)
Observations
85
42
43
R-squared
0.05
0.21
0.02
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Hence in this case the entire sample is negatively correlated with income inequality but
the correlation is stronger for countries with shorter life expectancy and weaker for
countries with longer life expectancy, the same pattern that we observed with the OECD
countries. Now I examine whether the regression becomes insignificant for above median
group.
Table 8 Correlation between inequality and health measures (World Bank countries)
Dependent Variable: GDP per capita growth
Life Expectancy
Below Average Above Average
inv
0.11**
0.14***
(0.05)
(0.05)
gini
-19.99***
-5.55
(6.43)
(14.12)
tax
-0.43**
-0.11
(0.17)
(0.37)
tax*gini
0.80**
-0.19
(0.33)
(0.89)
Constant
10.76***
5.61
(2.92)
(6.55)
Observations
42
43
R-squared
0.26
0.38
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Hence in this sample again the interaction between income tax and inequality is significant
only for countries where health is affected by inequality.
These results seem to support model 2.
5.4 IV Estimation
Another way to interpret the models and the regressions so far is that inequality causes
economic growth in face of high income taxes. This view, however, does not contradict the
other view that high income taxes cause economic growth in presence of high inequality.
After all in the models both inequality and income tax are underlying structures that
constitute workers’ incentives. Nonetheless this new perspective enables the use of
instrumental variable. This allows us to address the issue of causality. Easterly (2007)
suggests that the log of the ratio of land suitable for wheat to that for sugarcane is a good
instrument of inequality. The “wheat-sugar ratio” is defined as lwheatsugar=log[(1+share
of arable land suitable for wheat)/(1+ share of arable land suitable for sugarcane)]. That
this is indeed strongly correlated with inequality both for the OECD countries and the
World Bank countries can be seen from the graphs in Appendix E. The instrument is
rightly assumed to be exogenous because it is not affected by other variables that lead to
different inequality. Finally it also satisfies exclusion restriction which states the
instrument may affect economic growth only through inequality. Therefore, we can assert
that lwheatsugar is indeed a good instrument for inequality.
Since inequality also appears in the regression as an interaction with income tax, I use 2
stage least square estimation where the endogenous variable are inequality and
inequality*tax. The instrumental exogenous variables are lwheatsugar and
lwheatsugar*tax. The results are presented below.
Table 9 2SLS regression for GDP per capita growth on income tax while including other vairables (OECD countries)
Dependent Variable: GDP per capita growth
Other variables
inv
Gini
tax
tax*gini
None
export
GDP per
capita
0.00
(0.04)
-32.73***
(10.32)
-1.49***
(0.49)
3.45***
(1.17)
0.00
(0.05)
-32.92***
(9.64)
-1.49***
(0.48)
3.46***
(1.16)
0.00
(0.01)
15.02***
(4.67)
0.00
(0.05)
-32.77***
(9.49)
-1.49***
(0.51)
3.46***
(1.24)
0.00
(0.00)
1.61
(14.50)
Other
Constant
14.95***
(4.99)
Observation
s
20
20
R-squared
0.00
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
20
0.07
Labour
participation
rate
0.00
(0.05)
-32.73***
(11.68)
-1.41***
(0.43)
3.25***
(1.02)
0.02
(0.04)
13.98*
(7.24)
20
Public social
expenditure
0.00
(0.03)
-32.72***
(9.65)
-1.49***
(0.48)
3.45***
(1.14)
0.00
(0.03)
14.94***
(4.09)
20
Hence the IV estimations give very consistent and significant results for the OECD
countries. They are stronger than the previous OLS regressions. They suggest that if
income tax accounts for roughly more than 9.5% of GDP, which is the level of Austria,
more inequality leads to higher incentives for workers. In other words, anywhere below
that level, inequality is keeping workers from putting more efforts.
The same IV estimation for the World Bank countries is rather disappointing. None of the
regressions are significant and nor do they produce consistent coefficients. However, this
may be due to the fact that the variable used here are only proxies for what the models
deal with.
Table 10 2SLS regression for GDP per capita growth on income tax while including other variables (World Bank
countries)
Dependent Variable: GDP per capita growth
Other Variable
inv
gini
tax
tax*gini
None
GDP per capita
export
0.14
(0.09)
36.02
(79.49)
1.28
(2.15)
-2.86
(4.51)
0.08
(0.08)
21.14
(52.41)
1.13
(1.63)
-2.43
(3.34)
-0.00
(0.00)
-7.73
(24.40)
69
0.15
(0.10)
39.50
(89.56)
1.43
(2.52)
-3.10
(5.18)
-0.02
(0.05)
-17.05
(42.22)
69
Other
Constant
-15.76
(38.20)
Observations
69
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Government
expenditure
0.02
(0.17)
30.81
(87.69)
1.91
(3.43)
-3.71
(6.54)
-0.18
(0.27)
-9.77
(37.70)
68
6. Discussion and Conclusion
6.1 Discussion
The above results seem to contradict the previous findings that low income workers,
especially part time workers, reduce hours worked when income tax rises. The models in
this paper say that the very same low income workers can increase work efforts with
raised income tax if inequality is high. This contradiction may be due to two things. First
the part time workers may face different incentive problems than the models assumed,
such as other sources of income from families or governments. Second the regressions
gave support for the second model, which assumes that reduced inequality improve
workers’ productivity. This means that the effect of income tax is long-term and most
studies that only compare short-term changes just before and after tax reforms may be
misleading. After all if the main force of economic growth is full time workers, the part
time workers’ response to income tax should not interfere with the models’ prediction.
The apparent limitation of the models is that the link between workers’ effort and
economic growth is not straightforward. It is also important to remember that taxes can
alter other decisions such as accumulation of human capital that affect economic growth.
Although the correlations found here turned out fairly strong, to what extent it is causal
calls for further investigation. However, the variables in the regressions are the averages
of 10 years and in such time span workers’ incentives may play an important role in a long
term economic growth.
The regressions for OECD countries also suffer from the small sample size. One solution is
to use panel data regressions to increase the sample size. This may also solve the issue of
causality. However, some data, gini coefficients in particular, are not available every year.
Moreover, that the second model suggests long-term effects of income tax means that we
would need even longer period of data to gather enough sample size.
6.2 Conclusion
This paper suggested three models that imply income tax or income tax and social
expenditure combined can increase work incentives. Each model is based on a different
assumption as to what constitutes such incentive. This paper provided empirical tests for
the first two models. The first model did not have empirical support because government
subsidies were found insignificant. The second model, on the other hand, gave correct
predictions that if income inequality is linked with population health the proposition holds.
Therefore this paper found that there is evidence to support the second model.
It is important to be reminded that the regressions in the paper do not directly prove
causality of income tax on economic growth but the facts that many other variables, such
as government expenditure, income tax on corporate and tax on goods and services, that
should be influenced by the same endogenous factors that also affect income tax failed to
show correlations, and that the result was significant even among the OECD countries
which are likely to have similar economic conditions suggest that the correlations may be
indeed causations. It would be interesting to use an instrumental variable but finding a
good IV to prove the causation shall be left to further studies.
This paper provided another perspective whereby inequality causes economic growth in
face of high income tax. Here the IV method was used and the results for OECD countries
suggested causation while those for World Bank countries were rather disappointing.
Finally, the third model, which assumes that people look at their relative incomes, is
interesting in itself but this paper did not provide any empirical examination because it is
hard to test the impact of relative incomes while holding other variables constant. There is
a possibility for an experiment: we could ask subjects to take tests and reward them with
prizes based on their scores. If we make the result public, it would give subjects a way to
compare themselves to the average score. We could then see how subjects would be
incentivized to work harder or less hard towards the tests when the rewards are “taxed,”
depending on the inequality among the subjects’ abilities. This paper’s model predicts that
when inequality is high a tax will make it easier for low ability people to get closer to the
average score and hence they will work harder and perform better.
To my knowledge no study has examined an impact of income tax on economic growth
when income inequality is considered. I hope this paper encourages other researchers to
follow the path and conduct more detailed studies in this subject.
Appendix A
How output changes when inequality changes based on superstar hypothesis
GDP
1.0
0.8
0.6
0.4
0.2
1
2
3
4
(c,k,σ)=(0.5,4,0.5)
GDP
α
25
20
15
10
5
1
2
3
4
(c,k,σ)=(0.5,4,2)
In this case the optimal α that maximizes GDP
is closer to 1 compared to the case above
α
GDP
1.2
1.0
0.8
0.6
0.4
0.2
1
2
3
(c,k,σ)=(0.5,4,0)
When σ=0 GDP is strictly increasing as α increases
4
α
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
Iceland
Ireland
Italy
Appendix B
List of OECD countries used in the regression
Japan
Luxembourg
The Netherlands
New Zealand
Norway
Portugal
Spain
Sweden
Switzerland
United Kingdom
United States
Appendix C
Scattering plots of gin coefficients on health measures
Life Expectancy
Above Average
80.5
81
81.5
LifeEx
78.5
78
80
77.5
.25
.3
.35
.4
.26
.28
.3
gini
gini
.32
.34
HDI
Above Average
HDI
.86
.93
.88
.94
.9
.95
Below Average
.8
.9
.82
.91
.84
.92
HDI
LifeEx
79
82
79.5
80
82.5
Below Average
.25
.3
gini
.35
.25
.3
.35
gini
.4
Appendix D
How output changes depending on tax level based on model 3
GDP
120
115
110
0.2
0.4
0.6
0.8
1.0
0.8
1.0
Output vs. Tax rate
a=1, σ=1,k=12,μ=5,α=0.5
t
GDP
120
115
110
105
100
95
90
0.0
0.2
0.4
0.6
a=1, σ=0.5,k=12,μ=5,α=0.5
t
.5
.45
.4
.35
Gini before tax and transfer
.55
Appendix E
0
.2
.4
.6
lwheatsugar
.6
.5
.4
.3
Gini after tax and transfer
.7
Gini index before tax and transfer vs. lwheatsugar for OECD countries.
Data of lwheatsugar for Iceland and Luxemburg are missing
-.4
-.2
0
.2
.4
.6
lwheatsugar
Gini index after tax and transfer vs. lwheatsugar for World Bank countries
Source: Easterly(2007)
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