A model of international tax competition is developed in which taxes are raised in order to finance education which in turn raises income. It is shown that, in contrast to results from the tax competition literature, the outcome of a non-cooperative game can be to raise the tax rate, with the result that investment in education exceeds that which is globally socially optimal. This provides an explanation for the tendency for countries to emphasise growth as an objective in spite of what empirical studies tell us about the impact of income on happiness; it also identifies a new type of overeducation.

Geraint Johnes

English

Research Papers in Economics

 
 
 
 
 
 
 
Lancaster University Management School 
Working Paper  
2002/004 
 
 
 
 
 
Going for Growth: Overeducation in a Tax Competition 
Game  
 
 
 
 
 
Geraint Johnes 
 
 
 
The Department of Economics                        
Lancaster University Management School 
Lancaster LA1 4YX 
UK 
 
 
©Geraint Johnes  
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two paragraphs, may be quoted without explicit permission, 
provided that full acknowledgement is given. 
 
The LUMS Working Papers series can be accessed at http://www.lums.co.uk/publications 
LUMS home page: http://www.lums.lancs.ac.uk/ 
 
 
  
 
 
 
 
GOING FOR GROWTH: OVEREDUCATION IN A TAX COMPETITION GAME 
 
 
 
Geraint Johnes 
 
 
Department of Economics 
Lancaster University Management School 
Lancaster University 
Lancaster LA1 4YX 
United Kingdom 
 
Voice: +44 1524 594215 
Fax: +44 1524 594244 
E-mail: G.Johnes@lancs.ac.uk 
 
 
May 2002 
 
 
ABSTRACT 
 
A model of international tax competition is developed in which taxes are raised in order to 
finance education which in turn raises income. It is shown that, in contrast to results from the 
tax competition literature, the outcome of a non-cooperative game can be to raise the tax 
rate, with the result that investment in education exceeds that which is globally socially 
optimal. This provides an explanation for the tendency for countries to emphasise growth as 
an objective in spite of what empirical studies tell us about the impact of income on 
happiness; it also identifies a new type of overeducation. 
 
 
 
 
JEL Classification:  I20, H42, H21, H87, E62 
Keywords:  growth, overeducation, tax competition, income distribution, 
international social welfare function 1. Introduction 
 
Numerous recent studies have established that the distribution of income is an important 
determinant of happiness. Some of this evidence suggests that raising the income of all 
individuals will not raise well-being (Easterlin 1995; see also Alesina et al., 2001; Easterlin, 
2001; Oswald, 1997; Morawetz, 1977). In light of this, it is somewhat puzzling to observe 
that the authorities typically opt to pursue policies that are aimed at providing sustained 
growth, where inflation rather than inequality is seen as the limiting constraint. In this note, I 
provide one possible explanation for this.  
 
In order to render the analysis as simple as possible, I focus on educational policy as the 
route by which governments seek to stimulate growth. Inasmuch as it increases human 
capital and the productivity of the educated worker, education affects both the level and 
distribution of income within an economy. I develop a model of educational investment by 
societies where education is financed through the exchequer, and where the goal is to choose 
a tax rate that maximises social welfare. Social welfare in turn is a function of both the level 
and the distribution of income both within the domestic economy and abroad. Tax is 
therefore chosen in each country to maximise welfare in that country, given the actions of 
the government of the other country in the model. There is therefore a game being played by 
the governments of each country in the fashion of Nash (1951). The nub of the paper is that a 
prisoners' dilemma effect within this game can lead to countries investing more in education 
(that is, they pursue more growth oriented policies) than they would do in a cooperative 
solution. Note that this provides a counterexample to a well known finding in the tax 
competition literature: namely that the Nash equilibrium implies the setting of tax rates that are below the levels required to finance efficient quantities of publicly provided goods 
(Edwards and Keen, 1996). 
 
 
 
2. The Model 
 
The disposable income of individual i is given by  
 
Yi = (Y0 + sib)(1-τ)            ( 1 )  
 
where Y0 is basic income to be defined more precisely later, si is a binary variable that 
indicates whether the ith individual has undertaken schooling or not, τ is the proportional 
rate of income tax, and b is the income premium associated with schooling. Tax revenues are 
used solely for the purpose of financing education. I assume that education takes place 
instantaneously, and that the cost to the exchequer of educating an individual is a constant c.   
 
Denote by λ the proportion of the population n that undertakes education. Total tax revenue 
is given by  
 
τn(Y0 + λb )             ( 2 )  
 
This must equal the total cost of education cλn, in order for the exchequer's books to 
balance. Solving for λ, which must lie within the unit interval, yields  
 λ = τY0/(c-τb )             ( 3 )  
 
In order to express simply the emphasis that society places on the distribution of income, a 
weight of less than unity, say σ, where 0≤σ≤1, may be attached to the disposable incomes of 
those whose incomes exceed Y0. The weighted sum of disposable incomes is therefore given 
by  
 
V = n(1-τ)[Y0(1-λ)+σλ(Y0+ b ) ]          ( 4 )  
 
So far I have considered only one country. Suppose now that the world comprises two 
countries, labelled a and b. The above analysis applies within each country. A subscripted a 
or b could be attached to each variable in order to indicate the country to which it refers.  
 
To proceed further, I assume that there are positive and non-pecuniary externalities 
associated with education (McMahon, 1999). These may be country-specific or may spill 
over across country boundaries. Social welfare in a given country varies positively with 
disposable incomes and externalities due to education such that 
 
Wj = {ρ[(1-λj)Y0+λjσ(Y0+b)](1-τj)+(1-ρ)[(1-λk)Y0+λkσ(Y0+b)](1-τk)}λjαλkβ   (5) 
 
where 0≤ρ≤1, and n comes out in the wash. For simplicity, I shall assume that na=nb, ca=cb, 
σa=σb, Y0a=Y0b, ba= bb, ρa=ρb, αa=αb and βa=βb. These assumptions allow countries a 
and b to be regarded symmetrically. 
 Differentiating each Wj with respect to τj given τk and setting the results to zero defines the 
FOCs allowing the optimal τj to be evaluated for each country in the non-cooperative Nash 
game; in view of the symmetry of the problem, note that ex post τj = τk = τ*, say.  
 
Once τ* is known, it is a routine matter to work back through the equations to find the 
common level of education in each country in the optimum, λ*, and the level of global 
welfare, W* = 2Wj. 
 
To take an example, suppose that ρ=0.6, σ = 0.3, b = 5, Y0 = 20, c = 4, α = 1, and β = -0.5. 
In this case the FOCs are given by  
 
 (525τ*3 - 1540τ*2 + 1256τ* - 160) ξ  =   0           ( 6 )  
 
where ξ = 40√[5τ*/(4-5τ*)]/τ*(5τ*-4)2. From (6), (3) and (5) respectively, it is possible to 
establish that τ* = 0.155, λ* = 0.965 and W* = 13.18. 
 
How does this non-cooperative solution compare with the cooperative solution? In the case 
of co-operation between the countries the optimand is the international social welfare 
function 
 
W = Σm{ρ[(1-λj)Y0+λjσ(Y0+b)](1-τj)+(1-ρ)[(1-λk)Y0+λkσ(Y0+b)](1-τk)}λjαλkβ (7) 
 m=a,b; j=a,b; k=a,b; j≠k. Substituting from (3) into (7) yields an expression which may then 
be maximised with respect to the common tax rate, τ. Using the same parameter assumptions 
as earlier, the FOC satisfies 
 
(175τ*3 - 350τ*2 + 218τ* - 16) ξ  =   0           ( 8 )  
 
Once again, knowledge of the optimal τ*, obtained using numerical methods, permits simple 
calculation of the optimal values of education and social welfare. In the case of our example, 
the globally optimal values of the tax variables are τ*=0.084, yielding a value of λ*=0.471. 
From (6), W*=17.74.  
 
For certain parameters, then, it is readily observed that the value of λ* obtained in the 
cooperative solution is lower than the corresponding value in the non-cooperative solution. 
This finding suggests that the nature of the non-cooperative game is such that the authorities 
invest in growth enhancing activities to a greater extent than would occur in a situation of 
joint welfare maximisation, and this excess investment serves to reduce economic welfare. 
Moreover, and in contrast to standard findings in the tax competition literature, there exist 
parameter vectors that imply optimal tax rates that are greater under non-cooperation than 
under cooperation. 
 
 
3. Conclusion 
 
Recent empirical work has confirmed that aspirations rise as general incomes rise, and that 
the distribution of income has an impact on happiness. To resurrect an old catchphrase, it seems that indeed there are 'limits to growth' - or at least to the ability of growth to secure 
improvements in welfare. Governments have nonetheless been relentless in the pursuit of 
policies aimed at promoting growth. The thrust of this paper has been to argue that this may 
have resulted from the non-cooperative nature of games played between governments of 
different countries. The fragility of any cooperative agreement likely reinforces the tendency 
to grow at a rate that exceeds the global welfare optimum. In addition to providing a 
counterargument to the common finding that competitive taxation results in an inefficiently 
low level of provision, the arguments presented here provoke a new interpretation of the 
phenomenon of overeducation (Daly et al., 2000; Dolton and Vignoles, 2000). 
 
 
 
References 
 
Alesina, Alberto, Di Tella, Rafael and MacCulloch, Robert (2001) Inequality and happiness: 
are Europeans and Americans different?, NBER Working Paper 8198. 
 
Daly, Mary C., Büchel, Felix and Duncan, Greg J. (2000) Premiums and penalties for 
surplus and deficit education: evidence from the United States and Germany, Economics of 
Education Review, 19, 169-178. 
 
Dolton, Peter J. and Vignoles, Anna (2000) The incidence and effects of overeducation in 
the UK graduate labour market, Economics of Education Review, 19, 179-198. 
 
Easterlin, Richard A. (1995) Will raising the incomes of all increase the happiness of all?, 
Journal of Economic Behavior and Organization, 27, 35-47. 
 
Easterlin, Richard A. (2001) Income and happiness: towards a unified theory, Economic 
Journal, 111, 465-484. 
 
Edwards, Jeremy and Keen, Michael (1996) Tax competition and Leviathan, European 
Economic Review, 40, 113-134. 
 
McMahon, Walter W. (1999) Education and development: measuring the social benefits, 
Oxford: Oxford University Press. 
 
Morawetz, David (1977) Income distribution and self-rated happiness: some empirical 
evidence, Economic Journal, 87, 511-522 (with Ety Atia, Gabi Bin-Nun, Lazaros Felous, 
Yuda Gariplerden, Ella Harris, Sami Soustiel, George Tombros and Yossi Zarfaty). 
 
Nash, John F. (1951) Non-cooperative games, Annals of Mathematics, 54, 286-295.  
Oswald, Andrew J. (1997) Happiness and economic performance, Economic Journal, 107, 
1815-1831. 

Education and development: measuring the social benefits,

Going for growth: overeducation in a tax competition game

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