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GROWTH, FISCAL TRANSFERS AND DISTRIBUTIVE CONFLICT
Luigi Bonatti*
ABSTRACT
The link between endogenous growth and fiscal policy modeled in the paper depends on the depressing
impact on the rate of return to private investment that more massive redistributive transfers can cause by
increasing the tax rate and the wage pressure. Indeed, fiscal transfers in favor of the wage earners are
financed by taxing output, and a decrease in the policy parameter—the ratio of total tax revenues to GDP—
monotonically increases the economy’s growth rate. This notwithstanding, the paper shows that the
redistributive implications of such a decrease may induce the wage earners to oppose it.
JEL CLASSIFICATION NUMBERS: E25, H20, I38, O41.
KEY WORDS: endogenous growth, tax burden, welfare reforms, capital-labor conflict.
*University of Bergamo
<[email protected]>
1
INTRODUCTION
In recent years, it is increasingly common to hear economists, commentators, public officials and
institutions claiming that the disappointing growth performance of continental Europe vis-à-vis the United
States (see table 1) has to be attributed – among other factors – to the more costly welfare system and heavier
tax burden of the former (see table 2). The obvious policy implication of this claim for countries like France,
Germany or Italy is that they should implement structural reforms aimed at reducing both the amount of
redistribution operated through the welfare system and the associated tax burden if they want to boost longterm growth. Hence, those advocating the urgency of these reforms argue that the wage earners’
organizations and political representatives opposing them are myopic, since they do not fully appreciate the
long-term benefits that also their constituency can enjoy if the economy grows persistently at higher rates. In
contrast, this paper presents a simple general-equilibrium endogenous growth model where it can be
perfectly rational from the viewpoint of a wage earner to oppose these reforms even if they boost long-term
growth. Indeed, it is shown that workers can have good reasons to resist a cut in the share of GDP devoted to
redistributive transfers in their favor even in a set-up where i) they take into account the future benefits
accruing to them (or to their descendants) in case of higher growth, and ii) this cut has an unambiguously
positive effect on long-term growth. In other words, even conceding that these reforms will permanently
improve the growth performance of the economy and that their effects on workers’ well-being should be
evaluated in a very long-term perspective, their redistributive implications might be such that workers could
be better off if they are not implemented.
TABLE 1
REAL GDP: PERCENTAGE CHANGE, 1991-2001
France
20.39
Germany
15.76
Italy
16.22
United States
39.90
TABLE 2
TOTAL REVENUES AND EXPENDITURES AS A PERCENT OF GDP IN 1998
Tax burden
Expenditures
France
45.8
53.3
Germany
42.3
48.1
Italy
42.8
50.6
United States
29.8
32.6
1
The link between economic growth and fiscal policy modeled in the paper depends on the depressing
impact on the rate of return to private investment that more massive redistributive transfers can cause by
increasing the tax rate and the wage pressure. The former mechanism has been emphasized by the literature
studying the effects of tax policy in growth models (see Rebelo, 1991; Stokey and Rebelo, 1995; McGrattan
and Schmitz, 1999), the latter by those focusing on the so-called “labor-market channel” (see Alesina et al.,
2002), namely on the proposition that high public spending and taxation reduces profits and investment by
putting upward pressure on private sector wages. Indeed, fiscal redistribution can distort labor-supply
incentives,1 by affecting the ratio between the income conditional on working and the income conditional on
non working (see Phelps, 1997; Pissarides, 1998). Hence, the model presented in this paper is consistent with
the literature emphasizing that higher public trasfers and taxation tend to raise both the real wages and the
capital-labor ratio, and to lower both the employment rate (see table 3) and the expected return on capital,
thus depressing investment (see table 4) and growth (see Daveri and Tabellini, 2000). Within this
framework, the paper vindicates the intuition according to which the wage earners can be right in resisting a
cut in welfare programs and taxation, since they appropriate only a portion of the fruits of the higher growth
made possible by the cut, while bearing its entire impact in terms of less favorable income distribution.
TABLE 3
EMPLOYMENT RATE: NUMBER EMPLOYED RELATIVE TO WORKING-AGE POPULATION IN 1998
France
60.8
Germany
61.5
Italy
51.7
United States
75
TABLE 4
TOTAL GROSS INVESTMENT: AVERAGE ANNUAL PERCENTAGE CHANGE, 1991-1998
France
-0.3
Germany
1.1
Italy
-0.4
United States
4.9
The paper is organized as follows: section 2 presents the model; section 3 characterizes the
equilibrium path of the economy; sections 4 discusses the potential conflict between capitalists and wage
earners over the share of national product to be redistributed through the fiscal system; section 5 concludes.
1
See Bourguignon (2001). Prescott (2003) presents some evidence on the role of taxes in explaining the differences
2
2
THE MODEL
In the economy under consideration, there are the capitalists (who are the firms’ owners), the
workers and the government. All markets are perfectly competitive. Time is discrete and the time horizon is
infinite.
The firms
There is a large number (normalized to be one) of identical firms. The only good produced in this
economy is Yt, which is the numéraire of the system. Each firm produces this single good according to the
technology
Yt  A t Lt K1t- , 0    1,
(1)
where At is a variable measuring the state of technology, K t is capital (capital can be interpreted in a broad
sense, inclusive of all reproducible assets) and Lt is labor. It is assumed that At is a positive function of the
stock of capital existing in the economy: A t  Kt .2 Moreover, consistently with Frankel (1962), it is
supposed that although At is endogenous to the economy, each firm takes it as given, since a single firm
would only internalize a negligible amount of the effect that its own investment decisions have on the
aggregate stock of capital. Finally, note also that the price of Yt is set to be one.
Assuming that firms’ revenues are taxed, the period net (after taxes) profits t of a firm are given by:
 t  (1 -  )Yt - Wt L t - c(I t , K t ) , 0    1 ,
(2)
where  is the (fixed) tax rate, Wt is the real wage, and
2
I
c(It,Kt)=It+ t , I t  0 ,
Kt
(3)
are the investment costs, which are the sum of gross investment It and adjustment costs. In their turn, the
latter are assumed to be a quadratic function of It and a decreasing function of Kt.
The capital stock evolves according to
Kt+1=It+(1-)Kt , 01, K0 given,
(4)
where  is a capital depreciation parameter.
between the USA and continental Europe in labor supply across time.
2
Consistently with this formal set-up, one can interpret technological progress as labor augmenting.
3
The capitalists
The capitalists who are the firms' owners: for simplicity and without loss of generality, it is assumed that
each capitalist owns one firm, in the sense that s/he is the proprietor of the firm’s productive assets and is
entitled to receive its net profits. S/he has also full control on his/her own firm’s decisions. Moreover, the
capitalists take account of the welfare and resources of their actual and perspective descendants. Indeed,
following Barro and Sala-i-Martin (1995), this intergenerational interaction is modeled by imaging that the
current generation maximizes utility and incorporates a budget constraint over an infinite future. That is,
although individuals have finite lives, the model considers immortal extended families (“dynasties”).3 The
current adults expect the size of their extended family to remain constant, since expectations are rational (in
the sense that they are consistent with the true processes followed by the relevant variables). In this
framework in which there is no source of random disturbances, this implies perfect foresight. Finally, again
for simplicity and without loss of generality, bequests are assumed to be accidental.4
The representative capitalist’s problem amounts to deciding a contingency plan for consumption C t
Lt and It in order to maximize:


s t
 s-t v(C s ),
 (C )1-
 t
if   0 and   1
0<<1, v(C t )   1 - 

ln(C t ) if   1,
(5)
subject to (4) and to
C t  c(I t , K t )  (1 -  )A t Lt K1t- - Wt L t , K0 given.
(6)
In (5),  is a time-preference parameter, and  is the inverse of the intertemporal elasticity of substitution in
consumption.
3
As Barro and Sala-i-Martin (1995, p. 60) point out, “this setting is appropriate if altruistic parents provide transfers to
their children, who give in turn to their children, and so on. The immortal family corresponds to finite-lived indiiduals
who are connected via a pattern of operative intergenerational transfers that are based on altruism”.
4
In other words, it is ruled out the existence of actuarially fair annuities paid to the living investors by a financial
institution collecting their wealth as they die: the wealth of someone who dies is inherited by some newly born
individual.
4
The workers
For simplicity and without loss of generality, it is assumed that the working population is constant
and that its size is N. Moreover, workers are assumed to consume their entire income, which comes from two
sources. Indeed, a worker’s period utility is given by
u ( Wt  G t ) if employed
u (.)  
u(G t ), if not employed,   1, u '  0, u ' '  0,
(7)
where Gt is the workers’ non-labor income (namely the monetized value of the welfare entitlements and
government transfers made to all workers in period t), and >1 captures the fact that a worker can enjoy
more leisure (and/or undertake some home activity) when s/he is not employed.
It is apparent that market forces simultaneously determine Wt and Lt in such a way that one has or
Wt>(-1)Gt entailing Lt=N (full employment), or Lt<N entailing Wt=(-1)Gt.
The government
The government must balance its budget in each period. Hence,
Gt 
3
Y t
N
(8)
.
THE EQUILIBRIUM PATH
Capitalists’ optimal behavior
The optimality condition with respect to the choice of the labor input is
(1 -  )A t Lt -1K1t-  Wt ,
(9)
thus implying that employment is:
1
 (1 -  )A t  (1- ) .
Lt  Kt 

 Wt


 
By using (1), (3) and (10), one can rewrite (2) as  t  (1 -  )K t (1 -  )A t 

 Wt

(10)
1




  (1- )



I2
- It - t .
Kt
Hence, one can solve the intertemporal problem of the representative capitalist by maximizing
5
 
 

 

 s- t v (1 -  )K s (1 -  )A s 


 Ws

s t


 


1

  (1- )
 
 
 




   s [I s  (1 -  )K s - K s 1 ] with respect to It, Kt+1
- Is Ks 




I s2
and t, and then by eliminating the multiplier t, thus obtaining (4) and
1


    (1- )
 
(1 -  ) (1 -  )A t 1 
 X 2t 1  (1 -  )(1  2X t 1 )
 


W
t

1

 
I
1 C 

  t 1  , X t  t ,
1  2X t
  Ct 
Kt
(11)
where
1


    (1- )




C t  (1 -  )K t (1 -  )A t 
- K t (X t  X 2t ) .



 Wt 1  

(12)
Thus, an investor’s optimal plan must satisfy (11), (12) and the transversality condition
lim  s (X s  X s2 )K s Cs-  0 .
(13)
s
Labor-market equilibrium

 (1 -  )N
if  

Equilibrium in the labor market implies L t  L( )    ( - 1)
   -1
N otherwise,

thus entailing
Wt  (1 -  )A t L( ) -1 K1t- .
(14)
General equilibrium path
Considering (4), (11), (12), (14) and A t  Kt , one can obtain the system of equations governing the
general equilibrium path of the economy:
1  t  X t 1-  ,  t 
K t 1 - K t Yt 1 - Yt

,
Kt
Yt

(15)


(1 -  )(1 -  )[ L( )]  X 2t 1  (1 -  )(1  2X t 1 ) 1  (1 -  )(1 -  )[ L( )] - X t 1 - X 2t 1 (1   t ) 
 
 . (16)
1  2X t
 

(1 -  )(1 -  )[ L( )] - X t - X 2t
By using (15), one can rewrite (16) as the difference equation in X t that governs the evolution of the
economy:
6



(1 -  )(1 -  )[ L( )]  X 2t 1  (1 -  )(1  2X t 1) 1  (1 -  )(1 -  )[ L( )] - X t 1 - X 2t 1 (X t  1 -  ) 
(X t 1, X t ) 
- 
  0. (17)
1  2X t
 

(1 -  )(1 -  )[ L( )] - X t - X 2t
Long-run growth
Along a balanced growth path, one must have Xt+1=Xt=X* in equation (17) (“*” denotes the longrun equilibrium value of a variable). Given equation (15), one can verify that when X t+1=Xt=X* the
economy follows a balanced growth path along which Kt, Yt, Wt, Gt and Ct grow at the fixed rate *=X*-.
(.)
By linearizing (17) around X*, one can check that -
(.)
X t
 1 : the only path in
X t 1 X t 1  X t  X *
a neighborhood of X* consistent with lim X t  X * must be characterized by Xt=X* t (it is easy to verify
t 
that only this path can be an equilibrium trajectory).
As t, equation (17) becomes
f (X*,  ) 
(1 -  )(1 -  )[ L( )]  (X*) 2
(X * 1 -  ) 
1-  0.
1  2X *

Equation (18) implicitly defines X* as a function of
(18)
: X*=g(). One can verify that
f (.)
dX *
 = g’()<0. In other words, a larger tax rate lowers X*, thus depressing the
f (.)
d f (.)  0
X *
equilibrium rate of growth *=()= g()-, which is monotonically decreasing in the tax rate: ’()<0.
4
CLASS CONFLICT OVER THE DETERMINATION OF THE TAX BURDEN
The capitalists would prefer that the welfare entitlements and the government transfers in favor of
the workers will be suppressed, so as to avoid the tax burden financing the public outlays and the upward
pressure on the wage due to the non-labor income enjoyed by the workers. Indeed, by inserting the
equilibrium real wage (14) in the capitalists’ budget constraint (6), one can immediately see that =0 would
be optimal for the capitalists.
In contrast, this is not generally the case for the workers, since they may face a trade-off between
taking possession of a larger share of national product thanks to a larger  and benefiting from a more rapid
7
growth of national product thanks to a smaller . The possible existence of this trade-off can be seen by
considering that in period t the sequence of discounted utilities of the representative worker is given by


  s-t

 -1
s-t
if  
  u   (1 -  ) K t N [1   ( )]
   -1
 s  t
Ut  





s - t  (1 -  ) 
 -1
s- t 

u

K
N
[
1


(

)]

 otherwise, 0    1,
t



 ( - 1) 

 s  t

(19)

where  is a time-preference parameter. It is straightforward that
U t
 0 implies that it would be
  0
optimal for the workers to have >0, where



K t N  -1 (1 -  )  s- t [1   ( )]s- t u '   (1 -  ) K t N  -1[1   ( )]s-t 


s t










(
1

)


'
(

)
 s-t (s - t)[1   ( )]s-t -1 u '   (1 -  ) K t N  -1[1   ( )]s-t  if  

   -1

s  t 1
U t 








 (1 -  )  K N  -1 1 -  -    s-t [1   ( )]s- t u '  (1 -  )  K N  -1 [1   ( )]s-t  



t
t


  ( - 1) 
 (1 -  )  s  t
 ( - 1) 














s-t
s - t -1  (1 -  ) 
 -1
s - t 


'
(

)

(
s
t)
[
1


(

)]
u
'

K
N
[
1


(

)]

 otherwise.
t



(

1)




s

t

1


(20)








As the condition
U t
 0 is satisfied, a potential conflict between capitalists and workers on the
  0
determination of --namely on the share of national product devoted to finance welfare entitlements and
transfers in favor of the workers--arises in spite of the fact that a lower  unambiguously boosts growth. It is
not surprising that--given the other parameter values--the more heavily the workers discount the future (the
lower is ), the more likely is that this condition is satisfied since the workers attach less importance to the
slower growth brought about by a higher .5
5
For instance, in the case in which both the capitalists’ utility function and the workers’ utility function are logarithmic
U t
 0 if and only if    , where
(v(.)=ln (.) and u(.)=ln(.)),
  0
8
5
CONCLUSION
In the simplified formal treatment proposed in this paper, a decrease in a policy parameter—the ratio of
total tax revenues to GDP—can monotonically increase the economy’s growth rate. This notwithstanding,
the paper shows that the redistributive implications of such a decrease may induce the wage earners to
oppose it.
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Daveri, Francesco and Tabellini, Guido (2000), “Unemployment, growth and taxation in industrial
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Frankel, Marvin (1962), “The Production Function in Allocation and Growth: A Synthesis”. American
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Phelps, Edmund S. (1997), Rewarding Work, Harvard University Press, Cambridge Mass.
Pissarides, Christopher A. (1998), “The impact of employment tax cuts on unemployment and
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42: 155-183.
1-  -
 
[1  2(1 -  )(1 -  )]  [1  2(1 -  )(1 -  )] 2 (1 -  )(1 -  )  (1 -  )N  



2(2 -  )
(2 -  )
(2 -  ) 
4(2 -  ) 2

N   [1  2(1 -  )(1 -  )] 2 (1 -  )(1 -  )  (1 -  )N  



2(2 -  ) 
(2 -  )
(2 -  ) 
4(2 -  ) 2
-1
2
1
2
[1  2(1 -  )(1 -  )]  [1  2(1 -  )(1 -  )] 2 (1 -  )(1 -  )  (1 -  )N  
1-  


2(2 -  )
(2 -  )
(2 -  ) 
4(2 -  ) 2

1
.
2
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Prescott, Edward C. (2003), “Why do Americans work so much more than Europeans?”. Research
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