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Growth and Public
Infrastructure
Nigar Hashimzade
University of Reading
Gareth D. Myles
University of Exeter and Institute for Fiscal Studies
Introduction

The EU operates a system of revenue
collection and redistribution among member
states
 This has the aim of contributing to economic
convergence
 The policy has had considerable success



Ireland
Spain
But this policy has been challenged by
expansion
Introduction

The EU has a programme of research into the
“Quality of Public Funds”
 This term captures all aspects of good
governance



Structure of taxation
Allocation of expenditure
Guideline 3 of the Lisbon Strategy asserts the
promotion of growth as an objective
 The effect of redistribution between countries
has not been analyzed within a growth model
Introduction





Fiscal federalism has focused upon tax
externalities in a static setting
Growth theory has generally focused on
single-country models
The particular features of a customs union has
not featured prominently in growth theory
Nor has the role of public expenditure in a
union with integrated economies
Integration of these is needed to address the
QPF
Introduction

There has been considerable attention
devoted to the link between



This has been undertaken using



Taxation and growth
Public expenditure and growth
Tax regressions
Barro regressions
Some evidence will now be briefly reviewed
US Growth and Taxation
30
25
20
15
10
5
0
-51950
1960
1970
1980
1990
-10
-15
US Growth and Average Tax Rate
2000
UK Growth and Taxation
25
20
15
10
5
0
1910
-5
1920
1930
1940
1950
1960
-10
-15
UK Growth and Average Tax Rate
1970
1980
Plosser Evidence

Updated version of
Chart 6 in Plosser
(1993)
 Extends the sample
period through to 2004
 Trendline shows the
negative relationship
 Three countries that are
unusual



Korea
Czech Republic
Slovak Republic
Average Per
Capita
GDP Growth 7
1960-2004
6
5
4
3
2
1
0
0
10
20
30
Average Tax Rates
40
Homogenous Data
Average Per
Capita
GDP Growth
1960-2004 4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
y = -0.0025x + 2.7234
Average Per
Capita
GDP Growth 7
1960-2004
6
2
R = 0.0002
y = -0.0707x + 3.8778
R2 = 0.136
5
4
3
2
1
0
0
10
20
Average Tax Rate
Without Outliers
30
0
10
20
30
Average Tax Rates
With Outliers
40
Structural Relations

Slemrod (1995) suggests two structural
relations


Taxation causes distortions and lowers GDP
Growth in GDP raises demand for expenditure

Estimation has not resolved simultaneity
 If expenditure is chosen to maximize the rate
of growth


For similar countries observations clustered round
the maximum
If countries are different no meaningful relationship
OECD Data



Data on expenditure and
growth for OECD
No strong relationship is
apparent
Linear trend line shows
weak negative
Polynomial shows
observations around a
maximum
14
12
Growth rate
rate of
of GDP
GDP per
per capita
capita
Growth

10
8
6
4
R2 = 0.0128
R2 = 0.0454
2
0
-2 0
10
20
20
30
30
-4
-6
Government
GDP
Government expenditure
expenditure as
as aa proportion
proportion of
of GDP
40
40
Motivation

Paper explores the apparent absence of
relationship between taxation and growth in
cross-country data
 Two components to the ideas we explore



First, public sector expenditures are productive
Second, growth between countries are
endogenously equalized
Consequence is that taxation in one country
can raise growth in all countries
 Questions should focus on the similarity of
growth rates over time
Long-Run Growth
Public Infrastructure

Endogenous growth when capital and labour
are augmented by additional inputs
 Public infrastructure supports private capital



Provides a positive role for public expenditure
A direct mechanism for policy to affect growth
Develop the Barro (1990) model of productive
public expenditure
 Employ comparisons across balanced growth
paths
Barro Model

The Barro model includes public expenditure
as an input
Yt  AL1t Kt Gt1

The public input is financed by a tax on output
 t  1   AL1t Kt Gt1  rt Kt  wt Lt

The utility function of the consumer is
1

C
1
t t
U  
1
t 1
Barro Model

The growth rate of
consumption can be
written as
Ct 1  Ct
Ct



  1/  1  1   A1  1  
Ct 1  Ct
Ct
  1
1/
The figure shows the
relationship between the
tax rate and growth rate
The model provides a
positive role for taxation

Tax and Growth Rates
Spillovers

We employ a model with two countries and a
spillover of infrastructure
 The production function is
Yit 

α
AKit


1 ρ ρ 1 α
Git Γt
Global infrastructure is
Γ t  Git  G it
 Infrastructure is a durable good
 Infrastructure is financed by a tax on capital
Household

The focus is placed on balanced growth paths
 If the growth rate is g
ρ
Git1 ρ Γ tρ

 Γt
 Git 
 Git

ρ
Γ

t
  G0 1  γ   0

 G0






The level of consumption is



t
Cit  1  γ   AK0α  G0 Γ 0 G0


 The consumer chooses g

t

ρ
1 α



to maximize
max   lnCit 
g 
t 0
 K 0 γ  δK

 τ 

Household

We exploit two equivalences
 The standard result
Competitive equilibrium ≡ Consumer chooses {kt}

Plus the long-run result
Consumer chooses {kt} ≡ Consumer chooses {g}

This allows us to simplify to the choice of a
balanced growth rate
Household



The choice of growth
rate affects the value of
C0
As the growth rate
increases C0 rises then
falls
The optimum depends
on the intertemporal
trade-off
ln(C)
t
Household
The household treats G and G as given when
choosing g
 This distinguishes the household from the
government
 Household choice is characterized by the
growth rate



ρ 1 α 


1
G0 K0   1  δK  τ 
1  γ    A Γ 0 G0


Scenarios

We consider three different scenarios for the
government choice of tax rate




Independent choice: Nash equilibrium in tax rates
without coordination
Coordination: joint welfare maximization by the
governments
Redistribution: a central body that collects and
redistributes revenue
The maximum growth rate implies maximum
welfare
Independent Choice

The governments choose tax rates taking into
account







Effect on infrastructure
The choice of the households
But with initial capital given
We impose equality of growth rates
Optimization determines equations in  and g
A simulation illustrates the results
Assume symmetry and the parameter values
 = 0.9, r = 0.5,  = 0.5 dK = dG = 0.2, A = 0.5,
and K0 =2
Independent Choice




The figure shows the
equilibrium outcome
The tax rate chosen by
the government is too
low
It does not pass through
the maximum
This is a consequence
of the externality caused
by the spillover
Coordination

The coordinated governments choose the tax
rates to solve
maxU g   U g 
 , 


This is equivalent to
max g  with g  g
 , 
The necessary condition (with symmetry) is
  A2
r 1 
1
 1 g 

1   

g

d
G 

Coordination




The figure shows the
coordinated outcome
The tax rate chosen by
the governments
achieves the maximum
The coordination
succeeds in internalizing
the externality
A higher growth rate is
achieved
Central Body

A central body is now introduced that
redistributes revenue between countries
 A fraction q (q ) of revenue is collected and
fraction m (1 – m) of total is returned
 The law of motion for infrastructure becomes
Gt 1  1  dG Gt  1  q  t 1Kt 1  mt 1

This is now modelled as a three-stage game
Central Body

Stage 1: The central body announces the
share of tax revenue to be collected
 Stage 2: The countries independently choose
tax rates
 Stage 3: The central body chooses the
redistribution of collected revenues
 The solution for the optimal tax rate is
 1 g

qm
 r


 
 1  d K   1   1    
2  1  q  qm

 

Central Body



The figure shows the
optimal choice of the
central body
The selection of the
parameters for the
redistribution can secure
the optimum
The central body
encourages higher tax
(q < 0) and then claims
back (m)
Capital Mobility

The analysis above assumed balanced growth
for the world

For many parameter configurations cannot occur

Capital mobility is an additional link between
countries
 Capital flows to the country offering the
highest return



Return is dependent on taxation
Taxation affects the rate of growth
We demonstrate that the movement of capital
equalizes growth rates
Capital Mobility
Let lt  [0, 1] denote fraction of kt invested in
the home country
 Let lt denote fraction of k t invested in the
foreign country
 The home capital stock is
K t  lt kt  1  lt kt


This gives the accumulation condition


 
Gt 1  1  d G Gt   lt kt 1  1  lt kt 1
Capital Mobility

Iterating this equation over time
t 1

 1 g

1 g
1  l k0 
l k0  
G0   
g  dG

g  dG
 
t 1


1  g k 0 1  g 
1 g
  1  l 

l


g  d G k0 1  g 
g  dG 


Gt 1 1  d G 

kt 1  1  g 

1
k0
The first terms tends to zero
 The second term can only be constant if g  g
Capital Mobility

If the steady state is reached at 0
1 g

G0  
lk0  1  l k0 
g  dG

The level of consumption on the balanced
growth path is
Ct  1  g t C0

Where
 Y0

Y0
C0  l
 1  l 
 1  d K   l   1  l   1  g  k0
K0
 K0

Capital Mobility

The consumer chooses the allocation of
capital to maximise utility
 The necessary condition is
 
 
 l k0   1  l k0 Y0

1 dg lk0  1  l k0 Y0

  
 
 dl lk0  1  l k0 K0
 l k0  1  l k0 K0


This represents the equalization of net rates of
return
Capital Mobility

With capital flows there is a world balanced
growth path
 Our previous analysis can then be applied to
the issue of policy design
 One additional point


Tax policy in one country affects all countries
through capital flows
This increases the effect that taxation can
have

Additional to infrastructural spillover
Conclusion

The paper has investigated economic growth
with public infrastructure and spillovers
 We have adopted this as a model of tax and
redistribution policy for the EU
 The model has a natural role for a central body
to resolve a market failure
 The model also suggests an explanation for
the lack of a link between taxation and growth
in cross-country data