QPFpres (Paris) - University of Exeter
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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 lnCit
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 mt 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
Gt 1 1 d G
kt 1 1 g
t 1
1
k0
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
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 K 0
l k0 1 l k0 K 0
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