growth and public infrastructure nigar hashimzade university of reading gareth d. myles university...
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Growth and Public Infrastructure
Nigar HashimzadeUniversity of Reading
Gareth D. MylesUniversity 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 Taxation and growth Public expenditure and growth
This has been undertaken using Tax regressions Barro regressions
Some evidence will now be briefly reviewed
US Growth and Taxation
US Growth and Average Tax Rate
-15
-10
-5
0
5
10
15
20
25
30
1950 1960 1970 1980 1990 2000
UK Growth and Taxation
UK Growth and Average Tax Rate
-15
-10
-5
0
5
10
15
20
25
1910 1920 1930 1940 1950 1960 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
0
1
2
3
4
5
6
7
0 10 20 30 40
Average Tax Rates
Average Per Capita
GDP Growth 1960-2004
Homogenous Data
y = -0.0707x + 3.8778
R2 = 0.136
0
1
2
3
4
5
6
7
0 10 20 30 40Average Tax Rates
Average Per Capita
GDP Growth 1960-2004
y = -0.0025x + 2.7234
R2 = 0.0002
00.5
11.5
2
2.53
3.54
4.5
0 10 20 30
Average Tax Rate
Average Per Capita
GDP Growth 1960-2004
Without Outliers With Outliers
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
-6
-4
-2
0
2
4
6
8
10
12
14
0 10 20 30 40
Government expenditure as a proportion of GDPG
row
th r
ate
of G
DP
per
cap
ita
R2 = 0.0128
-6
-4
-2
0
2
4
6
8
10
12
14
0 10 20 30 40
Government expenditure as a proportion of GDPG
row
th r
ate
of G
DP
per
cap
ita
R2 = 0.0454
-6
-4
-2
0
2
4
6
8
10
12
14
0 10 20 30 40
Government expenditure as a proportion of GDPG
row
th r
ate
of G
DP
per
cap
ita
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 equalizedConsequence is that taxation in one country
can raise growth in all countriesQuestions 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
The public input is financed by a tax on output
The utility function of the consumer is
11tttt GKALY
tttttttt LwKrGKAL 111
1
1
1
1
t
tt CU
Barro Model
The growth rate of consumption can be written as
The figure shows the relationship between the tax rate and growth rate
The model provides a positive role for taxation
111/111/11
AC
CC
t
tt
t
tt
C
CC 1
Tax and Growth Rates
Spillovers
We employ a model with two countries and a spillover of infrastructure
The production function is
Global infrastructure is
Infrastructure is a durable good Infrastructure is financed by a tax on capital
αρt
ρit
αitit ΓGAKY
11
ititt GGΓ
Household
The focus is placed on balanced growth paths If the growth rate is
The level of consumption is
The consumer chooses to maximize
ρ
tρ
it
tit
ρt
ρit G
ΓγG
G
ΓGΓG
0
00
1 1
0lnmax
tit
t C
τδγKGΓGAKγC K
αραtit 0
1
00001
Household
We exploit two equivalencesThe standard result Competitive equilibrium ≡ Consumer chooses {kt}
Plus the long-run result
Consumer chooses {kt} ≡ Consumer chooses {}
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
t
ln(C)
Household
The household treats G and as given when choosing
This distinguishes the household from the government
Household choice is characterized by the growth rate
τδKGGΓA Kαρ
1γ1 100
100
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 ratesOptimization determines equations in and A simulation illustrates the resultsAssume symmetry and the parameter values = 0.9, = 0.5, = 0.5 K = G = 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
This is equivalent to
The necessary condition (with symmetry) is
UU
,max
with max
,
1
1 112
G
A
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 ( ) of revenue is collected and fraction (1 – ) of total is returned
The law of motion for infrastructure becomes
This is now modelled as a three-stage game
1111 11 ttttGt KGG
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
12111
1K
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 ( < 0) and then claims back ()
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 t [0, 1] denote fraction of kt invested in the home country
Let denote fraction of invested in the foreign country
The home capital stock is
This gives the accumulation condition
ttttt kkK 1
111 11 tttttGt kkGG
t tk
Capital Mobility
Iterating this equation over time
The first terms tends to zeroThe second term can only be constant if
G
t
G
GG
tG
t
t
k
k
kkGkk
G
1
1
111
11
11
1
1
1
0
0
0000
1
1
1
Capital Mobility
If the steady state is reached at 0
The level of consumption on the balanced growth path is
Where
000 11
kkGG
01 CC tt
00
0
0
00 1111 k
K
Y
K
YC K
Capital Mobility
The consumer chooses the allocation of capital to maximise utility
The necessary condition is
This represents the equalization of net rates of return
0
0
00
00
0
0
00
00
1
1
1
11
K
Y
kk
kk
K
Y
kk
kk
d
d
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 flowsThis 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