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