Chapter 21
Economic Growth
Reading
• Essential reading
– Hindriks, J and G.D. Myles Intermediate Public Economics.
(Cambridge: MIT Press, 2005) Chapter 21.
• Further reading
– Barro, R.J. (1990) “Government spending in a simple model of
endogenous growth”, Journal of Political Economy, 98, S103 –
S125.
– Barro, R.J. (1991) “Economic growth in a cross section of
countries”, Quarterly Journal of Economics, 106, 407 – 444.
– Barro, R.J. and Sala-I-Martin, X. (1995) Economic Growth (New York:
McGraw-Hill),
– Lucas, R.E. (1990) “Supply-side economics: an analytical
review”, Oxford Economic Papers, 42, 293 – 316.
– Slemrod, J. (1995) “What do cross-country studies teach about
government involvement, prosperity, and economic growth”,
Brookings Papers on Economic Activity, 373 - 431.
Reading
– Solow, R.M. (1970) Growth Theory: An Exposition (Oxford:
Oxford University Press).
– Stokey, N.L. and Rebelo, S. (1995) “Growth effects of flat-rate
taxes”, Journal of Political Economy, 103, 519 – 550.
• Challenging reading
– Aghion, P. and Howitt, P. (1998) Endogenous Growth Theory
(Cambridge: MIT Press),
– Chamley, C. (1981) “The welfare cost of capital income taxation
in a growing economy”, Journal of Political Economy, 89, 468 –
496.
– Chamley, C. (1986) “Optimal taxation of capital income in
general equilibrium with infinite lives”, Econometrica, 54, 607 –
622.
– De La Croix, D. and Michel, P. (2002) A Theory of Economic
Growth (Cambridge: Cambridge University Press).
Reading
– Dowrick, S. (1993) “Government consumption: its effects on
productivity growth and investment” in N. Gemmel (ed.) The
Growth of the Public Sector. Theories and Evidence (Aldershot:
Edward Elgar).
– Easterly, W. (1993) “How much do distortions affect growth?”,
Journal of Monetary Economics, 32, 187 – 212.
– Easterly, W. and Rebelo, S. (1993) “Fiscal policy and economic
growth”, Journal of Monetary Economics, 32, 417 – 458.
– Engen, E.M. and Skinner, J. (1996) “Taxation and economic
growth”, NBER Working Paper No. 5826.
– Jones, L.E., Manuelli, R.E. and Rossi, P.E. (1993) “Optimal
taxation in models of endogenous growth”, Journal of Political
Economy, 101, 485 – 517.
– Judd, K. (1985) “Redistributive taxation in a simple perfect
foresight model”, Journal of Public Economics, 28, 59 – 83.
Reading
– King, R.G. and Rebelo, S. (1990) “Public policy and endogenous
growth: developing neoclassical implications”, Journal of Political
Economy, 98, S126 – S150.
– Levine, R. and Renelt, D. (1992) “A sensitivity analysis of crosscountry growth models”, American Economic Review, 82, 942 –
963.
– Mendoza, E., Milesi-Ferretti, G.M and Asea, P. (1997) “On the
ineffectiveness of tax policy in altering long-run growth:
Harberger's superneutrality conjecture”, Journal of Public
Economics, 66, 99 – 126.
– Pecorino, P. (1993) “Tax structure and growth in a model with
human capital”, Journal of Public Economics, 52, 251 – 271.
– Plosser, C. (1993) “The search for growth”, in Federal Reserve
of Kansas City symposium series, Policies for Long Run Growth,
57 – 86, (Kansas City).
Introduction
• Economic growth is the basis of increased
prosperity
• Growth comes from capital accumulation and
innovation
• Taxation can affect incentives but can also
finance productive public expenditure
• The level of taxes has risen in most countries
• This raises questions about the effect of taxation
on growth
Exogenous Growth
• Exogenous growth theory developed in the
1950s and 1960s
• The theory assumes technical progress occurs
exogenously
– It does not try to explain technical progress
• In the Solow growth model capital and labor are
combined with constant returns to scale and
there is a single consumer
• Growth occurs through capital accumulation
Exogenous Growth
• Assume a production function Yt = F(Kt, Lt)
where Kt and Lt are capital and labor inputs at
time t
• Let the saving rate be fixed at s, 0 < s < 1
• Investment at time t is It = sF(Kt, Lt)
• With depreciation rate d capital stock at t + 1 is
Kt+1 = It + [1 – d]Kt
= sF(Kt, Lt) + [1 – d]Kt
• This capital accumulation equation determines
the evolution of capital through time
Exogenous Growth
• Constant returns imply
Yt = LtF(Kt/Lt, 1) = Ltf(kt), kt = Kt/Lt
• In terms of the capital-labor ratio the capital
accumulation condition becomes
[1 + n]kt+1 = sf(kt) + [1 – d]kt
• A steady state is achieved when the capitallabor ratio is constant
• The steady state capital-labor ratio k is defined
by
sf(k) - [n + d]k = 0
• This is interpreted as the long-run equilibrium
Exogenous Growth
kt
4
3.5
3
2.5
2
1.5
1
0.5
Figure 21.1: Dynamics of the
capital stock
49
46
43
40
37
34
31
28
25
22
19
16
13
10
7
4
0
1
• Fig. 21.1 plots the
evolution of kt assuming
that f(kt) = kta
• This gives the capital
accumulation equation
kt+1 = (skta + [1–d]kt)/(1 + n)
• Using k0 = 1, n = 0.05, d =
0.05, s = 0.2 and a = 0.5
the figure plots kt for 50
years
• The steady-state level is k
=4
t
Exogenous Growth
• The determination of the
steady state is shown in
Fig. 21.2
• The steady state is at the
intersection of (n + d)k
and sf(k)
• Consumption is the
difference between f(k)
and sf(k)
• In the steady state
consumption per capita
Ct/Lt is constant
• This places a limit on the
growth of living standards
Output
f k 
Consumption
n  d k
sf k 
k
Capital
Figure 21.2: The steady state
Exogenous Growth
• Policy can affect the outcome by changing the
saving rate, s, or shifting the production function,
f(k)
• But a one-off change cannot affect the long-run
growth rate
• A sustained increase in growth can only come
through continuous upward movement in f(k)
• This can occur through technical progress
– But the cause of the progress requires explanation
Exogenous Growth
• For each saving rate
there is an equilibrium k
• Consumption is given by
c(s) = f(k(s)) – [n + d]k(s)
• c(s) is maximized by s*
which solves
f′(k(s* )) = n + d
• The level of capital k* =
k(s*) is the Golden Rule
capital-labor ratio
• This is shown in Fig. 21.3
Output
f k 
Consumption
k*
n  d k
Capital
Figure 21.3: The Golden Rule
Exogenous Growth
• To see the effect of the
saving rate assume y =
k a, a < 1
• The steady state then
satisfies ska = [n + d]k so
k = (s/(n + d))1/(1-a)
• Consumption is plotted as
a function of s in Fig. 21.4
• The saving rate can have
a significant effect on
consumption
c
s
Figure 21.4: Consumption and
the saving rate
Exogenous Growth
• The Chamley-Judd
results shows that there
should be no tax on
capital income in the
long-run
• Table 21.1 reports the
welfare cost of imposing
a capital tax
• The increase in
consumption arises from
removal of the tax
• The welfare cost is large
as a percent of the tax
revenue
Initial tax
rate (%)
Increase in Welfare cost
consumption
(% of tax
(%)
revenue)
30
3.30
11
50
8.38
26
Source: Chamley (1981)
Table 21.1: Welfare cost of taxation
Endogenous Growth
• Endogenous growth models explain the causes
of growth through individual choices
• There are several explanations available
• These include:
– The AK model assumes constant returns
– Human capital can be incorporated alongside
physical capital
– Technological innovation can introduce new products
– The government can provide a productive public input
Barro Model
• The Barro model includes public expenditure as
an input
Yt  AL1ta Kta Gt1a
• The public input is financed by a tax on output
 t  1   ]
1a a 1a
ALt Kt Gt
 rt Kt  wt Lt
• The utility function of the consumer is
1

C
1
t t
U  
1
t 1
Barro Model
• Profit-maximization determines the demand for
capital and labor
• The model can be solved explicitly
• The growth rate of consumption can be written
as
Ct 1  Ct
Ct

1/ 

1  1   ]aA  1a ] a
1a
]
1/ 
1
• Taxation has both a positive and a negative
effect
Barro Model
• With a productive public
input there is a role for
taxation
• Taxation finances the
public input and can
generate growth
• Raising the tax rate too
high reduces growth
• This identifies the
concept of an optimal
size of public sector
Ct 1  Ct
Ct

Figure 21.5: Tax rate and
consumption growth
Policy Reform
• There is significant research on the form of the
best tax system for economic growth
• Much of this has focused on the effect of the
corporate tax
– In 2002 the top rate was 40 percent in the US, 30
percent in the UK and 38.4 percent in Germany
– These values are above the optimal value of zero
• Simulations have considered the welfare effect
of reforming the tax system
Policy Reform
• There is a distinction
between level and growth
effects
• In Fig. 21.6 the move
from a to c is a level effect
• The increase along a to e
is a growth effect
• Taxation can have level
and growth effects
Output
3
2
d
c
e
1
b
a
t0
t1
Time
Figure 21.6: Level and growth
effects
Policy Reform
Author
Features
Utility
Parameters
Initial Tax
Rates and
Growth Rate
Final Position
Additional
Observations
Lucas (1990)
Production of human
capital did not
require physical
capital
=2
a = 0.5
Capital 36%
Labor 40%
Growth 1.50%
Capital 0%
Labor 46%
Growth 1.47%
33% increase in
capital stock
6% increase in
consumption
King and Rebelo
(1990)
Production of human
capital requires
physical capital
(proportion = 1/3)
=2
a=0
Capital 20%
Labor 20%
Growth 1.02%
Capital 30%
Labor 20%
Growth 0.50%
Labor supply is
inelastic
Jones, Manuelli
and Rossi (1993)
Time and physical
capital produce
human capital
=2
a= 4.99
a calibrated
given 
Capital 21%
Labor 31%
Growth 2.00%
Capital 0%
Labor 0%
Growth 4.00%
10% increase in
capital stock
29% increase in
consumption
Pecorino (1993)
Production of human
capital requires
physical capital
=2
a = 0.5
Capital 42%
Labor 20%
Growth 1.51%
Capital 0%
Labor 0%
Growth 2.74%
Capital and
consumption
different goods,
consumption tax
replaces income
taxes
Figure 21.7: Growth effects of tax reform
Empirical Evidence
• There has been considerable empirical
investigation of the relation between taxation
and growth
• The prediction of theory is ambiguous
– Consider the model of a productive public good
– Relation between tax and growth was non-monotonic
– A similar outcome will apply for many models
• This motivate the analysis of empirical evidence
Empirical Evidence
• A first view of the data is
shown in Fig. 21.8
• This plots the US growth
rate (lower line) and tax
revenue as a proportion
of GDP (upper line)
• The trend lines show a
steady rise in tax but a
very minor decrease in
growth
• There is no obvious
relation
30
25
20
15
10
5
0
-51950
1960
1970
1980
1990
2000
-10
-15
Source: US Department of Commerce
Figure 21.8: US tax and growth rates
Empirical Evidence
• Fig. 21.9 reports tax and
growth data for the UK
• Tax revenues have grown
• The trend line for GDP
growth is upward sloping
• The figure provides
evidence of a positive
relation
• The difficulty in this
analysis is constructing
the counterfactual
25
20
15
10
5
0
1910
-5
1920
1930
1940
1950
1960
1970
1980
-10
-15
Source: Feinstein (1972),
UK Revenue Statistics, Economic Trends
Figure 21.9: UK tax and growth rates
Empirical Evidence
• It should be the marginal
rate of tax that matters
• Fig. 21.10 illustrates the
problem of defining the
marginal rate of tax
• There is no single rate
with a non-linear tax
• The construction is
further complicated by
deductions and incentives
• Many definitions of the
marginal rate have been
used in empirical work
Post-Tax
Income
Gradient  1  t 2
Gradient  1  t1
Gradient  1
Y1
Y2
Yˆ
Pre-Tax
Income
Figure 21.10: Average and
marginal tax rates
Empirical Evidence
• The figure shows GDP
and tax rates for a crosssection of countries
• It shows the negative
relation reported by
Plosser
• This has been presented
as evidence of a general
effect
Average Per
Capita
GDP Growth 1960-7
2004
6
5
4
3
2
1
0
0
10
20
Average Tax Rates
30
40
Empirical Evidence
• But the downward trend
is driven by the outliers
• Three countries that are
unusual
– Korea
– Czech Republic
– Slovak Republic
• The negative relation
almost disappears when
these are removed
Average Per
Capita
GDP Growth 7
1960-2004
6
5
4
3
2
1
0
0
10
20
30
Average Tax Rates
40
Empirical Evidence
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
Empirical Evidence
14
12
Growth rate
rate of
of GDP
GDP per
per capita
capita
Growth
• Data on expenditure and
growth for OECD
• No strong relationship is
apparent
• Linear trend line shows
weak negative
• Polynomial shows
observations around a
maximum
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
Empirical Evidence
• 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
Empirical Evidence
• Easterly and Rebelo show that the negative
relation virtually disappears when initial GDP is
added to regression
• They also consider alternative definitions of the
marginal tax rate and a range of determinants of
growth (school enrolments, assassinations,
revolutions, war casualties)
• Conclude there is little evidence of a link
between tax rates and growth
Empirical Evidence
• Are there any variables correlated with growth in
cross-country data?
• Barro (1991)
–
–
–
–
–
Initial GDP (-)
Education (+)
Government consumption (-)
Deviation from PPP (-)
Revolutions (-), Assassinations (-)
• Robustness tests reduced the set of variables to:
East Asian dummy, Investment price, Years
open, Primary schooling, Fraction Confucion
Empirical Evidence
• The evidence that taxation reduces growth is
weak
• Personal and corporate income taxes have the
strongest negative effect
• No empirical variable can summarise the tax
system
• There is an absence of structural modelling
• Causality is unclear