Chapter 21Economic 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 cross-country 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 capital stock at t + 1 is

Kt+1 = It + [1 – Kt

= sF(Kt, Lt) + [1 – 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 – kt

• A steady state is achieved when the capital-labor ratio is constant

• The steady state capital-labor ratio k is defined by

sf(k) - [n + k = 0• This is interpreted as the long-run equilibrium

Exogenous Growth

• Fig. 21.1 plots the evolution of kt assuming that f(kt) = kt

• This gives the capital accumulation equation

kt+1 = (skt + [1–]kt)/(1 + n)

• Using k0 = 1, n = 0.05, = 0.05, s = 0.2 and = 0.5 the figure plots kt for 50 years

• The steady-state level is k = 4

0

0.5

1

1.5

2

2.5

3

3.5

4

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 t

tk

Figure 21.1: Dynamics of thecapital stock

Exogenous Growth

• The determination of the steady state is shown in Fig. 21.2

• The steady state is at the intersection of (n + )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

kf

ksf

kn

k

Consumption

Capital

Output

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 + ]k(s)

• c(s) is maximized by s* which solves

f′(k(s* )) = n + • The level of capital k* =

k(s*) is the Golden Rule capital-labor ratio

• This is shown in Fig. 21.3

kf

kn

*k

Consumption

Capital

Output

Figure 21.3: The Golden Rule

Exogenous Growth

• To see the effect of the saving rate assume y = k, < 1

• The steady state then satisfies sk = [n + ]k so

k = (s/(n + ))1/(1-)

• Consumption is plotted as a function of s in Fig. 21.4

• The saving rate can have a significant effect on consumption

s

c

Figure 21.4: Consumption andthe 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

consumption (%)

Welfare cost

(% 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

• 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

• Profit-maximization determines the demand for capital and labor

• The model can be solved explicitly• The growth rate of consumption can be written

as

• Taxation has both a positive and a negative effect

111/111/11

AC

CC

t

tt

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

t

tt

C

CC 1

Figure 21.5: Tax rate andconsumption 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

Time

Output

1

2

3

a

c

b

e

d

0t 1t

Figure 21.6: Level and growtheffects

Policy Reform

Capital 0%

Labor 0%

Growth 2.74%

Capital 0%

Labor 0%

Growth 4.00%

Capital 30%

Labor 20%

Growth 0.50%

Capital 0%

Labor 46%

Growth 1.47%

Final Position Additional Observations

Initial Tax Rates and Growth Rate

Utility Parameters

FeaturesAuthor

Capital and consumption different goods, consumption tax replaces income taxes

Capital 42%

Labor 20%

Growth 1.51%

= 2

= 0.5

Production of human capital requires physical capital

Pecorino (1993)

10% increase in capital stock

29% increase in consumption

Capital 21%

Labor 31%

Growth 2.00%

= 2

= 4.99

calibrated given

Time and physical capital produce human capital

Jones, Manuelli and Rossi (1993)

Labor supply is inelastic

Capital 20%

Labor 20%

Growth 1.02%

= 2

= 0

Production of human capital requires physical capital (proportion = 1/3)

King and Rebelo (1990)

33% increase in capital stock

6% increase in consumption

Capital 36%

Labor 40%

Growth 1.50%

= 2

= 0.5

Production of human capital did not require physical capital

Lucas (1990)

Capital 0%

Labor 0%

Growth 2.74%

Capital 0%

Labor 0%

Growth 4.00%

Capital 30%

Labor 20%

Growth 0.50%

Capital 0%

Labor 46%

Growth 1.47%

Final Position Additional Observations

Initial Tax Rates and Growth Rate

Utility Parameters

FeaturesAuthor

Capital and consumption different goods, consumption tax replaces income taxes

Capital 42%

Labor 20%

Growth 1.51%

= 2

= 0.5

Production of human capital requires physical capital

Pecorino (1993)

10% increase in capital stock

29% increase in consumption

Capital 21%

Labor 31%

Growth 2.00%

= 2

= 4.99

calibrated given

Time and physical capital produce human capital

Jones, Manuelli and Rossi (1993)

Labor supply is inelastic

Capital 20%

Labor 20%

Growth 1.02%

= 2

= 0

Production of human capital requires physical capital (proportion = 1/3)

King and Rebelo (1990)

33% increase in capital stock

6% increase in consumption

Capital 36%

Labor 40%

Growth 1.50%

= 2

= 0.5

Production of human capital did not require physical capital

Lucas (1990)

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

-15

-10

-5

0

5

10

15

20

25

30

1950 1960 1970 1980 1990 2000

Source: US Department of CommerceFigure 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

-15

-10

-5

0

5

10

15

20

25

1910 1920 1930 1940 1950 1960 1970 1980

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

Figure 21.10: Average andmarginal tax rates

1Y 2Y Y

Post-TaxIncome

Pre-TaxIncome

1Gradient

11Gradient t

21Gradient t

Empirical Evidence

• The figure shows GDP and tax rates for a cross-section of countries

• It shows the negative relation reported by Plosser

• This has been presented as evidence of a general effect

0

1

2

3

4

5

6

7

0 10 20 30 40

Average Tax Rates

Average Per Capita

GDP Growth 1960-2004

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

0

1

2

3

4

5

6

7

0 10 20 30 40

Average Tax Rates

Average Per Capita

GDP Growth 1960-2004

Empirical Evidence

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

Empirical Evidence

• 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

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

• 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

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