Public Economics

1
Chapter 21 Economic Growth
2
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.

3
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).

4
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.

5
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).

6
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

7
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

8
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 lt s lt 1
• Investment at time t is It sF(Kt, Lt)
• With depreciation rate d capital stock at t 1
  is Kt1 It 1 dKt
• sF(Kt, Lt) 1
  dKt
• This capital accumulation equation determines the
  evolution of capital through time

9
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 nkt1 sf(kt) 1
  dkt
• 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 dk
  0
• This is interpreted as the long-run equilibrium

10
Exogenous Growth

• Fig. 21.1 plots the evolution of kt assuming that
  f(kt) kta
• This gives the capital accumulation equation
• kt1 (skta 1dkt)/(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

Figure 21.1 Dynamics of the capital stock
11
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

Figure 21.2 The steady state
12
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

13
Exogenous Growth

• For each saving rate there is an equilibrium k
• Consumption is given by c(s) f(k(s)) n
  dk(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

Figure 21.3 The Golden Rule
14
Exogenous Growth

• To see the effect of the saving rate assume y
  ka, a lt 1
• The steady state then satisfies ska n dk 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

Figure 21.4 Consumption and the saving rate
15
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
16
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

17
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

18
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

19
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

Figure 21.5 Tax rate and consumption growth
20
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

21
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

Figure 21.6 Level and growth effects
22
Policy Reform
Figure 21.7 Growth effects of tax reform
23
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

24
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

Source US Department of Commerce Figure 21.8 US
tax and growth rates
25
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

Source Feinstein (1972), UK Revenue Statistics,
Economic Trends Figure 21.9 UK tax and growth
rates
26
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 and marginal tax rates
27
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

28
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

29
Empirical Evidence
With Outliers
Without Outliers
30
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

31
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

32
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

33
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

34
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