Chapter 21 Economic Growth

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 < 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

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 + n]kt+1 = sf(kt) + [1 – d]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 + d]k = 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 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 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 + 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 Figure 21.3: The Golden Rule

14. Exogenous Growth • To see the effect of the saving rate assume y = ka, 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 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 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