Growth and Public Infrastructure

1. Growth and Public Infrastructure Nigar Hashimzade University of Reading Gareth D. Myles University of Exeter and Institute for Fiscal Studies

2. 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

3. 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

4. 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

5. 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

6. US Growth and Taxation US Growth and Average Tax Rate

7. UK Growth and Taxation UK Growth and Average Tax Rate

8. 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

9. Homogenous Data With Outliers Without Outliers

10. 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

11. 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

12. 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 equalized • Consequence is that taxation in one country can raise growth in all countries • Questions should focus on the similarity of growth rates over time

13. Long-Run Growth

14. 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

15. 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

16. 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 Tax and Growth Rates

17. 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

18. Household • The focus is placed on balanced growth paths • If the growth rate is g • The level of consumption is • The consumer chooses g to maximize

19. Household • We exploit two equivalences • The standard result Competitive equilibrium ≡ Consumer chooses {kt} • Plus the long-run result Consumer chooses {kt} ≡ Consumer chooses {g} • This allows us to simplify to the choice of a balanced growth rate

20. 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 ln(C) t

21. Household • The household treats G and G as given when choosing g • This distinguishes the household from the government • Household choice is characterized by the growth rate

22. 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

23. 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 rates • Optimization determines equations in t and g • A simulation illustrates the results • Assume symmetry and the parameter values b = 0.9, r = 0.5, a = 0.5 dK = dG = 0.2, A = 0.5, and K0 =2

24. 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

25. Coordination • The coordinated governments choose the tax rates to solve • This is equivalent to • The necessary condition (with symmetry) is

26. 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 Coordination

27. Central Body • A central body is now introduced that redistributes revenue between countries • A fraction q ( ) of revenue is collected and fraction m (1 –m) of total is returned • The law of motion for infrastructure becomes • This is now modelled as a three-stage game

28. 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

29. 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 (q< 0) and then claims back (m) Central Body

30. 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

31. Capital Mobility • Let lt[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

32. Capital Mobility • Iterating this equation over time • The first terms tends to zero • The second term can only be constant if

33. Capital Mobility • If the steady state is reached at 0 • The level of consumption on the balanced growth path is • Where

34. 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

35. 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 flows • This increases the effect that taxation can have • Additional to infrastructural spillover

36. 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