4. Productive Government Expenditures

Transcription

1 Prof. Dr. Thomas Steger Advanced Macroeconomics I Lecture SS Productive Government Expenditures Introduction A basic model Congestion Supply side policy and redistribution

2 Introduction Governments collect tax revenues to finance government consumption (including social transfers) and government investment (productive government expenditures). Aschauer (1989, pp. 178/79): The empirical analysis indicates that movements in public investment bring forth movements in private sector output which are as much as four to seven times as large as the public sector outlays, while changes in government consumption have, at best, a small positive influence on production. In what follows, we focus on the consequences of productive government expenditures, like Core infrastructure: streets, highways, airports, mass transit, sewers, water systems Homeland security, jurisprudence, property rights protection The standard approach rests on the assumption that public services are nonrival and nonexcludable. Public investments provide free public services to private producers. One firm s use of the public good does not diminish the quantity available to others. This amounts to saying that there is no congestion. 2

3 The Barro (1990) model market economy (1) Consider a perfectly competitive economy. There is a continuum of length one of identical firms, indexed by i [0,,1]. Output technology of firm i is given by (0<α,β<1) Notice that this technology exhibits CRS in private inputs (K i and L i ) G denotes a public input (productive government expenditures) We assume that the government runs a balanced budget Y= Y i di is aggregate output Solving G=τG β K α L (1 α) for G, plugging the result into Y=G β K α L 1 α (noting K i =K, L i =L and Y i =Y) gives the reduced form technology Notice that there are IRS at the aggregate level since 1/(1-β)>1. Notice also that, holding K fix, Y is increasing in the tax rate τ. 3

4 The Barro (1990) model market economy (1a) Solving G=τG β K α L (1 α) for G gives Plugging into the original Y-technology (aggregate level) yields The K-terms and the L-terms can be merged Hence, the reduced form technology may be expressed as 4

5 The Barro (1990) model market economy (2) The competitive rate of return to capital investments (before taxes) is given by (δ=0) Using K i =K, L i =L and G=τG β K α L (1 α) gives Plugging this result into the Keynes Ramsey rule yields This is the steady state growth rate of the economy. Notice that there are no transitional dynamics. This solution implies a scale effect. An increase in the tax rate τ unfolds two opposing effects The higher τ, the higher tax revenues and hence spending on productive government expenditures G (balanced budget rule). The larger G, the higher the MPC and hence the competitive rate of return before taxes to physical capital investments. This effect accelerates economic growth. The higher τ, the smaller the rate of return net of taxes to physical capital investments (1 τ)r. An increase in τ unfolds a disincentive to investment / saving and therefore decelerates economic growth. 5

6 The Barro (1990) model market economy (2a) The competitive rate of return to capital investments (before taxes) Noting G=τ 1/(1 β) K α/(1 β) L (1 α)/(1 β) gives Collecting the K-terms and the L-terms yields Hence, one gets 6

7 The Barro (1990) model market economy (3) Explain the shape of this graph! The tax rate which maximizes the growth rate is τ*=β. Empirical estimates indicate that β [0.16, 0.3]. Notice that the implied degree of IRS would then be something like 1/(1 0.23) 1.3. This appears empirically plausible since the degree of IRS ranges from 1.03 to 1.4 (Schmitt- Grohé, 1997, Table 4). Set of parameters: L=1, ρ=0.02, σ=1, α=0.4 7

8 The Barro (1990) model optimal tax rate The benevolent government chooses τ such that welfare of the representative individual is maximized, taking the decisions of the private sector (captured by the "policy function" C=C(K;τ)) as given. Welfare of the representative individual reads as follows (Chapter 3 Utility, AM Exercises) Notice that U increases with C(0) and g. The reason that the (benevolent) government may not wish, in general, to maximize the (long run) growth rate g is that an increase in g entails a reduction in C(0). Initial consumption is given by C(0)=Y(0) G(0) I(0) From K=I δk and K=g one gets I/K δ=g. Welfare is hence described by Maximizing U w.r.t. τ should yield τ=β. 8

9 The Barro (1990) model congestion Many public services are subject to congestion (highways, water systems, policy and fire services, and courts). Under congestion, the quantity / quality available to an individual declines, for a given quantity of aggregate services G, as other users congest the facilities. This idea can be formalized by the following output technology (again i [0,,1] indexes firms) The production process exhibits CRS in the single private input K i. The positive impact of G on private sector TFP is captured by f(g/y) with f (.)>0 and f (.)<0. Because of congestion, an increase in Y, for given G, lowers the public services available to each firm. The competitive rate of return to capital reads as follows (notice G=τY) Above we have seen that the competitive ROR (before taxes) increases with τ. Congestion weakens this effect as captured by the concave function f(τ). 9

10 Supply side policy and redistribution (1) Market structure and technology The economy under study is perfectly competitive. The production technology for the final output good is As in Barro (1990) the government provides productive public services G, which are financed according to (0<q<1) The reduced-form production function reads 10

11 Supply side policy and redistribution (2) Type of individuals There is mass L of identical workers. Each worker supplies u units of labor inelastically every period of time. Workers consume their complete income, i.e. do not save. The market income per worker is simply uw with w= Y/ (ul). Workers also receive social transfers such that total income of the typical worker is There is mass one of identical capitalists / entrepreneurs who own the capital stock and don't work. Entrepreneurs do save and choose the amount of labor they wish to employ. The problem of the typical entrepreneur reads 11

12 Supply side policy and redistribution (3) The government The government does two things: First, it collects taxes by levying a linear income tax on both capital and labor income. Second, it allocates total tax receipts to finance productive government expenditures and transfers in favor of workers. Notice that the government is assumed to run a balanced budget, i.e. G+Q=τY. Policy experiment The government increase the share of tax revenues devoted to productive government expenditures from q=0.5 to q=0.7. The short run as well as the dynamic implications of this policy are investigated taking the general equilibrium effects into account. 12

13 Supply side policy and redistribution (4) 13

14 Notation and abbreviations Notation A>0 total factor productivity C consumption C:=C/C growth rate of C G productive government expenditures Q social transfers g long run growth rate K i L i capital stock of firm i 0,,1] labor input of firm i 0,,1] Y i Y α β δ ρ σ τ output of firm i [0,,1] aggregate output technology parameter technology parameter depreciation rate time preference rate preference parameter tax rate τ* optimal tax rate 0<q<1 r t U u w share of tax revenues devoted to productive government expenditures interest rate time index life-time utility working time per worker wage rate Abbreviations CRS constant returns to scale i.e. id est IRS increasing returns to scale MPC marginal product of capital ROR rate of return TFP total factor productivity w.r.t. with respect to 14