Fiscal Policy and Unemployment Marco Battaglini Princeton University, NBER and CEPR and Stephen Coate Cornell University and NBER 1
Introduction During the Great recession, countries have pursued a variety of fiscal strategies - tax cuts, public works projects. Recent experience reveals that the willingness to use fiscal policy is tempered by the cost of high levels of debt. All this suggests an interesting and potentially important interaction between fiscal policy and unemployment. Fiscal policy has the potential to mitigate unemployment; The desirability of stimulus policies, on the other hand, depends on the country s debt position. 2
This paper explores this interaction between fiscal policy and unemployment. It constructs a dynamic economic model with a private and a public sector. Unemployment can arise because of sticky wages but can be mitigated by tax cuts and spending increases. The model allows government to finance stimulus activities by issuing debt. This model is used to explore the levels of unemployment that arise in steady state and the way in which fiscal policy is used. 3
Plan for today I. The model II. III. The optimal fiscal policy Static analysis Dynamic analysis The political equilibrium IV. The policy mix and the stimulus plan V. Conclusion 4
I. The model I. 1 The economy We consider an infinite horizon economy with: Two final goods, a private good x and a public good g; Two inputs: labor l and a natural resource z (say, oil) There are two types of citizens, workers and entrepreneurs: A mass n w of workers, endowed with 1 unit of labor each period which they supply inelastically. A mass n e of entrepreneurs produce the private good by combining labor and oil with their own effort. 5
The MRT g,l =1 Entrepreneurs production technology: x=a min{ l,ϵ,z } where ϵ represents the entrepreneur's effort. Workers' per period payoff function is x+γ ln g, where γ measures the relative value of the public good. Entrepreneurs' per period payoff function is x+γ ln g-ξ ϵ ²/2 where the third term represents the disutility of providing entrepreneurial effort. All individuals discount the future at rate β. 6
There are markets for the private good, oil and labor. The private good is the numeraire. The natural resource z has an exogenous price p : Pr(p =p H )=α and Pr(p =p L )=1-α The wage rate ω is endogenous: we assume that ω > ω This friction is the source of unemployment. There is a market for risk-free one period bonds: ρ=1/β-1. 7
I.2 Public policies The government can raise revenues in two ways: a tax on profits (τ) and borrowing (b). If the legislature borrows b in period t it must repay (1+ ρ)b in period t+1. The legislature can also hold bonds if it wants, so b can be negative. Public revenues are used to finance the public good. Surplus revenues are distributed to citizens by lump transfers. 8
I.3 Market equilibrium Assume the state of the economy is and that the tax rate is τ and the public good level is g. Entrepreneur choose l, z and ϵ to maximize: 2 ε max(1 τ)( Amin{ l, z, ε} pz ωl) ξ. (, lze, ) 2 Setting demand of l equal to supply, we obtain: where A =A-p. nw g ω if A ω+ ξ( n (1 )) e τ ω = nw g nw g A ξ( n (1 )) if A ( (1 )) e τ > ω+ ξ ne τ 9
so when A is small (relative to τ and g) we may have unemployment: u nw g ne(1 τ)( A ω)/ ξ nw g n if A ( (1 )) w ω+ ξ ne τ = nw g 0 if A > ω+ ξ( n (1 )). e τ Note: τ u and g u From these expressions we obtain the indirect utility functions v e (τ,g), v w, (τ,g) and output x (τ,g). 10
Given this, the public policies must satisfy the budget constraint: R (, τω) ωg b(1 + ρ ) b. The upperbound on debt is: b b= max τ R H ( τω, ) / ρ. 11
I.4 Politics We assume that the economy is divided into N identically sized political districts, each a microcosm of the economy as a whole. In each period, policy decisions are made by a legislature consisting of N representatives, one from each district. Each representative maximizes the welfare of his/her own district The budget surplus can be divided among the districts in any way the representatives choose. The affirmative votes of Q < N representatives are required to pass legislation. 12
II.1 The static case II. Optimal fiscal policy Consider the budget constraint: We start by fixing debt, so: R ( τω, ) ω g b( 1+ ρ) b R (, τω) ω g The planner s problem be written as: max (τ,g ) x (τ ) A A ( ) n e ξ r ( x (τ )) 2 An e 2 + γ ln g s.t. R (τ,ω ) ωg r & g + x (τ ) A n w 13
g A ( A ) x ( τ ) ( ) 2 An x () e τ neξ + γ l n g = U. 2 g nw ne A = (1 τ)( ω) / ξ o g R (, τω) ωg = r o τ 1/2 τ o o o When r r,, the solution is g o = R( τ, ω) ωg,τ o, independent from r. This allocation is efficient. 14
g g r τ When r > o r τ the efficient allocation is unfeasible. * o When, the solution is at a kink: g o r > g, τ > τ. r The output mix is distorted in favor of the public good. 15
g ĝ τˆ τ * When r > r, we have unemployment. Further increases in r induce a reduction in g and τ. 16
In summary: o If r r, the solution involves full employment with no distortions. ( *, r r r If o, the solution involves full employment with distorted output mix. * If r >, the solution involves unemployment. r The revenue requirement is endogenous. What is the relevant range of r? 17
To focus the analysis on the natural case of interest: R ( τ o, w) wg o < 0 < R ( τ o, w) wg o, H H H L L L with zero debt, the first best without borrowing is achievable in the low but not the high cost state. Proposition. In any solution to the government s problem, the economy converges to full employment with no distortions. 18
S((1 b + ρ) b ) + β EV ( b ) V () b = max. b s.. t b b 19
III. The political equilibrium One legislator is randomly selected to make the first policy proposal. If the proposal is accepted by Q legislators, the plan is implemented and the legislature adjourns until the next period. At that time, the legislature meets again with the only difference being that b and (maybe) are different. If the first proposal is rejected, another legislator is chosen. The proposer is forced to internalize the welfare of Q districts. 20
The proposer s problem can be written as: ( τ, gb, ) where q=n/q>1. x ( τ ) ( ) 2 ( A ) An ( ) e x τ A neξ 2 + γ ln g+ βev '( b ) max + ( q 1 )( R (, ) g. τ ω ω ) + q( b (1 + ρ) b) x ( τ ) s. tr. ( τω, ) ωg b(1 + ρ) b, g+ A n w This problem can be studied graphically as before. Since q>1, politicians put more weight on tax revenues and primary surplus. 21
In the short run, politicians trade-off distorting the mix of public and private outputs with minimizing unemployment. Now the trade off favors tax revenues to finance targetable transfers. The distribution of debt converges to an invariant distribution. However, in contrast to the planner's solution, this distribution is no longer degenerate. 22
Proposition. With political decision-making, the following is true in the long run: If q>q * L, there is always unemployment in both states. If q (q * H, q* L ), there is always unemployment in the high cost state. In the low cost state, there is full employment with a distorted output mix for low debt levels and unemployment for high debt levels. If q<q * H, in the high cost state, there is full employment with a distorted output mix for low debt levels and unemployment for high debt levels. In the low cost state, there is full employment with a distorted output mix for low debt and either full employment with a distorted output mix or unemployment for high debt. 23
The government mitigates this unemployment with debt financed fiscal stimulus plans. The government does not maintain an adequate stock of bonds: in the high cost state, unemployment arises. In the low cost state, the government reduces debt until it reaches a floor level. When debt reaches this floor, politicians devote revenues to transfers rather than debt reduction. Unemployment can arise even in the low cost state, depending on the parameters, but is always lower than in the high cost state. Irrespective of the cost state, when there is unemployment, it will be higher the larger the government s debt level. 24
IV. Policy mix and Stimulus plan How does the policy mix look like? With full employment, when: 1 2γ / A n e < 1+ A / 2ξ we have g (b) > g o (b) and τ (b) > τ o (b). (*). (*) is not true: we have g (b) < g o (b) and τ (b) < τ o (b). Condition (*) is more likely to hold the smaller is n e and the larger is γ. 25
With unemployment, equilibrium policies do not minimize unemployment (g *, τ * ). g Employment maximizing policy gh ( r( b) ) τ ( rb H ()) τ The government balances the benefits of reducing unemployment with the costs of distorting the output mix. 26
In equilibrium, tax cut and public production multipliers are not equal. When: 1 2γ / A n e 1+ A / 2ξ (*). we have τ (b) > τ * : in this case marginally reducing taxation implies an increase in employment (but a reduction in welfare). When (*) is not true, the impact of taxation depends on b. 27
If b is high enough we have τ (b)>τ * ; if b is low we may have τ (b) < τ *. g Employment maximizing policy τ M τ <M g M τ >M g 28
With political decision-making, the model generates a positive theory of stimulus plans. Stimulus funds are typically used to both cut taxes and increase public production. The magnitude of stimulus (the size of the debt increase) depends on the economy s debt level. As b approaches its maximum level, the size of stimulus must go to zero. It is natural to interpret economy s fiscal space. b b as a measure of the 29
IV. Conclusion This paper has explored the interaction between fiscal policy and unemployment. We have argued that when fiscal policy is endogenous, assuming market imperfections is not sufficient to obtain a theory of unemployment. We have proposed a political economy model that delivers an appealing theory of fiscal policy and unemployment. The theory provides a new perspective to evaluate and interpret fiscal policy. 30