Government Spending Macro-Economic Policy University of Lausanne Fall 2013 Macro-Economic Policy Government Spending 1 / 32
Motivation Financial crisis: huge fiscal packages. Rationale? No consensus at all among economists about the efficiency of fiscal policy, either theoretically or empirically Potential reasons: F F The baseline real business cycle model itself (this lesson) has ambiguous predictions No definite empirical answers (identification issues) Macro-Economic Policy Government Spending 2 / 32
Key Concepts The benefit of government spending should at least exceed the costs of additional taxes Holding resources constant, spending crowds out consumption and investment Y = C + + G mportant notion: fiscal multiplier @Y @G @Y @Y @G @Y @G @G > 0: additional government spending increases production < 1: additional government spending crowds out private resources > 1 is not sufficient to justify additional government spending when people suffer a disutility of labor F Ultimately, what matters is welfare! What happens to consumption and labor? Macro-Economic Policy Government Spending 3 / 32
ASimpleGovernment We want to know how the economy behaves given some level of spending We are not solving an optimal spending problem n light of Ricardian Equivalence, let s ignore borrowing and lending. Government Budget Constraint g t = T t Macro-Economic Policy Government Spending 4 / 32
Firm s Problem max n t,k t F (k t, n t ) w t n t r k t k t Optimal demand schedule of capital and labor F k (k t, n t )=r k t F n (k t, n t )=w t Constant returns to scale production function: F (k t, n t ) Profits must equal zero in equilibrium F (k t, n t ) w t n t r k t k t = 0 The labor demand schedule can be expressed as w t n t = F (k t, n t ) F k (k t, n t )k t Macro-Economic Policy Government Spending 5 / 32
nelastic Labor Supply Households endowed with 1 unit of labor No utility of leisure, so they work all of the time F (k t, n t )=F(k t, 1) f (k t ) The demand schedules become r k t =f 0 (k t ) w t =f (k t ) k t f 0 (k t ) Macro-Economic Policy Government Spending 6 / 32
Household Problem max 1X {c t,b t+1,x t,k t+1 } t=0 t U(c t ) x t + c t =w t k t+1 =(1 T t + r k t k t )k t + x t By substituting out investment, we can combine the two constraints: k t+1 + c t = w t T t +(1 + r k t )k t Macro-Economic Policy Government Spending 7 / 32
Optimal Consumption Dynamics Consumption Euler Equation U 0 (c t+1 ) U 0 (c t ) (1 + r k t )=1 Given log-utility and the firm demand-condition for capital: c t+1 = c t (1 + f 0 (k t+1 ) ) Macro-Economic Policy Government Spending 8 / 32
The Resource Constraint and Capital Dynamics Economy Resource Contraint c t + x t + g t = F t Substitute out investment, then we obtain the capital dynamics of the economy given a path for private and public consumption k t+1 = f (k t )+(1 )k t (c t + g t ) Macro-Economic Policy Government Spending 9 / 32
Steady State Assume all economic variables are constant in time Steady state capital depends only on parameters implies c t+1 = c t (1 + f 0 (k t ) ) f 0 (k) = 1 (1 ) What is the effect of g 0 > g in the long run? implies k t+1 = f (k t )+(1 )k t (c t + g t ) c + g = f (k) As g increases, consumption falls. What if the steady state is disrupted only temporarily? Consumption and investment decrease temporarily F nvestment falls because households want to smooth the fall in consumption F f investment falls, so does output Macro-Economic Policy Government Spending 10 / 32 k
Empirical Evidence Structural VAR Approach (Blanchard-Perotti 2002) unexpected output movements depend on tax and spending shocks make sufficient identification assumptions to calculate the spending and tax shocks show what are the effects on spending and tax shocks on output Macro-Economic Policy Government Spending 11 / 32
Blanchard Perotti (2002) Macro-Economic Policy Government Spending 12 / 32
Blanchard Perotti (2002) Macro-Economic Policy Government Spending 13 / 32
Try again We need a more realistic model in order to improve the ability of the theory to match empirical evidence n what follows, we allow labor supply to be flexible Macro-Economic Policy Government Spending 14 / 32
Elastic Labor Supply Household endowed with 1 unit of time - split between leisure and work n t + `t = 1 The household values leisure (in the utility function) U(c,`)=u(c)+v(`) where u 0 > 0, u 00 < 0, v 0 > 0, v 00 < 0. Macro-Economic Policy Government Spending 15 / 32
Household s Problem such that max {c t,k t+1 } t=0 1X t [u(c t )+v(1 n t )] k t+1 (1 )k t + c t = w t n t + r k t k t T t Macro-Economic Policy Government Spending 16 / 32
Optimality Conditions Consumption Euler equation U 0 (c t+1 ) U 0 (c t ) (1 + r k t )=1 Leisure/consumption trade-off Suppose u = log c and v = log ` v 0 (`t) u 0 (c t ) = w t c = 1 w t`t When agents consume less, they also enjoy less leisure. F People work harder. Does output increase? Macro-Economic Policy Government Spending 17 / 32
Household Budget Period by period constraint s=0 k t+1 + c t = w t n t +(1 + r k t )k t T t ntertemporal constraint (r t = rt k ) 1X c 1 Q t+s s i=1 (1 + r t+i) = X (w t+s n t+s T t+s ) Q s i=1 (1 + r t+i) s=0 +(1 + r k t )k t Leisure can be seen as a household s expense, affected by a household s revenues Substitute nt = 1 `t and g t = T t 1X c t+s + w 1 Q t+s`t+s s i=1 (1 + r t+i) = X (w t+s g t+s ) Q s i=1 (1 + r t+i) +(1 + r t k s=0 s=0 s there a wealth effect of government spending on leisure? Higher government spending decreases future cashflows, lowering household wealth Since leisure is an expense, it should decrease (along with consumption) Macro-Economic Policy Government Spending 18 / 32 )k t
How to solve the model? Use labor ratios Obtain a model solution similar to before, but in terms of labor ratios Solve for the level of labor Obtain the full solution Macro-Economic Policy Government Spending 19 / 32
Firm s Problem Recall the demand schedules from before F k (k t, n t )=rt k F (k t, n t ) F k (k t, n t )k t =w t n t Constant returns to scale implies F (k t, n t )=n t F (k t /n t, 1) F k (k t, n t )=F 0 (k t /n t, 1) Let k t = k t /n t,then where rt k =f 0 ( k t ) w t =f ( k t ) kt f 0 ( k t ) f kt = F (k t /n t, 1) Macro-Economic Policy Government Spending 20 / 32
Dynamic Equations Express everything as labor ratios Denote labor growth as t+1 = n t+1 n t Capital Dynamics t+1 k t+1 + c t + g t = f ( k t )+(1 ) k t Consumption dynamics with log-utility t+1 c t+1 = c t (1 + f 0 ( k t+1 ) ) Macro-Economic Policy Government Spending 21 / 32
Steady State Steady-state capital-labor ratio does not depend on government s spending But steady-state total capital stock k = n k can be affected if steady-state labor supply depends on government s spending What do you think will happen? Macro-Economic Policy Government Spending 22 / 32
ntuition for the Effect Higher government spending lowers private income the negative wealth effects makes people work harder Higher labor input increases the returns to capital higher investment leads to more capital The output multiplier can be positive, or even higher than 1! Macro-Economic Policy Government Spending 23 / 32
Results: Baxter and King (1993) Macro-Economic Policy Government Spending 24 / 32
Results: Baxter and King (1993) Macro-Economic Policy Government Spending 25 / 32
Distortionary Fiscal Policy Lump-sum taxes are not very realistic... Suppose current government expenditures financed through current distorsionary tax revenues on income: t = g t /y t The household s problem with taxes: 1X max t [u(c t )+v(1 n t )] such that {c t,k t+1 } t=0 k t+1 (1 )k t + c t =(1 t ) w t n t + rt k k t T t Macro-Economic Policy Government Spending 26 / 32
Optimality Conditions Euler Equation U 0 (c t+1 ) U 0 (c t ) (1 +(1 t )r k t )=1 Leisure/consumption trade-off v 0 (1 n t ) u 0 (c t ) =(1 t ) w t Negative substitution effect on labor supply Negative effect on capital accumulation r t =(1 t )r k t Macro-Economic Policy Government Spending 27 / 32
The Multiplier The total effect is ambiguous Wealth effect: poorer people work more Substitution effect on labor: since labor doesn t pay much, people substitute away Substitution effect on capital: since future capital returns are lower, people invest less Which effects are larger dictates how distortionary taxes affect the multiplier F substitution effects on capital accumulation are most important Macro-Economic Policy Government Spending 28 / 32
Results: Baxter and King (1993) Macro-Economic Policy Government Spending 29 / 32
Conclusion - Neoclassical consensus Main channels of government spending on economic activity in the neoclassical model? @Y /@G > 1? Effect on welfare? Still missing public investment! This helps a lot t s hard to know what kind of public spending is actually investment Macro-Economic Policy Government Spending 30 / 32
Conclusion - Limits Robust implication of the neoclassical model that contradicts empirical evidence: consumption falls at impact Solutions? What do you think? Macro-Economic Policy Government Spending 31 / 32
Conclusion - Recent Developments So, huge fiscal packages are a mistake? Actually, still no consensus. More recent empirical evidence suggests that fiscal multipliers can be very large under certain circumstances t s not yet clear what are the channels Active field of research Macro-Economic Policy Government Spending 32 / 32