Keynesian Views On The Fiscal Multiplier

Transcription

1 Faculty of Social Sciences Jeppe Druedahl (Ph.d. Student) Department of Economics 16th of December 2013 Slide 1/29

2 Outline th of December 2013 Slide 2/29

3 The For Today 1 Some 2 A Benchmark (a la Woodford) 3 A Approach (a la Woodford) 4 A Approach (a la Carroll) 16th of December 2013 Slide 3/29

4 Outline th of December 2013 Slide 4/29

5 Some Definition: How many percent does GDP increase when government spending increases one percent of GDP. Methodology: 1 Exogenous military spending. 2 SVARs with e.g. Cholesky decompositions. 3 Variation across U.S. states. Good Review: Valerie Ramey, Can Government Purchases Stimulate the Economy? (Journal of Economic Literature 2011, 49:3, ). General Conclusions: 1 The multiplier is between 0.8 and 1.5. Larger in recessions. Larger for more closed economies. 2 The effect on private consumption is significantly positive. 16th of December 2013 Slide 5/29

6 Outline th of December 2013 Slide 6/29

7 Consumers The objective of the consumers is to maximize β t E 0 [u (C t ) v (H t )] (1) t=0 u, v > 0, u < 0, v > 0 subject to the flow budget constraints P t C t + Q t B t B t 1 + W t H t T t (2) This implies two optimality conditions: v (H t ) u (C t ) [ u ] (C t+1 ) E t u (C t ) = W t (3) P t [ ] Q t /E Pt+1 t P t = (4) β 16th of December 2013 Slide 7/29

8 Firms The objective of the firm in each period is to maximize P t f (H t ) W t H t (5) f > 0, f < 0 This implies the optimality condition: f (H t ) = W t P t (6) 16th of December 2013 Slide 8/29

9 Equilibrium The goods market equilibrium is given by Y t = C t + G t (7) We assume that government spending is financed by lump-sum taxation. Ricardian Equivalence then implies that the timing of the taxation is irrelevant. The central equilibrium condition is: f (H t ) = v (H t ) u (C t ) f ( f 1 (Y t ) ) = v ( f 1 (Y t ) ) u (C t ) u (Y t G t ) = v ( f 1 (Y t ) ) f (f 1 (Y t )) = ṽ (Y t ) ṽ = v f 1 ṽ > 0, ṽ > 0 (8) 16th of December 2013 Slide 9/29

10 Fiscal u (Y t G t ) = ṽ (Y t ) Note: The multiplier is below 1, else constant RHS < LHS { Y t H t = f 1 v ( f 1 (Y t ) ) (Y t ) f ( f 1 (Y t ) ) ṽ (Y t ) Conclusion: Private consumption is always crowded-out. In terms of elasticities wrt. Y t we can write: The multiplier is small if: dy dg = η u η u + η v Γ (9) η u = Ȳ u u is small, i.e. the degree of intertemporal substitution is high, and Ȳ ṽ η v = ṽ is large, the marginal cost of employing additional resources in production is sharply rising. 16th of December 2013 Slide 10/29

11 Possible Extensions 1 Non-Separability Between Labor and Consumption: If more labor increases the marginal utility of consumption then the multiplier might increase. 2 Government Investment: If government investment (or spending) increases private sector productivity then the multiplier might increase. 3 Adding Capital: If the increase in government spending is persistent, then investment and thus the capital stock might increase, which might increase the multiplier. 4 Distortionary Taxes: If introduced immediately the multiplier will decrease, but it might increase if they are expected to be introduced in the future. 5 International Trade: Smaller if there is demand leakage, i.e. smaller for more open economies. 6 State Dependence: If e.g. the rate of utilization is low, η v might be low, increasing the multiplier. 16th of December 2013 Slide 11/29

12 Monopolistic Competition The firm optimality condition becomes P t = W t µ ( ) }{{} f (H t ) mark-up }{{} marginal costs The central equilibrium condition becomes u (Y t G t ) = µ ( ) ṽ (Y t ) Conclusion I: No effect on the multiplier if µ ( ) = µ is constant. Conclusion II: Might increase if µ/ G < 0 as e.g. collusion breaks down or prices and/or wages are sticky. 16th of December 2013 Slide 12/29

13 Outline th of December 2013 Slide 13/29

14 Consumers Return to the Euler-equation: [ u ] (C t+1 ) E t u = (C t ) A log-linearization gives an IS-curve [ ] Q t /E Pt+1 t P t β (10) Ĉ t = E t Ĉ t+1 σ (i t E t π t+1 r), σ ηu 1 (11) ] Ŷ t Ĝt = E t [Ŷt+1 Ĝt+1 σ (i t E t π t+1 r) where we have defined π t+1 E t [log P t+1 /P t ] i t log (Q t ) r log β ˆX t ( X t X ) /Ȳ Note: If monetary policy succeeds in setting i t such that r t i t E t π t+1 = r then a purely temporary increase in government spending will imply Ŷt = Ĝt. 16th of December 2013 Slide 14/29

15 Monetary Policy + Firms Monetary Policy: Assume that the central bank follows a Taylor-rule of the form: i t = r + φ π π t + φ y Ŷt, φ π > 1, φ y 0 (12) Calvo Price Setting: A randomly chosen α-fraction of firms cannot change their price in a given period. The aggregate inflation rate can then be shown to be given by ] π t = κ β j E t [Ŷt+j ΓĜt+j j=0 (13) where κ = (1 α) (1 αβ) (ηv + ηu) α > 0 Note: Increased price stickiness lowers κ, i.e. α κ. 16th of December 2013 Slide 15/29

16 Full Model The full model now is ] Ŷ t Ĝt = E t [Ŷt+1 Ĝt+1 σ (i t E t π t+1 r)(14) i t = r + φ π π t + φ y Ŷt (15) π t = ] κ β j E t [Ŷt+j ΓĜ t+j (16) j=0 16th of December 2013 Slide 16/29

17 Solution Government spending: Ĝt = Ĝ0ρ t for ρ [0, 1). The rational expectations solution must now be on the form: Ŷ t = γ y Ĝ t (17) π t = γ π Ĝ t (18) i t = r + γ i Ĝ t (19) Using the method of undetermined coefficients we find 1 ρ + (ψ σφy ) Γ γ y = 1 ρ + ψ [ ] ψ σ φ y + κ 1 βρ (φπ ρ) > 0 Conclusions: If φ y = 0 then Γ < γ y < 1, else we might have γ y < Γ. Increases for higher price stickiness (lower κ). Decreases for more aggressive monetary policy (higher φ π). The general conclusion is that the multiplier is very dependent on the stance of monetary policy. (20) 16th of December 2013 Slide 17/29

18 Zero Lower Bound Consider an extreme case: The central bank lowers the real interest rate in response to increased government spending. Relevant: YES, at the zero lower bound. Constant i t = 0, but increasing E t π t+1. Woodford sets up a formal model: The multiplier can be much larger than one. It is specially large if: The increase in government spending is small (or at least below some limit). The crisis is persistent (and exogenous to government spending). The fiscal spending is focused in the crisis period. (If government spending is increased permanently then future interest rates will increase reducing consumption today). Welfare: Government spending is clearly welfare increasing under ZLB, but so can unconventional monetary policy be. Always problems with implementation lags, and monetary policy does not use any resources. 16th of December 2013 Slide 18/29

19 Possible Extensions I Compared to the Benchmark: 1 The exchange rate regime will be important. 2 Investment is very interest rate sensitive in models, so introducing capital can change the multiplier considerably. 3 Effects which increases productivity can have the perverse effect of increasing the real interest rate by lowering inflation expectations decreasing the multiplier. (On the other hand increased productivity can convince the central bank to hold the real interest rate fixed, increasing the multiplier.) 16th of December 2013 Slide 19/29

20 Possible Extensions II Two Problems: We have a multiplier without multiplication. The effect of fiscal transfers is zero (or can only come from less tax distortion today). Towards old-school ism: 1 Introduce rule-of-thumb consumers who consume all of their income. A) Directly: More consumption. B) Indirectly: Might increase inflation, lowering the real interest rate, boosting consumption of the Ricardian households, and the investment of firms. 2 Make labor demand determined (i.e. completely flexible labor supply as under involuntary unemployment, intuitively η v Γ γ y ). 16th of December 2013 Slide 20/29

21 Outline th of December 2013 Slide 21/29

22 The Consumer Problem max E t s.t. n=0 β n c 1 ρ t+n, β (0, 1), ρ > 1 (21) 1 ρ a t = m t c t (22) m t+1 = R a t + y t+1, R > 1 (23) y t+1 = p t+1 ε t+1 (24) p t+1 = p t ψ t+1 (25) { µ with probability π [0, 1] ε t+1 = (26) with probability 1 π θ t+1 log ψ t+1 N ( ω ψ, σ 2 ψ), Et [ψ t+1] = 1 (27) log θ t+1 N ( ω θ, σ 2 θ), Et [θ t+1] = 1 (28) a t 0 (29) m 0 and p 0 are given Note: No income insurance or risk pooling/sharing. 16th of December 2013 Slide 22/29

23 he solid curve shows the consumption function for β-point model. The dashed curves show the con for the most patient and the least patient consumers for β-dist model. The histogram 16th of December 2013 shows Slide 23/29 the u n i v e r s i t y o f c o p e n h a g e n re 2 The Consumption Function β {0, 982, 0, 988, 0.994} Wealth Distribution and Consumption Functions of β and β-dist Models Representative agent's net worth Most impatient Identical patience Most patient 0.5 Histogram: empirical density of net worth m t

24 Clear Numerous empirical micro-studies have found that the majority of households have a marginal propensity to consume (MPC) out of transitory income shocks in the range percent. 1 Surveys. 2 Euler-equations (both macro-data and micro-data). 3 Event-studies (e.g. randomly timed tax-rebates) Especially large in recessions and for households with low wealth. Example: Kreiner, Lassen og Leth-Petersen, Consumption Responses to Fiscal Stimulus Policy and the Household Price of Liquidity (working paper, 2012). 16th of December 2013 Slide 24/29

25 Spending and the SP-payout Figure 4: Spending and the size of the SP payout Spending (DKK) SP payout (DKK) Data points Local polynomial regression NOTE: 5055 observations. 16th of December 2013 Slide 25/29

26 Full Model General Equilibrium. Demographics: Perpetual youth (a la Blanchard-Yaari) with constant mortality risk. Production: Cobb-Douglas. Price and Wage Setting: Fully flexible. Aggregate Shocks: Both permanent and transitory. Heterogeneity in: 1 Ex post income (after idiosyncratic shocks). 2 Discount rates (β) Calibration: Standard income processes. Aggregate capital-output ratio. 16th of December 2013 Slide 26/29

27 TheFigure Distribution 1 Distribution of Wealth of Net Worth (Lorenz Curve) KS JEDC 0.25 Β Dist Β Point 0 US data SCF, solid line Percentile es: The solid curve shows the distribution of net worth in the 2004 Survey of Consumer Finances. 16th of December 2013 Slide 27/29

28 baseline KS-JEDC model or from a representative agent 16th of model, December 2013 the Slide 28/29r u n i v e r s i t y o f c o p e n h a g e n TheFigure Marginal 4 Distribution Propensity of tompcs Consume Across Households Annual MPC Matching liquid financial assets retirement assets 0.25 Matching net worth KS JEDC Percentile

29 My Own Research Fundamental idea: Same as Carroll and co. authors. Differences: 1 Partial equilibrium. 2 Wealth more dispersed than income due to: A) Full life-cycle setup with inter generational links. B) Ex ante heterogeneous income. C) Heterogeneous interest rates (e.g entrepreneurial activity). D) A joy of giving bequest-motive as a luxury good. 3 More focus on the business cycle (e.g. persistent unemployment risk). 4 Aim at using Danish registry data for simulated minimum distance estimation (or some form of calibration). 16th of December 2013 Slide 29/29