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Harri Turunen. Government spending in a volatile economy at the zero lower bound

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University of Helsinki
University of Cambridge
February 16, 2015
Open Seminar at Eesti Pank

Published in: Economy & Finance
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Harri Turunen. Government spending in a volatile economy at the zero lower bound

  1. 1. Government spending in a volatile economy at the zero lower bound Harri Turunen University of Helsinki University of Cambridge February 16, 2015
  2. 2. Outline Motivation The model Generalized Stochastic Simulation Results
  3. 3. Outline Motivation The model Generalized Stochastic Simulation Results
  4. 4. Ramey (JEL 2011) Reasonable people can argue, however, that the data do not reject 0.5 or 2.0. Blanchard & Perotti (2002): SVAR-identified tax shocks imply multiplier of 0.9 to 1.29 Cogan, Cwik, Taylor & Wieland (2010): estimated Smets-Wouters model implies 0.64 at peak
  5. 5. ECB refi rate, Fed Funds rate, BoJ overnight rate, 2004-2014
  6. 6. Intuition on the multiplier at the ZLB Multiplier depends on response of hours worked to spending increase New Keynesian special case: when interest rates are low, the multiplier can be large With interest rates stuck, consumption level adjusted by working more
  7. 7. This paper/presentation How does uncertainty affect the multiplier at the ZLB? Uncertainty modeled as stochastic volatility in government spending and aggregate productivity Model solved using a global method that accommodates the ZLB Multipliers computed by simulating the model Not an explanation of causes of business cycles
  8. 8. This paper/presentation How does uncertainty affect the multiplier at the ZLB? Uncertainty modeled as stochastic volatility in government spending and aggregate productivity Model solved using a global method that accommodates the ZLB Multipliers computed by simulating the model Not an explanation of causes of business cycles
  9. 9. What is spending uncertainty? What causes it? Household uncertainty about government behavior Greek commitment to cuts and reforms (also in 2010!) U.S. government shutdown in 2013 More generally Uncertainty about a new party or politician Uncertainty about commitment Uncertainty about general economic conditions
  10. 10. Justiniano and Primiceri (AER 2008) DSGE-based estimate of volatility of U.S. government spending with confidence intervals
  11. 11. Baker et al (AER P&P 2014) Economic policy uncertainty index based on newspaper word count
  12. 12. Previous literature on multipliers at ZLB Christiano, Eichenbaum & Rebelo (2011): multiplier above 1 in a linearized model Aruoba & Schorfheide (2013): multiplier greater than 1 - if economy is in non-deflationary equilibrium Braun, K¨orber & Waki (2013): multiplier 1 or less, depending on parametrization Fernandez-Villaverde, Gordon, Rubio-Ramirez & Guerron-Quintana (2013): above bound 0.6, at bound 1.5
  13. 13. My results Volatility matters: 1. Spending volatility has a positive effect; high volatility increases the multiplier 2. Productivity volatility has a negative effect; high volatility decreases the multiplier Different shocks can take the economy to the bound; the multiplier depends on the shock 1. Shocks to discount rate result in large multipliers 2. Shocks to productivity yield small multipliers 3. Bond return shock and monetary policy shock in between Size of spending increase strongly affects size of multiplier
  14. 14. Outline Motivation The model Generalized Stochastic Simulation Results
  15. 15. Model foundations Representative household Calvo pricing in production Central bank follows Taylor rule Government levies lump sum taxes and spends, has balanced budget No capital, no distorting taxes
  16. 16. Shocks Discount rate (ut), labor preference (lt), bond return (bt), productivity (at), government spending (gt), monetary policy (rt) All follow ht = hρh t−1 exp (σhεh,t), εh,t ∼ N (0, 1) Two volatility shocks: productivity (σa,t), government spending (σg,t) log σj,t = (1 − j ) log σj + j log σj,t−1 + ςj ηj,t, ηj,t ∼ N (0, 1)
  17. 17. Central bank Nominal rate constrained by ZLB Rt = max {1, φt} Central bank follows Taylor rule: φt = rtR1−ρ (Rt−1)ρ πt π∗ φπ Yt Y ∗ φY 1−ρ Due to kink Rt non-differentiable =⇒ perturbation methods inapplicable!
  18. 18. Spending Government borrows Bt, levies lump-sum taxes Tt and spends Budget always balanced Spending shock gt subject to stochastic volatility: gt = g ρg t−1 exp (σg,tεg,t) log σg,t = (1 − g ) log σg + g log σg,t−1 + ςg ηg,t Government expenditure computed as Gt = gt ¯GYt
  19. 19. Households Households consume final good Ct, supply labor Lt to intermediate goods producers, put savings into government bonds, maximize max Ct ,Bt ,Lt E0 ∞ t=0 βt ut log (Ct) − lt L1+ϑ t 1 + ϑ subject to PtCt + Bt bt ≤ Rt−1Bt−1 + WtLt + Tt + Πt Standard intertemporal optimality condition for bonds: C−1 t = β bt ut RtEt ut+1C−1 t+1 In equilibrium Ct = 1 − gt ¯G atLt∆t
  20. 20. Firms Competitive production of final good Yt using Dixit-Stiglitz aggregation Monopolistic production of intermediate goods with aggregate productivity subject to stochastic volatility Calvo pricing implies optimality condition for reset prices ˜Pt ˜Pt Pt ≡ St Ft where St = utlt at Lϑ t Yt + βθEt πε t+1St+1 Ft = utC−1 t Yt + βθEt πε−1 t+1Ft+1
  21. 21. Calibration Objective of calibration: model hits the bound in roughly 6% of periods Shocks central: variances set to 0.005 in steady state, persistences 0.75, a = g = 0.9 and ςa = ςg = 0.1 Central bank reacts strongly to inflation: φπ = 2, φY = 0.15, π∗ = 1.004 and ρ = 0.8 Households: β = 0.994, ϑ = 1 Firms: ε = 6, θ = 0.75
  22. 22. Outline Motivation The model Generalized Stochastic Simulation Results
  23. 23. Nutshell Approximate equilibrium conditions with polynomials of state variables Polynomials found with fixed-point iteration: 1. Make a guess on parameters in polynomials 2. Simulate model for T periods using the polynomials 3. Regress “true” model outcomes on simulation outcome 4. Update guess using regression output. If no convergence, go to 2.
  24. 24. Nutshell Approximate equilibrium conditions with polynomials of state variables Polynomials found with fixed-point iteration: 1. Make a guess on parameters in polynomials 2. Simulate model for T periods using the polynomials 3. Regress “true” model outcomes on simulation outcome 4. Update guess using regression output. If no convergence, go to 2.
  25. 25. My implementation Third order polynomials for St, Ft and marginal utility Vector of state variables Xt = (∆t−1, Rt−1, at, bt, gt, lt, rt, ut, σa,t, σg,t) Dimension of polynomials large - 286 parameters! Initial values from second-order perturbation of Gomme and Klein (2011)
  26. 26. Other technicalities Problem: regression coefficients unstable between iterations Solution: “stabilize” regression using singular value decomposition Use numerical integration to compute “true” model outcomes of expectations Iterate over structural parameters - even with stabilization invertibility issues arise 10-20 minutes per iteration
  27. 27. Outline Motivation The model Generalized Stochastic Simulation Results
  28. 28. Results Which shocks are important for hitting the bound? What happens at the bound to output and inflation? How large is the multiplier?
  29. 29. Which shocks drive the economy to the bound? Probability of hitting the bound after a shock in the next 10 periods at least once Size of innov. at bt ut rt 2 s.d. 0.31 0.43 0.23 0.22 1 s.d. 0.28 0.34 0.24 0.23 0 s.d. 0.26 0.26 0.26 0.26 -1 s.d. 0.24 0.2 0.28 0.28 -2 s.d. 0.22 0.15 0.3 0.36 Legend: at productivity, bt bond return, ut discount rate, rt interest rate
  30. 30. Which shocks drive the economy to the bound? Realized and theoretical distributions of shocks at bound -0.03 -0.02 -0.01 0 0.01 0.02 0 1 2 3 x 10 4 Interest rate -0.04 -0.02 0 0.02 0.04 0 1 2 3 x 10 4 Bond premium -0.04 -0.02 0 0.02 0.04 0.06 0 1 2 3 x 10 4 Aggr. productivity -0.04 -0.02 0 0.02 0.04 0 1 2 3 x 10 4 Discount factor
  31. 31. Which shocks drive the economy to the bound? Realized and theoretical distributions of shocks at bound -6.5 -6 -5.5 -5 -4.5 -4 0 1 2 3 x 10 4 Vol. of productivity -6.5 -6 -5.5 -5 -4.5 -4 0 1 2 3 x 10 4 Vol. of spending -0.04 -0.02 0 0.02 0.04 0 1 2 3 x 10 4 Gov. spending -0.04 -0.02 0 0.02 0.04 0 1 2 3 x 10 4 Labor supply
  32. 32. “Primary” drivers of ZLB events bond return and monetary policy shocks 5 s.d. shocks guarantee hitting bound Productivity and discount rate shocks have lesser effects 10 s.d. shocks guarantee hitting bound Spending, labor and volatility shocks seem to have no effect Several different types of ZLB events!
  33. 33. Not all shocks are created equal Impulse responses to productivity and bond shocks that drive the economy to the ZLB 0 2 4 6 8 10 1 1.005 1.01 1.015 1.02 1.025 Aggr.product. Output 0 2 4 6 8 10 0.98 0.985 0.99 0.995 1 1.005 Inflation 0 2 4 6 8 10 0.94 0.96 0.98 1 Bondreturn 0 2 4 6 8 10 0.97 0.98 0.99 1
  34. 34. Not all shocks are created equal Impulse responses to productivity and bond shocks that drive the economy to the ZLB together with a government intervention 0 2 4 6 8 10 1 1.005 1.01 1.015 1.02 1.025 Aggr.product. Output 5 s.d. shock to spending No increase 0 2 4 6 8 10 0.98 0.985 0.99 0.995 1 1.005 Inflation 0 2 4 6 8 10 0.94 0.96 0.98 1 Bondreturn 0 2 4 6 8 10 0.97 0.98 0.99 1
  35. 35. Not all shocks are created equal Impulse responses to discount rate and monetary policy shocks that drive the economy to the ZLB together with a government intervention 0 2 4 6 8 10 0.96 0.97 0.98 0.99 1 1.01 Discountrate Output 0 2 4 6 8 10 0.985 0.99 0.995 1 1.005 Inflation 0 2 4 6 8 10 0.98 1 1.02 1.04 1.06 1.08 Interestrate 0 2 4 6 8 10 0.995 1 1.005 1.01 1.015
  36. 36. Simulation procedure for computing fiscal multipliers 1. Start from steady state. Hit the economy with a shock that drives it to the bound, a shock to volatility and a shock to spending. 2. Simulate 10 000 realizations for 10 periods. 3. Compute multiplier for period t as an average over realizations with formula Yt −Yt ∗ G1−G∗ 1 Five cases: economy not at bound, at bound due to productivity, discount rate, bond return or monetary shock Two volatility shocks: spending and productivity
  37. 37. Fiscal multiplier, not at bound Volatility in spending
  38. 38. Fiscal multiplier, not at bound Volatility in productivity Productivity volatility shock Spendingshock -10 -5 0 5 10 20 15 10 5 1 0 0.5 1 1.5 2
  39. 39. When not at the bound... Multipliers low Larger spending packages have significantly smaller multipliers Effects of uncertainty minor Spending volatility seems to have no clear effect Extremely low productivity volatility increases multiplier
  40. 40. Fiscal multiplier at ZLB 1. Bond return shock Spending volatility shock Spendingshock -10 -5 0 5 10 20 15 10 5 1 0.7 0.8 0.9 1 1.1 1.2 Productivity volatility shock Spendingshock -10 5 0 5 10 20 15 10 5 1 0.4 0.6 0.8 1 1.2
  41. 41. Fiscal multiplier at ZLB 2. Discount rate shock Spending volatility shock Spendingshock -10 -5 0 5 10 20 15 10 5 1 0 0.5 1 1.5 2 2.5 3 Productivity volatility shock Spendingshock -10 -5 0 5 10 20 15 10 5 1 -1 0 1 2 3
  42. 42. Some intuition 1. The economy is at the bound due to a high bond return shock or a low discount rate shock and there is a change in uncertainty 2. The government spends a portion of output greater than normal 3. Households would like to save less, but the interest rate is stuck From the household’s point of view, spending is taxation - thus uncertainty in spending is uncertainty in taxation
  43. 43. Fiscal multiplier at ZLB 3. Monetary policy shock Spending volatility shock Spendingshock -10 -5 0 5 10 20 15 10 5 1 0.2 0.4 0.6 0.8 1 1.2 Productivity volatility shock Spendingshock -10 -5 0 5 10 20 15 10 5 1 0 0.2 0.4 0.6 0.8 1 1.2
  44. 44. Fiscal multiplier at ZLB 4. Productivity shock Spending volatility shock Spendingshock -10 -5 0 5 10 20 15 10 5 1 -0.5 0 0.5 Productivity volatility shock Spendingshock -10 -5 0 5 10 20 15 10 5 1 -1.5 -1 -0.5 0 0.5
  45. 45. Conclusions Size of the multiplier often, but not always, greater than 1, when the economy is at the ZLB Strong dependence on volatility: high spending volatility can significantly increase the multiplier Size of spending increase has a strong impact on multiplier Different shocks lead to different types of ZLB events and different multipliers Caveats: lack of capital and distorting taxation probably skew results

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