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Systematic Component of Monetay Policy in Open Economy SVAR's: A New Agnostic Identi fication Procedure

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Master project by Adrian Ifrim and Önundur Páll Ragnarsson. Barcelona GSE Master in Macroeconomic Policy and Financial Markets

Published in: Economy & Finance
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Systematic Component of Monetay Policy in Open Economy SVAR's: A New Agnostic Identi fication Procedure

  1. 1. Introduction Econometric Methodology Identification Strategy Estimation Results Systematic Component of Monetary Policy in Open Economy SVAR’s: A New Agnostic Identification Procedure Adrian Ifrim and ¨Onundur P´all Ragnarsson July 16, 2015
  2. 2. Introduction Econometric Methodology Identification Strategy Estimation Results Introduction - the aim of our thesis • Time series analysis using an SVAR model to study monetary policy in the context of international macroeconomics • New approach to the identification of monetary policy shocks in SVARs, which is a combination of previously introduced methods • Contribution to empirical research on exchange rate dynamics, initiated by the Dornbusch (1976) model
  3. 3. Introduction Econometric Methodology Identification Strategy Estimation Results Motivation • Uhlig (2005) introduced agnostic identification of SVAR models • Found no clear effect of U.S. monetary policy on real GDP • Using an improved methodology, Arias et al. (2015) recover the real effects of monetary policy
  4. 4. Introduction Econometric Methodology Identification Strategy Estimation Results Motivation II • Scholl and Uhlig (2007) study the effects of monetary policy in an open economy SVAR using the Uhlig (2005) methodology • Find substantial evidence of delayed overshooting • This motivates us to apply the Arias et al. (2014) method to a similar setting as Scholl and Uhlig • Motivating questions: • Does delayed overshooting still appear? • Do the two identification methods yield plausible results? • Do they correctly identify monetary policy shocks?
  5. 5. Introduction Econometric Methodology Identification Strategy Estimation Results Literature review • Dornbusch (1976) model exchange rate dynamics: The long term depreciation, following expansionary shocks to monetary policy; exchange rate overshoots on impact • The initial overshooting is followed by a monotone adjustment to the new depreciated value • Empirical studies: Gradual appreciation, followed by gradual depreciation before converging on a long term value: delayed overshooting • Eichenbaum and Evans (1993): Peak response delay 1-3 years • Clarida and Gali (1994): Peak response delay 6-12 months • Grilli and Roubini (1996): Peak response delay several months • Scholl and Uhlig (2007): Peak response delay 1 to 2 years
  6. 6. Introduction Econometric Methodology Identification Strategy Estimation Results Overshooting
  7. 7. Introduction Econometric Methodology Identification Strategy Estimation Results The Model The reduced form VAR(p) model: yt = c + p l=1 Bl yt−l + ut, E(utut) = Σ = PP (1) ⇔ yt = B+xt + ut (2) where B+ = (B1 . . . Bp c) and xt = (yt−1 . . . yt−p 1). The structural model is: yt A0 = xtA+ + t (3) where A0 = (P−1) , A+ = B+(P−1) and t = ut(P−1) .
  8. 8. Introduction Econometric Methodology Identification Strategy Estimation Results The Model II Impulse Response Functions: Lh(A0, A+) = [Fh ]nnP (4) Define: f (A0, A+) =      A0 L0(A0, A+) ... Lk(A0, A+),      Notice that f (A0Q, A+Q) = f (A0, A+)Q
  9. 9. Introduction Econometric Methodology Identification Strategy Estimation Results The Model III • (A0, A+) and (A0Q, A+Q) are observationally equivalent • sign and zero restrictions are satisfied if: 1. Zj f (A0, A+)Qej = 0 2. Sj f (A0, A+)Qej > 0 • How to choose the Q matrix?
  10. 10. Introduction Econometric Methodology Identification Strategy Estimation Results Sign and Zero Restrictions: Intuition • Recall the WOLD decomposition Theorem: yt = B(L)PQQ P−1ut • we have to find an orthonormal matrix Q that satisfies the sign and zero restrictions • construct a random matrix Q such that it satisfies the zero restrictions • check if the sign restrictions are also satisfied • if yes keep the matrix Q and the structural parameters A0, A+ • if no, discard it and draw another Q
  11. 11. Introduction Econometric Methodology Identification Strategy Estimation Results Constructing the matrix Q Reformulate the Gram-Schmidt recursive algorithm Define: Rj (A0, A+) = Zj f (A0, A+) Qj−1 where Qj−1 = [q1 . . . qj−1] and qj = Qej . Theorem 1. Let j = 1. 2. Find a matrix Nj−1 whose columns form an orthonormal basis for the null space of Rj (A0, A+). 3. draw xj from a standard normal distribution on Rn. 4. qj = Nj−1(Nj−1xj / Nj−1xj ). 5. If j = n stop; otherwise let j = j + 1 and move to step 2.
  12. 12. Introduction Econometric Methodology Identification Strategy Estimation Results Algorithm for Sign and Zero Restrictions 1. Draw (B+, Σ) from the posterior distribution of the reduced form parameters. 2. Draw Q such that the structural parameters ((P−1) Q, B+(P−1) Q) satisfy the zero restrictions. 3. Keep the draw if Sj f (P−1) , B+(P−1) )qj > 0, where qj repre- sents the j th column of Q. 4. Return to Step 1 until the required number of draws from the posterior distribution conditional on the sign and zero restric- tions has been obtained.
  13. 13. Introduction Econometric Methodology Identification Strategy Estimation Results Baseline Identification I
  14. 14. Introduction Econometric Methodology Identification Strategy Estimation Results Baseline Identification I We adopt the EE(1993) specification: (yt, y∗ t , pt, nbrxt, rert, i∗ t , it) Identification 1.
  15. 15. Introduction Econometric Methodology Identification Strategy Estimation Results Baseline Identification I We adopt the EE(1993) specification: (yt, y∗ t , pt, nbrxt, rert, i∗ t , it) Identification 1. 1. The federal funds rate is the monetary policy instrument and it reacts contemporaneously only to output and prices.The re- sponse coefficients of output and prices are non-negative.
  16. 16. Introduction Econometric Methodology Identification Strategy Estimation Results Baseline Identification I We adopt the EE(1993) specification: (yt, y∗ t , pt, nbrxt, rert, i∗ t , it) Identification 1. 1. The federal funds rate is the monetary policy instrument and it reacts contemporaneously only to output and prices.The re- sponse coefficients of output and prices are non-negative. 2. For k periods the responses of prices and reserves are non- positive while the response of interest rates is non-negative.
  17. 17. Introduction Econometric Methodology Identification Strategy Estimation Results Baseline Identification II
  18. 18. Introduction Econometric Methodology Identification Strategy Estimation Results Baseline Identification II Label the first equation of the SVAR as the monetary policy equation:
  19. 19. Introduction Econometric Methodology Identification Strategy Estimation Results Baseline Identification II Label the first equation of the SVAR as the monetary policy equation: yt a0,1 = xtal,1 + 1t
  20. 20. Introduction Econometric Methodology Identification Strategy Estimation Results Baseline Identification II Label the first equation of the SVAR as the monetary policy equation: yt a0,1 = xtal,1 + 1t ⇔
  21. 21. Introduction Econometric Methodology Identification Strategy Estimation Results Baseline Identification II Label the first equation of the SVAR as the monetary policy equation: yt a0,1 = xtal,1 + 1t ⇔ it = φy yt + φy∗ y∗ t + φppt + φnbrx nbrxt + φrer rert + φi∗ i∗ t + a−1 0,71 1t
  22. 22. Introduction Econometric Methodology Identification Strategy Estimation Results Baseline Identification II Label the first equation of the SVAR as the monetary policy equation: yt a0,1 = xtal,1 + 1t ⇔ it = φy yt + φy∗ y∗ t + φppt + φnbrx nbrxt + φrer rert + φi∗ i∗ t + a−1 0,71 1t Part 1 of our identification implies: it = φy yt + φppt + a−1 0,71 1t with φy > 0 and φp > 0.
  23. 23. Introduction Econometric Methodology Identification Strategy Estimation Results Baseline Identification II Label the first equation of the SVAR as the monetary policy equation: yt a0,1 = xtal,1 + 1t ⇔ it = φy yt + φy∗ y∗ t + φppt + φnbrx nbrxt + φrer rert + φi∗ i∗ t + a−1 0,71 1t Part 1 of our identification implies: it = φy yt + φppt + a−1 0,71 1t with φy > 0 and φp > 0. For Part II we selected an horizont of 12 months
  24. 24. Introduction Econometric Methodology Identification Strategy Estimation Results Long-Run Multipliers
  25. 25. Introduction Econometric Methodology Identification Strategy Estimation Results Long-Run Multipliers • Is our identification consistent with the Taylor Principle?
  26. 26. Introduction Econometric Methodology Identification Strategy Estimation Results Long-Run Multipliers • Is our identification consistent with the Taylor Principle? • Including the lags: (1 − a−1 0,71 p i=1 ai,71Li )it = (a−1 0,71( p i=1 ai,11Li − a0,11))yt +(a−1 0,71( p i=1 ai,31Li − a0,31))pt
  27. 27. Introduction Econometric Methodology Identification Strategy Estimation Results Long-Run Multipliers • Is our identification consistent with the Taylor Principle? • Including the lags: (1 − a−1 0,71 p i=1 ai,71Li )it = (a−1 0,71( p i=1 ai,11Li − a0,11))yt +(a−1 0,71( p i=1 ai,31Li − a0,31))pt • The long run multipliers are:
  28. 28. Introduction Econometric Methodology Identification Strategy Estimation Results Long-Run Multipliers • Is our identification consistent with the Taylor Principle? • Including the lags: (1 − a−1 0,71 p i=1 ai,71Li )it = (a−1 0,71( p i=1 ai,11Li − a0,11))yt +(a−1 0,71( p i=1 ai,31Li − a0,31))pt • The long run multipliers are: Φy = ∂i∗ ∂y∗ = (a−1 0,71( p i=1 ai,11 − a0,11)) 1 − a−1 0,71( p i=1 ai,71) (5) Φp = ∂i∗ ∂p∗ = (a−1 0,71( p i=1 ai,31 − a0,31)) 1 − a−1 0,71( p i=1 ai,71) (6)
  29. 29. Introduction Econometric Methodology Identification Strategy Estimation Results Alternative Identifications
  30. 30. Introduction Econometric Methodology Identification Strategy Estimation Results Alternative Identifications 1. Scholl & Uhlig (2008): For 12 periods, the responses of prices and reserves are non-positive while the response of interest rates is non-negative.
  31. 31. Introduction Econometric Methodology Identification Strategy Estimation Results Alternative Identifications 1. Scholl & Uhlig (2008): For 12 periods, the responses of prices and reserves are non-positive while the response of interest rates is non-negative. 2. Arias, Caldara, Rubio-Ramirez (2015): The federal funds rate is the monetary policy instrument and it reacts contempo- raneously only to output and prices. The response coefficients of output and prices are non-negative.
  32. 32. Introduction Econometric Methodology Identification Strategy Estimation Results Estimation
  33. 33. Introduction Econometric Methodology Identification Strategy Estimation Results Estimation • Monthly data, 1978M1-2007M11, for the U.S and U.K economies, FRED Database
  34. 34. Introduction Econometric Methodology Identification Strategy Estimation Results Estimation • Monthly data, 1978M1-2007M11, for the U.S and U.K economies, FRED Database • Bayesian VAR(6) with a Normal-Wishart prior as in Uhlig (2005)
  35. 35. Introduction Econometric Methodology Identification Strategy Estimation Results Estimation • Monthly data, 1978M1-2007M11, for the U.S and U.K economies, FRED Database • Bayesian VAR(6) with a Normal-Wishart prior as in Uhlig (2005) • Following Fry and Pagan (2007) we use the closest to median IRF. Why?
  36. 36. Introduction Econometric Methodology Identification Strategy Estimation Results Estimation • Monthly data, 1978M1-2007M11, for the U.S and U.K economies, FRED Database • Bayesian VAR(6) with a Normal-Wishart prior as in Uhlig (2005) • Following Fry and Pagan (2007) we use the closest to median IRF. Why? Let Θmed and Θstd represent the median and the standard deviation of the IRF across the 1000 draws. Define:
  37. 37. Introduction Econometric Methodology Identification Strategy Estimation Results Estimation • Monthly data, 1978M1-2007M11, for the U.S and U.K economies, FRED Database • Bayesian VAR(6) with a Normal-Wishart prior as in Uhlig (2005) • Following Fry and Pagan (2007) we use the closest to median IRF. Why? Let Θmed and Θstd represent the median and the standard deviation of the IRF across the 1000 draws. Define: ˜Θt = (Θt − Θmed ) Θstd
  38. 38. Introduction Econometric Methodology Identification Strategy Estimation Results Estimation • Monthly data, 1978M1-2007M11, for the U.S and U.K economies, FRED Database • Bayesian VAR(6) with a Normal-Wishart prior as in Uhlig (2005) • Following Fry and Pagan (2007) we use the closest to median IRF. Why? Let Θmed and Θstd represent the median and the standard deviation of the IRF across the 1000 draws. Define: ˜Θt = (Θt − Θmed ) Θstd Closest to Median IRF: min vec( ˜Θt) vec( ˜Θt)
  39. 39. Introduction Econometric Methodology Identification Strategy Estimation Results Monetary Policy Shocks under Scholl & Uhlig (2008) 10 20 30 40 50 60 0 0.1 0.2 0.3 0.4 Fed Funds 10 20 30 40 50 60 −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 U.K Output 10 20 30 40 50 60 −0.1 −0.08 −0.06 −0.04 −0.02 U.S CPI 10 20 30 40 50 60 −0.35 −0.3 −0.25 −0.2 −0.15 −0.1 −0.05 0 Non−borrowed/Total reserves 10 20 30 40 50 60 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 Real Exchange rate U.K/U.S 10 20 30 40 50 60 −0.3 −0.2 −0.1 0 0.1 U.K interbank rate 10 20 30 40 50 60 −0.1 −0.05 0 0.05 0.1 0.15 U.S Output
  40. 40. Introduction Econometric Methodology Identification Strategy Estimation Results IRFs from a Monetary Policy Shock under Arias et al.(2015) 10 20 30 40 50 60 −0.25 −0.2 −0.15 −0.1 −0.05 0 U.S Output 10 20 30 40 50 60 −0.04 −0.02 0 0.02 0.04 0.06 0.08 U.K Output 10 20 30 40 50 60 −0.12 −0.1 −0.08 −0.06 −0.04 −0.02 0 U.S CPI 10 20 30 40 50 60 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 Non−borrowed/Total reserves 10 20 30 40 50 60 −0.4 −0.3 −0.2 −0.1 0 0.1 Real Exchange rate U.K/U.S 10 20 30 40 50 60 −0.05 0 0.05 0.1 0.15 U.K interbank rate 10 20 30 40 50 60 −0.2 −0.1 0 0.1 0.2 0.3 0.4 Fed Funds
  41. 41. Introduction Econometric Methodology Identification Strategy Estimation Results FEVD of the MP Shock under Arias et al.(2015) 10 20 30 40 50 60 0 5 10 15 20 25 U.S Output 10 20 30 40 50 60 0 0.5 1 1.5 2 U.K Output 10 20 30 40 50 60 0 10 20 30 40 50 U.S CPI 10 20 30 40 50 60 0 0.5 1 1.5 2 2.5 Non−borrowed/Total reserves 10 20 30 40 50 60 0 0.5 1 1.5 2 Real Exchange rate U.K/U.S 10 20 30 40 50 60 0 0.5 1 1.5 2 2.5 3 3.5 U.K interbank rate 10 20 30 40 50 60 0 2 4 6 8 10 12 14 Fed Funds
  42. 42. Introduction Econometric Methodology Identification Strategy Estimation Results Long-run multipliers under Arias et al.(2015) −16000−14000−12000−10000 −8000 −6000 −4000 −2000 0 2000 4000 0 1 2 3 4 5 6 7 8 x 10 −4 Inflation Long−Run Multipliers: Φp −4000 −3500 −3000 −2500 −2000 −1500 −1000 −500 0 500 1000 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Output Long−Run Multipliers: Φy . i P(Φi > 0) P(Φi > 1) P(Φi > 20) P(Φi > 50) P(Φi > 100) P(Φi > 150) P(Φi > 200) Φp 0.995 0.943 0.226 0.101 0.059 0.038 0.029 Φy 0.994 0.860 0.073 0.033 0.014 0.009 0.006
  43. 43. Introduction Econometric Methodology Identification Strategy Estimation Results Is this plausible?
  44. 44. Introduction Econometric Methodology Identification Strategy Estimation Results Is this plausible? Scholl & Uhlig(2008) Identification:
  45. 45. Introduction Econometric Methodology Identification Strategy Estimation Results Is this plausible? Scholl & Uhlig(2008) Identification: • A contractionary monetary policy shock raises output in the short-term (Is it expansionary?)
  46. 46. Introduction Econometric Methodology Identification Strategy Estimation Results Is this plausible? Scholl & Uhlig(2008) Identification: • A contractionary monetary policy shock raises output in the short-term (Is it expansionary?) Arias et al.(2015) Identification:
  47. 47. Introduction Econometric Methodology Identification Strategy Estimation Results Is this plausible? Scholl & Uhlig(2008) Identification: • A contractionary monetary policy shock raises output in the short-term (Is it expansionary?) Arias et al.(2015) Identification: • No significant effect of the identified monetary policy shock on the Federal Funds rate
  48. 48. Introduction Econometric Methodology Identification Strategy Estimation Results Is this plausible? Scholl & Uhlig(2008) Identification: • A contractionary monetary policy shock raises output in the short-term (Is it expansionary?) Arias et al.(2015) Identification: • No significant effect of the identified monetary policy shock on the Federal Funds rate • The shock explains only 13% on impact and 2% in the long-run from the variations in Fed Funds
  49. 49. Introduction Econometric Methodology Identification Strategy Estimation Results Is this plausible? Scholl & Uhlig(2008) Identification: • A contractionary monetary policy shock raises output in the short-term (Is it expansionary?) Arias et al.(2015) Identification: • No significant effect of the identified monetary policy shock on the Federal Funds rate • The shock explains only 13% on impact and 2% in the long-run from the variations in Fed Funds • 0.2% increase in interest rates causes output to fall by 1-1.2%
  50. 50. Introduction Econometric Methodology Identification Strategy Estimation Results Is this plausible? Scholl & Uhlig(2008) Identification: • A contractionary monetary policy shock raises output in the short-term (Is it expansionary?) Arias et al.(2015) Identification: • No significant effect of the identified monetary policy shock on the Federal Funds rate • The shock explains only 13% on impact and 2% in the long-run from the variations in Fed Funds • 0.2% increase in interest rates causes output to fall by 1-1.2% • Probability of an inflation multiplier ≥ 50 or 100 is 10% and 6% respectively
  51. 51. Introduction Econometric Methodology Identification Strategy Estimation Results Is this plausible? Scholl & Uhlig(2008) Identification: • A contractionary monetary policy shock raises output in the short-term (Is it expansionary?) Arias et al.(2015) Identification: • No significant effect of the identified monetary policy shock on the Federal Funds rate • The shock explains only 13% on impact and 2% in the long-run from the variations in Fed Funds • 0.2% increase in interest rates causes output to fall by 1-1.2% • Probability of an inflation multiplier ≥ 50 or 100 is 10% and 6% respectively • Hard to justify the presence of an inflation multiplier of 100.
  52. 52. Introduction Econometric Methodology Identification Strategy Estimation Results IRFs from a Monetary Policy shock under the Baseline Identification We restrict both the systematic component of monetary policy and the IRFs 10 20 30 40 50 60 −0.15 −0.1 −0.05 0 0.05 U.S Output 10 20 30 40 50 60 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 U.K Output 10 20 30 40 50 60 −0.12 −0.1 −0.08 −0.06 −0.04 −0.02 U.S CPI 10 20 30 40 50 60 −0.25 −0.2 −0.15 −0.1 −0.05 0 Non−borrowed/Total reserves 10 20 30 40 50 60 −0.4 −0.3 −0.2 −0.1 0 Real Exchange rate U.K/U.S 10 20 30 40 50 60 −0.05 0 0.05 0.1 0.15 0.2 U.K interbank rate 10 20 30 40 50 60 0 0.1 0.2 0.3 0.4 0.5 Fed Funds
  53. 53. Introduction Econometric Methodology Identification Strategy Estimation Results The MP Shock under the Baseline Identification Jul78 Mar80 Nov81 Jul83 Mar85 Nov86 Jul88 Mar90 Nov91 Jul93 Mar95 Nov96 Jul98 Mar00 Nov01 Jul03 Mar05 Nov06 −2 −1.5 −1 −0.5 0 0.5 1
  54. 54. Introduction Econometric Methodology Identification Strategy Estimation Results FEVD under the Baseline Identification 10 20 30 40 50 60 0 5 10 15 20 U.S Output 10 20 30 40 50 60 0 0.5 1 1.5 2 U.K Output 10 20 30 40 50 60 0 5 10 15 20 25 30 U.S CPI 10 20 30 40 50 60 0 2 4 6 8 Non−borrowed/Total reserves 10 20 30 40 50 60 0 2 4 6 8 10 12 14 Real Exchange rate U.K/U.S 10 20 30 40 50 60 0 2 4 6 8 10 U.K interbank rate 10 20 30 40 50 60 0 10 20 30 40 50 60 Fed Funds
  55. 55. Introduction Econometric Methodology Identification Strategy Estimation Results Long-run multipliers under Baseline Identification 0 5 10 15 20 25 30 35 0.02 0.04 0.06 0.08 0.1 0.12 Inflation Long−Run Multipliers: Φp 0 1 2 3 4 5 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 Output Long−Run Multipliers: Φy i P(Φi > 0) P(Φi > 1) P(Φi > 5) P(Φi > 10) P(Φi > 20) P(Φi > 50) Φp 1 0.9960 0.7650 0.2650 0.0390 0 Φy 1 0.5820 0 0 0 0
  56. 56. Introduction Econometric Methodology Identification Strategy Estimation Results Conclusions
  57. 57. Introduction Econometric Methodology Identification Strategy Estimation Results Conclusions • We propose a new agnostic identification for open economy SVARs...
  58. 58. Introduction Econometric Methodology Identification Strategy Estimation Results Conclusions • We propose a new agnostic identification for open economy SVARs... • ...restricting both the systematic component of monetary policy and the IRFs
  59. 59. Introduction Econometric Methodology Identification Strategy Estimation Results Conclusions • We propose a new agnostic identification for open economy SVARs... • ...restricting both the systematic component of monetary policy and the IRFs • this method yields more plausible results than the approches it builds on
  60. 60. Introduction Econometric Methodology Identification Strategy Estimation Results Conclusions • We propose a new agnostic identification for open economy SVARs... • ...restricting both the systematic component of monetary policy and the IRFs • this method yields more plausible results than the approches it builds on • we find that an increase of 0.4-0.5% increase in interest rates causes output to contract by 1.2% in the long-run
  61. 61. Introduction Econometric Methodology Identification Strategy Estimation Results Conclusions • We propose a new agnostic identification for open economy SVARs... • ...restricting both the systematic component of monetary policy and the IRFs • this method yields more plausible results than the approches it builds on • we find that an increase of 0.4-0.5% increase in interest rates causes output to contract by 1.2% in the long-run • exchange rate exhibits delayed overshooting

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