Flexible Inflation Forecast Targeting: Evidence for Canada (and Australia) Glenn Otto School of Economics UNSW g.otto@unsw.edu.a & Graham Voss Department of Economics University of Victoria gvoss@uvic.ca August 2011
Introduction What are the targets or objectives of central banks? Formal inflation targets Less (formal) information about other variables 2008 PTA (New Zealand) For the purpose of this agreement, the policy target shall be to keep future CPI inflation outcomes between 1 per cent and 3 per cent on average over the medium term. In pursuing its price stability objective, the Bank shall implement monetary policy in a sustainable, consistent and transparent manner and shall seek to avoid unnecessary instability in output, interest rates and the exchange rate. 2
With multiple targets and a single instrument, a central bank may have to trade-off various objectives. Flexible inflation targets: inflation plus other variables in target criteria Buiter (2006) argues for a lexicographic ordering of targets with inflation ordered first How successful are central banks at achieving their targets or objects? Do we see predictable deviations from the (stated, estimated) target of the central bank? 3
Forecast Targeting Rules Woodford (2003; 2007) and Svensson (2003) normative case We estimate and test following condition(s): E t [(π t+h π T ) + φδx t+h ] = 0 h = 0,1,.. h, π = inflation π T = inflation target Δx = change in the output gap φ 0 (relative) weight on activity Optimal monetary policy rule for a particular New Keynesian model 4
New Keynesian Model Central Bank Loss Function 1 h=0 2 ] E 2 t β h [(π t+h π T ) 2 + λx t+h Phillips Curve π t = βe t h π t+1 + κe t h x t + E t h u t Pricing decisions are pre-determined h periods in advance Central bank optimises under the assumption that it can influence future expectations of inflation Implements timelessly optimal policy φ = λ/κ 5
Generalization of Strict Inflation Targeting E t (π t+h π T ) = 0 h = 1,2,3. Are future deviations of inflation from target predictable? Rowe and Yetman (2002) test this condition on Canadian data (1992:4-2001:1) - What is BOC s inflation target? 1.6% - How well does it achieve its target? Are deviations from the estimated target predictable? Not at horizons of 6-8 quarters. Extension of Rowe and Yetman - What does the BOC do at horizons less than 6 quarters? - A more powerful test of strict inflation targeting? 6
Empirical Model Replace output gap with output growth E t [(π t+h π T ) + φδx t+h ] = 0 E t [(π t+h π T ) + φδ(y t+h y t+h )] = 0 E t [(π t+h π T ) + φ(δy t+h Δy t+h )] = 0 Assume Δy t+h = Δy E t [(π t+h π T ) + φ(δy t+h Δy)] = 0 7
Generalized Nominal Income Growth Targeting Rule E t [π t+h + φδy t+h ] = π T + φδy If φ = 1 E t [π t+h + Δy t+h ] = π T + Δy 8
Estimation E t [(π t+h π T ) + φ h (Δy t+h Δy)] = 0 h = 0,1,.. h,.. H Estimate by GMM for a range of h Set of potential instruments is large Instrument quality matters need good predictor of π t+h or Δy t+h Re-normalize the condition as: E t [Δy t+h + 1 φ h π t+h a 0h ] = 0 a 0h = π h φ h + Δy 9
Data Bank of Canada adopted inflation targeting framework in 1991 Current target band is 1-3 percent inflation (adopted in 1995) Monthly Canadian data from 1996:1-2007:12 π t = core inflation, 12-months ended Δy t = output growth, 3-month ended, annual rate cm π t = commodity price inflation, 12-months ended Δm t = M2 growth, 12-months ended 10
Instruments Instrument set 2-month lag E t [Δy t+h + 1 φ h π t+h a 0h ] = 0 h = 1,2,3,,18 Newey-West estimator: m=h-1 z t = (1, π t 2, π cm t 2, Δm t 2 ) Use Δy = 3.37 to recover an estimate of inflation target 11
Results Stock and Yogo (2002) test for weak instruments. Reject weak instruments at 5% level for h 11. Instrument quality may be more of an issue at longer horizons (not unexpected). Estimate of h. At what horizon is targeting rule non-rejected? J- statistic. Targeting rule is not-rejected at h 10 months. Interval estimates for φ h. Can reject φ = 0. But estimates suggest that φ varies across forecast horizons. Test φ 10 = φ 13 = φ 16 p-value = 0.002 Sensitivity Analysis 12
Test for Weak Instruments (IV bias relative to OLS) 40 35 30 25 F-statistic 20 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 F-stat 5% bias cv 10% bias cv h 13
Hansen s J-Statistic 1 0.9 0.8 0.7 0.6 p-value 0.5 0.4 0.3 0.2 0.1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 h 14
95% Interval Estimates of φ h 3 2.5 2 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18-0.5-1 h 15
Sensitivity Analysis (h=12) 10.0 8.0 6.0 4.0 2.0 0.0-2.0 baseline Δgap gap 2001m1-2007m12-4.0 16
Identification Robust Methods Anderson and Rubin (1949); Dufour (2003); Dufour, Khalaf and Kichian (2006) Re-write targeting rule as a regression model π t+h = π T φ(δy t+h Δy ) + u t+h If instruments are weak, we can still consider the condition that Basic Idea E(u t+h z t ) = 0 E([π t+h π T + φ(δy t+h Δy )]z t ) = 0 Search for values of π T and φ that make this condition hold 17
AR Regression z t = vector of instruments π t+h + φ h (Δy t+h Δy ) = α + z t β + v t+h Test: φ h = φ h 0 implies β = 0 (F-test) Search in range φ h = (0,1): Step size = 0.00001 - Report all p-values for F-statistics - Use maximum p-value as AR estimate of φ h - Use distribution of p-values to compute confidence intervals Standard or Robust F-statistic? 18
AR 95% Interval Estimates of φ h (h=12 18) 0.6 0.5 0.4 0.3 0.2 0.1 0 12 13 14 15 16 17 18 h 19
Australian Estimates RBA inflation target 2-3 percent Quarterly data from 1996:1-2010:2 π t = Trimmed mean inflation, 4-qrt-ended Δy t = Non-farm output growth, 4-qrt-ended Δy rt t = Real time output growth, 4-qrt-ended 20
Regression Model Instrument Set i t c = cash rate π t+h = c h + φ h Δy t+h + v t+h h = 1,2..,6 un t = unemployment rate c z t = (1, Δy t 1, i t 1, un t 1, Δcr t 1 ) Δcr t = credit growth, 4-qtr-ended 21
Estimates of φ h for Australia h π T φ h J-test IQ IQ(NW, m=4) 1 2.6 0.47 0.06 11.9 10.4 (0.05) 2 2.6 0.55 0.17 8.3 11.2 (0.09) 3 2.6 0.61 0.53 10.7 14.3 (0.12) 4 2.7 0.67 0.95 7.3 28.7 (0.10) 5 2.6 0.60 0.15 9.6 20.4 (0.08) 6 2.6 0.48 0.19 7.9 9.7 (0.09) 22
23 AR Estimate of φ h for h=4 0 0.2 0.4 0.6 0.8 1 1.2 0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30 0.33 0.36 0.39 0.42 0.45 0.48 0.51 0.54 0.57 0.60 0.63 0.66 0.69 0.72 0.75 0.78 0.81 0.84 0.87 0.90 0.93 0.96 0.99 1.02 1.05 1.08 1.11 1.14 1.17 1.20 1.23 1.26 1.29 1.32 1.35 1.38 1.41 1.44 1.47 p-value phi
Estimates of φ h for Australia Real Time GDP Data h φ h J-test IQ IQ(NW, m=4) 1 0.57 0.34 9.9 5.4 (0.08) 2 0.64 0.47 9.5 4.2 (0.15) 3 0.61 0.65 12.2 8.2 (0.14) 4 0.65 0.79 9.9 12.3 (0.13) 5 0.70 0.93 7.5 6.7 (0.13) 6 0.68 0.89 6.5 5.0 (0.14) 24
AR Estimate of φ h for h=4: 2010:Q2 Vintage and Real Time Data 1.2 1 0.8 0.6 0.4 0.2 0 0 0.029 0.058 0.087 0.116 0.145 0.174 0.203 0.232 0.261 0.29 0.319 0.348 0.377 0.406 0.435 0.464 0.493 0.522 0.551 0.58 0.609 0.638 0.667 0.696 0.725 0.754 0.783 0.812 0.841 0.87 0.899 0.928 0.957 0.986 1.015 1.044 1.073 1.102 1.131 1.16 1.189 1.218 1.247 1.276 1.305 1.334 1.363 1.392 1.421 1.45 1.479 2010:Q2_vintage realtime data 0.05 significance level 25
Estimates of φ h at One-Year Horizon 1.6 1.4 1.2 1 phi12 0.8 0.6 0.4 0.2 0 Can IV Can AR Aus IV Aus AR Aus IV realtime Aus AR realtime 26
A Final Concern Are our estimates biased? True forecast targeting rule E t [(π t+h π T ) + φ h (Δy t+h Δy) + γ h X t+h ] = 0 X = interest rate, exchange rate, omitted dynamics 27