Banque Nationale De Belgique Sa · EURONEXT:BNB
Banque Nationale De Belgique Sa — National Bank of Belgium biennial conference 2018
26 slides from Banque Nationale De Belgique Sa's conference presentation, October 2018
Slide 1: Quantile-based Inflation Risk Models
Quantile-based Inflation Risk Models Eric Ghysels 1 Leonardo Iania 2 Jonas Striaukas 2 1 UNC 2 UC Louvain National Bank of Belgiums biennial conference GIS Quantile-based Inflation Risk Models NBB 2018 10 1 / 23
Slide 2: Outline
Outline 1 Introduction 2 Modeling inflation quantiles Quantiles Summary of the analysis In- and out-of-sample analysis 3 Inflation risk measures Inflation risk measures: definitions The reaction of short-term interest rates to inflation risk 4 Conclusions GIS Quantile-based Inflation Risk Models NBB
Slide 3: Motivation
Motivation Figure: Fan chart of PCE Inflation ”In assessing the path for the federal funds rate [...] FOMC participants take account of the range of possible economic outcomes, the likelihood of those outcomes, and the potential benefits and costs should they occur.” Source: Minutes of the Federal O
Slide 4: Motivation
Motivation Figure: Risks to PCE inflation ”Because the fan charts are constructed to be symmetric around the median projections, they do not reflect any asymmetries in the balance of risks that participants may see in their economic projections.” Minutes of the Federal Open Market Committee. March 2
Slide 5: Motivation
Motivation Zarnowitz and Lambros (1987) propose uncertainty measure using the inter-quantile range of survey data Kilian and Manganelli (2008) develop structural model in which monetary authorities can have non-quadratic valuation of inflation costs Kilian and Manganelli (2007) estimate several infl
Slide 6: In this (ongoing) project...
In this (ongoing) project... We focus on quantile forecasting... ... in a mixed-frequency setting... ...and we construct quantile-based inflation risk measures GIS Quantile-based Inflation Risk Models NBB 2018 10 6 / 23
Slide 7: In this (ongoing) project...
In this (ongoing) project... We focus on quantile forecasting... (h) πt = log(Pt /Pt−h ) −→ qπτ h (t+h | t) ... in a mixed-frequency setting... ...and we construct quantile-based inflation risk measures GIS Quantile-based Inflation Risk Models NBB 2018 10 6 / 23
Slide 8: In this (ongoing) project...
In this (ongoing) project... We focus on quantile forecasting... (h) πt = log(Pt /Pt−h ) −→ qπτ h (t+h | t) ... in a mixed-frequency setting... qπτ h = µτ + ρτ πt + βτ Zt (θ) (t+h | t) ...and we construct quantile-based inflation risk measures GIS Quantile-based Inflation Risk Models NBB 2018 10 6 /
Slide 9: In this (ongoing) project...
In this (ongoing) project... We focus on quantile forecasting... (h) πt = log(Pt /Pt−h ) −→ qπτ h (t+h | t) ... in a mixed-frequency setting... qπτ h = µτ + ρτ πt + βτ Zt (θ) (t+h | t) ...and we construct quantile-based inflation risk measures I I@Rτt|t−h = Inflation-at-risk I IQRτ t|t−h = Interquan
Slide 10: Outline
Outline 1 Introduction 2 Modeling inflation quantiles Quantiles Summary of the analysis In- and out-of-sample analysis 3 Inflation risk measures Inflation risk measures: definitions The reaction of short-term interest rates to inflation risk 4 Conclusions GIS Quantile-based Inflation Risk Models NBB
Slide 11: Regression quantiles: intuition
Regression quantiles: intuition Linear regression (Blue line) E (rt |πt−1 ) = µ + ρπt−1 Quantile regression (Red lines) qτ (rt |πt−1 ) = µ(τ ) + ρ(τ )πt−1 GIS Quantile-based Inflation Risk Models NBB 2018 10 8 / 23
Slide 12: Models
Models Quantile autoregressive model (QAR) p−1 X q−1 X qπτ h = µτ + ατ,j πt−j ≡ µτ + ρτ πt + βτ,j ∆πt−j (t+h | t) j=0 j=0 QAR distributed lag model with MIDAS component (QADL-MIDAS) qπτ h = µτ + ρτ πt + βτ Zt (θ) (t+h | t) where h X Zt (θτ ) = ωm (θτ )|∆πt−m | m=0 GIS Quantile-based Inflation Risk M
Slide 13: Modeling inflation quantiles: analysis
Modeling inflation quantiles: analysis Setting 1 Based on monthly US CPI inflation (Headlines and CORE) 2 Period: 1960-01 to 2018-05 3 We focus on modeling/forecasting year-on-year inflation 4 Number of lags: 12. Model comparison 1 In-sample I Are the regression coefficients quantile-dependent? I Is
Slide 14: In-sample analysis
In-sample analysis Pq−1 qπ(h) (τ | Ft ) = µτ + ρτ πt + j=0 βτ,j ∆πt−j t+h Quantile 0.05 0.25 0.5 0.75 0.95 µ -0.454 0.569 0.952 1.471 2.597 (0.047) (0.000) (0.000) (0.000) (0.000) ρ 0.502 0.593 0.713 0.866 1.101 (0.000) (0.000) (0.000) (0.000) (0.000) qπ(h) (τ | Ft ) = µτ + ρτ πt + βτ Zt (θ) t+h Qua
Slide 15: Out-of-sample analysis
Out-of-sample analysis CPI 12-months 3-months 0.05 0.25 0.50 0.75 0.95 0.05 0.25 0.50 0.75 0.95 CW statistic 2.289∗∗ 0.677 2.304∗∗ 3.127∗∗∗ 3.364∗∗∗ -2.681 1.288 -3.172 3.507∗∗ 3.550∗∗ p-Value (0.015) (0.259) (0.014) (0.002) (0.001) (0.995) (0.109) (0.999) (0.000) (0.000) ratio 0.796 0.951 0.959 0.8
Slide 16: Outline
Outline 1 Introduction 2 Modeling inflation quantiles Quantiles Summary of the analysis In- and out-of-sample analysis 3 Inflation risk measures Inflation risk measures: definitions The reaction of short-term interest rates to inflation risk 4 Conclusions GIS Quantile-based Inflation Risk Models NBB
Slide 17: Inflation risk measures (based on Andrade et al. (2015))
Inflation risk measures (based on Andrade et al. (2015)) Inflation-at-risk I @R τ = q̂τ Interquantile range IQR τ = q̂1−τ − q̂τ Contitional (robust) asymmetry (q̂1−τ − q̂0.50 ) − (q̂0.50 − q̂τ ) ASY τ = IQRτ GIS Quantile-based Inflation Risk Models NBB 2018 10 14 / 23
Slide 18: Conditional asymmetry comparison
Conditional asymmetry comparison QAR(12) conditional asymmetry 1 0.5 0 -0.5 -1 1970 1980 1990 2000 2010 QADL-MIDAS conditional asymmetry 1 0.5 0 -0.5 -1 1970 1980 1990 2000 2010 GIS Quantile-based Inflation Risk Models NBB 2018 10 15 / 23
Slide 19: Conditional asymmetry regimes
Conditional asymmetry regimes 1 0.5 0 -0.5 -1 1970 1980 1990 2000 2010 Note: 12 months ahead conditional asymmetry (75%) for CPI data GIS Quantile-based Inflation Risk Models NBB 2018 10 16 / 23
Slide 20: Inflation risk measures and monetary policy
Inflation risk measures and monetary policy We study the relationship between federal fund rates and inflation risk via a two-step procedure: 1 Construct real-time risk measures 2 Regress federal fund rates changes on real-time risk measures and a set of control variables GIS Quantile-based Inflatio
Slide 21: Step 2: Federal fund rates changes and real-time risk measures
Step 2: Federal fund rates changes and real-time risk measures Following Andrade, Ghysels, and Idier (2015), our augmented Taylor Rule-type regression equation is: ∆it+1 = β0 + β1 IQRτt|t−h + β2 ASYτt|t−h + ρ0 Ct + t+1 where: ∆it+1 is the change in the effective federal funds rate (EFFR) Ct contains
Slide 22: Table: Parameter estimates and model fit
Table: Parameter estimates and model fit 01-Mar-1963 to 01-Apr-2018 IQR 5% ASY 5% IQR 25% ASY 25% coeff. -0.014 0.192∗∗ -0.033 0.120∗∗ p-Value (0.403) (0.012) (0.237) (0.043) 2 Radj 0.184 0.184 Dependent variable is real time change in effective federal funds rate. ∗∗∗ , ∗∗ and ∗ refer to 1, 5 and 1
Slide 23: Table: Parameter estimates and model fit
Table: Parameter estimates and model fit 01-Jan-1980 to 01-Apr-2018 IQR 5% ASY 5% IQR 25% ASY 25% coeff. 0.004 0.108∗ 0.001 0.072 p-Value (0.860) (0.068) (0.987) (0.190) 2 Radj 0.179 0.179 01-Mar-1963 to 01-Dec-1978 IQR 5% ASY 5% IQR 25% ASY 25% coeff. -0.054∗∗∗ 0.297∗∗ -0.101∗∗∗ 0.106∗∗ p-Value (0.
Slide 24: Outline
Outline 1 Introduction 2 Modeling inflation quantiles Quantiles Summary of the analysis In- and out-of-sample analysis 3 Inflation risk measures Inflation risk measures: definitions The reaction of short-term interest rates to inflation risk 4 Conclusions GIS Quantile-based Inflation Risk Models NBB
Slide 25: Summary of results
Summary of results 1 We propose a new approach to extract quantile-based inflation risk measures 2 Our model accounts for absolute past inflation changes in quantile modeling and can handle mixed-frequency data sampling 3 Our model performs favorably with respect to a standard QAR model in terms of
Slide 26: References I
References I Andrade, P., E. Ghysels, and J. Idier (2015): “Tails of Inflation Forecasts and Tales of Monetary Policy,” . Kilian, L. and S. Manganelli (2007): “Quantifying the risk of deflation,” Journal of Money, Credit and Banking, 39, 561–590. ——— (2008): “The central banker as a risk manager: Es
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