Detrending and nancial cycle facts across G7 countries: Mind a spurious medium term! Yves S. Schüler. 2nd November 2017, Athens

Transcription

1 Detrending and nancial cycle facts across G7 countries: Mind a spurious medium term! Yves S. Schüler Deutsche Bundesbank, Research Centre 2nd November 217, Athens Disclaimer: The views expressed in this presentation are those of the author and do not necessarily reect the views of the Deutsche Bundesbank or the European Central Bank. 1/21

2 Introduction Motivation and research question Analysis of expansions and contractions in nancial variables (or, nancial cycles): Critical to inform about the build-up of imbalances in the nancial sector For example, Basel III credit-to-gdp gap: Cycles guide the setting of countercyclical capital buers (CCyBs) Here, identication of cycles: HP lter with smoothing parameter 4, applied to trending credit-to-gdp ratio (medium-term cycles), where 1,6 is the commonly employed smoothing parameter 2/21

3 Introduction Motivation and research question Such and similar identication of cycles common practice for nancial variables 1 What are the consequences of these dierent detrending approaches for the analysis of cycles? Are extracted cycles spurious? (literature on spurious (business) cycles, e.g., Cogley and Nason (1995)) Are nancial cycle facts robust (dier to business cycles in amplitude, duration, and cross-country synchronisation) 2? (literature on detrending and non-robustness of business cycle facts, e.g., Canova (1998)) 1 e.g., Borio and Lowe (24), Drehmann et al. (212), Behn et al. (213), Borio (214), Meller and Metiu (215, forthcoming), Stremmel (215), Anundson et al. (216), Bauer and Granziera (216) 2 e.g., Claessens et al. (211, 212), Aikman et al. (215), Schüler et al. (217) 3/21

4 Introduction Preview of main results Main results: Signicant evidence of spurious cycles for HP and band pass lters, but not dierence lters Eects of spurious cycles particularly stark when extracting medium-term cycles (e.g., Basel III credit-to-gdp gap) (factor of amplication of a specic cycle: up to 24) Financial cycle facts broadly robust! Dierences marginal for HP and band pass lters (due to spurious cycles) 4/21

5 Introduction Illustration of main result (a) True gap (b) HP (16) gap (c) HP (4) gap Simulated data: Estimated dynamics in changes in US credit-to-gdp *Spurious cycles: cycle duration determined by smoothing parameter *Stronger distortion the λ in HP (λ) (no short-term uctuations) (a) US Basel III credit-to-gdp gap (λ = 4, ), 197Q1-213Q4 (b) France *Abrupt risk materialisation? *Changes in frequency of crises? *4, right parameter for French case? 5/21

6 Introduction Outline of the remaining parts 1 Methods of detrending 2 Theory of detrending 3 Empirical evidence 4 Summary and policy implications 6/21

7 Methods of detrending Methods of detrending Dierence lters (y t is time series of interest, t = 1,..., T ): lter: 3 y t = y t y t 1, 4 lter: 4 4 y t = y t y t 4. HP lter: λ = 16 and λ = 4. 5 Baxter and King (1999)'s (BK) lter (K = 4, lags): 1.5 to 8 years and 8 to 3 years. 6 3 e.g., Schularick and Taylor (212), Aikman et al. (215), Schüler et al. (215, 217) 4 e.g., Drehmann et al. (212), Strohsal et al. (215), Verona (216) 5 Basel III and, e.g., Borio and Lowe (24), Behn et al. (213), Bauer and Granziera (216) 6 similar to Drehmann et al. (212), Stremmel (215), Meller and Metiu (215) 7/21

8 Theory of detrending Theory of detrending 8/21

9 Theory of detrending Eects of detrending on trend (TS) and dierence stationary (DS) time series Let y t = τ t + ψ t (1) τ t is non-stationary component (trend) ψ t is stationary, non-deterministic, and possibly cyclical Assumptions on τ t : 7 TS: y t = α + βt + ψ t (2) DS: y t = α + y t 1 + ψ t (3) α is intercept (drift), t deterministic trend, and β slope coecient of trend. Goal: Extract ψ t (also called gap, y t τ t ) 7 e.g., Nelson and Plosser (1982) 9/21

10 Theory of detrending TS: Eect on ψ t (power transfer functions) 4 PTF Δ filter Δ 4 filter π/4 π/2 3π/4 π Notes: The blue area marks business cycle frequencies (1.5-8 years) and the purple area medium term cycles (8-3 years) assuming quarterly frequency. (a) Dierence lters HP (16) HP (4) 3 BK (1.5,8) BK (8,3) PTF 2 PTF π/4 π/2 3π/4 π π/4 π/2 3π/4 π (b) HP lter (c) BK lter 1/21

11 Theory of detrending DS: Eect on ψ t (power transfer functions) 15 PTF π/4 π/2 3π/4 π (d) lter (black) and 4 lter (red) 1 Peak at 7.5 years 2 15 Peak at 3 years PTF 5 PTF 1 5 π/4 π/2 3π/4 π π/4 π/2 3π/4 π (e) HP (16) (f) HP (4) 11/21

12 Theory of detrending DS: Eect on ψ t (power transfer functions, cont'd) 15 Peak at 6.2 years 1 Peak at 18 years PTF 1 5 PTF 5 π/4 π/2 3π/4 π π/4 π/2 3π/4 π (g) BK (1.5,8) (h) BK (8,3) Note: DS case has broad implications: near unit root trend stationary cases similar eects (Cogley and Nason (1995)) 12/21

13 Empirical evidence Empirical evidence 13/21

14 Empirical evidence Setup Data: G7 countries Financial cycle variables: credit (c), credit-to-gdp (c/q), house prices (p h ), equity prices (p e ), bond prices (p b ) Business cycle variable: GDP (q) 197Q1-213Q4, real terms and seasonally adjusted 14/21

15 Empirical evidence ADF test Trend or dierence stationary? H: y t = α + y t 1 + p i=1 θ i y t 1 + η t, η t iid normal H1: y t = α + βt + ρy t 1 + p i=1 θ i y t 1 + η t F -test: β =, ρ = 1 At 5% level, cannot reject H: 3 out of 42 cases (c: 5/7, c/q: 7/7, p h : 5/7, p e : 7/7, p b : 2/7, q: 4/7) Distortions under DS relevant? 15/21

16 Empirical evidence Estimated spectral densities (Ŝ(ω)) of detrended credit-to-gdp *Distortions in line with DS (shape and amplication) Ŝ(ω) Ŝ(ω) Ŝ(ω) π/2 π π/2 π π/2 π HP (16) BK (1.5,8) 1-3 Ŝ(ω) 2 Ŝ(ω).1 Ŝ(ω).1 π/2 π π/2 π π/2 π 4 HP (4 1 5 ) BK (8.3) Notes: Solid line is median across countries at frequency ω; dashed lines depict the 25% and 75% quantiles. 16/21

17 Empirical evidence Predicted cycle duration under DS relevant? *Yes! Estimated durations roughly coincide with predicted durations Cycle duration in years. Average across G7 countries. Predicted duration under DS c c/q p h p e p b q (4.3) (3.1) (2.4) (1.9) (5.4) (4.) (3.3) (2.4) (1.9) (4.1) HP (16) (1.1) (1.8) (.9) (.3) (.7) (.4) HP (4 1 5 ) (14.1) (3.6) (1.4) (5.5) (34.5) (.7) BK (1.5,8) (.6) (.8) (.4) (.2) (.4) (.2) BK (8,3) (6.) (5.) (9.5) (3.9) (32.5) (2.7) Notes: Table reports average of most important (w.r.t overall variance) cycle duration across countries. Standard deviation in parentheses. c is total credit, c/q credit-to-gdp, p h house prices, p e equity prices, p b bond prices, q GDP. 17/21

18 Summary and policy implications Summary and policy implications 18/21

19 Summary and policy implications Summary and policy implications Aim: Shed light on the eects of (popular) detrending methods for nancial variables and nancial cycle facts. Main conclusions: Strong evidence for spurious cycles using HP and band pass lters Distortions especially strong when extracting medium-term frequencies Robust empirical dierences between nancial variables and GDP 19/21

20 Summary and policy implications Summary and policy implications Policy implications: 1 Caution, when extracting medium-term nancial cycles (as in Basel III): Completely erases short-term uctuations Relevant for signalling of crises? Abrupt materialisation of systemic risk? If frequency of nancial crises changes, relevant uctuations missing 2 Same smoothing parameter (or frequency window) across countries most likely wrong: US credit-to-gdp gap peaks before crises, US GDP gap same duration as NBER estimate, but other countries? 3 Robust empirical dierences between nancial cycle and business cycle variables Substantiate argument of a complementary role of macroprudential policy 2/21

21 References References 21/21

22 References Aikman, D., Haldane, A. and Nelson, B.: 215, Curbing the credit cycle, The Economic Journal 125, Anundson, A., Gerdrup, K., Hansen, F. and Kragh-Sørensen, K.: 216, Bubbles and crises: The role of house prices and credit, Journal of Applied Econometrics 31, Bauer, G. and Granziera, E.: 216, Monetary policy, private debt and nancial stability risks, Bank of Canada Sta Working Paper Baxter, M. and King, R.: 1999, Measuring business cycles: Approximate band-pass lters for economic time series, The Review of Economics and Statistics 81, Behn, M., Detken, C., Peltonen, T. and Schudel, W.: 213, Setting countercyclical capital buers based on early warning models: Would it work?, ECB Working Paper 164. Borio, C.: 214, The nancial cycle and macroeconomics: What have we learnt?, Journal of Banking and Finance 45, Borio, C. and Lowe, P.: 24, Securing sustainable price stability: Should credit come back from the wilderness?, BIS Working Papers No 157. Canova, F.: 1998, Detrending and business cycle facts, Journal of Monetary Economics 41, Claessens, S., Kose, M. and Terrones, M.: 211, Financial cycles: What? How? When?, IMF Working Paper WP/11/76. Claessens, S., Kose, M. and Terrones, M.: 212, How do business and nancial cycles interact?, Journal of International Economics 87, Cogley, T. and Nason, J.: 1995, Eects of the Hodrick-Prescott lter on trend and dierence stationary time series. Implications for business cycle research, Journal of Economic Dynamics and Control 19, Drehmann, M., Borio, C. and Tsatsaronis, K.: 212, Characterising the nancial cycle: Don't lose sight of the medium term!, BIS Working Paper 38. Meller, B. and Metiu, N.: 215, The synchronization of European credit cycles, Deutsche Bundesbank Discussion Paper 2/215. Meller, B. and Metiu, N.: forthcoming, The synchronization of credit cycles, Journal of Banking and Finance. Nelson, C. and Plosser, C.: 1982, Trends and random walks in macroeconomic time series. Some evidence and implications, Journal of Monetary Economics 1, Schularick, M. and Taylor, A.: 212, Credit booms gone bust: Monetary policy, leverage cycles, and nancial crises, , American Economic Review 12, /21

23 References Schüler, Y., Hiebert, P. and Peltonen, T.: 215, Characterising the nancial cycle: A multivariate and time-varying approach, ECB Working Paper Schüler, Y., Hiebert, P. and Peltonen, T.: 217, Coherent nancial cycles for G-7 countries: Why extending credit can be an asset, ESRB Working Paper Series No. 43. Stremmel, H.: 215, Capturing the nancial cycle in Europe, ECB Working Paper Strohsal, T., Proaño, C. and Wolters, J.: 215, How do nancial cycles interact? Evidence for the US and the UK, SFB 649 Discussion Paper Verona, F.: 216, Time-frequency characterization of the U.S. nancial cycle, Economics Letters 144, references 21/21