The real-time predictive content of asset price bubbles for macro forecasts Benjamin Beckers DIW Berlin, Macroeconomics and Graduate Center June 23, 2015 Financial support by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged.
Research Questions and Contribution (How well) Can asset price bubbles be detected in real-time? Review performance of popular (HP-filter) and recently proposed bubble indicators (recursive ADF-tests by Phillips et al. (2011, 2013)). Propose combination indicators, aggregating the information contained in individual indicators. Can bubble indicators improve forecasts for output and inflation? Horse-race of indicators against a simple OLS-forecast model containing common predictors from Stock & Watson (2001) following Assenmacher-Wesche & Gerlach (2010). Extend analysis of Assenmacher-Wesche & Gerlach (2010) by acknowledging real-time dimension of the data.
Outline 1 Research Question 2 Bubble indicators 3 Simulation results 4 Forecast results 5 Conclusion
HP-filter indicator (Assenmacher-Wesche & Gerlach, 2010) Excessive price deviations from slow moving fundamentals 10% threshold for stock, 7.5% for house prices Strong trend smoothing with parameter 100, 000 3 4 Recursive or rolling trend estimates One-sided HP filter for real-time application
Detecting asset price bubbles by unit root tests Starting point: Rational bubbles P t = 1 1 + r E t [P t+1 + D t+1 ] ( 1 = 1 + r i=0 ) i E t [D t+i] + lim i = P f t + B t, with B t = 1 1 + r E t[b t+1 ]. ( ) 1 i E t [P t+i] 1 + r Test log real prices and fundamentals separately for explosive roots (H 0 : δ = 1 vs. H 1 : δ > 1) z t = µ z +δz t 1 + J iid φ j z t j +v t, v t N(0, σ 2 v ), z t = {p t, d t } j=1
Unit-root tests (PWY11, PSY13) Forward recursive regression to obtain sequence of right-tailed ADF-test statistics ADF τ, τ = τ 0, τ 0 + 1,..., T Binary bubble indicator with B τ = 1 if H 0 is rejected for prices but not for dividends PWY11: recursive or rolling estimation PSY13: forward recursive, backward rolling estimation to allow for an automatic restarting of the monitoring procedure after a bubble collapse Individual vs. log-ratio tests: Larger power vs. accounting for relative growth rates P t 1 ( ) 1 + r r D ( ) 1 i t = E t [ D t+i]+b t I (0) if B t = 0 r 1 + r i=1
Frequency of detecting X bubbles: One-bubble scenario Number of detected bubbles Zero One Two Zero One Two Emergence date τ e = 40 τ e = 120 HP rec 0.021 0.221 0.319 0.004 0.249 0.331 HP rol 0.006 0.085 0.348 0.001 0.216 0.328 PWY11 rec: individual 0.216 0.472 0.231 0.259 0.403 0.211 PWY11 rec: ratio 0.342 0.372 0.192 0.338 0.354 0.180 PWY11 rol : individual 0.026 0.125 0.234 0.024 0.130 0.229 PWY11 rol : ratio 0.042 0.134 0.239 0.026 0.130 0.237 PSY13: individual 0.318 0.443 0.175 0.229 0.520 0.194 PSY13: ratio 0.517 0.323 0.112 0.453 0.359 0.140 Combination: κ = 3 0.052 0.369 0.307 0.036 0.365 0.308 Combination: κ = 4 0.208 0.516 0.198 0.172 0.502 0.235 Combination: κ = 5 0.422 0.447 0.112 0.406 0.461 0.114
U.S. stock price bubbles
Direct OLS forecasts Direct h-step forecasts of IP and CPI y t+h = µ + P p=1+r δ p y t p+1 + Q q=1+s xi x t q+1β q + ε t+h r, s xi publication lags of dependent y and explanatory variable x i, respectively x t : IP, CPI, 3 month t-bill rate, 10Y-3M spread, unemployment rate, binary bubble indicator Fixed P and Q or specific-to-general variable and lag length selection by iterative addition of in-sample significant regressors Sample 1983M01-2013M12, Start of out-of-sample forecast period: 1997M12
Forecasting output with stock price bubbles Forecast horizon (in months) Model 0 1 3 6 12 24 Benchmark 0.007 0.012 0.022 0.035 0.054 0.101 HP rec 0.982* 0.971* 0.963* 0.981* 1.007* 0.982 HP rol 0.994* 0.984* 0.979* 0.995* 1.035* 1.080* PWY11 rec: ind 0.995* 0.986* 0.970* 0.976* 1.003* 0.959* PWY11 rec: ratio 0.999 0.994* 0.988* 1.003 1.024* 1.047 PWY11 rol : ind 0.979* 0.959* 0.942* 0.955* 0.996 0.996 PWY11 rol : ratio 1.021 1.032 1.042 1.056* 1.041* 1.000 PSY13: ind 0.994* 0.988* 0.976* 0.974* 0.972* 0.924* PSY13: ratio 1.024 1.036 1.041 1.046 1.030* 0.979 Combi: κ = 3 0.970* 0.956* 0.937* 0.950* 0.994 0.983* Combi: κ = 4 0.972* 0.957* 0.936* 0.952* 0.993* 0.985* Combi: κ = 5 0.975* 0.958* 0.940* 0.959* 0.996 0.996
Forecasting output with stock price bubbles No real-time data Forecast horizon (in months) Model 0 1 3 6 12 24 Benchmark 0.007 0.011 0.022 0.037 0.053 0.097 HP rec 0.989 0.976 0.970 0.981 1.008 0.992 HP rol 0.999 0.997 0.988 0.995 1.034 1.062 PWY11 rec: ind 1.001 0.995 0.981 0.987 1.020 1.000 PWY11 rec: ratio 1.009 1.010 1.004 1.016 1.050 1.068 PWY11 rol : ind 0.991 0.972 0.960 0.969 1.008 1.013 PWY11 rol : ratio 1.016 1.029 1.045 1.056 1.067 1.033 PSY13: ind 0.995 0.987 0.975 0.974 0.974 0.939 PSY13: ratio 1.021 1.032 1.038 1.043 1.044 0.996 Combi: κ = 3 0.985 0.970 0.957 0.966 1.009 1.007 Combi: κ = 4 0.986 0.971 0.955 0.966 1.010 1.012 Combi: κ = 5 0.987 0.973 0.957 0.972 1.012 1.020
Forecasting output with stock + house price bubbles Forecast horizon (in months) Model 0 1 3 6 12 24 Benchmark 0.007 0.012 0.022 0.035 0.054 0.101 HP rec 0.988* 0.979* 0.977 0.985 1.009 1.038 HP rol 0.994* 0.984* 0.979* 0.994* 1.033* 1.077* PWY11 rec: ind 0.995* 0.986* 0.970* 0.976* 1.003* 0.959* PWY11 rec: ratio 0.994* 0.987* 0.986 0.994 1.015 1.032* PWY11 rol : ind 0.977* 0.952* 0.936* 0.941* 0.968 0.993 PWY11 rol : ratio 0.999 0.999 0.998 0.993 0.982 0.994 PSY13: ind 1.000 0.994* 0.983* 0.989 0.986 1.002 PSY13: ratio 0.998 1.000 1.002 1.006 0.986 0.983 Combi: κ = 3 0.958* 0.934* 0.916* 0.917* 0.936 0.982 Combi: κ = 4 0.971* 0.952* 0.932* 0.933* 0.952 0.983 Combi: κ = 5 0.972* 0.950* 0.930* 0.932* 0.957 0.984
Conclusion HP-filter as used by AWG10 signals too many bubbles. Asset price bubble indicators by PWY11 and PSY13 can detect commonly accepted bubble periods in real-time but signals are often instable. Results are very sensitive to timing and number of bubbles in the sample, and the exact indicator specification. Testing prices and dividends separately is found to be superior over testing their log-ratio. Combination indicators can provide insurance against high uncertainty of individual signals. Bubble indicators by PSY13 and combination indicators significantly improve output forecasts. Real-time dimension needs to be acknowledged.
Thank you for your attention. DIW Berlin Deutsches Institut für Wirtschaftsforschung e.v. Mohrenstraße 58, 10117 Berlin www.diw.de
References Assenmacher-Wesche, K. & Gerlach, S. (2010). Monetary Policy and Financial Imbalances: Facts and Fiction. Economic Policy, 25, 437 482. Bernanke, B. & Gertler, M. (1999). Monetary Policy and Asset Price Volatility. Economic Review, Q IV, 17 51. Bordo, M. D. & Jeanne, O. (2002). Monetary Policy and Asset Prices: Does Benign Neglect Make Sense? International Finance, 5(2), 139 164. Campbell, J. Y. & Shiller, R. J. (1987). Cointegration and Tests of Present Value Models. Journal of Political Economy, 95(5), pp. 1062 1088. Cecchetti, S. G., Genberg, H., & Wadhwani, S. (2002). Asset Prices in a Flexible Inflation Targeting Framework. Working Paper 8970, National Bureau of Economic Research.
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