## _wp15135 ## Source details **Canonical URL:** [_wp15135](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15135.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15135.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15135.pdf.json) --- ### II. EMPIRICAL FRAMEWORK - Model structure - Core system includes: - IS-curve relating output gap to interest rate gaps. - Backward-looking Phillips curve relating core inflation to the output gap. - Equation linking the neutral rate to its determinants (trend potential output growth and an exogenous process z). - Key variable definitions: - x is the output gap defined as the difference between actual and potential log-output (y_t - y*_t). - r is the real (policy) interest rate; r^n is the neutral rate. - π is core inflation; π_m and π_o are oil and non-oil import relative price inflation. - Potential output growth g_t follows a random walk: g_t = g_{t-1} + η_t + ξ_t. - Neutral rate governed by trend growth g_t and exogenous process z_t with a positive constant ρ. - z-process specification (observable determinants included) - z_t = z_{t-1} + ϕ_2 z_{t-2} + ϕ_s ΔS_t + ϕ_e ΔEP_t + ϕ_u ΔU_t + ε_t - Observable components included in estimation: - Measure of global savings S (proxied by the current account surplus of emerging and developing economies in terms of US GDP). - Equity premium EP (summary indicator of equity premia as estimated by Duarte and Rosa (2015)). - Policy uncertainty U (Bloom index). - Identification and estimation approach - Bayesian methods with priors informed by a production function approach (CBO, 2001). - Priors on smoothed state vector are a mixture of uninformative priors and uniform distributions, equivalent to imposing bounds on output gap evolution around NBER peaks and troughs. - Output gap constraints: - Bounds of +/- 1.5 percentage point around the average output gap during 2 year periods around NBER peaks and troughs. - Larger bands of +/- 2 percentage point during and after the GFC. - Rationale for including observables in z: several candidate variables (global savings, uncertainty measures, equity premium) showed statistical significance and were included. ### III. RESULTS #### A. Baseline estimates - General findings - Approach yields more plausible estimates of unobserved variables (trend potential growth, output gap, neutral rate) than standard maximum likelihood. - Confirmed decline in trend potential growth and a significant fall in the output gap during the GFC. - Output gap estimates - Output gap at end-2014 estimated to range from -0.4 and -1.2 percent, broadly consistent with outside estimates (CBO, WEO, FRB/US). - Estimated output gap during the GFC is significantly lower than updated Laubach and Williams estimates and somewhat higher than outside estimates. - Trend growth and neutral rate dynamics - Trend growth fell below 2 percent during the crisis and its aftermath, moderated in the late 1990s (technology-driven expansion). - Neutral real rate: - Significant trend decline, especially in the mid 2000s. - Estimates suggest the neutral real rate in early 2015 was likely positive, but close to zero. - Estimates bottomed out as low as -1.5 percent in 2008 (with even the top centile of all estimates falling close to or below zero). - Range of estimates widens during the GFC, indicating higher uncertainty. - Projections conditional on WEO forecasts up to end-2020 - Projected neutral rate at the end of the projection horizon: estimates range from 0.4 to 1.6 percent. - Projected neutral rate stays well below FOMC participants’ median forecast for the long term real policy rate (about 1.75 percent). - Projection results: - Neutral rates bottomed shortly after the crisis, trended upwards thereafter, and likely turned positive in the course of 2014. - Projections imply only a very gradual increase in neutral rates looking forward; do not converge to projected equilibrium real rate within the forecast horizon. - Projection assumptions: - Liftoff in policy rates in the second half of 2015 and a gradual path towards an equilibrium real federal funds rate of 1.5 percent (25 basis points below the median FOMC projection for the appropriate longer term policy rate). #### B. Results with shadow rates - Motivation - Observed nominal policy rates constrained by the ZLB underestimate actual monetary policy accommodation post-GFC. - Large-scale asset purchases likely lowered term premia and contributed to stronger growth. - Findings using shadow policy rates - Shadow-based neutral rate is lower than the baseline neutral rate (close to zero in early 2015 versus a comparable positive neutral rate using observed real rates). - Shadow neutral rate increases with gradual normalization of policy interest rates and the Federal Reserve’s balance sheet over time but remains below neutral rate based on observed real rates. #### C. Policy stance - Real interest rate gaps (observed real rates minus estimated neutral rates) - Values below zero indicate observed policy rates were below neutral (accommodative). - Policy has been accommodative since the crisis started. - Baseline estimated gap is relatively small and comparable to gap in early 2000s slow growth period. - Shadow-rate gaps are more negative, implying unconventional policies added between 1-3 percentage points of policy accommodation during the GFC. - Forward-looking assessment - Assuming liftoff this year, gradual policy rate increases, and gradual normalization of the Fed’s balance sheet, monetary policy is likely to remain accommodative for some time. - Caveats - Rate gaps are useful summary indicators but incomplete and imprecise given uncertainty in neutral rate estimation. - Other factors (e.g., bank lending conditions, flat yield curve) may have contributed to financing conditions and stance assessments. #### D. Determinants - Drivers of neutral rate changes - Trend growth is an important but not sole driver of neutral rates. - Decline in trend growth since the 2000s is a significant determinant of the trend decline in neutral rates. - Other factors (z) played a key role: - Substantial increases in emerging market current account surpluses (excess global savings) increased demand for U.S. assets and contributed to lower neutral rates. - Increased risk aversion and preference for safer assets (e.g., higher equity premium) amplified the decline in the 2000s and during the GFC. - Forward projection drivers - Expected increase in neutral rates driven by a gradual recovery in trend growth (recovering to just above 2 percent) and declining downward pressure from other factors. ### IV. CONCLUSIONS - Summary of main findings - The semi-structural, Bayesian-augmented Laubach-Williams framework with observable z-determinants and shadow-rate treatment yields: - A significant trend decline in the neutral real rate over time driven by both a decline in trend growth and other factors, including excess global savings. - Neutral real rate fell below zero during the GFC (as low as -1.5 percent in 2008) before turning positive in the course of 2014. - Projections indicate the neutral rate is likely to increase only very gradually going forward (projected range at end-horizon: 0.4 to 1.6 percent, below FOMC median ~1.75 percent). - Re-estimation with shadow policy rates implies a lower neutral rate and larger implied interest rate gaps—hence more policy accommodation during the GFC. - Projected interest rate gaps show monetary policy likely to remain accommodative for some time. - Large uncertainty remains about time-varying neutral rates, particularly during periods of exceptional volatility such as the GFC. - Implications - Neutral rate estimates are imprecise and sensitive to model specification, treatment of the ZLB/unconventional policy, and inclusion of observable determinants such as global savings and equity premia. - Assessments of policy stance using rate gaps should be interpreted with caution given estimation uncertainty and omitted financing/credit conditions. ### Appendix B and estimation details (key technical points) - State-space formulation used to construct the likelihood. - Priors on smoothed series implemented as uniform distributions imposing restrictions. - Additional restrictions to avoid negative parameters and ensure stability. - Lower bound of 0.10 to ߣ ௭ imposed. - A sample from the posterior is drawn using the Metropolis-Hasting algorithm based on 100,000 draws from a symmetric proposal density. - Some parameters held fixed following Trehan and Wu (2007) to reduce computational intensity. - Constraints on Phillips curve coefficients: b2 = b3 = b4, b6 = b7 = b8 = 1 - b1 - b2, and b4 = 1 - b1 - b2 - b0. - Note: Neutral rate sensitive to the parameter on the relative oil import price variable in the Phillips curve, relatively insensitive to other parameters. - Table C1: Parameter values - a2 -0.27 - by 0.15 - bi 0.004 - bo 0.03 - b1 0.47 - b2 0.35 - b0 0.05 *Source: IMF working paper content provided in the supplied PDF excerpt.* ### 1.75 percent). Second, despite the decline in the neutral rate, we assess that monetary policy ### _wp15135 - 1.75 percent). Second, despite the decline in the neutral rate, we assess that monetary policy ### II. EMPIRICAL FRAMEWORK - Model structure - Core system includes: - IS-curve relating output gap to interest rate gaps. - Backward-looking Phillips curve relating core inflation to the output gap. - Equation linking the neutral rate to its determinants (trend potential output growth and an exogenous process z). - Key variable definitions preserved: - x is the output gap defined as the difference between actual and potential log-output (y_t - y*_t). - r is the real (policy) interest rate; r^n is the neutral rate. - π is core inflation; π_m and π_o are oil and non-oil import relative price inflation. - Potential output growth g_t follows a random walk: g_t = g_{t-1} + η_t + ξ_t (trend potential output growth plus noise component). - Neutral rate governed by trend growth g_t and exogenous process z_t with a positive constant ρ. - z-process specification (observable determinants included) - z_t = z_{t-1} + ϕ_2 z_{t-2} + ϕ_s ΔS_t + ϕ_e ΔEP_t + ϕ_u ΔU_t + ε_t - Observable components included in estimation: - Measure of global savings S (proxied by the current account surplus of emerging and developing economies in terms of US GDP). - Equity premium EP (summary indicator of equity premia as estimated by Duarte and Rosa (2015)). - Policy uncertainty U (Bloom index). - Identification and estimation approach - Use of Bayesian methods with priors informed by a production function approach (CBO, 2001). - Priors on smoothed state vector are a mixture of uninformative priors and uniform distributions, equivalent to imposing bounds on output gap evolution around NBER peaks and troughs. - Output gap constraints: - Bounds of +/- 1.5 percentage point around the average output gap during 2 year periods around NBER peaks and troughs. - Larger bands of +/- 2 percentage point during and after the GFC. - Rationale for including observables in z: some determinants are unobservable, but several candidate variables (global savings, uncertainty measures, equity premium) showed statistical significance and were included. ### III. RESULTS #### A. Baseline estimates - General findings - Approach yields more plausible estimates of unobserved variables (trend potential growth, output gap, neutral rate) than standard maximum likelihood. - Confirmed decline in trend potential growth and a significant fall in the output gap during the GFC. - Output gap estimates - Output gap at end-2014 estimated to range from -0.4 and -1.2 percent, broadly consistent with outside estimates (CBO, WEO, FRB/US). - Estimated output gap during the GFC is significantly lower than updated Laubach and Williams estimates and somewhat higher than outside estimates. - Trend growth and neutral rate dynamics - Trend growth fell below 2 percent during the crisis and its aftermath, moderated in the late 1990s (technology-driven expansion). - Neutral real rate: - Significant trend decline, especially in the mid 2000s. - Estimates suggest the neutral real rate in early 2015 was likely positive, but close to zero. - Estimates bottomed out as low as -1.5 percent in 2008 (with even the top centile of all estimates falling close to or below zero). - Range of estimates widens during the GFC, indicating higher uncertainty. - Projections conditional on WEO forecasts up to end-2020 - Projected neutral rate at the end of the projection horizon: estimates range from 0.4 to 1.6 percent. - Projected neutral rate stays well below FOMC participants’ median forecast for the long term real policy rate (about 1.75 percent). - Projection results: - Neutral rates bottomed shortly after the crisis, trended upwards thereafter, and likely turned positive in the course of 2014. - Projections imply only a very gradual increase in neutral rates looking forward; do not converge to projected equilibrium real rate within the forecast horizon. - Assumptions noted for projections: - Liftoff in policy rates in the second half of 2015 and a gradual path towards an equilibrium real federal funds rate of 1.5 percent (25 basis points below the median FOMC projection for the appropriate longer term policy rate). #### B. Results with shadow rates - Motivation - Observed nominal policy rates constrained by the ZLB underestimate actual monetary policy accommodation post-GFC. - Large-scale asset purchases likely lowered term premia and contributed to stronger growth. - Findings using shadow policy rates - Shadow-based neutral rate is lower than the baseline neutral rate (close to zero in early 2015 versus a comparable positive neutral rate using observed real rates). - Shadow neutral rate increases with gradual normalization of policy interest rates and the Federal Reserve’s balance sheet over time but remains below neutral rate based on observed real rates. #### C. Policy stance - Real interest rate gaps (observed real rates minus estimated neutral rates) - Values below zero indicate observed policy rates were below neutral (accommodative). - Policy has been accommodative since the crisis started. - Baseline estimated gap is relatively small and comparable to gap in early 2000s slow growth period. - Shadow-rate gaps are more negative, implying unconventional policies added between 1-3 percentage points of policy accommodation during the GFC. - Forward-looking assessment - Assuming liftoff this year, gradual policy rate increases, and gradual normalization of the Fed’s balance sheet, monetary policy is likely to remain accommodative for some time. - Caveats - Rate gaps are useful summary indicators but incomplete and imprecise given uncertainty in neutral rate estimation. - Other factors (e.g., bank lending conditions, flat yield curve) may have contributed to financing conditions and stance assessments. #### D. Determinants - Drivers of neutral rate changes - Trend growth is an important but not sole driver of neutral rates. - Decline in trend growth since the 2000s is a significant determinant of the trend decline in neutral rates. - Other factors (z) played a key role: - Substantial increases in emerging market current account surpluses (excess global savings) increased demand for U.S. assets and contributed to lower neutral rates. - Increased risk aversion and preference for safer assets (e.g., higher equity premium) amplified the decline in the 2000s and during the GFC. - Forward projection drivers - Expected increase in neutral rates driven by a gradual recovery in trend growth (recovering to just above 2 percent) and declining downward pressure from other factors. ### IV. CONCLUSIONS - Summary of main findings - The semi-structural, Bayesian-augmented Laubach-Williams framework with observable z-determinants and shadow-rate treatment yields: - A significant trend decline in the neutral real rate over time driven by both a decline in trend growth and other factors, including excess global savings. - Neutral real rate fell below zero during the GFC (as low as -1.5 percent in 2008) before turning positive in the course of 2014. - Projections indicate the neutral rate is likely to increase only very gradually going forward (projected range at end-horizon: 0.4 to 1.6 percent, below FOMC median ~1.75 percent). - Re-estimation with shadow policy rates implies a lower neutral rate and larger implied interest rate gaps—hence more policy accommodation during the GFC. - Projected interest rate gaps show monetary policy likely to remain accommodative for some time. - Large uncertainty remains about time-varying neutral rates, particularly during periods of exceptional volatility such as the GFC. - Implications - Neutral rate estimates are imprecise and sensitive to model specification, treatment of the ZLB/unconventional policy, and inclusion of observable determinants such as global savings and equity premia. - Assessments of policy stance using rate gaps should be interpreted with caution given estimation uncertainty and omitted financing/credit conditions. *Source: IMF working paper content provided in the supplied PDF excerpt.* ### References ### References ### Bibliographic sources - Baker, S., Bloom, N. and Davis, S. (2013): “Measuring Economic Policy Uncertainty”. - Barsky, R., A Justiniano, and L. Melosi, 2014, “The Natural Rate and its Usefulness for Monetary Policy Making”, American Economic Review Papers and Proceedings, 104(7), pp. 37 – 43. - Blanchard O., D. Furceri, and Pescatori A., (2014): “A Prolonged Period of Low Real Interest Rates?”, in “Secular Stagnation: Facts, Causes and Cures”. Edited by Teulings, C. and Baldwin, R. VoxEu Aug. 2014. - CBO (2001): “CBO's Method for Estimating Potential Output: An Update”, Congressional Budget Office. - CBO (2014): “The 2014 Long-Term Budget Outlook”, July 2014. - Clark and Kozicki, 2005: “Estimating Equilibrium Real Interest Rates in Real Time”, North American Journal of Economics and Finance 16. - Curdia, V., Ferrero, A., Ng, G. and Tambalotti, A. (2015): “Has U.S. Monetary Policy Tracked the Efficient Interest Rate?”, Journal of Monetary Economics 70. - Duarte, F. and Rosa, C. (2015): “The Equity Risk Premium: A Review of Models”, new York Federal Reserve Staff Report. - Engen, E., Laubach, T. and Reifschneider, D. (2015). “The Macroeconomic Effects of the Federal Reserve’s Unconventional Monetary Policies,” Finance and Economic Discussion Series 005. - Fernald, J. (2014): “Productivity and Potential Output Before, During and After the Greatr Recession”, Federal Reserve Bank of San Francisco working paper 2014-15. - Giammarioli, N. and Valla, N. (2004): “The Natural Real Interest Rate and Monetary Policy: a Review”, Journal of Policy Modelling 26. - Congressional Budget Office (2001): “CBO's Method for Estimating Potential Output: An Update”. - Hamilton, J, Harris, E., Hatzius, J. and West, K. (2015): ”The Equilibrium Real Funds Rate: Past, Present and Future”. - International Monetary Fund (2014): World Economic Outlook April. - Krippner, L. (2013): “Measuring the Stance of Monetary Policy in ZLB Environments”, Economics Letters 118. - Laubach, T. and Williams, J. (2003): “Measuring the natural Rate of Interest”, Review of Economics and Statistics 85(4). - Lombardi, M. and Zhu, F. (2014): “A Shadow Policy Rate to calibrate US Monetary Policy at the ZLB”, BIS working paper 452. - Orphanides, A., and Williams, J. (2002): “Robust Monetary Policy Rules with Unknown Natural Rates.” Brookings Papers on Economic Activity 2, pp. 63–145. - Stock, J. (1994): “Unit Roots, Structural Breaks and Trends”, in Engle, R. and McFadden, D.: Handbook of Econometrics 4. - Trehan, B. and Wu, T. (2007): “Time-varying Equilibrium Real Rates and Monetary Policy Analysis”, Journal of Economic Dynamics and Control 31. - Williams, John H. (1931): “The Monetary Doctrines of J. M. Keynes.” Quarterly Journal of Economics 45(4): 547–87. - Williams, J. (2015): “The Decline in the Natural Rate of Interest.” Manuscript, March. - Wicksell, K. (1898): “The Influence of the Rate of Interest on Commodity Prices,” reprinted in Lindahl, E. ed., (1958): Selected Papers on Economic Theory by Knut Wicksell. - Wu, J. and Xia, F. (2014): “Measuring the Macroeconomic impact of Monetary Policty at the ZLB”, NBER working paper 20117. ### Appendix A: Data definitions - Two endogenous variables are observable, core PCE inflation and log-GDP, while other various observable variables are treated as exogenous: real federal funds rate (deflated using one year ahead inflation expectations), the oil and import prices, the emerging market and developing economies current account as a share of US GDP, the equity premium, and a measure of policy uncertainty. - Real GDP (loggdp): 100*ln(real GDP), where real GDP is SAAR, Billions of Chained 2009 dollars. WEO projections. - Core inflation (coreinfl): 400*ln(P(t)/P(t-1)), where P is PCE less Food and Energy Chain Price Index (SA, 2009=100). WEO projections. - Oil import price gap (oilgap): oilinfl-coreinfl. Oilinfl is 400*ln(P(t)/P(t-1)), where P is Petroleum & Products Imports Price Index (SA, 2009=100). Gaps are assumed to equal zero for the projection period. - Import (ex-oil) price gap (impgap): impinfl-coreinfl. Impinfl is 400*ln(P(t)/P(t-1)), where P is Nonpetroleum Goods Imports: Chain Price Index (SA, 2009=100). Gaps are assumed to equal zero for the projection period. - Federal funds rate (ffr): Effective Federal Funds Rate (% p.a.). WEO projections. - Real federal funds rate (realffrrate): ffr-expinfl. Expinfl is Median 1-Year-Ahead CPI Inflation Expectation (%) from Survey of Professional Forecasters. Assumed to equal latest value for the projection period. - Shadow federal funds rate: simple average of estimates in Krippner (2013), Lombardi and Zhu (2014) and Wu and Xia (2014). Shadow rates are projected to normalize (i.e. approach projected policy interest rates) gradually over the projection horizon. - Potential output (based on CBO, 2001). - Emerging market current account surplus as a share of US GDP. WEO projections. - Policy uncertainty index. Based on Baker, Bloom and Davis (2013). http://www.policyuncertainty.com/ - Equity risk premium. Principal component derived from several models. Source: Duarte and Rosa (2015) ### Appendix B: Model estimation details - The model described in section 2 can be written in a state space form which allows us to construct the likelihood of observing the data (y) for a given set of parameters (ߠ): ሻߠ|ݕሺ݌. - To exploit prior information, ܫ ௢ , on some unobservable smoothed series we first define the mapping that from the parameter space Θ to the smoothed series as ሻߠሺ߮. Hence a prior on the smoothed series (e.g., the output gap) can be written as ܫ|ሻߠሺ߮ሺ݌ ௢ ሻ. - By letting ݌̂ ሺ ߠ | ܫ ௢ ሻ ൌ ܫ|ሻߠሺ߮ሺ݌ ௢ ሻ be a probability density function defined in the parameter space Θ we can write the posterior density function as: ݌ሻൌݕ|ߠሺ݌̂ ሺ ߠ | ܫ ௢ ሻ ሻߠ|ݕሺ݌. - Since the priors are uniform distributions the mapping from ݌ to ݌̂ can be trivially implemented as imposing restrictions. - Additional restrictions on the parameter space are included to avoid some parameters from taking negative values and/or in order to ensure a stable (non-explosive) system of equations. - In light of the pile-up problem discussed in Stock (1994) we impose a lower bound of 0.10 to ߣ ௭ . - A sample from the posterior is drawn using the Metropolis-Hasting algorithm based on 100,000 draws from a symmetric proposal density. - In the estimation some parameters were held fixed following Trehan and Wu (2007) to reduce computational intensity. - Constraints on Phillips curve coefficients: b2 = b3 = b4, b6 = b7 = b8 = 1 - b1 - b2, and b4 = 1 - b1 - b2 - b0. - Note: While the neutral rate is sensitive to the parameter on the relative oil import price variable in the Phillips curve, it is relatively insensitive to the other parameters. ### Table C1: Parameter values - a2 -0.27 - by 0.15 - bi 0.004 - bo 0.03 - b1 0.47 - b2 0.35 - b0 0.05 *Source: _wp15135 - References* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15135.pdf_