“The natural rate is an abstraction; like faith, it is seen by its works.” (Williams, J., 1931)
“There is a certain rate of interest on loans which is neutral in respect to commodity prices […] This is necessarily the same as the rate which would be determined by supply and demand if no use were made of money.” (Wicksell, 1898)
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.
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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.
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.
Orphanides, A., and Williams, J. (2002): “Robust Monetary Policy Rules with Unknown Natural Rates.” Brookings Papers on Economic Activity 2, pp. 63–145.
Trehan, B. and Wu, T. (2007): “Time-varying Equilibrium Real Rates and Monetary Policy Analysis”, Journal of Economic Dynamics and Control 31.
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.
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.
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
Since the priors are uniform distributions the mapping from p to
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. We also constrain coefficients in the Phillips curve such that b2 = b3 = b4, b6 = b7 = b8 = 1 - b1 - b2, and b4 = 1 - b1 - b2 - b0. 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.
It is important to note that further complications arise in the presence of the zero lower bound (ZLB), where considering the neutral rate requires ability of the central bank to influence inflation expectations through e.g. forward guidance.
Important dimensions that may matter for policy stance that are not explicitly considered in our empirical model include measures of monetary and financial conditions. The paper also abstracts from possible policy responses to address financial stability risks.
When the real policy rate is equal to the neutral rate at all times, in absence of transitory disturbances, the output gap will be closed and inflation will be stable.
In order to determine what other variables to include in the z process, we ran preliminary regressions with several candidate variables, including measures of global savings (current account surplus of emerging economies in terms of US GDP and global official reserves), uncertainty (realized and implied equity volatility and policy uncertainty), as well as preference for safe assets (equity premium). Three variables are statistically significant and are included in the estimation: (1) current account surplus of emerging economies in terms of US GDP; (2) policy uncertainty as measured by the Bloom index; and (3) a summary indicator of equity premia as estimated by Duarte and Rosa (2015).
Updated estimates of the original Laubach and Williams (2003) paper are available at http://www.frbsf.org/economicresearch/economists/john-williams/Laubach_Williams_updated_estimates.xlsx
Both estimates are so-called smoothed estimates. Laubach and Williams (2003) discuss a difference between one-sided and two-sided (smoothed) estimates and show that the former, also referred to as “real-time” estimates, are estimated less precisely. As in Laubach and Williams, this discussion abstracts from data revisions. Clark and Kozicki (2005) show that data revisions add another layer of uncertainty on neutral rate estimates available for the policymaker.
The projections assume 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). While using projections of real GDP, inflation and policy interest rates to back out current neutral rates is influenced by judgment included in the forecast, it is worth noting that the neutral rate based on the model does not converge to the projected equilibrium real rate within the forecast horizon. That is to say that while there is a degree of circularity in this approach the model provides additional information about the likely path of the neutral real rate.
An alternative approach would be to use observed long-term interest rates instead of the policy rate. However, while monetary policy effects go beyond the short term rate, and include expectations of the policy rate over time that are reflected in longer term interest rates, long-term rates are also influenced by a number of financial market factors that do not capture policy effects.