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posted on 05 September 2016 Projecting The LongRun Natural Rate Of Interestfrom the San Francisco Fed  this post authored by Kevin J. Lansing The "natural" rate of interest  the real rate consistent with full use of economic resources and steady inflation near the Fed's target level  is an important benchmark for monetary policy. Current estimates suggest that this rate is near zero, but it is expected to rise gradually in the years ahead as real GDP returns to its longrun potential. If the historical statistical relationship between the growth rate of potential GDP and the natural rate holds true in the future, then a 2% longrun growth rate would imply a longrun natural rate of around 1%.
The "natural" rate of interest, also known as r* (rstar), is the inflationadjusted interest rate that is consistent with full use of economic resources and steady inflation near the Fed's target level. The natural rate is an important benchmark for monetary policy because it determines the real interest rate that policymakers should aim for once temporary shocks to the economy have dissipated and the Fed's macroeconomic targets have been achieved (Hamilton et al. 2015). Over the past three decades, empirical estimates of rstar track reasonably well with the fourquarter growth rate of potential GDP, as estimated by the U.S. Congressional Budget Office (CBO 2016). The CBO currently projects potential GDP to the year 2026. This Economic Letter uses the historical statistical relationship between the growth rate of CBO's potential GDP series and estimates of rstar to construct a 10year projection for the natural rate. The exercise suggests a very gradual rise in rstar from a value near zero in early 2016 to a longrun value of around 1% in 2026. This longrun projected value is slightly below the central tendency midpoint for the longerrun real federal funds rate from the June 2016 Summary of Economic Projections (SEP) issued by the Federal Open Market Committee (FOMC). Empirical estimates of rstar Standard economic models imply that rstar is linked to households' degree of patience, which influences their choice of saving versus current consumption, and to the expected growth rate of potential GDP, which influences the rate of return from savings. However, these two factors are not directly observable. This means that the value of rstar must be inferred using data on economic variables that can be observed, such as nominal interest rates, inflation, and real GDP growth. Figure 1 plots estimated time series for rstar from two recent studies that employ different statistical methods. The rstar series from Laubach and Williams (2015, updated) is the red line denoted by LW, while that from Lubik and Matthes (2015, updated) is the dark blue line denoted by LM. Given the considerable uncertainty surrounding estimates of rstar, any observed differences between the two series are not statistically significant. Since rstar is adjusted for inflation, Figure 1 plots for comparison the inflationadjusted, or "real," federal funds rate, computed as the nominal federal funds rate minus the trailing fourquarter personal consumption expenditures (PCE) inflation rate, using both the headline measure and the core measure that removes volatile food and energy components. All of the series exhibit downwardsloping trends. This pattern is consistent with the declines in global real interest rates observed over the same period (International Monetary Fund 2014, Rachel and Smith 2015). Figure 1 Real interest rates, 1985:Q1 to 2016:Q1 Note: Shaded areas indicate recessions. Estimates of rstar are an important input for monetary policy decisions. Setting the real federal funds rate too high relative to rstar for an extended period could contribute to an undershooting of the central bank's inflation target or cause real GDP growth to fall below potential growth. Setting the real federal funds rate too low relative to rstar for an extended period could contribute to an overshooting of the inflation target or to a buildup of financial imbalances that would make the economy more vulnerable to a crisis or severe recession if the imbalances unwind. Figure 1 shows that the real federal funds rate remained consistently below rstar during the fiveyear period from the first quarter of 2001 through the first quarter of 2006. Some have argued that this period of "loose" monetary policy contributed to excessive runups in U.S. house prices and mortgage debt that subsequently reversed and triggered a severe crisis and recession (Taylor 2007 and Selgin, Beckworth, and Bahadir 2015). Others argue that low interest rates were not a major contributor to the U.S. housing boom (Dokko et al. 2011). Much evidence points to lax lending standards as a primary driver of the episode (see Gelain, Lansing, and Natvik 2015 for a summary of the evidence). Figure 1 shows that the real federal funds rate computed using either headline or core PCE inflation has remained below estimates of rstar for nearly seven years, indicating that the stance of monetary policy over this period, as reflected by this conventional metric, has been accommodative. Downward revisions to longrun potential growth Given the postulated links between rstar and the expected growth rate of potential GDP, it is useful to examine how estimates of potential growth have changed over time. Figure 2 shows the CBO's estimates of fourquarter potential GDP growth for various data vintages ranging from 2006 to 2016. In 2006, the longrun growth rate of potential GDP was estimated to be 2.5%, whereas in 2016 the number has been revised down to 2.0%. Figure 2 CBO estimates of potential output growth Standard economic models imply that a permanent downward adjustment to the longrun growth rate of potential GDP would imply a permanent downward adjustment to rstar. Consistent with this idea, the CBO's estimate of the real interest rate that will prevail in the long run has been revised down in tandem with the downward revisions to the longrun potential growth rate (Leduc and Rudebusch 2014). If the downward shifts in rstar turn out to be permanent, it would have important implications for monetary policy by making the prospects of encountering the effective lower bound on nominal interest rates more likely in future business cycle contractions. Given the presumed links between real interest rates, estimates of rstar, and the growth rate of potential GDP, the prevailing environment of low real interest rates has been cited by some commentators as evidence that the global economy has shifted to a lowgrowth regime, often referred to as "secular stagnation" (Summers 2014). Projecting rstar 10 years ahead The LW and LM estimates of rstar plotted in Figure 1 do not make explicit use of CBO potential GDP data. Nevertheless, Figure 3 shows that, over the sample period from the first quarter of 1985 to the first quarter of 2016, both rstar series track reasonably well over the medium and longer term with the CBO's implied estimate of fourquarter potential growth. The shortterm relationship between the two variables is less precise, however. CBO's most recent estimate of potential growth shows a declining trend through 2010, owing to headwinds from the Great Recession, and then a gradual recovery to 2% growth thereafter as the headwinds dissipate. Figure 3 Potential output growth and natural rate of interest A simple statistical model of the possibly complex relationship between rstar and potential growth can be constructed by regressing an estimated time series for rstar on a flexible functional form  specifically a thirdorder polynomial in CBO's potential growth estimate. This functional form could help capture nonlinearities in the relationship that may arise from the impact of timevarying uncertainty on household saving decisions and the existence of an effective lower bound on the nominal policy interest rate (Basu and Bundick 2015). Figure 4 plots the resulting fitted relationship using the LW estimate of rstar. All of the nonlinear terms in the regression equation are statistically significant and help improve the insample fit. Figure 4 Fitted and projected natural rate of interest Using the fitted relationship and CBO's projected path for potential growth to 2026, we can construct a 10year projected path for rstar. Such an exercise implies a gradual rise in rstar from a value near zero in early 2016 to a longrun value of around 1%, corresponding to a longrun potential growth rate of 2% in 2026. If we instead use the LM estimate of rstar to form the fitted relationship, then the resulting projected path for rstar looks similar but is slightly lower, reaching only 0.9% in 2026. Using a simple linear functional form to estimate the fitted relationship yields longrun projected values for rstar that are slightly higher by 10 to 30 basis points, or 0.10 to 0.30 percentage points. If the longrun value of rstar is indeed only around 1% or less, then the process of normalizing the federal funds rate may end up being more gradual than the midpoint paths implied by recent SEPs. The central tendency midpoint from the FOMC's June 2016 SEP implies a longerrun real federal funds rate of 1.15%. This corresponds to a longerrun growth rate of 2% for real GDP, which presumably also implies a longerrun growth rate of 2% for potential GDP. The three previous SEP central tendency midpoints for the longerrun real federal funds rate were each revised down relative to the prior SEP. The central tendency midpoint was 1.55% in September 2015, 1.4% in December 2015, and 1.25% in March 2016. If we go back even further to January 2012, the central tendency midpoint was 2.25%. Thus, incoming economic data over the past several years have caused SEP participants to lower their collective assessments of the longrun value of rstar. SEP participants have also tended to revise down their forecasts of real GDP growth over the same period (Lansing and Pyle 2015). Conclusion The CBO currently projects a 2% longrun growth rate for potential GDP. If we assume a stable empirical relationship between rstar and potential growth, then a 2% longrun growth rate would imply a longrun rstar value of around 1% or less. Current estimates of rstar are near zero. The CBO's projection of a gradual rise in potential growth over the next 10 years implies a similar gradual rise in rstar. If these projections are accurate, then a monetary policy designed to track the rise in rstar would imply a very gradual normalization of the federal funds rate. About the Author Kevin J. Lansing is a research advisor in the Economic Research Department of the Federal Reserve Bank of San Francisco. References Basu, Susanto, and Brent Bundick. 2015. "Endogenous Volatility at the Zero Lower Bound: Implications for Stabilization Policy." NBER Working Paper 21838. Dokko, Jane, Brian M. Doyle, Michael T. Kiley, Jinil Kim, Shane Sherlund, Jae Sim, and Skander Van Den Heuvel. 2011. "Monetary Policy and the Global Housing Bubble." Economic Policy 26 (66), pp. 237  287. Gelain, Paolo, Kevin J. Lansing, and Gisle J. Natvik. 2015. "Explaining the BoomBust Cycle in the U.S. Housing Market: A ReverseEngineering Approach." FRBSF Working Paper 201502. Hamilton, James, Ethan Harris, Jan Hatzius, and Kenneth West. 2015. "The Equilibrium Real Funds Rate: Past, Present and Future." Brookings, Hutchins Center Working Paper. International Monetary Fund. 2014. "Perspectives on Global Real Interest Rates." Chapter 3 inWorld Economic Outlook: Recovery Strengthens, Remains Uneven (April). Lansing, Kevin J. and Benjamin Pyle. 2015. "Persistent Overoptimism about Economic Growth."FRBSF Economic Letter 201503 (February 2). Laubach, Thomas, and John C. Williams. 2015. "Measuring the Natural Rate of Interest Redux."FRBSF Working Paper 201516. Leduc, Sylvain, and Glenn Rudebusch. 2014. "Does Slower Growth Imply Lower Interest Rates?"FRBSF Economic Letter 201433 (November 10). Lubik, Thomas, and Christian Matthes. 2015. "Calculating the Natural Rate of Interest: A Comparison of Two Alternative Approaches." FRB Richmond Economic Brief 1510 (October 15). Rachel, Lukasz, and Thomas D. Smith. 2015. "Secular Drivers of the Global Real Interest Rate."Bank of England, Staff Working Paper 571. Selgin, George, David Beckworth, and Berrak Bahadir. 2015. "The Productivity Gap: Monetary Policy, the Subprime Boom, and the Post2001 Productivity Surge." Journal of Policy Modeling37, pp. 189  207. Summers, Lawrence H. 2014. "U.S. Economic Prospects: Secular Stagnation, Hysteresis and the Zero Lower Bound." Business Economics 49(2), pp. 6573. Taylor, John B. 2007. "Housing and Monetary Policy." Remarks at symposium hosted by FRB Kansas City, Jackson Hole, WY (September 1). U.S. Congressional Budget Office. 2016. The Budget and Economic Outlook: 2016 to 2026. (January). Disclaimer Opinions expressed in FRBSF Economic Letter do not necessarily reflect the views of the management of the Federal Reserve Bank of San Francisco or of the Board of Governors of the Federal Reserve System. Source http://www.frbsf.org/economicresearch/publications/economicletter/2016/august/projectinglongrunnaturalrateofinterest/ >>>>> Scroll down to view and make comments <<<<<<
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