Economic Brief October 2015, EB15-10 Calculating the Natural Rate of Interest: A Comparison of Two Alternative Approaches By Thomas A. Lubik and Christian Matthes The natural rate of interest is a key concept in monetary economics because its level relative to the real rate of interest allows economists to assess the stance of monetary policy. However, the natural rate cannot be observed; it must be calculated using identifying assumptions. This Economic Brief compares the popular Laubach-Williams approach to calculating the natural rate with an alternative method that imposes fewer theoretical restrictions. Both approaches indicate that the natural rate has been above the real rate for a long time. The natural rate of interest is one of the key constantly react to economic shocks, gives rise concepts for understanding and interpreting to a natural rate of interest akin to Wicksell’s macroeconomic relationships and the effects of original concept. Woodford’s innovation was to monetary policy. Its modern usage dates back show how the natural rate relates to economic to the Swedish economist Knut Wicksell, who in fundamentals such as productivity shocks or 1898 defined it as the interest rate that is com- changes in consumers’ preferences. Moreover, patible with a stable price level.1 An increase in an inflation-targeting central bank can steer the the interest rate above its natural rate contracts economy toward the natural rate and price sta- economic activity and leads to lower prices, bility by conducting policy through the applica- while a decline relative to the natural rate has tion of a Taylor rule, which links the policy rate to the opposite effect. In Wicksell’s view, equality measures of economic activity and prices. of a market interest rate with its natural counter- part therefore guarantees price and economic Naturally, monetary policymakers should have a stability. deep interest in the level of the natural interest rate because it presents a guidepost as to whether A century later, Columbia University economist policy is too tight or too loose, just as in Wicksell’s Michael Woodford brought renewed attention original view. The problem is that the natural rate to the concept of the natural rate and connected is fundamentally unobservable. It is a hypotheti- it with modern macroeconomic thought.2 He cal construct that cannot be measured directly. demonstrated how a modern New Keynesian Instead, economists have developed various em- framework, with intertemporally optimizing pirical methods that attempt to derive the natural and forward-looking consumers and firms that rate from actual data.3 EB15-10 - Federal Reserve Bank of Richmond Page 1 The Unobserved Component Model relationships in a manner that is informed by theo- of Laubach and Williams retical reasoning but allows enough flexibility to The most commonly used approach to compute capture the data well. the natural rate was developed by Federal Reserve economists Thomas Laubach and John Williams in a In this empirical framework, the real natural rate is widely cited paper from 2003.4 Their approach uses an unobserved component in that it has to be in- a “state-space” model to calculate the fundamen- ferred from observable data, such as the inflation tally unobservable natural rate from actual data by rate, the growth rate of gross domestic product, and specifying a simple theoretical relationship that links the federal funds rate. This can be accomplished interest rates to measures of economic activity. This by means of the Kalman filter, which allows the re- relationship has an economic foundation in a tradi- searcher to predict the values of unknown variables tional Keynesian model, where movements in the through the restrictions implied by the empirical real interest rate affect consumption and investment model. The natural rate of interest is identified in decisions. For example, an increase in the real rate their paper as the variable in a regression of the out- due to a hike in the federal funds rate would, when put gap on past output gaps that best helps to fit prices are sticky, reduce consumption and invest- this theoretical relationship. ment. A similar relationship can be derived from a more modern forward-looking framework where Figure 1 shows the natural rate computed with the real rate movements affect intertemporal household Laubach-Williams framework for the data range from decisions on savings and portfolio allocation. 1961 through the second quarter of 2015.5 The esti- mate shows a secular decline of the rate from a high The insight that Laubach and Williams brought to of 4.5 percent at the beginning of the sample toward this discussion is Wicksell’s idea that what matters negative territory in 2011. According to their results, for economic activity in the short run—that is, for the natural interest rate has thus been negative for the business cycle and economic stabilization—is more than three years. the level of the interest rate relative to its natural rate. Moreover, they recognize that it is the real In line with the argument above, namely that the rate of interest—that is, the nominal rate net of natural rate of interest can be used as a measure of the effects of inflation—that underlies economic the stance of monetary policy, the findings by Lau- decisions. Laubach and Williams then develop a bach and Williams suggest that policymakers could small-scale economic model that connects these consider extending the current policy of a federal FFigureigure 1 1:: N Naturalatural RRateate ofof InterestInterest from from Laubach-Williams Laubach-Williams 55 44 33 t n e c r 22 e P Percent 11 00 -1-1 11961961 11966966 11971971 11976976 11981981 11986986 11991991 11996996 22001001 22006006 22011011 22016016 SSources:ources Laubach: Lauba candh a Williamsnd Wil l(2003)iams (with200 updated3) with estimatesupdated from esti thema Santes Franciscofrom th Fede San Francisco Fed. Page 2 funds rate close to zero and an enlarged balance consider a number of alternative specifications for sheet due to a policy of quantitative easing. However, their empirical framework. The overall impression what matters for this interpretation is not the absolute from their robustness checks is that natural rate level of the natural rate, but its level relative to the estimates can vary considerably.7 Moreover, the corresponding real rate. Figure 2 therefore shows the estimates come with considerable standard errors real interest rate computed as the difference between to the effect that the level of the natural rate cannot the federal funds rate and the expected personal be ascertained with a high degree of confidence. consumption expenditures (PCE) inflation rate. As can be seen, the real rate is lower than the natural rate The approach by Laubach and Williams relies on an by a full percentage point and has been that low or empirical model that has some underpinnings in lower since 2009. Based on this metric, this finding theoretical models of the economy. One alternative suggests that policy is not tight enough—and has would be to impose more theoretical rigor.8 Moving not been for a while.6 This impression also is sup- in the opposite direction, another alternative would ported by the accompanying estimate of the output be to take a less structural approach. gap from the Laubach-Williams framework, which has been positive since the middle of 2014. This implies An Alternative Approach: TVP-VARs that economic output is running above its potential, A time-varying parameter vector autoregressive (TVP- indicating that any inflationary pressures could be VAR) model is a flexible framework for studying the reined in by a higher federal funds rate. complex relationships among macroeconomic data.9 It is a time-series model that explains the evolution of In addition, the discussion above raises questions economic variables as a function of their own lagged about the robustness and precision of the Laubach- values and random shocks. What distinguishes a TVP- Williams natural rate estimates. In their paper, they VAR from the more standard VAR approach is that FFigureigure 22:: NNaturalatural RateRate from from Laubach-Williams Laubach-William vs.s v sthe. th Ex-Antee Ex-An tReale Re Rateal Rate 1100 L-W Natural Rate 88 Ex-Ante Real Rate 66 44 t n e c r 2 e 2 P Percent 00 -2-2 -4-4 -6-6 11961961 11966966 11971971 11976976 11981981 11986986 11991991 19961996 20012001 20062006 20112011 20162016 Sources: Laubach and Williams (2003) with updated estimates from the San Francisco Fed SNotes:ource Thes: L aex-anteubach realand rate Wil wasliam computeds (2003) w asit hthe up differencedated esti mbetweenates fr theom federalthe Sa nfunds Fran ratecisc oand Fe thed expected PCE inflation rate. NInterestotes: Trateshe e arex-a nreportedte real rasat annuale was crates,omp uwhileted athes t hinflatione differ eratence is b eannualizedtween th equarter feder aoverl fu nquarter.ds rate and the expected core PCE inflation rate. Interest rates are reported as annual rates, while the inflation rate is annualized quarter over quarter. Page 3 the parameters of the model, namely the lag coef- less of an economic structure. Whereas Laubach and ficients and the variances of the economic shocks, Williams posited economic relationships between are allowed to vary over time. This framework is thus the key macroeconomic variables that may or may capable of capturing a variety of nonlinear behaviors not be supported, a TVP-VAR is largely agnostic on that are apparent in macroeconomic time series, this dimension. It simply captures the co-movement such as asymmetric movements of variables over the between these variables in a flexible manner. The course of the business cycle or the overall decline in identification of the natural rate in Laubach and Wil- macroeconomic volatility since the mid-1980s.