The Equilibrium Real Funds Rate: Past, Present, And Future

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IMF Economic ReviewVol. 64, No. 4ª 2016 International Monetary FundThe Equilibrium Real Funds Rate: Past, Present,and FutureJAMES D. HAMILTON, ETHAN S. HARRIS, JAN HATZIUS,and KENNETH D. WEST*We examine the behavior, determinants, and implications of the equilibrium level ofthe real federal funds rate, interpreted as the long run or steady state value of the realfunds rate. We draw three main conclusions. First, the uncertainty around theequilibrium rate is large, and its relationship with trend GDP growth much moretenuous than widely believed. Our narrative and econometric analysis using crosscountry data and going back to the 19th century supports a wide range of plausibleestimates for the current level of the equilibrium rate, from a little over 0 per cent tothe pre-crisis consensus of 2 per cent. Second, a bivariate vector error correctionmodel that looks only to U.S. and world real rates well captures the behavior of U.S.real rates. The model treats real rates as cointegrated unit root processes. As of theend of our sample (2014), the model forecasts the real rate in the U.S. will asymptoteto an equilibrium value of a little less than half a percent by 2021. Consistent with ourfirst point, however, confidence intervals around this point estimate are huge. Third,the uncertainty around the equilibrium rate argues for more ‘‘inertial’’ monetarypolicy than implied by standard versions of the Taylor rule. Our simulations using theFed staff’s FRB/US model show that explicit recognition of this uncertainty results ina later but steeper normalization path for the funds rate compared with the median‘‘dot’’ in the FOMC’s Summary of Economic Projections.IMF Economic Review (2016) 64, 660–707. doi:10.1057/s41308-016-0015-z;published online 1 November 2016* James Hamilton is Robert F. Engle Professor of Economics at the University of California, San Diego(email: jhamilton@ucsd.edu). Ethan Harris is Head of Global Economics Research at Bank of AmericaMerrill Lynch Global Research (email: ethan.harris@baml.com). Jan Hatzius is Chief Economist and Head ofGlobal Economics and Markets Research at Goldman Sachs (email: jan.hatzius@gs.com). Kenneth West isJohn D. MacArthur and Ragnar Frisch Professor of Economics at the University of Wisconsin, Madison(email: kdwest@wisc.edu).We thank Jari Stehn and David Mericle for extensive help with the modeling work in ‘‘Implications forMonetary Policy’’ sections. We also thank Chris Mischaikow, Alex Verbny, Alex Lin, and Lisa Berlin forassistance with data and charts and for helpful comments and discussions. We also benefited fromcomments on earlier drafts of this paper by Mike Feroli, Peter Hooper, Anil Kashyap, Rick Mishkin, PauRabanal, Kim Schoenholtz, Amir Sufi, and two anonymous referees. This is a substantially revisedversion of Hamilton et al. (2015). West thanks the National Science Foundation for financial support.

THE EQUILIBRIUM REAL FUNDS RATE: PAST, PRESENT, AND FUTUREIntroductionWhat is the steady-state value of the real federal funds rate? Is there a newneutral, with a low equilibrium value for the foreseeable future?A consensus seems to be building that the answer to the second question isyes. Starting in 2012 FOMC members have been releasing their own estimates ofthe ‘‘longer run’’ nominal rate in the now somewhat infamous ‘‘dot plot.’’ AsTable 1 shows, the longer run projection for PCE inflation has remained steady at2.0 per cent, but longer run projections for both the GDP and the nominal fundsrate projections have dropped 50 bp. The implied equilibrium real rate has fallenfrom 2.0 to 1.5 per cent and the current range among members is between 1 and2 per cent. Indeed, going back to January 2012, the first FOMC projections forthe longer run funds rate had a median of 4.25 per cent, suggesting an equilibrium real rate of 2.25 per cent. Forecasters at the CBO, OMB, Social SecurityAdministration and other longer term official forecasts show a similar cut in theassumed equilibrium rate, typically from 2 to 1.5 per cent.The consensus outside official circles points to an even lower equilibriumrate. A hot topic of recent discussion is whether the U.S. has drifted into ‘‘secularstagnation,’’ a period of chronically low equilibrium rates due to a persistentweak demand for capital, rising propensity to save and lower trend growth in theTable 1. Economic Projections of Federal Reserve Board Members and FederalReserve Bank PresidentsGDPDecember 2015December 2014December 2012Unemployment rateDecember 2015December 2014December 2012PCE inflationDecember 2015December 2014December 2012Core PCE inflationDecember 2015December 2014December 2012Fed funds rateDecember 2015December 2014December 20122014201520162017Longer 53.754.0Note: Q4/Q4 percent changes, except unemployment (4Q average) and the fed funds rate (eop).Middle ofthe central tendency range, except fed funds rate (median).661

James D. Hamilton, Ethan S. Harris, Jan Hatzius, and Kenneth D. Westeconomy [see Summers (2013b, 2014)]. A similar view holds that there is a ‘‘newneutral’’ for the funds rate of close to zero in real terms [see McCulley (2003)and Clarida (2014)]. The markets seem to agree, with the yield on 10-yearTreasury Inflation Protected Securities having spent much of the last 5 yearsbelow 0.5 per cent.The equilibrium real rate is sometimes interpreted as the value of theintercept in a Taylor rule. In dynamic stochastic general equilibrium models, theequilibrium real rate is sometimes thought of as the value associated with thedeterministic steady-state growth path, which is a function of the discount factorand growth rates of technology and population. If these are constant, we shouldobserve a tendency of the real rate to return to a fixed long-run average over time.In richer models the equilibrium real rate is sometimes defined as the value thatwould be observed in the absence of monetary frictions. Empirical estimates ofthis magnitude often exhibit huge variation over time; see for example Justinianoand Primiceri (2010), Barsky et al. (2014) and Cúrdia et al. (2015). Laubach andWilliams (2003) obtained empirical estimates of the equilibrium rate assumingthat trend growth was a central determinant, and also found tremendousvariation.In this paper we evaluate some reduced-form evidence on this question. Wefocus on long run or steady state values, examining the behavior of the realinterest rate over long periods of time and its empirical relation to factors such asthe economic growth rate. We consider evidence from a large number ofcountries, though our primary focus will be on the United States. In ‘‘The RealRate and Aggregate Growth’’ section we describe the data and procedures thatwe will use to construct the ex-ante real rates used in our analysis. These go backas far as two centuries for some countries, and also include more detailed data onthe more recent experience of OECD economies. We also note the strategy weoften use to make empirical statements about the equilibrium rate: for the mostpart we will look to averages or moving averages of our measures of real rates; atno point will we estimate a structural model.‘‘The Real Rate and Aggregate Growth’’ section summarizes and interpretssome of the existing theoretical and empirical work and highlights the theoreticalbasis for anticipating a relation between the equilibrium real rate and the trendgrowth rate. In this and the next section, we look to moving averages as (noisy)measures of the equilibrium rate and the trend growth rate. Using both long timeseries observations for the United States as well as the experience across OECDcountries since 1970, we investigate the relation between safe real rates and trendoutput growth. We uncover some evidence that higher trend growth rates areassociated with higher average real rates. However, that finding is sensitive to theparticular sample of data that is used. And even for the samples with a positiverelation, the correlation between growth and average rates is modest. We conclude that factors in addition to changes in the trend growth rate are central toexplaining why the equilibrium real rate changes over time.In ‘‘The Secular Stagnation Hypothesis’’ section we briefly discuss the secular stagnation hypothesis in particular. We suggest that advocates of this vieware misinterpreting the delayed recovery from the Great Recession as evidence of662

THE EQUILIBRIUM REAL FUNDS RATE: PAST, PRESENT, AND FUTUREchronically weak aggregate demand. Our analysis suggests that the current cyclecould be similar to the previous two, with a delayed normalization of both theeconomy and the funds rate. A comparison with previous cycles, which isdetailed in Hamilton et al. (2015), suggests that the equilibrium rate may havefallen, but not as much as the secular stagnation hypothesis would imply. Thiscomparison is one source of the 0 to 2 per cent range for the equilibrium rategiven above.In ‘‘Long-run Tendencies of the Real Interest Rate’’ section we perform somestatistical analysis of the long-run U.S. data and find, consistent with our narrative history as well as with empirical results found by other researchers inpostwar datasets, that we can reject the hypothesis that the real interest rateconverges over time to some fixed constant. We do find a relation that appears tobe stable. The U.S. real rate is cointegrated with a measure that is similar to themedian of a 30-year-average of real rates around the world. When the U.S. rate isbelow that long-run world rate (as it was as of the beginning of 2015), we couldhave some confidence that the U.S. rate is going to rise. The model forecasts theU.S. and world long-run real rate settling down at a value around a half a percentwithin about six years. However, because the world rate itself is also nonstationary with no clear tendency to revert to a fixed mean, the uncertainty associated with this forecast is not only large, but grows larger the farther we try tolook into the future.More generally, the picture that emerges from our analysis is that thedeterminants of the equilibrium rate are manifold and time varying. We areskeptical of analysis that puts growth of actual or potential output at the center ofreal interest rate determination. The link with growth is weak. Historically, thatlink seems to have been buried by effects from other factors influencing the realrate. We conclude that reasonable forecasts for the equilibrium rate will comewith large confidence intervals.We close the paper in ‘‘Implications for Monetary Policy’’ section by considering the policy implications of uncertainty about the equilibrium rate.Orphanides and Williams (2002, 2006, 2007) have noted that if the Fed does nothave a good estimate of what the equilibrium real rate should be, it may bepreferable to put more inertia into policy than otherwise. We use simulations ofthe FRB/US model to gauge the relevance of this concern in the current setting.We conclude that, given that we do not know the equilibrium real rate, there maybe benefits to waiting to raise the nominal rate until we actually see someevidence of labor market pressure and increases in inflation. Relative to the‘‘shallow glide path’’ for the funds rate that has featured prominently in recentFed communications, our findings suggest that the funds rate should start to riselater but—provided the recovery does gather pace and inflation picks up—somewhat more steeply.To conclude, we think the long-run equilibrium U.S. real interest rate remainspositive, and forecasts that the real rate will remain stuck at or below zero for thenext decade appear unwarranted. But we find little basis in the data for stating withconfidence exactly what the value of the equilibrium real rate is going to be. In thisrespect our policy recommendation shares some common ground with the663

James D. Hamilton, Ethan S. Harris, Jan Hatzius, and Kenneth D. Weststagnationists—it pays for the Fed to be cautious about raising the nominal interestrate in the current environment until we see more evidence from the behavior ofthe economy and inflation that such increases are clearly warranted.The Real Interest Rate Across Countries and Across TimeOur focus is on the behavior of the real interest rate, defined as the nominal shortterm policy rate minus expected inflation. The latter is of course not measureddirectly, and we follow the common approach in the literature of inferringexpected inflation from the forecast of an autoregressive model fit to inflation.However, we differ from most previous studies in that we allow the coefficientsof our inflation-forecasting relations to vary over time. We will be making use ofboth a very long annual data set going back up to two centuries as well as aquarterly data set available for more recent data. The countries we will beexamining are listed in Table 2. In this section we describe these data and ourestimates of real interest rates.A Very Long-Run Annual Data SetOur long-run analysis is based on annual data going as far back as 1800 for 17different countries. Where available we used the discount rate set by the centralTable 2. Country Mnemonics and Start Dates for Real Interest Rate tzerlandGermanyDenmarkSpainFinlandFranceUnited KingdomIrelandItalyJapanSouth KoreaNetherlandsNorwayPortugalSwedenUSANew ZealandSample Start,Annual 8n.a.18931900n.a.185818581960185818581939Sample Start,Quarterly 1:21971:21971:21982:21958:1n.a.

THE EQUILIBRIUM REAL FUNDS RATE: PAST, PRESENT, AND FUTUREbank as of the end of each year. For the Bank of England this gives us a seriesgoing all the way back to 1801, while for the U.S. we spliced together values forcommercial paper rates over 1857–1913, the Federal Reserve discount rate over1914–1953, and the average fed funds rate during the last month of the year from1954 to present.1 Our interest rate series for these two countries are plotted in thetop row of Figure 1 and for 15 other countries in the panels of Figure 2.2 TheU.S. nominal rate shows a broad tendency to decline through World War II, risesharply until 1980, and decline again since. The same broad trends are also seenin most other countries. However, there are also dramatic differences acrosscountries as well, such as the sharp spike in rates in Finland and Germanyfollowing World War I.We also assembled estimates of the overall price level for each country. Forthe U.S., we felt the best measure for recent data is the GDP deflator which isavailable since 1929. We used an estimate of consumer prices for earlier U.S.data and all other countries. The annual inflation rates are plotted in the secondrow of Figure 1 for the U.S. and U.K. and for 15 other countries in the panels ofFigure 3. There is no clear trend in inflation for any country prior to World WarI, suggesting that the downward trend in nominal rates prior to that should beinterpreted as a downward trend in the real rate. Inflation rose sharply in mostcountries after both world wars, with hyperinflations in Germany and Finlandfollowing World War I and Japan and Italy after World War II. But the postwarspike in inflation was in every case much bigger than the rise in nominal interestrates.How much of the variation in inflation would have been reasonable toanticipate ex ante? Barsky (1987) argued that U.S. inflation was much lesspredictable in the 19th century than it became later in the 20th century. Moregenerally, we might expect predictions of inflation to be very different for episodes characterized by a gold standard or fixed exchange rates compared to afloating exchange rate regime. To deal with these issues we estimated a timevarying first-order autoregression to predict the inflation rate in country n for yeart:6 have been truncatedpnt ¼ cn þ /n pn;t 1 þ entð2:1ÞTo allow for variation over time in inflation persistence, we estimatedEq. (2.1) by ordinary least squares using a sample of thirty years of data endingin each year T. The resulting estimates of the persistence of inflation for countryb ; are plotted as a function of T for the U.S. and U.K. in row 3 ofn in year T, /nT1Values of the 3 separate U.S. series are very close to each other at the dates at which theywere spliced together.2Our data set is largely identical to Hatzius et al. (2014) and mainly comes from the GlobalFinancial Data Inc. database, supplemented with information from Haver Analytics. In most cases,the short-term interest rate series is a central bank discount rate (known as bank rate in UKparlance) or an overnight cash or repo rate. When more than one series is used for the same countrybecause of changes over time in definitions and market structure, we splice the series using thediscount rate as the basis.665

James D. Hamilton, Ethan S. Harris, Jan Hatzius, and Kenneth D. WestFigure 1 and for other countries in the panels of Figure 4. There is indeed littlepersistence in realized inflation for most countries during the 19th century,implying that changes in the nominal rate should be viewed as changes in the exante real rate. However, by World War I there is a fair amount of persistence inmost countries, suggesting that at least some degree of war-related inflationshould have been anticipated at the time. People knew there had been a war andthat last year there had been significant inflation. To maintain that they nevertheless anticipated stable prices for the following year in such a setting seems anunlikely hypothesis.In the last row of Figure 1 and the panels in Figure 5 we plot the value forthe ex-ante real interest rate that is implied by the above forecasting model, thatis, we plotb pntrnt ¼ int bc nt /ntð2:2Þb are the estimated intercept and slope for a regression estimatedwhere bc nt and /ntusing 30 years of data for that country ending at date t. These suggest that exFigure 1. U.S. and U.K. Nominal Interest Rate, Inflation Rate, Persistence ofInflation, and Ex-ante Real Rate, Annual 1800–2014USA Nominal Interest RateUK Nominal Interest Rate2020 201515 151010 102018161412108642055501800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000001800 1820 1840 1860 1880 1900 1920 1940 1960 1980 20003030303020202020101010100000USA InflationUK Inflation-10-10 -10-10-20-20 -20-20-301800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000-30 -301800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000-30USA Inflation PersistenceUK Inflation 0.2 -0.2-0.2-0.41800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000-0.4 -0.41800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000-0.4USA Real RateUK Real Rate151515151010101055550000-5-5-5-5-10-10 -10-10-15-15 -15-15-201800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000-20 -201800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000-20666

THE EQUILIBRIUM REAL FUNDS RATE: PAST, PRESENT, AND FUTUREFigure 2. Nominal Interest Rates for 15 Different Countries, Annual 03020France251501850861541052519001950200001850New Zealand20100

The equilibrium real rate is sometimes interpreted as the value of the intercept in a Taylor rule. In dynamic stochastic general equilibrium models, the equilibrium real rate is sometimes thought of as the value associated with the deterministic steady-stat

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