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

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Abstract

We examine the behavior, determinants, and implications of the equilibrium level of the real federal funds rate, interpreted as the long run or steady state value of the real funds rate. We draw three main conclusions. First, the uncertainty around the equilibrium rate is large, and its relationship with trend GDP growth much more tenuous than widely believed. Our narrative and econometric analysis using cross-country data and going back to the 19th century supports a wide range of plausible estimates for the current level of the equilibrium rate, from a little over 0 per cent to the pre-crisis consensus of 2 per cent. Second, a bivariate vector error correction model 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 the end of our sample (2014), the model forecasts the real rate in the U.S. will asymptote to an equilibrium value of a little less than half a percent by 2021. Consistent with our first point, however, confidence intervals around this point estimate are huge. Third, the uncertainty around the equilibrium rate argues for more “inertial” monetary policy than implied by standard versions of the Taylor rule. Our simulations using the Fed staff’s FRB/US model show that explicit recognition of this uncertainty results in a later but steeper normalization path for the funds rate compared with the median “dot” in the FOMC’s Summary of Economic Projections.

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Note: This figure plots the quarterly data in Table 4.

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Note: This figure plots the annual data in Table 4.

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Note: The two digit label identifies the observation corresponding to the fourth quarter of that year. For example, “08” labels the 2008:4 observation: over the 40 quarter period 1999:1–2008:4, the average value of r and GDP growth were average r = 1.08, average GDP growth = 2.14. See notes to Table 6.

Figure 12

Note: See notes to Table 6.

Figure 13

Note: This exhibit plots the data listed in Table 7. See notes to Table 7. Mnemonics for country names are given in Table 2.

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Note: Dashed: 1 per cent critical value if test were only performed at a single date (6.63). Solid: 1 per cent critical value if the maximal statistic over the range 1900–1976 were used (11.28, from Andrews (2003)). Top panel: U.S. real interest rate \( r_{US,t} ; \) middle panel: long-run world rate \( \ell_{t} ; \) bottom panel: difference between U.S. real rate and long-run world rate \( (r_{US,t} - \ell_{t} ). \)

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Note: Arrows indicate optimal inertia coefficients. *Relative to no-misperception optimum.

Figure 27

Note: Arrows indicate optimal inertia coefficients. *Relative to no-misperception optimum.

Figure 28

Note: Arrows indicate optimal inertia coefficients. *Relative to no-misperception optimum.

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Notes

  1. Values of the 3 separate U.S. series are very close to each other at the dates at which they were spliced together.

  2. Our data set is largely identical to Hatzius et al. (2014) and mainly comes from the Global Financial 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 UK parlance) or an overnight cash or repo rate. When more than one series is used for the same country because of changes over time in definitions and market structure, we splice the series using the discount rate as the basis.

  3. In preliminary work, we also experimented with keeping the window size fixed at 40 quarters through the whole sample. This led to a very similar series; the correlation was 0.98 between the expected inflation series with a 40 quarter window and the Eq. (2.3) version that we actually used.

  4. Using a different approach, Leduc and Rudebusch (2014) also conclude the link in the U.S. is weak.

  5. This is consistent with the formal econometric work of Clark and Kozicki (2005, p. 403), who conclude that the link between trend growth and the equilibrium real rate is “quantitatively weak.”

  6. Indeed, in “Implications for Future Real Rates” section we use a model that relies on a conventional link between real rates and growth.

  7. Elliott and Müller (2006) noted that departures from stationarity, whether in the form of structural breaks, unit roots, or time-varying parameters, can be embedded into a single unifying framework, and that, from the perspective of efficient tests of the null hypothesis, the seemingly different approaches are in fact equivalent. In most of what follows we will be using a finite number of structural breaks as specification of the alternative hypothesis against which the null of stationarity is being tested.

  8. Using a second-order autoregression for levels allows us to include as a special case a first-order autoregression for growth rates as one of the possible specifications that we will be considering.

  9. The test statistic using 5 lags and a constant is 0.55 for a p value of 0.025.

  10. The null hypothesis of a single structural break is rejected in favor of the alternative of two structural breaks with a p value less than 0.01 using the test described in Table 2 of Bai and Perron (1998).

  11. Our measure of the long-run real rate is very similar to an average value of r over the preceding 30 years. In fact, if (5.2) were estimated by OLS instead of with ARCH(2) residuals, and if the interest rate in year t was identical to the interest rate in year t -30, our estimate would be identical to the average rate over the 30 years ending in t. One can see this from the OLS identity that \( \overline{r} = \widehat{b} + \widehat{\psi }\overline{r}_{ - 1} \) and the fact that if \( r_{t} = r_{t - 30} \) then \( \overline{r} = \overline{r}_{ - 1} \) meaning that \( \widehat{b}/(1 - \widehat{\psi }) = \overline{r} . \) If \( r_{t} > r_{t - 30} \) then \( \ell_{t} \) will tend to be a little above the average rate over the 30 years ending in t. Also, since we estimate (5.2) allowing for ARCH errors, our estimate tends to down-weight observations that appear to be outliers in calculating the long-run real rate.

  12. The forward rates implied by yields as of December 20, 2014 were calculated as in Gürkaynak et al. (2010) using the spreadsheet available at http://www.federalreserve.gov/pubs/feds/2008/200805/200805abs.html. Note that the forward rate cannot be reliably calculated by this method for a horizon less than 2 years into the future, which is why the plotted curve only begins in 2016. We do not attempt to correct for risk premia and use these calculations only as a rough guideline.

  13. OW also consider uncertainty around u* and therefore also include a potential response to the change in the unemployment rate. We set aside this issue in our formal analysis but touch on it at the end of this section.

  14. For example, Chairman Bernanke said in the September 2013 FOMC press conference that the equilibrium rate would likely still be depressed by the end of 2016—the point at which the committee expected to hit its mandate at that time—and that it “…looks like it will be lower for a time because of these headwinds that will be slowing aggregate demand growth.”

  15. This assumption lies in between the very low aversion to changes in the funds rate in OW and the higher aversion in Yellen (2012). We explore the implications of varying it below.

  16. A different baseline for r* (e.g. resulting from a different assumption about the baseline policy reaction function) would generate different optimal values for a 0 . However, it would not change the result that greater uncertainty around r* increases the optimal value for a 0 .

  17. Haldane (2015) also concludes that delayed normalization is preferred.

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Authors and Affiliations

  1. University of California at San Diego, La Jolla, CA, USA

    James D. Hamilton

  2. Bank of America Merrill Lynch, New York, NY, USA

    Ethan S. Harris

  3. Goldman Sachs, New York, NY, USA

    Jan Hatzius

  4. University of Wisconsin, Madison, WI, USA

    Kenneth D. West

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  1. James D. Hamilton
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  4. Kenneth D. West
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Correspondence to Kenneth D. West.

Additional information

* 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 America Merrill Lynch Global Research (email: ethan.harris@baml.com). Jan Hatzius is Chief Economist and Head of Global Economics and Markets Research at Goldman Sachs (email: jan.hatzius@gs.com). Kenneth West is John 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 for Monetary Policy” sections. We also thank Chris Mischaikow, Alex Verbny, Alex Lin, and Lisa Berlin for assistance with data and charts and for helpful comments and discussions. We also benefited from comments on earlier drafts of this paper by Mike Feroli, Peter Hooper, Anil Kashyap, Rick Mishkin, Pau Rabanal, Kim Schoenholtz, Amir Sufi, and two anonymous referees. This is a substantially revised version of Hamilton et al. (2015). West thanks the National Science Foundation for financial support.

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Hamilton, J.D., Harris, E.S., Hatzius, J. et al. The Equilibrium Real Funds Rate: Past, Present, and Future. IMF Econ Rev 64, 660–707 (2016). https://doi.org/10.1057/s41308-016-0015-z

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