# R-star wars: the phantom menace.

Abstract The natural real rate of interest has been on a declining path for the past 30 years. I present a regimes-witching analysis of the natural rate, which suggests that the current low levels are likely to persist in the near future. I identify a high global demand for safe assets as the most important factor in keeping the natural rate low. I conclude that the current low levels of the policy rate are generally appropriate, with some upside risk, and that forward guidance should be characterized by a flat policy rate path.Keywords Natural real interest rate * Markov switching * Monetary policy rules

JEL Classification C24 E47 E58

1 Introduction

This article provides some commentary on issues around what is often called "r-star," denoted "r*", the natural real rate of interest. According to leading contemporary theories, policymakers need to know the value of r* to decide if the current policy rate setting is accommodative, neutral or restrictive. In practice, pinning down empirical values for the natural real rate of interest involves imputing an underlying trend from raw data, which can be difficult. Hence, this variable is something of a "phantom menace."

In this article, I will define the natural real rate of interest as a low-frequency trend measure of a short-term real interest rate. Further, I will take a regime-switching view of how to think about trend movements in the data. (1) Based on this analysis, I tentatively conclude that there appears to be a large demand for safe assets globally, and this may be the largest factor driving real interest rates to low levels over the past three decades. In addition, there appears to be only modest evidence that key trends influencing the natural rate of interest are changing today. At the end of this article, I will insert the current-regime low value of the natural rate in some Taylor-type monetary policy rules. These rules will generally recommend that the current low setting of the policy rate is broadly appropriate.

2 The r-star debate

There is a growing literature trying to understand the downward trend in the natural real rate of interest. Laubach and Williams (2003) impose a structural model and estimate a relatively low value for r*. Holston et al. (2017) extend the analysis to other countries. Curdia (2015) performs a similar analysis with somewhat altered assumptions and reports a very low value for r*. Del Negro et al. (2017) impose a structural model, including an evolving demand for safe assets and estimate a low value for r*. The analysis in this article imposes less structure along with an alternative stochastic conception, regime switching. This suggests a different view of mean-reversion properties. In particular, while most of the literature views the natural rate as having a unique long-run equilibrium to which it tends to revert, I view the natural rate as periodically visiting a set of possible regimes, each of which is persistent. I will call the natural rate of interest so-described "r-dagger" (or [r.sup.[dagger]]) to emphasize that my estimates use an alternative methodology and an alternative stochastic conception.

The analysis here considers three factors that are widely thought to influence the natural real rate of interest. More possible factors impacting real rates are analyzed in Rachel and Smith (2015). One could also take a longer-run view of the natural safe real rate of interest. For instance, Borio et al. (2017) consider a panel dataset for 19 countries from 1870 to the present and emphasize how monetary regimes apparently impact real interest rates over long eras. Homer and Sylla (2005) consider even more data from a wide variety of historical episodes.

In the following section, I discuss the raw data and various ways of detrending the data. In Sect. 4, I consider a decomposition of the natural interest rate into three factors, each of which follows a simple regime-switching process. Section 5 illustrates the monetary implications of the analysis by looking at the policy rate recommendations from standard Taylor-type rules. Section 6 concludes.

3 Raw data and the trend

Short-term real interest rates are at the center of macroeconomic theory and monetary policy. For the purposes of this article, I will view the natural real rate of interest as the trend component of a specific measure of a short-term real interest rate. The core idea in the literature is that the Fed can influence the real rate of interest but that it cannot influence the longer-run trend in the real rate of interest, which is viewed as driven by fundamental factors. The raw data I will consider are 1-year ex-post real interest rates on U.S. Treasury bills from 1984 to the present, constructed by subtracting the Dallas Fed trimmed-mean personal consumption expenditures (PCE) inflation rate over the previous year from the 1-year Treasury rate. (2)

The following are four methods that could be used to detrend these data: (1) Use a constant, as in Taylor (1993); (2) Use a linear trend; (3) Use an atheoretical filter, like the Hodrick-Prescott filter; (4) Use a model, as in Holston et al. (2017) or Del Negro et al. (2017).

Figure 1 portrays the raw data, as well as various trends. Most detrending methods suggest a relatively low value of the natural rate of interest in recent quarters.

The raw data in Fig. 1 show a declining trend on an expost real return to holding government paper. The declining trend does not appear to extend to ex-post real returns on claims to capital as measured from the U.S. national accounts. (3) That return has been fairly constant since the 1980s, as shown in Fig. 2.

The fact that real returns to government paper have a declining trend over the last three decades or more, while similarly measured real returns to capital do not, suggests that there has been an increased demand for safe assets relative to supply over this period. This helps to rationalize the idea that the demand for safe assets is an important factor, and perhaps the dominant factor, in driving the natural rate of interest to low levels over this time period.

4 The natural rate of interest in a Taylor-type policy rule

In a Taylor-type rule, the natural real interest rate, [r.sup.[dagger].sub.t], determines the intercept:

[i.sub.t] = [r.sup.[dagger].sub.t] + [[pi].sup.e.sub.t] + [[phi].sub.[pi]] [[pi].sup.GAP.sub.t] + [[phi].sub.y][y.sup.GAP.sub.t] (1)

where [[pi].sup.e.sub.t] = [pi]* = 2% is the inflation target of the Federal Open Market Committee (FOMC); [[pi].sup.GAP.sub.t] and [y.sup.GAP.sub.t] denote the inflation gap and the output gap, respectively. When the gaps are zero, [[pi].sup.GAP.sub.t] = [y.sup.GAP.sub.t] = 0, a Taylor-type rule simply recommends setting the policy rate equal to the natural real interest rale plus the inflation target, [i.sub.t] = [r.sup.[dagger].sub.t] + 2. The key issue is then to identify the value of the natural real interest rate. One way to think about [r.sup.[dagger].sub.t] is to decompose it into three factors:

[r.sup.[dagger].sub.t] = [[lambda].sub.t] + [[psi].sub.t] + [[xi].sub.t], (2)

where [[lambda].sub.t] denotes the growth rate of labor productivity, [[psi].sub.t], is the growth rate of the labor force and [[xi].sub.t] captures investors' desire for safe assets. A strong desire for safe assets would imply a relatively large negative value for [[xi].sub.t], whereas an ordinary desire for safe assets would imply a value closer to zero. (4)

This decomposition of [r.sup.[dagger].sub.t] can be rationalized by considering a T-periods overlapping generations model with consumers endowed with log preferences, no discounting, no fixed capital and without any other frictions. In this type of model, if there was no special desire for safe assets, [r.sup.[dagger]] would equal the real output growth rate (also the consumption growth rate), [lambda] + [psi], along the balanced growth path. This conception of the natural real rate of interest suggests that [r.sup.[dagger]] will have a constant mean associated with a single possible balanced growth path.

I will argue that this single mean may in practice be better modeled as shifting over time. Shifting means can be modeled as regime-switching processes. For example, relatively long eras of high productivity growth may be followed by relatively long eras of low productivity growth, and the natural rate of interest would be different in the two regimes.

Accordingly, I will treat each of the three factors, [[lambda].sub.t], [[psi].sub.t] and [[xi].sub.t] as following a two-state Markov-switching intercept process:

[x.sub.t] = x([s.sub.t]) + [[epsilon].sup.x.sub.t], (3)

where [[epsilon].sup.x.sub.t] is an i.i.d. error term and [s.sub.t] can take two values, high and low. The two possible mean values are called regimes. The idea is that these types of factors generally have constant means, but that there can be infrequent shifts in mean. I want to characterize these shifts statistically.

A statistical model that estimates the probability that the U.S. economy is in a low-productivity-growth or in a high-productivity growth regime puts nearly all the probability on the low-growth regime (Kahn and Rich 2006, 2007). As shown in Fig. 3, the most recent estimates based on Kahn and Rich's methodology put the growth rate in the low (high) state at 1.33% (2.90%). (5) The U.S. economy was in the high-productivity-growth regime from early 1997 to late 2004.

Let's now turn to the labor force growth factor. The U.S. labor force had been growing at a 1.33% average annual rate until the financial crisis (Fig. 4). The average growth rate has been 0.46% since the financial crisis. It appears that the U.S. is in a low-growth state, but statistically the two regimes are not precisely estimated. In discussing the policy implications below, I will consider the possibility that the U.S. is in either state.

To address the final factor, the demand for safe assets, I now remove the regime-switching trends for both labor productivity and labor force growth from the raw data on ex-post safe real returns. The result is a time series of adjusted safe real returns, and this series still has a downward trend. I then fit a two-state regime-switching process to these residual values (Eq. 3), and I interpret the two states as a strong desire for safe assets versus a more normal desire for safe assets. The estimated values for [[xi].sub.t] are - 3.06% in the high-desire-for-safe-assets regime and 0.57% in the normal-desire-for-safe-assets regime (Fig. 5). The U.S. is currently in the regime with a high desire for safe assets. The difference between the two regimes is largest for this factor; in some sense, it is the "most important" of the three.

Table 1 summarizes the results obtained using the regime-switching approach. Labor productivity appears to be in the low-growth regime, so set [lambda] = 1.33%. The labor force appears to be in the low-growth regime as well, so set [psi] = 0.46%. Plausibly, labor force growth could be interpreted as still consistent with the high-growth regime, [psi] = 1.33%. There also appears to be a high desire for safe assets, so set [xi] = - 3.06%. According to this analysis, the natural real interest rate from Eq. (2) is either--127 basis points or--40 basis points, depending on how one views labor force growth.

5 Implications for monetary policy

I now return to a Taylor-type monetary policy rule, Eq. (1), to give some sense of the policy impact of this analysis. As I noted above, if the gaps in a Taylor-type rule are viewed as close to zero, the rule would recommend a policy rate setting equal to the natural rate plus the inflation target. The gap variables are probably not exactly zero today, so I now turn to a brief discussion of the values for gap variables.

The U.S. inflation rate has been below the 2% inflation target since 2012. (6) Inflation measured from 1 year earlier is currently (December 2017) between 30 and 48 basis points below target, depending on which of the following measures one prefers:

* Dallas Fed trimmed-mean PCE: 1.67%;

* Headline PCE: 1.70%;

* Core PCE: 1.52%.

As for the remaining gap variable, I look at three ways to calculate an output gap. One method is to accept the Congressional Budget Office estimate of the output gap at 0.47% for 2017-Q4. Another method is to consider the deviation of real GDP from a HP(1600) trend, which was 0.14% in 2017-Q4. And finally, a third method uses Okun's law to relate the output gap to the deviation of unemployment from the natural rate:

[y.sup.GAP.sub.t] = -k ([u.sub.t] - u*). (4)

Assuming a slope of k = 2.3 and using the St. Louis Fed "no-recession regime" estimate of u* = 4.5%, (7) the current unemployment rate ([u.sub.t] = 4.1% in January 2018) gives an estimate for the output gap of 0.92%.

With these gap measurements in hand, I now consider two Taylor-types rules of the form of Eq. (1). The rule proposed by Taylor (1993) assumes [[phi].sub.[pi]] = 1.5 and [[phi].sub.y] = 0.5. These values, together with a real rate between -127 and--40 basis points, an inflation gap between -48 and--30 basis points, and an output gap ranging from 14 to 92 basis points, imply a recommended policy rate in the range of 8-161 basis points. The rule suggested by Taylor (1999) features the same response to the inflation gap, [[phi].sub.[pi]] = 1.5, but a more aggressive response to the output gap, [[phi].sub.y] = 1. These values imply a recommended policy rate ranging from 15 to 207 basis points.

The FOMC's target range for the federal funds rate today is 125-150 basis points, and the federal funds rate is trading at about 142 basis points (February 2018). This value is within the range of the recommendations. However, if the FOMC raises the policy rate substantially from here without other changes in the data, the policy setting could become restrictive.

The regime-switching approach suggests that the current setting of the policy rate is broadly appropriate. It also suggests that [r.sup.[dagger]] is unlikely to shift over a forecast horizon of 2 years (the typical time frame for monetary policy decisions). This suggests forward guidance should be characterized by a relatively flat policy rate path, as opposed to an upward-sloping one that would be appropriate if [r.sup.[dagger]] has strong mean reversion.

6 Conclusion

This analysis has provided some background on how one might begin to think about recent trends in the natural safe real rate of interest in a regime-switching context.

According to the analysis presented here, the natural safe real rate of interest, and hence the appropriate policy rate, is relatively low and unlikely to change very much over the forecast horizon.

A more rigorous and thorough analysis that reaches a similar conclusion is Del Negro et al. (2017).

https//doi.org/10.1057/s 11369-018-0077-1

References

Borio, Claudio, Piti Disyatat, Mikael Juselius, and Phurichai Rungcharoenkitkul. 2017. Why so low for so long? A longterm view of real interest rates. Bank for International Settlements Working Papers No. 685.

Bullard, James. 2016. The St. Louis Fed's new characterization of the outlook for the U.S. economy. Federal Reserve Bank of St. Louis. Announcement. https://www.sdouisfed.org/~/media/Files/PDFs/Bullard/papers/ Regime-Switching-Forecasts-17June2016.pdf?

Curdia, Vasco. 2015. Why so slow? A gradual return for interest rates. Federal Reserve Bank of San Francisco. Economic Letter No. 2015-32.

Del Negro, Marco, Domenico Giannone, Marc Giannoni, and Andrea Tambalotti, 2017. Safety, liquidity and the natural rate of interest. Brookings Papers on Economic Activity. Spring: 235-294.

Dupor, William. 2015. Liftoff and the natural rate of interest. Federal Reserve Bank of St. Louis. On the Economy. https://www.stlouisfed.org/on-the-economy/2015/june/ liftoff-and-the-naturalrate-of-interest.

Gomme, Paul, B. Ravikumar, and Peter Rupert. 2011. The return to capital and the business cycle. Review of Economic Dynamics 14 (2): 262-278. https://doi.org/10.1016/j.red.2010.11.004.

Gomme, Paul, B. Ravikumar, and Peter Rupert. 2015. Secular stagnation and returns on capital. Federal Reserve Bank of St. Louis. Economic Synopses 2015, No. 19.

Hamilton, James D. 1989. A new approach to the analysis of nonstationary time series and the business cycle. Econometrica 57 (2): 357-384. https://doi.org/10.2307/1912559.

Holston, Kathryn, Thomas Laubach, and John C. Williams. 2017. Measuring the natural rate of interest: International trends and determinants. Journal of International Economics 108 (SI): S59-S75. https://doi.org/10.1016/j.jinteco.2017.01.004.

Homer, Sidney, and Richard Sylla. 2005. A History of Interest Rates, 4th ed. Hoboken, NJ: Wiley.

Kahn, James A., and Robert W. Rich. 2006. Tracking productivity in real time. Federal Reserve Bank of New York. Current Issues in Economics and Finance 12 (8): 1-7.

Kahn, James A., and Robert W. Rich. 2007. Tracking the new economy: Using growth theory to detect changes in trend productivity. Journal of Monetary Economics 54 (6): 1670-1701. https://doi.org/10.1016/j.jmoneco.2006.07.008.

Kim, Chang-Jin, and Charles R. Nelson. 1999. State-space Models with Regime Switching. Cambridge, MA: MIT Press.

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Laubach, Thomas, and John C. Williams. 2003. Measuring the natural rate of interest. Review of Economics and Statistics 85 (4): 1063-1070. https://doi.org/10.1162/003465303772815934.

Monge-Naranjo, Alexander, Juan M. Sanchez, and Raul Santaeulalia-Llopis. 2015. Natural Resources and Global Misallocation. Federal Reserve Bank of St. Louis. Working Paper No. 2015-036A.

Rachel, Lucasz, and Thomas D. Smith. 2015. Secular Drivers of the Global Real Interest Rate. Bank of England. Staff Working Paper No. 571.

Taylor, John B. 1993. Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy 39: 195-214. https://doi.org/10.1016/0167-2231 (93)90009-L.

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James B. Bullard is the president and CEO of the Federal Reserve Bank of St. Louis. He oversees the activities of the Eighth Federal Reserve District, including operations in the St. Louis headquarters and its branches in Little Rock. AR, Louisville, KY, and Memphis, TN. He also participates on the Federal Reserve's Federal Open Market Committee, or FOMC, which meets eight times each year to set the direction of U.S. monetary policy. He is a noted economist and scholar, and his positions are founded on research-based thinking and an intellectual openness to new theories and explanations. He is often an early voice for change. In addition, he makes public outreach and dialogue a priority to help build a more transparent and accessible Fed. He regularly engages with many audiences--including academics, policymakers, business and labor organizations, charities, students and media, among other public groups--to discuss monetary policy and the U.S. economy and to help further the regional Reserve banks' role of being the voice of Main Street. He is active in the community. He is an honorary professor of economics at Washington University in St. Louis, where he also sits on the advisory council of the economics department, as well as several advisory boards. In addition, he is a member of the Greater St. Louis Financial Forum, the St. Louis Regional Chamber's board of directors and the St. Cloud State University School of Public Affairs advisory council. He is also chairman of the United Way's U.S.A. Board of Trustees and a member of the United Way Worldwide board. In addition, he is a member of the Central Bank Research Association's senior council. A native of Forest Lake, Minn., he received his doctorate in economics from Indiana University in Bloomington. He holds Bachelor of Science degrees in economics and in quantitative methods and information systems from St. Cloud State University in St. Cloud, Minn.

(1) For an introduction to regime switching, see Hamilton (1989) and Kim and Nelson (1999).

(2) This method is using ex-post inflation. Forward-looking measures, based on Federal Reserve Bank of Cleveland data on inflation expectations, are similar but more volatile.

(3) See Gomme et al. (2011, 2015), Monge-Naranjo et al. (2015), and Dupor (2015). For an alternative perspective on this issue, see Williams (2017).

(4) For some analysis along this line, see Lagos (2010).

(5) Available at https://www.newyorkfed.org/medialibrary/media/research/national_economy/richkahn_prodmod.pdf.

(6) The inflation target is in terms of the annual change in the price index for personal consumption expenditures (PCE).

(7) See Bullard (2016) for more details on the St. Louis Fed's approach to characterizing the U.S. economic outlook.

James B. Billiard (1)

Published online: 16 April 2018

This article is an extended version of remarks delivered at the 34th Annual NABE Economic Policy Conference, Washington, DC, February 26, 2018. The author appreciates the assistance and comments provided by colleagues at the Federal Reserve Bank of St. Louis. Any opinions expressed here are the author's own and do not necessarily reflect those of the Federal Open Market Committee.

[mail] James B. Bullard

bullard@stls.frb.org

(1) Federal Reserve Bank of St. Louis, St. Louis, MO, USA

Caption: Fig. 1 Real interest rate and trends. Sources Federal Reserve Board, Federal Reserve Bank of Dallas, Taylor (1993), Del Negro et al. (2017), Holston et al. (2017), and author's calculations. Last observation: 2017-Q4. (Color figure online)

Caption: Fig. 2 Real returns on capital and safe assets. Sources Gomme et al. (2015), Federal Reserve Board, Federal Reserve Bank of Dallas, and author's calculations. Last observation: 2017-Q4. (Color figure online)

Caption: Fig. 3 High- and low-productivity-growth regimes. Sources Kahn and Rich (2006, 2007) and Federal Reserve Bank of New York. Last observation: 2017-Q4. (Color figure online)

Caption: Fig. 4 High- and low-labor-force-growth regimes. Sources Bureau of Labor Statistics and author's calculations. Last observation: January 2018. (Color figure online)

Caption: Fig. 5 High- and normal-desire-for-safe-assets regimes. Source Author's calculations. Last observation: December 2017. (Color figure online)

Table 1 State values for each factor Factor High state Low state High-low state difference Labor productivity 290 133 157 growth, [lambda] Labor force 133 46 87 growth, [psi] Investor desire 57 - 306 363 for safe assets (inverse), [xi] Max/min natural rate, 480 - 127 607 [r.sup.[dagger]] = [lambda] [psi] + [xi] All values are expressed as basis points. The max (min) natural rate is the value corresponding to all three factors taking the value in the high (low) state

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Title Annotation: | ORIGINAL ARTICLE |
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Author: | Billiard, James B. |

Publication: | Business Economics |

Geographic Code: | 1U4MO |

Date: | Apr 1, 2018 |

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