Essays related to Marvin and his work:

# Interest Rate Smoothing

**Honoring Marvin Goodfriend**

**Goodfriend, Marvin. 1987. "Interest Rate Smoothing and Price Level Trend-Stationarity." Journal of Monetary Economics 19, no. 3 (May): 335-348.**

The concept of interest rate smoothing behavior by central banks is now standard, but it was not when Marvin Goodfriend wrote in the early 1980s.^{1} His "Interest Rate Smoothing and Price Level Trend Stationarity" made the concept into a distinct phenomenon to be explained, first in working papers that appeared in 1983 or earlier and then in a 1987 publication in *Journal of Monetary Economics*. At the time, the conduct of monetary policy as well as the interest rate and inflation outcomes produced by it were changing rather dramatically.

We begin with a summary of Marvin's "Interest Rate Smoothing" paper. We then use the paper as a window into the changes that were taking place, and continued to take place, both in the practice and the analysis of monetary policy. Next, we discuss how the literature on interest rate smoothing evolved after Marvin's work and reflect on how the practice of interest rate smoothing seems to have evolved in recent years in the US. In the concluding section, we offer some personal recollections from our time working with (and for) Marvin at the Richmond Fed.

## Summary of the paper

In the early 1980s, the US economy was emerging from a period of high and volatile inflation, accompanied by high unemployment and low output growth — the so-called stagflation of the 1970s. This was fertile ground for studying why the Fed made the policy choices it made, and how those choices determined the behavior of inflation and influenced the behavior of real variables. A large part of Marvin's career was devoted to studying these issues.

In "Interest Rate Smoothing," he focused specifically on the nontrend stationarity of the price level: amid calls for constant money growth rules that would presumably guarantee price-level trend stationarity as well as limit inflation, Marvin asked why was such a policy not chosen?

As a student of central banking, Marvin believed it unlikely that failure to follow a constant money growth rule was due to ignorance on the part of the central bank. Thus, to answer the question, Marvin developed a simple model where the monetary authority can choose a rule for money growth that may or may not result in a trend-stationary price level. He shows that if the monetary authority is only interested in stabilizing the macroeconomy, then the optimal policy will indeed result in a trend-stationary money stock and price level. But if the authority also cares about financial market stability, then they would accept random drift in the money stock and the price level would no longer be trend stationary.

His theoretical foundations were those of the times: a linear rational expectations model with a Lucas supply curve, a Fisher equation for nominal interest rates, and a money demand equation. Each one of the model's three equations is subject to an iid shock. The monetary authority observes the current interest rate but not the current price level or output, or the current shocks for that matter. The monetary authority chooses the parameters of a money supply growth rule that responds to contemporaneous interest rate surprises. In addition, the monetary authority can choose to offset last period's unanticipated money stock change that follows from the response to surprise movements in the interest rate. The objectives of the monetary authority relate to the stabilization of the macroeconomy and the financial sector. Instability of the macroeconomy is represented by the variance of price-level surprises and the variance of expected inflation. Instability of the financial sector is represented by the variance of nominal interest rates.

First, Marvin shows that if the monetary authority is only concerned with macroeconomic stability, the optimal policy will exactly offset any past surprise money stock change such that the money stock becomes trend stationary. With a trend-stationary money stock, the price level is also trend stationary. In particular, the price level is an iid random variable, so unconditional expected inflation is zero. Conditional on observing the current price level though, expected inflation is the opposite of the current price-level surprise, and therefore the variance of expected inflation and the price-level surprise are the same. The monetary authority's optimal contemporaneous response to the interest rate surprise is then set such that there is no expected price-level surprise. That is, based on the monetary authority's current information, the expected price level is the same as the unconditional expectation of the price level, which then implies that expected inflation is also zero.^{2}

After showing that optimal macroeconomic stabilization indeed implies trend stationarity of the money stock and the price level, Marvin then demonstrates that adding the additional objective of financial market stabilization — which translates into smoothing nominal interest rates — introduces random drift into the optimal money stock and the price level. To understand this result, first note that the Fisher equation determines the nominal interest rate as the sum of expected inflation and the stochastic real rate, which is iid. With the previously optimal trend-stationary policy, expected inflation conditional on the observed interest rate is always zero. This means that the observed nominal interest rate reflects the conditional expectation of the real rate shock. Now suppose that the nominal interest rate is above average and the inferred real rate shock is positive. Then the monetary authority could reduce the nominal interest rate by creating expected deflation, that is, an expected reduction in next period's price level. To reduce the price level, the monetary authority would reduce the money stock by more than expected; that is, it would more than offset last period's unanticipated money stock change. But this introduces drift into the money stock. Optimal policy then trades off reductions in interest rate volatility against increases in expected inflation volatility.

The monetary authority's objectives are crucial for Marvin's account of the stochastic drift in the price level under optimal policy. Given the reduced-form nature of the model, these objectives don't arise from the economic environment as in modern macroeconomics, but as a student of central banking Marvin motivates them by referring to expressed or inferred preferences of central banks. Minimizing the variance of price-level surprises is related to stabilizing employment, which seems reasonable in the context of the Lucas supply curve.^{3} Minimizing the variance of expected inflation is motivated by a reference to central banks' concern arising from imperfect indexation of nominal contracts. Finally, minimizing the variance of nominal interest rates is motivated by central banks' preference for "smooth nominal interest rates to maintain 'orderly money markets.'" Note that such behavior has the central bank working against "natural rate" movements to some degree, rather than simply tracking them, as in Goodfriend and King (1997) and much subsequent analysis with New Keynesian models.^{4}

## Marvin's evolving views about monetary policy

Marvin's paper provides a window, circa 1985, into how he thought about monetary policy and into the tools that were widely used for studying monetary policy. Both the conduct of monetary policy and the analytical tools changed substantially over the course of Marvin's career. As discussed in other essays in this volume, Marvin's work at the intersection of theory and policy put him at the center of these changes. We think it's interesting to use the paper as a departure point for a brief discussion of how the practice and analysis of monetary policy changed from the time Marvin began work on "Interest Rate Smoothing" to the early 21st century.

*The monetary policy instrument*

Although the title of Marvin's paper refers to "interest rate smoothing," it is notable that the money supply is the policy instrument in his model. This may suggest that Marvin's analysis reflects large differences in the way monetary policy was implemented in the 1980s compared to today. It is more likely though, that it reflects Marvin straddling the boundary of academic monetary economics and central bank practice.

At the time, there was much less transparency about policy than there is today (see Goodfriend, 1986, and Lars E.O. Svensson's essay in this volume). To the extent that the Fed did make public statements about policy, those concerned broad target ranges for money supply growth and the federal funds rate.^{5} Subsequently, policy has become much more transparent, and — at least away from the zero bound — policy decisions are framed in terms of short-term interest rates. Attention to the money supply gradually faded until it essentially disappeared from policy discussions by the early 2000s, if not earlier.

But it is also true that most academic research on monetary policy at the time treated the money supply as the central bank instrument. In particular, Marvin's paper is all about why optimal monetary policy would deviate from one leading optimal policy prescription, which called for a constant money growth rule. There was also an ongoing debate over whether the choice of the interest rate as a policy instrument would lead to instability, especially in the case of interest rate pegs, for example, in Sargent and Wallace (1975) and McCallum (1981). At the same time, as we noted above, Marvin was an avid student of central banking, and he saw that actual US monetary policy was implemented by means of an interest rate instrument. In fact, footnote six in "Interest Rate Smoothing" previews the main themes of his 1991 paper, "Interest Rates and the Conduct of Monetary Policy."^{6} There, Marvin writes that the Fed has "*always employed either a direct or indirect Federal Funds Rate policy instrument*."

*The meaning of interest rate smoothing*

Clearly, even in 1987 Marvin viewed interest rate smoothing as being related to the adjustment of the interest rate instrument over time. But the absence of any true dynamics in his theoretical framework con-strained him to identify interest rate smoothing with minimizing the variance of interest rates. The development of New Keynesian dynamic stochastic general equilibrium models, with nominal rigidities and interest rate rules for monetary policy, allowed for an expanded analysis of interest rate smoothing.

## Subsequent literature on smoothing

Over time, central banks moved to explicit interest rate policy and became more transparent. As analytical tools were developed, a large literature arose using the broader notion of interest rate smoothing as representing high persistence of policy interest rates. That the fed funds rate target is highly persistent at a quarterly frequency, in the sense of first-order autocorrelation, is an established fact. The interpretation, however, is not obvious. The more recent literature has addressed theoretical explanations for this persistence and then attempted to evaluate those candidate explanations with empirical studies.

*Why make interest rates persistent?*

Subsequently, in Goodfriend (1991), Marvin considered additional reasons for why central banks might want to smooth interest rates besides financial stability considerations. One of the reasons is Mankiw's (1987) observation that it is optimal to smooth the inflation tax and thus make inflation a random walk. Barro (1989) analyzed how a central bank would implement such a policy. Although the idea of an optimal inflation tax is intriguing, we know of no evidence that US monetary policymakers ever considered smoothing the Treasury's revenue stream as an important consideration for policy.

More persuasive is Marvin's observation that it is longer-term interest rates that primarily influence macroeconomic behavior, and having a substantial impact on longer-term rates generates a desire for persistence in short-term rates. Because financial markets are forward looking, inertial behavior by the central bank can translate a small change in the current funds rate into meaningful changes in longer-term rates of longer maturities. This feature is also highlighted by Sack and Wieland (2000). Not wanting to "whipsaw" financial markets based on every new piece of information also can explain why rates tend to be adjusted gradually and unidirectionally. Affecting market behavior at longer horizons is also part of the reason that starting in the early 2000s the FOMC has increasingly resorted to forward guidance.

Other potential reasons for interest rate smoothing involve the facts that data are imperfectly measured and often revised. Additionally, some of the important underlying variables such as the output gap and the natural rate of interest are not directly observable. A number of researchers have shown that these data features generate a rationale for interest rate smoothing, as can the presence of model uncertainty.^{7}

In addition to these heuristic motivations for interest rate smoothing, Woodford (2003b) has shown that even if the policymaker merely wants to minimize interest rate volatility, interest rate persistence may arise through history dependence of optimal policies with commitment. And it is history dependence that allows policy to influence views about the far future and therefore allows less aggressive policy to achieve desirable outcomes.

Woodford also shows that in the absence of full commitment, introducing an additional preference for low volatility of changes in the interest rate leads to time-consistent policies that achieve outcomes close to those that can be achieved by full commitment. Thus, far from being an unduly timid policy, interest rate smoothing can enhance the conduct of monetary policy.

Woodford's work builds on Marvin's insights, formalizing some of the ideas in "Interest Rate Smoothing" and Goodfriend (1991). Woodford argues that another reason for preferring low interest rate volatility, besides a preference for orderly markets, is to reduce the likelihood of very high interest rates (and their associated distortions) and the likelihood of hitting the zero lower bound. Of course, the latter consideration was not on the horizon of policymakers when Marvin originally wrote his paper.

*Empirics: purposeful smoothing or inherited persistence?*

Broadly speaking, the theories rationalizing interest rate smoothing can be classified as purposeful vs. incidental.^{8} In the latter case, the central bank has no inherent preference for smoothing, and the observed persistence reflects the nature of the data to which the central bank responds (with some of those data being perhaps unobserved by the researcher). Two notable attempts to sort out these issues are Rudebusch (2006) and Coibion and Gorodnichenko (2012).^{9}

Rudebusch (2006) characterizes the problem in the context of a Taylor-style rule for monetary policy. He asks: Is the lagged interest rate an argument of that rule (purposeful smoothing) or is there a persistent error term representing some misspecification (an omitted variable that is persistent)? As he explains, this is a classic econometric problem, and it is notoriously difficult to distinguish the two cases without auxiliary information.^{10} Rudebusch brings in auxiliary information from the yield curve and argues that purposeful smoothing would show up as predictability in short-term rates to a greater degree than is evident in the term structure. He thus concludes that persistence of short-term rates is inherited from other variables to which the policy rate responds.

Coibion and Gorodnichenko (2012) conduct an exhaustive study broadly in the same spirit as Rudebusch but reach a different conclusion. They first take a direct approach, using a more general specification of both the policy rule and shock persistence, and find that the evidence favors purposeful smoothing. With respect to the yield curve, they find that predictability may be reduced if the public has different information about the economy or policy than the Fed. They also show that Federal Reserve Board staff forecasts more accurately predict future interest rates than private sector forecasts. Their summary of the evidence favors purposeful smoothing, and they support this conclusion with narrative evidence from the public and private comments of FOMC members.

## Narrative evidence and recent policy history

The statistical analysis in Coibion and Gorodnichenko (2012) is impressively thorough. And yet, given the fundamental challenge described by Rudebusch (2006), it is conceivable that another study could push the dial back toward inherited persistence. For this reason, narrative evidence — of which there is a plethora — has great potential to inform the debate. By narrative evidence we mean material such as speeches by FOMC members and transcripts of FOMC meetings, which are released with a five-year lag.

Coibion and Gorodnichenko summarize the narrative evidence up to approximately 2011. Since then, 10 more years of FOMC transcripts have become available. In addition, over that period, the observed persistence of policy rates has been unusually high: the fed funds rate target range remained at its lower bound until December 2015, and then the Fed raised that range in nine 25-basis point increments from December 2015 to December 2018. On the surface, this certainly looks like purposeful smoothing, with Federal Reserve policy becoming more persistent as opposed to economic fundamentals becoming more persistent. Increased persistence on the part of the Fed is probably related to its experience with the effective lower bound. With rates constrained by the lower bound for some time, the FOMC then kept rates at that lower bound until it was nearly certain that the appropriate funds rate was positive. And once it lifted off, it behaved cautiously to avoid having to reverse course and once again be constrained by the lower bound. One does not need to comb the transcripts to find support for this view: from December 2015 to May 2018, the FOMC statements contained slight variations on the following sentence:* The Committee expects that economic conditions will evolve in a manner that will warrant only gradual increases in the federal funds rate; the federal funds rate is likely to remain, for some time, below levels that are expected to prevail in the longer run.*

As longtime Federal Reserve economists, we view narrative evidence as important and as supporting the view that the FOMC does purposefully impart persistence in the short-term rate. A simple way to make this case is to consider the following question: Does the FOMC view the short-term interest rate as a meaningful "state variable"? If there is not purposeful interest rate smoothing, then the answer should be "no."

To us, the answer is unambiguously "yes." Virtually all policy discussions (when the interest rate is in play) are of the form "how much – if at all – should the policy rate rise or fall?" If there were no concern for smoothing, then the discussion would be about the proper *level *of the interest rate, not how much of a change is appropriate.

## Concluding remarks

The three of us worked with Marvin at the Richmond Fed for a collective total of almost 40 years. He played a role in hiring each of us. We can't stress enough his role in guiding policy work and setting the tone for the research environment at the Richmond Fed, first as an economist and then as research director and policy advisor. If we had to sum up that tone concisely, it would be that research and policy work are complementary. Along with much of Marvin's work, "Interest Rate Smoothing" exemplifies that complementarity.

The lunch table was an important forum for Marvin. During his many years in Richmond, conversations with as many as 12 people crowded around a table meant for six were a critical ingredient in creating the unique mix of a policy and research environment. And Marvin as much as anyone else facilitated those conversations. Marvin's contributions were wide ranging, sometimes heated, sometimes bewildering, and always with his tie tucked into his shirt (when we still wore ties).

**References**

Barro, Robert J. 1989. "Interest-rate targeting." *Journal of Monetary Economics* 23, no. 1 (January): 3-30.

Bernanke, Ben S. 2004. "Gradualism." Remarks at an economics luncheon cosponsored by the Federal Reserve Bank of San Francisco (Seattle Branch) and the University of Washington, Seattle, Washington, May 20.

Coibion, Olivier, and Yuriy Gorodnichenko. 2012. "Why Are Target Interest Rate Changes So Persistent?" *American Economic Journal: Macroeconomics* 4, no. 4 (October): 126-62.

Goodfriend, Marvin. 1985. "Reinterpreting Money Demand Regressions." *Carnegie-Rochester Conference Series on Public Policy* 22: 207-241.

Goodfriend, Marvin. 1986. "Monetary Mystique: Secrecy and Central Banking." *Journal of Monetary Economics* 17, no. 1 (January): 63-92.

Goodfriend, Marvin. 1987. "Interest Rate Smoothing and Price Level Trend-Stationarity." *Journal of Monetary Economics* 19, no. 3 (May): 335-348.

Goodfriend, Marvin. 1991. "Interest Rates and the Conduct of Monetary Policy*." Carnegie-Rochester Conference Series on Public Policy* 34 (Spring): 7–30.

Goodfriend, Marvin, and Robert G. King. 1997. "The New Neoclassical Synthesis and the Role of Monetary Policy." In *NBER Macroeconomics Annual 1997*, edited by Ben S. Bernanke and Julio J. Rotemberg, 231-283. Cambridge and London: National Bureau of Economic Research.

Mankiw, N. Gregory. 1987. "The Optimal Collection of Seigniorage: Theory and Evidence." *Journal of Monetary Economics* 20, no. 2 (September): 327-341.

McCallum, Bennett T. 1981. "Price Level Determinacy with an Interest Rate Policy Rule and Rational Expectations." *Journal of Monetary Economics* 8, no. 3: 319-329.

Rudebusch, Glenn D. 2006. "Monetary Policy Inertia: Fact or Fiction*?" International Journal of Central Banking* 2, no. 4 (December): 85-135.

Sack, Brian, and Volker Wieland. 2000. "Interest-Rate Smoothing and Optimal Monetary Policy: a Review of Recent Empirical Evidence." *Journal of Economics and Business* 52, no. 1-2 (January-April): 205-228.

Sargent, Thomas J., and Neil Wallace. 1975. "'Rational' Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule." *Journal of Political Economy* 83, no. 2 (April): 241–254.

Woodford, Michael. 2003a. *Interest and Prices. Foundations of a Theory of Monetary Policy*. Princeton and Oxford: Princeton University Press.

Woodford, Michael. 2003b. "Optimal Interest-Rate Smoothing." *Review of Economic Studies* 70, no. 4 (October): 861-886.

**Cite as**: Dotsey, Michael, Andreas Hornstein, and Alexander L. Wolman. 2022. "Interest Rate Smoothing." In *Essays in Honor of Marvin Goodfriend: Economist and Central Banker*, edited by Robert G. King and Alexander L. Wolman. Richmond, Va.: Federal Reserve Bank of Richmond.

^{1}

A Google search on "interest rate smoothing" turns up only a handful of references that predate Marvin's paper. Most of those are also by Marvin and coauthors, the exception being an NBER working paper version of Ben McCallum's classic paper (1981) on price level determinacy with an interest rate instrument. But smoothing is not a central component of McCallum's analysis.

^{2}

Conditional on their information set, the monetary authority always expects next period's inflation rate to be zero. However, the monetary authority knows that in the current period it is offsetting last period's price-level surprise. This means that the monetary authority generally expects current-period inflation to be nonzero conditional on their information set, which does not include the current price level.

^{3}

On the other hand, Woodford (2003a, p. 92) notes that price-level trend stationarity is more attractive if the monetary authority's objective is the variance of long-horizon price-level forecast errors. In this case, the desire to smooth interest rates may well be consistent with trend stationarity, because otherwise the variance of long-horizon forecast errors is increasing with the horizon. Marvin does acknowledge that low variance of long-horizon forecast errors might be desirable since it reduces the real rate of return variance of long-term nominal assets.

^{4}

Goodfriend and King (1997) is the subject of an essay by Michael Woodford elsewhere in this volume.

^{5}

See, e.g., the record of policy actions from February 1983 https://www.federalreserve.gov/monetarypolicy/files/fomcropa19830209.pdf.

^{6}

Goodfriend (1991) is the subject of an essay by John Taylor elsewhere in this volume.

^{7}

See, for example, Sack and Wieland (2000). The effects of model uncertainty are sensitive to the details; if the policymaker has a preference for robust policies (minimizing the probability of the worst outcomes), model uncertainty tends to work in favor of more aggressive policy.

^{8}

Rudebusch (2006) refers to the former as endogenous and the latter as exogenous.

^{9}

See also Bernanke (2004) for a useful survey.

^{10}

Marvin himself studied this econometric issue in the context of money demand equations (Goodfriend, 1985). See Mark Watson's essay in this volume.