A New Approach to Estimating the Natural Rate of Interest

The approach estimates the natural rate of interest from the velocity of M1, on the premise — established in Benati (2020) and taken as given here — that M1 velocity is, to a close approximation, the permanent component of short-term nominal interest rates. The paper is explicitly built as the interest-rate analogue of Cochrane’s (1994) proposal to estimate the permanent component of GNP from consumption: “in the same way as, as argued by Cochrane (1994), consumption can be treated as a good estimate of permanent GNP, M1 velocity can be regarded as a reliable estimate of the permanent component of the nominal short-term rate” (Section 1). The supporting evidence is a set of cointegrated structural VARs identified via long-run restrictions in which a single permanent shock explains close to 100 per cent of the forecast error variance of M1 velocity at all horizons, while the short rate retains a sizeable transitory component — dominant, for the United States, at all horizons up to about five years (Section 3.2, Figure 2). Taiwan, and to a lesser extent Japan, are the exceptions the author names.

Two steps, under monetary regimes that make inflation I(0): project the short-term monetary policy rate onto M1 velocity by OLS to obtain the nominal natural rate, then subtract inflation’s sample average (or the inflation target) to obtain the real natural rate (Sections 1 and 3.3). The projection is a cointegrating regression, so the slope estimator is super-consistent; the paper argues this means the level of the natural rate “and therefore also” the estimate itself is “likely reliably estimated” for samples of typical size, “which is of obvious, paramount importance within a policy context” (Section 3.3). The choice between subtracting the sample average and subtracting the target is made to depend on how credible the central bank’s target is. The paper also reports that more complex implementations based on cointegrated SVARs identified via long-run restrictions produce qualitatively the same and quantitatively close estimates, and relegates those to the Online Appendix, preferring the simpler estimator on grounds of simplicity and robustness to lag-order selection and initial conditions (Section 4, result (i), and footnote 26).

Because the nominal natural rate is driven by two things — permanent inflation shocks, via the Fisher effect, and permanent shocks to the real natural rate — so only when the former is switched off do permanent movements in velocity identify the latter. Formally, the paper writes the permanent component of the nominal rate as the sum of the permanent component of inflation and the real natural rate (equation 9). Under regimes that make inflation I(0) the permanent inflation component is zero, so permanent shifts in velocity “uniquely reflect permanent fluctuations in the natural rate of interest” (Section 3.3). If instead inflation were I(1) over the sample, the nominal natural rate would have to be purged of permanent inflation shocks — feasible, the paper says, via a cointegrated SVAR for velocity, the short rate and inflation, but an avenue it does not pursue because Section 5’s evidence says the current regimes have made inflation I(0). This is the paper’s binding scope condition: outside such regimes the simple two-step recipe is not claimed to work.

Yes, and it treats the euro area as the one awkward case. Section 5 reports bootstrapped p-values from Elliott, Rothenberg and Stock (1996) unit root tests together with Hansen (1999) grid-bootstrap median-unbiased estimates of the sum of the autoregressive coefficients, both with 10,000 bootstrap replications, split into “regimes with clearly-defined nominal anchors” and the previous periods. Under the anchored regimes the point estimates range between −0.40 and 0.66 and the upper limits of their bootstrapped 90 per cent intervals between −0.16 and 0.88, so “based on Hansen’s procedure there is no evidence that, under these regimes, inflation may have been I(1)”; a unit root is strongly rejected for Canada, New Zealand, the United Kingdom and the United States. For the euro area alone a unit root cannot be rejected at any lag order. The author argues this should be “quite heavily discounted,” on two grounds: the post-Lehman fall in euro area inflation, from an average of 2.01 per cent over 1999Q1–2008Q3 to 1.05 per cent over 2008Q4–2017Q3, looks like a very large but ultimately transitory shock that a short sample can mistake for a permanent one; and ECB Survey of Professional Forecasters five-year-ahead expectations stayed between 1.8 and 2.0 per cent throughout, suggesting agents read the shift as temporary. Bai–Perron tests find no break in the mean of inflation for any country over the anchored samples. Over the earlier, Great-Inflation-dominated periods the opposite holds, confirming Benati (2008).

They trend downward in all eight countries over the whole sample, and by the end of the sample most are negative. The countries are Australia, Canada, the euro area, New Zealand, Norway, Sweden, the United Kingdom and the United States, with samples ending 2019Q4 (2020 is excluded throughout except in the COVID section, to avoid distortion from the pandemic). Since the first half of the 1990s “the point estimate of the natural rate has fallen by about 6 per cent” for Australia, New Zealand and the United Kingdom, “and by about 8 per cent” for Canada — the paper’s “per cent” here denotes percentage points of a rate, the units it uses explicitly for the United States, where the estimate falls “by about 6 percentage points since the peak of 4.1 per cent reached in the second half of the 1990s” around the time of the “New Economy”; in the euro area and Sweden the decrease since the start of the new millennium is “about 4 percentage points” (Section 6, result (i)). At the end of the sample the U.S. point estimate has been about −2 per cent since 2014, and Canada, the euro area and Sweden reach −1.9, −1.7 and −2.4 per cent respectively in 2019. New Zealand and Norway are the only two countries whose 2019 point estimate is still — “barely” — positive.

The paper reports them as bootstrap probabilities rather than as point estimates alone, and they are high at the end of the sample but not uniform. Using the fraction of 10,000 bootstrap replications in which the real natural rate is estimated to have been negative — which the author says he will refer to interchangeably as “the probability that the natural rate had been negative” — the end-of-sample figure is 100 per cent for both the euro area and Sweden and slightly greater than 90 per cent for Canada and the United States (Section 6, result (ii)). For the nominal natural rate the corresponding end-of-sample figures are lower and more dispersed: 95 per cent in Sweden, 50 per cent in Canada, and around 60 per cent in both the euro area and the United States (Section 4, result (v)). The paper also notes that for the real rate the probability was already rising before Lehman’s collapse in several countries, especially the euro area, Norway and the United Kingdom, whereas for the nominal rate it had been close to nil throughout before then.

The paper poses the question itself and answers it by appeal to the co-movement between the estimated natural rate and the ex post real rate, not by an independent validation exercise. Taking Sweden’s end-2019 estimate as the test case — a number the author concedes “might appear to some researchers as manifestly absurd” — the defence is that since Lehman’s collapse, and in fact since the beginning of the millennium, the estimated natural rate has closely tracked the fall in the ex post real rate. That pattern is read as saying Riksbank policy was on average broadly neutral and the fall in the ex post real rate was a reaction to the fall in the natural rate rather than a deviation from it; the corroborating evidence offered is that since the 2008–2009 recession Swedish annual inflation rose slowly from about 1 per cent in early 2010 to 2.5 per cent at the end of 2019 while GDP growth fluctuated around about 2 per cent, i.e. neither accelerating nor collapsing. The author states a very similar argument can be made for the remaining countries, which “suggests that the estimates in Figure 5 are likely plausible” — a calibrated claim, not a demonstration.

Very close to Fiorentini, Galesi, Pérez-Quirós and Sentana (2018); materially lower than Holston, Laubach and Williams (2017) and than the range in Williams (2017). The paper notes that in Fiorentini et al.’s Figure 10 the U.S. natural rate falls from 2.5–3 per cent in the second half of the 1990s to about −2 per cent in 2016 and the euro area rate from 2 per cent in 2000 to about −1 per cent in 2016, figures very close to its own. Its U.S. estimates are also “materially lower” than the roughly 0-to-1 per cent range for 2016 reported in Williams’ (2017) Figure 1. On Holston et al., the paper does not adjudicate directly but defers to Fiorentini et al.’s arguments that those estimates “should be regarded as less reliable.” It separately observes that DSGE-based estimates are often far more volatile, citing Barsky, Justiniano and Melosi (2014), whose U.S. natural rate fluctuates since the early 1990s between about −7 and about 12 per cent.

That unobserved-components filters impose orthogonality between the individual unobserved components, and if that assumption is wrong it will distort the estimates. The paper points out that in Holston et al. (2017) the permanent component of log real GDP, its time-varying drift, and an additional random-walk component of the natural rate are all postulated to be orthogonal to one another. “The assumption of orthogonality might be correct, but if it is not, imposing it upon the data is likely going to distort the estimates.” The approach proposed here imposes no such assumption; what it does instead is hinge everything on the single premise that M1 velocity is the long-horizon component of the short rate (Section 3.3). Whether that is a weaker or merely a different assumption the paper does not argue at length — it is, on the paper’s own presentation, the trade being made.

Monthly, unsmoothed estimates for Canada, the euro area, the United Kingdom and the United States show sharp and sudden declines in both the nominal and the real natural rate in three of the four countries after Lehman’s collapse on 15 September 2008. From August to October 2008 — one month before to one month after — the real natural rate declines by −0.30 per cent in Canada, −0.27 in the euro area and −0.42 in the United States, which the paper reports as −1.80, −1.62 and −2.52 per cent on an annual basis. The United Kingdom’s fall over the same window, −0.06 per cent (−0.36 annualised), is described as comparatively minor. From August to December 2008 the declines are −0.81, −0.37 and −0.71 per cent for Canada, the euro area and the United States, and through December 2009 they reach −1.13, −1.02 and −1.47 per cent; the United Kingdom’s decline from August 2008 to December 2009 is −0.40 per cent. The bootstrap probability of a negative real natural rate “literally skyrocketed” in October 2008 for Canada and the euro area and rose very sharply, though less dramatically, for the United States; for the United Kingdom the increase was continuous across the whole sample and apparently unaffected by Lehman.

The Great Depression and COVID, both explicitly flagged as to be “regarded with some caution” — the first because of lower pre-WWII data quality, the second because of the idiosyncratic nature of the COVID shock. For the interwar United States (1920Q1–1941Q3, bookended by the end of World War I and Pearl Harbor, using Friedman–Schwartz M1, the New York Fed discount rate and Balke–Gordon nominal GNP and deflator), the real natural rate is broadly stable through the 1920s apart from a temporary fall in the 1921 recession, then collapses from 5.6 to 2.8 per cent between the October 1929 crash and Roosevelt’s March 1933 inauguration; it stabilises around 2.8–3.0 per cent from 1933 and falls by nearly a further percentage point after “(the mistake of) 1938.” The paper reads this as according well with Eggertsson (2008), whose two tenets are that the Depression’s onset was caused by a dramatic fall in the real natural rate and that the post-1933 recovery came from the New Deal’s policy regime change rather than from a rebound in the natural rate. For COVID, monthly point estimates from January to June 2020 fall by −0.84 per cent in the United States, −0.76 in Canada, −0.75 in the euro area and −0.44 in the United Kingdom, which the paper describes as broadly comparable to Lehman’s impact — “taken at face value,” with the caveats restated.

Two things, both stated by the author rather than inferred here. First, the higher the data frequency, the harder it is for economic agents to perform the permanent–transitory decomposition the method attributes to them: “whereas it is by no means unreasonable to believe that, within the space of a quarter, agents may be able to effectively disentangle the permanent and transitory components of short-term nominal rates, this assumption becomes much less credible, e.g., at the weekly frequency” (Section 7.2, credited to a referee). Second, the entire analysis runs on the assumption that M1 velocity and the short rate feature exact unit roots; the author reports that Elliott et al. tests are consistent with either exact or near unit roots, that point estimates are identical by construction under the near-unit-root alternative, and that confidence bands bootstrapped from the corresponding near-unit-root VAR are virtually identical. He also addresses a referee’s prior that financial innovation injected a second stochastic trend into velocity, arguing that if it had there would be no cointegration between velocity and the short rate, and that the documented cointegration “logically refutes” the notion. Perron–Yabu tests detect no break in the projection regression’s intercept or slope in any case, and Hansen–Johansen tests detect no break in the cointegration vector.

That the post-1980 conventional wisdom is wrong on one specific point: a particular transformation of a monetary aggregate carries crucial information for policy. The conclusion puts it as follows: since the early 1980s “it has been conventional wisdom among macroeconomists and policymakers that monetary aggregates contain little useful information for monetary policy. In this paper I have shown that, in fact, a specific transformation of a monetary aggregate, the velocity of M1, contains crucial information about the evolution of the real natural rate of interest” (Section 9). The claim is deliberately narrow — it is about M1 velocity as an indicator of the natural rate, not a general rehabilitation of money growth as a policy target or an intermediate variable, and the paper nowhere argues for targeting a monetary aggregate.