The Submit-Pandemic r* – Liberty Avenue Economics


The talk concerning the pure price of curiosity, or r*, typically overlooks the purpose that there’s a whole time period construction of r* measures, with short-run estimates capturing present financial circumstances and long-run estimates capturing extra secular components. The entire time period construction of r* issues for coverage: shorter run measures are related for gauging how restrictive or expansionary present coverage is, whereas longer run measures are related when assessing terminal charges. This two-post sequence covers the evolution of each within the aftermath of the pandemic, with at this time’s submit focusing particularly on long-run measures and tomorrow’s submit on short-run r*.

There may be arguably some proof that short-run r* is at present elevated relative to pre-COVID ranges: The financial system has confirmed to be extraordinarily resilient and spreads stay comparatively low, despite the current banking turmoil. Estimates from the New York Fed DSGE mannequin, which we talk about in tomorrow’s submit, affirm this evaluation. As proven in June, the mannequin expects short-run actual r* to be 2.5 p.c by the tip of the 12 months. Proof on whether or not long-run r*—that’s, the persistent part, or pattern, in r*—has risen after COVID is way weaker. We use a battery of fashions, from VARs to DSGEs, to estimate these developments, and these fashions attain completely different conclusions. In line with VAR fashions, long-run r* has roughly remained fixed and, if something, declined a bit since late 2019, reaching 0.75 p.c in actual phrases. In line with the DSGE mannequin, long-run r* has as an alternative risen by nearly 50 foundation factors throughout this era, and is now about 1.8 p.c.

Lengthy-Run r*: Totally different Solutions from Totally different Fashions

The chart beneath reveals the developments in r* obtained from two fashions offered on this Brookings paper by Del Negro, Giannone, Giannoni, and Tambalotti (2017). The 2 fashions are a “stylish” VAR (or, VAR with frequent developments; black dashed line) and a DSGE (blue dashed line) mannequin able to capturing low-frequency actions in productiveness development and the comfort yield. A key results of that paper, reproduced within the chart beneath with up to date information, was that as much as the mid-2010s these two very completely different methodologies delivered practically equivalent outcomes. After the pandemic, the estimates diverge notably nevertheless, with the VAR estimates trending down barely, and the DSGE estimates trending up sharply.

The Low-Frequency Element of r* within the VAR and DSGE Fashions

Supply: Authors’ calculations.
Observe: The dashed black (blue) traces present the posterior medians and the shaded grey (blue) areas present the 68 p.c posterior protection intervals for the VAR (DSGE) estimates of the low-frequency part of the actual pure price of curiosity.

The desk beneath studies numerical values of the adjustments within the r* developments (that’s, long-run r*) in keeping with a wide range of fashions. It reveals that from the fourth quarter of 2019 (pre-COVID) to the second quarter of 2023 the pattern in r* has decreased by somewhat greater than 10 foundation factors, in keeping with the baseline stylish VAR. For a variant of this VAR the place we additionally use information on consumption development and therefore make inference on pattern development, the decline is a bit bigger at 20 foundation factors. In line with the DSGE, long-run r* as an alternative went up by nearly 50 foundation factors after COVID. We additionally report the outcomes from the international stylish VAR proposed by Del Negro, Giannone, Giannoni, and Tambalotti (2019). In line with this mannequin, which is estimated with annual information from seven superior international locations, each world and U.S. long-run r* rose by about 15 foundation factors from 2019 to 2022, though the rise isn’t important.

The pre-COVID decline in long-run r* because the late Nineties is similar to that reported within the Brookings paper, the place the pattern ends in 2016. In line with the stylish VAR, long-run r* had fallen pre-COVID by somewhat greater than 1.5 share factors. The VAR with consumption implied a bigger decline of just about 2 pp, whereas in keeping with the DSGE the decline was about 1 pp. Due to the divergence within the post-COVID developments the general decline in r* turns into a bit bigger in keeping with the 2 VAR fashions—1 and 1.75 pp, respectively—however falls to about 60 foundation factors in keeping with the Brookings DSGE mannequin.

Change in Lengthy-Run r* In line with Totally different Fashions

Submit-COVID Change
2023:Q2-2019:This autumn
r*t cyt gt
VAR -0.14
(-0.15, -0.12)
Pr>0: 9
(-0.09, -0.04)
Pr>0: 20
VAR with cons. -0.19
(-0.22, -0.18)
Pr>0: 7
(-0.11, -0.05)
Pr>0: 21
(-0.13, -0.09)
Pr>0: 16
Brookings DSGE 0.48
(0.06, 0.89)
Pr>0: 98
(-0.01, 0.57)
Pr>0: 96
(-0.04, 0.48)
Pr>0: 94
World VAR 0.14
(-0.44, 0.71)
Pr>0: 68
Pre-COVID Decline
2019:This autumn–1988:Q1
r*t cyt gt
VAR -1.61
(-1.78, -1.34)
Pr<0: 99
(-1.05, -0.89)
Pr<0: 99
VAR with cons. -1.88
(-2.08, -1.52)
Pr<0: 99
(-0.83, 0.66)
Pr<0: 99
(-1.13, -0.86)
Pr<0: 99
Brookings DSGE -1.03
(-1.51, -0.54)
Pr<0: 99
(-1.05, -0.14)
Pr<0: 99
(-0.62, -0.20)
Pr<0: 99
World VAR -1.69
(-3.27, -0.14)
Pr<0: 98
Submit-COVID Decline
r*t cyt gt
VAR -1.75
(-1.93, -1.46)
Pr<0: 99
(-1.13, -0.93)
Pr<0: 99
VAR with cons. -2.07
(-2.30, -1.71)
Pr<0: 99
(-0.93, -0.71)
Pr<0: 99
(-1.26, -0.95)
Pr<0: 99
Brookings DSGE -0.55
(-0.99, -0.24)
(-0.73, 0.09)
Pr<0: 93
(-0.44, 0.05)
Pr<0: 94
World VAR -1.56
(-3.17, 0.02)
Pr<0: 97
Supply: Authors’ calculations.
Observe: For every pattern, the desk studies the posterior median and the 95 p.c (parentheses) posterior protection intervals, in addition to the posterior chance in share factors that the change is optimistic (for the 2023:Q2-2019:This autumn interval) or unfavourable (for the 2019:This autumn-1998:Q1 and 2023:Q2-1998:Q1 durations).

The Time period Construction of r* within the DSGE Mannequin

What drives these variations throughout fashions? Since a lot of the post-COVID motion takes place within the DSGE mannequin, we flip to this mannequin with a view to perceive its interpretation of the information. The chart beneath reveals your entire time period construction of r* in keeping with the mannequin—specifically the short-run r* and the 5-year, 10-year, and 30-year r* measures (which now we have to date known as long-run r*), the place the x-year r* is the anticipated worth of r* x-years forward (that’s, the x-years r* is a ahead price). Whereas the short-run r* may be very risky, its fluctuations seize effectively the state of the enterprise cycle within the U.S.: short-run r* is low throughout recessions or durations of stagnation (for instance, early Nineties, early 2000s, the good recession and its aftermath, and the COVID recession) and excessive when the financial system is booming. Of late, the U.S. financial system has remained extraordinarily resilient whilst financial coverage has tightened, as mentioned in tomorrow’s submit, and the estimates of r* are elevated.

The chart additionally reveals that whereas the volatility of the r* measure not surprisingly diminishes with the horizon–5-year is much less risky than short-run r*, 10-year is much less risky than 5-year, and so forth—all these measures are correlated with each other. This statement factors to an essential distinction between stylish VAR and DSGE estimates of future r*. Whereas by design the stylish VAR separates the pattern from the cycle—in econometric parlance, the mannequin performs a pattern/cycle decomposition—within the DSGE mannequin all the varied frequencies are inextricably linked. This doesn’t imply that longer run DSGE measures of r* transfer with each motion of short-run r*—within the Nineties recession for example short-run r* falls fairly a bit however the different measures don’t budge. Nonetheless, it seems that within the DSGE, actions in short-run r* are inclined to have some data for longer run measures, whereas within the stylish VAR this data is ignored.

The Time period Construction of r* within the DSGE Mannequin

Supply: Authors’ calculations.

We conclude this submit by relating the DSGE estimates to the r* estimates from Laubach and Williams (2003, LW) and Holston, Laubach, and Williams (2017, HLW), obtained with post-COVID information utilizing the method in Holston, Laubach, and Williams (2023). The chart beneath plots the time sequence of those measures along with  the 5-year DSGE r*, which within the Brookings paper we discovered to be most correlated with the LW and HLW measures. The chart reveals that the LW and HLW r* estimates declined sharply with the Nice Recession, going from about 2.5 to 1 p.c, after which they continue to be roughly regular at about 1 p.c. The DSGE 5-year r* tracks the LW and HLW measures effectively from the early Nineties to the early 2010s. It then continues to say no going beneath zero, however finally rises to a degree akin to that of the LW mannequin on the finish of the pattern.

DSGE 5-12 months r* and the LW and HLW Measures

Supply: Authors’ calculations.

Conducting inference on latent variables akin to r* is a tough enterprise, as any estimate is inherently mannequin dependent. In lots of circumstances the completely different fashions agree: for example, there may be widespread proof that r* declined from the mid-Nineties till the aftermath of the Nice Recession and remained low till the COVID pandemic. Approaches disagree by way of assessing what occurred afterward, with fashions relying extra on long-run averages indicating that long-run r* remained low, whereas approaches such because the DSGE the place short- and long-run measures are extra tightly related point out that long-run r* has risen. Tomorrow’s submit focuses on short-run r* and its implications for the financial system.

Katie Baker is a former senior analysis analyst within the Federal Reserve Financial institution of New York’s Analysis and Statistics Group.

Logan Casey is a senior analysis analyst within the Federal Reserve Financial institution of New York’s Analysis and Statistics Group.

Marco Del Negro is an financial analysis advisor in Macroeconomic and Financial Research within the Federal Reserve Financial institution of New York’s Analysis and Statistics Group.

Aidan Gleich is a former senior analysis analyst within the Federal Reserve Financial institution of New York’s Analysis and Statistics Group.

Ramya Nallamotu is a senior analysis analyst within the Federal Reserve Financial institution of New York’s Analysis and Statistics Group.

The right way to cite this submit:
Katie Baker, Logan Casey, Marco Del Negro, Aidan Gleich, and Ramya Nallamotu, “The Submit-Pandemic r*,” Federal Reserve Financial institution of New York Liberty Avenue Economics, August 9, 2023,

The views expressed on this submit are these of the writer(s) and don’t essentially mirror the place of the Federal Reserve Financial institution of New York or the Federal Reserve System. Any errors or omissions are the accountability of the writer(s).


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