---
ticker: "USSHR"
title: "U.S. Shadow Federal Funds Rate"
unit: "%"
frequency: "Monthly"
source: "Wu and Xia (2016); Black (1995)"
release: "Updated Monthly"
category: "Interest Rates"
country: "US"
language: "en"
canonical: "https://kred.dev/en/series/USSHR"
license: "https://creativecommons.org/licenses/by-nc-nd/4.0/"
latest_value: 4.16
latest_date: "2026-09-30"
first_date: "1990-01-31"
observations_total: 441
observations_shown: 120
---

# U.S. Shadow Federal Funds Rate

## Overview

The shadow federal funds rate for the United States, the latent short rate the term structure implies while the policy rate is held at its floor, filtered monthly from forward rates at parameters estimated once on the paper's own sample.

## Key Figures

|  | Value | Date |
|---|---|---|
| Latest | 4.16 | 2026-09-30 |
| Change from previous | +0.07 | 2026-08-31 |
| Change over one year | +0.14 | 2025-09-30 |
| Highest on record | 8.14 | 1990-04-30 |
| Lowest on record | -2.89 | 2014-05-31 |
| Period covered | 1990-01-31 – 2026-09-30 |  |
| Observations | 441 |  |

## Recent observations

| Date | Value | Change |
|---|---|---|
| 2016-10-31 | 0.54 | +0.01 |
| 2016-11-30 | 0.44 | -0.09 |
| 2016-12-31 | 0.43 | -0.01 |
| 2017-01-31 | 0.39 | -0.05 |
| 2017-02-28 | 0.40 | +0.01 |
| 2017-03-31 | 0.64 | +0.24 |
| 2017-04-30 | 0.85 | +0.21 |
| 2017-05-31 | 1.03 | +0.18 |
| 2017-06-30 | 1.06 | +0.03 |
| 2017-07-31 | 1.08 | +0.02 |
| 2017-08-31 | 1.10 | +0.02 |
| 2017-09-30 | 1.11 | 0.00 |
| 2017-10-31 | 1.16 | +0.05 |
| 2017-11-30 | 1.28 | +0.13 |
| 2017-12-31 | 1.41 | +0.12 |
| 2018-01-31 | 1.40 | -0.01 |
| 2018-02-28 | 1.55 | +0.15 |
| 2018-03-31 | 1.65 | +0.10 |
| 2018-04-30 | 1.71 | +0.06 |
| 2018-05-31 | 1.77 | +0.06 |
| 2018-06-30 | 1.89 | +0.12 |
| 2018-07-31 | 1.92 | +0.03 |
| 2018-08-31 | 2.01 | +0.09 |
| 2018-09-30 | 2.17 | +0.16 |
| 2018-10-31 | 2.30 | +0.13 |
| 2018-11-30 | 2.40 | +0.10 |
| 2018-12-31 | 2.53 | +0.13 |
| 2019-01-31 | 2.49 | -0.04 |
| 2019-02-28 | 2.45 | -0.04 |
| 2019-03-31 | 2.40 | -0.06 |
| 2019-04-30 | 2.41 | +0.01 |
| 2019-05-31 | 2.41 | 0.00 |
| 2019-06-30 | 2.18 | -0.23 |
| 2019-07-31 | 2.17 | -0.01 |
| 2019-08-31 | 2.01 | -0.16 |
| 2019-09-30 | 1.96 | -0.05 |
| 2019-10-31 | 1.65 | -0.30 |
| 2019-11-30 | 1.64 | -0.02 |
| 2019-12-31 | 1.61 | -0.03 |
| 2020-01-31 | 1.62 | +0.01 |
| 2020-02-29 | 1.40 | -0.22 |
| 2020-03-31 | 0.68 | -0.73 |
| 2020-04-30 | 0.51 | -0.17 |
| 2020-05-31 | 0.53 | +0.02 |
| 2020-06-30 | 0.47 | -0.05 |
| 2020-07-31 | 0.33 | -0.15 |
| 2020-08-31 | 0.34 | +0.01 |
| 2020-09-30 | 0.14 | -0.20 |
| 2020-10-31 | 0.24 | +0.10 |
| 2020-11-30 | -0.17 | -0.40 |
| 2020-12-31 | -0.20 | -0.04 |
| 2021-01-31 | -0.33 | -0.13 |
| 2021-02-28 | -0.38 | -0.05 |
| 2021-03-31 | -1.43 | -1.05 |
| 2021-04-30 | -1.64 | -0.21 |
| 2021-05-31 | -1.83 | -0.19 |
| 2021-06-30 | -1.66 | +0.17 |
| 2021-07-31 | -1.77 | -0.10 |
| 2021-08-31 | -1.67 | +0.10 |
| 2021-09-30 | -1.69 | -0.02 |
| 2021-10-31 | -1.63 | +0.07 |
| 2021-11-30 | -1.78 | -0.16 |
| 2021-12-31 | -1.09 | +0.69 |
| 2022-01-31 | -0.20 | +0.89 |
| 2022-02-28 | 0.21 | +0.41 |
| 2022-03-31 | 0.50 | +0.28 |
| 2022-04-30 | 0.97 | +0.47 |
| 2022-05-31 | 1.13 | +0.16 |
| 2022-06-30 | 2.76 | +1.64 |
| 2022-07-31 | 2.79 | +0.03 |
| 2022-08-31 | 3.02 | +0.23 |
| 2022-09-30 | 3.75 | +0.73 |
| 2022-10-31 | 4.49 | +0.75 |
| 2022-11-30 | 4.85 | +0.35 |
| 2022-12-31 | 4.92 | +0.07 |
| 2023-01-31 | 5.11 | +0.20 |
| 2023-02-28 | 5.55 | +0.44 |
| 2023-03-31 | 5.08 | -0.47 |
| 2023-04-30 | 5.35 | +0.27 |
| 2023-05-31 | 5.79 | +0.43 |
| 2023-06-30 | 6.25 | +0.47 |
| 2023-07-31 | 5.83 | -0.43 |
| 2023-08-31 | 5.79 | -0.03 |
| 2023-09-30 | 5.96 | +0.16 |
| 2023-10-31 | 5.78 | -0.17 |
| 2023-11-30 | 5.67 | -0.11 |
| 2023-12-31 | 5.38 | -0.29 |
| 2024-01-31 | 5.30 | -0.08 |
| 2024-02-29 | 5.37 | +0.07 |
| 2024-03-31 | 5.37 | 0.00 |
| 2024-04-30 | 5.35 | -0.02 |
| 2024-05-31 | 5.44 | +0.09 |
| 2024-06-30 | 5.45 | 0.00 |
| 2024-07-31 | 5.28 | -0.16 |
| 2024-08-31 | 4.91 | -0.37 |
| 2024-09-30 | 4.39 | -0.52 |
| 2024-10-31 | 4.41 | +0.02 |
| 2024-11-30 | 4.47 | +0.06 |
| 2024-12-31 | 4.17 | -0.30 |
| 2025-01-31 | 4.16 | -0.01 |
| 2025-02-28 | 4.18 | +0.02 |
| 2025-03-31 | 4.19 | +0.01 |
| 2025-04-30 | 4.27 | +0.08 |
| 2025-05-31 | 4.50 | +0.23 |
| 2025-06-30 | 4.45 | -0.04 |
| 2025-07-31 | 4.54 | +0.08 |
| 2025-08-31 | 4.34 | -0.20 |
| 2025-09-30 | 4.02 | -0.32 |
| 2025-10-31 | 3.96 | -0.06 |
| 2025-11-30 | 3.94 | -0.02 |
| 2025-12-31 | 3.73 | -0.21 |
| 2026-01-31 | 3.69 | -0.04 |
| 2026-02-28 | 3.76 | +0.07 |
| 2026-03-31 | 3.84 | +0.07 |
| 2026-04-30 | 3.81 | -0.03 |
| 2026-05-31 | 3.83 | +0.02 |
| 2026-06-30 | 4.02 | +0.19 |
| 2026-07-31 | 4.08 | +0.06 |
| 2026-08-31 | 4.09 | +0.01 |
| 2026-09-30 | 4.16 | +0.07 |

## Definition

USSHR is the shadow federal funds rate, the latent short rate that stands in for the policy rate once that rate is pinned at its floor. The short rate that clears the market is the larger of the shadow rate and that floor, so the two coincide whenever the floor is slack and only the shadow rate keeps moving once the floor binds, which is the device Black (1995) proposed and Wu and Xia (2016) estimate. The floor used here is 0.25 %, the value the paper adopts. The series is a filtered latent state of KRED's own estimated model and never an observed rate, a measurement or a passthrough of anyone's published series.

The parameters are estimated once, on the paper's own sample of 282 months from 1990-01-31 to 2013-06-30, and are never re-estimated afterwards. The states are then filtered forward by a single causal pass over the whole sample of 438 months from 1990-01-31 to 2026-06-30 at that one parameter vector. Every value after the estimation sample is therefore produced at parameters fixed before it, which is a property of the construction rather than a detail of it, and it travels with the series on every surface (Joslin, Singleton, and Zhu 2011; Hamilton and Wu 2012).

Over the 108 months in which the floor binds, this path agrees with the published shadow-rate series that accompanies the original work to a mean absolute difference of 0.0609 pp, a maximum of 0.1668 pp and a correlation of 0.9992. That is agreement and nothing more. Whether the published series is produced by re-estimation, by fixed-parameter filtering or otherwise is unverified, so the agreement is not presented as a shared method, as a continuation of that series or as a newer vintage of it. Away from the floor the shadow rate should track the policy rate, and over the 330 unbound months it sits 0.293 pp from it on average, inside the tolerance of 0.3702 pp fixed before the comparison; measured with one comparator on both sides KRED's distance is 0.271 pp against the published series' 0.270 pp, so KRED sits slightly farther and no claim of equal closeness is made.

The level is not exact. Perturbing each gated parameter by one robust standard error in either direction moves the published path by as much as 0.9184 pp against a published rounding unit of 0.01 pp, and at the sample's lowest month, 2014-05-31, the envelope around a shadow rate of −2.8875 % runs from −3.0050 % to −2.7738 %. The forward-rate expression the filter is built on is an approximation whose error grows with maturity and with time spent at the floor, and whose fit degrades after the estimation sample, so the level of any single month is read inside that sensitivity rather than as a reading in its own right (Bauer, Rudebusch, and Wu 2012; Bauer and Rudebusch 2020).

Three statements bound what the series is. It is a latent state, so nothing here is a rate at which anything is borrowed or lent. The published surface is the monthly shadow rate and the date it carries, while the factors, the fitted forwards, every parameter and every likelihood stay unpublished. And the estimand is the shadow federal funds rate of this particular three-factor shadow-rate term structure model at this floor, so a shadow rate built for another market or from a different specification is a different object and no comparison of that kind is offered here (Krippner 2013; Christensen and Rudebusch 2015; Creal and Wu 2013; Kim and Wright 2005).

## Methodology

**(1) Model.** Three latent factors drive the whole curve. The shadow rate is affine in them, an intercept plus a fixed loading vector applied to the factors, and the factors follow a first-order vector autoregression under both the physical and the pricing measure, the two parameter sets differing only by the prices of risk that carry one measure into the other (Wu and Xia 2016; Joslin, Singleton, and Zhu 2011).

**(2) The floor.** A one-period forward rate under the floor is the expectation of a truncated normal, which the study writes in closed form as the floor plus the pricing-measure standard deviation of the shadow rate at that horizon multiplied by a function of the standardized distance between the unconstrained forward rate and the floor. That function is the standardized distance weighted by the standard normal distribution function plus the standard normal density, so far above the floor it approaches the distance itself and the expression collapses to the unconstrained forward rate, while far below it approaches zero and the forward rate settles onto the floor (Black 1995; Krippner 2013).

**(3) Inputs.** The observation vector is one-month forward rates at seven maturities out to ten years, read on the last parameter-bearing day of each month from a fitted zero curve of the extended parametric family that is standard for this panel (Nelson and Siegel 1987; Svensson 1994; Gürkaynak, Sack, and Wright 2007). Each forward is formed from continuously compounded zero yields as the longer maturity's yield scaled by its own tenor less the shorter maturity's yield scaled by its tenor, and the filter works in monthly decimal units.

**(4) Estimation.** Two deterministic stages. A Gaussian model without the floor is fitted first by linear filtering, and its optimum starts the fit of the floored model, which is estimated by an extended Kalman filter that linearizes the floor function around the current state estimate. Identification follows the study's normalization, with the loading vector fixed, the pricing-measure intercept set to zero, the pricing-measure transition matrix in real Jordan form with ordered eigenvalues and the volatility matrix lower triangular, leaving 22 free parameters and one common measurement variance. Estimation runs on the paper's own sample of 282 months and nowhere else, so the downward bias that afflicts estimated persistence in samples of this length is carried as stated rather than corrected here (Bauer, Rudebusch, and Wu 2012; Hamilton and Wu 2012).

**(5) Filtering forward.** The published path is a single causal pass of the same filter over all 438 months at that parameter vector, initialized once at the unconditional mean and covariance of the factor process and never re-initialized. No smoother touches the series, so a value at a past date is not revised by later information, which is the opposite of the vintage behaviour that filtered-and-re-estimated term structure states show (Kim and Wright 2005; Kim and Orphanides 2012).

**(6) Disclosures computed beside the path.** The approximation error of the forward expression is measured by simulation against an exact evaluation, averaging 4.41 basis points at the ten-year forward and 1.54 basis points at the ten-year yield across every January in the sample, against 2.50 and 1.02 basis points over the paper's own Januaries and the 2.30 and 0.78 basis points it reports. The error therefore grows with maturity and the fit degrades after the estimation sample. Sensitivity to the parameter vector is measured by perturbing each gated parameter by one robust standard error in both directions and re-filtering, which moves the path by as much as 0.9184 pp against a published rounding unit of 0.01 pp (Creal and Wu 2013; Bauer and Rudebusch 2020).

**(7) The bound months.** A month counts as bound when the month-end upper target is at or below 0.25 %, which gives 108 of the 438 months, the first at 2008-12-31. The original study's own shading of the bound period begins at 2009-01, and that one-month difference is disclosed here and never substituted. Part of any distance between the shadow rate and the policy rate outside those months is a timing mismatch rather than model error, since the shadow rate is a month-end quantity while the policy rate it is set against is a monthly average (Christensen and Rudebusch 2015).

## Applications in Economics

Once a policy rate reaches its floor it stops recording changes in the stance, while asset purchases, guidance about the path and the expected duration of the floor keep moving the curve. A shadow rate converts what the curve says about that stance back into rate units, which is the reason the construction exists at all (Black 1995; Wu and Xia 2016).

Substituted for the policy rate in a reaction function or a macroeconomic regression, it restores a continuous stance variable across the bound period, which is otherwise a stretch of constant readings that no rate-based comparison can use. The stance is set at the shortest maturity while transmission runs through longer rates, so a measure defined at the short end is what such comparisons need (Bindseil 2004; Borio 1997).

A shadow rate is not a single well-defined number. Different shadow-rate term structure models applied to the same curve return materially different paths, and the sensitivity of such estimates to the specification, to the number of factors and to the floor assumed is documented rather than disputed (Krippner 2013; Christensen and Rudebusch 2015; Bauer and Rudebusch 2020; Hamilton and Wu 2012). The estimand here is this particular three-factor model at this floor and nothing wider (Joslin, Singleton, and Zhu 2011).

Three limits bound the reading. The level is model-identified and its sensitivity to the parameter vector reaches 0.9184 pp, far larger than the unit at which it is published, so a difference of a tenth of a percentage point between two months is not a finding. The parameters are fixed on the paper's own sample and the fit degrades after it, which the approximation-error figures show directly (Creal and Wu 2013). And inside the bound months nothing observed pins the level down, so what is read there is the model's fixed dynamics applied to the observed forward curve rather than a statement about a stance anyone quoted (Kim and Wright 2005; Kim and Orphanides 2012).

No forecast is offered here, and no turning point is identified. What the series reports is the level the model assigns to each month, read inside the sensitivity band that travels with it, and nothing on this page is offered as agreement or disagreement with a shadow rate built for another market or by another design (Diebold 2015).

## Applications in Financial Markets

For a rates desk the shadow rate is the form in which the stance stays legible once the policy rate can fall no further, so it enters relative-value work as the stance variable that the front end of the curve is otherwise unable to express while the policy rate is pinned (Wu and Xia 2016; Black 1995). What a long forward rate prices is an expected path of short rates together with the compensation demanded for bearing risk, and the shadow rate speaks to the first of those two parts alone (Hicks 1939; Cochrane and Piazzesi 2005).

Three measurement facts bear on that use. The number is filter output rather than a price, so its level carries the specification's assumptions and a different shadow-rate model on the same curve returns a different answer (Krippner 2013; Christensen and Rudebusch 2015). The estimated persistence of the factors is biased downward in samples of this length and that bias transmits into the level (Bauer, Rudebusch, and Wu 2012; Bauer and Rudebusch 2020). And the inputs are read off a fitted curve rather than quoted, so the series inherits that curve's fitting conventions (Nelson and Siegel 1987; Svensson 1994; Gürkaynak, Sack, and Wright 2007).

A view formed on this reading is expressed through the curve rather than through the shadow rate, since the shadow rate is not an instrument and no market lends at it. Exposure is measured by the duration that maps yield changes into price changes and managed by immunization defined on the whole term structure (Macaulay 1938; Fisher and Weil 1971).

Two uses are ruled out. A threshold reading taken from the level alone is not supported, because a one-standard-error perturbation of the parameter vector moves that level by far more than the unit at which it is published. And the series is not a decomposition of the curve into expectations and compensation, since it is a single state of the short end and carries no such split (Kim and Wright 2005; Diebold 2015).

## Statistical Tests

USSHR is a latent short rate filtered from observed one-month forward rates by one causal pass of an extended Kalman filter at a parameter vector estimated once on the paper's own sample and never re-estimated afterwards, so the statistical object is a model-derived rate level whose persistence is inherited from the observed forward panel rather than manufactured by a smoother (Wu and Xia 2016; Black 1995). Because no smoother touches it and no variance is re-estimated as the sample grows, the integration battery that a filtered trend would rule out is appropriate here, and the deterministic specification was set by the platform's trend pre-test rather than pinned in advance. The battery runs on the 438 monthly observations spanning 1990-01-31 to 2026-06-30.

The augmented Dickey-Fuller test of Dickey and Fuller (1979), in the lag-augmented form of Said and Dickey (1984) with lag length chosen by an information criterion as in Ng and Perron (2001), does not reject a unit root with a statistic of −2.73628 at p = 0.221331, the nonparametric Phillips and Perron (1988) test concurs with a statistic of −2.25659 at p = 0.458095, and the KPSS test rejects the trend-stationary null with a statistic of 0.381639 at p < 0.01 (Kwiatkowski et al. 1992). All three point the same way, so the honest agreement carries a clean I(1) verdict on the level, and because this is not a lone-dissent reading the GLS-detrended escalation of Elliott, Rothenberg, and Stock (1996) is not required and was not run.

Because the level carries a stochastic trend, the portmanteau and the break search move to the first difference, where each is well defined. The Ljung and Box (1978) statistic, refining the original Box and Pierce (1970) form, rejects the no-autocorrelation null on the differenced series at both rungs of the monthly lag ladder over 437 observations, with Q = 273.378 at lag 12 and Q = 304.494 at lag 24 and p = 0.000 in both cases. The multiple-break procedure of Bai and Perron (1998), computed by the dynamic-programming algorithm of Bai and Perron (2003) on the same differenced object, finds no break in the mean of the differenced series, so no break date is printed (Perron 1989).

Four limits belong with the verdict. Inside the months in which the lower bound binds the level is model-identified rather than observed, so a unit-root reading there is a property of the model's fixed dynamics and never a statement about the policy stance (Joslin, Singleton, and Zhu 2011; Hamilton and Wu 2012). Any statement about the level travels with the parameter sensitivity recorded in the narrative, since a one-standard-error perturbation of the estimated parameters moves the path by far more than the unit the series is published in, and the closed-form forward expression the filter rests on is an approximation whose error grows with maturity and with time spent at the bound (Krippner 2013; Christensen and Rudebusch 2015). The platform's bound-period flag opens one month earlier than the shading in the paper, which is disclosed here and never substituted. And the series does not revise, since one causal pass at a fixed parameter vector rewrites nothing, a construction property stated here rather than a tested cell (Kim and Wright 2005).

This series is a monthly model-derived rate level with no posited seasonal quantity, so the seasonal-unit-root machinery of Hylleberg et al. (1990) and the Canova and Hansen (1995) seasonal-stationarity test are not applicable and were deliberately not run, the seasonal question being about a calendar component this object does not carry (Ghysels and Osborn 2001).

## Frequently Asked Questions

### What does the shadow federal funds rate describe?

It is the latent short rate that the whole shape of the curve implies while the observed rate can fall no further. Away from the floor the two agree, and once the floor binds only the latent one keeps moving, which is how easing delivered by means other than the headline rate is expressed in rate units.

### Why are the model's parameters not updated?

They are estimated once on the paper's own sample and are never re-estimated afterwards, while the states are filtered forward by one causal pass that looks only backwards. Everything after that estimation window is therefore produced at parameters fixed before it, and that fact travels with the series wherever it is shown.

### How exact is the level of any single month?

Less exact than the unit it is published in. Moving each estimated parameter by one standard error shifts the whole path by far more than that unit, so a small gap between two neighbouring months carries no meaning on its own and the level is read together with the sensitivity that accompanies it.