---
ticker: "USGDPGAP"
title: "U.S. Output Gap"
unit: "%"
frequency: "Quarterly"
source: "Holston, Laubach, and Williams (2023); Laubach and Williams (2003)"
release: "Updated Quarterly"
category: "Interest Rates"
country: "US"
language: "en"
canonical: "https://kred.dev/en/series/USGDPGAP"
license: "https://creativecommons.org/licenses/by-nc-nd/4.0/"
latest_value: -0.14
latest_date: "2026-06-30"
first_date: "1961-03-31"
observations_total: 262
observations_shown: 120
---

# U.S. Output Gap

## Overview

The natural rate of interest for the United States, reported together with the trend growth rate of potential output, the output gap and the real rate gap, all estimated as filtered latent states of one quarterly state space model on inputs KRED collects itself.

## Key Figures

|  | Value | Date |
|---|---|---|
| Latest | -0.14 | 2026-06-30 |
| Change from previous | -0.12 | 2026-03-31 |
| Change over one year | +0.01 | 2025-06-30 |
| Highest on record | 6.99 | 2021-06-30 |
| Lowest on record | -5.46 | 1982-12-31 |
| Period covered | 1961-03-31 – 2026-06-30 |  |
| Observations | 262 |  |

## Recent observations

| Date | Value | Change |
|---|---|---|
| 1996-09-30 | 0.20 | +0.12 |
| 1996-12-31 | 0.41 | +0.20 |
| 1997-03-31 | 0.20 | -0.21 |
| 1997-06-30 | 0.45 | +0.25 |
| 1997-09-30 | 0.29 | -0.16 |
| 1997-12-31 | 0.34 | +0.04 |
| 1998-03-31 | 0.27 | -0.07 |
| 1998-06-30 | 0.21 | -0.05 |
| 1998-09-30 | 0.29 | +0.08 |
| 1998-12-31 | 0.40 | +0.11 |
| 1999-03-31 | 0.38 | -0.02 |
| 1999-06-30 | 0.44 | +0.06 |
| 1999-09-30 | 0.52 | +0.08 |
| 1999-12-31 | 0.84 | +0.32 |
| 2000-03-31 | 0.88 | +0.04 |
| 2000-06-30 | 0.75 | -0.13 |
| 2000-09-30 | 0.69 | -0.05 |
| 2000-12-31 | 0.40 | -0.29 |
| 2001-03-31 | 0.11 | -0.29 |
| 2001-06-30 | -0.52 | -0.62 |
| 2001-09-30 | -1.09 | -0.57 |
| 2001-12-31 | -1.13 | -0.04 |
| 2002-03-31 | -1.25 | -0.12 |
| 2002-06-30 | -0.77 | +0.48 |
| 2002-09-30 | -0.56 | +0.21 |
| 2002-12-31 | -0.70 | -0.14 |
| 2003-03-31 | -0.69 | +0.01 |
| 2003-06-30 | -0.41 | +0.28 |
| 2003-09-30 | 0.17 | +0.58 |
| 2003-12-31 | 0.69 | +0.51 |
| 2004-03-31 | 1.10 | +0.42 |
| 2004-06-30 | 1.35 | +0.25 |
| 2004-09-30 | 1.34 | -0.02 |
| 2004-12-31 | 1.75 | +0.41 |
| 2005-03-31 | 2.20 | +0.46 |
| 2005-06-30 | 2.06 | -0.14 |
| 2005-09-30 | 1.89 | -0.17 |
| 2005-12-31 | 2.08 | +0.19 |
| 2006-03-31 | 2.05 | -0.04 |
| 2006-06-30 | 2.20 | +0.15 |
| 2006-09-30 | 1.63 | -0.58 |
| 2006-12-31 | 1.21 | -0.42 |
| 2007-03-31 | 1.21 | 0.00 |
| 2007-06-30 | 0.68 | -0.53 |
| 2007-09-30 | 0.54 | -0.14 |
| 2007-12-31 | 0.62 | +0.08 |
| 2008-03-31 | 0.12 | -0.50 |
| 2008-06-30 | -0.22 | -0.34 |
| 2008-09-30 | -0.39 | -0.17 |
| 2008-12-31 | -1.83 | -1.44 |
| 2009-03-31 | -2.57 | -0.75 |
| 2009-06-30 | -2.40 | +0.17 |
| 2009-09-30 | -2.23 | +0.17 |
| 2009-12-31 | -1.39 | +0.85 |
| 2010-03-31 | -1.20 | +0.19 |
| 2010-06-30 | -0.88 | +0.32 |
| 2010-09-30 | -0.63 | +0.25 |
| 2010-12-31 | -0.18 | +0.45 |
| 2011-03-31 | 0.08 | +0.26 |
| 2011-06-30 | 0.46 | +0.38 |
| 2011-09-30 | 0.47 | +0.01 |
| 2011-12-31 | 0.60 | +0.13 |
| 2012-03-31 | 1.25 | +0.65 |
| 2012-06-30 | 1.27 | +0.02 |
| 2012-09-30 | 1.16 | -0.10 |
| 2012-12-31 | 1.28 | +0.12 |
| 2013-03-31 | 1.38 | +0.09 |
| 2013-06-30 | 1.36 | -0.01 |
| 2013-09-30 | 1.62 | +0.26 |
| 2013-12-31 | 1.89 | +0.27 |
| 2014-03-31 | 1.71 | -0.18 |
| 2014-06-30 | 1.96 | +0.25 |
| 2014-09-30 | 2.21 | +0.25 |
| 2014-12-31 | 2.24 | +0.03 |
| 2015-03-31 | 2.20 | -0.04 |
| 2015-06-30 | 2.56 | +0.37 |
| 2015-09-30 | 2.45 | -0.12 |
| 2015-12-31 | 2.24 | -0.21 |
| 2016-03-31 | 2.35 | +0.11 |
| 2016-06-30 | 2.46 | +0.11 |
| 2016-09-30 | 2.37 | -0.09 |
| 2016-12-31 | 2.28 | -0.10 |
| 2017-03-31 | 2.36 | +0.09 |
| 2017-06-30 | 2.18 | -0.18 |
| 2017-09-30 | 2.14 | -0.05 |
| 2017-12-31 | 2.41 | +0.27 |
| 2018-03-31 | 2.76 | +0.35 |
| 2018-06-30 | 2.69 | -0.07 |
| 2018-09-30 | 2.35 | -0.34 |
| 2018-12-31 | 2.25 | -0.09 |
| 2019-03-31 | 1.99 | -0.26 |
| 2019-06-30 | 1.93 | -0.05 |
| 2019-09-30 | 1.92 | -0.01 |
| 2019-12-31 | 1.87 | -0.05 |
| 2020-03-31 | 1.90 | +0.03 |
| 2020-06-30 | -1.21 | -3.11 |
| 2020-09-30 | 5.13 | +6.35 |
| 2020-12-31 | 5.88 | +0.74 |
| 2021-03-31 | 6.47 | +0.59 |
| 2021-06-30 | 6.99 | +0.52 |
| 2021-09-30 | 6.65 | -0.34 |
| 2021-12-31 | 6.88 | +0.23 |
| 2022-03-31 | 6.31 | -0.57 |
| 2022-06-30 | 4.98 | -1.32 |
| 2022-09-30 | 4.66 | -0.32 |
| 2022-12-31 | 4.47 | -0.19 |
| 2023-03-31 | 4.03 | -0.45 |
| 2023-06-30 | 3.44 | -0.59 |
| 2023-09-30 | 2.10 | -1.34 |
| 2023-12-31 | 1.66 | -0.44 |
| 2024-03-31 | 1.65 | -0.01 |
| 2024-06-30 | 0.98 | -0.67 |
| 2024-09-30 | 0.48 | -0.49 |
| 2024-12-31 | 0.26 | -0.23 |
| 2025-03-31 | -0.01 | -0.27 |
| 2025-06-30 | -0.15 | -0.14 |
| 2025-09-30 | -0.18 | -0.04 |
| 2025-12-31 | -0.35 | -0.17 |
| 2026-03-31 | -0.02 | +0.34 |
| 2026-06-30 | -0.14 | -0.12 |

## Definition

USNR is the natural rate of interest, the real short rate consistent with output at its natural level and with stable inflation, and the same model delivers the trend growth rate of potential output as USTRGDP, the output gap as USGDPGAP and the real rate gap as USRRGAP. The four are states of one quarterly state space model in which the natural rate is a coefficient times trend growth plus a second slow-moving component, with that coefficient estimated rather than imposed at one, so its level is identified only jointly with the model that carries it (Laubach and Williams 2003; Holston, Laubach, and Williams 2017; Holston, Laubach, and Williams 2023). KRED estimates that model itself, in three stages, on a vintage of inputs KRED collects, so what this page carries is KRED's own estimate of the authors' model rather than anyone else's published estimate, and it is not a data series.

The published history is the filtered, one-sided path, so each quarter's value uses only information dated up to that quarter inside the estimated model. It is not a real-time series, since the parameters at which the filter runs are estimated on the whole sample, and it is not the best available estimate of the past either, since the two-sided smoothed companion that reads every date through the whole sample is the better-informed estimate of history and is withheld. The distance between the two is not a rounding matter, because over the 261 estimation quarters the one-sided and two-sided natural rates differ by 0.642 pp on average and by as much as 2.027 pp, the widest gap falling at 2007-12-31, which is the order of revision that Orphanides and van Norden (2002) report for trend and gap estimates of this kind.

The level carries a wide band. Standard errors computed by the Monte Carlo procedure of Hamilton (1986) put the natural rate's average standard error over the sample at 1.2012 pp and its standard error at the final observation at 1.5715 pp, and for trend growth the same two figures are 0.4037 pp and 0.5752 pp. A band of that width is wider than most of the movements a reader would want to interpret, so no level here is read as an exact quantity and no two quarters are set against each other without it.

Against the estimates the authors publish, KRED's natural rate sits within 0.0612 pp at its widest point and 0.0217 pp on average over the common quarters, measured against a tolerance of 0.50 pp fixed before the comparison was run. The estimate therefore replicates the published series within the paper's own fifty-basis-point statement about specification uncertainty, which is a statement of agreement and not a claim that the two are the same numbers. Part of what is left is a vintage effect rather than an estimation difference, since running the same code on the two input vintages moves the natural rate by 0.005 pp on average and by at most 0.034 pp (Holston, Laubach, and Williams 2023).

Three statements bound what these series are. They are latent states of an estimated model, so none of them is a measurement, an observation or a passthrough of anyone's published figures, and the inputs behind them are KRED's own collected vintage rather than the authors' panel. The decomposition itself is a modelling choice and not a fact the data settle, which is the standing objection to trend and cycle extraction generally (Hamilton 2018; Stock and Watson 1998; Hodrick and Prescott 1997). And the estimates stand on this design alone, since an estimate built for another economy under a different expectations rule and a different pandemic indicator is a different object, and no comparison of that kind is offered here (Taylor 1993; Fisher 1930).

## Methodology

**(1) Model.** Output, inflation and the real rate are linked by an aggregate demand relation in which the output gap depends on its own two lags and on the average distance of the real rate from the natural rate over the two preceding quarters, and by a Phillips curve in which inflation depends on its own lag, on an average of the three quarters before that and on the lagged output gap. The trend level of output, its growth rate and a second slow-moving component each follow a random walk, the trend level carrying its own lagged growth rate, and the natural rate is recovered as a coefficient times trend growth plus that second component, with the coefficient estimated rather than imposed at one (Holston, Laubach, and Williams 2023; Laubach and Williams 2003).

**(2) Inputs.** The quarterly frame is the log of real output, an annualized quarterly growth rate of a core consumption price index, and a nominal short rate placed on a 365-day annualized basis, with a discount rate standing in for the policy rate over the early years the authors specify. Expected inflation is the four-quarter moving average of current and past inflation, and the real rate is the nominal short rate less that expectation. Every input is collected by KRED on its own vintage (Holston, Laubach, and Williams 2017).

**(3) Pandemic terms.** Two devices carry the pandemic quarters. The innovation variances are scaled by factors estimated separately for the three pandemic years and held at one elsewhere, and an exogenous stringency indicator lifts the trend level of output in proportion to itself while removing the same amount from the gap, so the collapse in measured output is not read wholly as a fall in potential. KRED rebuilds that indicator itself from a committed daily stringency reference, taking calendar-quarter means over the observed window 2020-01-01 to 2022-12-31, holding it at zero for every quarter through 2019 and, once the observed window ends, letting it fall in eight equal steps to zero. That rebuild is KRED's own and is attributed to no one else. Measured against the indicator column the authors publish, it agrees exactly in 2 of the 12 observed quarters and departs by at most 3.4307 at the widest point, and the vintage of the stringency file behind their column is unverified, so the residual is disclosed rather than repaired (Hale et al. 2021; Lenza and Primiceri 2022).

**(4) Estimation.** Three stages. The first two fix the two signal-to-noise ratios, the one governing trend growth and the one governing the natural rate's second component, by the median-unbiased procedure of Stock and Watson (1998) built on the exponential Wald statistic of Andrews and Ploberger (1994), which is used because the maximum-likelihood estimate of a random-walk component's variance piles up at zero. The third stage maximizes the likelihood over the remaining parameters under the sign restrictions the authors impose on the two behavioural slopes, with the state initialized from a heavily smoothed trend of log output (Hodrick and Prescott 1997). The search is a seeded multi-start optimization, and reproducibility is claimed only as seed reproducibility on the Linux platform of record, where re-running it from each pre-registered seed moves the natural rate by at most 0.0000665 pp.

**(5) Filtering and the published path.** The states are read off the filter at each date, so the published series is the one-sided estimate and no smoother touches it. The estimation sample runs from 1961-03-31 to 2026-03-31, 261 quarters, with four further quarters of data before the start used only to initialize. Parameters are re-estimated whenever the series is rebuilt and the whole history is rewritten with them, so a value at a fixed past date is not stable across rebuilds, and no dated panel of earlier vintages is kept from which the size of that movement could be measured (Orphanides and van Norden 2002).

**(6) Standard errors.** Computed by the Monte Carlo procedure of Hamilton (1986) under the admissibility restrictions the authors place on the draws, persisted beside the states and never used to alter a published value. They are what the band quoted with every level comes from, and a trend and cycle split of this kind carries such a band by construction rather than by accident (Hamilton 2018; Stock and Watson 1991).

## Applications in Economics

The natural rate of interest is the benchmark against which a real policy rate is judged, since a real rate below it is accommodative and one above it is restrictive, and the reason for estimating it at all is that the benchmark itself moves (Laubach and Williams 2003; Holston, Laubach, and Williams 2017). The same model delivers trend growth and the output gap, so the four series here are one object read at four places rather than four independent readings, and the real rate gap USRRGAP is simply the distance of the real policy rate from the estimated natural rate (Fisher 1930).

A policy rule of the Taylor (1993) kind takes the natural rate as its intercept, so a decline in that intercept moves every prescribed rate computed from it, and much of the interest in the series follows from that dependence rather than from any property of the path itself. The stance is set at the shortest maturity while transmission runs through longer rates, which is why a benchmark defined in real short-rate space is where the comparison is made (Bindseil 2004).

Reliability here is a revision question rather than a measurement question. Orphanides and van Norden (2002) show that trend and gap estimates built on two-sided filters are revised heavily as data accumulate and that the revision can be of the same order as the quantity being estimated, which is why the one-sided path is the published object and why it is still not a real-time series. In this sample the one-sided and two-sided natural rates differ by 0.642 pp on average and by as much as 2.027 pp, so the choice between them is not a presentational detail.

Two further limits bound any reading. The estimated level carries a standard error of 1.2012 pp on average over the sample and 1.5715 pp at the final observation (Hamilton 1986), which is wide relative to the movements usually discussed, and the pandemic quarters are carried by devices the model imposes rather than discovers, namely scaled innovation variances and an exogenous stringency indicator, so the estimates through those quarters rest on choices the authors state and KRED implements (Lenza and Primiceri 2022; Hale et al. 2021). Whether a trend and cycle decomposition of this kind recovers anything the data identify is itself contested (Hamilton 2018; Stock and Watson 1998).

Three readings are therefore not supported. No turning point is identified here, because the filtered path at full-sample parameters is not what an observer would have had in front of them at the time. These series are not forecasts, since the unobserved components follow random walks and a random walk says nothing about its own future beyond its current level (Andrews and Ploberger 1994). And nothing on this page is offered as agreement or disagreement with an estimate produced for another economy or by another research design, since a different expectations rule and a different pandemic indicator define a different object (Holston, Laubach, and Williams 2023).

## Applications in Financial Markets

On a rates desk the estimated natural rate is the anchor of the far end of a policy path, since where the short rate is expected to settle once a cycle is over is much of what a long forward rate prices, alongside the compensation demanded for bearing risk (Hicks 1939). A move in the estimate therefore bears on the level around which forward rates are anchored rather than on any near-dated quotation, and the real rate gap is the form in which the same comparison reaches the front end (Laubach and Williams 2003).

Three measurement facts bear on that use. The series is a filtered model state rather than a price, so its level carries the specification's assumptions and a different identification of the same trend returns a different level (Hamilton 2018; Stock and Watson 1998). The history is rewritten whenever the model is re-estimated, so a backtest that treats today's path as what was visible at each past date overstates what a desk could have acted on, and no dated vintage panel is kept from which the size of that rewriting could be measured (Orphanides and van Norden 2002). And the standard error at the final observation is 1.5715 pp (Hamilton 1986), which is larger than the moves a positioning decision usually rests on.

A view formed on this reading is expressed through the curve rather than through the estimate, since none of these four series is an instrument. 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), and the discounting curve is itself a fitted construction whose conventions the position inherits (Nelson and Siegel 1987; Svensson 1994; Gürkaynak, Sack, and Wright 2007).

Two uses are ruled out. A threshold reading taken from the real rate gap alone is not supported, because a band well over a percentage point wide sits around the natural rate that would define the threshold. And the series is not a substitute for what the market prices, since a policy rule built on it is a benchmark for discussion rather than a path anyone is committed to (Taylor 1993; Holston, Laubach, and Williams 2017).

## Statistical Tests

USGDPGAP is the one-sided, Kalman-filtered output-gap state of a quarterly unobserved-components model, adjusted over the pandemic quarters by an exogenous stringency indicator the model treats as given, and never a two-sided smoothed path, so the statistical object is a persistence summary of that filtered series and not an integration order of the data. The integration order of the state is imposed by the random-walk state equation rather than estimated, and a one-sided filter at steady state is an exponentially weighted one-sided average whose gain, set by signal-to-noise ratios fixed before the likelihood is maximized, dominates the path's serial correlation.

The augmented Dickey and Fuller (1979) regression, the nonparametric Phillips and Perron (1988) test and the KPSS stationarity test of Kwiatkowski et al. (1992) were deliberately not run on this path, because a verdict from them would re-import the very inference the model was built to avoid, the signal-to-noise ratios having been fixed by the median-unbiased procedure of Stock and Watson (1998) built on the exponential Wald statistic of Andrews and Ploberger (1994). The GLS-detrended escalation of Elliott, Rothenberg, and Stock (1996) was not run for the same reason, and neither was the modified-statistic battery of Ng and Perron (2001), since both confirm an integration reading this archetype does not take. The level break search of Bai and Perron (1998) was likewise not run, because a break in the mean of a filtered latent state reflects the filter's response to its inputs rather than a change in the economy (Perron 1989). A level portmanteau such as Ljung and Box (1978) is not applied here either, since on a filtered path it reads the filter gain rather than evidence about the data-generating process.

What the matrix mandates in their place is a descriptive persistence summary and a statement about revision. Over the 261 quarters spanning 1961-03-31 to 2026-03-31 the first-order autoregressive coefficient of the filtered series is 0.950577 and the implied half-life is 13.6754 quarters, reported as a property of the filtered series and not as an order of integration, and read with the small-sample downward bias that afflicts near-unit autoregressive estimates in mind (Andrews 1993). The revision cell records that the parameters are re-estimated on every rebuild by a seeded multiple-start search and that the whole history is rewritten by a full-replacement load, so the value at a fixed past date moves across rebuilds and no dated vintage panel exists from which the size of that movement could be measured (Orphanides and van Norden 2002).

Three limits are stated rather than implied. No order of integration is assigned to this series, by ruling and not by an inconclusive test, so nothing here is evidence that the series does or does not carry a stochastic trend (Hamilton 2018). The published path is one-sided but it is not a real-time estimate, since the parameters at which the filter runs are estimated on the whole sample, which makes it a quasi-final estimate in the sense of Orphanides and van Norden (2002), and no turning point is identified from it. And the frequency is quarterly, so the half-life above is measured in quarters and is not comparable with a half-life measured at another frequency (Holston, Laubach, and Williams 2023; Laubach and Williams 2003; Hamilton 1986; Taylor 1993).

## Frequently Asked Questions

### What does the natural rate of interest describe?

It is the real short-term interest rate that would be consistent with output at its natural level and with inflation stable. Nothing observes it directly, so it is treated as a hidden state of a model and estimated along with the trend growth of the economy that moves it.

### Why is the published history a one-sided estimate?

Every point uses only information dated up to its own quarter inside the estimated model. A companion estimate that reads each date through the whole sample fits history better and is not published here, so what this page shows is the more conservative of the two and is not the best available reading of the past.

### How much uncertainty surrounds the estimate?

A great deal. The band around the level is wider than most of the movements a reader would want to interpret, so a level is read together with that band, and two nearby quarters are not treated as different from each other without it.