South Korea Output Gap

The output gap measures the percentage difference between actual real GDP and the COVID-adjusted level of potential output, capturing the degree of slack or overheating in the economy.

Formally, the output gap $\tilde{y}_t$ is the log level of real GDP minus COVID-adjusted potential output:

where

is the log level of actual real GDP and $y^{*,COVID}_t$ adjusts potential output for the transitory supply disruptions caused by COVID-19 lockdowns.

The COVID adjustment prevents the pandemic-era GDP collapse from being misattributed to a permanent decline in potential output, and is constructed as:

where $d_t$ is the OxCGRT Government Stringency Index and $\phi$ is an estimated coefficient capturing the supply-side impact of lockdown measures.

A negative output gap indicates economic slack, where the economy operates below its potential, suggesting underutilized labor and capital resources and downward pressure on inflation through the Phillips curve. A positive output gap indicates overheating, where demand exceeds the economy's sustainable production capacity, with upward pressure on inflation.

The COVID-adjusted output gap reported in this series should be distinguished from the unadjusted output gap $y_t - y^*_t$, which is available as a secondary field in the chart. The unadjusted gap attributes all of the pandemic-era GDP decline to demand deficiency, while the adjusted gap correctly reclassifies the portion attributable to government-mandated supply restrictions.

Estimated jointly with the natural rate of interest ($r^*$, KRNR), trend growth (KRTRGDP), and the real rate gap (KRRRGAP) within the HLW (2023) 3-stage MLE state-space model. The full model specification, data inputs, and estimation procedure are described in detail in the KRNR methodology section; this section highlights the aspects specific to the output gap.

(1) Output gap within the structural model. The output gap

is not directly a state variable but is derived as the difference between observed GDP and the one-sided Kalman-filtered estimate of potential output. It enters the IS curve as the dependent variable:

It also enters the Phillips curve as a determinant of inflation through the $b_y \tilde{y}_{t-1}$ term, where $b_y > 0$ captures the effect of demand pressures on price dynamics.

(2) COVID-19 adjustment. The COVID-adjusted potential output is:

where $d_t$ is the quarterly average of the Oxford COVID-19 Government Response Tracker (OxCGRT) Stringency Index for Korea. The stringency index is constructed from daily observations, averaged to quarterly frequency, and zero-padded after the last observed quarter to ensure the adjustment phases out as pandemic restrictions end. The coefficient $\phi < 0$ is freely estimated in Stage 3 of the model, capturing the percentage-point reduction in output per unit increase in the stringency index. Time-varying measurement error variances $\kappa_{2020}$, $\kappa_{2021}$, $\kappa_{2022}$ account for the increased macroeconomic volatility during the pandemic period, and these are freely estimated scale factors that multiply the observation covariance matrix.

(3) Estimation uncertainty. The output gap inherits substantial estimation uncertainty from the filter's estimate of potential output. The standard error is:

since observed GDP is known exactly and all uncertainty resides in $y^*_t$. This standard error is conditional on the estimated parameters and excludes parameter uncertainty (Hamilton 1986). Because every published quarter is a one-sided estimate that never draws on later observations, the whole path, not only its latest quarters, carries the imprecision that Orphanides and van Norden (2002) document for gap estimates made at the end of a sample. The parameters are estimated on the full sample and the filter starts from a full-sample trend of log GDP, so the first quarters lean on that start value, and every quarter is revised when the model is re-estimated, which makes the series a quasi-final estimate filtered at parameters estimated on the full sample rather than a real-time one (Orphanides and van Norden 2002).

The output gap is a core input for monetary policy decisions and macroeconomic assessment, connecting the real side of the economy to inflation dynamics through the Phillips curve.

The output gap enters the Phillips curve in the HLW structural model through the coefficient $b_y$, where a positive gap exerts upward pressure on inflation and a negative gap is disinflationary. This channel is central to the BOK's monetary policy framework, where the central bank estimates the current output gap to assess whether aggregate demand conditions are consistent with the inflation target. The HLW output gap provides a model-consistent estimate that is jointly estimated with the natural rate and trend growth, ensuring internal coherence across the monetary policy assessment variables.

Output gap estimates are revised heavily as data accumulate (Orphanides and van Norden 2002). The published path can differ substantially from later estimates because (i) GDP data are revised multiple times, (ii) every published quarter is a one-sided Kalman-filtered estimate that never uses later observations, while the parameters behind it are re-estimated on the full sample at every update, so the whole history moves, and (iii) trend growth itself is imprecisely estimated. The series is therefore not a real-time estimate, and policymakers should treat every observation, the latest included, with appropriate caution and compare with alternative output gap measures.

The HLW output gap can be cross-referenced with other estimates. These comprise (i) the Hodrick-Prescott (HP) filter output gap, a purely statistical detrending method widely used in policy institutions; (ii) the production function approach used by the OECD, IMF, and the BOK's own Research Department, which explicitly models labor, capital, and TFP; and (iii) multivariate filter approaches (e.g., IMF's Flexible System methodology). These methods differ in their structural assumptions and can yield materially different point estimates. The HLW approach has the advantage of being grounded in economic theory (the IS-Phillips curve structure) and jointly estimated with the natural rate, but the disadvantage of imposing a specific functional form on the IS curve dynamics.

During 2020–2021, the COVID adjustment significantly affects the output gap estimate. Without the OxCGRT adjustment, the massive GDP decline in the second quarter of 2020 would appear entirely as a demand shortfall, generating an unrealistically large negative output gap and biasing the estimated natural rate. The adjusted gap reclassifies part of the decline as a transitory supply disruption caused by lockdown measures. The parameter $\phi$ quantifies this reclassification, where a more negative $\phi$ implies a larger supply-side attribution. This distinction matters for policy analysis, as supply-driven output declines call for different policy responses than demand-driven declines.

The output gap is a key cyclical indicator for fixed income positioning, credit analysis, and cross-asset allocation.

A large negative output gap typically precedes monetary policy easing and rate cuts as the BOK acts to close the gap and return inflation to target, creating a bullish signal for KTB prices, particularly at the front end of the curve. Conversely, a closing or positive output gap signals the BOK is likely to tighten, favoring defensive positioning. The output gap can be combined with the real rate gap (KRRRGAP) for a more complete policy stance assessment, where a negative output gap combined with a positive real rate gap is a particularly strong easing signal.

The output gap correlates with corporate default rates and credit spreads in the Korean won bond market. Large negative gaps coincide with economic weakness, elevated default risk, and wider spreads on AA- and BBB rated won-denominated corporate bonds. Positive output gaps compress spreads as corporate earnings and cash flows improve. The output gap thus provides a macroeconomic input for credit cycle timing, signaling an underweight in credit risk during large negative gaps and an overweight during positive gaps.

Output gap dynamics may correlate with term premium regime shifts (KRTPCR series). During recessions, which correspond to a large negative output gap, flight-to-quality demand compresses term premiums as investors seek duration. During expansions, which correspond to a positive gap, term premiums tend to rise as inflation uncertainty increases. Monitoring the output gap alongside the term premium weight (KRTPCR10) helps distinguish between yield curve movements driven by growth expectations versus risk premium repricing.

The output gap provides a macro-cyclical timing signal for equity allocation. A closing negative output gap, where the economy recovers toward potential, is typically associated with improving corporate earnings and positive equity market performance, particularly for cyclical sectors. A positive and widening output gap is associated with inflationary pressures and eventual monetary tightening, which tends to be negative for equity valuations after an initial lag.

KRGDPGAP is the COVID-adjusted output-gap state of KRED's quarterly Holston-Laubach-Williams model on Korean data, a one-sided Kalman-filtered estimate and never a smoothed path, so the statistical object is a persistence summary of that filtered series and not an integration order of the data. The gap's dynamics are imposed by the model's autoregressive IS equation around a random-walk potential output rather than estimated, and a one-sided filter at steady state is an exponentially weighted one-sided average whose gain, set by the median-unbiased signal-to-noise ratios, dominates the path's serial correlation.

The augmented Dickey and Fuller (1979) regression with the lag augmentation of Said and Dickey (1984), 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 test 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 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 117 quarters from 1997-03-31 to 2026-03-31 the first-order autoregressive coefficient of the filtered output gap is 0.855 and the implied half-life is 4.43 quarters, reported as a property of the filtered series and not as an order of integration, and read with the small-sample downward bias of autoregressive estimates in mind (Andrews 1993). The revision cell records that the signal-to-noise ratios and the model parameters are re-estimated at every update, the parameters by a seeded basin-hopping search, and that each load rewrites the whole stored history, so the value at a fixed past quarter moves across updates although no smoothing enters it, 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 output gap 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, the signal-to-noise ratios and the filter's start value, a Hodrick and Prescott (1997) trend of log GDP, are all estimated on the full sample, which makes it a quasi-final estimate in the sense of Orphanides and van Norden (2002), a filtered latent state of a model rather than observed data. Unlike the one-sided credit and house-price gaps on this site, whose fixed parameters leave them unchanged across vintages, this gap moves with every re-estimation. 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).