South Korea Natural Rate of Interest

The natural rate of interest ($r^*$) is the real short-term interest rate consistent with output at its potential level and stable inflation in the absence of transitory shocks. It represents the equilibrium real rate that neither stimulates nor restrains aggregate demand, the rate at which saving and investment are in balance when the economy operates at full capacity.

The Holston, Laubach, and Williams (2023) framework decomposes the natural rate as:

where $g_t$ is the quarterly trend growth rate of potential output, annualized by the factor $4c$ with $c$ estimated from the IS curve, and $z_t$ captures all other low-frequency determinants including the household discount rate, demographic shifts, fiscal policy stance, and global savings patterns. Both $g_t$ and $z_t$ evolve as independent random walks, allowing the natural rate to shift smoothly over time in response to structural economic changes.

The natural rate is fundamentally unobservable and must be inferred from the joint dynamics of output, inflation, and interest rates using state-space methods. This distinguishes it from the ex-ante real policy rate (KREARPR), which is computed directly from observable data using the Fisher equation with model-estimated expected inflation. The natural rate anchors the short end of the real yield curve; for model-based real rates at longer maturities derived from the ACM term structure decomposition, see the KRRR series (KRRR1, KRRR3, KRRR5, KRRR10), and for trend growth, a key driver of the natural rate through the $4cg$ channel, see KRTRGDP. The natural rate ultimately serves as the benchmark for assessing the monetary policy stance, where an ex-ante real policy rate above $r^*$ makes policy contractionary (positive real rate gap, KRRRGAP) and a rate below $r^*$ makes it accommodative.

Estimated using the Holston, Laubach, and Williams (2023) three-stage MLE state-space model, applied to Korean macroeconomic data and incorporating COVID-19 adjustments.

(1) Model specification. The structural model consists of two observation equations governing the joint dynamics of the output gap and inflation, together with transition equations for three unobserved state variables. The IS curve governs the output gap dynamics:

where the innovation term follows

Here the output gap

is log real GDP minus log potential output, both scaled as $100 \times \ln$, the ex-ante real interest rate

is the MSB 91-day yield minus expected inflation, and the natural rate is

The coefficient $a_r < 0$ captures the contractionary effect of a positive real rate gap on output, entering as a two-period average to reflect the lagged transmission of monetary policy.

The Phillips curve governs the inflation dynamics:

where the innovation term follows

Here $\pi_t$ is annualized quarterly core CPI inflation and $\bar{\pi}_{t-2:4}$ is the average of inflation lags 2 through 4. The coefficients on lagged inflation are constrained to sum to unity, imposing a vertical long-run Phillips curve. Expected inflation is implicitly backward-looking as a weighted average of recent inflation realizations, consistent with the original Laubach and Williams (2003) specification.

The transition equations are defined for the three unobserved states. Potential output follows

with innovation

The trend growth rate $g_t$ is itself a random walk:

The natural rate is determined by trend growth and other structural factors through

where the other structural factors follow

capturing shifts in household discount rates, demographics, and fiscal stance.

Potential output $y^*_t$ follows a random walk with drift $g_{t-1}$, and $g_t$ is the quarterly trend growth rate, reported after annualization as $4g_t$ (KRTRGDP). The component $z_t$ captures the portion of $r^*$ not explained by trend growth. The Kalman filter and Rauch-Tung-Striebel (RTS) smoother operate on the 9-dimensional state vector

(2) Data inputs. Three quarterly time series enter the model. The first is real GDP in $100 \times \ln$ scale, constructed by chain-linking quarterly quarter-on-quarter growth rates from the Bank of Korea national accounts, seasonally adjusted with base 2020:Q1 = 100. The second is annualized quarterly core CPI inflation

where $\bar{CPI}^Q_t$ is the quarterly average of the monthly core CPI index (excluding food and energy). The third is the MSB 91-day yield, computed as a quarterly average of daily observations. Expected inflation $\pi^e_t$ is constructed within the model as a 4-quarter trailing moving average of past core CPI inflation, with an expanding window for the first 4 observations. The estimation sample begins in 2000:Q4, determined by the availability of the MSB 91-day rate after VECM backcasting of the pre-2006 period, and extends through the latest available quarter. To accommodate the lag structure, the effective sample begins at $t_0 = 4$, yielding approximately 100 observations.

(3) Three-stage MLE estimation. Following the original HLW (2017, 2023) procedure, the parameters are estimated by three-stage maximum likelihood (MLE). In Stage 1, a reduced model excluding the interest rate channel is estimated by MLE, and the exponential Wald test of the Stock-Watson (1998) median unbiased estimator (MUE) applied to smoothed potential output yields the signal-to-noise ratio

In Stage 2, the interest rate channel ($a_r$) is added and MLE is run with $\lambda_g$ fixed, after which a second MUE test on the IS residuals yields $\lambda_z$. In Stage 3, with both $\lambda_g$ and $\lambda_z$ fixed, the full model is estimated by MLE via basin-hopping global optimization (with L-BFGS-B as local minimizer). The structural parameters ($a_{y,1}$, $a_{y,2}$, $a_r$, $b_\pi$, $b_y$, $\sigma_{\tilde{y}}$, $\sigma_\pi$, $\sigma_{y^*}$, $\phi$, $c$) are estimated jointly with the COVID variance scaling parameters ($\kappa_{2020}$, $\kappa_{2021}$, $\kappa_{2022}$). The key constraints impose $a_r \leq -0.0025$, requiring a negative interest rate channel, and $b_y \geq 0.025$, the Phillips curve slope. The innovation variances are parameterized as $\sigma_g = \lambda_g \sigma_{y^*}$ and

(4) COVID-19 adjustments. Following Holston, Laubach, and Williams (2023), the model incorporates three pandemic-related modifications. First, the Oxford COVID-19 Government Response Tracker (OxCGRT) Stringency Index for Korea $d_t$ enters both observation equations as a supply-shock control with an estimated coefficient $\phi$, where $d_t$ is computed as a quarterly average of daily observations and zero-padded after the last observed quarter. The IS curve observation is adjusted by

and the Phillips curve by $-b_y \phi d_{t-1}$. COVID-adjusted potential output, the measure used for the output gap series KRGDPGAP, is defined as

Second, the time-varying measurement error scale factors $\kappa_{2020}$, $\kappa_{2021}$, $\kappa_{2022}$ multiply the observation covariance matrix during the pandemic period,

with each $\kappa$ freely estimated in Stage 3. Third, the MUE regressions in Stages 1 and 2 use WLS with COVID-period downweighting

to prevent outliers from distorting the structural break tests.

(5) Estimation uncertainty. All four HLW outputs ($r^*$, $g$, $\tilde{y}$, real rate gap) are estimates of unobservable variables carrying substantial uncertainty. Standard errors are derived from the diagonal elements of the RTS smoother's state covariance matrix and are combined as follows:

In the MUE procedure, if $\lambda_z = 0$ is obtained so that there is no evidence of time variation in $z_t$, then $z_t$ becomes a fixed parameter and $se(z_t)$ is set to zero. End-of-sample estimates carry larger uncertainty than mid-sample estimates because the RTS smoother has access to future data in only one direction. In particular, the last two quarters typically display identical $r^*$, $g$, and $z$ values, because $g_t$ and $z_t$ follow random walks with small innovation variances ($\sigma_g \approx 0.04$, $\sigma_z \approx 0.4$) relative to the observation noise ($\sigma_{\tilde{y}} \approx 0.9$), so that the Kalman gain for these states at the terminal observation falls below machine precision and the smoother cannot distinguish $g_T$ from $g_{T-1}$. This is an inherent property of the HLW state-space structure shared by the NY Fed's own U.S. estimates, and it resolves naturally as new quarterly data arrive and the backward pass revises previously terminal estimates. The NY Fed's own HLW estimates likewise emphasize this caveat, noting that confidence intervals for $r^*$ are typically on the order of ±1–2 percentage points.

The natural rate of interest is central to modern monetary policy analysis, serving as the benchmark against which the central bank's policy stance is assessed.

The concept of the natural rate is defined as the interest rate at which the demand for loan capital equals the supply of savings at full employment, and originates with Wicksell (1898). Laubach and Williams (2003) introduced the empirical state-space framework for estimating $r^*$, finding a significant decline in the U.S. natural rate from the 1960s through the early 2000s. Holston, Laubach, and Williams (2017) extended the framework to the U.S., Canada, Euro area, and UK, documenting a common downward trend across advanced economies. The 2023 update incorporated COVID-19 adjustments to prevent pandemic-era disruptions from distorting the estimates. KRED applies this framework to Korean data, providing a directly comparable estimate of Korea's natural rate.

The secular decline in advanced-economy natural rates has been interpreted through the lens of the secular stagnation hypothesis advanced by Summers (2014), where a persistent excess of desired saving over desired investment depresses the equilibrium real rate, potentially below zero. Korea's case is particularly striking. It faces the fastest rate of population aging among OECD member states, with the working-age population already declining and the total fertility rate falling to 0.72 in 2023, the lowest globally (Statistics Korea). Household debt exceeding 100% of GDP constrains consumption and amplifies the transmission of interest rate changes to the real economy. Korea's semiconductor-dependent export structure generates terms-of-trade volatility that adds to macroeconomic uncertainty, potentially depressing $r^*$ through precautionary saving channels (Carroll 1997).

Korea's $r^*$ can be compared with the NY Fed's HLW estimates for the United States, the ECB's estimates for the Euro area, and the Bank of Japan's assessments for Japan. While methodological differences (different data sources, sample periods, and COVID adjustments) limit strict comparability, the common finding of declining natural rates across advanced economies reflects shared structural forces, namely demographic aging, productivity growth slowdowns, and the global savings glut (Bernanke 2005). Korea's natural rate estimate has been among the lower in recent years, consistent with its demographic trajectory and the structural deceleration of trend growth (KRTRGDP).

The HLW identification of the natural rate rests entirely on New Keynesian demand-side frictions, which contrasts with the production-function (neoclassical) approach used by the Bank of Korea, OECD, and IMF. In the production-function approach, potential output is constructed as

and the natural rate is tied to the marginal product of capital. The structural difference lies in the $z_t$ component, where in HLW $z_t$ absorbs demand-side headwinds such as aging, household debt, and precautionary saving as a persistent downward pressure on the equilibrium rate. Production-function models lack this channel, so they tend to yield higher $r^*$ estimates, particularly for Korea, where demand-side headwinds are severe.

The natural rate provides the benchmark for the real rate gap (KRRRGAP). A positive real rate gap

indicates contractionary policy, and a negative gap indicates accommodative policy. Because this assessment reflects the time-varying equilibrium real rate, it is more informative than simply comparing the nominal policy rate to inflation. A 3% nominal base rate may be accommodative when $r^*$ is high and inflation expectations are elevated, but deeply contractionary when $r^*$ has fallen to near zero. For the model-free, forward-looking real rate based on UCSV expected inflation rather than backward-looking moving averages, see KREARPR.

If $r^*$ is near or below zero, the effective lower bound (ELB) on nominal interest rates becomes a binding constraint on conventional monetary policy. With the BOK's inflation target at 2%, a natural rate near zero implies an equilibrium nominal rate of approximately 2%, leaving minimal room for conventional rate cuts during downturns. This has implications for the design of unconventional monetary policy tools such as quantitative easing, forward guidance, and yield curve control, and for the fiscal-monetary policy mix (Blanchard 2023). Korea's experience during the COVID-19 pandemic, when the base rate was cut to a then-record 0.50%, illustrates the practical relevance of ELB constraints.

The natural rate provides a fundamental anchor for long-term interest rate forecasts and fixed income valuation.

In equilibrium, the nominal 10-year KTB yield should converge to the following level:

where $\pi^{target}$ is the BOK's inflation target (currently 2%) and $TP(10Y)$ is the 10-year term premium (KRTP10). A structural decline in $r^*$ directly lowers the fair-value anchor for long-term government bond yields, independent of cyclical fluctuations. When the observed 10Y KTB yield significantly exceeds this anchor, the excess reflects either an elevated term premium or temporary risk repricing, forming a mean-reversion signal for duration-oriented investors. This decomposition can be operationalized using KRED's term premium estimates, where the observed yield minus KRTP10 minus $\pi^{target}$ yields a market-implied $r^*$ that can be compared with the model estimate.

The real rate gap (KRRRGAP), namely the difference between the current real rate and $r^*$, informs tactical duration decisions. When the gap is wide and positive (tight policy relative to equilibrium), mean reversion suggests the BOK will eventually ease and short-term rates will fall toward $r^*$, favoring long-duration positions on KTB futures (the 3-year and 10-year contracts on KRX) and IRS receivers. When the gap is negative (easy policy), the short end is likely to rise as the BOK tightens, favoring short duration and IRS payers. The speed of convergence depends on the Bank of Korea's reaction function and the persistence of the output gap (KRGDPGAP).

The structural differential between Korea's $r^*$ and that of other economies provides a long-run anchor for real exchange rate expectations. If Korea's $r^*$ is persistently lower than the U.S. $r^*$, real interest rate parity implies a long-run tendency toward KRW real depreciation, with implications for the attractiveness of KRW-denominated assets to foreign investors and for optimal FX hedging ratios in international KTB portfolios. Macro hedge funds use cross-country $r^*$ differentials as a structural input for carry trade positioning, since the attractiveness of KRW carry depends not just on the current rate differential but on whether that differential is above or below its $r^*$-implied equilibrium.

The natural rate anchors the very short end of the real yield curve. For the model-free forward-looking ex-ante real policy rate, see KREARPR. For market-implied ex-ante real rates at longer maturities (1Y, 3Y, 5Y, 10Y), derived from the ACM term structure decomposition and Nelson-Siegel expected inflation, see the KRRR series (KRRR1, KRRR3, KRRR5, KRRR10). The spread between longer-maturity real rates and $r^*$ reflects the real term premium and expectations of future real rate changes, providing information about the market's assessment of the future monetary policy path relative to the structural equilibrium.

KRNR is the natural rate of the HLW natural-rate model, a two-sided Kalman-filtered and RTS-smoothed latent state estimated over 117 quarters from 1997-03-31 to 2026-03-31, so the persistence figures below are stated in quarters. Because it is a two-sided smoother output, its measured serial correlation is dominated by the filter's gain rather than by any data-generating process.

For that reason the integration-order battery is deliberately not run. The augmented unit-root regression of Dickey and Fuller (1979) with the lag augmentation of Said and Dickey (1984), the semiparametric Phillips and Perron (1988) test, the KPSS stationarity test (Kwiatkowski et al. 1992), the efficient GLS-detrended test of Elliott, Rothenberg, and Stock (1996), and the modified M-tests of Ng and Perron (2001) are all excluded, because a two-sided smoother is a symmetric moving average whose gain, not the underlying process, drives the serial correlation an integration test reads, and the random-walk-versus-constant character of the latent state is not point-identified by the likelihood (Stock and Watson 1998; Orphanides and van Norden 2002). The level mean-break search of Bai and Perron (1998) is likewise not run, since its asymptotics require a stationary object and a filter-persistent path spuriously segments (Perron 1989).

The matrix-mandated replacement is a descriptive persistence summary, labeled as a property of the smoothed series rather than of the data. The lag-one autocorrelation and implied half-life are 0.991 and 75.22 quarters, so the natural-rate level is highly persistent. These figures describe how slowly the smoothed path decays and carry no integration-order claim, and the strong lag-one autocorrelation a portmanteau such as that of Ljung and Box (1978) would register on this level is itself a property of the smoother's gain.

No order of integration is assigned, by ruling rather than by an inconclusive test. The lag-one coefficient carries the familiar downward small-sample bias near unity on a quarterly sample of 117 observations, so the half-life is a lower-leaning descriptive figure whose median-unbiased interval would follow the grid of Andrews (1993). Because the HLW loader rewrites the full state history on every re-estimation, the smoothed natural rate at any fixed past quarter revises across vintages and no stored vintage panel exists to quantify the magnitude (Orphanides and van Norden 2002). The model-implied content is honest as an assumption rather than a discovery, namely the random-walk state equation for the natural rate and the median-unbiased signal-to-noise ratios the model pins by the method of Stock and Watson (1998).