South Korea Trend Growth Rate of Potential Output

The annualized trend growth rate of potential output is the long-run growth rate that the economy can sustainably achieve, excluding business-cycle fluctuations. It is estimated as a stochastic drift in the log level of potential output within the Holston, Laubach, and Williams (2023) structural model (HLW).

In the HLW model, the log level of potential output $y^*_t$ follows a random walk with trend growth $g_{t-1}$ as its drift:

Trend growth $g_t$ itself is a quarterly-frequency variable that follows a driftless random walk with innovation variance $\sigma^2_g$:

The reported series is $4 \times g_t$, annualizing the quarterly rate to facilitate comparison with standard macroeconomic aggregates.

Trend growth abstracts from the business-cycle fluctuations captured by the output gap (KRGDPGAP) and reflects the economy's sustainable long-run growth capacity. It captures the combined effects of labor force growth, capital accumulation, and total factor productivity (TFP), though the HLW model estimates aggregate trend growth without decomposing it into these supply-side components. Because trend growth is a key determinant of the natural rate of interest $r^*$ (KRNR), a decline in trend growth directly lowers $r^*$, tightening the effective lower bound constraint on monetary policy and reshaping the long-run interest rate environment.

Estimated jointly with the natural rate of interest ($r^*$, KRNR), the output gap (KRGDPGAP), 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, and this section highlights the aspects specific to trend growth estimation.

(1) State dynamics. Trend growth $g_t$ enters the model as the drift term in the log level of potential output:

Trend growth itself follows a driftless random walk

with innovation variance $\sigma^2_g$. The ratio

governs the relative variability of trend growth shocks versus potential output level shocks. A small $\lambda_g$ implies a slowly evolving trend, and a value near zero implies near-constant growth.

(2) Estimation of $\sigma_g$. Within the 3-stage MLE framework, $\sigma_g$ is not estimated directly but is derived from the signal-to-noise ratio

obtained in Stage 1 via the Exponential Wald test statistic of the Stock-Watson (1998) median unbiased estimator (MUE). The MUE procedure tests whether a structural break exists in the trend growth of smoothed potential output, and a value of $\lambda_g$ equal to zero reduces trend growth to a constant.

(3) Extraction. The Kalman filter, run with the MLE parameters, gives the one-sided estimate of $g_t$ as element [3] of the 9-dimensional state vector

The reported series multiplies by 4 to annualize. Each quarter's value uses the data only up to that quarter, and the smoother that enters the median-unbiased test above is used nowhere in the published path. The parameters are estimated on the full sample and re-estimated at every update, and the filter starts from a full-sample Hodrick and Prescott (1997) trend of log GDP, as in the authors' code, so the first quarters lean on that start value, and the series is not a real-time estimate but a quasi-final one filtered at parameters estimated on the full sample (Orphanides and van Norden 2002).

Trend growth is a fundamental structural indicator for macroeconomic analysis, fiscal planning, and monetary policy calibration.

Korea has experienced a pronounced structural deceleration in trend growth. In the committed one-sided record trend growth is 4.99% at 1999Q4, 3.87% at 2009Q4, 3.09% at 2019Q4 and 1.99% at 2026Q1, with filtered standard errors of 0.62, 0.59, 0.59 and 0.59 percentage points at those quarters, conditional on the estimated parameters. This trajectory reflects the exhaustion of catch-up growth (convergence to the technology frontier), rapid demographic aging (the working-age population peaked in 2017 and is now contracting), and a structural slowdown in total factor productivity growth as the economy matured. The HLW estimate filters out business-cycle fluctuations and provides a model-consistent measure of this secular trend.

While the HLW model estimates aggregate trend growth without explicit decomposition, this decline can be interpreted through three channels of growth accounting. The first is labor input contraction, where Korea's working-age population (15–64) is projected to decline by roughly 30% by 2050 (Statistics Korea, UN Population Prospects), creating a structural drag on potential output. The second is diminishing returns to capital deepening, as Korea's capital-output ratio has risen toward advanced-economy norms. The third is a slowdown in total factor productivity growth, although Korea's R&D intensity of 5.2% of GDP, the highest among OECD countries, may partially offset this through innovation in semiconductors, batteries, and other technology sectors.

The HLW estimate of trend growth is cross-validated against independently produced official estimates. The Bank of Korea publishes its own potential growth estimates, typically derived from a production function approach, and the OECD Economic Outlook provides HP-filter-based and production-function-based estimates for Korea. Differences arise from methodological choices, where the HLW trend growth is a one-sided Kalman-filtered latent variable from a structural model, while the BOK and OECD estimates use supply-side production functions with explicit labor, capital, and TFP components.

Lower trend growth has direct implications for fiscal sustainability analysis. Korea's government debt-to-GDP ratio, while still moderate by international standards, is on a rising trajectory driven by population aging (pension and healthcare costs) and expanded fiscal commitments. The Blanchard (2023) framework emphasizes the $r - g$ differential, and when the real interest rate $r$ exceeds growth $g$, the debt-to-GDP ratio rises unless offset by primary surpluses. A declining trend growth narrows the margin of safety, making the $r > g$ scenario more likely and fiscal consolidation more pressing.

Trend growth is a key determinant of the natural rate of interest. The natural rate is determined by

where $c$ is a Stage-3 parameter, estimated at 0.65 in KRED's committed record for the core-CPI specification. Declining trend growth is one of the two channels through which the natural rate falls in this framework, the other being the non-growth component described next. The trend growth series (KRTRGDP) and the natural rate series (KRNR) should therefore move broadly in parallel, with divergences attributable to changes in the $z_t$ component (shifts in the discount rate, demographics beyond the growth channel, and global savings patterns).

Trend growth is a key structural input for long-term asset valuation, sovereign credit analysis, and fixed income strategy.

Trend GDP growth provides a ceiling for long-run aggregate corporate earnings growth. In the absence of rising profit shares, economy-wide earnings cannot sustainably grow faster than potential output. For the KOSPI composite index, a trend growth rate that in the committed record falls from 4.99% at 1999Q4 to 1.99% at 2026Q1, with filtered standard errors of 0.62 and 0.59 percentage points, implies a proportional reduction in the terminal growth rate used in discounted cash flow (DCF) models and equity risk premium calculations. This structural shift contributes to the "Korea discount" (the persistent undervaluation of Korean equities relative to international peers) through lower justified P/E ratios.

Trend growth is a primary determinant of sovereign creditworthiness through its impact on the debt-to-GDP trajectory. Rating agencies (S&P, Moody's, Fitch) explicitly incorporate potential growth estimates into their sovereign rating models. A sustained decline in Korea's trend growth, coupled with rising age-related fiscal expenditures, is a medium-term credit risk factor, even though Korea's current fiscal position remains strong by international standards.

A lower trend growth rate implies a structurally lower equilibrium interest rate environment. This is because trend growth feeds directly into $r^*$ via

This supports the view that long-term KTB yields will remain lower than historical averages on a structural basis, independent of the cyclical monetary policy stance. Fixed income investors with long-horizon mandates (pension funds, insurance companies) use trend growth estimates to calibrate their strategic asset allocation and liability-matching assumptions.

The trend growth rate provides a benchmark for the sustainable real return on the aggregate capital stock. In standard neoclassical theory, the marginal product of capital is linked to the growth rate through the capital accumulation equation. A lower trend growth rate implies lower equilibrium returns across real assets (real estate, infrastructure, and private equity), with implications for institutional portfolio construction and actuarial assumptions for pension fund adequacy.

KRTRGDP is the annualized trend-growth 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 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 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 trend growth is 0.940 and the implied half-life is 11.17 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 near-unit 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 trend growth 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. 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).