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 RTS smoother, run with the MLE parameters, extracts the smoothed estimate of $g_t$ as element [3] of the 9-dimensional state vector

The reported series multiplies by 4 to annualize.

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. Trend growth has fallen from over 7% in the 1990s during the late stages of export-led industrialization, to approximately 4% in the 2000s following the 1997–98 Asian financial crisis, to roughly 2% by the 2010s, and approximately 1.6% in recent estimates. 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 Kalman-smoothed 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 typically close to 1. Declining trend growth is the primary channel through which the natural rate has fallen in Korea and other advanced economies. 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 declining trend growth rate from 4% to 1.6% 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 Holston-Laubach-Williams trend potential growth, a latent random-walk state extracted by a two-sided Kalman filter and RTS smoother. Over 117 quarterly observations from 1997-03-31 to 2026-03-31, its measured serial correlation is dominated by the smoother's gain rather than by the data-generating process, so the object framed here is a persistence summary of the smoothed path and not an integration order of the data.

The integration-order battery is therefore 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 symmetric two-sided filter manufactures the persistence 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 the filter-persistent path spuriously segments (Perron 1989).

The matrix-mandated replacement is a descriptive persistence summary labeled as a property of the smoothed series. The lag-one autocorrelation is 1.001 and the implied half-life is undefined, since the coefficient sits at essentially unity, the very value a naive procedure would misread as a random walk, a description of how slowly the smoothed path decays that carries no integration-order claim. Because the HLW loader rewrites the full state history on every re-estimation, the smoothed state at any fixed past quarter revises across vintages, and no stored vintage panel exists to quantify the revision magnitude (Orphanides and van Norden 2002).

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, so the half-life is a lower-leaning descriptive figure whose median-unbiased interval would follow the grid of Andrews (1993), and the lag-one autocorrelation a portmanteau such as that of Ljung and Box (1978) would register is a filter-gain reading rather than evidence about the process. The model-implied content is honest as an assumption rather than a discovery, namely the random-walk state equation for trend growth and the median-unbiased signal-to-noise ratio the model pins by the method of Stock and Watson (1998), which is precisely why the near-unity persistence above must be read as the smoother's and not as an estimated integration order.