South Korea Near-Term Recession Probability

The near-term recession probability is the model-implied likelihood that the Korean economy will be in a business-cycle contraction three months ahead of the observation date, estimated by entering the shape of the government bond yield curve into a probit model. Because the conventional yield-curve recession literature operates at a twelve-month horizon, a companion estimate at that horizon is reported alongside as a transparency reference.

The probability is obtained from a probit model

where $R_{t+h}$ is a binary indicator equal to one when the economy is in contraction $h$ months after date $t$, $\Phi(\cdot)$ is the standard normal cumulative distribution function, and $x_t$ is a yield-curve predictor. Business-cycle contractions are dated by the official reference turning points published by Statistics Korea, which determines them from the cyclical movements of the coincident composite index, real GDP, and related indicators, and the contraction indicator is set to one for the months running from the period after a reference peak through the trough. This dating follows the convention used in the U.S. recession-probit literature.

What distinguishes this series from a textbook slope probit is the decomposition of the predictive spread into an expectations component and a term premium component. Under the no-arbitrage affine term structure model of Adrian, Crump, and Moench (2013), the slope separates exactly into a difference of risk-neutral rates and a difference of term premiums

The model enters the expectations slope and the term premium slope as separate predictors, and also reports as an alternative predictor the near-term forward spread (NTFS) built from the risk-neutral forward curve.

A rising fitted probability signals that a flattening or inverting yield curve is pricing in near-term policy easing and that contraction risk has risen, while a falling probability signals the opposite.

Estimated as a probit forecasting model on predictors derived from the ACM affine term structure decomposition (Adrian, Crump, and Moench 2013) at monthly frequency.

(1) Predictor construction. Three month-end predictors are formed from the fitted yield curve. The conventional term spread is the difference between the ten-year and three-month zero-coupon yields,

The expectations slope and the term premium slope are the risk-neutral and term premium components of the fitted spread,

so that

recovers the fitted spread up to the affine fitting error. The near-term forward spread compares the risk-neutral implied three-month rate six quarters ahead with the current three-month rate,

where $f^Q_t(6\text{Q})$ is obtained from the log-price identity

as

in months, using continuous-compounding risk-neutral yields recovered from the ACM affine coefficients.

(2) Probit estimation. For each predictor $x_t$, the contraction indicator $h$ months ahead is mapped to a probability through the probit link

estimated by maximum likelihood. The headline specification enters the expectations slope and the term premium slope as separate regressors,

, while the single-spread and near-term forward specifications are estimated alongside for comparison. Because the $h$-month horizon induces overlapping observations, inference uses Newey and West (1987) heteroskedasticity and autocorrelation consistent standard errors with the lag truncation set to the horizon minus one.

(3) Dual-horizon reporting. Two horizons are reported. The headline prob corresponds to a three-month forecast lead, the horizon at which the Korean data carries out-of-sample receiver operating characteristic discrimination above 0.6 for all three specifications in the expanding-window exercise described in step 5. A canonical twelve-month estimate is reported alongside for transparency and for contrast with the U.S. literature, where the twelve-month horizon is conventional. In the Korean sample the twelve-month estimate carries little discrimination, and it is exposed in the data and as a hidden chart line rather than as a headline forecast.

(3a) Display cadence. Coefficient estimation runs at monthly frequency, since the contraction target is monthly. The displayed series is daily, where the monthly-fitted coefficient vector is applied pointwise to the daily predictor grid, refreshing the fitted probability with each new daily yield-curve observation. Daily moves reflect daily changes in the yield curve passed through the probit link rather than additional recession signal. The recession signal itself is a slowly evolving cyclical indicator, so day-to-day fluctuations should not be over-interpreted. All performance metrics in step 5 are computed only on the monthly path; no metric is computed on the daily series.

(4) Re-estimation and revision. The model is re-estimated on the full sample at each update, so fitted probabilities for past dates revise as additional turning points are confirmed and as new predictor data shift the coefficient estimates. The likelihood contribution is omitted for the most recent $h$ months, where the contraction indicator is not yet observable, while the fitted probability is still reported as a forecast.

(5) Discrimination and fit. Model fit is summarized by the McFadden pseudo-coefficient of determination

and by the area under the receiver operating characteristic curve, computed in sample and through an expanding-window out-of-sample exercise that retrains the model at each step on data up to $t-1$ and predicts at $t$.

The estimates here rest on a short post-Global-Financial-Crisis sample, containing only three completed contraction episodes (2008–2009, 2011–2013, 2017–2020) within the predictor window. Confidence bands around the fitted coefficients are wide, no individual coefficient is statistically significant at conventional levels, and the indicator should not be treated as decisive on its own. The series' principal contribution is the decomposition framework rather than precise point estimates, and a reading should be corroborated by the output gap (KRGDPGAP), the real rate gap (KRRRGAP), and the term premium series (KRTP) before any inference is drawn.

The ability of the yield curve to carry information about future recessions is among the most robust empirical regularities in macroeconomics, because the curve embeds market expectations about the future path of monetary policy. When investors anticipate that the central bank will cut rates in response to a deteriorating outlook, long-term yields fall relative to short-term yields and the curve flattens or inverts (Estrella and Mishkin 1998). Estrella and Hardouvelis (1991) established that this signal leads real activity in the United States, and Rudebusch and Williams (2009) document that the curve forecasts U.S. recessions more reliably than professional forecasters, a puzzle given that the curve is public information. Ang, Piazzesi, and Wei (2006) found that the short-rate expectations extracted from a no-arbitrage model carry more predictive power for output than any single observed spread, locating the signal in the expectations channel.

The affine decomposition makes this channel observable. Hamilton and Kim (2002) separated the spread into expectations and term premium components and showed that the two contribute distinct information, with the expectations part dominating the forecast of future growth. Benzoni, Chyruk, and Kelley (2018) reached the same conclusion, finding that a decline in the expectations component, which reflects anticipated easing, is the strong recession signal, whereas a compression of the term premium carries weaker and sometimes offsetting information. Greenwood and Vayanos (2014) emphasize that term premium movements can be driven by demand-for-duration shocks unrelated to growth expectations, providing a theoretical basis for treating the two components asymmetrically. Reporting the expectations slope and the term premium slope separately therefore lets a reader judge whether a flat curve reflects a market that expects rate cuts, which is the genuine warning, or merely a depressed term premium.

The near-term forward spread of Engstrom and Sharpe (2019) sharpens the same idea. Rather than measuring the slope out to ten years, it compares the rate the market expects to prevail on a short instrument roughly six quarters ahead with the current short rate, isolating the near-term policy expectation that does most of the predictive work in the U.S. evidence. They show that once the near-term forward spread is included the conventional long-term spread adds little, consistent with the view that the recession signal is fundamentally about expected near-term monetary easing.

The strength of the yield-curve-recession relationship varies markedly across countries and over time. Chinn and Kucko (2015) caution that the relationship holds qualitatively across a panel of advanced economies while its strength varies across countries and time periods and has weakened in some, and the Korean evidence assembled here is consistent with that caution.

The sample caveat applies first to any positioning use. Three completed contraction episodes in the predictor sample is too few to support tactical decisions based on this series in isolation. Any portfolio action prompted by a movement in the fitted probability should be cross-checked against the term premium series (KRTP), the real rate gap (KRRRGAP), and the implied rate path (KRIMPR), and the position size should be scaled to reflect the wide confidence bands documented in the validation output.

With that constraint in mind, an elevated fitted probability has historically been associated with subsequent declines in the front end of the curve as the central bank eases, favoring receivers on the Korean interest rate swap curve and long positions in three-year Korea Treasury Bond futures. Harvey (1989) showed that the term structure's forecast of consumption growth maps into expected equity and bond returns, providing a theoretical link between the recession probability and cross-asset positioning, and Ilmanen (2011) provides a general framework for incorporating business-cycle signals into systematic bond allocation.

Separating the expectations slope from the term premium slope adds discrimination that a single spread cannot provide. A flattening driven by the expectations component, which signals that the market prices in monetary easing ahead of a downturn, warrants more caution than a flattening driven by a compressed term premium, which may reflect duration demand from price-insensitive investors (Hamilton and Kim 2002; Benzoni, Chyruk, and Kelley 2018). Bauer and Rudebusch (2014) document how the U.S. term premium during the large-scale asset purchase era complicated interpretation of the slope, and the decomposed signals here are intended to give a reader the tools to make the same distinction in Korean data.

The near-term forward spread is especially useful at the operational level because it expresses the priced-in easing expectation in basis points directly comparable to the policy rate, so the magnitude of the implied near-term policy shift can be read off the curve (Engstrom and Sharpe 2019). The companion twelve-month probability is reported in the data and exposed as a hidden chart line for readers interested in the canonical horizon of Estrella and Mishkin (1998). In the Korean post-GFC sample it carries little discrimination, and it is included for transparency rather than as a forecasting tool.

KRRECP is a model event probability, the probit fitted value $\Phi(\hat{\beta}^{\top} x)$ of a near-term recession on the ACM-decomposed yield-curve slope and the near-term forward spread, evaluated against the realized 0/1 recession outcome, so its scientific content is calibration and discrimination rather than any property of its own path.

Because the probability is a deterministic transform of fitted probit coefficients and is bounded in the unit interval, the standard unit-root battery of the augmented Dickey and Fuller (1979) regression, the Phillips and Perron (1988) test, and the KPSS stationarity test of Kwiatkowski et al. (1992) was deliberately not run, since a bounded fitted probability cannot be an unbounded random walk and its integration order is a property of the predictors rather than of the recession signal (Cavaliere 2005; Cavaliere and Xu 2014). Descriptive AR(1) persistence and its half-life were likewise forgone, and the level Ljung and Box (1978) portmanteau was excluded, because the autocorrelation of a fitted probability measures the smoothness of the conditioning variables and not forecast quality (Murphy and Winkler 1987). A level Bai and Perron (1998) break search was ruled out, since a break in a fitted probability reflects a predictor regime already inside the model rather than a shift in skill (Perron 1989), and seasonal-frequency tests carry no meaning for a model probability and were not applied (Ghysels and Osborn 2001).

The battery appropriate to a probability forecast is calibration and discrimination. Over the reused validation panel the Brier (1950) score for the headline three-month specification is 0.211 across 231 labeled months from 2000-12 to 2020-02, and 0.239 across 222 months to 2019-05 at the twelve-month horizon. Its Murphy (1973) vector partition into reliability, resolution, and uncertainty,

computed on equal-count deciles, returns reliability 0.040, resolution 0.073, and uncertainty 0.244 at three months, and reliability 0.021, resolution 0.024, and uncertainty 0.243 at twelve months, so the probabilities are well calibrated with the small reliability term while the resolution that carries information content is modest and collapses at the longer horizon. Discrimination is read from the area under the ROC curve with the Hanley and McNeil (1982) standard error. The in-sample AUROC is 0.706 at three months with a standard error of 0.036 and a z-statistic of 5.75 against the no-discrimination value, against an out-of-sample expanding-window figure of 0.670, while at twelve months the AUROC is 0.540 with a standard error of 0.040 and a z-statistic of 0.99, statistically indistinguishable from chance.

Two limits are stated as such. The recession event is rare, so the uncertainty ceiling is small and a low raw Brier score is largely the base rate, which is why the resolution term and the skill against climatology, not the raw score, carry the reading, and the upper-probability deciles hold few months so the within-bin frequencies and the reliability term are noisy in this sample (Brocker and Smith 2007). The number of recession-labeled positive months is the binding sample size for the discrimination standard error rather than the full count of labeled months, so the twelve-month AUROC near one-half is weak evidence of discrimination rather than strong evidence against it, and a formal calibration test is left to the reliability diagram rather than a grouped chi-squared or z-test (Spiegelhalter 1986).