South Korea DB Core CPI 12-Month Inflation-at-Risk

This gauge applies quantile regression to Korean DB core CPI as an Inflation-at-Risk measure, with the conditional distribution of the 12-month-ahead average annualized inflation rate as the headline object (López-Salido and Loria 2020). With $\pi_{t\to t+h}$ the average annualized inflation rate from month $t$ to month $t+h$, this series is the $h=12$ horizon, and its headline is the two-sided quantiles $\{Q_{0.05},\,Q_{0.50},\,Q_{0.95}\}$ reported jointly in percent. The quantile fan running from $q_{05}$ to $q_{95}$, the two-sided expected shortfalls, and the downside-minus-upside asymmetry $(q_{50}-q_{05})-(q_{95}-q_{50})$ are provided as auxiliary series for reading which part of the distribution current conditions are acting on.

The interest is in both tails, with the 95th percentile answering how deep the inflation tail can run when financial conditions tighten and the 5th percentile answering the low-inflation and deflation risks. This gauge is a characterization of the conditional distribution, not a point forecast.

Computed in five steps that combine quantile regression with a skew-t expected-shortfall layer.

(1) Conditional quantile regression. The conditional quantiles come from quantile regression fit in inflation-gap form (Koenker and Bassett 1978),

where

is the 3-month trailing annualized inflation, $\pi^{\text{long}}_t$ is a long-run anchor that combines the Bank of Korea inflation target, the Stock and Watson (2007) UCSV trend, and a survey-expectations component, $\text{gap}_t$ is the one-sided HLW Kalman-filtered output gap (Holston, Laubach, and Williams 2023), and $\text{FCI}_t$ is the level of KRFCI. The slack regressor is the Kalman-filtered estimate rather than the two-sided RTS-smoothed series the HLW step publishes as its headline, and the filter at $t$ uses only data through $t$, so it carries no look-ahead. Fitting in gap form automatically imposes the implicit coefficient $1-\lambda_\tau$ on $\pi^{\text{long}}_t$, so the accelerationist sum-to-one restriction holds mechanically without a separate explicit constraint, which is the discipline Faust and Wright (2013) identify as the price of admission for any modern Phillips-curve specification. The level quantiles are recovered as

and per-row monotonicity across $\tau$ is enforced by the Chernozhukov, Fernández-Val, and Galichon (2010) rearrangement.

(2) Estimation frequency and HAC standard errors. Coefficients are estimated at monthly frequency on the target's natural cadence, with Newey-West HAC standard errors at lag $h-1$, namely 11 months, to absorb the overlapping 12-month targets. Monthly inputs are step-held onto the business-day grid at a publication-lag stamp matching the official CPI release timing, the fitted betas are evaluated on the daily regressor frame, and KRFCI enters as its daily level, so the daily variation is FCI-driven exactly as in KRGAR.

(3) Seasonal handling. The DB core CPI series published by the Bank of Korea is not seasonally adjusted, and at the 12-month horizon seasonal noise is material both in the trailing inflation regressor and in the forward target. Each pipeline run performs the seasonal-and-trend decomposition of Cleveland, Cleveland, McRae, and Terpenning (1990) on the log level and, when the Wang, Smith, and Hyndman (2006) seasonal-strength statistic exceeds 0.20, substitutes the deseasoned reconstruction for the raw level, recording both the choice and the strength value so the vintage stays reproducible.

(4) Expected shortfall and asymmetry. The two-sided expected-shortfall and asymmetry layers come from an Azzalini-Capitanio skew-t (Azzalini and Capitanio 2003) fit to the rearranged conditional quantiles. The full four-parameter $(\xi, \omega, \alpha, \nu)$ is fit per month on the monthly-fit-evaluated level quantiles, the shape $(\alpha, \nu)$ is carried forward to daily, and the daily $(\xi, \omega)$ are recovered in closed form by ordinary least squares against the standardized quantiles

. This extends to a daily display the per-period shape discipline KRGAR uses at quarterly cadence, and it mirrors the location-scale recovery pattern Korobilis (2017) lays out for daily quantile forecasting. The lower-tail expected shortfall is $E[\pi\mid \pi < q_{05}]$ with the threshold pinned to the QR-direct $q_{05}$, the upper-tail expected shortfall is $E[\pi\mid \pi > q_{95}]$ with the threshold pinned to the QR-direct $q_{95}$, and hard clips $\text{ES}_{\text{low}}\le q_{05}$ and $\text{ES}_{\text{high}}\ge q_{95}$ absorb residual grid-interpolation noise. The asymmetry is

with the same sign convention as KRGAR, so positive values mark a fatter conditional low-inflation tail than high-inflation tail.

(5) Real-time re-estimation. Coefficients refit on the full sample every run, so the latest published days are the least settled.

This gauge models the tails of the inflation distribution directly by treating each conditional quantile as a separate object of interest rather than the mean (López-Salido and Loria 2020). It extends the Vulnerable Growth template of Adrian, Boyarchenko, and Giannone (2019) to the inflation distribution, taking the Koenker and Bassett (1978) quantile regression as its workhorse and imposing an accelerationist sum-to-one anchor that ties the regression to a long-run trend, so the conditional distribution reaches for an inflation target instead of drifting on a full-sample average. The conditioning set follows the financial-conditions logic of Hatzius, Hooper, Mishkin, Schoenholtz, and Watson (2010), with the level of KRFCI entering the regression alongside the look-ahead-free one-sided Kalman-filtered HLW output gap (Holston, Laubach, and Williams 2023) and the trailing three-month gap to the Bank of Korea 2 % point inflation target in force since 2016. KRFCI enters as its raw level rather than the macro-orthogonalized variant KRGAR uses, since KRIAR already controls for slack and the anchor inside the regression, so orthogonalizing would project away the financial-conditions channel López-Salido and Loria set out to identify.

The single most honest headline statement on this sample is that FCI conditioning helps describe disinflation risk at the 12-month horizon but does not improve high-inflation risk and out-of-sample worsens it. Mean inflation forecasts have long been extremely hard to beat (Atkeson and Ohanian 2001), and the value of the quantile decomposition is precisely that it makes visible the at-risk signal the centre of the distribution loses, in the spirit of the inflation-forecast literature Faust and Wright (2013) survey.

Conditioning on the anchored Phillips structure changes where this gauge sits at the centre. At the median the implicit coefficient on $\pi^{\text{long}}_t$ is

, so the conditional median rides the BOK-target, UCSV-trend, and survey composite anchor rather than a full-sample average, which is the persistence-modelling discipline Stock and Watson (2007) document for advanced-economy inflation and Mertens and Nason (2020) carry across countries. Anchored expectations are the primary reason an anchored conditional distribution behaves well in the first place (Coibion and Gorodnichenko 2015). On the Korean sample the 12-month conditional median climbs from about 1.0–1.5 % over 2017–2020 to 2.7 % in 2022 and then normalizes near 1.5 % over 2024–2026, tracking realized 12-month-ahead inflation and the era-level anchor the Bank of Korea and the official CPI vintages publish, which is the kind of behaviour Korobilis (2017) reports for analogous direct-quantile inflation models elsewhere.

The Korean sample does not statistically identify an FCI asymmetry direction at the 12-month horizon. The conditional FCI slope $\hat\theta_\tau$ runs over a narrow band around zero with no individual $t$-statistic crossing one, the diagonal-HAC joint Wald test on equality across $\tau$ does not reject at any conventional level, and all pairwise contrasts carry $p$-values well above 0.85. The sample therefore does not reproduce the lower-tail asymmetry direction López-Salido and Loria (2020) document for the U.S., nor does it support the upper-tail rising channel Banerjee, Contreras, Mehrotra, and Zampolli (2020) record in emerging-market samples where currency depreciation lifts the upper inflation quantile, so only the point profile is reported descriptively. The methodological citation for the accelerationist quantile Phillips curve with the sum-to-one restriction stands, although the empirical asymmetry direction is not asserted as a Korean result.

The sample is what bounds the framework. The only two full inflation episodes in the post-2006 record are the 2007–2008 oil shock and the 2022–2023 supply-chain shock that the official CPI vintages document at the headline level, and the effective number of independent observations for the 12-month overlapping-target panel is roughly nineteen against roughly seventy-five at the 3-month horizon, so the better-identified calibration read lives in the companion 3-month series rather than here. In-sample PIT and pinball metrics within one or two percentage points of nominal at all seven $\tau$ are near-mechanical against that count and cannot themselves be evidence of calibration. The honest reading is therefore that the 12-month gauge is descriptive of how current conditions tilt the inflation distribution and is correctly anchored to the trend, while statistical inference on the FCI channel is left for a richer sample.

For monetary surveillance and the rates desk the headline reads on both sides, with the weight on each tail calibrated to what the out-of-sample block shows. At the 12-month horizon the conditional pinball ratio against the unconditional benchmark sits well below one in the lower tail, near one at the median, and well above one in the upper tail, and the upper-tail PIT runs roughly nine percentage points below nominal, which is the order of magnitude at which an out-of-sample claim has to be downgraded rather than presented as a sharper signal. The lower-tail gain is not crisis-driven, as an ex-crisis recomputation that excludes the 2008–2009 and 2020 windows leaves the lower-tail ratio essentially unchanged, while the upper-tail miss almost halves under the same exclusion and is therefore episode-concentrated rather than structural. The opposite asymmetry, namely a confident lower tail and an uncertain upper tail, is what the rates desk should carry into a stress scenario.

The fan and the two-sided expected shortfalls are where the construction repays its complexity over a single inflation nowcast, although the same out-of-sample limitation applies. A widening upside spread with a stable median reads as a descriptive statement of how current conditions are pricing the upper quantile rather than a quantitative ceiling for future risk. The lower-tail expected shortfall is the more coherent input for deflation-scenario design, since the data say it is the side where the conditional quantile actually carries information, and the asymmetry channel is read as a description of the point profile rather than a directional statement, since the FCI direction is not statistically distinguishable on this sample.

The gauge is meant to be read alongside KRFCI and KRGAR. KRGAR draws growth tails that respond to the macro-orthogonalized KRFCI variant, while KRIAR draws inflation tails on both sides that respond to the raw level of KRFCI, so how the two gauges respond differently to the same KRFCI event is the first-order policy variable. Adrian, Boyarchenko, and Giannone (2019) frame the growth-tail cadence and López-Salido and Loria (2020) the inflation-tail cadence, and Hatzius, Hooper, Mishkin, Schoenholtz, and Watson (2010) close the loop with the financial-conditions link, so the three gauges read as a coherent macro-risk dashboard rather than three independent panels. The surveillance schedule these tails naturally fit is the Bank of Korea Financial Stability Report cycle, and the 12-month horizon is the standard horizon over which monetary-policy transmission operates and matches that reporting cycle.

As with KRGAR and KRFXAR the gauge is descriptive rather than predictive and refits on the full sample every run, so history revises as the panel grows and the latest published days are the least settled. The upper tail in particular carries less out-of-sample weight than the lower tail and concentrates its miss in the 2008–2009 and 2020 windows, and that asymmetry of out-of-sample confidence is what determines where the rates desk should pay attention rather than the level of the headline alone.

KRIAR12M is an estimated conditional quantile path of twelve-month-ahead inflation, $\hat{q}_t(\theta)=x_t^{\top}\hat{\beta}(\theta)$ from the gap-form quantile regression, so its persistence is inherited from the conditioning variables and the object that carries forecast quality is the violation-indicator sequence, not the path. Unit-root, structural-break, and level Ljung and Box (1978) batteries on the path were deliberately not run, because coverage is a property of the joint forecast-outcome distribution that a univariate path diagnostic cannot address (Christoffersen 1998; Engle and Manganelli 2004; Murphy and Winkler 1987), and a bounded estimated quantile cannot be an unbounded unit-root process on which standard inference over-rejects (Cavaliere 2005; Cavaliere and Xu 2014). The appropriate evidence is coverage backtesting at the two pinned extreme tails, the fifth and ninety-fifth conditional quantiles.

At a twelve-month horizon the violation sequence overlaps across a full year of adjacent months, so no size-correct unconditional-coverage test exists on the full sample. A literal Kupiec (1995) likelihood-ratio test on the overlapping sample and a Newey and West (1987) autocorrelation-robust coverage statistic constructed to repair it were both found materially oversized in a pre-registered Monte-Carlo size check recorded in the model specification, so a formal unconditional-coverage verdict is withheld on the full sample and the full-sample record is reported descriptively.

Two coverage panels appear because they measure different things. The reused validation panel is the in-sample probability-integral-transform hit rate over the estimation panel, the empirical frequency that the realized outcome falls at or below the fitted conditional quantile, so it targets the quantile level itself and reads 0.062 at the fifth-percentile quantile and 0.942 at the ninety-fifth over 225 months, the upper figure being cumulative coverage near its ninety-five-percent target rather than a breach rate. The pinned monthly-sampled backtest of 226 observations from 2006-09-30 to 2025-06-30 instead counts tail exceedances directly, the breaches below the fifth-percentile quantile and above the ninety-fifth, recording seventeen lower-tail exceedances at a rate of 0.075 and sixteen upper-tail exceedances at 0.071, both a little above the five-percent tail mass.

The size-correct check on the offset-zero non-overlapping subsample is itself uninformative at this horizon, because the eighteen-observation subsample expects only 0.9 exceedances at the five-percent tail, fewer than one, so it records zero lower-tail and one upper-tail exceedance, 1.847 at p = 0.174 and 0.011 at p = 0.915, with too little power to distinguish correct from incorrect coverage. The subsample check is exact under the hypothesis of correct conditional coverage, which renders the spaced violation indicators independent Bernoulli draws (Christoffersen 1998), and it does not claim size control for exceedances of a fixed unconditional quantile of a persistent process, where dependence can cross the non-overlapping window boundaries. The exceedance rate ranges from zero to 0.167 at the lower tail and from zero to 0.111 at the upper tail across the twelve admissible offsets, and no formal coverage verdict is drawn at this horizon.

The Christoffersen (1998) independence and conditional-coverage tests reject strongly at both tails, the independence statistics 22.861 at p = 0.000 and 32.184 at p = 0.000 and the conditional-coverage statistics 25.554 at p = 0.000 and 34.061 at p = 0.000, which is the serial dependence that the overlapping twelve-month target mechanically induces in the hit sequence rather than a coverage failure and is consistent with the verdict withheld on the full sample. The Engle and Manganelli (2004) dynamic-quantile test is run in its constant-only binomial-score form because the overlap removes the eligible instruments, and it fails to reject at both tails, 3.027 at p = 0.082 and 2.058 at p = 0.151, with the full instrument set deferred. The cross-quantile monotonicity check confirms a non-crossing fan (Chernozhukov, Fernandez-Val, and Galichon 2010).

The limits are stated as such. At a twelve-month horizon the effective number of independent windows is a small fraction of the 226 sampled points, so the non-overlapping subsample expects fewer than one exceedance and delivers no formal coverage verdict, and the descriptive exceedance rate and the reused validation coverage are read as the honest content while the overlapping-sample tests are withheld (Kupiec 1995; Berkowitz 2001; Diebold, Gunther, and Tay 1998; Rosenblatt 1952). Because these are estimated quantiles whose parameter uncertainty is not absorbed into the reference distribution, the coverage reading is descriptive of how current conditions place the inflation distribution rather than a validated forecast (Campbell 2005; Escanciano and Olmo 2010).