South Korea House Price Gap

KRHPI is Korea's real residential house price index, net of general price-level changes, and KRHPGAP expresses in percent how far that index has departed from its own trend. Formally, KRHPI is the nominal residential property price deflated by the consumer price index and normalized to 2010 = 100. KRHPGAP is the one-sided Hodrick-Prescott gap that measures the deviation of its log level from a recursively estimated trend $\tau_t$:

where $\tau_t$ is the real-time trend estimated using only the data available through $t$. A positive and widening gap means that real house prices exceed a slow-moving trend, which commonly appears together with a build-up of household leverage and tends to precede financial instability. A negative gap points to a correction phase in which prices fall below trend.

(1) Real house price index. KRHPI is the Bank for International Settlements real residential property price series for Korea, the nominal residential property price deflated by the consumer price index, redistributed at index 2010 = 100 and dated to the end of each quarter, the construction documented by Scatigna, Szemere, and Tsatsaronis (2014). It is cross-validated against the Korea Real Estate Board national house sale price index, with which it co-moves closely on the overlapping sample.

(2) One-sided Hodrick-Prescott gap. KRHPGAP is the one-sided gap of the log real house price index, built identically to the credit-to-GDP gap KRCGAP. At each quarter $t$ a two-sided Hodrick and Prescott (1997) filter with smoothing parameter $\lambda = 400{,}000$ is fit on the sub-sample through $t$ and the endpoint trend value is kept, giving a recursive expanding-window trend $\tau_t$ that uses only information available at $t$. The trend minimizes

over $\tau$, where $x_s = \ln \text{HPI}_s$, and the gap is

in percent.

(3) Smoothing parameter. The setting $\lambda = 400{,}000$ is the Basel quarterly standard for slow-moving financial trends (Borio and Lowe 2002; Bank for International Settlements 2016; Drehmann et al. 2010). This value lies far above the Ravn and Uhlig (2002) business-cycle setting, so the trend absorbs only the lowest-frequency movement and the gap retains the medium-term cycle, with Mehra (2004) providing the frequency interpretation.

(4) Real-time property and burn-in. Because the trend at $t$ uses only data through $t$, the gap is real-time and does not revise as later data arrive. This non-revising property is central for early-warning use and is the reason a one-sided rather than two-sided filter is used (Borio and Drehmann 2009). The trade-off is that the one-sided filter's trend estimate becomes imprecise near the sample end, which Edge and Meisenzahl (2011) analyze, with the spurious-dynamics critique of Hamilton (2018) providing the general case. The first forty quarters are a burn-in and report no value, following the Drehmann and Tsatsaronis (2014) and Drehmann and Yetman (2018) convention for the credit-gap family.

House prices transmit to the real economy through the household balance sheet. A house-price decline destroys collateral and net worth at once, forcing a sharper consumption contraction the more levered the household (Mian and Sufi 2014), and this mechanism extends to a panel of thirty countries, where a rise in the household debt-to-GDP ratio predicts slower output growth two to three years later (Mian, Sufi, and Verner 2017). Residential investment, which house prices lead, is the most reliable single cyclical indicator (Leamer 2007), and the collateral channel formalizes the mechanism by which house prices amplify the business cycle (Iacoviello 2005).

House prices sit at the center of financial-stability analysis (Borio and Lowe 2002; Borio and Drehmann 2009). Recessions accompanied by a house-price boom and its collapse are deeper and longer (Claessens, Kose, and Terrones 2012), and booms financed against housing collateral are the credit booms most likely to end in crisis (Jordà, Schularick, and Taylor 2016). The property-and-credit cycle forms the core of the medium-term financial cycle that policy tends to neglect (Aikman, Haldane, and Nelson 2015), and house-price overvaluations are persistent while their unwinding is costly (Igan and Loungani 2012).

The house-price deviation is among the most informative crisis predictors when combined with credit. Property-price collapses are among the defining features of severe financial crises (Reinhart and Rogoff 2009), and the combination of house-price and credit booms is the most informative crisis predictor (Cerutti, Dagher, and Dell'Ariccia 2017). The policy tools deployed against such real-estate booms have also been catalogued extensively (Crowe et al. 2013).

The object of interest is the deviation from trend, not the price level. The level reflects long-run fundamentals that vary across countries and over time, so it cannot by itself indicate overheating, and the diagnostic object is therefore the degree to which prices depart from their own trend (Glaeser and Nathanson 2015; Muellbauer 2012).

Korea combines a high household-debt-to-income ratio with a housing market that has gone through repeated policy-driven cycles. The loan-to-value and debt-to-income limits the authorities deploy measurably slow house-price appreciation and transaction volume (Igan and Kang 2011), and the structural and cyclical drivers of the Korean house-price cycle and the role of metropolitan supply constraints have also been analyzed (Geng 2018). The KRHPGAP gauge places the current real house price against its own recursive trend, so the recent reading of about minus six percent indicates that Korean real house prices sit below their slow-moving trend after the 2022–2024 correction. This is a within-Korea cyclical signal rather than a cross-country valuation comparison, consistent with the Cerutti, Claessens, and Laeven (2017) finding that the credit-and-house-price cycle should be read against a country's own history.

House-price gaps are among the most reliable medium-term early-warning indicators for systemic banking crises. The joint property-price-and-credit gap outperforms either indicator alone (Borio and Drehmann 2009), and the property-price gap's forecasting value holds across horizons (Drehmann and Juselius 2014). Several early-warning studies consistently rank house-price-gap measures among the top predictors. The European Systemic Risk Board early-warning work (Detken et al. 2014), the optimal-threshold analysis (Alessi and Detken 2018), and the model comparison (Anundsen et al. 2016) all do so, and the combined credit-and-property-price gap is identified as the highest-conviction crisis signal (Aldasoro, Borio, and Drehmann 2018).

The house-price gap is a direct input to macroprudential policy timing. Property-price gaps enter the countercyclical-capital-buffer decision (Gerdrup, Kvinlog, and Schaanning 2013), and the loan-to-value, debt-to-income, and capital tools mobilized against real-estate booms have also been catalogued (Crowe et al. 2013). Because these borrower-based limits actually work in Korea (Igan and Kang 2011), KRHPGAP, read alongside the credit-to-GDP gap KRCGAP and the debt service ratio KRDSR, is a leading indicator of when Korean macroprudential limits are next tightened or loosened.

For credit investors, a high and rising house-price gap signals a build-up of collateral-driven leverage that tends to precede wider credit spreads and a turn in the bank-credit-loss cycle (Jordà, Schularick, and Taylor 2015). Conversely, a low or negative gap, as in Korea's recent reading, signals the correction phase, where the risk shifts from overheating to a balance-sheet drag (Mian and Sufi 2014).

KRHPGAP is most useful when read alongside the other credit and financial-cycle series. KRCGAP captures the credit-stock dimension (Borio and Lowe 2002), KRDSR captures the cash-flow dimension (Drehmann and Juselius 2014), and the house-price gap captures the collateral-and-asset dimension, so the three together give a layered read that no single series delivers alone.

KRHPGAP is a one-sided Hodrick and Prescott (1997) real house-price gap with the smoothing parameter set to 400000, built recursively through each quarter from contemporaneously available data, so it is a stationary-by-construction object rather than an observed level. The augmented Dickey-Fuller, Phillips and Perron (1988), and KPSS (Kwiatkowski et al. 1992) unit-root battery, with the DF-GLS test of Elliott, Rothenberg, and Stock (1996) and the Ng and Perron (2001) refinement, was deliberately not run, because an HP cycle of a driftless random walk is judged stationary by the Dickey and Fuller (1979) test in a large majority of replications and a rejection would confirm the filter rather than discover mean reversion (Hamilton 2018).

Its first-order autoregressive coefficient is 0.988 over 164 quarterly observations from 1985-03-31 to 2025-12-31, a half-life of about 59.6 quarters reported descriptively and not as an order of integration and read with the near-unity small-sample bias of Andrews (1993) in mind, with a standard deviation of 12.39 percentage points and a range whose bounds are −33.91 and 14.94 percentage points.

The Bai and Perron (1998, 2003) break procedure, admissible because the gap is stationary by construction, locates three breaks in the mean at 1992-06-30, 2002-03-31, and 2012-12-31, and the gap is non-revising by construction, a fixed past-quarter value identical across three committed vintages at a revision of 0.0000 percentage points (Orphanides and van Norden 2002).