South Korea Employment Growth (YoY)

The series in this group are year-over-year growth rates of the seasonally-adjusted-at-source activity and employment levels, each reported as an annual percentage change. A growth rate of this kind is a derived transform rather than a directly observed quantity, obtained by comparing a level index or count with its own value twelve months earlier. Writing $x_t$ for the seasonally-adjusted level in month $t$, the year-over-year rate expresses the proportional change from $x_{t-12}$ to $x_t$ in percent. Because this is a ratio of the same series at two dates, any fixed base-year normalization of the underlying index cancels, so the growth rate is invariant to the reference year and to the units in which the level is measured. The twelve-month difference also filters the series at the seasonal frequency and removes the fixed within-year pattern that source seasonal adjustment does not fully absorb, which centers the measure on the cyclical pace of activity. The resulting object is a stationary rate rather than a trending level, and it summarizes how fast production, sales, service output, or employment is expanding or contracting relative to the same month of the previous year.

Each series is the year-over-year percentage change of the seasonally-adjusted level. Let $x_t$ be the level in month $t$. The growth rate is

with a twelve-month lag for these monthly series. No additional seasonal adjustment, smoothing, or detrending is applied, because the source level is already seasonally adjusted and the twelve-month difference removes any residual fixed seasonal pattern. The base-year normalization cancels in the ratio $x_t / x_{t-12}$, so the growth rate does not depend on the index base or on the level units. The first growth observation becomes available twelve months after the first level observation, and each value uses the most recent published vintage of the underlying level, so the growth series inherits any later revisions to that level.

Year-over-year growth rates of production, sales, and employment are among the most widely used coincident indicators of the business cycle, and their measurement traces to the reference-cycle program of Burns and Mitchell (1946). Because the twelve-month change removes seasonality and low-frequency base effects, it isolates the cyclical component that dating committees and forecasters monitor, and it aligns closely with the coincident-index tradition of Stock and Watson (1989). Industrial-production and all-industry output growth capture the goods and broad-economy side of the cycle, retail-sales growth proxies household demand, services-production growth reflects the largest and least cyclically volatile sector, and employment growth summarizes the labor-market response that typically lags output.

The stationarity of these rates makes them convenient inputs to the dynamic-factor and vector-autoregression models popularized by Sims (1980), where trending levels would otherwise require differencing. Comovement across the five rates is informative about the breadth of an expansion, a property emphasized in the diffusion-index work of Stock and Watson (2002), whereas divergences, such as employment growth holding up while production growth turns negative, help characterize the nature of a slowdown. Because the growth rate discards the level, it is silent about the absolute scale of activity and about slow-moving structural change in potential output, so it is best read alongside the level indices and trend-output measures rather than on its own (Zarnowitz 1992).

For investors, year-over-year activity and employment growth are macro conditioning variables that shape the path of policy rates, earnings, and credit. Because the Bank of Korea weighs real-activity momentum in its rate decisions, turning points in production and employment growth carry information for the front end of the government-bond curve, and surprises relative to expectations move yields much as data surprises do in the event-study tradition of Kuttner (2001). Retail-sales and services growth are timely reads on domestic demand that feed nowcasts of quarterly GDP, complementing the mixed-frequency factor approach of Giannone, Reichlin, and Small (2008).

Across asset classes, the breadth and direction of these growth rates inform cyclical positioning. Broad-based acceleration tends to support cyclically sensitive equities and to sustain credit-spread compression, whereas synchronized deceleration in production and employment growth is a classic late-cycle signal that argues for defensive rotation and duration extension. Because the rates are stationary and comparable across sectors, they are natural regressors in return-predictability and sector-rotation frameworks in the spirit of Chen, Roll, and Ross (1986), who linked industrial-production growth and other macro factors to equity risk premia. As with any coincident indicator, these series describe the current pace of activity rather than forecast it, and their tendency to be revised means real-time trading signals should treat the latest print as provisional (Zarnowitz 1992).

KREMPYOY is the year-over-year growth rate of the seasonally-adjusted-at-source employment level, and this rate rather than the underlying count is the candidate stationary object the battery assesses. The sample is 311 monthly observations spanning 2000-06 to 2026-04, and the unit-root triplet is fitted on the level of the rate with a constant and trend. The augmented Dickey-Fuller regression of Dickey and Fuller (1979), in the lag-augmented form of Said and Dickey (1984), rejects the unit root at p = 0.008, the nonparametric test of Phillips and Perron (1988) concurs at p = 0.001, and the stationarity-null test of Kwiatkowski et al. (1992) does not reject trend stationarity at p > 0.10, so all three procedures agree on a clean I(0) reading. Because the three readings already concur, the agreement is not an artifact of the Phillips-Perron over-rejection toward spurious stationarity documented by Ng and Perron (2001), since the augmented Dickey-Fuller and stationarity-null legs corroborate it independently.

On the level of the rate, which is the candidate stationary object, the portmanteau statistic of Ljung and Box (1978) rejects the no-autocorrelation null at both the lag-12 and lag-24 rungs, with Q = 865.23 and Q = 919.53 respectively, each at p = 0.000, confirming the strong serial dependence expected of a persistent growth rate. Because the rate itself rather than its difference is the candidate stationary object, a level break search is the appropriate mean-shift diagnostic (Perron 1989), and the procedure of Bai and Perron (1998), computed by the dynamic-programming algorithm of Bai and Perron (2003), locates four mean shifts, at 2005-01, 2010-04, 2015-03, and 2021-03.

Because the year-over-year construction is itself the seasonal-differencing filter that removes the seasonal unit roots the HEGY class interrogates, the HEGY and Canova-Hansen seasonal-unit-root tests are deliberately not run, since testing seasonal unit roots the transform has already annihilated would be circular (Hylleberg et al. 1990; Canova and Hansen 1995; Ghysels and Osborn 2001).