South Korea Industrial Products CPI

KRCPIAGRI, KRCPIINDGOODS, KRCPIUTIL, KRCPIRENT, KRCPIPUBSVC, and KRCPIPRIVSVC are six raw consumer price sub-index levels recorded without transformation, each the monthly index-number level (2020 = 100) for one commodity-nature partition of the same consumer basket that underlies the headline index, namely agriculture-livestock-fisheries products, industrial products, electricity-gas-water, housing rent, public services, and private services.

Each sub-basket level is computed as a base-period-quantity-weighted aggregate over the items assigned to that partition, and because the weights are held fixed within each partition, movements in a sub-index reflect price change within that commodity class alone rather than a shift in its composition (Laspeyres 1871).

The current-period-weighted counterpart and the ideal index that is the geometric mean of the two bound each sub-basket's fixed-base level from above and below, and this ideal index satisfies the time- and factor-reversal tests (Paasche 1874; Fisher 1922). The expenditure-share-weighted log-change form gives the superlative approximation against which any fixed-basket sub-level is read (Törnqvist 1936).

The quantity each sub-index ultimately approximates is a partition-specific true cost-of-living index, the expenditure ratio that holds household utility fixed within that commodity class (Konüs 1939). This target is made precise within the four-approach taxonomy of index-number theory (Diewert 2002), whose economic approach is grounded in the exact and superlative aggregators (Diewert 1976).

Because each sub-basket is held fixed, its level departs from its own cost-of-living target by the substitution and quality-change wedge and by measurement bias, the same wedge documented for the headline aggregate (Diewert 1998; Boskin et al. 1996). The axiomatic consistency the construction does satisfy belongs to the test-approach lineage (Balk 1995).

Unlike a core measure formed by removing volatile items from the full basket (Eckstein 1981), a commodity-nature sub-basket instead partitions the full basket by economic classification, so no item is excluded and each of the six levels sums, at its own expenditure weight, back to the headline index.

KRED applies no transformation to any of the six sub-index levels, loading each published figure as recorded with only a date parse and a reshape into the long store. It therefore performs no re-indexing, deflation, smoothing, annualizing, or year-over-year differencing on any of the six.

The measurement basis by which each level comes to exist is the same fixed-basket aggregation as the headline index, restricted to the items assigned to one commodity-nature partition, where the base-period expenditure survey fixes the quantity weights within that partition and the elementary price relatives are combined into a sub-index anchored at 2020 = 100 (Laspeyres 1871).

Each sub-basket construction sits within the same index-number framework whose alternatives are the current-weighted index, the symmetric ideal index, and the expenditure-share log-change index (Paasche 1874; Fisher 1922; Törnqvist 1936), the last two being the superlative formulas exact for flexible aggregators (Diewert 1976).

The four conceptual routes to the same number, fixed-basket, test, stochastic, and economic, apply identically at the sub-basket level (Diewert 2002). The axiomatic properties each sub-level satisfies are characterized within the test approach (Balk 1995). The cost-of-living concept each targets is defined as the expenditure ratio that holds utility fixed within that commodity class (Konüs 1939).

The gap between each fixed-base sub-level and its own economic target consists of substitution bias and broader measurement bias, and because each series is served exactly as measured, KRED does not correct it (Diewert 1998; Boskin et al. 1996).

Unlike the exclusion rule that defines a core aggregate by removing the most volatile components from the full basket (Eckstein 1981), the six commodity-nature partitions instead cover the full basket exhaustively, so summing the six at their own expenditure shares reconstructs the headline level rather than a narrower core variant.

As sub-baskets of the consumer price index, these six levels are the empirical counterparts of the cost-of-living concept applied within one commodity-nature partition at a time, and their use for a decomposed reading of price stability turns on how closely each fixed-basket level tracks its own partition's cost-of-living concept (Konüs 1939), the same base-period-quantity-weighted construction underlying every fixed-basket sub-level (Laspeyres 1871).

Each sub-index carries the same known upward-biased character as the headline aggregate. The fixed-base Laspeyres level overstates true cost-of-living growth by a substitution wedge, and the combined commodity-substitution, outlet, quality-change, and new-goods bias widens that wedge within each partition (Diewert 1998; Boskin et al. 1996).

For monetary-policy purposes the headline level is routinely decomposed into a persistent component and transitory noise framed as trend plus transitory disturbance plus bias (Cecchetti 1997; Eckstein 1981), and the six commodity-nature sub-baskets offer a complementary decomposition by economic origin rather than by the statistical volatility that motivates trimming (Bryan and Cecchetti 1994; Bryan, Cecchetti, and Wiggins 1997).

Reading the utility, industrial-goods, rent, and services sub-baskets separately isolates which economic channel, namely supply cost, administered pricing, housing, or labor-intensive services, is driving a given headline move, a decomposition the core-versus-headline split by volatility does not itself provide (Quah and Vahey 1995).

The trend extracted from the aggregate series by the unobserved-components stochastic-volatility model remains the slow-moving inflation objective against which policy is calibrated, and the sub-baskets here are read as its economic-origin decomposition rather than as a substitute trend estimate (Stock and Watson 2007). The four-approach index-number taxonomy explains why a single partition-level index can still anchor sector-specific expectations (Diewert 2002).

For asset pricing each sub-index level is a partition-specific deflator, and index-number theory formalizes the reversal properties any such deflator should satisfy through the time- and factor-reversal tests (Fisher 1922). The base-quantity weights, their current-weighted dual, and the expenditure-share log-change form bound the deflation error within each partition just as for the headline aggregate (Laspeyres 1871; Paasche 1874; Törnqvist 1936).

Inflation-linked instruments settle on the realized path of the headline level rather than any single sub-basket, but the substitution and quality-change wedge priced into the basis between indexed and nominal instruments is itself an aggregation of the same wedge documented within each fixed-base sub-index (Diewert 1998; Boskin et al. 1996).

Because no sub-basket level is the superlative cost-of-living target, the convexity and seasonality of each published sub-index, rather than a smoothed economic index, feed into how a sector-specific read carries relative-value information (Diewert 1976, 2002). Axiomatic consistency governs whether successive vintages of each sub-basket chain coherently for such use (Balk 1995).

For relative-value and macro positioning the six sub-baskets let a trader separate an administered-price move in utilities or rent from a market-driven move in industrial products or private services, a read the headline print alone cannot supply and that the trend-versus-noise framing addresses only in aggregate (Cecchetti 1997; Bryan and Cecchetti 1994; Stock and Watson 2007). The cost-of-living anchor still frames the long-horizon real-return target within each partition (Konüs 1939).

KRCPIINDGOODS is published as a not-seasonally-adjusted consumer price sub-index level for industrial products, and the appropriate statistical object is its logarithm, expected to be integrated of order one. The sample is 318 monthly observations spanning 2000-01 to 2026-06, and the unit-root triplet is fitted on the log level 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), does not reject the unit root at p = 0.776, the nonparametric test of Phillips and Perron (1988) agrees at p = 0.811, and the stationarity-null test of Kwiatkowski et al. (1992) rejects trend stationarity at p < 0.01, so all three procedures concur on a clean I(1) classification without ambiguity.

On a clean I(1) reading the level is not the stationary object, so the portmanteau and the break search are run on the first difference of the log level, since a level portmanteau reads the near-unit autocorrelation of a stochastic trend and a level mean-break search spuriously segments it (Perron 1989; Hamilton 2018). The portmanteau statistic of Ljung and Box (1978), refining the form of Box and Pierce (1970), rejects the white-noise null on the differenced log level, with Q = 29.94 at lag 12 at p = 0.003 and Q = 41.00 at lag 24 at p = 0.017, while the multiple-break procedure of Bai and Perron (1998), computed by the dynamic-programming algorithm of Bai and Perron (2003), finds no break in the mean of the differenced series.

Seasonal tests are appropriate on this unadjusted monthly sub-index. The seasonal-unit-root test of Hylleberg et al. (1990), with the monthly mechanics of Beaulieu and Miron (1993), rejects unit roots at the seasonal frequencies with a statistic of 530.887 at p = 0.000, and the seasonal Ljung-Box statistic at the seasonal lags is significant at p = 0.006, while the joint seasonal-dummy F test does not reach significance at the 5% level with a statistic of 1.524 at p = 0.122, so the seasonality reads as present and deterministic on the HEGY and seasonal-portmanteau legs even though the dummy-regression leg alone does not detect it, consistent with the stationary-seasonality reading of Canova and Hansen (1995) and with the not-seasonally-adjusted character of the series (Ghysels and Osborn 2001).