South Korea Income Terms of Trade

This series is a raw external-price or terms-of-trade index recorded without transformation, the monthly index-number level that measures either the average price of a country's internationally traded goods or the ratio between those traded-goods prices. The import and export price indices are base-period-quantity-weighted aggregates of the prices of goods crossing the border, so that with the weights held fixed across the comparison the level reflects price change alone rather than shifts in the traded basket (Laspeyres 1871). The current-period-weighted counterpart and the ideal index that is their geometric mean bound the fixed-base level, and the last of these satisfies the time- and factor-reversal tests (Paasche 1874; Fisher 1922). The expenditure-share log-change form gives the superlative approximation against which a fixed-basket external-price level is read (Törnqvist 1936).

The net barter terms of trade published here is the ratio of the export price index to the import price index expressed as an index number, the quantity of imports obtainable per unit of exports, while the income terms of trade scales that ratio by an export volume index so as to measure the import purchasing power of total exports (Fabricant 1940). Read as a relative price, the terms of trade is the traded-goods counterpart of the real exchange rate, the consumer-price-deflated nominal rate whose deviations index the departure of traded prices from purchasing-power parity (Rogoff 1996; Cassel 1918).

The measurement distinction between an absolute price-level ratio and a price-index ratio times a base-period rate defines what such an external-price index equates (Officer 1976), and the doctrinal choice of which price index enters the comparison and the homogeneity postulate behind it govern the construction (Frenkel 1978). The single-price law of one price is the arbitrage foundation the traded-goods indices approximate (Isard 1977). The economic target these fixed-basket comparisons approximate is the utility-fixed expenditure ratio made precise within index-number theory (Konüs 1939; Diewert 2002). The terms of trade in turn enters the intertemporal accounting identity that links the current account and the change in net foreign assets (Obstfeld and Rogoff 1995).

KRED applies no transformation to this series, loading each published index level as recorded with only a date parse and a reshape into the long store. It therefore performs no re-indexing, deflation, smoothing, annualizing, ratio-taking, or year-over-year differencing.

The measurement basis by which the import and export price levels come to exist is fixed-basket aggregation, where a base-period trade survey fixes the quantity weights and the elementary price relatives are combined into an all-items external-price index (Laspeyres 1871). The construction sits within the 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 are the superlative formulas that are exact for flexible aggregators, and the axiomatic properties the levels satisfy are characterized within the test approach (Diewert 1976; Balk 1995).

The net barter terms of trade is published as the export-to-import price-index ratio and the income terms of trade as that ratio scaled by the export volume index, and because each is served exactly as measured KRED itself performs neither the ratio nor the volume scaling (Diewert 1998). The volume component behind the income terms of trade is a quantity relative built by the same base-weighted and current-weighted aggregation as the price side (Fabricant 1940; Kuznets 1941). Chain-linking of successive base periods and the fixed-base-versus-chain choice belong to the same index-number lineage, and the continuous-time limit of that aggregation is the Divisia index (Hill 1988; Frisch 1936; Divisia 1925). The four conceptual routes to any one of these numbers are the fixed-basket, test, stochastic, and economic approaches (Diewert 2002).

As measures of traded-goods prices and their ratio, these indices are the empirical counterparts of the real exchange rate and the cost-of-living concept, and their use in policy turns on how closely a fixed-basket comparison tracks those concepts (Konüs 1939; Rogoff 1996). The terms of trade is a relative price whose movements are read against purchasing-power parity, the benchmark anchoring the nominal rate to the ratio of national price levels (Cassel 1918). The absolute-versus-relative measurement distinction and the choice of price index determine what deviation from parity the series records (Officer 1976; Frenkel 1978), and the law of one price is the arbitrage condition the traded-goods prices are tested against (Isard 1977; Dornbusch 1987).

An import price level enters the domestic cost-of-living target as a known biased proxy, since the fixed-base aggregate overstates true cost growth by a substitution wedge widened by the commodity-substitution, outlet, quality-change, and new-goods bias (Diewert 1998; Boskin et al. 1996). A worsening terms of trade is a real-income loss whose national-accounts counterpart is the trading gain or loss on the traded basket (Kuznets 1941). The demand-elasticity framework that distinguishes goods by country of origin supplies the weights through which relative traded prices move (Armington 1969).

For external-balance analysis the terms of trade enters the intertemporal identity linking saving, investment, the current account, and the change in net foreign assets (Obstfeld and Rogoff 1995), and the trade and valuation channels through which that position evolves are measured on the external asset and liability stocks (Gourinchas and Rey 2007b; Lane and Milesi-Ferretti 2018). Gross and net external positions carry information beyond the current-account flow the terms of trade helps drive (Obstfeld 2012).

For asset pricing the external-price level is a deflator and a relative-price signal, and index-number theory formalizes the deflation operation through the time- and factor-reversal tests a deflator should satisfy (Fisher 1922). The base-quantity weights, their current-weighted dual, and the expenditure-share log-change form bound the deflation error in converting traded-goods values to real terms (Laspeyres 1871; Paasche 1874; Törnqvist 1936).

Currency positioning reads the terms of trade as a fundamental for commodity- and trade-sensitive exchange rates, since the real rate reverts toward purchasing-power parity over long horizons (Rogoff 1996; Cassel 1918). A rising import price index feeds the inflation basis priced into linkers and inflation swaps through the traded-goods component of the consumer basket (Boskin et al. 1996). Trade-weighted currency indices aggregate the bilateral rates against which these traded prices are quoted, using geometric-mean weighting aligned to trade shares (Loretan 2005; Pauls 1987).

For cross-border balance-sheet analysis the terms of trade drives the trade channel of external adjustment, while the valuation channel operates through the currency and asset composition of the external position (Gourinchas and Rey 2007a; Gourinchas and Rey 2007b). The measurement of returns on external claims and liabilities, and the distinct information in gross versus net positions, frame how a terms-of-trade shock transmits to national wealth (Curcuru, Dvorak, and Warnock 2008; Obstfeld 2012; Lane and Milesi-Ferretti 2007). The same relative price enters the current-account and net-foreign-asset accounting on this platform rather than any reweighted index (Obstfeld and Rogoff 1995).

KRITOT is published as a not-seasonally-adjusted income-terms-of-trade index level, and the appropriate statistical object is its logarithm, which is expected to be integrated of order one. The sample is 461 monthly observations spanning 1988-01 to 2026-05, 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 = 0.427, and the stationarity-null test rejects trend stationarity at p < 0.01 (Kwiatkowski et al. 1992), so the augmented Dickey-Fuller and KPSS legs concur on an I(1) reading. The nonparametric test of Phillips and Perron (1988) is the sole dissenter, rejecting the unit root at p = 0.000, which is the documented Phillips-Perron over-rejection toward spurious stationarity under near-unit moving-average errors rather than independent evidence of stationarity (Ng and Perron 2001), so no clean order of integration is assigned and the concurring reading is I(1).

Because the log level is not a clean stationary object, the portmanteau and the break search are run on its first difference, since a level portmanteau on a near-unit-root index reads mechanical near-unit autocorrelation and a level mean-break search spuriously segments a stochastic trend (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 at p = 0.000, and 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 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 at p = 0.000, while the seasonal dummies are jointly significant at p = 0.000, so the seasonality is present and deterministic rather than stochastic, 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).