U.S. Personal Consumption Expenditures Price Index

USPCEPI is the seasonally adjusted chain-type price index for personal consumption expenditures recorded as published, the monthly index-number level (2017 = 100) that measures the average change over time in the prices paid for the goods and services making up personal consumption. The seasonal adjustment belongs to the measurement basis by which the published level comes to exist, and KRED adds nothing to it.

The consumer price indices served alongside this one hold base-period quantity weights fixed across the comparison, whereas a chain-type index updates its weights from expenditure shares period by period and links successive comparisons together, so the two families answer the same question with different weighting rules, and they price different universes, one the expenditures of urban consumers and the other personal consumption expenditures (Laspeyres 1871; Fisher 1922; Hill 1988; Diewert 1998).

The current-period-weighted form is the dual of the base-weighted one and the two together bound the comparison they approximate (Paasche 1874), while the expenditure-share-weighted log-change form is the superlative discrete-time aggregator that chain-linked practice approaches (Törnqvist 1936; Diewert 1976). Whether to chain or to hold a base fixed is itself the classical index-number problem (Frisch 1936), and period-by-period chaining tends in the limit toward the continuous-time aggregate of price and quantity components (Divisia 1925).

The aggregate whose prices this index measures is the consumption expenditure of the national accounts, whose definitional boundary and double-entry structure fix what enters the basket (Meade and Stone 1941), and the economic target the price measure approximates remains the expenditure ratio that holds utility fixed (Konüs 1939).

Within the four-approach taxonomy of index-number theory the construction is placed and its axiomatic properties characterized (Diewert 2002; Balk 1995), and the substitution and quality-change bias that separates any measured price index from its theoretical target is catalogued in the same literature (Boskin et al. 1996).

The level served here covers the whole consumption basket and no exclusion of volatile components is applied to it, the core counterpart being served separately as USCOREPCEPI.

KRED applies no transformation to USPCEPI, loading the 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, or year-over-year differencing, and it applies no seasonal filter of its own, since the adjustment already belongs to the measurement basis by which the published level comes to exist.

That measurement basis is chain-linked aggregation, in which expenditure shares of adjacent periods supply the weights for each link and the links are multiplied into a continuous series anchored at 2017 = 100, the practice for which the case is set out in the national-accounts index-number literature (Hill 1988). The share-weighted log-change form is the superlative aggregator such chaining approaches (Törnqvist 1936).

Each two-period comparison stands on the classical alternatives, the base-weighted form and the current-weighted form, with the symmetric ideal index built from them and the log-change index filling the space between (Laspeyres 1871; Paasche 1874; Fisher 1922). The last two belong to the superlative family that is exact for a flexible aggregator function (Diewert 1976).

Whether to chain those comparisons or to hold a base fixed is the classical index-number choice (Frisch 1936), and continuous-time aggregation is the limiting case toward which period-by-period chaining tends (Divisia 1925).

The consumption aggregate being priced is defined by the double-entry accounting framework of national income and expenditure and by the consistency rules later codified from it (Meade and Stone 1941; Stone 1947).

The four conceptual routes to the same number and the axiomatic properties the construction satisfies are set out in the index-number literature (Diewert 2002; Balk 1995), the economic target remains the expenditure ratio that holds utility fixed (Konüs 1939), and the residual substitution and quality gap is not corrected by KRED because the series is served exactly as measured (Diewert 1998). None of these constructions are applied to USPCEPI itself, which remains at the recorded level.

As a measure of consumption prices the index is the empirical counterpart of the cost-of-living concept, and its use as a reference for price stability turns on how closely a chain-type level tracks that concept (Konüs 1939). The consumption aggregate it prices is itself a national-accounts construct whose boundary and netting conventions decide what the measure covers (Kuznets 1941).

Because the weights are updated period by period, the chain-type construction narrows but does not remove the substitution wedge that separates a measured index from the cost-of-living target, and the broader commodity-substitution, outlet, quality-change, and new-goods biases remain (Hill 1988; Diewert 1998; Boskin et al. 1996).

For monetary-policy purposes the level is decomposed into a persistent component and transitory noise, a separation framed as trend plus transitory disturbance plus bias and originally defined as the core rate on the economy's long-run growth path (Cecchetti 1997; Eckstein 1981).

The supply-shock robustness of that underlying signal is supplied by the limited-influence estimators and the optimally trimmed means (Bryan and Cecchetti 1994; Bryan, Cecchetti, and Wiggins 1997), the core component is identified as the part of measured inflation with no long-run effect on real output (Quah and Vahey 1995), and the trend extracted by the unobserved-components stochastic-volatility model is the slow-moving objective against which policy is calibrated (Stock and Watson 2007).

The reasoning that lets a single consumption price level anchor expectations across the economy rests on the same index-number foundations that define what the level is (Diewert 2002; Fisher 1922). Because the level is seasonally adjusted at source, its month-on-month change is read directly as a rate of price change rather than only against a year-earlier comparison.

For asset pricing a consumption price level is the deflator that converts nominal cash flows into real terms, and index-number theory formalizes this operation through the time- and factor-reversal tests a deflator should satisfy (Fisher 1922). The share-weighted log-change form and the superlative family it belongs to describe the weighting rule the chained level actually applies (Törnqvist 1936; Diewert 1976).

Read against a fixed-basket level, the chained level answers the same deflation question under a different weighting rule, and the base-weighted and current-weighted forms bound the difference between the two answers (Laspeyres 1871; Paasche 1874; Hill 1988).

Indexed instruments settle on a consumer price basket rather than on this aggregate, so the level enters the analysis as an analytical deflator and not as a settlement reference, while the residual substitution and quality-change wedge is priced into the basis between indexed and nominal instruments and axiomatic consistency governs whether successive vintages chain coherently for valuation (Diewert 1998; Boskin et al. 1996; Balk 1995).

For relative-value and macro positioning the persistent component matters more than the monthly print, so the level is read against the underlying-inflation gauges and the extracted trend (Cecchetti 1997; Stock and Watson 2007). The cost-of-living anchor frames the long-horizon real-return target, and the taxonomy of index-number approaches fixes which properties survive when the level is used to deflate a cash-flow stream (Konüs 1939; Diewert 2002).

USPCEPI is published as a seasonally-adjusted monthly index level of personal consumption expenditures chain-type prices, and the statistical object is that published level, expected to be integrated of order one. The sample is 809 monthly observations spanning 1959-01-01 to 2026-05-01, and the unit-root triplet is fitted on the 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) with lag length set as in Ng and Perron (2001), does not reject the unit root with a statistic of −1.1527 at p = 0.9198, the nonparametric test of Phillips and Perron (1988) concurs with a statistic of −1.0141 at p = 0.9422, and the stationarity-null test rejects trend stationarity with a statistic of 0.2511 at p < 0.01 (Kwiatkowski et al. 1992), so the three procedures concur on a clean I(1) classification. The GLS-detrended escalation of Elliott, Rothenberg, and Stock (1996) is reserved for ambiguous outcomes and is not required on this clean reading.

On a clean integrated reading the level is not the stationary object, so the portmanteau and the break search are run on the first difference, 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; Bai and Perron 1998). The portmanteau statistic of Ljung and Box (1978), refining the form of Box and Pierce (1970), rejects the white-noise null on the differenced level at lags 12 and 24, with Q = 1295.32 and Q = 1743.59 and p = 0.000 in both cases. The multiple-break procedure of Bai and Perron (1998), computed by the dynamic-programming algorithm of Bai and Perron (2003), locates three mean shifts in the differenced series, at 1973-02-01, 1990-11-01, and 2016-03-01.

The index is seasonally adjusted at source, so under the platform convention whatever the seasonal battery detects is attributed to that adjustment and its revisions and is never presented as a KRED discovery (Ghysels and Osborn 2001). The seasonal-unit-root test of Hylleberg et al. (1990), with the monthly mechanics of Beaulieu and Miron (1993), is run on the level and rejects unit roots at the seasonal frequencies with a statistic of 6136.4979 at p = 0.000, so any seasonal signal that survives the adjustment is deterministic rather than stochastic. The seasonal portmanteau leg is the cumulative statistic through lag 24 on the first difference, 1743.586, numerically the lag-24 rung already reported rather than an independent second test, and it rejects the no-autocorrelation null at p = 0.000, while the joint test of monthly dummies on the first difference does not reject at the 5 percent level, though it would at the 10 percent level, with F = 1.6721 at p = 0.075182. The battery therefore disagrees with the adjusted designation the series carries, and the disagreement is stated as it stands, the series being neither declared seasonally clean nor credited with a newly found seasonal pattern. The reverse-null seasonal-stationarity test of Canova and Hansen (1995) is optional under the matrix and was not computed for this member.