U.S. Median CPI Inflation

USMEDCPI is the published weighted-median measure of consumer price inflation recorded as-is, a percent change from a year earlier rather than an index level, so it carries no reference base and is not comparable in units with the index levels served beside it. The published rate is seasonally adjusted at source and KRED adds nothing to it.

The measure belongs to the class of limited-influence estimators, which summarize the central tendency of the cross-section of component price changes by setting the tails of that cross-section aside, and which were introduced because the cross-section is strongly non-normal and its ordinary weighted mean is dominated by a few large relative-price moves (Bryan and Cecchetti 1994). The weighted median is the limiting member of that family, the point at which cumulated expenditure weight first reaches half of the basket, so it keeps the single component straddling that midpoint and lets every other component fall away (Bryan, Cecchetti, and Wiggins 1997; Meyer and Venkatu 2014).

The object being summarized is the cross-section of component price changes underlying the all-items consumer price index, the same aggregate whose seasonally adjusted level is served as USCPISA, and the weights that locate the midpoint in that cross-section are the expenditure shares of that basket (Laspeyres 1871; Hill 1988). The index-number formulas that define such an aggregate remain the base-weighted, current-weighted, ideal, and superlative forms (Paasche 1874; Fisher 1922; Diewert 1976), and the economic target of the underlying price measure is the expenditure ratio that holds utility fixed (Konüs 1939).

The concept the estimator addresses is underlying inflation, defined originally as the rate prevailing on the economy's long-run growth path with supply shocks absent and demand neutral (Eckstein 1981), framed elsewhere as measured inflation decomposed into trend plus transitory disturbance plus bias (Cecchetti 1997), identified structurally as the component with no long-run effect on real output (Quah and Vahey 1995), and modeled as the permanent component of an unobserved-components stochastic-volatility decomposition (Stock and Watson 2007).

The series is a descriptive gauge of the central tendency of the current cross-section of price changes and nothing more. It is not a forecast of headline inflation, no accuracy or superiority claim attaches to it, and any comparison with the headline rate is left to the reader.

Within its group the series is one of the few rates among index levels, and it reaches the underlying-inflation concept by reading whichever component sits at the weighted midpoint of the current month rather than by deleting the same named strata every month, which is the route the exclusion-based core measures take. The trimmed-mean rates served beside it average an interior band instead, so they are separate estimators of the same concept rather than confirmations of this one (Bryan and Cecchetti 1994; Meyer, Venkatu, and Zaman 2013).

KRED applies no transformation to USMEDCPI and stores the published rate exactly as recorded. It performs no conversion of the rate into an index, no re-annualizing, no smoothing, and no re-computation of the median, and it applies no seasonal filter of its own. Ordering the components and cutting at the weighted midpoint belongs to the measurement basis by which the number comes to exist and is not a KRED computation.

That basis is a limited-influence estimator of the central tendency of the cross-sectional distribution of component price changes, in which the components are ordered by the size of their price change, expenditure weight is cumulated along that ordering, and the price change of the component at which the cumulated weight first reaches half of the basket is taken as the summary (Bryan and Cecchetti 1994). The weighted median is the most aggressive member of that family, since it retains one component rather than an interior average (Bryan, Cecchetti, and Wiggins 1997), and the reason for setting the tails aside at all is that measured inflation is trend plus transitory disturbance plus bias (Cecchetti 1997). Median and trimmed measures built on consumer price components have been studied together as one family (Meyer and Venkatu 2014; Meyer, Venkatu, and Zaman 2013).

The distribution being summarized comes from a fixed-basket consumer price aggregate, whose weights are expenditure shares and whose construction is the standing index-number practice of consumer price measurement (Laspeyres 1871; Hill 1988).

The base-weighted and current-weighted forms and the symmetric ideal index built from them are the formulas against which such an aggregate is read (Paasche 1874; Fisher 1922; Törnqvist 1936), and the superlative family they belong to is exact for flexible aggregators (Diewert 1976).

The taxonomy within which the underlying index is placed and the axiomatic properties it satisfies are set out in the index-number literature (Diewert 2002; Balk 1995), and the economic target of the price measure remains the expenditure ratio that holds utility fixed (Konüs 1939).

The alternative routes to the same underlying-inflation concept delete named strata before aggregation (Eckstein 1981), identify the component structurally by its long-run neutrality for real output (Quah and Vahey 1995), or extract a permanent component with an unobserved-components stochastic-volatility decomposition (Stock and Watson 2007). None of these constructions are applied to USMEDCPI itself, which remains at the recorded rate.

The series is read as a gauge of the persistent component of consumer price inflation, the concept defined as the rate on the economy's long-run growth path once supply shocks are absent and demand is neutral (Eckstein 1981) and framed as trend plus transitory disturbance plus bias in the measurement literature (Cecchetti 1997).

The median route to that concept keeps every component in the basket and lets the current month's own ordering decide which one is read, which is what makes it robust to asymmetric supply shocks (Bryan and Cecchetti 1994), and the same robustness argument is what the wider limited-influence family rests on (Bryan, Cecchetti, and Wiggins 1997; Meyer and Venkatu 2014).

Alternative readings of the same concept identify it structurally as the part of inflation with no long-run effect on real output (Quah and Vahey 1995) or as the permanent component of an unobserved-components decomposition (Stock and Watson 2007), and the readings need not coincide in any given month.

Because the underlying aggregate is a fixed-basket consumer price index, the rate inherits that aggregate's weighting rule and its coverage, and the substitution and quality-change biases that separate any measured price index from the cost-of-living target carry through to it (Laspeyres 1871; Hill 1988; Konüs 1939; Diewert 1998; Boskin et al. 1996).

Where a headline level anchors expectations through the index-number foundations that define it, the median rate is read alongside that level rather than in place of it (Diewert 2002; Fisher 1922). The series is descriptive of the current cross-section and is never presented as a forecast, so no claim is made here about how it performs against future headline inflation.

For market participants the value of a median rate lies in its signal-to-noise property, since a monthly headline print mixes a persistent component with transitory relative-price moves while the median reading is untouched by how far the tails of that month's distribution reach (Cecchetti 1997; Bryan and Cecchetti 1994; Bryan, Cecchetti, and Wiggins 1997).

Desks that price inflation-linked instruments and breakevens settle on headline outcomes rather than on any underlying-inflation measure, so the median rate enters the analysis as a read on the persistent component and not as a settlement reference (Eckstein 1981; Quah and Vahey 1995; Stock and Watson 2007).

What a contract deflates with or settles on is an index level rather than a rate, and the properties that govern such a level are the reversal tests, the share-weighted superlative form, the exactness of that family for flexible aggregators, and the axiomatic consistency of successive vintages (Fisher 1922; Törnqvist 1936; Diewert 1976; Balk 1995).

The substitution and quality-change wedge that separates a measured index from the cost-of-living target is carried by the median rate as well, so a real-return calculation built on it inherits the same bias (Diewert 1998; Boskin et al. 1996; Konüs 1939). The rate is used as a descriptive gauge of the current central tendency of price changes, never as a forecast of the inflation a contract will settle on.

The weighted-median consumer price inflation rate is a twelve-month rate published as its own series rather than an index level, and it is read as a descriptive gauge of the central tendency of the current price-change distribution, never as a forecast and never with any accuracy claim attached (Bryan, Cecchetti, and Wiggins 1997; Meyer and Venkatu 2014; Meyer, Venkatu, and Zaman 2013). The sample is 511 monthly observations spanning 1983-12-01 to 2026-06-01, a window that begins at the first month for which a twelve-month change exists rather than at the first month of the underlying index, and the unit-root triplet is fitted on the level of the rate with a constant and trend. The augmented Dickey-Fuller test 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 a unit root with a statistic of −2.8453 at p = 0.180806, the nonparametric test of Phillips and Perron (1988) concurs with a statistic of −2.77687 at p = 0.205571, and the stationarity-null test rejects with a statistic of 0.468233 at p < 0.01 (Kwiatkowski et al. 1992), so the three procedures concur and a clean I(1) verdict is assigned on this sample. The GLS-detrended escalation of Elliott, Rothenberg, and Stock (1996) is reserved for ambiguous outcomes and is not required on this clean reading.

The rate itself is the candidate stationary object for this class of series, so the portmanteau and the break search are both run on its level. The portmanteau statistic of Ljung and Box (1978), refining the form of Box and Pierce (1970), rejects the no-autocorrelation null at lags 12 and 24, with Q = 4654.91 and Q = 6131.82 and p = 0.000 in both cases, the very strong dependence a twelve-month moving construction carries by design. The multiple-break procedure of Bai and Perron (1998), computed by the dynamic-programming algorithm of Bai and Perron (2003), was run on that same level and does return mean shifts, but the level is exactly the object the triplet declines to certify as stationary, so under the platform's break-date traceability rule those shift dates are not citable in any form, including as descriptive segmentation, and none is printed here (Perron 1989). The level portmanteau is read the same way, as a description of a persistent rate rather than as evidence about stationarity.

Because the twelve-month construction is itself the seasonal-differencing filter that removes the seasonal unit roots the HEGY class interrogates, the HEGY seasonal-unit-root test and the Canova and Hansen (1995) seasonal-stationarity test are deliberately not run, since testing for seasonal unit roots the transform has already annihilated is circular (Hylleberg et al. 1990; Ghysels and Osborn 2001). The evolving-seasonality companions on the difference of the rate are a documented deferral rather than a silent omission, since the pinned battery restricts them to two other members of this class and switching them on for one series alone would leave the family inconsistently evidenced, so no claim is made about residual seasonality in either direction. The loss-differential comparison of Diebold and Mariano (1995) and the unbiasedness regression of Mincer and Zarnowitz (1969) were likewise not run, so the series carries no forecast-performance claim and no predictive claim at any horizon.

Two limits close the reading. No dated vintage panel is stored for this member, so nothing is claimed about the rate as first published or about its invariance across vintages. And the verdict stands on its own, since the trimmed-mean rates served beside it are different estimators, one of them on a different price index, so a matching reading there would be neither independent evidence nor corroboration (Atkeson and Ohanian 2001; Rich and Steindel 2007).