The BEA announced that the PCE price index for July rose 1.89% at a seasonally adjusted annual rate. The year over year rate increased 3.70% and our trend measure increased 2.84% after an increase of 3.31% in June and 5.52% in May.
The PCE ex food and energy increased 2.99% at a seasonally adjusted annual rate. The year over year increase came in at 3.44%, the same as in June. Our trend measure increased 3.14% (interesting, economists typically use to indicate inflation!), a slight easing from the 3.22% reading in June.
Some readers may recall that Fed chairman Kevin Warsh has been talking about trimmed mean measures of inflaton. Fortunately for us, folks at the Dalls Fed have done the hard work of producing such measures. The monthly series is extremely volatile and so it’s not clear it’s a very good measure of `trend’ inflation (meaning: where is inflation going). The annual version is much smoother, but probably suffers from issues we’ve discussed before: as an annual measure, it responds slowly to changed in the underlying trend. As with other measures of PCE inflation, these series exhibit a downward trend starting in 2023. And as with other measures of PCE inflation, the Fed still has work to do to bring inflation down to its 2% target.
The inflation numbers remain elevated and are certainly front and center at the Jackson Hole meeting this week.
The BLS announced that the CPI rose 0.89% on an annualized basis. The year over year increase was 3.30%. Our trend measure came in at 1.92%. The CPI ex food and energy saw a 2.62% increase on an annualized basis with the year over year measure at 2.47% and the trend measure at 2.17%.
It is obvious from the graphs that inflation has been trending down over the past few years. The new Fed Chair, Kevin Warsh, has mentioned that he is thinking about alternative measures of inflation, such as some form of trimming. See the recent post on this here. The 16% trimmed mean, first introduced by the Cleveland Fed came in at 2.71%.
Since the spike in 2021-22, inflation has receded but remains somewhat elevated. Although the Michigan consumer inflation expectations consumer’s expectations shows inflation near 5% one year out, the implied measure from the Cleveland Fed shows a much tamer view.
Inflation expectations can also be derived from financial data. For a particular maturity, breakeven inflation is defined as the difference between the nominal return on government securities (Treasury Constant Maturity Securities) and the real return on government securities (Treasury Inflation-Indexed Constant Maturity Securities). Breakeven inflation represents market participants’ expectations for inflation at various horizons, from 5 to 30 years. Since 2021, markets have consistently priced in expectations for inflation that exceed the Fed’s 2% inflation target. However, we should adjust breakeven inflation to account for the fact that the Treasury Securities pay out based on the all items CPI, not core PCE, inflation. Historically, CPI inflation runs between 1/3 and 1/2 percentage points higher than PCE inflation. On this basis, markets may be pricing in inflation at the Fed’s stated 2% target.
It is evident that by almost any measure, the Fed has its work cut out. As always, it is a balancing act. If indeed, as Warsh has admitted, 2% will be hit, then it is much more likely to see rate increases going forward.
When Kevin Warsh told the Senate Banking Committee that the standard inflation numbers are “quite imperfect” and that he prefers “trimmed averages,” he pushed a wonky corner of inflation statistics into a political spotlight—and, with it, an old and worthwhile question: underneath the monthly noise, what is the underlying rate of inflation, and how should we estimate it?
The debate that followed mostly talks past itself, because it runs together things that ought to be kept apart. The central confusion is this: the trimmed mean is not a different, softer inflation number you choose. It is a more efficient estimate of the same inflation the headline is already trying to measure. Once that is clear, the case for it comes in three parts—a theoretical case for why trimming is the right way to estimate the center of price-change data, an empirical case for what the CPI data actually show when you do it, and a practical case for why the CPI is the index to trim and why trimming is the sensible tool to reach for.
The Theoretical Case
The CPI is an estimate
Start with what the headline number actually is. The all-items CPI is a weighted average of price changes across hundreds of components—a sample estimate of an unobservable quantity: the true central tendency of price change across the basket households buy. The ordinary average is one estimator of that quantity. The trimmed mean is another. They aim at the same target; the only question is which recovers it more reliably.
Efficiency: fat tails break the sample mean
For the kind of data inflation produces, the ordinary average is the worse estimator. In any given month the cross-section of price changes is not spread out smoothly—most components cluster tightly while a handful sit far out in the tails, a “fat-tailed” (leptokurtic) distribution. For such data the sample mean is inefficient: those few extreme values grab the average and jerk it around, so the headline lurches from month to month even when the underlying rate has not moved. Trim the tails and you recover the same central tendency with far less noise.
We can say precisely how this plays out. Simulating from distributions of increasing tail-heaviness, the efficient estimator shifts in a clear sequence: for near-Gaussian data the sample mean is best; once the excess kurtosis climbs above about one-half the trimmed mean overtakes it; and as the tails grow heavier still the median overtakes them both. Real CPI data sits well inside that range—a typical monthly cross-section has an excess kurtosis around 6—and there both robust estimators beat the sample mean handily: on the Cleveland Fed’s components the trimmed mean is roughly 2.2 times as efficient an estimator of the center as the simple average, and the median about 6 times. The plain average is the efficient choice only in a narrow near-Gaussian sliver that inflation never occupies. The empirical points sit above the simulated curves—the median markedly so—because a real CPI month is the extreme case the smooth model only approximates: a tight cluster of prices plus a lone outlier like gasoline, which is exactly the structure the median is built to ignore.
Mike Bryan’s first rule: every price is idiosyncratic
The deepest objection to trimming is that by discarding an outlier we might throw away real information—that today’s extreme mover is the leading edge of tomorrow’s trend. This rests on an assumption worth naming and challenging.
The economist Michael Bryan, then at the Federal Reserve Bank of Cleveland, did more than anyone to bring robust estimators into inflation measurement: the weighted-median and trimmed-mean CPI both grew out of his work with Stephen Cecchetti in the 1990s, which showed that trimming a fixed fraction from each tail of the monthly price-change distribution yields a markedly more efficient estimate of trend inflation than the simple average (Bryan and Cecchetti 1997). Call it Bryan’s first rule of prices: there is no such thing as a price change without an idiosyncratic component. Every price is the outcome of a particular market with its own trend and its own shocks. Some idiosyncratic movements are larger than others, but there is no way to know, a priori, how large—a big observed change might be a large idiosyncratic shock sitting on top of a downward trend, the two partly cancelling. You cannot read a single month’s outlier and know whether it is signal or noise. That is exactly why an agnostic statistical estimator is called for, rather than a judgment about which movements are “really” informative.
A rule, not a judgment
This is the cleanest reason to prefer the trimmed mean over the traditional “core” fix, and it is a point of principle. There is a real difference between blindly trimming the tails of a distribution and targeting specific goods for exclusion. Core inflation—the CPI stripped of food and energy—makes a judgment: it decides in advance that food and energy are the noisy items and removes them every month, whether or not they were the problem that month, and it leaves in whatever else happens to be lurching. The trimmed mean makes no such judgment. It applies a rule: rank the components this month, remove whatever sits in the tails, average the rest. It never has to know in advance where the noise will come from—which is fortunate, because by Bryan’s first rule, no one does.
The Empirical Case
Theory says trimming should work. Whether it is needed, and whether the objections to it actually bite, is an empirical question about a particular index. To answer it we rebuilt the Cleveland Fed’s exact 45-component measure from the underlying BLS data, using the weights from their own component table (including their four census-region owners’ equivalent rent splits). It reproduces their published trimmed-mean and median series closely—a correlation of about 0.97, root-mean-squared error under half a percentage point, over 172 months. Everything below is computed on that measure—theirs, not an approximation.
Two concrete months: March and June 2026
The mechanism shows up in single months, and the last few have supplied an almost laboratory-clean pair.
In March 2026 the headline CPI rose at a 12.6 percent annual rate—taken at face value, an inflation emergency. But look at where the components actually sat. The great majority were rising in the low single digits. The number was driven by energy: gasoline jumped more than 21 percent in the month, and fuel oil nearly 19 percent. Those are not signals about underlying inflation; they are two fat tails in a fat-tailed month. The simple average hands them their full weight and is dragged to 12.6. The trimmed mean sets them aside and estimates the same underlying rate at 2.4 percent; the median, at 2.8. Same target, cleaner reading.
Then June, and this is the part that should settle the charge that trimming is a dovish trick. The headline fell, at a 4.0 percent annual rate, as the energy spike unwound. The trimmed mean read 0.6 percent—that is, higher than the headline. In March the trim read ten points cooler than the simple average; three months later it read more than four points hotter. It is not biased down. It is biased toward the middle, which is the whole point. Which direction that lands in any given month is not the analyst’s to choose.
Trimming halves the noise
March and June are not flukes. Over the full sample the measures rank by month-to-month volatility exactly as the theory predicts—the trimmed mean cuts the headline’s noise roughly in half (a standard deviation of 1.8 against the headline’s 3.4), and the median is steadier still at 1.6. Core, at 2.2, is noisier than either.
The skewness question, and Waller’s example
The one serious way trimming could go wrong is skewness. If the price-change distribution is persistently skewed, a symmetric trim no longer recovers the mean—it drifts toward the median and biases the estimate. Governor Christopher Waller illustrates this with a three-good economy in which sharp price increases rotate across goods period after period: trim the extremes each period and you report 2 percent while true inflation is 3, because the extra inflation lives entirely in a tail that keeps refilling.
The example is valid—and it quietly names its own fix. Waller has built a persistently skewed distribution, and the answer to persistent skew is not to abandon trimming; it is to trim asymmetrically, cutting more from one tail than the other so the estimator is unbiased again. That is exactly what was done for Brazil, what Rogers did for New Zealand, and what the Dallas Fed does today for the PCE, whose distribution is genuinely skewed. Persistence is not a defeater; it is information you use to set the trim.
And whether that calibration is even needed is empirical—for the CPI, it mostly is not. The CPI cross-section is left-skewed on average (robust skewness about −0.2) and left-skewed over the past year, the opposite of the regime Waller’s example requires; if anything a symmetric trim runs slightly hot on the CPI, not cold. Over the last three years the headline has averaged 3.02 percent and the trimmed mean 3.01 — a gap of +0.01 percentage points, essentially zero. The headline and the trimmed mean track within a hundredth of a point. There is no 2-versus-3 wedge to find.
The tails carry no signal
Bryan’s first rule is testable. If the discarded tails carried early information about the trend, the gap between the headline and the trimmed mean would forecast where the trend is heading. It does not: regressing future trend inflation on the current headline-minus-trimmed gap, holding the current trend fixed and using standard errors robust to the overlapping windows, the gap’s coefficient is essentially zero (t ≈ 0.6). The trimmed-away tails do not lead the trend.
There is a deeper way to see why. Waller’s rotating-spike story needs a hidden common force pulling prices the same way period after period. We looked for one — extracting the single strongest common factor across the components (the 41 with a complete common history) and tracking its share of variance. Through 2019 it sits essentially at the pure-noise floor: co-movement no greater than chance would produce. From 2020 it climbs with the inflation surge and stays elevated — prices did move together more during the shock and its aftermath. But it never comes close to dominating: even at its 2023 peak the strongest factor explains under a quarter of the variance, and it takes eight separate factors to reach even half. There is co-movement, but no hidden common force strong enough to give the trimmed mean a persistent bias to exploit. (Three series that BLS begins publishing later are dropped from this factor analysis, along with the months that precede them.)
The Practical Case
Theory and evidence settle how to estimate inflation. Two practical questions remain: which index to estimate, and why trimming is the sensible instrument rather than an exotic one.
Why the CPI, not the PCE
Which price index to trim—the CPI or the PCE—is a question of weights and coverage, not of estimation, and it is where the practical considerations live. They point to the CPI.
The CPI is the number the public actually lives with, and it lives with it contractually. Social Security cost-of-living adjustments are set by the CPI, moving benefits for some seventy million people. Many union and private wage agreements carry CPI escalators. Rent-control and rent-stabilization formulas in a large number of cities tie the allowable annual increase to the CPI—in some places the cap is written directly as a CPI-linked number. Inflation-protected Treasuries pay off the CPI. When the CPI prints, real dollars change hands; the PCE, a national-accounts construct, has no comparable direct claim on anyone’s income.
The PCE is also, in practice, downstream of the CPI. The Bureau of Economic Analysis builds much of the PCE from CPI source prices and imputes a good deal of the rest, so the PCE is in substantial part a re-weighting of CPI data—and it arrives about two weeks later. Its weights are revised continually, which injects a revision volatility of its own. So the later, less-familiar index is largely assembled from the earlier, more-familiar one. Whichever index you target, the trimmed version is the more efficient monthly estimate of it—but there is no practical reason to reach past the CPI for a downstream index that fewer people use and that lands later.
Why trim: the company it keeps
The last objection to answer is the intuitive one—that trimming “throws away data.” It does not, and the surest way to see this is to notice how many other fields, facing the same problem, arrived independently at the same tool.
Olympic figure skating, gymnastics, diving, and ski jumping all drop the highest and lowest judges’ scores and average the rest—a literal trimmed mean, adopted precisely so one erratic or biased judge cannot swing the result. Metrologists and experimental physicists trim repeated measurements to blunt instrument glitches; the field of robust statistics grew up around exactly this problem. Signal and image processing use the “alpha-trimmed mean filter,” which sits deliberately between the mean and the median depending on how impulsive the noise is. Even LIBOR was, by construction, a trimmed mean of banks’ submitted rates, chosen to defang both outliers and manipulation.
None of these fields believes it is throwing away information. Each is using the estimator that the shape of its data selects—the mean when the data is well-behaved, something more robust when it is not. Inflation’s cross-section is emphatically not well-behaved; it is among the fatter-tailed distributions one encounters. To insist on the raw average there, alone among all these applications, is the genuinely idiosyncratic choice.
One honest wrinkle, since it recurs: at the CPI’s tail-heaviness the median is even more efficient than the 16 percent trim. Pure variance-reduction would push you all the way to the median. But the 16 percent trim tracks the headline’s underlying trend more faithfully, because it keeps more of the distribution—so the trimmed mean is the better all-round estimate of the same basket, while the median is the steadier but more austere summary. That is why the Cleveland Fed publishes both, and why watching them together tells you more than either alone.
Putting it together
The trimmed mean is not a controversial object once it is seen for what it is. Theoretically, it is the efficient estimator of the center of a fat-tailed distribution, an agnostic rule rather than a judgment about what to exclude. Empirically, in the CPI, the skewness that could bias it is absent, the outliers it discards carry no forecastable signal, and no single common factor is strong enough for the feared bias to run on. Practically, the CPI is the index that matters to real contracts and arrives first, and trimming is the same battle-tested tool that Olympic judges, physicists, and financial benchmarks all rely on.
The debate worth having is not whether the Fed should “switch” to a softer gauge. It is the narrow, almost technical question of whether, having chosen what to measure, one estimates it with the noisy tool or the precise one. Put that way, it scarcely looks like a controversy at all.
A note on the numbers: the trimmed-mean and median series here are built from the Cleveland Fed’s 45 CPI components, drawn from BLS and weighted with the Cleveland Fed’s own component table; they reproduce the Cleveland Fed’s published series at a correlation of about 0.97. The volatility, skewness, forecasting, efficiency, and common-factor results are computed on that same 45-component panel.
The BEA announced that inflation as measured by the Personal Consumption Expenditures was -1.30% (the price index actually fell) in June following a 5.67% rate in May. The monthly volatility is well-known and so our preferred trend measure smooths out these fluctuatons; this measure of trend inflation fell from 5.40% to 3.17%. On a year-over-year basis, inflation fell more modestly, from 4.08% to 3.67%.
Core PCE inflation (removing food and energy) fell from 4.06% to 1.60% on a month-over month basis, and from 3.42% to 3.29% measured on a year-over-year basis. Our trend measure fell from 3.79% to 3.06%.
It’s no longer clear which measure of inflation the FOMC pays attention to. For quite some time, the committee focused on core PCE inflation (although no idea if they ever specified monthly or annual rates, or something else). Chairman Warsh favors a so-called “trimmed mean” PCE measure. The Federal Reserve Bank of Dallas produces two such measures. Basically, a trimmed mean inflation measure computes inflation rates for each of the components of the PCE, then drops out a certain fraction of the components based on whether they are exceptionally high or low. Finally, the trimmed mean inflation rate is computed as a weighted average of the remaining components. Pretty straightforward, right 😉 The trimmed mean based on month-over-month inflation fell from 2.66% to 1.44%. In other words, by this measure, inflation has fallen below the Fed’s stated 2% target — at least for one month. It’s not clear that other members of the FOMC are convinced; three members dissented at the July’s FOMC meeting, preferring raising rates (tightening monetary policy).
The BEA also announced the advance estimate for Q2 GDP was 1.5%, not a particularly strong or weak number…one that will not change anyone’s mind about where the economy may be headed. The largest contributor to the growth was consumption
While the PCE price index is the so-called Fed’s preferred measure, tracking purchases by domestic consumers, the Q2 GDP report provides a broader statistic than the PCE, it is the price index for domestic purchases that adds to the PCE private investment and government spending and that popped to 5.7%
The labor market provides a scad of measures that are used to determine the state of the economy. The most common of these are the unemployment rate and payroll employment that are delivered monthly. On a weekly basis there is an indicator that counts the number of people applying for state unemployment insurance. The Department of Labor (DOL) announced that initial jobless claims sank to their lowest level since 1969: 187,000. Initial jobless claims (formally “initial claims”) count the number of unemployed individuals filing a first-time claim for unemployment insurance benefits after separating from an employer. Note, however, “separation” in the initial claims data isn’t neutral about cause. The general rule across states: to collect benefits, workers must be out of work through no fault of their own — layoffs and most non-misconduct firings clearly qualify. Those fired with cause do not quality. Voluntary quits are the opposite default: in every state, an employee who quits without good cause is not eligible for unemployment. So ordinary quits — leaving for a better job, personal preference, etc. — generally don’t generate an eligible claim and don’t show up in the initial claims count. Moreover, it is important to distinguish the number of people who are unemployed is substantially different from the people who claim unemployment insurance since many people who become unemployed do not qualify for unemployment insurance. As already discussed, those quitting their jobs generally do not quality. There are also work and wage criteria to quality for unemployment insurance; for example, an individual must have been employed for a certain number of weeks in the year leading up to an unemployment spell. And since unemployment insurance is a state-run program, there are differences in eligibtility criteria across states.
Once claims have been filed, the DOL tracks “continued claims,” or insured unemployment): people who already filed an initial claim, experienced a week of unemployment, and filed again to collect benefits for that week. The data are dated by the week of unemployment rather than the week the initial claim was filed, so they lag initial claims by one week in each release. Where initial claims measure the inflow into unemployment, continuing claims measure the stock. The stock itself provides one measure addressing how difficult it is to exit unemployment.
It is important to understand the distinction between continued claims and the stock of the unemployed. Many people who become unemployed do not quality for unemployment insurance (see the discussion above). And roughly half of those who do quality do not apply. Some choose not to apply because they feel they may not be unemployed for long; or they may experience stigma from receiving UI; or maybe they think applying is just a pain in the ass. In particular, the July 23 release showed that seasonally adjusted insured unemployment was 1,796,000 for the week ending July 11, down 2,000 from a downward-revised 1,798,000 and the four-week average at 1,805,250. The number of unemployed persons according to the household survey from the BLS was a seasonally adjusted 7,094,000 in June. In other words, only ¼ of unemployed people received unemployment insurance benefits.
The BLS announced that the Consumer Price Index (CPI) fell 5.0% on an annualized basis after rising 5.80% in May. The decline was largely due to energy prices, with energy commodity prices falling almost 10%. The year-over-year number came in at 3.46%. The large discrepancy between the monthly annualized number and the year-over-year number highlights the reason for our preferred trend measure, which rose 2.44%. That is, it damps the highly volatile monthly number while responding faster to changes in trend than the year-over-year measure.
The core CPI measure (which excluded food and energy) showed almost no decline, dropping 0.20%. The year-over-year increase was 2.6% and our trend measure grew 1.94%.
While the reduction is certainly welcomed, it appears to be short-lived. The June decline saw an easing in energy prices due to a “potential” scaling back of the crisis in the middle east. More recently, the battles have escalated and so too energy prices.
The BLS announced that payroll employment increased 57,000, and has been ratcheting down since March. The Dow Jones consensus forecast was 115,000. In addition, there were downward revisions over the past two months totaling 74,000. Employment in health care and social assistance grew 46,000. The largest decline came from leisure and hospitality, falling
Average hours of work remained at 34.3 for the third consecutive month. Hourly earnings rose from $37.54 to $37.64. With the recent uptick in inflation real wages have declined after several years of real wage growth.
The household survey revealed a large decline in employment, down 507,000; and the number unemployed also fell by 213,000, leading to a decline in the labor force participation rate, 61.8% to 61.5%. Taken together, these changes resulted in the unemployment rate moving down from 4.30% to 4.19%.
Another labor market indicator, the Jobs Openings and Labor Turnover Survey revealed no change in the number of job openings and hires, once again leading to more job openings than unemployed persons.
The BEA announced that the PCE price index rose 4.90% in April, down from the 8.27% March reading. The year over year number increased from 3.53% to 3.77% and our preferred trend measure rose 5.22% after a 5.38% increase in March. All well above the Fed’s 2.0% target.
The PCE price index excluding food and energy fell from 3.60% to 2.91%, the year over year number rose to 3.77% from 3.53% increase in March and the trend measure fell to 5.22% in April compared to 5.38% in March. Again, these inflation rates are well above the Fed’s stated 2% target.
In it’s second estimate of GDP for the first quarter, real GDP growth was revised down from 2.0% to 1.6%, mostly due to investment and consumer spending revisions.
The two reports don’t add much in the way of clarity as to future Fed Funds moves. The Fed-favored PCE is still solidly above the 2.0% target and the economy remains strong despite the downward revision to GDP. New Chair Kevin Warsh also adds to the uncertainty it becomes clearer what kind of Chair he will become.
The BLS announced that payroll employment increased 115,000 in April and March employment was revised up 7,000 to 185,000 and February was revised down 23,000 to 156,000.
The private sector added 123,000 jobs while the government sector shed 8,000, falling for seven consectutive months. Nearly all of the increase in employment came from the service producing sector, up 113,000.
Average hours of work rose from 34.2 to 34.3 and has been see-sawing between these two over the past few months. The increase in both private employment and average weekly hours means that total hours of work showed a strong increase. Average hourly earnings increased to $37.41 from $37.35.
According to the household survey the civilian labor force declined 92,000, the number unemployed increased 134,000 and then number employed fell 226,000. The end result was a slight uptick in the unemployment rate, from 4.26% to 4.34%. Note that, due to rounding, the BLS reported that the unemployment rate was unchanged at 4.3%.
While the establishment survey beat “expectations” and was taken as good news by the market, the household survey poured a little cold water on the outlook. Having said that, the labor market continues to exhibit more strength than weakness.
The BEA came out with two important announcements on the heels of the FOMC decision to not raise the Federal Funds Rate (good call). While the price indices were higher than the Fed’s 2% target, they were in the “what should we do now” range. That is, the members of the FOMC were debating whether to lower or keep the rate at its current level and what to say about future policy.
Voting for the monetary policy action were Jerome H. Powell, Chair; John C. Williams, Vice Chair; Michael S. Barr; Michelle W. Bowman; Lisa D. Cook; Philip N. Jefferson; Anna Paulson; and Christopher J. Waller. Voting against this action were Stephen I. Miran, who preferred to lower the target range for the federal funds rate by 1/4 percentage point at this meeting; and Beth M. Hammack, Neel Kashkari, and Lorie K. Logan, who supported maintaining the target range for the federal funds rate but did not support inclusion of an easing bias in the statement at this time.
The PCE price index rose 8.23% in March. Year-over-year it rose 3.5% and our preferred trend measure rose 5.30%.
The core PCE (ex food and energy) rose 3.58% on an annual basis, year-over-year 3.2% and the trend measure up 3.86%.
REal GDP
The BEA also announced that the advance estimate of real GDP for Q1 increased 2.0%. Personal Consumption Expenditures rose 1.6% and Private Investment rose 8.7% with the equipment component of investment rising 17.2% and Intellectual property products rising 13.0%. The Government sector rose 4.4%.
On a more negative note, both residential and non-residential structures investment have been in negative territory for quite some time.
Policy outlook
The real side of the economy continues a steady increase at the same time inflation has moved up considerably. It is interesting to conjecture what the Fed votes would have been had these reports come out before yesterday’s meeting. Mind you, today’s releases should not be a huge surprise to the FOMC. The Consumer Price Index release earlier this month signaled higher inflation, and economists at the Board of Governors are really good at now casting, so the National Income and Product Accounts data was almost certainly largely known.
