Methods & Data

• $\pi_{\text{yoy}}(t)$ — the 12-month inflation rate at month t
• I(t) — the price-index level (e.g. NSA CPI-U) at month t
• I(t−12) — the index level twelve months earlier

Used by: Estimated Personal Inflation

Inputs: monthly index level I (CPI, PCE, or a component). The annual figure is the annual-average YoY. A 12-month change that needs a month BLS never produced (October 2025) is not computed: the CPI and its components have no year-over-year rate for October 2025, nor for October 2026, whose month a year earlier is the missing one.

• wi — the user's spending weight on category i
• YoYi — the category's NSA CPI-U inflation
• personal YoY — the weight-averaged rate across the 11 categories

Builds on #1 — Year-over-year (YoY) inflation rate.

Used by: Estimated Personal Inflation

Inputs: user weights (presets or sliders, normalized); official weights = BLS relative importance, December 2025 (to one decimal). The gap is the difference between the personal and headline rates as shown, each to one decimal; a gap of 0.0 points is reported as matching the CPI. An approximation of Laspeyres aggregation on national-average category prices — not a literal cost of living. BLS never produced the CPI for October 2025, so the personal and headline rates have no figure for that month: a 12-month change needs the CPI in both months.

• sharek(t) — the share of components whose YoY inflation exceeds threshold k
• N — the component count in the fixed basket

Builds on #1 — Year-over-year (YoY) inflation rate.

Used by: no tool page. The Inflation Dashboard's breadth lens (#77) reads the CPI diffusion buckets (#54) since October 2026, so breadth has one meaning on the site.

Inputs: thresholds k of 0, 2 and 3%, over about 39 CPI expenditure categories; the median category YoY is shown alongside.

• buckets — ~49 CPI components sorted into deflation / 0–2% / 2–4% / >4% YoY bands
• share — each band's unweighted share of components (every component counts once)

Builds on #1 — Year-over-year (YoY) inflation rate.

Used by: Inflation Dashboard, through its breadth lens (#77)

Inputs: about 49 CPI-U component indexes from the BLS, not seasonally adjusted (NSA); fewer in the early years (41 in 1991). Counts are unweighted: every component counts once, because BLS relative-importance weights are not in the data set. Bucket edges belong to the higher bucket: 2.0% is moderate and 4.0% is hot. The four shares print to one decimal and are rounded together, by the largest remainder, so they add to exactly 100.0%. The Inflation Dashboard's breadth lens is this basket's share at 2% or more (moderate plus hot), in the dashboard's month. This share is a separate measure from the CPI's category-level figures, so each number keeps one meaning.

• DF(t) — the discount factor bootstrapped from the par CMT curve (semiannual)
• $f(\tau)$ — the implied six-month rate starting $\tau$ years ahead, as in the formula above

Used by: What's Priced In

Inputs: the Treasury par curve on each SEP release date (1M–7Y tenors, linear interpolation to semiannual nodes; log-linear discount factors, flat-forward extrapolation). The annualized 6-month forward starting at each projection year-end is the "market path", scored against the same realized value as the dots: the year-end target range's midpoint (or lower bound, the toggle) for every release, the January 2012 to June 2014 target-level releases included (calc #24). Their dots sat at 0.25 for the 0 to 0.25 range, so a 0.25 dot misses the 0.125 midpoint by 0.125 percentage points, and the chart shades those releases' target range, bottom to top, at each completed year-end. Treasury forwards embed term premium and the Treasury-vs-funds basis; no adjustment is applied.

• $f(\tau)$ — implied six-month rates at the next eight quarter-ends, from the bootstrapped discount curve and expressed as money-market rates (simple interest, actual/360, over the half-year of 182.625 days), the basis of the fed funds target they are compared with; the par yields that feed the bootstrap are bond-equivalent (semiannual)
• vs target — each forward minus the target-band midpoint on the curve date — what the curve has 'priced in'

Builds on #25 — Bootstrapped implied forward short rates.

Used by: What's Priced In

Inputs: the newest CMT curve, dated on the page (same bootstrap as calc #25), and the fed funds target band on that date. The page prints each quarter-end as its quarter (2026Q3: the forward from the quarter's last day). Its "Direction priced" card reads the two-years-out forward against the band midpoint in whole basis points, as printed: more than 10bp above is "Higher rates", more than 10bp below is "Lower rates", and anything within 10bp either way is "Roughly on hold". The bootstrap's first node is six months, so the 1- and 3-month points do not enter, and the forwards shown (at most two and a half years out at eight quarter-ends) depend only on the 6-month, 1-, 2- and 3-year par yields (DGS6MO, DGS1, DGS2, DGS3). Embeds term premium and Treasury-vs-funds basis — not meeting-dated odds, not a forecast.

• curve snapshot — the Treasury constant-maturity (CMT) par yields published on the chosen day, per published tenor, the same points and day calc 5 reads — no interpolation across missing tenors, no carry-forward; pages that read it with no date get the month-end 11-tenor set
• step — Daily = every publication day; Weekly, Monthly, Quarterly, Annually = the LAST publication day of each ISO week, month, quarter or year (a period-end value, never an average)
• note-rung interest — the ACTUAL auction coupon of the assigned CUSIP × its payment schedule

Used by: Curve Through Time · T-Bill Ladder

Inputs: Treasury CMT yields via FRED (DGS1MO…DGS30, daily from 1962-01-02; TIPS real DFII5, DFII7 and DFII10 from 2003, DFII20 from July 2004 and DFII30 from February 2010) plus the 1.5-, 2- and 4-month points from the U.S. Department of the Treasury par-yield file (UST6WK, UST2MO, UST4MO); no earlier or non-Treasury source is used for the curve; NBER recession months; the curve animator plots only published tenors (no interpolation of missing ones): the Treasury did not publish a 20-year constant-maturity yield from January 1987 through September 1993, and the Treasury did not publish a 30-year constant-maturity yield from February 18, 2002 until February 9, 2006, so neither point plots on those dates (FRED's stand-in 30-year values are left out, as are month-end 30-year points in that stretch); the calendar leaves out statistical-release dates instead of approximating them; ladder note rungs use the latest auction's actual coupon (or stop, or curve interp — labeled per rung).

• high–median spread — the stop yield minus the median accepted yield, in bp — the tail proxy (labeled "Tail proxy" on the page)
• takedown % — each bidder class's share of competitive accepted awards
• percentile — the share of the comparison group at or below the latest auction's figure. The comparison group is every earlier auction of the same security type and term, reopenings included, in the 10 years before the latest auction (all earlier auctions when there are fewer than 8), whatever history the page shows; each card names the group and its size
• recap rule — the recap's closing sentence comes from the average of four percentiles: bid-to-cover, indirect take, 100 minus dealer take and 100 minus the high–median spread. At 65 or above it reads "A firm auction", at 35 or below "A soft auction", and in between "A near-median auction"

Used by: Auction Demand · T-Bill Ladder

Inputs: TreasuryDirect results. Stop = high yield (coupons) / high discount rate (bills) / high discount margin over the 13-week bill index (floating-rate notes), never mixed. The true tail vs the 1 p.m. when-issued quote is not public — the high–median spread stands in for it. The bidder split is published from April 2008. Treasury's $25 million small-value test auctions (primary dealers only) are left out of the history and the ranks. The recap paragraph is generated deterministically from these figures.

• rungs — allocations snapped to available bill (and note) terms and matched to the next ANNOUNCED auction, real CUSIPs and dates
• est. interest — allocation × rate × days/365, priced indicatively off the newest constant-maturity curve, dated on the page (a bond-equivalent yield for every rung; auction discount rates are not used as yields), with a note rung's coupon from its latest auction where one priced in the last 45 days

Builds on #26 — Auction demand metrics (tail proxy & takedown).

Used by: T-Bill Ladder

Inputs: amount / horizon / rung count. Yields are interpolated from the newest CMT curve (its date is on the page and in the files) — indicative only; the rate on any bill is set at its auction. Allocation in $100 increments, remainder to the shortest rung. Horizons beyond 52 weeks use 2-/3-year NOTE rungs (semiannual coupons — the interest estimate is a simplification); if the note auction isn't announced yet the ladder tops out at the longest announced term and says so.

• gross issuance — the sum of the offering amounts of every auctioned security, reopenings included, by auction quarter and security type: the one term the Treasury Supply Monitor, Treasury Auction Demand (where one auction's offering amount is its gross issuance) and their files use for what is sold at auction. It is not net issuance (gross issuance less the debt that matures), not debt outstanding (the stock of debt) and not the deficit
• bill share of gross issuance — bills and cash-management bills as a share of a quarter's gross issuance (the bill share of debt is of debt outstanding, calc 37)
• average size — last four complete quarters versus the prior four

Used by: Supply Monitor

Inputs: Treasury auction results from TreasuryDirect (public domain), every auction with results (floating-rate notes from January 2014). Gross (no maturities netted); reopenings count; buybacks/SOMA out of scope; the current quarter, or one the records do not yet reach the last week of, is flagged partial.

• reserves/GDP — bank reserves scaled by the nominal GDP of the last quarter at or before each month
• QT pace — the 12-month change in total Fed assets
• ON RRP card — reads "Drained" below $50 billion and "Parked cash" at or above it

Used by: Fed Liquidity

Inputs: H.4.1 weekly levels via FRED (WALCL, RRPONTSYD, WTREGEN, WRESBAL), monthly-sampled from January 2003 (the weekly series begin in December 2002), all shown in $ billions: FRED publishes the H.4.1 levels in $ millions and ON RRP usage (RRPONTSYD) already in $ billions. RRP + TGA are the drains in the reserves identity.

• level — underlying inflation = median{core PCE, core CPI, median CPI, trimmed-mean PCE, sticky-core CPI} YoY, scored against the Fed's 2% goal as 50 + (u−2)·25
• momentum — core PCE 3-month annualized minus its 12-month rate (accelerating vs decelerating), scored 50 + accel·20
• breadth — the share of CPI components with 12-month inflation at 2% or more: the moderate and hot buckets of CPI diffusion (#54: the same components, buckets and printed shares), scored as the share itself; expectations — market-implied inflation (the 10-year breakeven) at the end of the month, scored 50 + (be−2)·30 + 10·(six-month change), the change from the end of the month six months earlier

Reuses the median-of-many-gauges idea (#72) and CPI component diffusion (#54); the verdict pairs the level read (cool/near-target/warm/hot) with the momentum read (rising/steady/cooling).

The verdict's rule. Each read is a fixed threshold on its figures at two decimals, as the page prints them. Level, from underlying inflation: cool (below target) below 1.5%; near target from 1.5% to below 2.5%; warm from 2.5% to below 3.5%; hot at 3.5% or more. Momentum, from the acceleration (core PCE's 3-month annualized rate minus its 12-month rate) and the 6-month trend (underlying inflation minus its reading six months earlier): rising when the acceleration is above +0.15 pp or the trend is above +0.2 pp; cooling when the acceleration is below −0.15 pp and the trend is below 0; steady otherwise. Both figures are printed on the page's Momentum card; when underlying inflation has no reading six months earlier, the trend is not available and counts as 0 pp in these tests. The dial's colors are the score's zones, read on the whole number the dial prints: cool below 38, near target 38 to below 55, warm 55 to below 72, hot at 72 or more.

Used by: Inflation Dashboard

Inputs: FRED PCEPILFE, CPILFESL, MEDCPIM094SFRBCLE, PCETRIM12M159SFRBDAL, CORESTICKM159SFRBATL, T10YIE, and the CPI-U component indexes of CPI diffusion (#54). The score is for the newest month in which every core measure is published (PCE trails CPI by a month), and all four lenses read that month: breadth in the same month (or the latest month before it with a figure, named on the page) and market-implied inflation at that month's end. Weights and thresholds are a house judgment, not a market standard; the score is a descriptive summary, not a forecast. Market-implied inflation is the 10-year breakeven, the gap between the nominal and TIPS yields. It includes an inflation risk premium (which pushes it up) and a TIPS liquidity premium (which pushes it down), so it is not a pure forecast of inflation. CPI and the Fed's goal. The Federal Reserve's 2% goal is defined for the PCE price index. Three of the five core gauges (core CPI, Cleveland median CPI, Atlanta sticky-core CPI) and the breadth lens are CPI-based, and CPI inflation has usually run above PCE inflation, mostly because the two baskets weight shelter and health care differently (#31, the CPI–PCE gap). The level is scored against 2% as one common reference for all five gauges, not as a CPI target.

• episode — two or more consecutive month-ends with the spread below zero
• lead — months from the episode's first month to the next NBER recession start

Used by: Curve & Recession

Inputs: month-end 10Y−2Y (from June 1976, when the 2-year CMT begins) and 10Y−3M (from September 1981, when the 3-month CMT begins); NBER peak-to-trough dates (public record). Leads vary widely, and an inversion does not guarantee a recession. The data bar's word for each spread reads it as printed, in percentage points at two decimals: below zero is "INVERTED", a printed 0.00 is "Flat", above zero is "Positively sloped".

• Sahm ≥ 0.50pp — the real-time Sahm-rule trigger
• 2s10s < 0 — curve inversion
• credit gap ≥ 10pp — the BIS Basel early-warning line
• HY OAS ≥ 80th pctile — spread stress versus its own history (ICE BofA)
• CFNAI 3m ≤ −0.70 — the Chicago Fed activity line

Used by: Recession Dials

Inputs: SAHMREALTIME, DGS10−DGS2, BIS CG (US), BAMLH0A0HYM2 percentile since 1996 (ICE BofA), CFNAI. Canonical published thresholds only; count of tripped dials is context, not probability. The status words come from this fixed rule: a gauge reads "Tripped" when its reading, compared with its line as the page prints it (two decimals; the percentile as a whole number), is past the line; a reading exactly at the line trips every gauge except the 2s10s slope, which trips only below zero; otherwise it reads "Calm". The HY OAS percentile is the share of complete month-ends from December 1996 on which the spread was below its newest reading; the page names the month-ends ranked and their count.