Labor hours per CPI basket, indexed to 2007

Labor hours per CPI basket, indexed to 2007, version 1.0

Classification. Derived: deterministic arithmetic over stored values; every number is reproducible from the stored ids named in the observation's metadata.

Formula. For each month, CPI-U all items divided by its 2007 calendar-year mean (the price of the basket relative to the base), divided by average hourly earnings divided by their 2007 calendar-year mean (the wage relative to the base). The result is hours per 2007 hour-basket, 1.000 on average over 2007 by construction. The base-year means are computed from the stored months of that year and those months' ids are recorded on every row (custom function labor_hours_cpi_basket; the engine's index transform takes a single base period, not a year mean).

Engine rendering: The custom function labor_hours_cpi_basket over the whole component dataset, for each geography and period. A period with any component missing produces no value. Rounded to 4 decimals.

Components.

• cpi_all_items, metric us-cpi (USA). CPI-U all items, US city average, seasonally adjusted (FRED CPIAUCSL).
• hourly_earnings, metric us-average-hourly-earnings (USA). Average hourly earnings of all employees, total private (BLS CES0500000003 via FRED).

Windows and alignment. Monthly, United States, matched on the month. Base period: calendar year 2007. No value is produced until both series have at least one stored month in 2007.

Missing data. A period is produced only when every component has a value for it; nothing is interpolated, carried forward or estimated.

Rationale. The two physical labor-hour measures cover energy; the CPI basket covers everything an urban household buys, at the cost of being an index. Stating it as hours per base-year basket is honest about that: it is the inverse of real average hourly earnings rebased to 2007, written in work time.

Limitations. The roadmap asked for a year-2000 base. CES0500000003 (all employees) starts in March 2006, so a 2000 base would need a different earnings series (CES0500000008, production and nonsupervisory employees, from 1964); that is a candidate for version 1.1 and would be a separate metric, not a silent substitution. Average hourly earnings are a mean across all private employees, not a median and not after tax, so the hours are those of an average earner, and a distribution shift changes them without any change in prices. Prices are national averages; households in different states face different electricity and gasoline prices. Both components are nominal, which is the point: no deflator is involved, the measure is a physical quantity against a wage.

Revision. Recomputed at every derived pass; a changed component value produces a new observation row and earlier rows are kept. A change to anything that affects the numbers is a new formula version (the spec hash is on every row and a changed spec under a used version is refused).