From Threshold Reporting to Denomination: Administrative Labels and the Limits of Supervised Text Measurement

Supervised text measurement treats labels as ground truth and the fitted model as the source of measurement error. Where the label is administrative, the institution is itself an upstream measurement model, so measurement runs in two stages. The state maps the construct into a record, and the researcher then maps features into an approximation of that record. Cross-validation evaluates the second mapping and is uninformative about the first. Held-out fit is also close to silent about the first mapping. In a controlled setting it moves by about a seventh across the full range from invariance to complete suppression, while the estimated group contrast moves by more than two units and reverses sign. This paper formalises the two-stage structure, derives a mechanical test for the case where the institution's rule differs across groups through a parameter it publishes, demonstrates the test in a controlled setting where the truth is known, and then shows it catching a regression of my own that four conventional robustness checks did not. The setting is Germany's database of ex ante regulatory compliance costs, covering 29,434 legal obligations. The German costing handbook directs that citizens' compliance time be recorded in hours but not priced at the level of the individual regulation, and the database follows that instruction closely. A wage rate appears for 54.8 per cent of business obligations, 27.8 per cent of public administration obligations, and none of the 2,681 citizen obligations. The convention is not German but a property of the international Standard Cost Model. Training on the obligations costed above Germany's reporting gate, which discards 91.3 per cent of the corpus, leaves the addressee-group difference undetectable, and worst-case bounds do not identify its sign even after granting an assumption the reporting rule does not supply. A matched design over textually identical obligations returns the difference at overwhelming significance while measuring nothing, because the outcome is an algebraic consequence of the wage rule. Applied instead across policy areas, where the published tariff differs without vanishing, the same test attributes almost exactly half of the recorded personnel-cost gap between health and tax regulation to the tariff rather than to the work. Linking each obligation to the statutory provision that creates it supplies text the costing officials did not write, and within the 604 provisions binding both citizens and firms, holding the provision fixed leaves a large gap in recorded time per case that disappears once the obligation description is also held fixed.