Hourwise

Why an hourly wage is rarely observed directly

For most of the workforce there is no hourly rate written down anywhere. The hourly figure that appears in statistics is constructed by dividing one measured quantity by another, and it carries the errors of both.

A ratio, not a reading

A minority of jobs carry a posted hourly rate. For everyone else — salaried staff, commission and piece-rate workers, the self-employed, anyone whose pay is tipped or variable — an hourly wage has to be built. The standard construction divides reported earnings over a period by reported hours over the same period.

That construction is unremarkable until the inputs contain error. Hours are reported by a respondent from memory, subject to the rounding and heaping that affects every recall measure. Earnings are reported the same way, or taken from a different source entirely. The quotient inherits both.

Division bias

George Borjas set out the specific consequence in the Journal of Human Resources in 1980, in work on the relationship between wages and weekly hours. When the hours figure appears in the denominator of the constructed wage and again as the dependent variable in an analysis of labour supply, error in that single reported quantity enters both sides of the relationship — and it enters with opposite signs. Overstated hours push the constructed wage down while raising measured hours. The result is a spurious negative association between wages and hours that has nothing to do with anyone's behaviour.

The effect is now standard in the econometrics literature under the name division bias, and it is one reason estimates of labour supply elasticity vary so widely across studies that appear to be asking the same question with the same kind of data.

How the error in hours was established

The size of reporting error in hours is not a matter of speculation, because validation studies exist. John Bound, Charles Brown, Greg Duncan and Willard Rodgers compared workers' survey reports against their employers' administrative records in a validation study conducted alongside the Panel Study of Income Dynamics. Reported hours and recorded hours diverged, and the divergence was not random noise: it correlated with the characteristics of the respondent and with the size of the quantity being reported. Bound, Brown and Nancy Mathiowetz later synthesised this literature in their chapter on measurement error in survey data for the Handbook of Econometrics.

Those validation studies come with a caveat their authors state plainly. Each draws on a small number of employers, often a single firm, and cannot be treated as representative of the labour force. Employer records are also not ground truth in any absolute sense — a payroll system records hours the firm accounts for and pays, which is its own definition rather than a neutral one.

The aggregate version of the same problem

Published average hourly earnings, computed at the aggregate level from payroll data, avoid individual recall error but acquire a different one. Aggregate payroll divided by aggregate hours is sensitive to which jobs are in the sample. When employment changes unevenly across the wage distribution, the average moves because the composition moved, not because any rate changed. The Bureau of Labor Statistics issued explicit cautions to this effect during the employment disruption of 2020, when sharp job losses concentrated in lower-paying industries lifted the average without any individual receiving a raise.

None of this makes the hourly wage unusable. It means the number is an estimate assembled from two imperfect inputs, and that it is most fragile exactly where an analysis leans on it hardest: comparisons across groups whose hours are reported with different degrees of error.

References

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