Earnings Dynamics and Measurement Error in Matched Survey and Administrative Data

This paper analyses the measurement error and earnings dynamics of two sources of individuals' annual earnings from Statistics New Zealand's Survey of Family, Income and Employment (SoFIE) and administrative linked employer-employee data (LEED) earnings reported in the Integrated Database Infrastructure (IDI).

First, SoFIE reported earnings are 2-4% lower than LEED earnings on average, and slightly more variable; while the difference between the two reported earnings accounts for 25-30% of the variance in either report.

Second, we reject the joint hypothesis that SoFIE earnings are reported with classical measurement error and LEED earnings are recorded without error. We estimate that the statistical reliability of LEED measured earnings (0.87{0.91) is higher than that of SoFIE earnings (0.83{0.85).

Third, the differences between SoFIE and LEED earnings are negatively correlated with both individuals' average (LEED) earnings over the sample period and their annual transitory deviations. These differences can be characterised longitudinally by both persistent and serially correlated transitory factors.

Fourth, we formulate and estimate a model for SoFIE and LEED earnings, which includes dynamics for true earnings and for measurement errors in both SoFIE and LEED. Female earnings are more variable than males', due both to permanent and transitory effects, and transitory shocks are relatively stronger for women. Allowing for measurement error in LEED, we find no evidence of mean-reverting error in SoFIE.

Fifth, the models imply measurement errors dominate the observed changes in male earnings, and account for large fractions of the changes in female earnings.