Measurement error in the outcome variable and its consequences for first-difference and fixed-effects panel models

Studies analyzing panel data have gained popularity during the last decades, especially due to the availability of long-running panel surveys and the increasing interest in estimating causal effects. While researchers have investigated the magnitude of measurement error in survey data, little is known about the consequences of measurement error in outcome variables for longitudinal analyses, such as first-difference and fixed-effects models. In this paper, we investigate this issue using the example of monthly earnings and Mincer-style regressions, which are applied to survey data from the German Socio-Economic Panel (SOEP) linked with administrative data from the Institute for Employment Research (IAB). Assuming that administrative earnings information reflects true earnings, we show that individuals typically underreport short-term earnings changes in survey data, which can lead to increasing biases with shorter panel durations. We demonstrate that this problem is substantially mitigated when using fixed-effects models, particularly when longer panels are available. Our findings thus imply that measurement error in the dependent variable can bias estimates for models focusing on short-time changes, but has negligible impacts when using long-running data and adequate methods.