Over the last few decades, international trade has increased at a rapid pace, altering domestic production and labor demand in different sectors of the economy. A growing literature has studied the heterogeneous effects of trade shocks on workers’ industry and occupation employment and on welfare when reallocation decisions are costly. The estimated effects critically depend on data on workers’ reallocation patterns, which is typically plagued with coding errors. In this paper, I study the consequences of misclassification errors for estimates of the labor market effects of international trade and show that structural parameter values and the estimated effects are biased when the analysis uses uncorrected data. I develop an econometric framework to jointly estimate misclassification probabilities, corrected mobility matrices, and structural parameters in a unified way. Under different model specifications, I compare how the estimated effects of a trade shock differ on whether the analysis uses correct mobility measures and parameters. The results show that estimated employment and welfare effects of a trade shock are substantially different, raising an important warning for quantitative exercises using mobility data with coding errors.