First, we re-estimate moving costs with these alternative definitions, since the moving costs are estimated based on mobility observed from changes of positions. The results are summarized in Table A3. We find that the first two moving cost parameters from all three definitions are very similar. The additional cost of changing both sector and region is more different overall, but it is relatively insignificant for the overall moving cost level compared to the other two cost components.

Second, we re-estimate the implications of export shocks for welfare, the number of job options, and option values reported in Table 5, using alternative definitions of positions. We use the same IV strategy discussed in the earlier sections, where the first-stage results are presented in Table 4. The new results are presented in Table A4. We find that most results are very close across all definitions of a position. We can conclude that as long as the detailed occupation is a part of the definition of position, as suggested by the theoretical framework, the model produces very robust results.

# **8 Conclusion**

We introduce a new general equilibrium framework to quantify the impacts of trade shocks on labor mobility and workers’ welfare, combining the advantages of the structural and reduced-form methodologies. The key new mechanism of our model is the endogenous number of job options workers can choose from. We show that a labor market experiencing a positive trade shock attracts more workers because of the larger number of job options that are created there. More job options translate into higher welfare, as workers can choose the best job after comparing more options.

We first provide empirical evidence on the causal effects of export shocks on labor markets using rich employer-employee panel data combined with customs records on export transactions from Brazil during 2003-2015. Using changes in import demand directed to the labor market as a source of variation in exports, we document a positive causal effect of positive export shocks on employment, residual wages, and job turnover rates in the corresponding labor market.

Motivated by this reduced-form evidence, we develop a dynamic general equilibrium model of labor mobility and trade, featuring the endogenous number of job options as well as frictional labor mobility between and within labor markets. Our model characterizes the mechanism through which trade shocks affect the number of job options, labor mobility, and workers’ welfare. We provide a sufficient statistic result showing that the effects of a trade shock on relative welfares are fully embedded in the gross flows between labor markets. This is a powerful result that greatly simplifies the analysis of the welfare impacts of trade shocks. We then structurally estimate the model using the same administrative data from Brazil and the same IV strategy used in our reduced-form analyses. Armed with the estimates of the structural parameters and the sufficient statistic result, we find that a 10% change in exports during the sample period increases the lifetime welfare of a median worker in the formal labor market by 2.99% of the annual wage.

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