for country _n_ = 1. The equilibrium labor supply for each labor market of country 1, _L_<sup>_k_</sup> 1 _,t_<sup>,ispinned</sup> down by the labor model taking into account workers’ mobility decisions in each period, whereas the labor supply _Ln_ for other countries _n_ = 1 is assumed to be exogenously fixed.

� � A temporary equilibrium at _t_ is a vector of nominal wages **w** _t_ = � _w_ 1<sup>1</sup> _,t_<sup>_, . . . ,w_�</sup> 1<sup>_K_</sup> _,t_<sup>_,w_�2</sup><sup>_,t, . . . ,w_�</sup><sup>_N,t_</sup> � and a vector of prices of the fixed factor in country 1 **b** _t_ = � _b_<sup>1</sup> 1 _,t_<sup>_, . . . , b_</sup> 1<sup>_K_</sup> _,t_ � which satisfy (16)-(28), conditional on the labor supply **L** _t_ = � _L_<sup>1</sup> 1 _,t_<sup>_, . . . , L_</sup> 1<sup>_K_</sup> _,t_<sup>_, L_2</sup><sup>_,t, . . . , LN,t_</sup> � and other fundamental parameters. A sequen� _K,K_ tial competitive equilibrium is the period-by-period sequence of **L** _t_ , **w** _t_ , **b** _t_ , and **m** _t_ = � _m_<sup>_kl_</sup> 1 _,t_ � _k_ =1 _,l_ =1 which solve the labor mobility model in every period, conditional on the initial labor allocation **L** 0 and fundamental parameters of the model.

# **4 Estimation**

In this section, we describe how we structurally estimate the labor part of our model using RAIS from Brazil. The main objects to be estimated are the moving probabilities, between-market moving costs, and the inverse labor supply elasticity _ν_ which is identified by the empirical strategy described in Section 2. With these estimates, we turn to our variables of interest: changes in relative welfare, option values, and the number of job options due to trade shocks. In our reduced-form analysis, we did not study the effect of trade shocks on these variables, because they do not have direct data counterparts. Once we estimate our model, we can use the sufficient statistic result in equations (14) and (15). In other words, we can study the effect of trade shocks on the welfare-related variables in a reduced-form way, before doing full general equilibrium counterfactuals in the next section.

We restrict the sample to the labor markets where at least 100 workers move in and out respectively in every year of our sample period 2004-2015. Since the identification of moving probabilities is based on workers’ mobility, values of labor markets with little labor mobility cannot be identified. Unlike ACM or CDP, we include corridors with zero mobility.<sup>38</sup> After this restriction, we have 804 labor markets in our sample.

## **4.1 Estimation of the Flows**

In practice, it is not possible to obtain _m_ �<sup>_kl_</sup> _t_ directly from data without any estimation. The binestimator for a moving probability, i.e., the number of switchers divided by the number of workers in origin, only works with a large sample size and a small number of choices. Since we have 804 labor markets each of which offers multiple job options, the bin-estimator is infeasible. Therefore, instead of using the bin-estimator, we estimate log _m_ �<sup>_kl_</sup> _t_<sup>byimposingaparametricstructureonthemovingcosts.</sup>

> 38For example, if less than 100 workers move out of or into labor market A, we drop A. However, if no worker moves from labor market B to labor market C, but there are more than 100 workers in total moving out of B, then we keep the labor market B and the B-C corridor in the estimation. All main results we present are robust to the mobility cutoff.

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