is equal to one if labor markets _k_ and _l_ are associated with different sectors; and **1** _sk_ = _sl∧rk_ = _rl_ is an indicator function that is equal to one if _k_ and _l_ are associated with different sectors and regions.<sup>39</sup> Based on PPML estimation result reported in Table A2, we find that the moving cost coefficient between regions, _C_<sup>�</sup> _t_<sup>1,iscloseto1,wherethetotalcostisproportionaltologdistance.Themoving</sup> cost between sectors, _C_<sup>�</sup> _t_<sup>2,isaround1</sup><sup>_._6.Toputthesenumbersinperspectivebasedondistance,the</sup> moving cost between S ̃ao Paulo and Rio de Janeiro is about 5 _._ 76, while that between S ̃ao Paulo and Salvador is about 7 _._ 5. The average moving cost between region pairs is around 7 _._ 62. Therefore, the moving cost between regions is more than four times larger than the moving cost across sectors. We find that moving both regions and sectors makes the total cost slightly lower, with _C_<sup>�</sup> _t_<sup>3around</sup><sup>_−_0</sup><sup>_._18.40</sup> As reported in Table A2, the estimated coefficients are not identical but very similar between years. With the estimates of Γ<sup>�</sup><sup>_k_</sup> _t_<sup>,</sup><sup>_V_�</sup> _t_<sup>_l_, and</sup><sup>_C_�</sup><sup>_t_(</sup><sup>_k, l_), we can simply compute the estimates for log</sup><sup>_m_�</sup><sup>_kl_</sup> _t_<sup>from (29).</sup>

# **4.2 Estimation of the Labor Supply Elasticity**

The key structural parameter we need to pin down for quantification is the labor supply elasticity 1 _/ν_ . We estimate this parameter by embedding the reduced-form approach into our structural model. We derive a regression equation similar to Autor, Dorn, and Hanson (2013), where the reducedform coefficient has a direct link to _ν_ .<sup>41</sup> The model results depend on this key parameter, since the responsiveness of labor market outcomes depends on how elastic labor mobility is.

Once we estimate _V_<sup>�</sup> _t_<sup>_k_asthedestinationfixedeffectinthePPMLequation,wecancalculatethe</sup> present discounted value of the expected wage as with the bin-estimators of _μ_<sup>_k_</sup> 0 _,t_<sup>and</sup><sup>_μk_</sup> 1 _,t_<sup>.Then,wecanestimate</sup><sup>_ν_byestimating</sup> � where we set _Yt_<sup>_k_=</sup><sup>_V_�</sup> _t_<sup>_k_+</sup> �log _μ_<sup>_k_</sup> 0 _,t_<sup>_−_log</sup><sup>_μk_</sup> 1 _,t_ � _− β_ � _Vt_<sup>_k_</sup> +1<sup>_−_log</sup><sup>_μk_</sup> 1 _,t_ +1� and _Zt_<sup>_k_=</sup><sup>_w_</sup> _t_<sup>_k_</sup> +1<sup>.Conditionalon</sup> _β_ = 0 _._ 95, we back out the elasticity _ν_ from the estimate of _ψ_ .<sup>42</sup> As in Section 2, we measure _wt_<sup>_k_</sup> +1<sup>frompurgedwagesfromindividualcharacteristicsandadopt</sup>

> 39Alternatively, we can have **1** _rk_ = _rl_ instead of _Dkl_ , but we use the information on physical distance to back out the region-level mobility friction following the migration literature. We impose _D_<sup>_kk_</sup> = 0 for every _k_ and _D_<sup>_kl_</sup> = 0 if _rk_ = _rl_ . Distance is measured in kilometers.

> 40We can compare the sectoral moving cost estimate to earlier findings in the literature after multiplying the number by _ν_ . In the next section, we will find _ν_ is equal to 0 _._ 493 which translates into a moving cost of approximately 0 _._ 80 times annual average wage which is significantly smaller than ACM’s estimates, and closer to Dix-Carneiro (2014) results.

> 41Our estimation strategy is in a similar spirit of Galle, Rodriguez-Clare, and Yi (2017) and Ad ̃ao, Arkolakis, and Esposito (2019). The labor market adjustment in our model is dynamic and subject to mobility friction, while these two papers interpret the elasticity in a static setting without explicit mobility frictions.

> 42Our main results are robust to the choice of the discount factor.

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