where ∆ _z_ denotes the linear change induced by a change of _z_ . Next, our model shows that the change in the number of job options in each labor market driven by a change in _z_ is Equations (14) and (15) suggest that the labor supply elasticity and changes in moving probabilities are the sufficient statistics for changes in the relative welfare and the number of job options.

# **3.4 International Trade with Love for Variety of Tasks**

The dynamic labor mobility model we introduce can be used to quantify the effect of various labor demand shocks on workers’ welfare. In this paper, we focus on the effect of international trade. We introduce trade to our model as a static problem, where trade endogenously affects both wages and the number of job options, and eventually dynamic labor mobility as well as welfare.

The international trade part of our model is based on Eaton and Kortum (2002, EK, hereafter), where trade is driven by the standard Ricardian force. We assume that there are _N_<sup> ̄</sup> countries ( _n_ = 1 _, . . . , N_<sup> ̄</sup> ), but only country 1 has more than one region. For other countries _n_ = 1, there is only one region which is the country itself. We now introduce a country subscript _n_ to all relevant variables, and the labor mobility model described previously applies only to country _n_ = 1 for which we study the effect of trade shocks on dynamic labor mobility and welfare in quantification.<sup>30</sup> There is a continuum of products on [0 _,_ 1] in each of _S_ sectors. Consumers have identical nested CES preferences with a common elasticity of substitution _σ >_ 0 across products and a Cobb-Douglas aggregation across sectors with the expenditure share _φ_<sup>_s_</sup> for each sector _s_ . To characterize trade between countries, while we have multiple regions only in country 1, we assume that there is a national aggregator for each sector in country 1. The aggregator of each sector can source each product of that sector from the lowest cost region within the country at no trade cost. The national price of each product is thus equalized across consumption locations within the country. Then, this aggregator trades with partner countries. If no region in country 1 is the lowest cost supplier of a certain product for country 1, after taking into account cross-country differences in production cost and bilateral trade costs, then country 1 imports that product, and no region in country 1 produces that product at the equilibrium. To simplify our analysis, we assume that there is no production in the residual labor market of country 1 and further assume that there are only formal sectors in other countries _n_<sup>_′_</sup> = 1.<sup>31</sup> Labor, fixed factor, and composite intermediate inputs are used for production in country 1.

> 30Our model is able to allow for multiple regions and dynamic labor mobility for all countries. For quantification, however, we would need detailed labor mobility data from each country. Therefore, we restrict the analysis of the effect of trade shocks on internal labor mobility only to one country, which will be Brazil empirically. The general equilibrium feature of the trade part applies to all of _N_<sup> ̄</sup> countries.

> 31Combined with the previous assumption on the systematic component of the utility of workers in the residual labor market, we effectively allow for neither production nor consumption in the residual market.

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