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- i Ii, (10) National income consists of labor income, tariff rebates Ri and the trade surplus, which is exogenous Si, i. e. Ii = wiLi + Ri â Si and X j i is country iâs expenditure on sector j goods.- 14 Demand of sectors k in all countries i for intermediate usage of sector j varieties produced in country n is given in the first term on the right hand side. The second term denotes the final demand. Tariff rebates are Ri = J j=1 X j i 1 â N n=1 j ni (1+t j ni) .15 14 Aggregate trade deficits in each country are exogenous in the model, which follows the theoretical framework of Caliendo and Parro (2015). All counterfactuals are calculated by holding the countriesâ aggregate trade deficits constant, as a share of world GDP. 15 Instead of the goods market clearing condition, one can also use the expenditure equation X j i = J k=1 γ j,k i (1 â k i )(Fk i Xk i + Sk i ) + ! j
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- n, while trade cost changes directly affect it (see eq. (13)). Trade shares change as a reaction to changes in trade costs, unit costs, and prices. The productivity dispersion (j indicates the intensity of the reaction. The higher (j, the bigger trade changes. Goods market clearing is ensured in eq. (15). Equation (16) provides the new equilibrium and the counterfactual income-equals-expenditure, thus balanced trade condition. The framework of Caliendo and Parro (2015) is exploited to solve the system for multiple sectors, which is an extension of the single-sector solution algorithm proposed by Alvarez and Lucas (2007). The initial guess is made about a vector of wage changes. Using eqs. (12) and (13), it then computes changes in prices, trade shares, expenditure levels, evaluates the trade balance condition eq. (16), and updates the change in wages based on deviations in the trade balance. Revisiting the Euro 945 A.3 Detailed Gravity Results
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