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We do not attempt to calculate optimal tariffs. We assume that trade liberalization begins at factual tariff rates.
The Frisch elasticity is the elasticity of labor supply with respect to the wage, holding the marginal utility of wealth constant.
Abstracting from seignorage in practice, however, we keep the money supply constant.
We motivate the demand for money using the money-in-the-utility function approach. As usual in the macro literature, however, we focus the welfare analysis on the real component of the utility function, ignoring the welfare effect of money balances. The derivation of the welfare results follows that of Tervala (2012).
We use a first-order approximation of the utility function, whereas several authors who have used the method of Schmitt-Grohe and Uribe (2007) has focused on stabilization policy using stochastic models, implying that one should take into account the volatility of consumption and the labor supply. We focus on a policy which aims to increase consumption and the labor supply and solve the model around a perfect-foresight path.
Hwang and Turnovsky (2013) analyze the macroeconomic effects of tariffs using an open-economy model and find that the short-term effects of unanticipated tariffs on welfare depend on the currency of export pricing, the monetary policy rule, the share of non-traded goods in the consumption basket and the share of exports in total production. However, they do not show that even the short-term welfare effect of an increase in tariff would be negative under plausible parameter combinations.
The assumption of log utility implies that the intertemporal elasticity of consumption is one. Therefore, domestic and foreign goods are Edgeworth-Pareto substitutes (complements) in our model when ρ > 1 (ρ < 1).
The only asymmetry in the model is that the bond is denominated in the domestic currency. This does matter because the nominal interest rate is identical in both countries.
We calculate the DPV using 1,000 periods.