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In this paper the authors consider a two-country New Open Economy Macroeconomics model, and analyze the optimal monetary policy when countries cooperate in the face of a "Global Liquidity Trap" - i.e., a situation where the two countries are simultaneously caught in liquidity traps. The notable features of the optimal policy in the face of a global liquidity trap are history dependence and international dependence. The optimality of history dependent policy is confirmed as in local liquidity trap. A new feature of monetary policy in global liquidity trap is whether or not a country's nominal interest rate is hitting the zero bound affects the target inflation rate of the other country.
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