Currency Invoicing,incomplete Exchange Rate Pass-Through And Optimal Monetary Policy

Optimal monetary policy rules in the open economy have been the hot topic in monetary policy research.One of the most discussed issues about this topic is which kind of inflation should central bank targets to and whether the central bank needs to control the fluctuation of exchange rate.Currency choice is one of the most crucial factors which determines the optimal monetary policy.By assuming all the exporters choose to price in producer currency,some scholars find that optimal policy in open economy should be consistent with the closed,which is the so-called inward-looking policy,and that means all central bank needs to do is simply stabilizes domestic inflation and reach the maximization of welfare.Another part of scholars adopted the setup that all the exporters choose to price in local currency and find that incomplete exchange rate pass-through triggered by currency invoicing will not only have impact on the expenditure-switching effect of variation of exchange rate but distort the real exchange rate,and finally reduce the welfare.Thus,for improving the welfare,central bank should target to the group of price inflation like consumed price,which contains some"external" targets such as foreign price inflation and variation of exchange rate.Most of researches above,however,only considered the polar setup that all the exporters in two country only price in producer currency or local currency,and missed the asymmetric and some other complex characters each country shows in reality.So,once considering the complex situations of currency invoicing in reality,it will be so hard for us to make trade-off between the conclusion of the researches which derived under different polar setup of currency choice.Based on such consideration,we introduce a more general setup of currency choice,there are two kinds of exporters price in different currency in one country.We also derive the purely second-order household-based welfare loss function and use it to investigate the optimal monetary policy under full commitment.On the other hand,for investigating the optimal choice of inflation target,we constructed some representative rules which derived under the polar setup,such as domestic inflation targeting(DIT)and consumer inflation targeting(CIT).Basing on the simple rules above we also constructed other rules by introducing some extra targets like lag interest rate and variation of exchange rate.By using the method of optimal simple rule and welfare loss function,we derived the optimal parameters to targets under given policy rule,and compared the welfare of different rules.Our conclusion points out that,under non-inertial interest rule,the optimal choice of inflation target depends on the proportion of exporter’s currency choice,the more pricing in producer currency the better DIT is.While under inertial interest rule,DIT is almost always the best choice.In addition,the result of impulse response also indicate that dynamic adjustment to exogenous shocks under DIT is mostly close to the optimal rule under commitment.At last we assess the welfare of simple rules above and find that additionally stabilizing the fluctuation of exchange rate can remarkably improves the welfare.Finally,for explaining the principle of that we need to stabilize the variation of exchange rate,we analyzed the result of impulse response under various rules and currency choice.We find the spontaneous adjustment of exchange rate to exogenous shocks can not only stabilizes the inflation and price dispersion through terms of trade and improve the welfare,but also triggers the deviation of law of one price which distorts the composition of consumer’s final consumption and thus reduces the welfare.So,except to face the trade-off between inflation and output gap,central bank will also face the trade-off between the stabilized effect and distorted effect which induced by variation of exchange rate.