Optimal Monetary Policy Analysis:from The Perspective Of Payment Lag And Currency Choice

The time lag between invoicing and receiving the payment for a manufacturing firm is called Payment Lag,which causes time mismatch between income and expenditure and influences price-setting in two aspects.First,the delay of payment leads to a loss of interest earnings,giving rise to an important role played by the interest rate in price-setting.Second,the exchange rate changes that may occur during the period of payment collection can be another important factor affecting the price-setting.The interest rate is a key monetary policy tool and the exchange rate is the channel for transmission of economic fluctuations across borders.Thus,the payment lag will have a great impact on transmission channels of monetary policy through the interest rate and the exchange rate,affecting the optimal monetary policy.We also note that although the existing literature has analyzed the policy implications of Producer Currency Pricing(PCP)and Local Currency Pricing(LCP)separately,in practice the PCP and the LCP coexist.This coexistence has a special compound effecton equilibrium due to a new friction:the price discrimination by different invoicing currencies.The price discrimination will reduce the efficiency of resource allocation and increase the welfare loss of households.Based on the economic observations and the related literature,this paper builds an open economy two-country DSGE model to analyze the interplay of the payment lag and the invoicing currencies and the resulting impact on equilibrium,the transmission of monetary policy,and the design of optimal monetary policy.On the basis of the rigorous theoretical analysis,we conclude as follows:(1)The exchange rate peg can eliminate the inefficiency of LCP,but can not eliminate the inefficiency of the payment lag.When a central bank pegs the exchange rate,the price of traded goods is the same no matter which currency is used to invoice goods,and thus the impact of invoicing currency is eliminated.However,the payment lag affects the price-setting by the firms through the interest rate channel,an impact that can not be fully eliminated through the exchange rate peg.(2)The existence of the payment lag results in a higher cost that government must pay to realize efficient resource allocation in steady state.The payment lag increases the real marginal cost of firms through interest loss and the government must give higher subsidies to firms to eliminate such loss.(3)The trade-off between inflation and output gap does not hold under a discretionary monetary policy when a payment lag is present.In addition,the inflation targeting is no longer the optimal monetary policy.Given the payment lag,the interest rate can affect inflation through the price-setting by the firms and through the consumption-saving decision of the households,with the two offsetting each other,leaving the inflation as a function of expectational variables.Under a discretionary monetary policy,the expected variables are taken as given and hence the authorities need not respond to inflation.(4)Under commitment,inter-temporal but not intra-temporal trade-off between output gap and inflation is faced by a central bank when the payment lag exists.The expected output affects the current aggregated demand through consumption-savings decisions and in turn the current aggregated output,which then affects the interest rate.Due to the payment lag,the interest rate will affect the current inflation.Therefore,the expected output will influence the current inflation due to the payment lag,and the central bank should consider the inter-temporal trade-off between the output gap and the inflation.(5)If there were no payment lag,the dynamic system would have a unique equilibrium under the optimal monetary policy.When the payment lag does exist,the dynamic system has a unique equilibrium under the optimal monetary policy if and only if the parameters satisfy a set of conditions.The traditional restrictions on the coefficients in a simple Taylor rule is no longer sufficient to guarantee the uniqueness of the equilibrium.We use the method in Blanchard&Kahn(1980)to solve the model and analyze the impact of the invoicing currency and the payment lag on the economic fluctuations and the social welfare loss.Some conclusions are given as follows:(6)No matter whether there exists a payment lag,the optimal monetary policy can significantly reduce economic fluctuations and social welfare losses compared with the simple Taylor rule.(7)When there does not exist a payment lag,the optimal monetary policy under discretion has the same effect as under commitment on economic fluctuations and the social welfare loss.Also,the more the number of LCP firms,the greater the welfare loss.(8)When there exists a payment lag,the optimal monetary policy under discretion has a significantly different impact as under commitment on economic fluctuations and the social welfare loss.Generally,the social welfare loss under commitment is less than under discretion.(9)The currency misalignment as an economic friction does not affect the fluctuations of the world economy as a whole but transmits the economic fluctuations between countries.The payment lag,however,not only transmits fluctuations between countries but also increases the fluctuations of the world economy.On the basis of the conclusions above,the following policy recommendations are given:(1)Paying attention to the management of expectation.This study shows that economic fluctuations and the social welfare loss are lower under commitment than under discretion.Commitment stresses the management of expectation,and more effective techniques of expectation management can mitigate the negative effects of the payment lag on economic fluctuations.(2)Take note of the inter-temporal relationship between economic variables.When there exists a payment lag,inter-temporal rather than intra-temporal trade-off between output gap and inflation is faced by the monetary authorities.(3)The corresponding fiscal policy should support the implementation of monetary policy.The payment lag will reduce the efficiency of resource allocation similar to the presence of monopolistic competition.The monetary policy can only reduce the economic fluctuations that is amplified by the payment lag,but it can not eliminate the inefficiency at steady state.Fiscal policy can directly affect the markup of firms and reduce or even eliminate the inefficiency caused by the payment lag.(4)Given that the PCP reduces the social welfare loss,China should continue to promote the internationalization of RMB and increase the proportion of Renminbi as an invoicing currency in foreign trade.