Dynamic Programming Model And Numerical Solution For Optimal Monetary Policy

In this paper,a dynamic programming model for optimal monetary policy,which adjustsdomestic money supply to achieve both monetary independence and the stability of import and export trading is constructed.Exchange rate bands gives central bank some control over the domestic interest rate and allow the central bank some freedom to adjust the domestic interest rates to local conditions to avoid the disturbance from foreign economy,in other words,exchange rate bands make monetary independence possible.On the other hand,for the stability of import/export trading,we hope the bands of exchange rate as small as possible since the variability of exchange rate induce the change of transaction amount.The monetary policy is to find the optimal adjustment of money supply to minimize the weighted sum of variability of exchange rate and interest rate and transaction amount.According to Bellman principle,we transform the infinite period dynamic programming problem into a sequence of single period optimization problems to find the optimal adjustment of money supply and the motion of the system.Since there exist forward-looking variables,we modify the solution which is optimal from the government's viewpoint to make the market participants' expectation consistent to the government's decision.To solve the nonlinear matrix equations involved in the solution procedure,3 iterative methods--Newton method,implicit alternating direction method and explicit alternating direction method are used.Numerical experiments are made to compare 3 methods and numerical results show that the solutions obtained by these 3 methods are the same and that explicit alternating direction method is the most efficient.Using the spot exchange rate,treasury bond's interest rate and different kinds of trade goods' transaction amounts between China and USA,empirical analysis has been made.It shows that,in the long-term,the optimal monetary policy with exchange rate bands can keep monetary independence and import/export trading stability at the same time.