Modelling & Controlling Monetary and Economic Identities with Constrained State Space Models

The paper presents a method for modeling and controlling time series with identity structures. The approach is presented in the context of monetary targeting where the monetary identity (e.g. reserve money equals net foreign assets plus domestic credit) is modeled using a constrained state space model and next-period changes in domestic credit (policy variable) are estimated to reach the target level of reserve money. The constrained modeling ensures that aggregation and identity relations among items are dynamically satisfied during estimation, leading to more accurate forecasting and targeting.Application to Germany, U.K and U.S.A. show that the constrained state space model provides significant improvements in targeting and forecasting performance over the AR(1) benchmark and the unconstrained model. The reduction in mean square error of targeting over AR(1) are in the range 76%-95% for the three countries while the gain in targeting efficiency over unconstrained modeling is between 21%-55%. Beyond monetary targeting, the method has wide application to the dynamic modeling and control of economic and financial time series with identity and aggregation constraints (e.g. balance of payment, national income, purchasing power parity, company balance sheet)