Studies of Economic Interdependence by State-Space Modelling of Time Series: U.S. Japan Example

This paper proposes a new way of studying interdependence of countries by building models for selected macroeconomic time series of the countries involved, by a state space model which incorporates moving average components in addition to autoregressive ones. The singular value decomposition is performed of the covariance matrix between the data and future realization of the data vector. A crucial step is the choice of a particular coordinate system which resolved indentifiability question and leads to estimates of the model system matrices which enjoy certain nesting or orthogonality properties. The estimates are consistent even when the state vector dimension is unspecified. The paper then discusses the possible presence of unit roots in the time series and develops a canonical representation of time series containing unit root components. Unit roots are removed by prior detrending in this paper. (The author has since developed a two-step procedure that eliminates the need for this prior detrending in AOKI (1987a)). The method is then applied to study interaction of the industrial production indices and ex ante real interest rates in the USA and Japan.