The Dynamic Components Model (DCM) is a form of State Space Model where the approximate state variables are first computed using Principal Components Analysis (PCA). The difference between a standard State Space Model and the DCM are (1) how the Measurement Matrix (see graphic above) is computed (with PCA) and (2) how the state variables are analyzed directly. The advantage of the DCM is that it separates the growth and control state variables so that growth and control can be analyzed independently (the PCs are statistically independent). In the Cannonical DCM, there are only three state variables (one for growth and one for control) that explain at least 80% of the variation in the Output Variables. The control components are typical made up of Error Correcting Controllers (ECCs). In SocioEconomic systems the ECCs are typically associated with a theoretical tradition. For example, the Malthusian Controller is presented here and generalized here. ECCs are key elements of Cybernetics and the dominant growth component is a key element of Systems Theory and Economic Growth Theory.
The DCM is implemented in the public domain R Programming language as an extension to the dse (Dynamic System Estimation) package. The dse package can be downloaded on all Computer platforms and can be run on line with a web browser (here). The DCM extensions with documentation are available here.
In the dse package, a state space model can be created using the SS command in R:
