Estimating Dynamic Models Using Kalman Filtering

The Kalman filter is useful to estimate dynamic models via maximum likelihood. To do this the model must be set up in state space form. This article shows how various models of interest can be set up in that form. Models considered are Auto Regressive-Moving Average (ARMA) models with measurement error and dynamic factor models. The filter is used to estimate models of presidential approval. A test of rational expectations in approval shows the hypothesis not to hold. The filter is also used to deal with missing approval data and to study whether interpolation of missing data is an adequate technique. Finally, a dynamic factor analysis of government entrepreneurial activity is performed. Appendices go through the mathematical details of the filter and show how to implement it in the computer language GAUSS.