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Abstract The paper formulates and estimates a single-factor multivariate time series model. The model is a dynamic generalization of the multiple indicator (or factor analysis) model. It is shown to be a special case of the general state space model and can be estimated by maximum likelihood methods using the Kalman filter algorithm. The model is used to obtain estimates of the unobserved metropolitan wage rate for Los Angeles, based on observations of sectoral wages within the Standard Metropolitan Statistical Area. Hypothesis tests, model diagnostics, and out-of-sample forecasts are used to evaluate the model.
Engle et al. (1981) studied this question.