Interrupted time-series analysis for panel data

Question

I am familiar with using regression with ARIMA errors to model interrupted time-series, in order to estimate the change in magnitude caused by a policy intervention. These models seem to be designed for a single time series, and thus if multiple time-series are analysed a model must be fit separately for each time-series.

I am interested in analysing the national impact of a policy intervention, the implementation of which was staggered in time across all (eight Australian) states. I can see three possible analysis approaches here:

1. Fit a separate ARIMA model for each state
2. Attempt to fit an aggregate national model, perhaps with one dummy variable indicating partial implementation and another indicating complete implementation
3. Find a different model that works explictly on panel data. This would hopefully bring some kind of compromise between the no-pooling approach 1 and the complete pooling approach 2.

What sort of approach would you recommend here?

Answer 1

I would identify the true date of the intervention i.e. when it was fully realized for each state separately using Intervention Detection schemes. The true date (de facto) can often be different from the "known date" (de jure) because of either a pre or a post effect (delay). With a common ARIMA model and one composite intervention variable constructed from the de facto dates, I would then globally estimate all parameters ie. the ARIMA coefficients and the national impact. The coefficient for the composite Intervention Variable would then reflect the national effect. When conducting this Global estimation you need to ensure that the prediction/fitted value for the first reading in the second state is not affected by the latest readings for the first state. For example if the ARIMA model is an AR(12) the first 12 expectations for each state would be the 12 observed values thus generating 12 zero errors. Commercial software with this built-in feature is rare but available.