Estimating regional level data from national data I am trying to estimate regional unemployment rate. I understand unemployment rate is calculated as (number of people unemployed/total labour force). For the national level, I have historical rates as well as forecast unemployment rate and labour force values.
However, I am keen to draw out a way to link regional unemployment rate to the national unemployment rate estimates (using some kind of weights). So that if I have forecasts of national unemployment rates, I could use some mechanism to calculate regional unemployment using these forecasts. Any ideas?
Data Available:
Historical National Data: Number of unemployed, unemployment rate, total labour force
Forecast National Data: Unemployment Rate
Historical Regional Data: Number of unemployed, unemployment rate, total labour force per region.
 A: Here is one way of doing this, probably as straightforward as possible.  This could form a base case for comparing to more sophisticated methods.
To have the regional unemployment rates consistent with the national unemployment rate, you need the weighted average regional rate (weighted by forecast labour force) to be the forecast national rate.  So the overall strategy is to forecast the individual regions' unemployment rates, then make the minimum changes to bring about that consistency.
Step 1 - forecast national and regional labour force sizes
You need to do this, even at the national level, because you only have forecast rates, not volumes.
This could be done any number of ways, but I think the simplest is to forecast them simultaneously using a hierarchical method for grouped data.  Rob Hyndman's hts R package does this nicely.  Basically, individual forecasts at both levels (regional and national) are combined optimally in such a way that correlation is made the most of, and the regional forecasts add to the national.
Step 2 - Infer the national unemployment volume
This is obviously just the national labour force volume multiplied by the forecast unemployment rate.
Step 3 - Forecast individual unemployment for each region
This can be done using whatever method is available - for example, either univariate (one at a time) or simultaneously through a Vector Auto Regression (probably better).
Step 4 - Calibrate the regional totals to be consistent with the national.
This is just a matter of arithmetic.  From your forecast regional unemployment rates, calculate unemployed volumes. Multiply them by whatever constant adjustment is needed to match the national unemployed volume.  Recalculate the unemployment rates.
This will work in that it will give you a credible set of regional forecasts that are consistent with the national total.  How well it will work is another matter.  Improvements would come in various ways eg just better methods for step 3, combining step 3 and 4, or combining the entire thing into a more formal statistical model.
