How to correlate closed data? could anyone help me with a correlational analysis between compositional variables and non-compositional ones. To make it clear I am interested in the correlations between the shares of employees in agriculture, services and manufacturing in total employment and GDP. The shares, obviously, add up to 100% (closed data). In other words, my goal is to correlate first the share of agriculture with GDP, then the share of manufacturing with GDP and so on. I would be more than grateful for any hints.
 A: One can look at this as a constraint modelling exercise, but my personal observation of poor performance with this path suggests a different approach.
I would start by identifying the employment segment that is apparently in decline, and just leave it out of the analysis. Then, attempt to forecast the missing segment by a difference from the Total Employment forecast.
If this missing segment value is negative or realistically too low,I would base a forecast for this segment based on a model of people (not percent change) which includes an intercept (which may represent a base of insulated workers). Employ this forecast for this segment and slightly prune the larger segment respective forecasts.
Alternatively, look for other higher figures for the Total Employment projection, which then allows a difference from total forecast that is seemingly more reasonable.
So, to directly answer the question how to correlate closed data, try to avoid doing so, and only address the constraint issue (by segment model choice, for example) upon review of a unconstrainted approach with an apparent issue.
