Correlation of composite indicator dimensions I have a composite indicator that works very well for my purposes and is made of 3 dimensions (dim1, dim2, dim3). The 3 dimensions are different measures that are, in many cases, highly correlated (let's say around 0.8). The final indicator is obtained by the sum of the standardized values of the 3 dimensions.
In the forecasting exercises I carry out, it is a matter of fact that the composite indicator works much better than taking the 3 dimensions separatedly.
Now my problem is that I need to justify, from a theoretical perspective, that it is ok to make an indicator from the sum of 3 correlated dimensions. Is that ok? Could you point me to some reference that supports this choice? Some people are telling me that my composite measure could carry too much redundancy. Is that a problem?
I apologize in advance if my question is naive or too general in some aspects. In case, please help me improve it. I am here to learn :)
 A: 
Now my problem is that I need to justify, from a theoretical perspective, that it is ok to make an indicator from the sum of 3 correlated dimensions.

Consider test construction in Psychology or Sociology. Those people tend to ask a number of associated questions (don't call them questions, they are items), each of them representing an underlying common idea (don't call it that, call it a common construct or trait) and then the answers to all of the items are added (or their mean is computed) to compute a scale value that is then taken as a measure for the underlying construct.
This is very similar to your question, just that most of these scales have more then 3 items, often much more. You have to take care that you only build the sum or the mean of things that represent a common trait/construct. You cannot add the number of apples you eat to your political orientation. That does not make sense.
Your observations regarding correlation are a good indication, that these three measures have some construct in common which their sum can then represent. A more formalized way of investigating the common pattern of n correlated measures is factor analysis. Either exploratory factor analysis or confirmatory factor analysis are possible routes to show, what these measures have in common.
Not the same but much easier to compute are measures of internal consistency (Cronbach's $\alpha$ probably being the best known). Depending on your circumstances you could compute either to formally justify your procedure.
Should you use R, the package psych comes with lots of usefull functions and good explanation/documentation, the package lavaan can be used for CFA.
Search terms for my analogy are "Classical Test Theory", "Test construction" and "Scales Psychology".
Starting points for further reading:

*

*https://en.wikipedia.org/wiki/Internal_consistency

*https://benwhalley.github.io/just-enough-r/cfa.html

*https://www.sciencedirect.com/science/article/pii/B9780126913606500045
