Multisector vs single contribution analysis

Hi, 

There have been lot of discussion regarding single sector vs multi-sector contribution analysis. Some use internal adjustment method (in IMPLAN software - changing commodity production and making RSC to zero) while some use matrix inversion method (using SAM matrix to create square matrix for sectors of interest, inverting it, and multiplying with output from study area data to get adjusted values). Results from both methods tend to differ slightly and its up to investigator objective to chose one. 

My question here is, suppose we would like to do contribution analysis for sectors A, B, and C individually as well as a whole. Summing the total contributions reported by individual sector A, B, and C analysis will be higher than that of running multi-sector analysis (A, B, C, together) because by summing individual sector total contribution, some of the indirect and induced effect (say A) happens to be direct effect for other sector (say B or C). So there is some double counting.

While if we do internal adjustment for all sectors (A, B, and C) and do single sector analysis in the same model we will get the sum of individual sectors total contribution equal to multi-sector (A, B, C together) total contribution. But doing so, aren't we losing individual sector identity. Is it a good idea to run individual sector (say A) analysis in the same model where we did internal adjustment for A, B, and C to run multi-sector analysis? 

Also, for matrix inversion, is it advisable to use same adjusted value that we derive from 3x3 matrix (SAMs for sector A, B and C) to shock the mode for single sector analysis? 

I would like to report results for A, B, and C individually as well as a whole. 

Thank you.