Example: Mapping skill shares from broad to detailed sectors

Suppose that the IO table gives us a vector of wage payments by 100 sectors (set IND). We wish to split up each payment by skill (set OCC), using a supplementary source that only distinguishes 30 broad sectors (set BROAD). Luckily, each IND element fits wholly into just one BROAD sector; ie, there is a mapping from IND to BROAD. Shares from the BROAD data are applied to corresponding numbers in the IO wage data to produce a matrix size IND*OCC which must add up to the IO wage vector.

Set

IND # industries # read elements from file infile header IND;

BROAD # broad sectors # read elements from file infile header BIND;

OCC # skill types # (Professional,Clerical,Skilled,Other);

Mapping (onto) IND2BROAD from IND to BROAD;

Read (by_elements) IND2BROAD from file infile header MIND;

Coefficient ! given !

(all,i,IND) LAB_O(i) # wages by ind #;

(all,b,BROAD)(all,o,OCC) BLAB(b,o) # wages by broad ind and occ #;

Read

LAB_O from file infile header LABO;

BLAB from file infile header BLAB;

Coefficient ! to compute !

(all,b,BROAD) BLAB_O(b) # wages by broad ind #;

(all,b,BROAD)(all,o,OCC) OCCSHR(b,o) # skill shares by broad ind #;

(all,i,IND)(all,o,OCC) LAB(i,o) # wages by ind and occ #;

Formula

(all,b,BROAD) BLAB_O(b) = sum{o,OCC,BLAB(b,o)};

(all,b,BROAD)(all,o,OCC) OCCSHR(b,o) = BLAB(b,o)/BLAB_O(b);

(all,i,IND)(all,o,OCC) LAB(i,o) = OCCSHR(IND2BROAD(i),o)*LAB_O(i);

Write LAB to file outfile header LAB;