Problems aggregating shares

If your database contains shares you may encounter difficulties in using AggHAR to aggregate them, especially if you aggregate 2 dimensions at once.

For example, the ORANI-G database contains a header R001 with coefficient:

(all,i,IND)(all,r,REG) REGSHR1(i,r) # Regional output shares #;

The shares add to 1, ie,

(all,r,REG) sum{,i,IND, REGSHR1(i,r)} = 1

Clearly, some type of weighted aggregation is needed for header R001 if you are aggregating sectors.

Equally clearly, unweighted aggregation is needed if you are aggregating over regions.

Supposing national outputs to be given by:

Coefficient (all,i,IND) V1TOT(i) # National outputs #;

then the weight matrix

(all,i,IND)(all,r,REG) REGWGT(i,r) = V1TOT(i);

will correctly aggregate R001, if you are aggregating only over sectors.

But those weights will not correctly aggregate R001, if you are aggregating over regions.

You need to run AggHAR twice, aggregating REG and IND separately (either order is fine), and using no weights for the REG aggregation.

A better solution

A neater solution would be replace the R001 shares on the data file with actual regional outputs, given by REGSHR1(i,r)*V1TOT(i). The model TAB file would be changed to read:

Coefficient

(all,i,IND)(all,r,REG) REGV1TOT(i,r) # Regional outputs #;

(all,i,IND) TEMTOT(i) # Temporary total #;

(all,i,IND)(all,r,REG) REGSHR1(i,r) # Regional output shares #;

Read REGV1TOT from file InFile header "R001";

Formula

(all,i,IND) TEMTOT(i) = sum{r,REG, REGV1TOT(i,r)};

(all,i,IND)(all,r,REG) REGSHR1(i,r) = REGV1TOT(i,r)/TEMTOT(i);

In many other cases you will find that puzzling problems about the correct way to aggregate shares are easily resolved if the database shares are replaced by flows, from which shares can be calculated, if necessary.

URL of this topic: www.copsmodels.com/webhelp/viewhar/hc_aggshares.htm

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