I want to calculate the Gross Value Added for different countries and industries using multi-regional input-output (MRIO) tables. However, I struggle to find a good explanation of how this is done based on the data available. The definition of the GVA (Gross Value Added) is the output of a country/industry less the intermediate consumption, and it is related to the GDP by:
GVA = GDP + subsidies - taxes
So far, I have used the "extensions" or "satellite accounts" that provide the Value Added (VA) disaggregated across different flows, i.e. example from Exiobase in the picture. The VA is the sum of all 12 to my understanding. However, based on the definition of the GVA, I have subtracted 1-3 since these are taxes (so GVA = sum of line 4-12). To me, this seems like the correct approach, but I have not succeeded in finding an explanation that could confirm/disprove. I also become uncertain due to the naming of the extension, i.e. "value added" sounding like "gross value added". Does anyone know the correct way of doing this?
Finally, in MRIO x is termed "gross output" being the total output to final demand + intermediate consumption:
x = Ax + y (Ax = intermediate, y = demand)
or
x = (I-A)^-1 * y = L*y (L = Leontif inverse/requirement matrix)
Does this mean that I can also derive the GVAs from x by subtracting the intermediate consumption? In my mind, this will just leave me with "y", but there might be a another smart way?
Thanks in advance!
From what I understand, yes you can !
You have to differentiate Z = Ax summed along its rows or along its columns
x - rowSum(Z) is the GVA.
x - colSum(Z) is the total final demand.
Regarding Exiobase, I don't have a real answer.
I found that summing all lines of the VA (keeping lines 1-3), I get "quasi" the same results as subtracting the row sum of Z to x. Which is stange...