I have been struggled to understand basic decomposition equation of final demand (Casler & Rose, 1998 p. 354, equation (7)). Because this equation does not deliver clear economic implication by itself.
(Where, Y is final demand. t is period.)
First term of second line is final demand level effect, and second term is final demand mix effect. Level effect means pure change in final demand that would happen if final demand of each industry in period t had increased in the same proportion with total production increase between two periods. Mix effect means change in the mix of final demand while assuming the same level of final demand at the control period.
But the decomposition equation does not match with the definitions and is not explanatory; first term is comparing Yt and Yt, and second term is comparing Yt and Yt-1. Equation itself is correct and holds, but it does not explain. Instead, we can consider to compare Yt and Yt-1 for first term, and Yt-1 and Yt-1 for second term.
Here sigm Yt over sigma Yt-1 is GDP growth rate. Instead using GDP scalinging down factor as in Casler and Rose (sigma Yt-1 over sigma Yt), using GDP growth rate makes things much clear and matches with original definition of level & mix effect. Although we follow which ever decomposition equation, Casler & Rose's equation or mine, there will be no difference. I do not understand why the authors use the equation in their analysis. There must be some reason, for example to make calculation easier.
After all, it seems a tedious thing in the whole analysis. But just for record, I have been suffering for long time to understand their equation. It must be their intention to torture graduate students.
2. Next Goal
Understanding method of Gowdy & Miller (1987) Technological and demand change in energy use: an input-output analysis
3. House Keeping
My abstract for Nairobi ISEE conference got accepted. I will work with Carol to find a ticket.