Recently, I found one article which points out a silly and embarrassing error of SDA application: Dietzenbacher, E. & J. Stage. 2006. Mixing oil and water? Using hybrid input-output tables in a structural decomposition analysis. Economic systems research. 18(1):85-95. The silly error is about unit problem at final demand decomposition: when units of energy or money changes, the results of level and mix effect change arbitrarily. For example, first I use million dollars for non-energy sectors and 10^15 Btus for energy sectors. Then I use the same million dollars for non-energy sectors but now 10^12 Btus for energy sectors. Now, I still get the same result for total final demand effect but totally different level and mix effects.
They presented mathematical proof of the problem and also showed the results from SDA with two different units tables using data from the famous Miller and Blair text book (1985). At first time, I couldn't believe what they found. Because if it is true, then many previous literatures become questionable... I ran through many times over their findings and then finally couldn't but accept them.
(Source: Dietzenbacher and Stage, p. 90. You can see level and mix effect are not consistent, although total effect does)
It is a major embarrassment in hybrid SDA. Monetary input-output analysis is utit-free. That must be one reason why no body has paid much attention on it. Who could have possibly imagined this? The authors of this paper proposed two solutions to get rid of unit problems. I tested the solutions using data from Miller & Blair (1985) by myself and found that they seamlessly work without any unit problem. One question is economic meaning of the new decomposition sets. I need consider more about this.
I had chance to send email to the corresponding author, Dr. Jesper Stage to clarify some points in their paper. I complimented him that this paper seemed to be a classic in this field. Dr. Stage is a Swedish economist at University of Gothenburg. He had his master's degree in Physics. I thought that his background might help him to find this problem. At the end of his email, Dr. Stage emphasized that this finding does not weaken analytical power of hybrid power, although they found serious but solvable problem in "application" of SDA; hybrid SDA is a still useful tool.
My advisor has not been fully convinced by this paper. He encouraged me to write email to big names in this filed. So far, I am waiting for responses from Drs. Casler and Rose. I wonder what their reaction to the finding and their critique on the proposed solutions will be.
Abstract of the paper;
Mixing Oil and Water? Using Hybrid Input-Output Tables in a Structural Decomposition Analysis
ERIK DIETZENBACHER* & JESPER STAGE**
*Faculty of Economics, University of Groningen, The Netherlands, **Department of Economics, Umea° University, Sweden
(Received October 2003; revised September 2005)
Input-output studies of energy use frequently adopt the so-called hybrid table, where the rows corresponding to energy sectors are in energy units rather than in monetary units. However, we show that, in structural decomposition analyses, this hybrid approach may induce arbitrary results that depend on the choice of units, rather than on changes in economic structure. This is because an economically meaningless sum of monetary and energy units enters the calculations. Our proposed solution to this problem is based on using a sum of monetary units instead, thus avoiding this attempt to mix oil and water.
KEY WORDS: Structural decomposition analysis, input-output analysis, energy use, hybrid input-output tables
Correspondence Address: Jesper Stage, Department of Economics, Umea° University, SE 901 87 Umea°, Sweden.