Examples - Decomposing All or One Side of an Equation

In ORANIG, the equation which describes the demands for household consumption of domestic and imported commodity c is:

Equation E_x3 # Source-specific commodity demands #

(all,c,COM)(all,s,SRC) x3(c,s) - a3(c,s) =

x3_s(c) - SIGMA3(c) * [p3(c,s) + a3(c,s) - p3_s(c)] ;

The x3_s(c) term on the right-hand side is the expansion term and the term

- SIGMA3(c) * [p3(c,s) + a3(c,s) - p3_s(c)]

on the right-hand side is the substitution term in this Armington nest.

You can ask AnalyseGE to decompose the right-hand side of this equation in two slightly different ways. To do this, click anywhere on this equation in the TABmate form, then right click and select the menu item Decompose All or One Side of this Equation. In the selection form which appears we assume below that you have selected "RHS" to decompose the right-hand side (rather than the left-hand side) and that you have selected First as the Toggle position. You get two different decompositions depending on whether you select "Complete" or "Intelligent" as the type of decomposition. We describe these below.

Intelligent decomposition. An intelligent decomposition respects brackets and SUMs.

In this case the software produces a coefficient TempCoeff with 3 arguments. The first argument ranges over the toggle set with elements called x3_s and e1_SIGMA3. The second and third arguments range over the sets COM and SRC from the equation. For each c in COM and s in SRC,

· the values of TempCoeff("x3_s",c,s) show the expansion term x3_s(c),

· the values of TempCoeff("e1_SIGMA3",c,s) show the substitution term (see above).

For example, it is easy to see whether an increase in x3(c,s) for particular c and s is due to an expansion effect or a substitution effect, or both.

AnalyseGE makes up toggle names (for example, "x3_c" and "e1_SIGMA3" above) based on the names of the Coefficients and Variables in the different expressions.

Complete decomposition. A complete decomposition of an expression in an equation is designed to show the separate effects of the changes in each of the variables involved, one at a time.

Again the software produces a coefficient TempCoeff with 3 arguments. This time the first argument has four possible values corresponding to the 4 different variables x3_s, p3, a3 and p3_s on the RHS of the equation. As before the second and third arguments ranges over COM and SRC. For each c in COM and s in SRC,

· the values of TempCoeff("x3_s",c,s) show the value of x3_s(c),

· the values of TempCoeff("p3",c,s) show the value of term involving variable p3(c,s), namely

-SIGMA3(c) * p3(c,s),

· the values of TempCoeff("a3",c,s) show the value of term involving variable a3(c,s), namely

-SIGMA3(c) * a3(c,s), and

· the values of TempCoeff("p3_s",c,s) show the value of term involving variable p3_s(c),

namely SIGMA3(c) * p3_s(c).

Compared to the intelligent decomposition above, the substitution term is here split into 3 parts. When doing a complete decomposition, AnalyseGE uses the names of the variables as the toggle names (for example, "x3_s" and "a3" above).

The general idea is that the intelligent decomposition takes notice of brackets such as those grouping "p3(c,s)+a3(c,s)-p3_s(c)", while the complete decomposition is designed to show the separate effects of changes in the variables one at a time.

On each occasion, you can choose which sort of decomposition you prefer. You can also modify a decomposition produced by AnalyseGE if you wish by editing the expressions it leaves in the AnalyseGE memo. [To do so, you will need to understand the implementation of toggles in a little detail.]

Exactly What Are You Seeing?

As with all decompositions, if you are at all unsure exactly what values you are seeing in each toggle, you can look at the Exxx header on the ViewHAR form or in the Evaluate memo on the AnalyseGE form.

We are grateful to Hans van Meijl for suggesting that we develop automatic decompositions of equations.

URL of this topic: www.copsmodels.com/webhelp/analysege/hc_decompall.htm

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