Why Results Do Not Always Add Exactly

If you look at a simple linearized equation such as

(All,i,SECT) p_XH(i) = p_Y - p_PC(i) ;

from Stylized Johansen, you may find that the results for these percentage-change variables do not add exactly. [For example, the 1,2,4-Euler results from simulation SJLB for "s2" are P_XH("s2")=6.899, p_Y=5.885 and p_PC("s2") = -0.949. If you calculate the RHS of the above equation with these values you get 6.834 rather than the LHS value of 6.899.] These results do not add exactly since you are looking at the linearized equation. While Johansen results would add exactly, accurate multi-step results should not add exactly. [In the example, the "-" in the linearized equation corresponds to division in the levels.]

This can be further complicated when Coefficients are involved in the expressions. The values of Coefficients are updated through a multi-step calculation. When you work in AnalyseGE, you see either the pre-simulation values (if you load the SLC file), or the post-simulation values (if you load the UDC file) or the average of these (if you load the AVC file). How accurately linearized equations or Formulas involving Coefficients are satisfied depends on which Coefficients values you have loaded and on the sort of expression you are looking at. See section 8.2 in the Hands-on introduction to AnalyseGE for an example where Coefficients are involved.

You can find more details about this

•in the Frequently Asked Questions section of the GEMPACK web site. This contains an explanation as to why linear equations are not satisfied exactly by the results from multi-step simulations.

•in Appendix 1 in the Hands-on introduction to AnalyseGE.

Although the LHS and RHS are not equal for many equations when you decompose them in AnalyseGE, they should always be equal for various types of equations (adding-up equations) which occur frequently in GE models. Examples include market clearing equations and equations adding up values or quantities.

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

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