I am trying to isolate the effect of two different drivers/factors over time. For example, consider the following:
Factor 1 x Factor 2 = Value
Year 1: Factor 1 = 10, Factor 2 = 40, Value = 400
Year 2: Factor 1 = 12, Factor 2 = 41, Value = 492
The Year over year change of value is 23%
I am trying to figure out what portion of that change is accounted for by each factor. The approach I have been trying to take is to hold one factor at a time constant and see what the resulting value would be. For example:
Holding factor 1 constant gives value = 10 * 41 = 410
- 410/400 - 1 = 2.5% Year over year change
Holding factor 2 constant gives value = 12 * 40 = 480
- 480/400 - 1 = 20% Year over year change
I take this to mean that factor 1 accounted for 2.5% of the growth and factor 2 accounted for 20%. However, adding these two together gives a year over year change of 22.5% when the actual change was 23.0%.
Could someone please let me know why this analysis does not seem to be very exact and if there is a better way to approach it?
Thank you Malay, that is very helpful explains why the numbers weren't adding up exactly. Is there any way to completly capture the change due to a particular factor, or will you always have some "left over" change due to the interplay between the factors?
20/23=87% ...change due to fist is 87% of total change
2.5/23=11%...change due to 2nd is 11% of total change
.5/23=2%.....change due to interplay is 2% of total change
hence, you can see that change due to interplay is considerably less than others.
Thanks again Malay. It appears this method does not scale beyond more than two factors. For example, if we change the function to look like the following, I am no longer able to isolate the effect of the different factors.
Factor1 x Factor2 x Factor3= Value
Year 1: Factor1 = 10, Factor2 = 40, Factor3 = 20, Value = 8000
Year 2: Factor1 = 12, Factor2 = 41, Factor3 = 17, Value = 8364
Year over Year change = 4.6%
Factor 1 isolation:
Holding Factor2 & 3 constant yields 12 * 40* 20 = 9600
- 9600/8000 - 1 = 20% change attributed to Factor1
Factor 2 isolation:
Holding Factor1 & 3 constant yields 10 * 41* 20 = 8200
- 8200/8000 - 1 = 2.5% change attributed to Factor2
Factor 3 isolation:
Holding Factor1 & 2 constant yields 10 * 40 * 17 = 6800
- 6800/8000 - 1 = -15% change attributed to Factor3
If I sum the impact of these changes up I get 7.5%. If I then try to add the "interplay" of the three factors (20% * 2.5% * -15%), it comes to 7.4%, which is significantly different than the actual total year over year change of 4.6%.
Is this a flawed approach when there are more than two variables (e.g., is it applying a linear approach to a non-linear problem, or something similar to that). If so, is there a better approach to isolate the impact of changes in factors, when three factors are involved?
Thank you again for the help,
Thanks again Malay. It seems the logic of trying to use this approach for analayzing the relative impact of the factors may breakdown somewhat for when there are three factors since the interplay effect is getting so large, but it is very helpful to at least be able to explain the interplay effect and bridge it back to the total change as you have illustrated.