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?