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State a fictional matched-unit product
Prior activity 100 and factor 0.5 give emissions 50. Current activity 120 and factor 0.4 give emissions 48. Units and factor coverage are held compatible for this arithmetic exercise.
Inspect both valid bridges
| Order | Activity component | Factor component | Total |
|---|---|---|---|
| Activity at prior factor, then factor at current activity | +10 | −12 | −2 |
| Factor at prior activity, then activity at current factor | +8 | −10 | −2 |
Explain the two-unit allocation difference
The product of the activity change 20 and factor change −0.1 is −2. The sequential orders assign that interaction to different components. The total product change remains −2.
Avoid treating components as proven causes
A factor update can reflect a method or dataset change rather than a company action. The bridge explains arithmetic under chosen inputs; causal attribution needs separate evidence.