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An activity and factor change bridge

For E = A times f, one sequential bridge attributes activity change at the prior factor and factor change at current activity.

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Write the exact bridge

E1−E0=(A1−A0)f0+A1(f1−f0)E_1-E_0=(A_1-A_0)f_0+A_1(f_1-f_0)

This is a chosen arithmetic ordering. Activity and factor units/coverage must match across periods.

Calculate a fictional product change

Prior activity 100 at factor 0.5 gives 50. Current activity 120 at factor 0.4 gives 48. The activity component is +10; the factor component is −12; their sum is −2.

Explain another valid ordering

Using the current factor for the activity component gives +8 and the prior activity for the factor component gives −10. The total remains −2, but the interaction is allocated differently. Label the chosen decomposition instead of claiming the components are unique causal effects.

Keep the calculation separate from attribution

A factor can change because of a dataset update, geographic mix or another reason. A product bridge alone does not establish why it changed or whether a company caused the difference. Retain the underlying evidence.

Further references