Two firms experience a seal change within the same year or within a shared time-window within a 52-week window.
According to the current selection criteria, we sample (i, j, t) as follows:
(I): Select TOP_N=200 products based on clicks, filtered by the condition that firm j offers them.
(II): Select 10 counterfactual firms j through a deterministic random sampling process.
It is possible for two firms to overlap in (I), meaning they may share the same counterfactual firm j from (II). Under Proposition 1, the (i, j, t)-tuple may no longer be unique.
Thus, a unique row is only identified by (i, j, t, S), where S serves as an additional identifier (denoting a Seal Provider World).
Appendix/Remark: Is not problem for estimation of various models with the data-set, but DUPLICATES of (i,j,t)-Rows are not something that should be dropped.
Suppose:
Proposition 1:
Two firms experience a seal change within the same year or within a shared time-window within a 52-week window.
According to the current selection criteria, we sample
(i, j, t)as follows:It is possible for two firms to overlap in (I), meaning they may share the same counterfactual firm j from (II). Under Proposition 1, the
(i, j, t)-tuple may no longer be unique.Thus, a unique row is only identified by
(i, j, t, S), where S serves as an additional identifier (denoting a Seal Provider World).Appendix/Remark: Is not problem for estimation of various models with the data-set, but DUPLICATES of (i,j,t)-Rows are not something that should be dropped.