Understanding Consumer Reactions to Assortment Unavailability

Table 4.2: Overview of separate analyses
Analysis Description Sample
1. Total category sales analysis Total
2. Decomposition: Former category buyers delisted
items – former category buyers nondelisted items
101
Category buyers before assortment
reduction (former buyers)
3. Decomposition: Sales of new buyers New category buyers after
4.4.3 Econometric modeling
assortment reduction
To estimate the effect of the assortment reduction on the category sales in the test stores, we
specify an econometric model in terms of the log category sales of specific sets of households.
Thus, the parameters should be interpreted as relative effects; that is, they represent percentage
changes. An advantage of such a specification is that sales of populations of different sizes can
be compared easily. For ease of exposition, we start by specifying the model for the comparison
of the total category sales across the four stores. For this case, the model can be presented
compactly as follows:
] { f ( t | γ ) + g(
t | θ ) } + ε 1,
3 ( test stores)
] { f ( t | γ ) } + ε 2,
4 ( control stores),
log = α + β ' x + I[
t ≥ T1
i =
(2a)
Sit i it
it
log = α + β ' x + I[
t ≥ T1
i =
(2b)
Sit i it
it
where Sit denotes the sales for store i = 1,2,3,4 at time t = 1, …, T; xit denotes a vector of
explanatory variables, such as promotion dummies or dummies for aberrant observations; I[t ≥
T1] denotes an indicator function that equals 0 before the time of delisting (T1) and 1 after the
delisting; and f(t|γ) and g(t|θ) denote flexible functions of the time index that measure the change
in category sales in the period after the delisting. These functions depend on unknown
parameters γ and θ. In this specification, we explicitly use the control stores to identify the effect
of the delisting. The function f(t|γ) gives the baseline changes in category sales in all stores,
irrespective of the delisting, whereas g(t|θ) gives the (additional) change in the test stores due to
the assortment reduction. Note that these functions capture everything that is different after the
delisting versus prior to the delisting. They are therefore not specified for t < T1. We estimate the
model based on the entire sample (t = 1, …, T), so the estimates of f() and g() depend on the