Biomedical Engineering Reference
In-Depth Information
Table 22.3
Descriptive statistics
DTCA ($)
Detailing ($)
PJA ($)
Sales ($)
Pre-peak window (1996-2004)
Mean
27,774,640
57,927,635
2,482,573
12,687,292
Standard deviation
47,159,463
46,374,352
3,671,366
12,178,225
Minimum
0
60,146
0
831
Maximum
240,354,997
223,023,132
20,106,593
62,540,586
Count
141
141
141
141
Post-peak window (2005-2007)
Mean
23,213,881
51,989,808
1,183,187
9,498,299
Standard deviation
53,834,173
70,012,387
2,560,772
14,384,164
Minimum
0
0
0
215
Maximum
225,843,864
243,330,312
9,943,405
63,218,640
Count
66
66
66
66
All years (1996-2007)
Mean
26,320,485
56,034,415
2,068,276
11,670,512
Standard deviation
49,299,702
54,917,372
3,405,590
12,972,946
Minimum
0
0
0
215
Maximum
240,354,997
243,330,312
20,106,593
63,218,640
Count
207
207
207
207
the first window covers the “pre-peak” DTCA spending period between 1996 and
2004, while the second window covers the 3 years following the DTCA peak
between 2005 and 2007 (see Table
22.3
for descriptive statistics). We then per-
formed cross-sectional sales response analyses for the “pre-peak” and “post-peak”
windows, respectively, as well as for the whole observation window. A couple of
points are worth mentioning here. First, the data exhibit enough variance in promo-
tional spending across agents in each window as coefficients of variation for each
year range between 1.28 and 2.78. Second, our main point of interest lies in the
change of average response pattern rather than agent heterogeneity, which would
have imposed more data requirements. For this reason, we pool the data across
agents and over time for each window, assuming no agent-specific effects.
22.5.2
Model Specification
Advertising response often exhibits threshold and saturation effects (Simon and Arndt
1980
; Vakratsas et al.
2004
), requiring a specification that accommodates both increasing
and decreasing returns to scale. In order to capture the nonlinear nature of advertising
response and allow for a possible S-shaped pattern, we employ the logistic specification
in (
22.1
) (Leeflang et al.
2000
, p. 81, Equation 5-53). We account for category-specific
idiosyncrasies through the use of dummy variables in the numerator:
j
j
αα α
ββ β
exp(
+
DD
+
)
j
0
1
1
it
2
2
it
S
=
(22.1)
it
j
j
β
3
PJA
i
j
))
1
+−+
exp( (
DTCA ET
+
+
0
1
it
2
it
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