coupons included in this study, six possible pairs
of relationship could be found, i.e., magazine
coupons versus newspaper coupons, magazine
coupons versus direct mail coupons, and so on.
The Chow F-ratios of these six possible pairs for
equation (2) are presented in Table 2, and those
for equation (3) are presented at the bottom of
the same table. The results suggest that, in all
cases, the equality hypothesis is rejected at 0.01
level. In other words, the relaxation of the as-
sumption of equal impacts of face value of the
coupon, size of distribution, and age of the pro-
gram on coupon redemption for different types of
coupon programs should provide better parame-
ter estimates than those reported by Ward and
Davis.
ANALYSIS
Couponing Effort
Redemption models estimated in Table 1 im-
plicitly assume that the redemption response or
elasticity of coupon redemption is conditional on
the media, coupon value, and juice price. For
given media, coupon value, and juice price, the
redemption elasticity (μ,) is fixed, i.e., a !-per-
cent change in couponing effort will lead to a
fixed percentage change in redemption where:
(4) μ = β2 * FV∕P + β3 for equation (2), and
(5) μ = β2* FV + β3 for equation (3),
where “*” indicates multiplication.
Estimated elasticities of coupon redemption by
method of distribution are given in Table 3.
These estimates are higher, and the rankings are
different from those estimated by Ward and
Davis.
The results in Table 3 show that the estimated
elasticities from both equations (2) and (3) for
magazine and direct mail coupons are statisti-
cally less than 1.0, which suggests that any in-
crease in couponing effort using magazines or di-
rect mail would result in reduced rates of rede-
mption.5
The estimated elasticity from both equations
for 10-cent newspaper coupons are not statisti-
cally different from 1.0, which indicates that
doubling 10-cent newspaper couponing effort
would also double the level of redemption, i.e.,
the rate of redemption remains constant. For
15-cent newspaper coupons, the estimated elas-
ticities are statistically greater than 1.0, which
implies that any increase in couponing effort
would increase the rate of redemption.
The results from equations (2) and (3) for in∕on
pack coupons are not consistent. The estimates
from equation (2) show that the elasticities are
not statistically different from 1.0, while those
TABLE 3. Estimated Redemption Elasticities3
|
Face Value |
Magazine |
Newspaper |
Direct Mail |
In∕0n Pack |
|
Equation (2) 10-cent |
.8272 |
1.0054 |
.9383 |
.8876 |
|
(.0107) |
(.0323) |
(.0111) |
(.0864) | |
|
15-cent |
.8410 |
1.0796 |
.9467 |
.8846 |
|
(.0104) |
(.0299) |
(.0102) |
(.1016) | |
|
Equation (3) 10-cent |
.8454 |
1.0473 |
.9495 |
2.2719 |
|
(.0104) |
(.0318) |
(.0125) |
(.0713) | |
|
15-cent |
.8204 |
1.1397 |
.9500 |
2.9145 |
|
(.0107) |
(.0291) |
(.0104) |
(.0968) |
a The numbers in parentheses are estimated standard er-
rors of elasticities. The following formula was used in compu-
tation (Kmenta, p. 372).
var (ax + by) = a2 var(x) + b2 var(y) + 2 a b Cov(x,y)
estimates from equation (3) indicate that the elas-
ticities are greater than 2.0. The estimates ob-
tained using equation (3) appear to be far too
large, therefore only equation (2) for in∕on pack
coupons will be used in the following discussion.
The point in time when the maximum redemp-
tion rate occurs can be estimated by setting the
second derivatives of equation (2) with respect to
variable T equal to zero and solving for T, i.e.,
(6) ÜÇR _/i.CR [2+Aj.0
ð-pa ɪɜ r[,
which results in
(7) T = -β1∕2
Using these results and the estimates in Table 1,
one finds that the maximum redemption rate oc-
curs during the third month for magazine and di-
rect mail coupons, during the fourth month for
newspaper coupons, and during the fifth month
for in∕on pack coupons.
Price Effect6
Another major difference between this study
and the Ward and Davis study is that the price
effect on coupon redemption can be studied with
the revised model specification presented in
equation (2). The empirical results in Table 1
showed the significance of price on the level of
redemption for magazine, newspaper, and direct
mail coupons. Using equation (2), the changes in
the level of redemption resulting from juice price
changes can be estimated as
(8) = —∕32*CR*<ρn C*FV∕P2
where all variables are as previously defined.
5 At 0.05 level. This same level was used in the discussion of elasticities.
6 In the previous section, we fail to establish a relationship between juice price and the level OfredemptionforinZonpack coupons, therefore, no discussion will be given to
in∕on pack coupons in this section.
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