The name is absent

to effort, value, price and time parameters, ex-
cept for in/on pack coupons which estimates a
negative sign for β₂ (Table 1) and the sign for the
estimate of β₂ in equation (3) for magazine cou-
pons. The estimated standard error for β₂ is also
large relative to the estimate of β₂ for direct mail
coupons. Other statistics also are included in
Table 1, where, specifically, the R²s show that
more than 80 percent of the variation in redemp-
tion is explained by the equations, except for
in/on pack coupons, equation (2).

The negative sign of parameter β₂ in equation
(3) for magazine coupons indicates that 15-cent
coupons had lower redemption than 10-cent cou-
pons. There were 26 magazine programs. Of
these 26 programs, 8 programs occurred before
1975, of which 5 programs used 10-cent coupons
and 3 used 15-cent coupons. Between March and
October, 1975, the FDOC had 7 programs, and
all of them used 10-cent coupons. The last 11
programs occurred in the fall of 1976, and all of
these programs used 15-cent coupons. If one
examines the face values of magazine coupons
during the study period, one finds that the nega-
tive sign of β₂ would indicate that the programs in
1976 were less effective than the programs before
1976. This result suggests the possible downward
influence of price, i.e., when price increases, re-
demption level decreases. The results in equation
(2) for magazine coupons support this hypothe-
sis.

The results of equations (2) and (3) for in∕on
pack coupons indicate that price may not be a
relevant variable in explaining coupon redemp-
tion, because the inclusion of a price variable in
the model caused R² to decrease and the esti-
mated parameter β₂ is estimated with large stan-
dard error and unexpected sign.

One of the major differences between this
study and the Ward and Davis (1978a) study is
that the revised model allows the impacts of the
face value of the coupon, size of distribution, and
age of the program on coupon redemption to vary
for different types of coupon programs. In other
words, the hypothesis is that the four separate
regression equations for the four media do not
have the same structure, i.e., the same parameter
estimates as Ward and Davis have hypothesized.
Since these four regression equations are identi-
cally specified, Chow’s F-ratio is used to test the
equality among the coefficients for these four
types of coupons and the results are presented in
Table 2.

Chow’s test is developed to determine whether
two sets of observations come from the same re-
lation, e.g., whether the observations on news-
paper coupons and those on magazine coupon
have the same relationship. With four types of

TABLE 2. Chow’s F-ratio for Tests of Equality
Between Coefficients in Two Relations³

^a If Chow’s F-ratio is greater than 3.48 (f_o.oι.₄,ι₂o), one
would reject the equality hypothesis.

TABLE 1. OLS Estimates of Coupon Redemption Model (see equations (2) and (3))^a

^a The numbers in parentheses are estimated standard errors of parameters.

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