The name is absent

Davis (1978a, p. 52) proposed the following
model:

(1) CR_ijt=C₁A_{t e}χp (β₀ + ∕3₁T→)

r

where A=( Σ a _jM_lj) + α_r+ιFV_ij, and,
J=I

CR_ijt = total coupon redemption at time t for
program i using medium j,

C_ij = total coupon drop or coupon effort for
program i using medium j,

M_lj = zero-one variable to indicate the
medium (j) for program i,

FV_ij = face value of coupon for program i
using medium j,

T_ijt = the age of program i using medium j at
time t, and a's and β^,s are parameters
to be estimated.

In their study, Ward and Davis (1978a) as-
sumed that the level of redemption should in-
crease with increased volume. Yet the rate of
increase in redemption may decline as total effort
is increased. A declining rate of redemption de-
picts the frequently observed phenomenon of
diminishing returns to advertising and/or promo-
tion efforts. It may further suggest that larger
coupon distributions reach marginal consumers
and, hence, it is more difficult to achieve a re-
demption response among that group of consum-
ers. In addition, for a sufficiently long time span
the redemption level will approach some upper
limits, i.e., redemption of a particular coupon
program will not continue indefinitely.

The model developed by Ward and Davis
(1978a) did not allow for the impact 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.² Their
model allowed only for shifts in the intercept of
equation (1). In addition, Telser’s hypothesis
could not be tested with equation (1).

In order to estimate the impact of price on the
level of coupon redemption, and relax the con-
straints on the impact of the face value of the
coupon,³ size of distribution, and age of the pro-
gram on coupon redemption, equation (1) was
modified and presented as follows,

(2) CR_lt = C¹? exp (β₀ + ∕3₁T_u¹),

where B = ∕3₂FV_i∕P_t + β₃, and P_t = retail orange
juice price at time t. And one equation was esti-
mated for each type of coupon program.

According to Telser’s hypothesis and results
from the Ward and Davis study (1978a), the sign
of β₂ is expected to be positive, i.e.,

For comparison purposes, the following re-
vised Ward and Davis model was also estimated,

(3) CR_lt = СГ exp (∕3₀+∕3₁T_lt¹),
where A'=_j8₂FV_i + β₃.

DATA SOURCES AND RESULTS

Florida Department of Citrus (FDOC) coupon
program data were obtained from the FDOC’s
accounting department. The time period studied
is from April, 1973, through January, 1981. The
most recent coupon program included in this
study originated in October, 1977. There are at
least three years of data available on each cou-
pon program. All coupon programs were classi-
fied into four major categories according to the
distribution media used, i.e., magazine, news-
paper, direct mail, and in-pack or on-pack. In
general, FDOC’s coupons do not have an expira-
tion date, thus redemption may continue indefi-
nitely. Retail orange juice price data were ob-
tained from Marketing Research Corporation of
America and NPD Research, Inc., for periods
from April, 1973, through November, 1977, and
December, 1977, through January, 1981, respec-
tively. The prices used in the study were the
weighted average retail prices of frozen concen-
trated orange juice and chilled orange juice ex-
pressed in cents per 24 ounces of single strength
equivalent (SSE) orange juice. Prices ranged
from 22 cents to 43 cents during the sample
period.

The empirical estimates for equations (2) and
(3) for each distribution method using ordinary
least squares⁴ are as hypothesized with respect

² Defined by the distribution method used.

³ Both face value of coupon and price variables should be deflated. The special functional form used in equation (2), i.e., the ratio of these two variables, makes the use of a
deflator unnecessary.

⁴ There have been two approaches to combining cross-section with time series data. First, the method of dummy variables has been suggested to account for constant
effects associated with both the time direction and cross-sectional units, but is not readily attributable to identifiable causal variables (Hoch; Mundlak; Johnson). The second
approach is to account for possible correlations among the error terms of the model in order to increase the asymptotic efficiency of the estimates of the causal parameters
(Wallace and Hussian; Maddala; Fuller and Battese). Because the number of active coupon programs at a specific time is not fixed, a method similar to the dummy variable
approach is used, where variables FV, C, and T are used to account for cross-section variations and retail prices are used to account for time series variation. Durbin-Watson
test cannot be applied in this case. MuIticolinearity problem is not serious. The sample correlation coefficients between ç>n C*FV∕P and ⅛>nC and the ones between ∣pnC*FV
and 0iC are:

The correlations between T^-‘ and other independent variables are smaller than the ortes presented above.

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