Coupon Redemption and the Demand for Frozen Concentrated Orange Juice: A Switcl~g Regression Analysis Jonq-Ying Lee and Mark G. Brown

Key words: coupon redemption, demand, orangejuice, switching regression.

Coupon programs are initially implemented In recent years, product promotion and advertising related to cents-off coupons has grown by dropping or mass distributing coupons via a dramatically. Coupons distributed by man- number of alternative media. Once the disufacturers rose from 16 billion in 1970 to a tribution is made, consumers redeem the level of slightly over 100 billion in 1981, with coupons over the life of the program. Because the most rapid growth occurring after 1974 redemptions represent individual uses of when the number of coupons rose at an annual coupons, changes in individual consumption rate of 20%. Coupons have become more behavior can be related to the coupons repopular not only with manufacturers but with deemed. Further, the effectiveness of coupon consumers also. In 1973, 58% of households programs may differ depending on the characused coupons, while in 1975 and 1980, 65% teristics of the redeemer. In this analysis, a and 76%, respectively, used coupons (A. C. switching regression model was used to study the influence of household characteristics on Nielsen Co. 1983). Coupons offer a price reduction directly to coupon redemption and the relationships bethe consumer. There is no need to rely on an tween household consumption behavior and intermediary to pass the savings along. Fur- coupon redemptions. In the remaining sections, we will discuss thermore, since coupons can be directed to specific areas, the manufacturer can reduce the estimation procedures and provide a direct the price where a problem exists. In addition, measure of the effect of coupons on the retail the manufacturer does not have to change the consumption of frozen concentrated orange basic price, since the concession is for a tem- juice (FCOJ). Monthly panel data from 9,552 households for July 1981 through June 1982 porary period. are used for the analysis. NPD Research, Inc., maintains a national panel of consumers who keep a weekly diary of their purchases. The Jonq-Ying Lee and Mark G. Brown are research economists in the panel participants are selected by NPD ReEconomic Research Department, Florida Department of Citrus, and an associate professor, and an assistant professor, respec- search to provide a representative sample of tively, Department of Food and Resource Economics, University the consumer demographics in the United of Florida. States. Al1 data relating to the purchases of Florida Agricultural Experiment Station Journal Paper No. FCOJ, as reported by the panel, have been 6232. The authors would like to thank two anonymous reviewers for used in this study, and the weekly diary data helpful comments. Review was coordinated by Robert G. Chambers, associate from each panelist were aggregated to a monthly basis. editor. Copyright 1985 American Agricultural Economics Association

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A switching regression model was estimated and used to study the impact of Florida Department of Citrus coupon promotionai programs on the demand for frozen concentrated orange juice. The empirical results show that discounts and information provided by coupons were effective in increasing the demand for FCOJ, and that the FDOC's coupon programs had positive impacts on the probability of using coupons for purchasing FCOJ. Moreover, different types of coupon promotions had different impacts, and coupon users and nonusers demonstrated different degrees ofresponse to price changes.

648

August 1985

Amer. J. Agr. Econ.

Econometric Model and Estimation Method

(1)

Qlt

:

(2) (3)

Q2t

= X2,f12 +

X l t ~ l + Elt

I*t = Z,T -

iff

I*t > ' 0

E2t iff I*t < 0

et

where Qlt is the FCOJ purchase rate during month t for a household redeeming coupons; Q2• is the FCOJ purchase rate during month t for a household not redeeming coupons; l*t is an unobservable index which determines the choice; X~t, X2,, and Zt ate vectors of exogenous variables; fil, ti2, and y are parameter vectors to be estimated and e~,, e2t, and et are trivariately normally distributed disturbance terms with zero means a n d a common nonsinguiar covariance matrix, invariant across time. Also, it is assumed that var (e,) = 1 for identification purposes (Lee and Trost, p. 359), and the sample observations belonging to different regimes can be distinguished, i.e., sample separation is available. Furthermore, only contemporaneous correlation between the dis-

[Q,t, Q2t, I't]' - N3(q E) t= 1,2,...,T, ate independently distributed where m = [X,,~,, X~,#2, Z M ' , t= 1,2,...,T, and Z is a positive definite matrix O"110"120"1,

(4)

E

--

o'2~0.._-0.2,. 0"l'02"

1

Since Qlt and Q2t are assumed to be mutually exclusive, they cannot be observed simultaneously for any one household. What one does observe is the binary index I,, which indicates whether or not coupons were redeemed and the quantity of the commodity purchased, Qt, i.e., (5)

Qt = Q,t, I, = 1

if l* >_ 0

(6)

Qt = Q2t, Ir = o

otherwise.

In addition, the exogenous variables Xlt, X 2 , and Zt are always observable. The model characterized by (1) through (3) together with data (5) and (6), and (7)

o'1, = 0"2,., = 0

defines the basic switching regression model with exogenous switching. When (7) does not hold, then the model is said to involve endogenous switching (Poirier and Ruud). Lee and Trost proposed a two-stage estimation procedure for the model represented by equations (1) through (3). In the first stage, one estimates the probit model (8)

Ir = F(Zt3/) + ut,

to get consistent estimates ~) of 3/. In equation (8), F(.) denotes the standard normal cumulative distribution function and uf is a disturbance term. As in this study, the maximum likelihood method (Maddala, pp. 26-27) can be used to obtain consistent estimates of 3/. In the second stage, one can substitute into the two nonlinear equations o ' , . f (Zt~)/F(Zt'~) + ~ql,

(9)

Qt

(10)

Qt = X2tfl2 + o'2,f (Zt~)/[1

= XI,j~I -

-

F(Zt~)] + "q2,

where f(.) denotes the standard normal den-

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In this study the sample data are divided into coupon users and nonusers, and demand equations are estimated separately for each group. Alternatively, the entire sample can be used to estimate a single equation (Ward and Davis). Another approach models only the choice of whether to redeem coupons or not. This can be accomplished with either a linear probability, probit or logit model. With this method, one does not obtain demand equations but rather an equation to predict the probability that a given household will use coupons. Typical sample data include the quantity purchased by households (whether redeeming or not redeeming cents-off coupons). A complete model then should take into account the joint determination of whether or not to redeem coupons and how much to purchase. In the above two approaches only one part of this complete model is emphasized. Furthermore, separate ordinary least squares (OLS) demand estimates for coupon users and nonusers will be biased ir there is simultaneity between the demand and choice equations. One may argue that this simultaneity does not occur, and hence the OLS approach is valid. However, before drawing this conclusion, a rigorous statistical test should be performed. To formulate the joint determination of whether to redeem a coupon and how much to purchase, the following model was used.

turbances is allowed (Lee and Trost). In other words,

Lee and Brown

649

coupons distributed in the second program do not have an expiration date, and there is a place that the customer can scratch off a printing mate¡ and find out whether he has won other prizes. In order to take these two promotions into account, five variables were employed in equations (1) and (2) to capture the effects of distribution sizes, media used, and any lagged effects related to coupon promotions. The first two variables were used for the first coupon promotional program mentioned above, i.e., Program One (t) = l 11 if month was August, and Program One (t + l) = 111 if month was September, otherwise both Program One variables were zeroes. Similar definitions were used for the second coupon program, i.e., Program Two (t), Program Two (t + 1), and Program Two (t + 2) equal 25.559 if month was January, February, and March, respectively, otherwise they are zeroes. The same variables were used in the decision equation (3) except the value of coupons redeemed and the value of other specials were deleted. Results

Table 1 shows the maximum likelihood estimates of the decision equation. The Akaike information crite¡ (Amemiya, p. 1505) were used to select the decision equation. The family size variable was deleted from the equation, because its t-ratio was insignificant and the inclusion of family size also increased the Akaike information criterion.

Table 1. Function

Probit Estimates of the Decision

Variables a Intercept Full price Market size Race d u m m y Presence of children d u m m y Income Age < 40 Age -> 55 Program One (period t) Program One (period t + 1) Program T w o (period t) Program T w o (period t + 1) Program T w o (period t + 2) Observations

Estimates - 2.0640 .0184 .0460 .1297 -.0414 .0047 -.0965 .0622 .0013 .0006 .0028 .0042 .0028 29,218

Standard Error .0671 .0009 .0037 .0425 .0269 .0017 .0235 .0258 .0003 .0003 .0011 .0012 .0012

a The Akaike information criterion equals 14,437. Dependent va¡ able = 1 if household redeems coupons, = 0 otherwise.

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sity function and r/,t and ~2t are disturbance terms. Equations (9) and (10) are based on the conditional expectations E(Qlt]It = 1) and E(Q2tllt = 0), respectively. With the sample observations from the first regime, one can obtain OLS estimates of/3, and o-~,. Similarly, one can obtain OLS estimates of/32 and 0-2, using the sample observations from the second regime. The resultant estimates are consistent. The tests for selectivity bias ate tests that cr,, = 0 and o2, = 0 in equations (9) and (10). The model represented by equations (1~ through (3) was estimated using panel data for 9552 households reporting intermittently over a twelve-month period, i.e., from July 1981 through June 1982. The Q,t's in equations (1) and (2) are ounces of FCOJ purchased per capita by a given household in month t. The same explanatory variables are used in the two demand equations, except that the nonuser equation does not have a variable for total value of coupons redeemed. The full set of variables includes the full price (price paid plus special discounts) in cents per six ounces of FCOJ; the per capita value of coupons redeemed in cents; the per capita value of other specials in cents; market size where the household resides (0 for non-SMSA, 1 through 6 for population sizes from 50,000 to 2,500,000 and over); race dummy (1 for white, 0 otherwise); presence of children dummy (1 for households with children younger than 18 years old, 0 otherwise); per capita income in thousands of dollars; two dummies for the age of the female head of the household, i.e., A G E < 40 for female heads younger than 40 years old, and A G E > 55 for female heads older than 55 y e a r s old; a n d a family size variable to capture the effects of economies of scale in orange juice consumption. One of the major purposes of this study is to investigate the effect of Florida Department of Citrus (FDOC) coupon promotional programs on coupon redemption behavior. During the period from July 1981 through June 1982, the FDOC had two coupon promotional programs. The first one was a newspaper promotion which used an advertisement with three 25r coupons each expiring within a week covering a period of three consecutive weeks. These coupons were distributed in August 1981 with a size of 111 million coupons. The second promotion happened in January 1982. The face value of these coupons was 15r They were distributed as magazine inserts with a size of 25.559 million coupons. The

Coupon Redemption and Orange Juice

650

August 1985

pected. The impact of scratch-off magazine coupons, lasting for three months, increases from period t to t + 1 and then decreases in t + 2 and dissipates thereafter. In addition, Program Two seems to have a heavier impact on the likelihood of redeeming coupons than Program One. For example, the estimated impact of Program One is about .21 [(.0013 + .0006) 111] while it is about .25 [(.0028 + .0042 + .0028) 25.559] for Program Two. Since we do not have information about the coupon promotions carried out by manufacturers and retailers, the estimates may capture some of the impact of these promotions. Lacking equality constraints on the coefficients in the two demand equations, consistent two-stage estimates are obtained by splitting the sample into two groups, coupon users and nonusers, inserting selectivity correction variables based on the probit estimates in each demand equation as in equations (9) and (10), and estimating separate equations using the OLS method. Table 2 presents the two-stage estimates of these two demand equations. The results in table 2 show that ~1. is statistically different from zero and has a negative sign. The estimate of d-~ is insignificant. This result suggests selectivity bias in the user group, and the correction for this bias was necessary. However, the bias in the nonuser group was insignificant, and hence the OLS method can be used to estimate the parameters for the nonuser group excluding the selectivity bias correction variable. Accordingly, such OLS results are presented in table 3. In the following discussion, the focus is on the two-stage estimates for the user group and the OLS estimates for the nonuser group (the two sets of estimates for the nonuser group in tables 2 and 3 are roughly the same). The coefficient estimate for the full price variable is insignificant for the user group and negative for the nonuser group. This implies that the demand for FCOJ for households which chose to use coupons is not affected by the container price, while the demand for FCOJ for those households who chose not to use coupons is inversely related to the container price. The estŸ price elasticity at the sample means is -.9549 for the nonuser group. The dŸ impact of coupons is measured through the increased income provided by coupon price discounts, the coupon cents-off variable (the coupon price discounts can be

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The coefficient estimate for the full price variable indicates the shelf price of FCOJ increases the likelihood that a household will redeem coupons. This result is consistent with the argument made by A. C. Nielsen Company (1980) and Gallo, Hauim, and Zeller. The positive coefficient estimate for the market size variable indicates that households living in larger metropolitan areas are more likely to redeem coupons than those living in smaller metropolitan areas. This could be because most of the coupons are dist¡ in areas with large population concentrations; hence, the result may reflect the availability of coupons to households. The coefficient estimate for the race dummy is significant and positive, indicating that whites are more likely to use cents-off coupons. This could be due to either differences in education or merely different lifestyles between white and other races, or both. The negative coefficient estimate for the dummy variable for children indicates that households with children are less likely to use cents-off coupons. This may be because these households have to spend more time with their children; therefore, the costs of searching and redeeming coupons in terms of their limited leisure time may become prohibitive. The coefficient estimate for income is significant and positive, implying high-income households are more likely to use coupons and perhaps reflecting differences in occupations and education between high-income and low-income households. The coefficient estimates for the age dummy variables show that the female head's age influences the household's decision to redeem coupons. The results indicate that households with female heads less than forty years old have the lowest probability of redeeming coupons, households with female heads from forty to fifty-four have a higher probability, and households with female heads equal or greater than fifty-five have the greatest probability. Different lag lengths were t¡ for the Program One and Program Two variables. Based on asymptotic t-ratios, one lag was chosen for Program One, and two lags for Program Two. The results show that FDOC coupon promotion programs have increased the likelihood that households use coupons. For the newspaper coupons with definite expiration dates, the promotion impact on the likelihood of redeeming coupons decreases quickly as ex-

Amer. J. Agr. Econ.

Lee and Brown

Table 2.

Coupon Redemption and Orange Juice 651

Two-Stage Estimates of Demand Equations Nonusers

Users

Estimate

Standard Error

Intercept Full price Cents-off (coupon) Cents-off (other special) Market size Race d u m m y (white) Presence of children Income Age < 40 Age --- 55 Family size Program One (period t) Program One (period t + 1) Program T w o (period t) Program T w o (period t + 1) Pro gram T w o (period t + 2) ~/~b ^ (~/(I - 6 ) F-Value Observations

- 39.6051 .1138 .2395 .3501 .4237 .9951 -9 9 -4.2200 2.2968 - 1.7790 .0356 .0226 .1494 .0708 9 33.3471

21.1988 91249 .0061 .0131 .3347 1.2987 .6877 .0489 .8437 .6979 .2082 .0107 .0072 .0309 .0382 .0314 9.1367

217.37 6,027

translated into increases in income that can be used directly to purchase more FCOJ or indirectly to purchase other commodities). In this case, the price discount per unit of FCOJ is not appropriate for investigating the impact of price discounts on the demand for FCOJ because there are quantity requirements for coupon redemption, e.g., a minimum purchase of six cans of 6-oz. FCOJ or three cans of 12-oz. FCOJ. In addition, both coupons and other p¡ promotions may bear an advertising function. Therefore, the total price discount in cents-off is used as the explanatory variable instead of a per unit discount variable. The coefficient estimates for the centsoff variables in both demand equations are positive and significant. The results show that for each 10r discount (per capita) on a purchase of FCOJ the per capita pur=hase would be increased by 2.4 to 3.5 ounces depending on the type of discount and whether it was a coupon user or not. In order to measure the importance of the price related variables in explaining variations in the demand for FCOJ, beta coefficients were calculated (Goldberger, pp. 197-200). The beta coefficients were .4164 and .2765 for the coupon cents-off and other specials cents-off variables, respectively, for the user group, indicating that coupons played a more important role than other price specials in ex-

Estimate

Standard Error

33.2135 - .2829

19 .0517

.2811 - .0919 .6800 - 1.9291 .2438 -.5487 .5055 - 1.4585 - .0014 .0009 .0954 -0123 - .0107

.0042 .1252 .5810 .3724 .0253 .3717 .3653 .1143 .0049 .0037 .0154 .0182 .0160

-3.4778 437.21 23,191

6.2869

plaining variations in the demand for FCOJ for this group. The beta coefficients were - . 1916 and .3895 for the full price and other specials cents-off va¡ respectively, for the nonuser group, indicating that price specials played a more important role in explaining variations in the demand for FCOJ than the price variable for this group. The coefficient estimate for the market size variable for the user group is not different

Table 3. Ordinary Least Squares Estimates of Nonuser Demand Equation Variable

Estimate

Intercept Full price Cents-off (special) Market size Race d u m m y (white) Presence o f children Income Age < 40 Age ~ 55 Family size Program One (period Program One (period Program T w o (period Program T w o (period Program T w o (period F-Value Observations

33.8045 - .3109 .2812 - . 1570 .4997 - 1.8721 .2366 -.4141 .4112 - 1.4601 -.0034 -.0001 .0913 -.0183 -.0146 468.43 23,191

t) t + 1) t) t + 1) t + 2)

Standard Error .8728 .0107 .0042 .0428 .4810 .3579 .0216 .2810 .3230 .1143 .0034 .0032 .0136 .0146 .0144

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Variable

652

August 1985

ing value to the consumer which positively affects consumption, i.e., the informational effect. Moreover, coupon programs may have impacts on the demand for FCOJ for both the user and nonuser groups. Consequently, coupon program variables were included in the demand equations to capture this informational effect. The coefficient estimates for the FDOC coupon program variables show that both FDOC coupon programs had a positive impact on the user group FCOJ demand while having only a limited positive impact on the nonuser group FCOJ demand. The result shows that scratch-off magazine coupons (Program Two) seem to have a greater impact on the demand for FCOJ for the user group than newspaper coupons (Program One). The estimated impact of Program One is 6.56 ounces per person [i.e., (.0365 + .0226) l l l ] , while it is about 7.45 ounces [(.1494 + .0708 + .0714) 25.559] per person for Program Two. The result also shows that the newspaper coupon program did not have ah impact on the nonuser group demand; and the scratch-off magazine coupon program had only a small impact on the demand during the month when coupons were distributed. The estimated impact of this coupon program on the nonuser group demand for FCOJ is 2.33 ounces per person.

Concluding Remarks The empirical results of the present study show that discounts and information provided by coupons were effective in increasing the demand for FCOJ, and that the F D O C ' s coupon programs had positive impacts on the probability of using coupons for purchasing FCOJ. Moreover, different types of coupon promotions had different impacts. For both coupon users and nonusers, special price discounts, either a s a result of coupon redemption or other store specials, explained more variations in the demand for FCOJ than the p¡ variable. Coupon users and nonusers demonstrated different degrees of response to price changes. In general, coupon users were less responsive to price changes than nonusers. This result may have important implications on the pricing strategies of FCOJ and the timing of coupon promotions. If coupon promotions ate used in conjunction with p ¡ increases (e.g., price increases after freezes) the negative impact of the p¡ increases on

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from zero, while for the nonuser group it is significantly negative. This result indicates that non-coupon-using households located in less-populated areas purchased more FCOJ per capita than those located in more-populated areas. This result is consistent with the ranking of household consumption of FCOJ by county sizes reported by A. C. Nielsen Company. The latter reported that, on the average, smaller counties, i.e., B, C, and D counties (A's are the most-populated counties and D's are the least-populated counties) had higher consumption rates per household than A size counties. The race dummy variable coefficient estimates indicate that both the coupon user and nonuser demands are unaffected by race, i.e., the coefficient estimates are not significantly different from zero. The negative signs for the coefficient estimates for the presence of children are not consistent with the results reported by Ward and Davis. Our result indicates that households which have children purchase less FCOJ per capita. Note that the dependent variable of the demand equations in the present study is the per capita purchase made by the household instead of the total household purchase which was used in the Ward and Davis study. Therefore, the present result may reflect that children consume less FCOJ than adults. The coefficient estimates for the income variable indicate a positive relationship between income and the consumption level. The estimated income elasticities~ at the sample means are small and similar, i.e., .1150 and .1154 for the user and non-user groups, respectively. As indicated by the age coefficient estimates, there appears to be a positive relationship between FCOJ consumption and the age of the female head. The coefficient estimates for the household size variable show that as household size increases, per capita consumption of FCOJ decreases, perhaps indicating economies of scale in consumption. In addition, household size has a larger negative impact for the user group than for the nonuser group. The estimates show that every additional household member would decrease the demand for FCOJ by 1.78 ounces per person for the user group and 1.46 ounces per person for the nonuser group. In addition to the income effect associated with coupons, Ward and Davis indicate that coupons have an informative and/or stimulat-

Amer. J. Agr. Econ.

Lee and Brown t h e d e m a n d for F C O J m a y b e a l l e v i a t e d , a n d t h u s a l l o c a t e d freezer s p a c e in r e t a i l s t o r e s c a n be maintained.

[ R e c e i v e d F e b r u a r y 1984; final revision r e c e i v e d S e p t e m b e r 1984. ]

References

Amemiya, T. "Qualitative Response Models: A Survey." J. Econ. Lit. 19(1981):1483-1536. Gallo, Anthony E., Larry G. Hauim, and James Z. Zeller. "Couponing's Growth in Food Marketing." Washington DC: U.S. Department of Agriculture, Econ. Res. Serv. Agr. Econ. Rep. No. 486, 1982. Goldberger, A. S. Econometric Theory. New York: John Wiley & Sons, 1964. Lee, Lung-Fee, and Robert P. Trost. "Estimation of Some Limited Dependent Variable Models with Application to Housing Demand." J. Econometrics 8(1978):357-82. Maddala, G. S. Limited-Dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press, 1983. Poirier, O. J., and P. A. Ruud. "On the Appropriateness of Endogenous Switching." J. Econometrics 16 (1981):249-56. Ward, Ronald W., and James E. Davis. "A Pooled Cross-Section Time Series Model of Coupon Promotions." Amer. J. Agr. Econ. 60(1978):393-401.

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A. C. Nielsen Company. "Coupons: The Consumer Speaks Out." Reporter, no. 3, 1980. ~ . "Information for Marketing Decisions." Presentation to State of Florida Department of Citrus on Orange Juice and Grapefruit Juice, selected issues. "The Growing Importance of Coupons--and How to Use Them Effectively." Reporter, no. 1, 1983.

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