FOR MANUFACTURER'S COUPONS. IN BRAND CHOICE MODELS. Gwen Ortmeyer and. David B. Montgomery. Research Paper No. 1099. August 1990.
A SCANNER-BASED PROXY FOR MANUFACTURER’S COUPONS IN BRAND CHOICE MODELS Gwen Ortmeyer and David B. Montgomery Research Paper No. 1099 August 1990
Cwen Ortmeyer is Assistant Professor ofMarketing, Harvard Graduate School of Business and David B. Montgomery is Robert A. MagowanProfessor of Marketing, Stanford Graduate School ofBusiness.
A SCANNER-BASED PROXY FOR MANUPACTUR~ER’S COUPONS
IN BRAND CHOICE MODELS
Gwen Ortmeyer
Harvard University
IDavid B. Montgomery Stanford University
ABSTRACT A potentially serious threat to the validity of estimates of predictor variable impact in logistic models of brand choice is the om.ission of important explanatory variables from the empirical analysis. An obvious omission from most previous models has been manufacturer’s coupons, which are time consuming, expensive, and often difficult to measure. Further, the measures are lacking from most historical databases used to test consumer brand choice models. This paper proposes a proxy measure for manufacturer’s coupons which is readily calibrated from available scanner panel data. The empirical results show that the proposed proxy measure ~empiricallyexhibits the expecte4 sign and is statistically significant in the case of the IRI instant coffee data. Further, the results show that the misspecification error in previous models from the omission of manufacturer’s coupons is not serious for the instant coffee data.
I.
Introduction Sales promotion has become an increasingly important marketing
activity and, as such, has been the focus of substantial, empirical research, particularly with household level purchase data becoming more widely available.
In particular, competitive effects models such as the
multinomial logit have been used to characterize.the impact of in-store promotions, and retailer featuring and couponing on individual brand choice (Guadagni and Little, 1983; Ortmeyer, L.attin, and Montgomery, forthcoming; Fader and McAlister, 1988) and purchase incidence (Lattin and Bucklin, 1989; Gupta, 1988). Response to manufacturers’ couponing has not been incorporated into such competitive effects models to date, due to the limitations of the scanne~r panel data typically used in empirical studies--the data contain information about coupon redemption only.
Therefore, a óompetitive effects
model, such as the multinomial logit choice model, which requires information on the availability of all competitors’ coupons, cannot easily incorporate manufacturer-distributed coupons as an explanatory variable. In the context of controlled experiments involving direct mail coupons, however, Bawa and Shoemaker have shown that manufacturers’ coupons can produce significant brand switching and household incremental purchasing (Bawa and Shoemaker, 1987 and 1989).
Other studies have shown
manufacturers’ coupons to have a strong impact on incremental purchasing, market share, brand switching, and brand sales (see Irons, Little, and Klein, 1983; Klein, 1981; Johnson, 1984; Schindler, 1984; Neslin, 1990). Beyond inherent interest in the effects of manufacturer’s coupon availability on brand choice and/or purchase incidence, the omission of
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this explanatory variable is potentially a serious specification issue and may affect the integrity of the estimates of the included explanatory variables.
~tpirical tests of omitted variable error in probabilistic
discrete choice models indicate that error due to an omitted variable will become a problem if the omitted variable (1) is correlated with one of the included variables, (2) does not have equal mean across alternatives, (3) is not lID across alternatives, (4) has a different distribution, on the forecast population than in the population used for model calibration, or (5) substantially alters the parametric form of the random component of utility (Horowitz, 1981).
If, for example, manufacturers’ coupon avail-
ability were highly correlated with the in-store promotion variable, as may be the ‘case If the retailer regularly provides in-store support for a manufacturer’s coupon drops, the integrity of the parameter estimate for the in-store promotion variable might be highly suspect. A direct measure of manufacturer’s coupon availability may be derived through extensive investigation of coupon drops
(Neslin, 1990).
Such gathering of data on coupon distribution is both time consuming and expensive.
We propose a proxy measure for manufacturer’s coupon availa-
bility which is derived from the coupon redemptions contained in the scanner panel data used for model estimation.
Incorporating this measure
into a multinomiai. logit model of brand choice (Guadagni and Little, 1983) allows us to investigate empirically the impact of manufacturer’s coupon availability on brand choice,
~
determine the impact of its omission on
,the parameter estimates of the other variables included in the choice model.
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II.
Measuring Coupon Availability from Coupon Redemptions The multinomial logit model that characterizes brand choice
assumes that an individual’s choice on a particular purchase occasion is determined by her relative utilities across the available items (items are a unique combination of brand and size).
Utility for an item is given as a
linear combination of the attributes that describe the item on the particular choice occasion.
In Guadagni and Little’s (1983) choice model,
for example, the attributes describing the item included its price, the individual’s brand and size’ loyalty for the item, an indicator of in-store promotion, and an indicator of past promotional purchase of the item. Estimation of such a model requires, for each purchase observation, the values of the attributes for the alternative chosen and for the other alternatives available at the time of purchase. This poses a problem when one considers including manufacturer’s coupon availability as an additional explanatory variable.
The scanner
data typically available for estimation of such models indicate only that a manufacturer’s coupon was redeemed for a given purchase--distribution and therefore the consumer’s access to each brand’s coupons is not given in the data.
Given these data constraints, we propose a proxy measure for
manufacturer’s coupon availability that is constructed directly from the coupon redemptions found in the panel data.
The variable is individual,
item, and purchase occasion specific and is defined as: MFR(i,k)1
—
item k’s coupon’ availability to individual i at purchase n.
1This and subsequent variables are specific to purchase n; the subscript a has been omitted for expositional simplicity. “
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MPR (i,k) is itself given as the product of two factors:
P(i),
the individual’s propensity to search for and have access to coupons and A(k), item k’s relative coupon distribution at purchase
xi.
Thus, the
greater i’s propensity to clip coupons and the greater brand k’s distribution of coupons, the greater is brand k’s coupon availability to i. P(i) and A(k) are measured from panel data as follows:
P(i):
Individual i’s Coupon Propensity P(i) acconmiodates individual differences in coupon acquisition--
many consumers ignore the Sunday newspaper’s collection of free-standing inserts that include manufacturer’s coupons, while others are avid coupon clippers.
The most appropriate indicator of an individual’s likely
interest in and attention to coupons is the individual’s past use of coupons.
Thus, individual i’s coupon propensity is specified as the ratio
of i’s past coupon purchases to i’s total past purchases:
P(i)
—
the number of i’s pastpurchases in which a coupon was redeemed the total number of i’s past purchases
Only past purchases (i.e., purchases 1 to n-i) are used in’ the construction of this measure--as i’s past behavior reflects a greater tendency to redeem coupons, we assume i will be more likely to search for coupons currently available.
A(k):
Item k’s Coupon Availability This measure indicates the relative availability of the item’s
coupons during the week in which the nth purchase takes place--does item k have more coupons in distribution than its competitors?
An indication of
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relative distribution of coupons is relative redemption of coupons.
Thus,
we measure A(k) as item k’s share of total coupon redemptions in the week previous to the one associated with purchase n:
A(k)
—
item k’s coupon redemptions in the week previous all coupon redemptions in the week previous
We compute A(k) from the previous week’s ‘redemptions so as not to contaminate the test of our model with explanatory variables constructed from the contemporaneous choice behavior we are trying to predict.
This induces
error specifically in the manufacturer’s coupon variable, however.
Neslin
(1990) found that the majority of the redemptions for a coupon drop occur in the week of the coupon distribution.
This suggests that our measure
will underestimate A(k) in the week of distribution and overestimate A(k) in the following week.
The error induced by the lagged measure was
preferred to the econometric’ difficulties in using contemporaneous redemptions.
This error is likely to attenuate our empirical results;
thus, if a significant effect is found for MPR(i,k), we might expect the true, effect to be even stronger. In computing MFR(i,k) as the product of the individual’s propensity (P(i)) and the brand’s coupon distribution (A(k)), both of which are between 0 and 1, we find that MFR.(i,k) will be between 0 and 1.
At
levels of ~Th’R(i,k) close to one, the individual is highly prone to have access to coupons (P(i) is close to one), and the brand’s coupons are much more available than competing brands’ coupons (A(k) is close to one).
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III.
Empirical Results The impact of the proposed measure for coupon availability,
MFR(i,k) must be assessed both for its direct
impact in a model of
aggregate choice behavior and how its inclusion impacts the parameter estimates of the other explanatory variables included in the brand choice model.
We use a multinomial logit choice model with a utility formulation
consistent with, though not precisely identical ,to Guadagni and Little’s 1983 model.
Variables characterizing item utility include:
*
Price(k):
the observed purchase price on occasion n--the purchase price may include a promotional discount.
*
Prom(k):2
1 if item k is offered at special price or is specially displayed or featured in a store flyer or advertisement on occasion xi, o otherwise.
*
Lag(i,k):
1 if individual i purchased item k on promotion without the use of a coupon on occasion (n-’l).
*
D(k):
an item-specific constant for item k.
Guadagni and Little
also included brand and size loyalty variables given as
exponentially weighted averages of the individual’s past purchase behavior. Our brand and size loyalty characterization
is more general and differs,
from this specification in that it separates population heterogeneity in loyalty from within individual
changes in loyalty over time (see Ortmeyer,
Lattin, and Montgomery, forthcoming, and Lattin,
1987 for full, description
and justification). Thus, we include two loyalty variables each for brand and size. •
For example, the brand loyalty variables are: BLOY(i,k) is a static measure of the average loyalty exhibited by individual i toward item k’s brand. This is
2Guadagni and Little also included a promotional price cut variable. This ‘added explanatory variable was not included due to excessive collinearity with the promotion variable.
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measured by computing the proportion of times individual i chose brand k in the initialization time period. •
.
BLOY*(i,k) is a measure of changes in i’s loyalty over time to brand k and is given as the difference between the exponentially smoothed model of loyalty proposed_by Guadagni and Little and the static measure of loyalty BLCY(i,k) above. The smoothing constant used for the exponentially weighted average was 0.7.~
‘To assess the impact of manufacturer’s coupon availability in the crosssectional model of brand choice and to determine the effect of its inclusion on the other parameter estimates, we compare the results of nested multinomial logit models, one including only the variables listed above, and the second with MFR(i,k) added. Ta calibrate
the two nested’ models, we used IRI scanner panel
data for instant caffeinated
coffee.
purchases over a two-year-period)
Only heavy users (at least 15
were included to ensure that the loyalty
measures, BLOY(i,k) and SL.OY(i,k) were based upon a reasonable number of observations.
The 13 brand-size combinations having greater than 2.5%
market ,share’were used as the choice alternatives
or items. The static
measures of average loyalty were calculated from the first 30 weeks of data (corresponding~to. the first 30% of all purchases).
These data were also
used for the initial calculations of the exponential smoothed purchase histories which were needed to calculate the loyalty difference variables, BLOY*(i,k) and SLOY*(i,k).
31n choosing the exponential decay constant, we began by setting the constant to 0.70 a priori, calculating the loyalties and calibrating the model. We then increased and decreased the smoothing constant, recalculated the loyalties and recalibrated the model. In each case the model fit deteriorated slightly and the t-statistics diminished. While this was not equivalent to a full grid search over all possible values for the smoothing constant (which would have been prohibitively expensive), we took it as evidence that 0.70 was a reasonable choice.
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Table 1 presents the parameter estimates, t-statistics and fit Statistics for the two models, one with MFR(i,k), and one without, each calibrated using data from the 45-week period following the 30-week initialization period (1074 purchases). Table 1 omits the item-specific effects as they are not directly relevant to the interpretation of the model.
Before discussing the empirical results it is useful to note that
the estimates for other model parameters are of the predicted sign, and all but the lagged promotional purchase variable are statistically significant. The price coefficient is negative, all four loyalty variables are positive and the promotion variable is positive.
The estimate for lagged
promotional purchase, negative but not statistically significant, is consistent with Guadagni and Little’s empirical finding of a negative but statistically insignificant coefficient for the first lagged promotional purchase and a negative and statistically significant coefficient for the second. MFR(i,k) was not found to be highly correlated with any of the other explanatory variables (no correlation exceeded 0.15 in absolute magnitude).
This suggests the parameter estimates are likely to be quite
robust against the inclusion ofMPR(i,k), a proposition that is corroborated by looking at the consistency in the parameter estimates and t-statistics given in Table 1.
In no case does the absolute magnitude of
the parameter estimate change by more than 5% as MFR(i,k) is added as an explanatory variable. MFR(i,k).
The t-statistics are also robust to the inclusion of
Thus, our empirical results indicate that the inclusion of
MFR(i,k) does not noticeably impact the estimates of the other explanatory variables.
These results for instant coffee indicate that’ the exclusion of
manufacturer’s coupons as a variable in previous models may not have
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resulted in serious parameter estimate bias in earlier brand choice model research. Tue empirical results in Table 1 also indicate that MPR(i,k) does contribute significa
ly to the model of aggregate choice. The parameter
estimate for MFR(i,k) is in the predicted direction (positive) a significant t-statistic.
and exhibits
With MPR(i,k) having a maximum value of one and
a positive in-store promotion indicator variable, we find that the impact of MPR(i,k), 1.07, is roughly comparable to that of an in-store promotion, 1.37.
This implies that, for a consumer with high propensity to use
coupons and a brand with extensive coupon distribution at a particular occasion, the coupon effect is roughly equivalent to the effect of an in-store promotion. The likelihood ratio tests in Table 1 indicate that the improvement in fit, as MFR(i,k) is added is significant, with a X2 value of 4.6 for the nested models comparison (one degree of freedom).
The U2 statistic
indicates that the model that includes manufacturer’s coupon availability explains less than 1% of the uncertainty not explained by the model ignoring those effects, however. These results are robust to the choice model specification. MFR(i,k) was also incorporated into a more complex model, of brand choice, one in which in-store promotional effects were characterized as individual and brand specific (Ortmeyer, L.attin, and Montgomery, forthcoming).
In
that model formulation, response to in-store promotions and lagged promotional purchases are given as a function of the individual’s brand preference.
Adding MFR(i,k) to this more complex model formulation
produced similar empirical results--adding MFR(i,k) to the model did not ‘substantially alter the parameter estimates of the other explanatory
-
variables.
10
—
Moreover, MPR(i,k) was found to have the expected positive sign
and was statistically
significant.
Discussion and Conclusion We have proposed a measure for manufacturer’s coupon availability ‘to an individual that is simple to construct from the scanner panel purchase data typically used to calibrate brand choice models.
Our
empirical results suggest that manufacturer’s couponing is important to the ‘explanation of brand choice, but that its exclusion from the brand choice does not seem to produce bias in the estimates of other explanatory variables. A major caveat to the results we have presented concerns the integrity of the measure we have constructed.
Our measure provides a
convenient method of including manufacturer’s couponing in competitive models of choice; however, in gaining this convenience, how much do we lose in the accuracy of the measure to underlying construct?
That is. how
closely does our measure reflect the individual’s actual access to the different coupons in the marketplace at a given purchase occasion? One source of error in our measure derives from our use of redemptions to reflect the intensity of distribution of a brand’s coupons in calculating A(k).4
Redemption rate may, for example, be highly
correlated with market share.
Thus, a small share brand will have a lower
A(k) value even if it distributes the same coupons as a large share brand. Similarly, if redemption is highly correlated with coupon face value, a brand with a coupon drop having high face value will have a higher A(k) 4The authors are indebted to Scott Neslin for suggesting this source of error. ‘
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11
-
brand with a coupon drop having high face value will have a higher ACk) than a coupon of lower face value even if both distribute ‘the same number of coupons. A second source of error in A(k) is a result of the use of lagged redemptions instead of contemporaneous redemptions.
As a consequence, the
measure is always a step behind the actual coupon drop and actual availability.
The results of Neslin (1990) suggest that the majority of the
redemptions occur in’ the week of the coupon distribution.
This suggests
that our measure, A(k), underestimates in the week of the distribution and overestimates in the following week.
However, ‘with this measurement error,
we should anticipate attenuated empirical results.
Interestingly, the
MFR(i,k) parameter estimate was in the anticipated direction, was significant, and its inclusion significantly improved the’fit of the brand choice model.
Given the measurement error, these manufacturer’s coupon
effects may in fact be somewhat stronger. A final source of error lies in our use of an individual’s redemptions to reflect the individual’s propensity to search and have access to coupons.
An individual’s high redemption rate may, for example,
result from a coupon drop with a particularly, high face value-—one that the consumer couldn’t afford to ignore. Judging from the above, it would seem that our measure for,. manufacturer’s coupon availability measures the true construct with a large degree of error.
,
As a result, one might expect additional noise in the
analysis and a decrease in the statistical significance of the coupon variable.
Given dur significant empiricairesults, the true effect of
manufacturer’s couponing may be even stronger.
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Despite these errors in measurement, we feel that the’ measure is an’ important step in research focused on coupon effectiveness.
It shows
that coupons have an important effect, even when a somewhat errorful measure of’ coupon availability is used.
Furthermore, as managers use brand
choice models to plan and evaluate promotional activities, the measure provides a convenient and inexpensive scanner based means of including couponing in the model.
Finally, our results suggest that although
manufacturer’s coupons have’a significant positive impact on brand choice, its omission in earlier empirical analyses probably did not result in substantial bias.
‘
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13
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Table 1 Parameter Estimates, t—statistics, and Model Fit Statistics for Nested Models Ct-statistics are in parentheses)
Expected Sign
Variable 1.
Price (Price(k))
2.
Promotion (PROM(k))
3.
Lagged Promotional Purchase (Lag(i,k))
4.
Brand Loyalty
,5.
6.
+
BLOY(i,k)
+
BLOY*(i,k)
+
Basic Model (without MFR(i,k)
Basic Model (with MFR(i,k)
-.7.04 (—3.91)
—6.86 (-3.81)
1.36 (10.30)
1.37 (10.36)
-0.06 (—0.31)
—0 06 (—0.32)
3.02 (21.25) 2.29 (11.97)
3.03 (21.25) 2.30 (12.00)
3.02 (21.61) 2.24 (12.05)
3.01 (21.58) 2.22 (11.92)
.
Size Loyalty SLOY(i1k)
+
SLOY*(i,k)
+
Manufacturer’s Coupon (MFR(i,k))
+
Log-Likelihood U2
‘
Chi-Square Test
1.07 (2.17)
—1,278.8 0.490
—1,276.5 0.49]. 2 —
4.6
’
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References Bawa, Kapil and Robert W. Shoemaker. 1989, “Analyzing Incremental Sales From a Direct Mail Coupon Experiment,’ Journal of Marketing, Vol. 53, July, pp. 61-78. 1987, ‘The Effects of a Direct Mail Coupon on Brand Choice Behavior,’ Journal of Marketing Research, Vol. 21, November, pp. 370376.
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Irons, Karl W., John D.C. Little, and Robert L. Klein. l98~, ‘Determinants of Coupon Effectiveness,’ in Fred Zufryden (ed), Proceedings of the Marketing Science Conference, University of Southern California, pp. 157-164. Johnson, Todd. 1984, ‘The Myth of Declining Brand Loyalty,’ Journal of Advertising Research, Vol. 24, February/March, pp. 9-17. Klein, Robert L. 1981, Usii~g Supermarket. Scanner Panels to Measure the Effectiveness of Coupon Promotions,’ in John V. leon (ed.), Proceedings: Third ORSAJTIMS Special Interest Conference on Market Measurement and Analysis (Providence, RI: The Institute of Management Science), pp. 118-124. Lattin, James M. 1987, ‘A Model of Balanced Choice Behavior,’ Marketing Science, Vol. 6, Winter, pp. 48—65. / Lattin, James M., and Randolph P. Bucklin. 1989, ‘Reference Effects of Price and Promotion on Brand Choice Behavior,’ Journal of Marketing Research, Vol. 26, August, pp. 299-310. .
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McFadden, D. 1981, ‘Econometric Models of Probabilistic Choice,’ in C. Manski and ID. McFadden (eds), Structural Analysis of Discrete Data with Econometric Applications, (Cambridge, MA: MIT Press). 1973, ‘Conditional Logit Analysis of Qualitative Choice Behavior,’ in P. Zarembka, Frontiers in Econometrics, (New York: Academic Press).
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