APPROACH 71 and discounts are personalized according to the customers’ purchase histories. For

random coupons, the retailer randomized brands and discounts at the coupon level.

The analyses in the following sections rely on results from two models, one for each type of coupon. In both data sets, we estimate a model that predicts redemption probabilities as a function of discounts and the brand score. We use binary logistic regression with random effects. The probabilitypr^R/T that customer i redeems a random (R) or a targeted (T) coupon for brand b in stores at time t is

pr^{R/T (︂}y^R/T_ibst = 1^)︂= 1

1 + exp{−u^R/T_ibst }, (4.1)

where the utility function (for simplicity, we omit the data set labels here)

uibst =α0+αs+αt+αb +γbsibt+ (β₀+βb)d_ibst (4.2) depends on the model intercept α₀, the average discount effect β₀, store random effects α_s ∼ N(0, σ_s), year-week random effects α_t ∼ N(0, σ_t), correlated brand random effects and random discount coefficients [α_b, β_b]^′ ∼ M V N(0,Σ_b), the discountd_ibst, and the effect of the customer-, brand-, and time-specific brand score γbs_ibt. We estimate a separate model for each type of coupon (see Appendix 4.8 for a discussion of five nested model specifications).

Given that we only have two continuous covariates, binary logistic regression with random effects is a good model choice because it is the most parsimonious model that fully leverages the strength of our data set. It also offers “borrowing strength”

across brands, which is essential for brands with few observations. Because we only use one observation for each customer/brand combination, we cannot estimate a model that accounts for unobserved heterogeneity. However, given that the brand score for each customer and brand (and time) is available in the data and we know from the analysis of the targeting mechanism, that this variable plays a key role in the RTO engine, it is well-suited for modelingobserved customer heterogeneity.

The brand score should be positively related to the coupon redemption probability.

The discount variation for random coupons is exogenous, so price endogeneity is not an issue when we model redemptions. For targeted coupons, the discounts are endogenous and related to the customer’s brand preferences. Including the brand score in the model for targeted coupons mitigates the endogeneity issue to some extent. More importantly, we only use the model for targeted coupons to predict redemption probabilities of observed coupons and discounts in-sample and we do not claim to estimate a causal effect. Differences across brands are accounted for by the brand-level random interceptsα_b, so we standardize brand scores within a brand to ensure that we only explain differences within brands. In the estimation,

Table 4.4. Estimation results for redemption models.

Random Data Targeted Data

Variable Est. Sig. Est. Sig.

Interceptα0 −5.579 *** −4.116 ***

Discountβ0 3.928 *** 1.430 ***

Brand-scoreγ .523 *** .492 ***

SD(Brand)αj .896 *** .865 ***

SD(Discount)βj 1.183 *** 1.612 ***

Cor(α_j,β_j)ρ −.784 *** −.782 ***

SD(Year-Week)α_t .222 *** .301 ***

SD(Store)αs .133 *** .096 ***

N 750,876 750,876

LL −55,370 −123,264

Note: Sig. label: *** p<0.01.

we randomly subsample the full data for targeted coupons to the same size as the random coupon data set to speed up the estimation and simplify the model comparison.

Table 4.4 summarizes the estimated coefficients for the redemption models. All model coefficients are significant atp < .01. For the model estimated on the random coupon data, the average discount effect is positive, as expected for price-offs. The average of the brand-specific price elasticities is −2.96 (SD = .51), with 90% of the values in [−3.74, −2.12]. This result is in line with the promotional price elasticities for grocery products (accounting for price endogeneity) reported in the meta-analysis by Bijmolt et al. (2005). As expected, the effect of the brand score is positive, such that higher brand scores result in higher redemption probabilities for the corresponding brands. The standard deviations (SD) of three random effects are all relevant in magnitude. We observe the largest heterogeneity in the brand dimension, followed by the dimensions store and week. It makes sense that redemption probabilities vary over stores and weeks, but the variation over brands should be larger, given that we analyze 1,116 brands from 115 categories.

Customers are known to be less price sensitive when it comes to attractive brands (Bolton, 1989), so the negative correlation between the brand random effect and

the random price coefficient is intuitive.

The results for the targeted coupons are quite similar. The signs for the estimates are the same compared to the model for random coupons. It is noteworthy that the discount parameter is considerably lower in magnitude, which translates into

4.4. APPROACH 73 average brand-specific price elasticities of about−.94 (SD = .60). This is in line with the results in Section 4.3.2: the RTO engine sets prices according to the brand preferences and the price sensitivities of the customers, such that customers with higher brand scores receive lower discounts. Hence, even after controlling for brand preferences via the brand score variable, the observed reaction to discounts is lower for targeted coupons, compared to random coupons. As mentioned above, we use the model based on targeted coupons only for in-sample predictions, so this downward “bias” is irrelevant. The other estimates have a similar magnitude as the estimates in the model that is based on random data.

4.4.2 Analysis Overview

Combining the predictions of the two models is the basis for studying the effect of personalization by comparing the outcomes for different targeting mechanisms (e.g., targeted and random). The clean and exogenous variation in the random coupon data is the foundation for evaluating outcomes for unobserved coupon policies.

Using a parametric model (instead of a nonparametric approach) enables us to control for confounding factors and to run simulations of promotion policies which were not observed in the data. We leverage this in deepening our understanding of coupon personalization.

Figure 4.1 systematically summarizes the main steps of our approach. In part 1 (Section 4.5) we use the estimated models to compare the coupon redemption probabilities for targeted coupons with the redemption probabilities of the random baseline. In the coupon data set, two factors lead to higher redemption rates in the case of targeted coupons: the targeting itself and the higher average discount (see Table 4.3). The exogenous variation of discounts in the random coupon data set enables us to control for the latter by stratifying the discount distribution for random coupons, so it equals the discount distribution for targeted coupons. This isolates the redemption rate uplift through targeting. We extend the redemption probability analysis by investigating the systematic differences in redemption probabilities across brands and categories. In part 2 (Section 4.6), we focus on revenues and profits, thereby measuring the financial impact of targeting. Both metrics directly penalize for larger discounts so we can analyze both dimensions of targeting (brand and discount) simultaneously. In doing so, we compare the RTO engine targeting (i.e., one-to-one marketing) to mass marketing policies for which all customers receive the same coupons and discounts. We then explicate how the selectiveness of brand targeting affects financial outcomes by systematically decreasing the size of the sub-population that is targeted with brand coupons. As in the first part of our analysis, we rely on the exogenous variation in the random coupon set to evaluate outcomes under unobserved pricing and brand targeting policies.

Figure 4.1. Analysis overview.

Note: Best viewed in color.

The two parts differ in their outcome variables (redemption probabilities in part 1, revenues and profits in part 2) but they share one important similarity: The first step in each part focuses on the performance of the specific RTO engine that produced the targeted coupons studied here. The second step then generalizes the insights by studying how mediator variables explain the variation in redemption rates and how the degree of personalization affects financial outcomes. This widens the applicability of our findings.