How causal machine learning can leverage marketing strategies: Assessing and
improving the performance of a coupon campaign

Henrika Langen and Martin Huber

University of Fribourg, Dept. of Economics

Abstract: We apply causal machine learning algorithms to assess the causal
effect of a marketing intervention, namely a coupon campaign, on the sales of
a retail company. Besides assessing the average impacts of different types of
coupons, we also investigate the heterogeneity of causal effects across
subgroups of customers, e.g. across clients with relatively high vs. low
previous purchases. Finally, we use optimal policy learning to learn (in a
data-driven way) which customer groups should be targeted by the coupon
campaign in order to maximize the marketing intervention’s effectiveness in
terms of sales. Our study provides a use case for the application of causal
machine learning in business analytics, in order to evaluate the causal impact
of specific firm policies (like marketing campaigns) for decision support.

Keywords: causal machine learning, coupon campaign, marketing

JEL classification:  M30, C21

##  1 Introduction

In the last two decades, the amount of customer data available to marketers
has increased dramatically with new data types such as social media,
clickstream, search query and supermarket scanner data on the rise. The
emerging availability of customer Big Data has spawned a new stream of
literature on machine learning (ML) methods and tools in the field of business
and marketing. The ML literature on designing marketing campaigns ranges from
research on modeling customer behavior (e.g. Xia, Chatterjee, and May (2019),
Hu, Dang, and Chintagunta (2019)), price sensitivity (e.g. Arevalillo (2021))
and choices (e.g. Donnelly, Ruiz, Blei, and Athey (2021)) to studies on the
development of personalized product recommendation systems (e.g. Ramzan,
Bajwa, Jamil, Amin, Ramzan, Mirza, and Sarwar (2019), Anitha and Kalaiarasu
(2021)), customer churn management (e.g. Gordini and Veglio (2017)) and
acquisition of new customers (e.g.Luk, Choy, and Lam (2019)).

A common feature of these studies is that they are based on predictive ML,
i.e., on identifying patterns of variables in the data in order to use them
for predicting an outcome of interest (e.g. sales). This is done by training
predictive models in one part of the data and determining the best performing
model (with the smallest possible prediction error) in the other part of the
data. Under some of the commonly used ML algorithms, the identified model
serves as a black box, i.e., it relies on functions that are too complex for
any human to understand (like in so-called deep learning), while in other
cases, the model has an explicit (and thus comprehensible) structure. In any
case, however, such predictive ML models do generally not provide insights
about the causal effects of specific variables or interventions (like a
marketing campaign) on the outcome of interest. Thus, predictive ML, while
appropriate for making educated guesses about outcomes given specific patterns
observed in the data, is not well suited for determining and comparing the
effectiveness of possible courses of action, which would be relevant as
decision support, e.g. for optimally designing a marketing campaign.111In
order to predict an outcome of interest based on predictor variables, ML aims
at minimizing the prediction error by optimally trading off prediction bias
and variance. If several variables capture the same relevant predictive
feature, i.e., are correlated with that feature, ML algorithms may identify
some of these variables as relevant predictors while giving little importance
to others, regardless of the variables’ causal effect on the outcome. For
instance, variables that do not directly or only modestly affect the outcome
might enter the prediction model as relevant predictors, simply because they
are correlated with other variables that actually affect the outcome. For this
reason, it can happen that these other variables play little or no role in the
predictive model even though they causally affect the outcome, simply because
they provide little additional information for prediction. Therefore,
predictive ML is generally not suitable for the causal analysis of ‘what if’
questions, like the behavioral effects of different coupon campaign
strategies.

To improve on the shortcomings of predictive ML for evaluating the impact of
implementing vs. not implementing a specific intervention, a fast growing
literature in econometrics and statistics has been developing so-called causal
ML algorithms. In this paper, we demonstrate the application of such methods
in the context of business analytics for decision support, namely for
evaluating a marketing intervention. More concisely, we make use of the so-
called causal forest approach by Athey, Tibshirani, and Wager (2019) to assess
the causal effect of coupon campaigns, in which customers were provided with
coupons for different product types, on customers’ purchasing behavior, i.e.
the difference in their expected behavior with and without being addressed by
a coupon campaign. While predictive ML algorithms cannot isolate the causal
effects of coupons on customers’ purchasing behavior from the influence of
background characteristics (e.g. socio-economic characteristics and price
sensitivity) which jointly influence coupon reception and purchasing behavior,
the causal forest approach can do so under specific assumptions.

One crucial condition is that all variables jointly affecting coupon reception
and purchasing behavior are observed in the data and can thus be controlled
for, known as selection-on-observables or unconfoundedness assumption. Under
further conditions on the quality of the estimated ML models for the outcome
and the treatment as a function of the observed variables, the causal forest
approach permits evaluating the mean impact of the coupons among all
customers, as well as across specific subgroups or customer segments (e.g.
different age groups). Our results for instance suggest a positive overall
effect of coupons for grocery and drugstore items. For coupons applicable to
ready-to-eat food, on the other hand, we do not find a statistically
significant overall effect. An analysis of the effect of ready-to-eat food
coupons in different customer subgroups, however, reveals that these coupons
positively affect customers with low levels of expenditures prior to the
campaign, while having a statistically significant negative effect on
customers with relatively high expenditures.

Furthermore, we apply optimal policy learning based on ML as suggested by
Athey and Wager (2021), in order to learn in the data which customer segments
should optimally be targeted by coupon campaigns such that the overall effect
(or net effect after subtracting the costs) is maximized. In contrast to
predictive ML, optimal policy learning allows under certain conditions
identifying the coupon provision policy which is most effective in terms of
its impact on sales. This is done by first assessing the expected effects
across different customer segments and then selecting those as target groups
in which the effects are sufficiently high. The estimated optimal policy for
coupons applicable to plants and flowers, for instance, suggests that such
coupons should be provided to low-middle-income customers who did not purchase
anything from the store in the period prior to the campaign, and to customers
aged 36 years or older whose pre-campaign spending did not exceed a certain
level.

The paper proceeds as follows. Section 2 outlines the current state of
quantitative research in the marketing literature and motivates the
application of causal ML methods in the field of marketing. Section 3
introduces and describes our retailer sales data to be analyzed. Section 4
defines the causal effects of interest based on so-called counterfactual
reasoning, discusses the conditions (such as the selection-on-observables
assumption) required for applying causal ML and describes the algorithms for
causal analysis and optimal policy learning. Section 6 provides the results of
the evaluation of the retailer’s coupon campaigns as well as the optimal
coupon assignment. Section 7 concludes.

##  2 Motivation

The evaluation of the causal impact of discount campaigns plays a significant
role in the earlier marketing literature from the ‘pre-Big-Data era’, see e.g.
Inman and McAlister (1994), Raju, Dhar, and Morrison (1994), Leone and
Srinivasan (1996) and Krishna and Zhang (1999) for studies on causal effects
of coupon provision. However, the last two decades have seen a surge of
predictive ML applications in business analytics, which appear to be
increasingly dominating causal analysis in marketing as well. In a keyword-
search-based literature review, Mariani, Perez-Vega, and Wirtz (2021) find
that the number of publications on predictive ML and Artificial Intelligence
(AI) in marketing, consumer research and psychology has grown exponentially in
the last decade (2010-21). The systematic literature reviews by Mustak,
Salminen, Plé, and Wirtz (2021) and Ma and Sun (2020) paint a similar picture,
with the latter stating that the rise of ML in marketing began with
applications of support vector machines, a specific type of ML algorithm. This
was then followed by studies that introduce text analysis, topic modelling and
reinforcement learning into marketing research, as well as by marketing
applications of deep learning, and network embedding. Questions about the
impact of marketing campaigns, the influence of certain external factors on
the success of a campaign and the heterogeneity of campaign effects across
customer segments appeared to become relatively less important (see e.g. Hair
Jr and Sarstedt (2021), Ma and Sun (2020)), even though most recently, the
literature saw first applications of causal ML alogithms (such as causal
trees).

The following sections summarize the current state of research on discount
campaigns using causal inference (Section 2.1) and predictive ML (Section
2.2). This serves as base for motivating the use of causal ML to evaluate and
optimize discount campaigns and to approach various other marketing and
business decisions in Section 2.3.

###  2.1 Causal Inference in Marketing

A range of studies assess the causal effects of specific marketing campaigns
on consumers’ response to campaigns. These studies typically rely on (field)
experiments or traditional methods for causal inference based on observational
data. In the latter case, researchers must assume that all variables that
jointly affect the intervention and purchasing behavior are observed in the
data and can thus be controlled for. Rubin and Waterman (2006) apply
propensity score matching to evaluate the effect of marketing interventions
aimed at doctors in order to promote the prescription of a “lifestyle” drug.
They also rank the doctors according to their estimated expected individual-
level effects which in turn can be used to derive a tailored marketing
strategy. Reimers and Xie (2019) assess the effect of e-coupon provision on
alcohol sales by means of a difference-in-differences approach, exploiting the
fact that the restaurants in their sample issued e-vouchers at different
points in time. See also Xing, Zou, Yin, Wang, and Li (2020), Halvorsen,
Koutsopoulos, Lau, Au, and Zhao (2016) and Zhang, Dai, Dong, Qi, Zhang, Liu,
and Liu (2017) for further examples of observational and experimental studies
assessing the effect of coupon provision or other discount campaigns on
consumer behavior.

Other contributions analyze the heterogeneity of marketing effects across
customer characteristics and the circumstances under which customers are
targeted by coupon and other promotion campaigns. Among them, Gopalakrishnan
and Park (2021) investigate whether high- and low-consumption customers, as
defined by their purchasing behavior during the 12 months prior to the
experiment, differ in their responsiveness to coupon campaigns. Andrews, Luo,
Fang, and Ghose (2016) study whether the level of capacity utilization (or
crowdedness) of a subway affects the response of its passengers to mobile
advertising campaigns and find a statistically significant positive
association. Based on a field experiment, Spiekermann, Rothensee, and Klafft
(2011) conclude that proximity to the place for which coupons are distributed
influences coupon redemption, and that this association is much more
pronounced in the city center than in suburban areas.

Furthermore, several studies evaluate how specific configurations of coupons
such as face value, method of distribution and expiry date affect consumer
behavior. The experimental studies by Zheng, Chen, Zhang, and Che (2021) and
Biswas, Bhowmick, Guha, and Grewal (2013) assess how the size of discounts
affects consumers’ perception of product quality and purchase intentions.
Leone and Srinivasan (1996) use supermarket scanner data to analyze the effect
of coupon face value on sales and profits, while Anderson and Simester (2004)
study the long-term effects of the discount size on the purchasing behavior
among new and established customers in an experimental setting. Other
contributions as e.g. Gopalakrishnan and Park (2021), Jia, Yang, Lu, and Park
(2018), Choi and Coulter (2012), Krishna and Zhang (1999) and Inman and
McAlister (1994) analyze how further aspects of the configuration of coupon
and discount campaigns affect consumer behavior.

###  2.2 Predictive ML in Marketing

In recent years, many studies have focused on the ML-based prediction of
coupon redemption and related sales. They use ML algorithms to model customer
behavior as a function of customers’ previous transactions, their response to
previous coupon/discount campaigns and their socio-economic characteristics,
in order to predict the likelihood of customers to redeem coupons or take up
discounts and make purchases.

Pusztová and Babič (2020) and He and Jiang (2017) compare the performance of
different ML-based classification algorithms in predicting coupon redemption
in digital marketing campaigns. The former study concludes that so-called
Support Vector Machines provide the most accurate predictions, the latter that
it is the gradient boosting framework ‘XGBoost’ which performs best.
Greenstein-Messica, Rokach, and Shabtai (2017) introduce an algorithm that
combines co-clustering and random forest classification to predict mobile
restaurant coupon redemption based on demographic and contextual variables
such as the consumer’s distance to the restaurant relative to the depth of the
coupon’s discount. Ren, Cao, Xu, et al. (2021) develop a two-stage model for
estimating the probability of coupon redemption consisting of a first stage in
which customers are clustered based on their past purchase and redemption
behavior, followed by a second stage of fitting prediction models for the
different customer clusters. Several studies such as Koehn, Lessmann, and
Schaal (2020), Xiao, Li, Xu, Zhao, Yang, Lang, and Wang (2021) and Zheng,
Chen, Zhang, and Che (2021) predict customer behavior in the context of coupon
or other discount campaigns by means of several ML methods.

###  2.3 Causal ML in Marketing

Under certain conditions like the selection-on-observables assumption,
implying that all variables that jointly affect the intervention and
purchasing behavior are observed in the data and can thus be controlled for,
causal ML methods allow for the evaluation of causal effects of
coupon/discount campaigns as well as effect heterogeneity across customer
segments. In contrast to more traditional methods of causal inference, they
can take advantage of the full amount of information available to marketers,
which might be large in the era of ‘Big Data’, and in a data-driven way. That
is, causal ML can address research questions such as those described in
Section 2.1 based on high-dimensional observational data that contain a large
set of observed background variables which could serve as control variables.
Examples are customers’ socio-economic characteristics, geographic or time-
related information, weather, economic circumstances and many more. Causal ML
is based on combining causal inference approaches with ML algorithms for the
data-driven selection of control variables when estimating causal effects
and/or their heterogeneity across customer segments.

The rise of predictive ML has e.g. motivated Anderson (2008), Lycett (2013)
and Erevelles, Fukawa, and Swayne (2016) to argue that theory-based causal
inference has lost some of its relevance for business decisions in the light
of large datasets and sophisticated predictive ML methods available to
marketers today. However, these views were soon challenged in several studies
that emphasize the importance of causal reasoning and risks of basing
decisions solely on correlations, see e.g. Cowls and Schroeder (2015) and
Golder and Macy (2014). In more recent years, a growing number of
contributions have further stressed the importance of integrating ML and
causal inference, see e.g. Hair Jr and Sarstedt (2021). Among them, Hünermund,
Kaminski, and Schmitt (2021) investigate the use of causal methods in business
analytics by combining qualitative interviews and quantitative surveys among
data scientists and managers in a mixed-methods research design. They document
an on-going shift in corporate decision-making away from focusing solely on
predictive ML and towards using causal methods, based on both observational
and experimental data.

Yet to date, applications of causal ML to marketing research appear to be
relatively scarce, with the exception of large tech companies operating in
social media or online market platforms. To the best of our knowledge, there
are virtually no studies evaluating the causal effect of coupon campaigns on
customer behavior by means of causal ML, as we do in this paper. Smith,
Seiler, and Aggarwal (2021) use predictive ML for deriving optimal coupon
targeting strategies and estimate the profits that would accrue under those
strategies out of sample, i.e. in parts of the data not used for deriving the
strategies. The profits are estimated based on the potential outcomes
framework, which is also the basis of causal ML. However, the study by Smith,
Seiler, and Aggarwal (2021) is conceptually different from ours in that it
uses the potential outcomes framework to compare coupon targeting strategies
inferred from different predictive ML algorithms, while we apply an algorithm
based on the potential outcomes framework (namely the optimal policy learning
approach of Athey and Wager (2021)) to infer a coupon targeting strategy.

One study in the broader field of marketing which does consider causal ML is
Gordon, Moakler, and Zettelmeyer (2022). They assess the performance of so-
called Double Machine Learning (DML), see Chernozhukov, Chetverikov, Demirer,
Duflo, Hansen, Newey, and Robins (2018), and propensity score matching, see
Rosenbaum and Rubin (1983), for estimating the causal effect of conversion ads
on Facebook. Such ads aim to increase online activity such as page visits,
sales and views on an external website. For their analysis, the authors take
advantage of the fact that Facebook offers businesses to assess their ad
campaigns by means of randomized experiments. Gordon, Moakler, and Zettelmeyer
(2022) compare the effect estimates based on DML and propensity score matching
with those from the experiments, finding that DML outperforms propensity score
matching but that both approaches overestimate the effect substantially. This
highlights the importance of observing and appropriately controlling any
factors jointly affecting the intervention and customer behavior when causally
assessing marketing interventions. Also Huber, Meier, and Wallimann (2021)
consider DML when analyzing observational data to investigate whether
discounted tickets induce Swiss railway customers to reschedule their
journeys, e.g. to shift demand away from peak hours.

Narang, Shankar, and Narayanan (2019) apply so-called causal forests, an
alternative causal ML framework developed by Wager and Athey (2018) and Athey,
Tibshirani, and Wager (2019) (see Section 5), to assess the heterogeneity
across shoppers in how mobile app failures affect their purchasing frequency,
volume and monetary value. Guo, Sriram, and Manchanda (2021) assess the effect
of a law requiring pharmaceutical firms to disclose their marketing payments
to physicians on the firms’ payments to physicians by means of a Difference-
in-Differences approach and assess expected individual-level effect
heterogeneity by means of causal forests. Zhang and Luo (2021) incorporate
causal forests in their study on restaurant survival as a function of photos
posted on social networks. They find that the total volume of user-generated
content and the extent to which user photos are rated as helpful have a
significant positive effect on the likelihood of restaurant survival.

In the following, we will use coupon promotions as a running example for
highlighting the merits of causal ML in business analytics and marketing
research. In the context of coupon campaigning strategies, marketers are
arguably not only interested in predicting customer behavior, but in measuring
the causal effects of alternative campaigns on customer behavior. Such effects
correspond to the difference in the customers’ (average) behavior when being
vs. not being addressed by a specific campaign. Intuitively, this requires
comparing a customer’s observed behavior under the actually assigned coupon
with the potential (and not directly observed) behavior that would have
occurred had coupon provision been different to the actually observed one, an
approach commonly referred to as counterfactual reasoning. Such a causal
assessment is necessary for determining whether and to which extent a campaign
is effective in altering customer behavior and for understanding how customer
behavior would change if coupons were distributed differently.

In a predictive ML model, however, the predictive power of coupon provision on
customer behavior does generally not correspond to such a causal effect,
because it is affected by so-called regularization bias. The latter is related
to shrinking the importance of some predictor with the aim of reducing the
variance of ML, in order to improve overall predictive performance.
Regularization bias may for instance occur if coupon provision is strongly
correlated with other (good) predictors (like previous purchases) and/or that
its effect on consumer behavior is comparably small, such that coupon
provision has little predictive value. A further issue is selection bias,
meaning that coupons may pick up the effects of other variables whose
importance has been shrunk by the ML algorithm. To provide proper decision
support for the implementation of coupon campaigns, it important to rely on an
appropriately estimated causal effect that avoids regularization and selection
bias, as implemented in causal ML algorithms like DML and causal forests.

The necessity of estimating the causal effect of coupon campaigns rather than
merely predicting customer behavior can be illustrated by means of a simple
example. Suppose a retailer estimates a sales prediction model based on
observational data from a previous coupon campaign, in which (in an attempt to
re-activate dormant customers) coupons were predominantly distributed among
those customers who had not been in the shop for a while, rather than among
frequent shoppers. The estimated predictive model might indicate a negative
association between coupon provision and sales as the coupon campaign is
likely to re-activate only some inactive customers, so that on average the
(formerly) inactive customers purchase less than the frequent shoppers. The
true effect of receiving a coupon, however, might actually be positive. A
positive effect implies that when comparing two groups of (formerly) inactive
customers with comparable background characteristics (like the willingness to
buy), where the first receives coupons while the second does not, then the
average purchases of the first group is higher. The predictive model therefore
confuses (or confounds) the causal effect of the coupon campaign with that of
being a dormant vs. a frequent shopper, thus incorrectly pointing to a
negative effect.

In a second scenario, the retailer decides to issue coupons in the shop. This
way, frequent shoppers are regularly provided with coupons while dormant
customers rarely if ever receive any. A predictive model now detects a
positive relationship between coupon provision and sales although the actual
effect of providing coupons might be negative, namely if frequent customers
use the coupons for products they would have bought anyway. When evaluating
the campaigns by predictive methods and incorrectly interpreting the results
as causal, marketers would come to the conclusion that the first campaign is
ineffective while the latter is effective. Causal methods, on the other hand,
enable marketers under specific conditions to control for such biases, in our
example due to differences in purchasing behavior between frequent and dormant
customers, and consistently estimate the effect of coupon campaigns. Further,
these methods can also be applied for assessing effect heterogeneity and
identifying an optimal coupon distribution scheme (or policy) that targets
those customers whose average purchases respond sufficiently strongly to
receiving a coupon.

In causal studies on discounts, the impact of providing coupons is typically
assessed either based on random experiments or observational data from
previous campaigns by controlling for observed characteristics or covariates
that are likely associated with both coupon provision and consumer behavior.
The covariates to be controlled for are conventionally selected using
theoretical considerations, domain knowledge, intuition and/or previous
empirical findings. Examples for such covariates in the context of campaign
evaluations are the previous purchasing behavior, exposure to earlier
campaigns and socio-economic characteristics like age, gender or income. The
conventional, i.e. non-ML-based, causal inference methods require the
researcher or analyst to manually select covariates. This entails the threat
of missing important control variables and may even be practically infeasible
in big data contexts with a very large set of potential covariates (collected
e.g. on online platforms), including unstructured data containing e.g. text or
clickstreams. Furthermore, conventional causal inference methods require the
researcher to specify how, i.e., through which functional form (like e.g. a
linear model), the selected covariates are associated with coupon provision
and purchasing behavior. In contrast, causal ML methods permit taking
advantage of the full amount of information in the data to detect and control
for relevant covariates (importantly affecting coupon provision and consumer
behavior) in a data-driven way and to flexibly estimate the functional form of
statistical associations. Still, the observational data have to meet certain
conditions, as described in Section 4.2.

The argument for counterfactual reasoning made further above also applies to
efforts of optimizing the distribution of coupons across segments of
customers, i.e. optimal policy learning as discussed e.g. in Manski (2004),
Hirano and Porter (2009), Stoye (2009), and Kitagawa and Tetenov (2018).
Basing optimization on predictive ML models as advocated in several studies on
predicting coupon redemption (e.g. Koehn, Lessmann, and Schaal (2020), Ren,
Cao, Xu, et al. (2021), Greenstein-Messica, Rokach, and Shabtai (2017))
ignores the fact that predictive models do generally not provide information
on causal effects and their heterogeneity across different customer segments.
Causal ML-based policy learning as suggested by Athey and Wager (2021), on the
other hand, is a causal ML approach to inferring allocation schemes which
ensure that those customers for whom sufficiently large effects can be
expected are targeted by the campaign. In our empirical application, we
demonstrate how causal ML methods can help evaluate coupon campaigns and
support marketing-related decision making. We analyze customer data from a
retail store and first evaluate the average effect of providing customers with
a coupon (of a certain type) on the monetary value of their purchases. In a
second step, we demonstrate how optimal policy learning can be used for
detecting customer segments that should be targeted or not targeted by coupon
campaigns to maximize the effectiveness of these campaigns.

##  3 Data

In our empirical application, we analyze sales data on coupon campaigns of a
retailer, which are available on the data science platform Kaggle (2019) under
the denomination ‘Predicting Coupon Redemption’. The dataset contains
information on socio-economic characteristics of retail store customers, on
the coupons they have received during the campaigns as well as on their coupon
redemption and purchasing behavior. The retail store has run several campaigns
to issue coupons with discounts for certain products, with some coupons being
applicable to individual products only and others to a range of products. In
each of the 18 partly time-overlapping campaigns falling into the time span
covered by the dataset, the store has distributed 1 to 208 different coupon
types each applicable to up to 12,000 products which mainly belong to the same
product category. The coupons were distributed in such a way that each
customer received 0 to 37 different coupons per campaign with the composition
of this set of coupons differing between the recipients. Apart from the
information on provided coupons, the dataset contains details on all purchases
made by each registered customer between January 2012 and July 2013, including
the date of the transaction, the redeemed coupons, the product type of each
purchased product and the price paid.

For our analysis, we group the coupons into five broad categories mirroring
the products they can be used for. More concisely, we distinguish between
coupons applicable for ready-to-eat food items, groceries, plants and flowers,
drug store items and other products. One could arguably also be interested in
more fine-grained coupon categories to focus on a specific coupon or discount
type than on our broader coupon categories, which would, however, require a
larger dataset to obtain satisfactory statistical power. Due to the temporal
overlap of campaign periods, we need to redefine them such that each of the
resulting artificially generated campaign periods coincides with the validity
period of a given set of coupons. That is, all coupons which are valid in some
artificial campaign period are valid during the entire period. By doing so, we
can fully attribute changes in the buying behavior from one artificial
campaign period to another to the coupons valid in the respective periods.
From now on, the 33 newly defined artificial campaign periods are simply
referred to as campaign periods. In order to take into account the differences
in the duration of campaign periods, we consider the average per-day
expenditures per customer and campaign period as our outcome of interest. For
estimating the causal effect of coupon provision on the buying behavior, we
pool the customer-specific purchases across campaign periods, thus entailing
33 observations per customer.

Table 1 provides some descriptive statistics for our data, namely on the daily
expenditures, the share of coupons redeemed and observed customer
characteristics. The table reports the mean of these variables in the total
sample of 50,624 observations, as well as among observations that received a
coupon and among those that did not. Further, it contains the mean difference
across variables among coupon receivers and non-receivers, as well as the
p-value of a two-sample t-test. For some 30% of the observations, customers
received at least one coupon. Furthermore, customers who received a coupon had
on average higher expenditures in the retail store than customers who did not,
suggesting that the retailer did not target its previous campaigns to re-
activate dormant customers. We also see that the retailer does not have
information on the socio-economic characteristics of all customers in the
registry, but only for about half of them, as the respective variable values
are unknown for many observations (see the coding ‘unknown’). Such a high rate
of non-response when measuring the variables can entail selection bias when
estimating the effects of interest and for this reason, we will conduct
several robustness checks in the empirical analysis to follow further below
(see Section 6.5). The descriptive statistics also reveal that some socio-
economic characteristics as well as their observability are correlated with
the reception of coupons. For example, customers aged 70 years or older are
less likely to be targeted by a coupon campaign. The main difference in the
probability of receiving a coupon seems to be between customers whose
socioeconomic characteristics are not available and those whose
characteristics are known, with the former less likely to receive a coupon.

As is noted in several studies (e.g. Danaher, Smith, Ranasinghe, and Danaher
(2015), Spiekermann, Rothensee, and Klafft (2011)) coupon redemption rates are
typically low and on average not higher than 1 to 3 percent. This is also the
case in our data, as only 3% of coupon receivers did actually redeem any of
them within the respective period of coupon validity. However, as mentioned
before, coupons might not only influence customer behavior when redeemed, but
may also serve as advertising tool which attracts customers to the store, even
when not redeeming the coupon.

variable |  Overall |  Coupon Receivers |  Non-Receivers |  Diff |  p-val
---|---|---|---|---|---
N |  50,624 |  15,327 |  35,297 |  |
daily expenditures |  202 |  245 |  184 |  61 |  0
age: |  |  |  |  |
18-25 |  0.028 |  0.031 |  0.027 |  0 |  0.02
26-35 |  0.082 |  0.102 |  0.074 |  0.03 |  0
36-45 |  0.118 |  0.141 |  0.108 |  0.03 |  0
46-55 |  0.171 |  0.191 |  0.163 |  0.03 |  0
56-70 |  0.037 |  0.045 |  0.034 |  0.01 |  0
70+ |  0.043 |  0.039 |  0.045 |  -0.01 |  0
unknown |  0.52 |  0.451 |  0.55 |  -0.1 |  0
family size: |  |  |  |  |
1 |  0.157 |  0.171 |  0.15 |  0.02 |  0
2 |  0.192 |  0.213 |  0.182 |  0.03 |  0
3 |  0.066 |  0.079 |  0.06 |  0.02 |  0
4 |  0.03 |  0.04 |  0.026 |  0.01 |  0
5+ |  0.036 |  0.047 |  0.031 |  0.02 |  0
unknown |  0.52 |  0.451 |  0.55 |  -0.1 |  0
marital status: |  |  |  |  |
married |  0.2 |  0.234 |  0.186 |  0.05 |  0
unmarried |  0.072 |  0.084 |  0.067 |  0.02 |  0
unknown |  0.728 |  0.682 |  0.747 |  -0.07 |  0
dwelling type: |  |  |  |  |
rented |  0.026 |  0.033 |  0.023 |  0.01 |  0
owned |  0.454 |  0.516 |  0.428 |  0.09 |  0
unknown |  0.52 |  0.451 |  0.55 |  -0.1 |  0
income group: |  |  |  |  |
1 |  0.037 |  0.042 |  0.035 |  0.01 |  0
2 |  0.043 |  0.051 |  0.04 |  0.01 |  0
3 |  0.044 |  0.049 |  0.042 |  0.01 |  0
4 |  0.104 |  0.113 |  0.1 |  0.01 |  0
5 |  0.118 |  0.137 |  0.11 |  0.03 |  0
6 |  0.056 |  0.061 |  0.053 |  0.01 |  0
7 |  0.02 |  0.023 |  0.019 |  0 |  0.01
8 |  0.023 |  0.03 |  0.021 |  0.01 |  0
9 |  0.018 |  0.024 |  0.016 |  0.01 |  0
10 |  0.006 |  0.006 |  0.006 |  0 |  0.89
11 |  0.003 |  0.003 |  0.003 |  0 |  0.43
12 |  0.006 |  0.01 |  0.005 |  0 |  0
unknown |  0.52 |  0.451 |  0.55 |  -0.1 |  0
coupons redeemed |  |  0.030 |  |  |
Table 1: Mean of the variables in the total sample (”Overall“), among the
treated (”$D=1$“) and the non-treated (”$D=0$“) as well as the mean difference
across treatment states and the p-value of a two-sample t-test.

##  4 Identification

###  4.1 Causal Effect

We are interested in estimating the causal effect of a specific intervention,
commonly referred to as ‘treatment’ in causal analysis and henceforth denoted
by $D$, on an outcome of interest, denoted by $Y$.222Throughout this paper,
capital letters denote random variables and small letters specific values of
random variables. In our context, $D$ reflects the reception or non-reception
of coupons and $Y$ the purchasing behavior, measured as the average per-day
expenditures during the coupon validity period. In the simplest treatment
definition, $D$ is binary and takes the value 1 when the respective customer
is provided with a coupon and 0 if this is not the case. Mathematically
speaking, the value $d$ which treatment $D$ might take satisfies
$d\in\\{0,1\\}$. Our subsequent discussion of causal effects and the
statistical assumptions required for their measurement will focus on this
binary treatment case for the sake of simplicity. However, our empirical
analysis will also separately consider the effects of receiving coupons for
five product categories, by running separate estimations for the comparison of
each category to not receiving any coupons. This implies that the assumptions
introduced in Section 4.2 need to hold for each of these categories, see e.g.
Imbens (2000) and Lechner (2001) for discussions of multi-valued treatments.

For defining the causal effect of coupon provision, we rely on the potential
outcome framework pioneered by Neyman (1923) and Rubin (1974). Let $Y(d)$
denote the potential (rather than observed) outcome under a specific treatment
value $d\in\\{0,1\\}$. That is, $Y(1)$ corresponds to a customer’s potential
purchasing behavior if she received a coupon, while $Y(0)$ is the behavior
without coupon. The causal effect of the coupon thus corresponds to the
difference in the purchasing behavior with and without coupon, $Y(1)-Y(0)$,
but can unfortunately not be directly assessed for any customer. This is due
to the impossibility of observing customers at the very same time under two
mutually exclusive coupon assignments (1 vs. 0), which is known as the
‘fundamental problem of causal inference’, see Holland (1986). This follows
from the fact that the outcome $Y$ which is observed in the data corresponds
to the potential purchasing behavior under the coupon assignment actually
received, namely $Y=Y(1)$ for those receiving a coupon ($d=1$), while $Y(0)=Y$
for those who do not ($d=0$). For receivers, however, $Y(0)$ cannot be
observed in the data, while for customers without coupon, it is $Y(1)$ which
remains unknown.

Even though causal effects are fundamentally unidentifiable at an individual
level, we may under the assumptions outlined further below evaluate them on
more aggregate levels, i.e. based on groups of treated and nontreated
individuals. One causal parameter which is typically of crucial interest is
the average causal effect, also known as average treatment effect (ATE), i.e.
the average effect of coupon assignment $D$ on purchasing behavior $Y$ among
the total of customers. Formally, the ATE, which we henceforth denote by
$\Delta$, corresponds to the difference in the average potential outcomes
$Y(1)$ and $Y(0)$:

$\displaystyle\Delta=E[Y(1)-Y(0)],$ (1)

where $`E[...]^{\prime}$ stands for ‘expectation’, which is simply the average
in the population.

###  4.2 Identifying Assumptions

In order to identify the ATE defined in the previous section, we need to
impose several identifying assumptions, which are outlined in this section. We
note that in the subsequent discussion, ‘$\bot$’ stands for statistical
independence. Further, $X$ denotes the set of covariates that should not be
affected by treatment $D$ and therefore be observed before or at, but not
after, treatment.
Assumption 1 (Conditional Independence of the Treatment):
$Y(d)\bot D|X$ for all $d\in\\{0,1\\}$. Assumption 1 states that the treatment
is conditionally independent of the outcome when controlling for the
covariates, and is known as ‘selection on observables’, ‘unconfoundedness’ or
‘ignorable treatment assignment’, see e.g. Rosenbaum and Rubin (1983). The
assumption implies that there are no unobservables jointly affecting the
treatment assignment and the outcomes conditional on the covariates. This
condition is satisfied if the coupons are quasi-randomly distributed among
observations with the same values in $X$. The retailer may therefore base the
distributing of coupons on customer or market characteristics observed in the
data, however, not on unobserved characteristics that affect purchasing
behavior even after controlling for the observed ones.

We control for the variables in Table 1, for period fixed effects, as well as
for the customers’ average daily pre-campaign expenditures and the coupons she
received and redeemed in the period prior to the campaign. When evaluating the
effect of specific coupon categories, we also include dummies that indicate
whether a customer received coupons from another category at the moment of
treatment assignment. This is because the availability of other coupons
influences purchase behavior and is likely to be correlated with the
probability of receiving coupons of the category under study. The reason for
including period fixed effects is that there is no information available on
holidays or weekdays on which the store is closed or has shortened opening
hours, that is, circumstances that might affect purchasing behavior. Also, the
retailer is likely to distribute coupons differently across campaign periods.
We control for pre-campaign expenditures, as well as coupon reception and
redemption in order to account for potential coupon-induced inter-temporal
purchase shifts, i.e. receipt of coupons in one period might motivate
customers to shift purchases of products covered by the coupons to the
respective period. Including pre-campaign expenditures further allows
controlling for general differences in purchasing behavior between customers
that might be correlated with the likelihood of receiving coupons.

The set of covariates considered in our estimation is similar to those in
studies on the effect of coupon campaigns that rely on traditional causal
inference approaches, see e.g. Xing, Zou, Yin, Wang, and Li (2020) and Hsieh,
Shimizutani, and Hori (2010) who both control for some demographic
characteristics as well as for a proxy for the customers’ economic situation
and their purchasing behavior before the coupon campaign under study. Other
than the methods used in these studies, however, the causal ML approach allows
the covariates to enter into the estimation in a flexible, possibly non-linear
way, and does not require to pre-select variables based on theoretical
considerations. Studies on predicting coupon redemption by means of ML mainly
rely solely on observable customer behavior and coupon characteristics as
predictors for coupon redemption while not including socio-demographic
characteristics of the customers, see e.g. Greenstein-Messica, Rokach, and
Shabtai (2017) use and He and Jiang (2017).

In their study on the performance of causal ML in evaluating facebook ads,
Gordon, Moakler, and Zettelmeyer (2022) include the users’ gender, age and
household size but - unlike our data - their data lack information on the
users’ economic situation, such as their income, employment status or wealth.
They also use several facebook-specific covariates measuring the customers’
activity on facebook (likes, posts, type of device used and interests
explicitely expressed on facebook). Furthermore, they take into account the
users’ response to earlier ads by other companies which is comparable to the
covariates on pre-campaign purchasing behavior, coupon reception and coupon
redemption considered in our analysis. Despite the large differences in the
amount of information available in the facebook study and our analysis, we
cannot conclude that the set of covariates in our estimation is insufficient.
For one, the algorithms used by facebook to determine the target audience for
ad placement are far more complex and information-hungry than a retailer’s
coupon strategy; and facebook users’ decision about whether or not to respond
to a facebook ad, on the other hand, is likely to be complex and dependent on
several of the characteristics considered in the algorithm (which is why they
are considered in facebook’s ad placement algorithm). In order to successfully
apply causal ML methods, the authors of the facebook study had to take into
account all the information that is incorporated in facebook’s ad placement
algorithms, while we only need to consider the information based on which the
retailer distributed its coupons, namely the information available in the
customer database.
Assumption 2 (Common Support):
$0<Pr(D=1|X)<1$.

Assumption 2 states that the conditional probability of being treated given
$X$, in the following referred to as the treatment propensity score, is larger
than zero and smaller than one. This so-called common support condition
implies that for any values the covariates might take, customers have a non-
zero chance of being treated and a non-zero chance of not being treated. While
this assumption is imposed w.r.t. to the total of a (large) population,
meaning that both treated and non-treated customers exist conditional on $X$,
we can and should also verify it in the data. In our sample, common support
appears to be satisfied, as there exist no combinations of covariate values
for which either only customers with coupons (of a certain category) or no
coupons exist.

Furthermore, another condition that needs to be satisfied is the so-called
Stable Unit Treatment Value Assumption (SUTVA), see e.g. Rubin (1980). In our
context, SUTVA rules out that the coupons provided to one individual in a
certain campaign period affect the potential outcome of another individual at
any point in time or that they affect the potential outcome of the same
individual in a different period. This implies that there are no inter-
personal or inter-temporal spillover effects of coupon campaigns. In addition,
SUTVA requires that for every individual in the population, there is a single
potential outcome value associated with each treatment state, meaning there
are no different versions of the coupons leading to different potential
outcomes. In many empirical applications, it appears likely that at least some
aspects of SUTVA are violated and for this reason, there exist several
relaxations of this assumption. In our case, the requirement to not have
different treatment versions is particularly problematic, as we group
different coupons into broader categories. The treatment of being provided
with coupon(s) from one category comprises the receipt of different coupons,
each applicable to a distinct set of products from the product category. If a
customer is not equally interested in all products belonging to that product
category, the customer might only redeem a coupon and/or change her purchasing
behavior if the coupon is applicable for certain products. For this reason, we
are in a setting in which there are different treatment versions, each
possibly associated with a different potential outcome.

VanderWeele and Hernan (2013) relax the original SUTVA by allowing for the
existence of different unobservable versions of the treatment, as long as
there are no different versions of non-treatment. This permits assessing the
average effects of certain bundles of coupons (rather than specific coupons as
under the original SUTVA) vs. not receiving any coupons. Indeed, the
assumption that there is only one version of non-treatment is satisfied in our
analysis of the effect of receiving some vs. no coupons, under the assumption
that the marketer has not run any undocumented discount campaigns during the
study period. Furthermore, when assessing the effects of coupons applicable to
specific product categories, we control for any other coupons that each
customer received at treatment assignment, which again creates non-treatment
states which are necessarily equal after controlling for other coupons.

Table 1 and the tables in Appendix A show that the coupons were distributed
under consideration of the covariates in the customer registry. We must now
assume that the propensity of receiving a coupon (of a certain category)
differs only depending on observed characteristics, but not on characteristics
that are not available to us. This issue can be easily circumvent in practice
as long as the information on customers available to marketing campaign
planners is also available to those evaluating the campaign.

We point out that other aspects of SUTVA, namely the requirement that there
are no inter-personal or inter-temporal spillover effects, may also be
problematic in our setting. By including pre-campaign coupon reception and
redemption as control variables, we for this reason aim at accounting for
potential intra-personal spillovers, i.e. that previous coupons might
influence customer behavior in later periods. However, there could also exist
inter-personal spillovers, e.g. if customers receiving vouchers also induce
their peers to make purchases, for instance by telling peers about the
products bought when redeeming the voucher or by visiting the shop together
with peers. This appears particularly likely when there are several members of
the same household in the customer base. There is ongoing research on how to
deal with such SUTVA violations under specific assumptions like the
observability of groups that are affected by spillovers, see e.g.Sobel (2006),
Hong and Raudenbush (2006), Hudgens and Halloran (2008) Tchetgen and
VanderWeele (2012), Aronow and Samii (2017), Huber and Steinmayr (2021) and
Qu, Xiong, Liu, and Imbens (2021). However, in our dataset, the relationships
between customers are not observable, meaning the data does not allow
accounting for possible spillovers of treating one customer on the outcomes of
other customers. If such spillovers occurred in our case, they would likely
entail an underestimation of the effect of coupons on purchasing behavior.
This is due to the likely scenario that treated customers induce non-treated
peers to make purchases for the reasons previously mentioned, which entails an
overestimation of the outcome under non-treatment.

##  5 Causal Machine Learning

In the following, let $i\in\\{1,....,n\\}$ be an index for the $n=1,582$
customers in the dataset and $t\in\\{1,...,T\\}$ with $T=32$ an index for the
campaign period. Then, $\\{Y_{i,t},D_{i,t},X_{i,t}\\}$ denote the outcome, the
treatment and the covariates, respectively, for individual $i$ in campaign
period $t$. Treatment $D_{i,t}$ is a binary indicator measuring exposure to a
coupon campaign (of a specific type) and $Y_{i,t}$ denotes the outcome,
defined as average per-day expenditures of customer $i$ in period $t$. The
covariates $X_{i,t}$, all measured prior to or at the moment of treatment
assignment, include socio-economic variables (see Table 1) as well as the
average per-day expenditures in the period prior to the campaign $t-1$, i.e.
the pre-treatment outcome, and variables that measure both whether the
customer received coupons in $t-1$ and whether he/she redeemed any. For
estimating the effect of a particular coupon type, $X_{i,t}$ also includes
variables on which other coupon types were provided to the customer in $t$;
further, it not only includes information about whether the customer received
any coupons in $t-1$ but also about the type of coupons.

Under the identifying assumptions outlined in Section 4.2, the ATE $\Delta$
defined in equation (1) corresponds to $\theta$:

$\theta=E[\mu(D=1,X)-\mu(D=0,X)]$ (2)

where $\mu(D=d,X)$ denotes the conditional mean outcome given treatment state
$D=d$ and covariates $X$. As long as the function $\mu$ is of a known
functional form and $X$ is low-dimensional, we can estimate $\hat{\mu}(D,X)$
by regressing $Y$ on $D$ and $X$ and then determine the ATE according to
equation 2. However, the amount of data on customers available to marketers is
often extensive and the functional form of relationships between observable
customer characteristics and purchasing behavior is often unknown and complex.
It may, therefore, in many cases be preferable to use an approach that
integrates ML algorithms into the estimation of the causal effect in order to
take advantage of the functional flexibility and the ability to deal with
high-dimensional data inherent in ML algorithms. Put simply, ML algorithms are
used to estimate models for predicting $Y$ as a function of $D$ and $X$
($\mu(D,X)$) as well as for predicting the probability of being treated
conditional on $X$, which is commonly referred to as the propensity score
$p(X)=Pr(D=1|X)$. These predictions are then integrated into the estimation of
the treatment effects.

We assess the causal effect of receiving coupons (of a certain category) on
the average per-day expenditures by means of causal forests, a causal ML
method developed by Wager and Athey (2018) that draws on the ML technique of
random forests. While the causal forest framework primarily aims at estimating
treatment effect heterogeneity, i.e., how the effect of coupons is distributed
across different clients and time periods (see Section 5.1), the estimated
causal forests can also be used to estimate the ATE of coupon provision (see
Section 5.2). Both, the causal forest algorithm for assessing treatment effect
heterogeneity as well as the estimation procedure used for determining the
ATE, rely on combining orthogonal score based estimation with sample
splitting. While orthogonalization ensures robustness to regularization bias
in the models for estimating $\mu(D,X)$ and $p(X)$, in the following referred
to as plug-in parameters $\eta=(\mu_{D}(X),p(X))$, the purpose of the latter
is to avoid overfitting in the estimation of treatment effects. In Section
5.3, we utilize the estimated causal forest for determining the treatment
effect in different customer segments as defined by selected covariates. In
Section 5.4, finally, the estimated causal forest is used to determine which
customers should optimally be targeted with the different coupon campaigns.

###  5.1 Treatment Effect Heterogeneity

The causal forest approach by Wager and Athey (2018) is a modified version of
the regression forest algorithm aimed at determining splitting rules that
maximize the heterogeneity of treatment effects in the resulting subsamples.
The causal forest provides individual treatment effect estimates for every
observation in the sample, thereby providing an impression of the
heterogeneity in the effect of coupon provision across customers and campaign
periods.

Causal forests are built from causal trees just as random forests are built
from regression/classification trees. In order to learn a causal forest, the
algorithm repeatedly (2,000 times in our case) draws a random sample from the
data containing 50% of the observations in the dataset that then serves as
training data. Further, it generates a random subset of $min(\sqrt{(}k)+20,k)$
covariates, which in our case amounts to 28 of our $k=72$ covariates. Based on
the resulting sample and under consideration of the set of 28 covariates, it
estimates a causal tree as follows: the algorithm splits the sample at every
possible value of each covariate in the covariate subset; for every split, it
calculates the expected ATE in each of the two resulting subsamples and
determines the splitting rule that yields the largest difference in ATEs
across the two subsamples, where the subsamples obtained when using the
identified splitting rule are commonly referred to as nodes. In each of the
nodes, the algorithm again searches for the splitting rule that maximizes the
ATE heterogeneity between the resulting subsamples. This procedure is repeated
until it is no longer possible to split any final node of the tree in such a
way that the resulting nodes would contain at least 5 treated as well as 5
controlled observations and that they would differ in ATEs. The causal forest,
finally, is generated by averaging over all 2000 causal trees.

The ATE in the subsamples resulting from each potential split is estimated by
means of an approach proposed by Robinson (1988) that allows estimating the
ATE with $\sqrt{n}$ consistency. The approach builds on first predicting the
plug-in parameters $\eta=(\mu_{D}(X),p(X))$, where the plug-in parameters can
be estimated using any predictive ML algorithm as long as the plug-in
estimates converge at least at rate $n^{-1/4}$, and then using the predicted
plug-in parameters for estimating the ATE. In our case, the plug-in parameters
are predicted by means of regression forests with out-of-bag
prediction.333First, the sample is split into two subsamples, each of which is
used to learn regression forests for predicting $(\mu_{D}(X),$ and $p(X))$,
respectively. Then, in both subsamples, the plug-in parameters are estimated
using the forests learnt in the other subsample. The final estimate of the
plug-in parameters is obtained by averaging over the estimates from both
samples. In a second step, the algorithm calculates the residuals
$Y_{i,t}-\hat{\mu}_{D_{i,t}}(X_{i,t})$ and $D_{i,t}-\hat{p}(X_{i,t})$ for all
observations $i,t$ in the sample that is used for learning the causal tree.
Then, after performing all possible splits, it regresses
$Y_{i,t}-\hat{\mu}_{D_{i,t}}(X_{i,t})$ on $D_{i,t}-\hat{p}(X_{i,t})$ in each
of the resulting subsamples. That is, for every potential node, the algorithm
estimates the following function, where $\hat{\theta}$ denotes the estimated
ATE.

$Y-\hat{\mu}_{D}(X)=(D-\hat{p}(X))\hat{\theta}$ (3)

By comparing the estimated ATEs in all potential nodes, the algorithm
determines the splitting rule for which the estimated ATEs differ most between
the two resulting subsamples.

The approach of first predicting the plug-in parameters and then incorporating
them into the estimate of ATE as described above ensures that the estimate of
$\hat{\psi}$ is robust to slight approximation errors in the plug-in parameter
estimates that may arise from regularization biases.

The causal forest algorithm further addresses another source of bias, namely
overfitting, i.e. not only modelling the ATE but also random noise in the
training data. In order to prevent such overfitting bias, the sample used for
learning each causal tree is randomly split into two subsamples, one for
building the tree by following the above mentioned procedure while the other
one is used for estimating the treatment effect in every leaf node of the
learnt causal tree. That is, by following the splitting rules learnt in the
first subsample, the algorithm populates the leaf nodes of the estimated tree
with the observations from the second subsample and calculates the ATE in each
leaf node based on the observations that have fallen into the respective node.
Trees that are estimated based on this sample splitting procedure are commonly
referred to as “honest” trees.

For computational efficiency, the splitting rules are not determined by
estimating the ATEs in all possible subsamples; the algorithm rather
approximates the between-node ATE heterogeneity generated through every
potential split by means of a gradient for each observation. Then, the
algorithm involves several conditions for formulating splitting rules that aim
at avoiding imbalance in the size of the nodes. Explaining all these rules in
detail would go beyond the scope of this discussion, the manual to the grf
package however provides all the details (see Athey, Friedberg, Hadad,
Hirshberg, Miner, Sverdrup, Tibshirani, Wager, and Wright (2022)). In our
application, we keep all these options at their default values.

Through averaging over 2000 causal trees, the causal forest provides
estimations of individual-specific treatment effects for every point in $X$,
commonly referred to as Conditional Average Treatment Effect (CATE). To
account for the issue that the behavior of one and the same customer is in
general not independent across different campaign periods we cluster standard
errors at the customer level. The estimation is performed in the statistical
software R (R Core Team (2022)) by means of the causal_forest function
provided in the grf package by Athey, Friedberg, Hadad, Hirshberg, Miner,
Sverdrup, Tibshirani, Wager, and Wright (2022).

###  5.2 Average Treatment Effect

The estimated causal forest can further be used to estimate the ATE of coupon
provision and thus to assess the overall effectiveness of the coupons (and
that of selected coupon types). The ATE of coupon provision can be identified
in a similar manner to how the ATE is estimated for building causal trees.
First, the sample is randomly split into two subsamples. In one of the
subsamples, we derive the models for both plug-in parameters based on the
estimated causal forest. The other subsample is used to predict the plug-in
parameters and estimate the ATE using the orthogonalization approach by
Robinson (1988) described further above. Then, in order to take advantage of
all observations in the sample, the roles of both subsamples are switched and
the estimated ATE is obtained by averaging the estimates from both subsamples.
This approach of learning the prediction models in one subsample, predicting
the plug-in parameters in the other subsample and then switching the roles of
both subsamples is commonly referred to as cross-fitting.

Just as the approach for estimating CATEs, the estimation procedure for the
ATE addresses overfitting bias as well as regularization bias. The former is
avoided through cross-fitting, the latter through orthogonalization, i.e.
including the predicted plug-in parameters in the estimation in such a way as
to ensure that small estimation errors in either predictor result in an
overall negligible error and thus do not introduce bias in the estimation of
the ATE. Orthogonalization and cross-fitting are also central to the so-called
double machine learning (DML) framework of Chernozhukov, Chetverikov, Demirer,
Duflo, Hansen, Newey, and Robins (2018), another causal ML approach to
estimating the ATE. Both, the DML framework as well as the causal-forest based
procedure for estimating the ATE outlined above, ensure that the ATE is
estimated while maintaining $\sqrt{n}$ consistency, i.e. the estimated ATE
converges to the true ATE with a convergence rate of $1/\sqrt{n}$.

The estimation is performed in the statistical software R (R Core Team (2022))
by means of the average_treatment_effect function provided in the grf package
by Athey, Friedberg, Hadad, Hirshberg, Miner, Sverdrup, Tibshirani, Wager, and
Wright (2022) with standard errors clustered at the customer level.

###  5.3 Group Average Treatment Effects

In order to assess the impact of coupon provision in different customer
groups, we also estimate selected Group Average Treatment Effects (GATEs),
i.e., the average treatment effects in different subgroups as defined by age,
income, family size and pre-campaign expenditures, respectively. The variables
used to distinguish these subgroups are the age group and family size
variables as defined in the original dataset, a variable for average daily
expenditures that divides the sample into four subgroups of similar size, and
a variable measuring income in broader categories, each of which combines two
of the more fine-grained income groups of the original variable. Using a
doubly robust estimator with heteroscedasticity and cluster-robust standard
errors, we estimate a linear model of personalized treatment effects (CATEs)
as a function of one of the variables indicating which subgroup each client
belongs to (see Semenova and Chernozhukov (2021) for more details). This
approach also allows assessing effect heterogeneity in customer segments
defined by more than one variable, the score must simply be regressed on the
respective identifiers. We estimate the GATEs by means of the
best_linear_projection function provided in the grf-package.

###  5.4 Optimal Policy Learning

The optimal policy learning approach by Athey and Wager (2021) goes one step
further as it not only estimates the effect of coupon provision in selected
customer groups. It rather exploits the heterogeneity in coupon effects for
determining a coupon distribution rule that is optimal in the sense that it
maximizes the expected ATE. The coupon distribution rule distinguishes
customer segments as defined by observable customer characteristics that are
likely to positively change their purchasing behavior when receiving a coupon
from those customer groups that are not anticipated to respond positively to
the campaign. To put it formally, the algorithm learns a strategy for
distributing coupons $\pi$ that maps an individual’s characteristics $X_{i}\in
X$ to the binary treatment decision of whether or not to target the individual
with the coupon campaign: $\pi:X\rightarrow{0,1}$.

For learning the optimal coupon distribution, the algorithm uses the causal
forest to estimate the treatment effect for every observation in the dataset.
It then plugs these personalized treatment effects, $\hat{\psi}_{i,t}$, into
the following objective function that gives the expected ATE as a function of
coupon distribution rules $\pi$:

$\phi=argmax\Bigg{\\{}\frac{1}{N*T}\sum_{i\in{1,...,N}}{}\sum_{t\in{1,...,T}}(2\pi(X_{i,t})-1)\hat{\psi}_{i,t}:\pi\in\Pi\Bigg{\\}}$
(4)

In order to find the distribution rule that maximizes the objective function,
the algorithm calculates the value of the objective function for each possible
covariate-defined sample split into groups of coupon receivers and non-
receivers. That is, the first step is to split the sample into two subsamples
at every possible value of each covariate, calculate the expected ATE for
defining each of the two resulting groups as coupon recipients, and determine
the splitting rule for which the largest ATE is expected. Then, the same is
done for each of two resulting subsamples and the procedure is repeated as
many times as specified by the researcher. The resulting coupon distribution
rule can be represented as a decision tree, i.e., a tree-shaped graph
indicating at which values of which observed characteristic to split the
sample and which of the resulting subsamples to give a coupon.

We estimate depth-3 decision trees representing the optimal distribution of
each coupon category by means of the R (R Core Team (2022)) policytree package
by Sverdrup, Kanodia, Zhou, Athey, and Wager (2020) using all customer
characteristics available in the dataset, i.e., the customers’ age and income
group, family size, marital status and dwelling type, as well as the pre-
campaign average daily expenditures. Since the algorithm performs a sample
split at every possible value of each covariate, i.e., at each observed value,
continuous variables can cause performance issues by driving up the number of
sample splits. We, therefore, round the pre-campaign average daily
expenditures to round values, namely to nearest 50 for values between 0 and
1,000 and to the nearest 100 for values between 1,000 and 2,000. Further, we
group all 157 observations with 2,000 or more average daily expenditures into
one category. This way, we capture pre-campaign differences in purchasing
behavior well while substantially reducing the number of sample splits that
need to be performed.

##  6 Empirical Results

###  6.1 Treatment Effect Heterogeneity

Figure 1 shows the distribution of the individual treatment effects (across
all customers and time periods) as estimated by means of the causal forest
algorithm. We can see that the treatment effect of being provided with any
coupon is positive for the vast majority of observations and ranges - except
for some outliers - between -100 and 200 monetary units. Similarly, provision
of grocery coupons and coupons applicable to drugstore products have a
positive effect for the majority of observations. The distribution of coupons
applicable to ready-to-eat food and other products however seem to be rather
centered around zero, with the estimated effect being positive for about half
of the observations and negative for the other half. For plant and flower
coupons, we can even observe a negative effect on daily expenditures for the
majority of observations. The plots suggest greater heterogeneity in the
treatment effects of the individual coupon categories than when all coupons
are analyzed together. It appears that the effects of the different coupon
categories cancel each other out to some extent when combined in one analysis,
suggesting that the different coupon categories should best be analyzed
separately.

The differences in individual treatment effects as revealed by the causal
forest approach suggest to not just assess the ATE, as is done in Section 6.2.
Rather, it also invites to analyze how the effect of coupons from certain
categories differs between customer groups as defined by covariates $X$
(Section 6.3) and to learn an optimal coupon distribution scheme that
maximizes the expected ATE of coupon provision (Section 6.4).

Figure 1: Distribution of CATE by coupon type.

###  6.2 The Causal Effect of Receiving Coupons

Table 2 shows the estimated ATE of receiving any coupon as well as that of
receiving coupons from each of the five coupon categories. The results show
that receiving any coupon has a positive and statistically significant effect
on daily expenditures. Providing a customer with a coupon increases her
expected daily expenditures by some 45 monetary units. The effect estimates
for the different coupon categories provide a more nuanced picture. Provision
of coupons for grocery and drugstore items has a statistically significant
positive effect on daily expenditures. Receiving coupons that belong to these
categories increases expected average daily expenditures during the validity
period by some 74 and 60 monetary units, respectively. Handing out coupons
applicable to plants and flowers, on the other hand, is estimated to decrease
a customer’s expected average daily expenditures by some 50 monetary units,
with this results also being statistically significant. The estimated ATE of
providing coupons from the other two categories does not have a statistically
significant effect on customers’ expected daily spending, with the estimated
effect of coupons for ready-to-eat foods being positive but close to zero and
that of coupons for products from other categories being slightly negative. A
possible explanation for the insignificant or significantly negative effect of
these latter three coupon types is that receiving such coupons does not
incentivize people to buy, but that such coupons are mainly used for products
that the coupon recipient would have bought anyway.

| Coef. | Standard Error | Sign. Level
---|---|---|---
ATE: Receiving any coupon | 45.27 | 6.969 | ***
ATE: Receiving coupon for ready-to-eat food | 8.50 | 20.063 |
ATE: Receiving coupon for groceries | 74.46 | 22.118 | ***
ATE: Receiving coupon for plants/flowers | -49.54 | 24.054 | *
ATE: Receiving coupon for drugstore items | 60.20 | 19.891 | **
ATE: Receiving coupon for other | -6.81 | 15.371 |
Table 2: ATE of receiving any coupon as well as the ATEs of receiving coupons
applicable to specific product categories, each with standard error and
significance level. Significance levels: . p<0.1, * p<0.05, ** p<0.01, ***
p<0.001.

Despite not having a statistically significant effect on the overall customer
base, the provision of coupons of these latter categories could still
significantly increase the expenditures of certain customer groups. Similarly,
providing coupons applicable to grocery or drugstore items could have a
significant impact on purchasing behavior only among certain subgroups of
customers. For this reason, the next section examines effect heterogeneity
with regard to selected customer characteristics.

###  6.3 Group Average Treatment Effects

In this section, we assess how the provision of coupons affects different
customer groups. We illustrate how the effect of providing coupons differs
depending on the customers’ age, income, family size and pre-campaign
expenditures. Further, We also examine the GATEs of those coupon categories
with a highly statistically significant ATE, i.e., grocery and drugstore
coupons.

Figure 2: GATEs of receiving any coupon with 95% confidence interval.

Figure 3 shows the GATEs of receiving any coupon by age, income, family size
and pre-campaign expenditures, respectively. The graphs show that providing
coupons has a positive effect on purchasing behavior in almost every customer
group, but that in most subgroups the effect of coupons is not statistically
significant. The effect of providing coupons tends to be particularly large
among low-income customers, customers from smaller households and among those
who made no purchases in the period prior to the campaign.

Figure 3: GATEs of grocery coupons with 95% confidence interval.

The GATE charts in Figure 3 show that in all subgroups considered, the
provision of coupons for grocery items has a positive, in many cases
statistically significant, effect on daily spending. The most pronounced
differences in GATEs can be found between the customer subgroups defined by
average daily spending prior to the campaign period. The effect of grocery
coupons tends to be positive and statistically significant for previously
inactive customers, while it is close to zero for customers with high pre-
period spending. This may suggest that grocery coupons have the potential to
reactivate dormant customers. This hypothesis is also supported by the fact
that the provision of grocery coupons has a relatively large statistically
significant444the small confidence interval around this GATE estimator can be
explained with the large number of observations with no information on socio-
economic characteristics available effect among customers for whom information
on socioeconomic characteristics is not available. Customers for whom no
information is available may be more likely to have low loyalty/commitment to
the store and to be rather inactive customers who can be reactivated by the
provision of grocery coupons. From these results, we can deduce the hypothesis
that the grocery coupons provided by the retailer are efficient for inactive
and non-frequent customers, while they have little effect on the purchasing
behavior of frequent shoppers or even lead to crowding out effects.

Figure 4: GATEs of drugstore coupons with 95% confidence interval.

Figure 4 displays the GATEs of receiving any coupon by age, income, family
size and pre-campaign expenditures, respectively. The graphs show that
providing drugstore coupons has a positive effect on daily spending for almost
all subgroups considered, and that the effect is statistically significant in
most cases. We can see that the largest difference from the GATE estimates for
grocery coupons is in the GATEs by pre-campaign spending. The effect of
drugstore coupons on daily spending is larger the higher the customer’s pre-
campaign spending, while we find the reverse pattern for grocery coupons. This
suggests that grocery coupons are more efficient in re-activating dormant
customers and drugstore coupons in retaining frequent shoppers. The GATE plots
for the other three coupon categories can be found in Appendix B.

While ML-based estimation of ATEs and GATEs is an excellent tool for
evaluating the effect of coupon campaigns, it is not the best choice for
deriving strategies for later coupon campaigns. For this purpose, the optimal
policy learning framework by Athey and Wager (2021) is by far the better
choice as it determines which customer groups to provide with coupons in order
to maximize the ATE.

###  6.4 The Optimal Distribution of Coupons

Figure 5 shows the optimal distribution rules for each coupon category. The
optimal distribution rule for ready-to-eat food coupons (decision tree (a))
suggests to provide customers who spent 100 or less monetary units per day in
the pre-campaign period with ready-to-eat food coupons if they are not older
than 45 years, if their age is unknown555Please note that for family size, age
group and income group the value zero denotes that information about these
variables is unavailable, see also the data description in Section 3 or if
they are older than 55 years and live in a single household. The retailer
should further provide ready-to-eat food coupons to all customers with average
pre-campaign spendings of 100 to 300 monetary units per day as long as their
marital status is known. Customers younger than 36 years and those whose age
is unknown should receive coupons even if their spendings in the pre-period
exceeded 300 monetary units per day.

The optimal distribution rule for grocery coupons (decision tree (b)) proposes
to provide grocery coupons to those customers with low or very low income as
well as to those whose income is unknown, if their average spendings at the
store did not exceed 350 monetary units per day in the period prior to the
campaign and/or if they spent more than 400 monetary units daily and own the
dwelling they live in. Customers belonging to income groups 5 and 6 (lower
middle income) should receive grocery coupons if their average daily spending
in the period prior to the campaign did not exceed 400 monetary units.
Customers with higher middle to very high income, finally, should receive
grocery coupon independently of their pre-campaign expenditures at the store
and their living situation.

The distribution rules paint a similar picture as the GATE estimates in
Section 6.1 about which customer groups are likely to be positively impacted
by the provision of certain coupon types. In contrast to the assessment of
effect heterogeneity across pre-specified broad categories in Section 6.1, the
optimal policy learning algorithm finds the covariate values at which the
sample should optimally be split to maximize the ATE and defines groups of
coupon recipients and non-recipients based on multiple covariates.

The other decision trees can be interpreted accordingly. A look at the
covariates used for sample splitting in those other decision trees shows that
each observed customer characteristic but the marital status is used for
distribution rules of at least one coupon type.

(a) (b) (c) (d) (e)

Figure 5: Depth-3 trees for coupons applicable to (a) ready-to-eat food, (b)
groceries, (c) drug store items, (d) plants and flowers as well as (e) other
products.

###  6.5 Robustness Checks

As described in Section 3, our dataset contains a large number of observations
with missing socio-economic information. To investigate the robustness of our
results with respect to these missing values, we performed the entire analysis
on a reduced dataset containing only observations of customers whose
socioeconomic background is known, i.e., on a dataset with 13,792 observations
on the purchasing behavior of $n=431$ individuals. The estimated ATEs can be
found in Table 3. They are close to the ATE estimates from the full dataset,
although the standard errors are of course considerably larger - due to the
much smaller number of observations.

| Coef. | Standard Error | Sign. Level
---|---|---|---
ATE: Receiving any coupon | 46.27 | 13.97 | ***
ATE: Receiving coupon for ready-to-eat food | 7.70 | 39.754 |
ATE: Receiving coupon for groceries | 73.89 | 37.908 | .
ATE: Receiving coupon for plants/flowers | -35.14 | 38.517 |
ATE: Receiving coupon for drugstore items | 24.99 | 39.59 |
ATE: Receiving coupon for other | -7.94 | 24.335 |
Table 3: ATE of receiving any coupon as well as the ATEs of receiving coupons
applicable to specific product categories in the reduced dataset (without
observations with missing socio-economic information), each with standard
error and significance level. Significance levels: . p<0.1, * p<0.05, **
p<0.01, *** p<0.001.

The GATE and policy tree plots are provided in Appendix C. The GATE plots show
similar patterns in how different customer groups are affected by each coupon
type, although of course they are not exactly identical with the GATEs
estimated in the full sample. The policy tree plots show that the splitting
rules are based on a similar set of variables with similar cutting points as
those estimated in the full dataset. These results suggest that the large
number of observations with missing socio-economic information does not
introduce systematic bias into the estimation of the treatment effects and the
optimal coupon distribution scheme.

##  7 Conclusion

The paper has presented different causal ML methods with multiple potential
applications in marketing research and business development. The application
of these methods to evaluate a retailer’s coupon campaign and optimize the
distribution of coupons has illustrated their potential in identifying the ATE
of coupon provision, effect heterogeneity, as well as optimal coupon
distribution rules. The proposed causal ML methods can further be applied to
evaluate and optimize a variety of other marketing and business strategies,
requiring only observational data from the context of previous campaigns or
business decisions, and utilizing all available (big) data, whether structured
or unstructured. Other potential applications for the proposed causal ML
methods are the evaluation and optimization of targetable (online) marketing
campaigns, loyalty programs and campaigns handling customer attrition but also
the assessment of different employee benefit plans, designs of job postings or
in-house training programs. The potential use cases of causal ML in business
and marketing are manifold.

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Appendices

##  A Descriptive Statistics

| ready-to-eat food coupons | grocery coupons | plant/flower coupons
---|---|---|---
variable | received | not received | received | not received | received | not received
daily expenditures | 233 | 253 | 241 | 335 | 228 | 246.3
age: 18-25 | 0.034 | 0.029 | 0.031 | 0.033 | 0.024 | 0.032
26-35 | 0.104 | 0.101 | 0.099 | 0.159 | 0.082 | 0.104
36-45 | 0.14 | 0.142 | 0.142 | 0.132 | 0.133 | 0.142
46-55 | 0.194 | 0.19 | 0.191 | 0.208 | 0.225 | 0.188
56-70 | 0.048 | 0.043 | 0.046 | 0.029 | 0.047 | 0.045
70+ | 0.045 | 0.035 | 0.04 | 0.021 | 0.055 | 0.037
unknown | 0.437 | 0.46 | 0.452 | 0.418 | 0.434 | 0.452
family size: 1 | 0.174 | 0.17 | 0.172 | 0.164 | 0.188 | 0.17
2 | 0.228 | 0.202 | 0.215 | 0.175 | 0.235 | 0.211
3 | 0.081 | 0.078 | 0.078 | 0.092 | 0.059 | 0.081
4 | 0.039 | 0.04 | 0.038 | 0.073 | 0.035 | 0.04
5+ | 0.041 | 0.05 | 0.045 | 0.078 | 0.049 | 0.046
unknown | 0.437 | 0.46 | 0.452 | 0.418 | 0.434 | 0.452
marital status: married | 0.249 | 0.223 | 0.235 | 0.207 | 0.256 | 0.232
unmarried | 0.083 | 0.085 | 0.084 | 0.097 | 0.076 | 0.085
unknown | 0.669 | 0.691 | 0.681 | 0.696 | 0.668 | 0.683
dwelling type: rented | 0.032 | 0.034 | 0.032 | 0.06 | 0.028 | 0.034
owned | 0.531 | 0.506 | 0.516 | 0.521 | 0.539 | 0.514
unknown | 0.437 | 0.46 | 0.452 | 0.418 | 0.434 | 0.452
income group: 1 | 0.051 | 0.036 | 0.043 | 0.022 | 0.069 | 0.039
2 | 0.049 | 0.052 | 0.05 | 0.057 | 0.046 | 0.051
3 | 0.047 | 0.05 | 0.049 | 0.041 | 0.032 | 0.051
4 | 0.121 | 0.108 | 0.111 | 0.164 | 0.125 | 0.112
5 | 0.138 | 0.137 | 0.137 | 0.14 | 0.131 | 0.138
6 | 0.063 | 0.06 | 0.062 | 0.052 | 0.065 | 0.061
7 | 0.025 | 0.022 | 0.023 | 0.016 | 0.028 | 0.022
8 | 0.03 | 0.03 | 0.03 | 0.038 | 0.034 | 0.03
9 | 0.021 | 0.027 | 0.023 | 0.043 | 0.025 | 0.024
10 | 0.009 | 0.005 | 0.006 | 0.008 | 0.003 | 0.007
11 | 0.002 | 0.004 | 0.003 | 0 | 0.002 | 0.003
12 | 0.008 | 0.011 | 0.01 | 0 | 0.006 | 0.01
unknown | 0.437 | 0.46 | 0.452 | 0.418 | 0.434 | 0.452
coupons redeemed | 0.044 | 0.02 | 0.031 | 0.006 | 0.037 | 0.029

Table A.1: Mean of the variables among the treated who received a coupon of a certain category and of those who did not | drug store item coupons | other coupons
---|---|---
variable | received | not received | received | not received
daily expenditures | 243 | 282 | 249 | 242.36
age: |  |  |  |
18-25 | 0.031 | 0.031 | 0.036 | 0.029
26-35 | 0.104 | 0.055 | 0.114 | 0.096
36-45 | 0.142 | 0.126 | 0.153 | 0.136
46-55 | 0.191 | 0.203 | 0.198 | 0.188
56-70 | 0.046 | 0.034 | 0.047 | 0.044
70+ | 0.039 | 0.035 | 0.039 | 0.039
unknown | 0.447 | 0.517 | 0.413 | 0.468
family size: |  |  |  |
1 | 0.172 | 0.164 | 0.178 | 0.168
2 | 0.215 | 0.175 | 0.227 | 0.206
3 | 0.08 | 0.069 | 0.083 | 0.077
4 | 0.04 | 0.034 | 0.044 | 0.037
5+ | 0.047 | 0.042 | 0.054 | 0.043
unknown | 0.447 | 0.517 | 0.413 | 0.468
marital status: |  |  |  |
married | 0.235 | 0.217 | 0.264 | 0.219
unmarried | 0.085 | 0.079 | 0.074 | 0.089
unknown | 0.681 | 0.704 | 0.662 | 0.691
dwelling type: |  |  |  |
rented | 0.032 | 0.051 | 0.03 | 0.035
owned | 0.521 | 0.432 | 0.557 | 0.497
unknown | 0.447 | 0.517 | 0.413 | 0.468
income group: |  |  |  |
1 | 0.041 | 0.053 | 0.052 | 0.037
2 | 0.051 | 0.04 | 0.05 | 0.051
3 | 0.05 | 0.035 | 0.048 | 0.05
4 | 0.114 | 0.095 | 0.119 | 0.111
5 | 0.138 | 0.118 | 0.154 | 0.129
6 | 0.062 | 0.055 | 0.065 | 0.06
7 | 0.023 | 0.019 | 0.023 | 0.023
8 | 0.031 | 0.018 | 0.031 | 0.03
9 | 0.024 | 0.029 | 0.022 | 0.025
10 | 0.006 | 0.006 | 0.009 | 0.005
11 | 0.003 | 0.005 | 0.004 | 0.003
12 | 0.01 | 0.009 | 0.011 | 0.009
unknown | 0.447 | 0.517 | 0.413 | 0.468
coupons redeemed | 0.031 | 0.005 | 0.045 | 0.022
Table A.2: Mean of the variables among the treated who received a coupon of a
certain category and of those who did not

##  B GATE Estimates for Coupons Applicable to Plants, Drugstore Items and
Other Products

Figure B.1: GATEs of ready-to-eat food coupons with 95% confidence interval.

Figure B.2: GATEs of plant/flower coupons with 95% confidence interval.

Figure B.3: GATEs of other coupons with 95% confidence interval.

##  C Robustness Checks

###  C.1 Reduced Dataset: GATE Estimates

Figure C.4: GATEs of receiving any coupon with 95% confidence interval,
estimated in reduced dataset.

Figure C.5: GATEs of ready-to-eat food coupons with 95% confidence interval,
estimated in reduced dataset.

Figure C.6: GATEs of grocery coupons with 95% confidence interval, estimated
in reduced dataset.

Figure C.7: GATEs of plant/flower coupons with 95% confidence interval,
estimated in reduced dataset.

Figure C.8: GATEs of drugstore coupons with 95% confidence interval, estimated
in reduced dataset.

Figure C.9: GATEs of other coupons with 95% confidence interval, estimated in
reduced dataset.

###  C.2 Reduced Dataset: Policy Trees

(a) (b) (c) (d) (e)

Figure C.10: Depth-3 trees for coupons applicable to (a) ready-to-eat food,
(b) groceries, (c) drug store items, (d) plants and (e) other, estimated in
reduced dataset.