Dutch healthcare industry, correcting
for sample selection bias
Master’s thesis Econometrics, Operations Research and Actuarial Studies
Laura Oudman
S2992337
23 April 2017
Master’s Thesis Econometrics, Operations Research and Actuarial Studies
Supervisor: prof. dr. T.H.A. Bijmolt
Co-assessor: prof. dr. L. Spierdijk
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Abstract
Health insurance companies aim to minimize the amount of customers that leave at the end of their contract period (i.e., customer churn). In this study, we estimate the effects of participation and different forms of collection and redemption behavior in a loyalty program (LP) on customer churn in the Dutch health insurance industry. Prior studies showed that in general customers who are participating in a LP, churn less. We use data from the health insurance company Menzis about its LP SamenGezond, gathered in 2015 and 2016. Menzis is with 2.2 million policyholders in 2016 a large player in the Dutch health insurance market.
Customers are not randomly assigned to participate in the LP, they decide themselves to participate or not. Presumably, unobserved variables influence both the decision to participate in the program and the decision to churn. Hence, estimates of the effect of LP membership on churn will contain sample selection bias; LP membership is in that case a endogenous variable. When not correcting for sample selection bias, estimates of the effects of participation and different forms of collection and redemption behavior in a loyalty program on customer churn are inconsistent.
We first estimate a so-called main effect ‘churn model’ to estimate the overall effect of participation in a LP on churn. Not correcting for sample selection bias leads to an estimated significant positive effect of participation on churning probability (which means that the program leads to increased churn). After this, we estimate the parameters of a main effect bivariate probit model, where the decision to churn and the decision to participate in the LP are modelled simultaneously to correct for sample selection bias. We find evidence that LP membership decreases churn. Diagnostic tests lead to the conclusion that LP membership is indeed endogenous and the bivariate model is thus the correct specification.
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Table of Contents
Abstract ... 1
1. Introduction ... 4
2. Literature review ... 7
2.1 Loyalty and loyalty programs ... 7
2.2 Sample selection bias in LPs ... 8
2.3 Expected effect of participation in a LP ... 9
2.4 Expected effect of different forms of collecting ... 9
2.4.1 Expected effect of active point collection ... 10
2.4.2 Expected effect of passive point collection ... 11
2.5 Expected effect of different forms of redemption ... 11
2.5.1 Expected effect of month of redemption ... 12
2.5.2 Expected effect of cash rewards ... 12
2.5.3 Expected effect of point-only versus copayment ... 12
3. Data & model ... 14
3.1 Data description ... 14 3.1.1 Churn ... 15 3.1.2 LP membership ... 15 3.1.3 Point collection ... 15 3.1.4 Point redemption ... 15 3.1.5 Control variables ... 16 3.2 Data characteristics ... 17 3.3 Model ... 18 3.3.1 Model ... 18 3.3.2 Instrumental variables ... 20 3.4 Data analysis ... 22 4. Results ... 23 4.1 Main effect ... 23 4.2 Interaction effects ... 25
4.2.1 Effects of collection behavior ... 25
4.2.2 Effects of redemption behavior ... 25
4.2.3 Graphic representation ... 26
4.3 Model evaluation ... 27
4.4 Effect of control variables on churn ... 28
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5. Conclusion & discussion ... 30
5.1 Conclusion ... 30
5.2 Limitations & further research ... 32
Literature ... 34
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1. Introduction
Since 1 January 2006 all Dutch residents are obligated to buy a standardized health insurance package from a private health insurance company. In general, consumers are allowed to switch from health insurance provider only at the end of each year. When a consumer leaves a company this is called “customer churn”. In the past three years the market switch percentages for health insurance companies in the Netherlands at the end of the year were 6,5% (2013), 6,8% (2014) and 6,3% (2015) (Vektis, 2014, 2015, 2016), which boils down to more than a million churning customers per year. Health insurance companies aim to have a large and balanced customer base to maximize their profits. A large customer base can be achieved in two ways: retaining customers and attracting new customers. To maximize their profits, retaining their customers is essential for health insurance companies.
Churning behavior is a measure of behavioral loyalty. One way to increase customers’ loyalty might be to start a loyalty program (LP): empirical findings generally indicate positive effects of loyalty programs on customer retention (Bijmolt et al., 2011). The SamenGezond (SG) program, started by Menzis is 2012, is the only LP in the Dutch healthcare industry. Menzis is the fourth largest health insurance company in the Netherlands, with 2.2 million policyholders (Vektis, 2016). In this thesis, we use this program as a case study.
Since starting a LP is costly for an organization, the firm wants to examine whether participating in the program indeed leads to increased customer loyalty. Without controlling for other characteristics, the churning probability at the end of 2015 was 3.0% for non-participants of SamenGezond, whereas this percentage was 5.0% for participants of SamenGezond. Correcting for characteristics like age, gender etc. in a probit model also lead to significant higher churning probabilities for members of SG. This can be caused by sample selection bias: customers are not randomly subscribed for the program, but choose themselves. Perhaps customers who are more likely to churn anyhow, are also more (or less) likely to sign up for the SG program. When there is sample selection bias and we do not correct for this, estimates of the effects of participation and different forms of collection and redemption behavior in a loyalty program on customer churn are inconsistent.
Knowledge of what behavior of participants within the LP leads to more behavioral loyalty can be useful to set up effective LPs or to improve existing LPs. If specific behavior in a LP leads to more or less behavioral loyalty, health insurance companies can anticipate to this to maximize the effectiveness of the LP.
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churn ratio. We do this by answering the research questions (RQs) below. We first investigate the effect of participation itself.
RQ1: What is the effect of participating in a loyalty program in the Dutch healthcare industry on
churn ratio?
In most LPs, participants can earn points both actively or automatically. Active point collection might be by buying items from the store that offers the LP and earning promotional currency for that. An example of automatic point collection is when the participant earns points at the start of each year. Since points are related to monetary value, the company that sets up a LP aims to be effective in handing out points. Both active and automatic point collection could have effects on the churn ratio. This leads to the second research question:
RQ2: What are the effects of active and of automatic point collection in a loyalty program in the
Dutch healthcare industry on churn ratio?
Customers do not participate in a LP if there are no rewards. Knowing the effect of different characteristics of redemption (timing, type of reward) on customer churn leads to useful insights for a company that owns a LP. The timing of redemption might be important, because certain redemption behavior might lead to certain churn behavior through the year. Hence, the third research question is:
RQ3: What is the effect of month of redemption in a loyalty program in the Dutch healthcare
industry on churn ratio?
In some LPs the participants can redeem promotional currency for cash. Dorotic et al. (2012, p. 228) argue that “cash rewards are often inefficient for a firm since they offer high unit costs”. It is thus essential for a firm to investigate whether cash rewards are effective. This leads to the fourth research question:
RQ4: What is the effect of redeeming points for cash rewards compared to non-cash rewards in a
loyalty program in the Dutch healthcare industry on churn ratio?
Some LPs offer the option of copayment. Some rewards can only be ‘bought’ with promotional currency, whereas other gifts can be bought with a combination of promotional currency and cash. We aim to gain insights of the effects of these different types of rewards on customer churn. This results in the last research question:
RQ5: What is the effect of redeeming points for rewards with copayment, compared to rewards
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2. Literature review
In this section we provide a theoretical background of the definition of loyalty and loyalty programs, and formulate our hypotheses, based on prior studies.
2.1 Loyalty and loyalty programs
Customer loyalty is defined as the likelihood to buy from a specific brand or firm. Following Bijmolt et al. (2010), we adopt the framework for customer loyalty derived by Dick and Basu (1994). Dick and Basu state that customer loyalty has two dimensions: behavioral loyalty and attitudinal loyalty. Measures of behavioral loyalty are for example probability of purchase, purchase sequence and purchase volume. Attitudinal loyalty refers to how much the customer favors the brand or firm. In our study, we focus on behavioral loyalty. According to Dick and Basu behavioral loyalty is driven by attitudinal loyalty. In this study, we use “customer churn” (i.e., customers who discontinue their contract at the firm) as a measure for behavioral loyalty. Minimizing customer churn is an important challenge for many firms. To understand and/or predict churning behavior, churn models have received a lot of attention in literature for many types of industries, among others: telecom (Ahn et al., 2006; Hung et al., 2006; Richter et al., 2010), financial services (Larivière & van den Poel, 2004), banking (Mutanen, 2006) and insurance (Günter et al., 2014; Saunders & Alexander, 2009).
In the Netherlands it is in general only possible to switch from health insurance provider at the end of the year. Therefore customer churn is in this context defined as customers who are insured at the firm in December of the past year but not in January in the new year, leaving out the people who are deceased in that period.
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with the earned points. Fifth, the LP provider should offer LP members special offers: participants can choose in the webshop a discount on their additional insurance. Also direct mailings are send to participants with information about health.
2.2 Sample selection bias in LPs
In this study we examine the effect of participation in a LP on customer churn. We take into account that customers are not randomly assigned to participate in the program, but they choose themselves, which is called self selection (Heckman, 1979). Perhaps customers who are more likely to churn anyhow, are more (or less) likely to sign up for the LP. Previous studies have shown that participants and non-participants of a LP are a different kind of consumer: for instance, Meyer-Waarden and Benavent (2009) found, by using longitudinal scanner-panel data, that heavier, more frequent customers of a grocery store enroll more often in the grocery stores’ loyalty program. Heckman (1979) argues that when estimating the effect of “treatment” (in this case: LP participation), one should correct for the fact that members are not randomly selected, to avoid sample selection bias.
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is modelled by using different instruments, for example ‘if the customer watched world cup soccer matches in 2010’ (all premiums were related to the matches).
In sum, prior studies show that when estimating the effect of participation in a LP on customer churn, correcting for sample selection bias might lead to more accurate effect estimates. Some authors did this by using 2SLS and others by a CF approach.
2.3 Expected effect of participation in a LP
Many researchers argued that LPs positively affect behavioral loyalty (Eason et al., 2015; Leenheer et al., 2007; Taylor & Neslin, 2005) and especially negatively affect customer churn, which means the LP is effective (Bolton et al., 2000; Verhoef, 2003). Bijmolt et al. (2010) find in general negative effects of a LP on consumer churn, also in industries with high exit barriers, such as a healthcare insurer. Bolton et al. (2000) found that members of a firm’s LP value the quality and service of the company higher than non-members, and thus are more likely to stay at the company although another firm offers a better service or price. Participants feel as if they get more service for the price they are paying than non-participants. Verhoef (2003) concludes that LPs that create economic incentives, such as rewards and pricing discounts, have a small but negative effect on customer churn.
Based on the above literature we formulate the following hypothesis: H1: Participating in a LP decreases churn.
2.4 Expected effect of different forms of collecting
Participants in LPs can often collect points by active or passive behavior. In the LP that we study, we make a distinction of 4 collecting categories: in an automatic way, by questionnaire, by the use of apps or by other activities.
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of apps. When for example a member installs the app ‘Runkeeper’ and walks at least one kilometer (confirmed by this app) the member earns 25 points. The last category are other activities, such as the ‘health check’, where the participants fill in an extensive questionnaire to receive an advise to improve their health.
We define active point collection as points where the customer has to perform an action right before getting the points. These collection activities are in the category ‘apps’ or ‘other activities’. We define passive point collection as point transactions where the customer does not have to act in order to get the points. These collection transactions are in the categories ‘automatic’ and ‘questionnaire’ in this case. Table 1 is a graphic overview of the different point collection categories. Table 12 in the Appendix shows for every collection possibility its category.
Point collection
Passive Active
Automatic Questionnaire Apps Other activities
Table 1 Point collection categories
In the next two sections we describe the expected effects of those two different collection behaviors on customer churn .
2.4.1 Expected effect of active point collection
By performing activities in a LP the member gets more promotional currency (often points). Bijmolt et al. (2010) argue that owning more promotional currency in a LP will lead to more activities because of the points-pressure mechanism: “the closer members feel to obtaining a reward, the more likely they will make additional purchases to gain the reward” (Bijmolt et al., 2010, p. 203). The LP studied is not a standard LP, where purchases at the firm lead to promotional currency and thus these purchases themselves are a measure of behavioral loyalty. The LP we study rewards healthy activities (e.g. participating in a running race) instead of purchases. However, we expect that the more (active) points members collect, the healthier they become and for this reason like the program and firm more. This expected increase in attitudinal loyalty will lead to more behavioral loyalty and thus to less churn.
Apart from the economic incentives created by the point-pressure mechanism, more collected points will lead to a creation of psychological incentives: “as members learn how to use a LP, they become more efficient in the use of the LP. This may increase psychological barriers due to increased motivation and perceived selfefficacy” (Bijmolt et al., 2010, p. 213). We assume that this, like the economic incentives, leads to more attitudinal loyalty and thus more behavioral loyalty. Hence, we formulate the following hypothesis:
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2.4.2 Expected effect of passive point collection
For passive point collection, the customer does not have to act in order to get the points. In the studied LP, these collection transactions are in the categories ‘automatic’ and ‘questionnaire’. We expect that passive point collection leads to more active behavior in the LP because of the point pressure mechanism, and thus to less churn, as explained in the previous section. Attitudinal loyalty (and as a consequence, behavioral loyalty) can also increase because the member is grateful to the firm and for this reason more committed.
However, Capizzi and Ferguson (2005, p. 73) find that in LPs “active program participation rates are modest in many sectors, with typically only 20-25 percent of enrolled members earning or redeeming promotional currency within the past 12 months”. Bolton et al (2000) studied a LP of a worldwide financial services company and found that 43% of the LP members had zero transactions in the past 12 months, and another 36% had 1-5 transactions in that period of time. Thus, being a member in a LP does certainly not mean that the customer is actively participating in the program. In most LPs (as well in the LP studied in this thesis) members get points in an automatic way (automatic point collection), for example when it’s the birthday of the member. This kind of point endowment might not be noticed by the member when he does not check his account. For these members, passive point collection might not lead to more loyal behavior, since the raise in points might not even be noticed.
Overall, we expect that passive point collection leads to more loyalty. H2B: Passive point collection decreases churn.
2.5 Expected effect of different forms of redemption
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2.5.1 Expected effect of month of redemption
A health insurance policy is a contract for a whole year (January until December). In November the premiums for the next year are announced by the healthcare insurer. We assume that a part of the LP members are considering to switch to another insurer from that moment on. When members know that they are going to switch, they may redeem their points. However, there can also be members who redeem points in November and December and have no intentions to churn. Redeeming points in November and December might decrease the negative impact on churn, or even turn the effect into a positive one, that is, it increases churn. We expect that redeeming points in the other months negatively affect churn because of the rewarded behavior mechanism explained above. This reasoning leads to the following hypothesis.
H3: Redeeming points in January until October decreases churn, whereas redeeming points in November and December increases churn.
2.5.2 Expected effect of cash rewards
The firm offering a LP can choose to offer a cash reward. In the LP studied in our study, participants can choose to redeem points to obtain a 15 or 30 euro discount on its additional insurance. Since the participant is obligated for its additional insurance the whole year, this discount can be seen as a cash reward; especially because the 15 or 30 euro is transferred to the participants’ bank account.
According to Nunes and Drèze (2006, p. 128-129), customers “respond more dramatically to performance incentives that promise pleasure (like luxe vacations (…)) than to purely utilitarian incentives (like cash bonuses)”. As Dorotic et al. (2012, p. 228) argue, cash rewards “may draw attention away from the brand and move it toward the reward, which induces spurious loyalty and decreases customers’ intrinsic relationship motivation”. We formulate the following hypothesis:
H4: Redeeming points for cash rewards increases churn more than redeeming points for other rewards.
2.5.3 Expected effect of point-only versus copayment
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loyalty. We thus expect redeeming points for rewards for point-only products decreases churn more than redeeming points for products with a copayment.
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3. Data & model
In this study we use the LP of the health insurance company Menzis as a case study. First, we will examine the setup of the LP studied and describe the data we are going to use. After this, we describe the model we will use to analyze the data.
3.1 Data description
Menzis consist of 4 labels, of which the ‘Menzis’ label is the largest with 1,8 million policyholders. In order to improve the health of their policyholders and to make them more loyal, Menzis (label) developed the loyalty program SamenGezond (SG) in 2012, for which members have to create an online account.
Our sample consists of customers who have been insured at Menzis from 1 January 2015 until 1 December 2015. Persons who deceased between 1 December 2015 and 19 January 2016 were excluded from the study. Since only members above 18 can make the decision to churn, we excluded members younger than 18 at 1 January 2015. Our sample consists of 1,250,695 customers. For every LP member, cross-sectional data are available concerning point collection, point redemption, participation in the SamenGezond program, churning behavior and some additional characteristics. The variable definitions are summarized in Table 2. In the next sections we describe the variables in more detail.
Variable Definition
y1,i 1 if customer i churned at the beginning of 2016, 0 otherwise
y2,i 1 if customer i was a member of SG from 1 April 2015 until 31 December 2015, 0 otherwise
Pas_Auti Amount of points customer i collected with passive activities that fall in the category ‘automatic’, from 1
April 2015 until 31 December 2015, divided by 10,000
Pas_Quei Amount of points customer i collected with passive activities that fall in the category ‘questionnaire’, from
1 April 2015 until 31 December 2015, divided by 10,000
Act_Appi Amount of points customer i collected with active activities that fall in the category ‘apps’, from 1 April
2015 until 31 December 2015, divided by 10,000
Act_Othi Amount of points customer i collected with active activities that fall in the category ‘other activities’, from
1 April 2015 until 31 December 2015, divided by 10,000
Apri Amount of points customer i redeemed in April, divided by 10,000 Mayi Amount of points customer i redeemed in May, divided by 10,000 Juni Amount of points customer i redeemed in June, divided by 10,000 Juli Amount of points customer i redeemed in July, divided by 10,000 Augi Amount of points customer i redeemed in August, divided by 10,000 Sepi Amount of points customer i redeemed in September, divided by 10,000 Octi Amount of points customer i redeemed in October, divided by 10,000 Novi Amount of points customer i redeemed in November, divided by 10,000 Deci Amount of points customer i redeemed in December, divided by 10,000
CRi Amount of points customer i redeemed for cash rewards from 1 April 2015 until 31 December 2015,
divided by 10,000
NCRi Amount of points customer i redeemed for non-cash rewards from 1 April 2015 until 31 December 2015,
divided by 10,000
POi Amount of points customer i redeemed for point-only rewards from 1 April 2015 until 31 December 2015,
divided by 10,000
CPi Amount of points customer i redeemed for rewards with copayment from 1 April 2015 until 31 December
2015, divided by 10,000
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3.1.1 Churn
The variable y1,i indicates whether or not the insured churned at the beginning of 2016. This
variable is 1 for churning customers and 0 for customers who did stay. Churning customers are the persons who were insured at 1 December 2015 but not at 18 January 20161, leaving out the persons who are deceased in that period.
3.1.2 LP membership
The variable y2,i indicates whether the policyholder was a member of the SG program from 1
April until 31 December. This variable is 1 for members and 0 for non-members. We set the subscription deadline at 1 April to give new insured a chance to subscribe. We exclude the customers from the data who were a SamenGezond member only for a part of the year 2015, or had double SamenGezond accounts. Of these customers 437,027 were SG member (34.9%).
3.1.3 Point collection
Points can be earned in an active (i.e., the collection of points where the customer has to peform an action in order to get the points) or passive way (i.e. the customer does not have to (necessary) perform an action in order to get the points). In Section 2.4 the difference between these types of point collection are explained.
Passively earned points can be earned in two ways, automatic or by questionnaire. To estimate the effect of automatic point collection (i.e., the participant does not influence whether or not he gets the points) we use the variable Pas_Auti, the amount of points customer i collected with
passive activities that fall in the category ‘automatic’, from 1 April 2015 until 31 December 2015. The variable Pas_Quei is used to measure the effect of the points earned by questionnaire. These
monthly earned points are earned in a fairly easy way, since the member only has to fill in this questionnaire once.
Actively earned points can also be earned in two ways, by apps or by other activities. The variables to measure these points are Act_Appi (for the points earned by apps) and Act_Othi (for
the points earned by other activities).
3.1.4 Point redemption
The points earned can be redeemed in the SG webshop. The variables Apri, Mayi, Juni, Juli, Augi,
Sepi, Octi, Novi, and Deci are measures of the amount of points that customer i redeemed in these
months in 2015. The first three months are not taken into account, to give new insured a chance to subscribe for the program. A special kind of gift is a 15 or 30 euros discount on one's additional insurance at Menzis, a cash reward. The variable CRi expresses the amount of points
1 This is the first date in the Menzis customer database where customer statistics for 2016 were first
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customer i redeemed for cash rewards from 1 April 2015 until 31 December 2015, whereas the variable NCRi is the number of non-cash rewards. Some rewards can be ‘bought’ with only
points, for other products the customer has to make a copayment. The variable POi is the amount
of points customer i spend on point-only products, whereas CPi is the amount of points customer
i spend on products with a copayment.
3.1.5 Control variables
Per customer there is a set of variables available about their characteristics. These variables are summarized in Table 3. We use these variables as control variables.
Variable Definition
Geni Gender of customer i; M when customer i is a man, V if customer i is a female
PSi Price sensitivity of customer i; increase in probability that the insured churns when the
monthly premium increases with 1 euro (estimated by Menzis) at 1 January 2015
ICi 1 if customer i is collected through a collective at 1 January 2015, 0 otherwise
YIMi Years insured at Menzis (label); number of months insured/12 at 1 January 2015
Edui Education level of customer i: L = low, M = medium, H = high (estimated by external company,
based on zipcode) at 1 January 2015
Soci Social class of customer i: : A (highest), B1, B2, C and D (lowest) at 1 January 2015
THCi Type health client of customer i: focused on consumption (CS), own opinions (OO), comfort
(CF), quality (QU), luxury (LU), society (SO), result (RE) or unfocused (UF) (estimated by external company, based on zipcode) at 1 January 2015
Regi Region of customer i: Drenthe (DR), Flevoland (FL), Friesland (FR), Gelderland (GE),
Groningen(GR), Limburg (LI), Noord-Brabant (NB), Noord-Holland (NH), Overijssel (OV), Utrecht (UT), Zeeland (ZE) or Zuid-Holland (ZH) (estimated by external company, based on zipcode) at 1 January 2015
Agei Age of customer i at 1 January 2015
EDi Chosen extra excess deductible of customer i in euro’s, divided by 100 at 1 January 2015
BIi Type of basic insurance: natura (N), budget (B) or restitution (R) at 1 January 2015
LSi Life stage of customer i: Families with children > 18 (FLC), Families with children < 18 (FOC),
Young singles (YS), Young couples without children (YC), aged singles (MS), Middle-aged couples without children (MC), Elderly singles (ES), Elderly couples without children (EC) (estimated by external company, based on zipcode) at 1 January 2015
Table 3 Overview of control variables
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3.2 Data characteristics
From April until December 2015 there were in total around 7 million collection point transactions performed (see Table 13 in the Appendix) and in total more than 110 million points were earned (Table 4). Of these collected points, no less than 50% falls in the automatic category, whereas another 19% falls in the questionnaire category, see Figure 1. This means that almost 70% of the earned points in the LP in 2015 is earned by ‘passive point collection’. The remainder of the points is collected by ‘active point collection’, namely by the use of apps (23%) and other activities (8%).
Total points Average per LP member Passive Automatic 55,562,118 127 Questionnaire 20,644,735 47
Active Apps 25,374,111 58
Other active 8,969,324 21
Total 110,550,288 253
Table 4 Collected points to category
From April until December 2015 around 90 million points were redeemed in the webshop (Table 5). This means that every LP participant redeemed on average 206 points. From October until December we observe a severe increase in redeemed points, see Figure 2. Striking is that most points are redeemed in December, almost a third of all points redeemed from April until November.
Month Total Average per LP member
April 6,953,584 16 May 5,795,206 13 June 5,746,662 13 July 7,426,678 17 August 7,110,303 16 September 7,760,948 18 October 10,689,119 24 November 14,068,972 32 December 24,261,258 56 Total 89,812,730 206
Table 5 Redeemed points per month
Figure 1 Collected points to category
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Of the redeemed points, one third went to cash rewards, whereas two third was spend on other gifts, as can be seen in Table 6. Striking is that by far most points are redeemed for point-only products, more than 95% of the points (Table 7).
Amount of points Percentage Cash reward 29,874,002 33,3% Non-cash rewards 59,938,728 66,7%
Total 89,812,730 100,0%
Table 6 Redeemed points, cash/non-cash rewards
Amount of points Percentage Point-only 85981760 95,7% Copayment 3830970 4,3% Total 89,812,730 100,0%
Table 7 Redeemed points, point-only/copayment
3.3 Model
3.3.1 Model
In this section we will motivate the model we are going to use to evaluate the effect of participation in a LP on churn. Customer churn (𝑦1) is a binary variable; this variable 𝑦1 is 1 if
the customer churns at the end of the contract period and 0 if the customer stays at the company. The variable ‘participating in a LP’ (𝑦2) is also binary; this variable takes value 1 for a policyholder that participates in the program and 0 if one is not a participant. The simplest model to describe these variables is by the following model:
𝑦1= 𝐼(𝛼1𝑋1+ 𝛽𝑦2+ 𝜀1> 0) (1)
𝑦2= 𝐼(𝛼2𝑋2+ 𝜀2> 0) (2)
𝐶𝑜𝑣(𝜀1, 𝜀2 ) = 𝜌 (3)
Equation (1) is the ‘churn equation’ where 𝑋1 is a set of control variables and 𝛽 the effect of
participating in the LP on churn. This is a so-called ‘main effect model’, where the overall effect of participation in the LP on churn is measured. No interaction variables are included in this model, only the average effect of participating in the program is estimated. Equation (2) models the decision to participate in LP, where 𝑋2 is a set of regressors. If the error terms 𝜀1 and 𝜀2 are uncorrelated (implying 𝜌 = 0), the parameters of the models can consistently be estimated by probit estimation (assuming (𝜀1, 𝜀2 ) is bivariate normal distributed with mean zero).
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(because another company can be cheaper). Thus, we cannot assume 𝜌 = 0 which means we have to take sample selection bias into account.
To correct for sample selection bias, we first divide 𝑋2 in two parts: 𝑋2= [𝑋1 𝑍]. The above equations can then be written as:
𝑦1= 𝐼(𝛼1𝑋1+ 𝛽𝑦2+ 𝜀1> 0) (4)
𝑦2= 𝐼(𝛼2𝑋1+ 𝛾𝑍 + 𝜀2 > 0) (5)
𝐶𝑜𝑣(𝜀1, 𝜀2 ) = 𝜌 (6)
In this case 𝑍 is a set of variables (instruments) that are correlated to 𝑦2 but not correlated with the error term of the structural equation, 𝜀1.
The most often used way to handle sample selection bias is by 2SLS. Although this method requires linearity of the model, we might try to mimic this method in this nonlinear case, where the dependent and endogenous explanatory variable are both binary. 2SLS is a two-step procedure, where the first step would be to estimate equation (5) by maximum likelihood estimation (MLE), which is in this case probit estimation. The second step is to include the fitted values of 𝑦2, defined as 𝑦̂2, into equation (4) and estimate the parameters of this model. However, this method does not produce consistent parameter estimates since the indicator function is nonlinear and the expected value cannot be passed through (Wooldridge, 2010, p.597).
Another two step procedure is the CF (Control Function) approach. This is also a two-step procedure where the first step is the same as 2SLS: equation (5) is estimated by probit estimation. Now the residuals are computed: 𝑟̂2 = 𝑦2− 𝑦̂2. In the second step these residuals are included in equation (4). The idea is that 𝑟̂2 captures the endogenous part of 𝑦2 and thus ‘controls’ for sample selection bias. This method also makes use of expected values which cannot be passed through. Wooldridge (2015, p. 442) argues that using so-called “generalized residuals” (a function that is zero conditional on [𝑋1 𝑍]) leads to consistent parameter estimates. A disadvantage of this method is that the standard errors of the structural equation need to be corrected, because the parameters are estimated in two steps (Wooldridge 2010, p. 652).
However, when 𝑦2 is included in the structural model in a non-linear way, for example as an
interaction effect or as (𝑦2)2 these effects cannot be consistently estimated by the CF approach,
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model”. We make use of this technique, since we include interaction effects of 𝑦2 in the model (namely point collection and redemption behavior). When we include the interaction variables in the model, to estimate the parameters of an ‘interaction effects model’, equation (4) is replaced by the following equation:
𝑦1= 𝐼(𝛼1𝑋1+ 𝛽𝑦2+ 𝜃𝑦2𝑊 + 𝜀1> 0) (7)
In equation (7), W is a set of variables that measure behavior within the LP. Note that 𝑦2𝑊 is 0 for non-participants, because 𝑦2 is 0 for these customers. The variables captured in W are
Pas_Aut, Pas_Que, Act_App, Act_Oth, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec, CR, NCR, PO and CP (see Table 2 for the definition of these variables).
To evaluate whether there is indeed sample selection bias, a Wald test of the significance of 𝜌 can be used. If 𝜌 = 0, there is no sample selection bias. In that case probit estimation of equation (4) leads to consistent estimators. If 𝜌 is non-zero, then LP membership is endogenous and the bivariate probit model is the appropriate method.
3.3.2 Instrumental variables
To model the decision to participate in the LP, we have to find instruments that are correlated to LP participation (y2), but uncorrelated to the error term in the churn (y1) model. Figure 3 shows
that the instrumental variables (Z) have to be correlated with y1 only through the endogenous
variable y2. The instrumental variables we use are summarized in Table 8.
Figure 3 Instrumental variables not correlated to error term of churn model
Variable Definition
supi 1 if customer i is insured through a collective that is Jantje Beton Members, Jantje Beton Employees, KWF Kankerbestrijding Members, KWF Kankerbestrijding Employees, IVN Members, IVN Employees,
Natuurmonumenten Members, Natuurmonumenten Volunteers at 1 January, 0 otherwise
CSRi 1 if customer i is insured through a collective that is in the segment ‘Culture, Sports and Recreation’ at 1
January, 0 otherwise
acti 1 if customer i is a ‘active 50+’ at 1 January (estimated by external company, based on zipcode), 0
otherwise
beni 1 if customer i is a ‘benefactor’ at 1 January (estimated by external company, based on zipcode), 0
otherwise
crei 1 if customer i is a ‘creative organic enthusiast’ at 1 January (estimated by external company, based on
zipcode), 0 otherwise
inti 1 if customer i is a ‘intellectual culture enthusiast’ at 1 January (estimated by external company, based on
zipcode), 0 otherwise
spoi 1 if customer i is a ‘sports enthusiast’ at 1 January (estimated by external company, based on zipcode), 0
otherwise
21 0 otherwise
trai 1 if customer i is a ‘traditional from a village’ at 1 January (estimated by external company, based on
zipcode), 0 otherwise
Table 8 Overview of instrumental variables
One type of reward in the SG webshop is a donation to a charity. This can be to ‘KWF Kankerbestrijding', ‘Natuurmonumenten' and 6 other alternatives. Some of these charities offer a collective insurance for their members and employees. In general members of such collectives are more intended to join SamenGezond: 42% of the members of such a collective is a participant in SG, whereas 32% of the other policy holders is a member. There are not a lot of policyholders involved in such collectives (1% of the total number of policy holders). We expect that if a customer is insured through one of these collectives, he might be more intended to join the program, because he can be stimulated by the charity to join the program. As a control variable we include the dummy variable ‘insured through a collective’ (IC) to the model, to correct for the fact that being insured through a collective can affect churn. Whether or not a customer is part of such a collective (sup) is used as an instrumental variable.
Since the SG program is related to health, we expect that a customer that is insured through a collective related to ‘culture, sports and recreation’ (CSR) is more intended to participate in the SamenGezond program, because of the sportive nature of the program. We use this variable as a second instrumental variable. Since we include if a customer is ‘insured to a collective’ as a control variable in the churn model, we expect that these IV’s do not affect churn.
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informative about type of person and not type of health client. ‘Type of health client’ (THC, see Section 3.1.5) is added to the churn equation as a control variable.
3.4 Data analysis
In this section we describe how we analyze the data. To estimate the main effect of participation in a LP in the Dutch healthcare industry on churn, two different ‘churn models’ are estimated. First, we estimate a probit model assuming no sample selection bias of LP membership. The dependent variable in this model is churn (y1). We include as a regressor LP membership (y2)
and the control variables described in Setion 3.1.5. Second, we estimate a bivariate probit model to correct for sample selection bias. In the bivariate probit we model two dependent variables simultaneously: customer churn (y1) and LP membership (y2). We make use of the same control
variables as in the probit equation. For the LP membership equation, the IV’s described in Section 3.3.2 are included as well.
We will consider which model is the right specification, by testing wether there is exogeneity and by testing the validity and strength of the instrumental variables. Since standard tests are not appropriate when both the dependent and (possibly) endogeneous variable are both binary, we make use of analysis techniques used in prior literature, explained below.
Hereafter, we estimate an interaction effects model to analyze the effect of specific collection and redemption behavior on churn. To estimate these effects, we estimate a bivariate probit model including the interaction variables of y2and Pas_Aut, Pas_Que, Act_App, Act_Oth, Apr, May, Jun, Jul,
Aug, Sep, Oct, Nov, Dec, CR, NCR, PO and CP as well as the independent variables used in the prior models. Behavior in the months January until March is not included, to give new customers a change to subscribe for the LP.
To measure the effect of the control variables on churn properly, control variables that correlate extremely positively or negatively with each other are excluded from all models. Correlation matrices of the dependent variables show that education level and social status correlate highly to each other: social class A is highly correlated with high education (0.9). Social class B1 highly correlated with medium education (0.6). The variable ‘life stage’ is highly correlated to ‘persons in household’. The variable ‘education level’ is negatively correlated with ‘income level’ (-0.5)2. To measure the effect of the control variables properly, we exclude the variables ‘income level’, ‘social class’ and ‘persons in household’ from the control variables.
2 Since this correlation is not extremely negative, we initially made a model with the income effects
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4. Results
In this section we discuss the results of these models.
4.1 Main effect
The main effects of participation in a LP on churn are reflected by the estimates of the probit model as displayed in Table 9. ‘LP membership’ has on average a significant positive main effect on churn of 0.122. If we do not control for sample selection bias, the LP seems to be ineffective: LP members churn more often than non-LP members, when all other variables are held constant (ceteris paribus). The estimated marginal effect (at sample means) is 0.0079 (p = 0.001, SE = 0.0045), meaning that customers who have all variables set at the sample mean are 0,8% more likely to churn if they participate in the LP.
24 Probit model Bivariate probit model
Dependent variable y1 y1 y2
Estimate S.E. Estimate S.E. Estimate S.E.
y2 0.122* 0.0045 -0.157* 0.0525 Intercept -0.748* 0.0197 -0.582* 0.0378 0.139* 0.0114 Gen M -0.036* 0.0044 -0.041* 0.0045 -0.046* 0.0024 F¯ PS 2.088* 0.3568 1.846* 0.3581 -2.155* 0.2497 IC -0.042* 0.0059 0.009* 0.0115 0.485* 0.0032 YIM -0.049* 0.0007 -0.048* 0.0007 0.001* 0.0004 Edu L -0.095* 0.0085 -0.128* 0.0103 -0.312* 0.0047 M -0.041* 0.0065 -0.056* 0.0070 -0.144* 0.0038 H¯ THC CS 0.049* 0.0098 0.063* 0.0101 0.151* 0.0047 OO 0.051* 0.0124 0.055* 0.0123 0.060* 0.0065 CF 0.010* 0.0117 0.011* 0.0116 0.036* 0.0060 QU 0.064* 0.0122 0.069* 0.0121 0.071* 0.0065 LU 0.037* 0.0123 0.041* 0.0122 0.049* 0.0061 SO 0.030* 0.0120 0.033* 0.0119 0.065* 0.0062 RE 0.036* 0.0110 0.039* 0.0109 0.051* 0.0056 UF¯ Reg DR -0.096* 0.0143 -0.101* 0.0142 -0.054* 0.0083 FL -0.022* 0.0169 -0.026* 0.0168 -0.033* 0.0107 FR 0.083* 0.0177 0.076* 0.0176 -0.060* 0.0116 GE -0.271* 0.0079 -0.287* 0.0083 -0.178* 0.0046 GR -0.309* 0.0092 -0.326* 0.0095 -0.191* 0.0051 LI 0.059* 0.0146 0.063* 0.0145 0.038* 0.0094 NB 0.052* 0.0101 0.055* 0.0100 0.030* 0.0065 NH -0.023 0.0091 -0.027* 0.0091 -0.038* 0.0057 OV -0.286* 0.0085 -0.296* 0.0085 -0.121* 0.0049 UT -0.137* 0.0102 -0.144* 0.0102 -0.084* 0.0061 ZE 0.058* 0.0244 0.063* 0.0242 0.059* 0.0155 ZH¯ Age -0.012* 0.0002 -0.013* 0.0003 -0.012* 0.0001 ED 0.038* 0.0017 0.043* 0.0019 0.047* 0.0011 BI N -0.088* 0.0081 -0.093* 0.0081 -0.061* 0.0048 B 0.123* 0.0150 0.136* 0.0151 0.130* 0.0105 R¯ LS FLC 0.046* 0.0083 0.040* 0.0084 -0.017* 0.0048 FOC 0.046* 0.0092 0.044* 0.0092 0.024* 0.0055 YS 0.015* 0.0117 -0.012* 0.0128 -0.213* 0.0071 YC 0.064* 0.0131 0.044* 0.0136 -0.132* 0.0079 MS -0.007* 0.0104 -0.027* 0.011 -0.154* 0.0058 MC 0.026* 0.0099 0.020* 0.0099 -0.035* 0.0053 ES 0.008* 0.0100 -0.010* 0.0105 -0.152* 0.0046 EC¯ sup (IV) 0.147* 0.0165 CSR (IV) 0.066* 0.0119 act (IV) 0.137* 0.0051 ben (IV) 0.100* 0.0049 cre (IV) 0.016* 0.0060 int (IV) -0.008* 0.0060 spo (IV) -0.026* 0.0048 soc (IV) -0.097* 0.0078 tra (IV) 0.024* 0.0057
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4.2 Interaction effects
Table 10 shows the estimators of the interaction effects (Table 14 in the Appendix shows the full model).
Bivariate probit model
Dependent variable y1 Estimate S.E. y2 -0.205* 0.0510 y2*Pas_Aut 0.335* 0.2161 y2*Pas_Que -1.403* 0.3665 y2*Act_App -1.659* 0.0865 y2*Act_Oth -2.770* 0.2497 y2*Apr 0.029* 0.3456 y2*May 0.759* 0.3431 y2*Jun 0.089* 0.3603 y2*Jul 0.704* 0.3362 y2*Aug 0.898* 0.3343 y2*Sep 1.037* 0.3296 y2*Oct 0.912* 0.3089 y2*Nov 1.601* 0.2994 y2*Dec 3.743* 0.2840 y2*CR -0.843* 0.0838 y2*NCR¯ y2*PO 0.283* 0.2890 y2*CP¯
Table 10 Bivariate probit model, interaction variables, *=significant at 1% significance level, ¯ = ref. category
4.2.1 Effects of collection behavior
Table 10 shows the estimates of the interaction effects. Points earned with ‘automatic’ activities (Pas_Aut) seem to have no significant effect on churn (p = 0.121). Points earned by questionnaire (Pas_Que) seem to decrease churn significant (estimate = -1.403, p = 0.001). Actively earned points are negative related with churn: both points earned by the use of apps (Act_App) and other activities (Act_Oth) seem to decrease churn significant with estimated coefficients -1.659 (p = 0.001) and -2.770 (p = 0.001), respectively. Points earned by active point collection decrease customer churn more than points earned by passive behavior. Points earned with ‘other activities’ decrease customer churn most heavily.
4.2.2 Effects of redemption behavior
As can be seen in Table 10, point redemption in the months August until December is related to higher churning probabilities, with effects ranging from 0.898 to 3.743 (p ranging from 0.007 to 0.001). Point redemption in the other months has no significant effect on churn.
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Redeeming points for point-only products (PO) do not significantly affect churn, comparing to redeeming points for products making a copayment (CP) (p = 0.327).
4.2.3 Graphic representation
We define the average main effect m of LP participation on churn as:
𝑚 = 𝛽 + ∑𝑘𝑖=1𝜃𝑖𝑊̅𝑖 (8)
Where 𝛽 and 𝜃 are the parameters from equation (7). The vector 𝜃 consist of k elements 𝜃1, … , 𝜃𝑘, where k is the number of interaction variables. In equation (7) W is a matrix of
interaction variables, and 𝑊̅𝑖 is the sample mean of interaction variable 𝑊𝑖 for LP members (𝑦2= 1). When 𝑚 is positive (negative), participation in the LP overall positively (or negatively)
affects the probability to churn. The value of m does not represent to what extent this probability increases or decreases, since this depends on the level of the independent variables. To measure the change in the estimated main effect when varying 𝑊̅𝑗 for a certain j, keeping all other 𝑊̅𝑖 (𝑖 ≠ 𝑗) constant, we estimate these effects for the interaction variables that have a
significant effect on customer churn: Pas_Que, Act_App, Act_Oth, Aug, Sep, Oct, Nov, Dec and CR, by replacing 𝛽 and 𝜃 by their estimated values (see Table 10). Figure 4 graphically depicts how the estimated average main effect of LP participation on churn changes when varying the value of these interaction variables, holding all other variables at the sample mean.
Figure 4 Estimated main effects
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points in December, his probability to churn increases most. When keeping all other variables at their sample mean, the average main effect even gets positive around 600 redeemed points. As shown in Table 5, the average amount of points that a participant redeems in December is 56, so this should increase by more than 10 times to turn the average main effect into a positive effect. Redeeming points in August, September, October and November seem to increase customer churn, whereas points collection by questionnaires and active activities (apps and ‘other activities’) and points redeemed for cash rewards decrease churn. Points collected by ‘other activities’ have the largest negative effect on churn.
We compare the most extreme positive and negative effect of customer churn. Redeeming points in December increases the probability to churn most heavily, whereas collecting points by ‘other activities’ decreases churn most heavily. Figure 5 shows the estimated average main effects for different combinations of collected or redeemed points in these categories.
Figure 5 Estimated main effect, comparing points redeemed in Dec with Act_oth
For example, when 2000 points are collected by ‘other activities’, but these 2000 points are redeemed in December by the customer, the estimated main effect of the LP is 0, all other variables held at the sample average.
4.3 Model evaluation
In this section we evaluate the models. First we discuss the validity and strength of the instrumental variables. Second, we evaluate whether the probit or bivariate probit model was the right specification.
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instruments by using the method as Martínez-Espiñeira and Lyssenko (2011). The authors estimate a bivariate probit model and evaluate the validity of the instruments by adding the instrumental variables to the structural equation and testing for joint significance. When the IV’s affect ‘churn’ significantly, the instruments are not valid. We add the instrument to the churn equation, perform a Wald test and find a χ2(9) value of 21.42, resulting in a p-value of 0.011. We thus cannot reject the hypothesis that these instrumental variables add significant value to the structural model, and thus the instruments seem to be valid. All separate variables are nonsignificant (p ranging from 0.258 to 0.743; see Table 15 in the Appendix), except for ‘being insured trough a collective related to culture, sports and recreation’ (CSR) (p = 0.001). This is another indicator for the validity of the instruments.
A second requirement is that the IV’s are strong: the IV’s have to explain variation in the ‘LP membership’ variable. We evaluate the strength of the IV’s by testing the joint significance of the instruments in the ‘LP membership’ equation. We perform a Wald test and find a χ2(9) value of 1806.20, resulting in a p-value of 0.001. The null hypothesis that 𝛾 = 0 in equation (5) is rejected and thus the instruments seem to be strong.
We also test for exogeneity. The factor 𝜌 is a measure for the correlation between the error terms in the churn and ‘LP membership’ model. The null hypothesis that ‘LP membership’ is exogenous corresponds with the hypothesis 𝜌 = 0. The estimated value of 𝜌 is 0.178. We perform the Wald test and obtain an χ2(1) value of 30.97, corresponding with a p-value of 0.001. Thus, ignoring the endogeneity of LP membership would lead to inconsistent estimators: the bivariate model is the appropriate model. That 𝜌 is positive means that there are unobserved factors that influence churn negative (positive) and also LP membership negative (positive).
4.4 Effect of control variables on churn
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churn than customers with a restitution polis (R), whereas customers with a restitution polis are more likely to churn than customers with a natura polis (N). Young couples without children (YS) and families with children above 18 (FOC) are most likely to churn, compared to customers in other life stages.
Comparing the probit and bivariate probit model, the estimators of the effects of the control variables on churn have the same signs, apart from ‘being insured through a collective’ (IC). So even if a probit model is not the right specification for a churn model, it generates a good approximation of the effects of the control variables on customer churn.
4.5 Factors that affect LP membership
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5. Conclusion & discussion
5.1 Conclusion
In this study we estimated the effects of participation and different forms of collection and redemption behavior in a LP in the Dutch healthcare industry on churn ratio. In this section we will answer our research questions. Table 11 shows an overview of the conclusions.
Hypothesis Conclusion Comment
H1: Participating in a LP decreases churn. Accepted H2A: Active point collection decreases churn. Accepted H2B: Passive point collection decreases churn. Partially
accepted ‘Automatic’: no significant effect ‘Questionnaire’: decreases churn H3: Redeeming points in January until October decreases
churn, whereas redeeming points in November and December increases churn.
Rejected March – July: no effect
August – December: increases churn H4: Redeeming points for cash rewards increases churn more
than redeeming points for other rewards. Rejected Cash rewards decrease churn more H5: Redeeming points for point-only products decreases
churn more than redeeming points for products with a copayment.
Rejected No significant difference
Table 11 Overview of the conclusions
RQ1: What is the effect of participating in a loyalty program in the Dutch healthcare industry on
churn ratio?
When assuming no sample selection bias (participation in the LP is random), participation significantly positively affects churning probability, meaning that the program leads to increased churn. When estimating a bivariate probit model to correct for sample selection bias, LP membership significantly negatively affect churn: LP membership leads relates to a lower churn probability. Diagnostic tests lead to the conclusion that LP membership is indeed endogenous and the bivariate model is thus the correct specification. We thus conclude that LP membership decreases churn. As Bolton et al. (2000) argues, LP members can feel as if they get more service for the price they are paying than non-participants and thus churn less. To minimize customer churn, health insurance companies in the Dutch market could set up a LP (if the gain in customers compensates the costs of this LP). Although there has been extensive research at the effectiveness of LPs, sample selection has hardly been taken into account. We conclude that sample selection bias in LPs should gain more attention, and that a bivariate probit model is an appropriate method for this (if both the dependent and endogenous variable are binary).
RQ2: What are the effects of active and of automatic point collection in a loyalty program in the
Dutch healthcare industry on churn ratio?
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use of apps and other activities are (significant) related to lower churning probabilities. This can be due to the point-pressure mechanism, since the more points a member collects, the healthier he becomes and thus likes the program and firm more. He will thus be more committed to the firm. This expected increase in attitudinal loyalty will lead to more behavioral loyalty and thus to less churn.
For passive point collection the customer does not have to (necessary) perform an action in order to get points. The points come in the category ‘automatic’ (for example at the start of the year) or ‘questionnaire’ (participants can fill in a questionnaire at the start of their membership and then earn points every month). Points earned with ‘automatic’ activities seem to have no significant effect on churn, although 50% of the earned points comes in this category. It might be that a lot of LP members are not actively participating in the LP and thus not notice these points. Points gathered by questionnaires seem to decrease churn significant, which can be caused by gratefulness: the member is grateful to the firm and thus more committed.
In the LP studied, 23% of the points was earned by the use of apps and 8% by ‘other activities’. Health insurance companies can try to enlarge the group of active members, since collecting points by the use of apps and other activities are related to lower churning probabilities, especially point collection through ‘other activities’. A second advantage of these points is that these contribute to the other goal of the LP: increasing the health of the participants. A health insurance company should try to hand out not too much points in the ‘automatic’ category, because these are not effective, only expensive for the owner of the LP. These points also do not contribute to goal of increasing the health of the LP member.
RQ3: What is the effect of month of redemption in a loyalty program in the Dutch healthcare
industry on churn ratio?
We find that points redeemed from August until December are related to higher churning probabilities. This can be because policyholders already decide they want to leave the company and are thus “spending” their points. Since the premiums and policy conditions for the new year are announced in November, redeeming points in August, September and October can be an early indication for churning customers. Health insurance companies should try to target these customers to prevent churn.
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RQ4: What is the effect of redeeming points for cash rewards compared to non-cash rewards in a
loyalty program in the Dutch healthcare industry on churn ratio?
Redeeming points for cash rewards seem to decrease churn more than other type of rewards. We thus do not endorse the argument of Nunes and Drèze (2006) and Dorotic et al. (2012) that cash rewards lead to decreased loyalty, but the reverse. Health insurance companies might consider to include a cash reward in their assortment of rewards.
RQ5: What is the effect of redeeming points for rewards with copayment, compared to rewards
that are point-only in a loyalty program in the Dutch healthcare industry on churn ratio?
We found no significant effect of redeeming points on point-only products comparing to products with copayment, thus this hypothesis is not supported. Since point-only products are often more expensive for the firm, offering only pay-extra products could be a valuable intervention.
5.2 Limitations & further research
We did not correct for the fact that redeeming points is only possible if one has collected these points. It is possible that a part of the effect of redeeming points on churn is captured in the effect of collecting points. We also did not account for the fact that being a more active member of the program can be correlated with the decision to churn through unobservable variables: an active member can be more committed to the firm than a less active member of the program. The instrumental variables might be slightly weak. Although we did not reject the hypothesis about the invalidity of the instruments, the p-value was only 0.0109. This small p-value seems to be caused by including the instrument “being insured through a collective related to culture, sports or recreation” (CSR), because when we include this instrument in the structural equation, it has a p-value of 0.001. It seems to capture a part of the effect of ‘being insured through a collective’ (IC), because the coefficient of this variable varies for the probit (a significant negative) and bivariate probit model (no significant effect). However, if we exclude this instrumental variable, the instruments are not strong anymore.
Future research can avoid these limitations by developing more and better instrumental variables. Participation in multiple LPs or the sportivity of a costumer might be more accurate instrumental variables.
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