Identification of customer groups in the German term life market: a benefit segmentation

Abstract

We run a benefit segmentation of 2017 insurance consumers in order to analyze the structure and heterogeneity of the German term life insurance market. The consumers’ preference information has been obtained through a choice-based conjoint (CBC) experiment and a subsequent hierarchical Bayes (HB) estimation routine. Drawing on their part-worth utility profiles, we first construct a diverse cluster ensemble, comprising a total of 1624 hierarchical and k-means solutions based on different linkage criterions and sensibly drawn starting points. Then, final group memberships are determined by means of consensus clustering. Our empirical results indicate that the market divides into three segments characterized by substantially different consumer types with distinct demands and needs. While the first group is clearly driven by the premium, the opposite holds true for the brand-loyal group. Additionally, the market is completed by a third segment with in-between preference structures. Hence, both brand insurers and companies with a lower reputation face consumer groups that almost perfectly fit their provider profiles. More specifically, by offering segment-oriented products, an efficient resource allocation is fostered and the basis for long-term business relationships is laid. This is becoming increasingly important, because ongoing regulatory efforts, low interest rates, and market entrances from InsuranceTech start-ups and tech giants aiming to utilize the market’s enormous hidden potential are changing the competitive environment significantly. A consequent alignment of important strategic decisions related to product innovations, pricing, and distribution channels to our identified consumer segments enables incumbents to maintain a stable and sustainable market share and profitability.

Appendices

Appendix 1: CBC experiment and consensus clustering

1.1 Levels for the attribute insurance premium

Table 6 Insurance premium levels for the 10 mortality risk groups

1.2 Illustration of consensus method

The approach applied in this paper goes back to the work of Strehl and Ghosh (2002). Later, it has then been adapted by Orme and Johnson (2008), who suggest to follow the subsequent steps: First, one needs to derive multiple solutions from various clustering algorithms and techniques in order to generate a diverse cluster ensemble. In the second step, for each ensemble partition $P_i$ ($i=1,\ldots ,M$) and individual j ($j=1,\ldots ,n$), the assigned group labels (e.g. 1, 2 for a two-group solution) are transformed into dummy coding such that every group represents a single column in the dummy matrix. Generally, “1” indicates “Group member”, whereas “0” stands for “No group member”. Then, the M dummy matrices are used to construct the so-called indicator matrix. In contrast to Strehl and Ghosh (2002), who employ a so-called graph partitioning approach at this stage to achieve correspondence between the labels of the individual solutions, Orme and Johnson (2008) refrain from this step. Instead, they suggest to take the columns of the indicator matrix as new clustering variables and directly subject them to the consensus analysis, which can be regarded as clustering on cluster solutions.

This short example illustrates how the input matrix for the consensus stage is generated.⁴² Let us assume that we have a total of five respondents j ($n = 5$) and four ensemble partitions $P_i$ ($i=1,\ldots ,4$) as shown in Table 7.

Table 7 Individual group memberships in an exemplary cluster ensemble

It can be seen that partitions $P_{2}$ and $P_{4}$ are two-group solutions with inverse labeling, while $P_{1}$ is a three-group solution, and $P_{3}$ a four-group solution. The dummy coding of partition $P_{1}$ results in the following three-column matrix as shown in Table 8.

Table 8 Dummy coding per group for ensemble partition $P_1$

Table 9 Indicator matrix of the exemplary cluster ensemble

By converting all M ensemble partitions into the form of Table 8, the so-called indicator matrix is obtained (see Table 9), which is then subjected to the final consensus clustering.

Appendix 2: Sensitivity analyses

According to Retzer and Shan (2007), two critical aspects in cluster analysis exist: deciding on the appropriate number of clusters and differentiating between their quality. In order to demonstrate that the results presented in this paper are robust and meaningful, we now run several sensitivity analyses on our selected number of segments and our selected ensemble. Additionally, we further show that the results remain stable if the sample is randomly reduced to 1000 persons.

1.1 Number of market segments

We construct six reduced ensembles based on different selections of clustering techniques and numbers of groups, which are then subjected to the consensus approach. The reduced ensemble A consists of 784 partitions with 2- to 15-group solutions derived by our eight clustering strategies on all seven clustering bases ($7\,\times \,8\,\times \,14 = 784$), while ensemble B has 504 partitions with 2- to 10-group solutions ($7\,\times \,8\,\times \,9 = 504$). Ensemble C, in turn, consists of 609 pure k-means strategies ($7 \times 3 \times 29 = 609$) that cover 2- to 30-group solutions. Its counterpart ensemble D, in contrast, is derived by the five hierarchical methods ($7 \times 5 \times 29 = 1015$). Finally, ensembles E ($1 \times 8 \times 14 = 112$) and F ($1 \times 8 \times 9 = 72$) exclusively resort to the combination of all six attributes.⁴³ As becomes apparent from the last row, diversity generally increases with the number of partitions.

Table 10 Adjusted reproducibility rates per ensemble

The adjusted reproducibility rates in Table 10 provide evidence that the three-cluster solution is first-best for at least two reasons. First, although reproducibility generally falls with an increasing number of segments, the reverse holds true for three segments, independent of the selected ensemble. Second, it reaches the highest absolute values at almost equal to 100.0%. As pointed out by Orme and Johnson (2008), such high reproducibility rates clearly indicate that a reasonable structure has been found. Additionally, it can be seen that the second-best solution is a division into two segments, with an average adjusted reproducibility of 91.8%.

Table 11 Segment sizes: two- vs. three-group solution

In order to further illustrate that three segments should be chosen, Table 11 shows its cross-tabulation with the two-group solution. As can be seen, the latter consists of two almost equally sized segments with 776 and 734 respondents. More specifically, it assigns all price-sensitive consumers to its first cluster (upper left cell), while all brand-loyal respondents are allocated to the second segment (cell at bottom center). However, since the algorithm was forced to form two groups, the waverers are distributed to both clusters. That is, 347 to $C_1$ and 211 to $C_2$. As a consequence, the preference distributions in the groups are diluted and less clear-cut than in our three-segment solution. In the first cluster, for instance, the average relative importance of the premium amounts to 59.5%, which equals a decline of 8.3 percentage points (p.p.). The importance of the attribute brand in the brand-loyal group, in turn, decreases by 2.8 p.p. to approximately 24.3% on average. At the same time, it increases by 5.5 p.p. to 23.9% for the insurance premium. Thus, the two-group solution ignores an important market segment that is substantially different from the price-sensitive and the brand-loyal groups.

Table 12 Relative attribute importances and market shares across ensembles

1.2 Selection of the ensemble

In the next step, we analyze how individual group membership assignments depend on the ensemble composition. To do so, we take all reduced ensembles from Table 10 as clustering bases and examine their three-segment solutions by calculating the corresponding average relative attribute importances. Table 12 shows all results.⁴⁴

The upper part of the table contains both the importances for the full sample and our final ensemble with 1624 partitions from Table 5. At first glance, it becomes evident that the price-sensitive, the brand-loyal, and the waverer groups are obtained under all ensembles. Moreover, the absolute relative attribute importances are almost constant for all three segments and similar to those of the full ensemble. For the price-sensitive and waverer segments, the importance ranking of the six attributes remains unchanged, while some minor deviations can be observed for the brand-loyal consumers. Regarding the segment sizes, the price-sensitives always account for the lowest market share, amounting to approximately 20.0% to 22.0%.⁴⁵ The brand-loyal market share, on the other hand, varies between 26.0% and 33.0%, while the waverers are associated with market shares between 21.0% and 29.0%. As can be seen from the last column, approximately 25.0% of the respondents are classified as outliers under all ensembles. Particularly when comparing the reduced ensembles E and F with our full ensemble, however, some differences in both the relative attribute importances and market shares emerge. This can be explained by the fact that the former are based on the combination of all six attributes only, while the single attributes have not been considered.⁴⁶ To sum up, this sensitivity analysis is a further indication of the robustness of our approach.

1.3 Number of respondents

Finally, we construct a subsample of 1000 respondents at random and reconstruct selected ensembles from Table 10 (Full, A, C, D), for which we then calculate adjusted reproducibilities, relative attribute importances, as well as market shares. Similar to our previous analyses, Fig. 7 shows that the adjusted reproducibilities for the three-cluster solutions exhibit an atypical trend. That is, for all ensembles, it increases compared to the respective two-group solution. In contrast to the full sample with 2017 persons, however, our full ensemble achieves a slightly lower reproducibility figure (96.3%), while the reduced ensemble A with a total of 784 partitions is associated with the maximum of 99.4%.⁴⁷

Fig. 7

Adjusted reproducibility rates per ensemble (1000 respondents). This figure shows the adjusted reproducibility rates (in percent) for selected cluster ensembles (see Table 10) based on a randomly drawn subset of 1000 respondents

Table 13 Relative attribute importances per segment (1000 respondents)

Table 13 shows that we were able to reproduce the preference patterns from the full sample.⁴⁸ As can be seen from the first row, both the absolute relative attribute importances and attribute rankings are almost identical (see Table 5). While the premium is by far the most dominant product characteristic, the remaining five attributes are of minor importance. Regarding the segments, the first group ($\mathrm {C_1}$) accounts for an equal market share (22.0% vs. 21.3%) and exhibits a similar price sensitivity. Within the second cluster ($\mathrm {C_2}$), the average relative attribute importance for the brand (26.9%) corresponds to the full sample analysis, which also holds true for its market share. Moreover, the importance distribution of the product attributes remains unchanged, with the insurance premium being ranked third. The members of the waverer group, in turn, have an average preference structure that lies between the price-sensitive and brand-loyal customers. A comparison of rows one and four shows that these respondents almost resemble the one-group solution. Finally, regarding the aggregated market share, we also identified 25.0% of the respondents as outliers.