Relationship value benefits of membership programs, heterogeneous stakeholders and museum impact beyond fees

In times of decreasing public funding, cultural institutions such as museums increasingly develop new stakeholder management practices to build a different or more diversified support base. Recently, membership programs have especially been gaining popularity. In this paper, we adopt a relationship value approach to study the poorly understood behaviors of members that can benefit museums beyond membership fees. In particular, we focus on the extent to which membership level and the perceived prestige of the museum drive value co-creation through prestige leveraging. We study this by using a sample of 430 members and non-members of the Hermitage Museum in Amsterdam. We find that membership level is positively related with cross-buying behavior at the museum store and restaurant, and recommending the museum. In addition, these value creating behaviors are mediated by members leveraging the museum ’ s prestige in their social environment. In contrast, we find a negative relationship between membership level and recruiting new members into the program, which could be explained by status dilution effects.


INTRODUCTION
As a result of the current Western trend of eroding public support and increasing competition for funds in the cultural sector, patronage relations between private actors and cultural organizations such as museums have regained importance (Thompson, Berger, Blomquist, & Allen, 2002;O'Hare, 2008). While visitors of museums pay only a portion of the actual cost of the experience, a large part of the costs is born by public subsidies, corporate sponsoring, or other sources of funding (Wallace, 2016). However, public subsidies, which for some organizations account for up to 70% of income, have decreased substantially and are often no longer sufficient (Gilmore & Rentschler, 2002). Consequently, many museums, and other cultural organizations, have been building closer relationships with a range of stakeholders (Della Torre, Eikhof, Montanari & Sikora, 2018).
In recent years, especially membership programs have been gaining in popularity. Membership programs allow individuals to financially support cultural organizations by becoming a "member"' or a "friend." In return, members receive specific benefits that depend on the size of their financial contribution. However, little is known about how exactly membership programs add value to cultural organizations and whether there are downsides that need to be recognized and managed. On the one hand, prior research in the context of museums shows that membership programs have the potential to generate a stable stream of income that make cultural organizations less vulnerable to external shocks, fickle government funding, and the unpredictable success of temporary exhibitions (Bhattacharya, Rao, & Glynn, 1995;Kadoyama, 2018). On the other hand, membership programs are likely to further complicate stakeholder management, especially when it comes to balancing artistic versus commercial objectives (Wallace, 2016;Della Torre et al., 2018). For example, while wealthy patrons tend to prefer more scholarly exhibitions, corporate sponsors may press for accessible popular exhibitions to enhance public relations and publicity (Gallagher & Weinberg, 1991;Alexander, 1996). Besides membership programs adding a new type of stakeholder to manage as such, it is also one that involves a relatively large number of individuals who, especially those that strongly identify with the museum (Bhattacharya et al., 1995), may want to exert some form of influence.
Most major museums, including the Metropolitan Museum of Art in New York (MET), the Louvre in Paris, and the Tate in London have a membership program. Although these programs come in many shapes and forms, many have a hierarchical design with different membership levels with the highest levels paying the most for exclusive services and perks. Lower level membership privileges include free admission, subscription to the members-only newsletter, access to the members-only lounge at the museum, and numerous discounts including a 10% discount on purchases at the museum store. Higher level membership privileges are more exclusive and may include behind the scenes events with curators, a special event with the museum's director, or a private reception with the museum's president. Fundamentally, the leveled design of a membership program indicates that not all members are equal or the same and that different members get different benefits and pay different fees.
The aim of this paper is to study the extent to which museums, and cultural organizations more broadly, are able to benefit from hierarchical membership programs by exploring a range of behaviors of members that can be beneficial to the museum. While the main rationale behind offering membership programs may be to generate a stable stream of revenue through annual membership fees, these formal practices may also have informal-positive but also negative-effects (Della Torre et al., 2018), which museums may want to take into consideration when designing membership programs. In particular, we focus on the broader relationship value of the membership program as members (co-)create value for themselves and the museum. The relationship value approach (Ravald & Grönroos, 1996;Leary, 2005;Biggemann & Buttle, 2012) in the museum context refers to the value derived from the broader relationship with the museum (or any organization), rather than the transaction itself. Besides understanding basic financial outcomes, such as purchasing goods in the museum shop, the relationship value approach can also be used to understand more complex and indirect network behaviors, such as members liaising with third parties who are not yet a member, to increase their self-esteem or status (Leary, 2005;Biggemann & Buttle, 2012).
In this study, the theoretical and managerial contribution results from the exploration of different relationship value behaviors for stakeholders within the same membership system. In particular, the focal relationship value behaviors from which both the members and the museum can benefit are the following: (1) cross-buying at the museum; (2) recommending the museum to others; (3) jointly visiting the museum with non-members; and (4) recruiting new members for the program. It is important to note that these behaviors are not a part of the membership deal or requirement to be a member. Rather, we theorize that the degree to which these behaviors emerge, relate to the level of the member in the program through a relationship value mechanism. For example, higher level members perceive more relationship value in their extended network-such a leveraged prestige for being associated to the museum, which is valuable in social settings-and therefore will engage more in mutually beneficial behaviors. Potential anomalies with respect to specific behaviors will be picked up in our empirical study, which will open up pathways for further theorization and future empirical work.
Our study has three contributions. First, using a relationship value approach, we provide theoretical underpinnings and extend prior work on membership programs by studying a range of specific member behaviors and the benefits (and potential pitfalls) to the museum (Bhattacharya et al., 1995;Glynn, Bhattacharya, & Rao, 1996). Second, while there are a number of studies about the effects of membership duration (e.g. Knoke, 1988;Hager, 2014), there is a paucity of studies about the effects of a tiered system with different membership levels, particularly in relation to a range of relevant behaviors such as word of mouth (WoM), joint visits, and recruiting new members for the program. Third, while Glynn et al. (1996) studied the relationship between the perceived prestige of the museum and members identifying with the museum, little is known about potential prestige leveraging by members in social contexts driving their behavior and consequently the value obtained by the museum through increased sales, additional visits, or new members.
This article is structured as follows. First, we provide a literature overview about museum membership programs. Second, we discuss the benefits of membership programs to both the museum and its members. Third, we hypothesize about the effect of membership level on the benefits that members provide for the museum using a relationship value lens. Fourth, we hypothesize about the role of perceived organizational prestige, and how it mediates the relationship between membership level and the behavioral benefits provided by its members. Fifth, these hypotheses are tested with data collected from the Hermitage Museum Amsterdam and the theoretical and managerial implications of this study are discussed.

THEORETICAL FRAMEWORK
Relationship value approach to museum membership programs Many heritage institutions, public spaces, and increasingly museums have set up membership programs (Holmes & Slater, 2012). Prior research in the context of museums shows that roughly 80% of the members use their benefits infrequently and do not visit the museum enough to recover their basic membership fee (Glynn et al., 1996). This suggests that membership programs can provide a relatively stable income at a comparatively low cost. However, besides direct material value, in a broader sense, membership programs also create relationship value.
The relationship value approach (Ravald & Grönroos, 1996;Leary, 2005;Biggemann & Buttle, 2012) reaches beyond the mere transactional nature of exchange relationships based on a cost/benefit conception of value. Instead, relationship value theory regards relationships, and the value created for all parties within these relationships, as social constructions that result from interactions over an extended period of time. It distinguishes between four dimensions of relationship value. First, personal value is about liking or disliking the other and can lead to customer retention and referrals. Second, financial value is about economic satisfaction and can, for example, lead to a higher willingness to pay. Third, knowledge value is about information sharing and can lead to benefits such as market intelligence and innovation. Fourth, strategic value is about improving the competitive position of the partners involved in the relationship, which can be beneficial in terms of longterm planning and social networks (Biggemann & Buttle, 2012).
Similarly, previous studies on membership suggest that the decision to become a member depends not only on material needs satisfied by the membership, but also on social needs (Truong & McColl, 2011;Holmes & Slater, 2012). The social context of a membership program may be a key reason why many membership programs have more expensive top levels as they offer value through benefits from which non-members and low level members are excluded. These particular benefits, privileges and degree of exclusivity are reflected in the membership fee and corresponding membership level (Liebermann, 1999). Conversely, membership programs should not only benefit its members but eventually also create value for the organizations offering them. Research in the field of professional industry associations, for example, shows that members often recommend their association in their social networks (Hager, 2014), and nearly half of the volunteers in the cultural heritage sector actively recruit new members for their institutions (Holmes & Slater, 2012). Membership programs can therefore be a tool to create relationship value (Biggemann & Buttle, 2012). However, a systematic study about the benefits of membership programs beyond direct membership fees is largely lacking.

Member behaviors that benefit museums
In response to the customer lifetime value model, Bolton, Lemon, & Verhoef (2004) argue that in addition to length, relationship management has to focus on the depth and width of the relationship. Generally, it is found that membership-like programs increase the number and value of transactions as a result of the incentives to stay and do more business with the supplier (Lewis, 2004). Besides customer retention for the museum, factors such as cross-buying and increased service usage also have great potential to enhance profits (Dowling & Uncles, 1997;Bolton et al., 2004;Biggemann & Buttle, 2012). Moreover, the devotion to, and identification with, the company rather than its products, leads to a positive valuation of both the actions and products generated by the firm (Bhattacharya & Sen, 2003). Research on membership in a regular business environment found that only 20% of the members buy significantly more, while 36% buy slightly more during their membership (Liebermann, 1999). Generally, additional revenues may also be generated directly through purchases at the museum shop or restaurant as retail is often on site.
Consumers who actively advertise and endorse the company have been labeled champions, advocates, evangelists or representative consumers (Keller, 2001;Jain & Singh, 2002;Bhattacharya & Sen, 2003;Varley, 2008). A key goal of relationship management is to create consumer champions, who actively endorse the organization and its products they are loyal to and identify with. Similarly, Biggemann & Buttle (2012) argue that an important sub-dimension of personal relationship value are referrals or the "willingness to share positive experiences with other parties". Endorsements often take the form of WoM, where champions attempt to provide a favorable image of the company (Bolton, Kannan, & Bramlett, 2000;Bhattacharya & Sen, 2003). Because of its perceived trustworthiness, WoM is found to be more influential in affecting "awareness, expectations, perceptions, attitudes, behavioral intentions and behavior" (Buttle, 1998: p. 242), than any other marketing efforts and nine times more effective than advertising in generating a positive opinion (Day, 1971). WoM can take the form of referrals where existing customers recruit new customers for which in certain cases they may be rewarded (Biyalogorsky, Gerstner, & Libai, 2001) but in other cases not. So rather than a financial relationship value, the driver for this behavior can be more strategic (Biggemann & Buttle, 2012) and relates to the role of the relationship with the museum in the broader social network of the member.
In the setting of museums, and cultural organizations more generally, WoM can be very important. First, consumers are more likely to exhibit WoM after emotional experiences (Dick & Basu, 1994). Considering that the objective of exhibitions in museums generally is to trigger emotional reactions, the role of WoM is expected to be especially relevant in this context. Second, WoM is more influential with respect to services compared to goods because services are intangible and perceived to be riskier (Murray & Schlacter, 1990). This may also explain why WoM is especially influential when the sender has a high degree of expertise (Bansal & Voyer, 2000). This is confirmed by McLean (1994) who found WoM to be the most important source of promotion in the context of museums, easily beating advertising. Such referrals appear to be particularly prevalent in the case of memberships, where individuals are actively involved recommending products and services (Liebermann, 1999;Jain & Singh, 2002;Bolton et al., 2004). Interestingly, a relationship value approach can explain a range of member behaviors such as purchasing, recommendation, and potentially recruitment behavior and why members engage in these behaviors without a specific incentive in the membership program itself.

Hierarchical membership programs and relationship value theory
While to date no overarching theoretical framework has been applied to get a more comprehensive understanding of how membership programs work, relationship value theory shows a lot of promise since it focuses on a broad range of benefits for both the member and the museum. Relationship value theory (Ravald & Grönroos, 1996;Biggemann & Buttle, 2012) argues that that financial or personal benefits are not so much different value components, but that financial, personal, knowledge and strategic relationship value dimensions together constitute an extended relationship value concept (Biggemann & Buttle, 2012). In the context of museums, relational benefits include the feeling of making a financial difference, the opportunity to communicate and interact with others, gain knowledge and even develop self-esteem or status in social settings (Leary, 2005).
Membership programs come in many forms and shapes and often share that they comprise of a hierarchical or tiered membership structure. Members in higher levels pay a higher fee, in return for which they receive more, and often increasingly exclusive, benefits. As such, membership provides the opportunity for raising and signaling social status, from which members derive utility (Bhattacharya et al., 1995). In addition, through the accumulation of information, experience, and intimacy with the organization, the relationship between the member and the organization evolves over time, resulting in stronger benefits for the organization as well (Baumeister & Leary, 1995;Jain & Singh, 2002;Bolton et al., 2004). These member behaviors, for example, create value for the museum through increased revenue streams, market intelligence and brand recognition. However, given the different membership levels and accompanied different benefits, not all member stakeholders will be equal and heterogeneity in select behaviors may occur. The goal here is to explore these differences in the specific setting of museums.
While all types of members will see value in being a member, high-rather than low-level members are more likely to benefit across all dimensions of relationship value: personal, financial, knowledge, and strategic (Biggemann & Buttle, 2012). Higher level members tend to have a more intimate and exclusive relationship with the museum while operating in higher worth networks. Higher level members are particularly likely to benefit in the strategic relationship value dimension because of the social (network) benefits of exclusive interactions through, for example, behind the scenes events with curators, invitations for new exhibition opening events, and (personal) meetings with the museum director or president. On the other hand, from a relationship value theory perspective, museums are more likely to benefit from their relationships with higher-rather than lower-level members because they are more likely to allocate more time, money, and other resources to the organization as well as its endorsement (Day, 2000;Keller, 2001;Jain & Singh, 2002). Finally, Payne et al. (1995) and others have argued that relationship value is generated by a summation of all the above mentioned (positive) value effects. We therefore hypothesize that: Hypothesis 1 There is a positive relationship between membership level and (a) cross-buying behavior, (b) recommendation behavior, (c) joint visiting behavior, and (d) recruitment behavior.

Prestige leveraging as a mediator
Prior research has identified two competing social needs among consumers: a need for uniqueness and a countervailing need for conformity (Amaldoss & Jain, 2005). First, when consumers purchase a product to satisfy their need for uniqueness, the value of the product increases as its perceived exclusivity increases. In other words, consumers could value a product less when more consumers own it. This also relates to the concept of conspicuous consumption or displaying wealth by purchasing lavish and unnecessary things (Veblen, 1899). Second, the need for conformity works the other way around and expresses the need to be perceived similar in a certain way. Conformity can play an important role in purchasing conspicuous goods as well (Amaldoss & Jain, 2005), including fashion purchases and music festival visiting behavior (Bruggeman et al., 2012). If more people become members, or worse, claim equally high positions in the membership program, the status differences become less apparent and the individual's status goals may not be achieved. As a result, this study may provide important clues as to why certain valuable outcomes may or may not materialize. Part of the reason why a tiered membership program with levels might lead to different types of member behaviors across stakeholder groups, which ultimately also provide different types of benefits for museums, is that the level of membership enhances the members' potential for leveraging the prestige associated with being a member in their social network or environment (Biggemann & Buttle, 2012). For example, they can leverage this prestige by spending time in the membersonly lounge, having dinner at the museum restaurant with friends or business partners as a specific form of conspicuous consumption (Veblen, 1899), and impressing non-members by demonstrating their knowledge of the museum and its collection through joint visits. While in Hypothesis 1 we argue that there is a direct relationship between membership level and (a) cross-buying behavior, (b) recommendation behavior, (c) joint visiting behavior, and (d) recruitment behavior, we expect that this mechanism operates through individual members' perceptions of the degree in which they can (socially) leverage the museum's prestige. We therefore hypothesize that: Hypothesis 2 Museum prestige leveraging mediates the positive relationship between membership level and (a) cross-buying behavior, (b) recommendation behavior, (c) joint visiting behavior, and (d) recruitment behavior.
Finding support, or anomalies, with respect to the above hypotheses will enable us to provide specific managerial recommendations and infer theoretical relationship value clues as to how these systems work across different stakeholders in the same system.

Empirical setting
Museums are a global industry and attendance is growing steadily around the world. From a regional perspective, Europe is an important player when it comes to museums. The Louvre in Paris, for example, is the most popular museum in the world with a total attendance of more than 10.2 million visitors in 2018 and just below 10 million in 2019. As a reference, Disneyland is the top theme park in Europe with 9.8 million visitors in 2018. Total attendance for the top 20 museums in the world was 108.1 million visitors in 2018, which is practically the same compared to 2017 with 108 million, including 7.4 million for the Metropolitan Museum of Art (MET) in New York and 8.6 million for the National Museum of China in Beijing. Museums play an important role in cities and local governments are often keen to help build new museums. In China, many museums in the top 20 showed double digit growth, with the re-opened Hunan Provincial Museum occupying 6th place with 3.6 million visitors in their first year of operations after reopening in a new building (Museum Index, 2019). However, as museum supply is growing and governments tighten public spending for running museums, membership programs emerge across the globe.
The data collection for this research was conducted at the Hermitage Amsterdam museum. The Hermitage Amsterdam is a subsidiary of the renowned State Hermitage Museum, located in St. Petersburg, Russia. This museum is in the global top 20 museums in terms of attendance and was founded by Empress Catherine the Great in 1764 and is one of the largest and oldest museums in the world. It has over three million items in its collection including the largest collection of paintings in the world. Since only a small part of their vast collection is on permanent display, they set up a number of local subsidiaries, including the one in Amsterdam, which organize temporary exhibitions that change roughly every six months with items borrowed from the State Hermitage. The Hermitage Amsterdam has a permanent building in the center of Amsterdam and was opened by then Russian President Dmitry Medvedev and Dutch Queen Beatrix in 2004. The Hermitage Amsterdam has to compete with Amsterdam's dense and wide range of cultural offerings but has established itself prominently in the top 10 list of museums in the Netherlands, being one of the largest and most visited museums in the city (van Lent & van Os, 2013).
The Hermitage Museum Amsterdam does not receive government subsidies to run its cultural and creative operations. This makes it an appropriate and relevant case for two main reasons. First, government subsidies affect the (entrepreneurial) behavior of museums and other types of cultural institutions in a unique way, depending on the specific local institutional context and specific contractual terms with respect to the subsidies that are granted. For example, some governments require cultural institutions to pay back (part of) the received subsidies when certain success milestones are reached, while others do not. The fact that the Hermitage Museum does not receive government subsidies makes our study more generalizable. Second, as a consequence of cuts in government subsidies that can be observed in many western countries, cultural institutions such as museums need to become more entrepreneurial in attracting alternative revenue streams and building a network of members that act as ambassadors for their organization. This makes our study of the Hermitage Museum particularly relevant also from a practical management point of view.
The Hermitage Museum Amsterdam has developed a membership program called "Friends of the Hermitage," and people pay an annual fee to become a member and get the benefits. The membership program includes four types of membership that can be viewed as hierarchical levels: "Friend of the Hermitage," "Friend of the Hermitage Duo," "Catherina Circle," and "Peter Circle" with annual fees of €35, €55, €500, and €5,000 respectively. Members enjoy free access to the Hermitage in both Amsterdam and St. Petersburg, two exclusive preopenings per year, exclusive access to the members-only lounge, direct mail updates, a 20% discount at the Hermitage shops, and fast lane access to the museum. Higher level members enjoy some additional privileges such as family member benefits, receiving catalogues of all exhibitions, invitations to openings of all new exhibitions, attendance of special travel events, and preferential access to special events. Members in the highest level-or "Peter Circle"-who pay €5,000 per year have the right to use the exclusive members-only lounge for hosting one private dinner per year. In addition, they are invited for pre-opening previews of new exhibitions, including an exclusive tour by the curators.

Questionnaire and sampling
Research access was granted by the Hermitage Museum in Amsterdam to collect data from both members and non-members. No additional requirements were imposed on the researchers. Access was granted to one of the authors of this study who had been employed at the Hermitage Museum as a floor manager before the start of the research project. In terms of the sampling procedure, only paying members with an active email address were considered as members. This led to a database of 776 members. From this group, 13 members were excluded because the registered membership level did not correspond with the recorded paid membership fee. Finally, 104 persons were left out of the sample because of delivery failure notifications and out-of-office replies to the announcement of the survey via e-mail. This means that the questionnaire reached 659 members. A reminder was sent 4 days after distribution of the survey, resulting in a usable sample of 308 members and a response rate of 47%. Table 1 shows the percentages of each of the four membership levels for both the population and the sample. Table 2 shows that all 2,482 members of the Hermitage Museum combined paid a total of €146,560 in annual membership fees.
In addition, we surveyed 122 random non-members within the museum. We made a number of decisions to minimize the potential bias in the sample of nonmembers that we surveyed at the museum premises. First, we surveyed non-members spread throughout the day at normal opening hours. Second, we surveyed nonmembers during the week as well as during the weekend. Third, we surveyed non-members only after (not before) they visited the museum to make sure that they actually experienced the museum before they were surveyed. Fourth, non-members were approached in the foyer that everyone needs to pass through on their way out to the exit. Note that only Dutch nationals were included in the sample because this enabled us to compare these nonmembers with members, which are also mostly Dutch nationals. In addition, a focus on Dutch nationals also enabled us to control for the barrier of geographical distance that prevents potential repeat visits by tourists. The total sample of members and non-members is 430 respondents.
There could be a bias in our sample resulting from the fact that we used e-mail to reach members and ask them to fill out the questionnaire online. A potential lack of IT savviness by relatively older members might lead to a bias towards relatively young members in the sample. However, this could be offset by the fact that older (and particularly retired) people tend to have more spare time to fill out the questionnaire. While O'Hare (2008) finds that the audience for high arts is clearly aging, unfortunately the age of the members is not documented in the database of the Hermitage. Consequently, a direct comparison between the age of the members in the population and the sample is not feasible. However, it is possible to compare the age of members and nonmembers surveyed in this study. Table 3 shows that in the members sample there are relatively many people in the age bracket of 71-80 (20.4%), while in the nonmembers sample there are relatively many people in the age bracket of 21-30 (16.4%). Finally, members spend more than 4 times as much on cross-buying compared to non-members, respectively €105.01 and € 23.54.
The questionnaire was designed after reviewing various studies, adapting existing scales as much as possible, and transforming them to fit the museum setting. Since five-point and seven-point Likert scales are similar in terms of effectiveness (Nunnally, 1978), for consistency and ease of use, seven-point Likert scales were used throughout the questionnaire. After constructing the questions, the initial survey was pretested using four random visitors and members, three employees of the Hermitage Amsterdam and three academics. The length of the survey was limited to a few pages to avoid response fatigue. Since many items were translated from existing English scales, reverse

Variables and operationalization
Four potential types of value across personal, financial, and strategic value dimensions are included (Biggemann & Buttle, 2012): (1) cross-buying at the museum; (2) recommendation behavior; (3) joint visiting with non-members, and (4) recruitment of new members into the program.
• Cross-buying behavior. This variable is operationalized as the total expenditures in the restaurant and the museum store measured in Euro over the past year. We measured this by asking the following two questions: "How much do you estimate to have spent at restaurant Neva [the name of museum restaurant] over the past year?" and "How much do you estimate to have spent in total at the Hermitage stores over the past year?" • Recommendation behavior. This variable is operationalized as the total number of people to which the museum is recommended by the respondent. More specifically we asked the following question: "How many persons did you recommend to visit the Hermitage over the past year?" • Joint visiting behavior. This variable is operationalized as the number of individuals brought along on a visit to the Hermitage museum and was stated as follows: "How many paying people did you bring along with you on your visits to the Hermitage over the past year?" • Recruitment behavior. This is operationalized as the total number of people recruited as a new member of the museum. In the survey this was formulated as follows: "How many persons have become a member of the Hermitage thanks to you?" • Membership level. Membership level is measured using an ordinal variable ranging from 0 to 4: Non-members get a score of "0." The basic "Friends of the Hermitage" level is scored as "level 1" and the highest "Peter Circle" level is scored as "level 4." However, none of the respondents in the sample are from the "Peter Circle", which makes up 0.1% of the member population. • Museum prestige leveraging. For this variable we used the perceived prestige scale developed by Mael & Ashforth (1992) and adapted by Glynn et al. (1996). This scale measures prestige leveraging in social contexts and consists of the following items: "Membership of the Hermitage is highly valued in my community," "in my community it is considered prestigious to be a member of this museum," "the Hermitage is an excellent conversation topic on parties and social events" and "membership of this museum raises my status among friends and other social contacts." One of the original items-"The Museum does not have an outstanding reputation in my community"-was deleted because of lower reliability, possibly because the item was reverse coded in the questionnaire. The resulting Cronbach's alpha of this four-item scale is 0.8.

Control variables
We controlled for a number of variables that might provide alternative explanations for our results.
• Organizational identification. Consumers that identify with an organization or brand are more likely to say positive things about the organization or brand and to recommend it to others (Bhattacharya & Sen, 2003). We therefore expect that organizational identification might affect each of our dependent variables as well.
To measure identification with the museum, an existing organizational identification scale developed by Mael & Ashforth (1992) was employed. This scale was adapted by filling in the name of the focal organization: Hermitage Amsterdam (Bhattacharya et al., 1995). The Cronbach's alpha of this five-item scale is 0.875. • Satisfaction. We included a satisfaction scale because one might expect that members and visitors of museums are more likely to recommend a museum and its membership program if they are satisfied with the organization and its services. The scale that we used is similar to Bhattacharya et al.'s (1995) and respondents could indicate their level of satisfaction with each of the following aspects: exhibitions, programming, museum shop, museum restaurant, organizational goals, website and communication, personnel, facilities and the building. The Cronbach's alpha of this nineitem scale is 0.805. • Membership duration. Years of membership has a positive effect on recommendations (Hager, 2014). In addition, one might expect that recent members visit the museum more often and as a result spend more money annually in the museum store and restaurant, while long time members might be more active in recruiting new members. We measured membership duration in the number of years since becoming a member. • Visits to other museums. This is a count variable for the number of other museums visited in the last year. It is included because people who visit many museums, have a positive attitude towards museums and would therefore be more inclined to promote museums in general, and the Hermitage in specific (Bhattacharya et al., 1995). • Age. Volunteers (Holmes & Slater, 2012) of cultural institutions tend to be relatively old. This variable is included because one might expect that older peopleespecially pensioners-have more time to be actively involved with the museum of which they are a member. • Gender. Finally, we included a dummy variable to distinguish between females and males with females being coded as 2 and males as 1.
All Cronbach alphas are good (above 0.8), indicating high reliability. In addition, a confirmatory factor analysis was performed using all multi-item scales. No significant cross item loadings were identified and all items loaded significantly on their expected dimension. The results are presented in the next section, including a more detailed description of the sample. Table 4 shows the descriptive statistics for the complete sample of 430 respondents. We first highlight some of the descriptive statistics related to the control and independent variables. First, the satisfaction with the museum is high with an average of 5.96 on a seven-point scale. Second, there are slightly more females (55%) than males (45%) in the sample. Third, the average age score is 4.37. Because we used age brackets in the questionnaire, this translates into an average age of about 54. This is very close to the average age of 52 found in other studies about museum members (Glynn et al., 1996). Finally, the average level of perceived prestige of the Hermitage Museum (that is leveraged) is 3.84 on a Likert scale from 1 to 7.

RESULTS
With respect to the dependent variables there are a few interesting descriptive statistics. First, cross-buying behavior in the museum store and restaurant is on average €82.09 per person per year. However, there is a high standard deviation with annual spending ranging from €0 to €1,280. Second, the average individual in the sample recommends the museum to 6.35 individuals per year and it ranges from 0 to 150. Third, on average visitors bring in 2.03 other paying visitors, with at least one individual having brought along 46 paying visitors in a single year. Finally, the average recruitment behavior score is 0.45. This variable has a relatively large standard deviation with many individuals not recruiting at all, and at least one person recruiting 27 new members in a single year. The skewed nature of most variables is indicative of count data requiring a different approach than ordinary least squares (OLS) regression. Table 4 also shows the correlations of the variables. A few notable correlations provide some interesting insights. First, membership level is significantly correlated with age (r = 0.207, p < 0.001), which is an indication that members in higher levels of the membership program are older than those in lower levels. Second, a higher-level member is more likely to be male (r = À0.180, p < 0.001). Third, the level of membership is significantly correlated with museum prestige leveraging (r = 0.307, p < .001). Finally, the correlations between the independent variables are modest, and the variance inflation factors are below 2, which indicates that multi-collinearity is not a concern.
The central hypotheses are tested using a series of 3-step generalized linear model (GLM) regression analyses in line with Baron & Kenny (1986). Next, these results are validated using simultaneous estimation using the Preacher & Hayes (2004)  model estimations on a sample that excludes nonmembers, and some other model specifications were used as robustness checks. In the first step, the independent variables are regressed on the proposed mediator. Next, we estimate the model with all the controls, and the independent variables for each of the four different dependent variables. The results can be found in Tables 5 and 6 (see  models 1, 3, 5 and 7). Next, we add the museum prestige leveraging variable and test for mediation. These results can also be found in Tables 5 and 6 (see models 2, 4, 6 and 8). The first dependent variable-cross-buying behavior-is measured in euros. However, the other three dependent variables-recommendation, joint visiting and recruitment behavior-are count data, which make OLS regressions problematic. First, to estimate the crossbuying behavior model we used a GLM regression using a gamma distribution because there are non-negative outcome values. Second, to estimate the three count data models we first performed a Poisson model estimation. However, the log-likelihood test of alpha indicated that the variance of our dependent variable exceeds the mean (p < 0.01), meaning that over dispersion is high resulting in high deviance. When the assumption of equidispersion is violated in the Poisson model, standard errors may be underestimated and results unreliable (Cameron & Trivedi, 2009). We therefore used a negative binomial model instead (Hausman, Hall, & Griliches, 1984). Tables 5 and 6 show the results of respectively the gamma and negative binomial GLM regressions. In all models, the independent variables explain a significant amount of variance (p < 0.001). GLM allows for fixed factors so that the associations can be estimated across the levels of the membership program.
First, model 1 shows that membership level is positively related to cross-buying behavior: (Level 1, β = 0.72, p < 0.001; Level 2, β = 0.83, p < 0.001; Level 3, β = 1.41, p < 0.001). When the mediator variable museum prestige leveraging is added to the regression in model 2 it obtains a positive and significant coefficient (β = 0.13, p < 0.05) and the magnitude of the relationship between membership level and cross-buying behavior drops significantly (Level 1, β = 0.66, p < 0.001; Level 2, β = 0.76, p < 0.001; Level 3, β = 1.26, p < 0.01), which offers support for mediation. We also tested for mediation using basic PROCESS model and Sobel tests (Preacher & Hayes, 2004). The results show that museum prestige leveraging is a significant (partial) mediator through an indirect effect (z = 2.86, p < 0.01). Similar results were also found across all dependent variables using SEM and sample splits. These findings offer support for Hypothesis 1a stating that there is a positive relationship between membership level and cross-buying behavior, and Hypothesis 2a stating that the positive relationship between membership level and cross-buying behavior is mediated by museum prestige leveraging. Second, in model 3 we find a positive and significant relationship between membership level and recommendation behavior regarding the Hermitage Museum (Level 1, β = 0.63, p < 0.01; Level 2, β = 0.77, p < 0.001; Level 3, β = 1.14, p < 0.01). When the mediator variable museum prestige leveraging is added to model 4 (β = 0.11, p < 0.10), the magnitude of the direct relationship between membership level and recommendation behavior T A B L E 5 OLS regression results for cross-buying at the museum drops significantly (Level 1, β = 0.56, p < 0.01; Level 2, β = 0.70, p < 0.001; Level 3, β = 1.03, p < 0.01) offering support for partial mediation. Similarly, the PRO-CESS and Sobel test supports (partial) mediation through an indirect effect (z = 2.73, p < 0.01). These findings offer support for hypothesis 1b stating that here is a positive relationship between membership level and recommendation behavior, and Hypothesis 2b stating that the positive relationship between membership level and recommendation behavior is mediated by museum prestige leveraging. Third, in models 5 and 6 we find no significant relationship between membership level and joint visiting behavior (Level 1, β = 0.35, ns; Level 2, β = 0.12, ns; Level 3, β = 0.65, ns). In addition, we find no significant relationship between museum prestige leveraging and joint visiting behavior (β = À0.02, ns). This means that we do not find support for Hypothesis 1c stating that here is a positive relationship between membership level and joint visiting behavior, and Hypothesis 2c stating that the positive relationship between membership level and joint visiting behavior, is mediated by museum prestige leveraging.
Fourth, in models 7 and 8 we find a significant but negative-instead of a hypothesized positiverelationship between membership level and recruitment behavior (Level 1, β = 3.33, p < 0.001; Level 2, β = 2.90, p < 0.001; Level 3, β = 2.29, p < 0.05). When the mediator variable museum prestige leveraging is added to model 4 (β = 0.21, p < 0.10), the magnitude of the direct relationship between membership level and recruitment behavior drops significantly (Level 1, β = 3.18, p < 0.001; Level 2, β = 2.77, p < 0.001; Level 3, β = 2.04, p < 0.05). However, including the variable museum prestige leveraging in model 8 does not affect the coefficient for membership level, showing that there is no mediation. This means that we do not find support for Hypothesis 1d stating that here is a positive relationship between membership level and recruitment behavior, and Hypothesis 2d stating that the positive relationship between membership level and recruitment behavior, is mediated by museum prestige leveraging.
As stated previously, these results are robust across of range of models and approaches. During the analyses, competing models with additional mediators and even moderators were considered resulting in insignificant models, lower fit, and similar results in the core of the study. The estimation of a sequence of path models also provided similar results as those reported above. In the next chapter we will discuss the results of our empirical study for theory and practice and provide possible explanations for some unexpected findings that offer avenues for future research.

DISCUSSION AND CONCLUSION
Membership programs play an important role in a growing number of cultural organizations. Since membership T A B L E 6 Negative binomial regression for recommending the museum, joint visits to the museum, and recruitment of new members programs have the potential to yield various financial and non-financial advantages (Bhattacharya et al., 1995;Glynn et al., 1996), cultural organizations, and not just museums, should at least consider the implementation of a membership program. However, there are still a lot of questions about how membership programs exactly work. While many design choices can be expected to have positive effects, some may backfire in unexpected ways.
In this paper, we studied the degree to which museums can benefit from their members beyond their annual membership contributions in the form of cross-buying behavior during their museum visits, recommending the museum to others, joint visits with non-members, and recruitment of new members into the program. Moreover, we take a relationship value approach to study how members and the museum benefit through a multidimensional relationship value mechanism that benefits the member as well as the museum. We did this by analyzing survey data of both members and regular visitors of the Hermitage Museum in Amsterdam, an iconic museum in a European market where competition is growing, government subsidies are becoming scarcer, and the COVID-19 pandemic has decreased number of visits in general and those by tourists more specific. As a result, museums need to adopt new approaches to generate alternative revenue streams (Kadoyama, 2018).
The benefits of a membership program with different hierarchical levels are not always straightforward but the relationship value approach argues that there are benefits to both sides. These benefits can be financial, personal, knowledge related, or strategic. First, the results of our empirical study show that higher-level members display a stronger degree of cross-buying behavior during museum visits in the form of spending money at the museum restaurant and museum store (financial relationship value). In addition, higher level members also recommend the museum to people in their social network more often (personal and strategic relationship value). Moreover, both these relationships are partially mediated by the leveraging of the museum's prestige by the members in their social network (e.g., Leary, 2005).
No significant results were found for the hypothesized positive relationship between membership level and joint visiting behavior to the museum with non-members. This is in line with previous findings that customers with a membership do not necessarily visit the museum more often (Glynn et al., 1996). Our findings show that there is no reason to think that they bring more people along either. As a result, no support was found for a mediation effect of museum prestige leveraging with respect to this relationship. In addition, and contrary to what was hypothesized, a negative (instead of a positive) relationship was found between membership level and the degree to which members recruit new members into the membership program. This interesting anomaly might be explained by the fact that the value of higher-level membership derives from its exclusivity. From a stakeholder perspective, this shows that rather than members behaving as a homogeneous stakeholder group, members behave differently depending on their membership level. As a consequence, museums, and other cultural institutions that want to derive more (relationship) value from their membership program, may need to apply a multi-stakeholder approach in dealing with members in different levels.
Prior research has identified two competing relationship needs of consumers: a need for uniqueness and a countervailing need for conformity (Amaldoss & Jain, 2005). Our finding across different member behaviors indicate that there may be status increasing behaviors (recommendation) and a status diluting behavior (recruitment) at play that create different outcomes. The higher the membership level, the more exclusive its benefits, the more they satisfy consumers' need for uniqueness. Relatedly, it might be that higher level members are more likely to be status consumers with a strong need for exclusivity (Veblen, 1899). While spending money at the museum store and restaurant, as well as recommending the museum to others, enable members to leverage the status associated with their (especially high level) membership, recruiting (especially high level) new members is likely to lead to status dilution (Dreze & Nunes, 2009), which runs directly counter to the exclusivity and status benefits that (especially high level) membership offers. Interestingly, WoM and referrals are often seen as similar (Biggemann & Buttle, 2012). However, our study shows there are fundamental differences in the context of hierarchical membership programs as referrals may relate to status dilution.
Prior studies about membership programs lack an overarching theoretical underpinning and mostly focus on explaining member identification with the museum (Bhattacharya et al., 1995) and the cost effectiveness and use of these programs (Glynn et al., 1996). These studies tend to ignore other forms of value generating behaviors that can benefit museums, and arguably other non-profit cultural institutions that are running them. Our study shows that some member behaviors that benefit museums, namely cross-buying and recommending the museum, depend on the hierarchical level of the membership. In particular, we show that the relationship value approach has merit at the level of personal value relationship (e.g., increased WoM by higher tier members) and the financial value relationship (spending more in the museum store by higher tier members). We also show that these relationships are driven by higher level members leveraging prestige in social contexts and these behaviors are clearly offering value for both the members and the museum.
In addition, this study finds that membership level is negatively related with member recruitment behavior into the membership program. In a way, this is in line with Dreze & Nunes (2009) who found that increasing the population size in tiered loyalty programs dilutes the perception of status by existing consumers. Our findings suggest that high level members might recruit fewer new people for the membership program because it dilutes the status and exclusivity that they themselves derive from being a member. From a theoretical perspective, our study shows that relationship value consists of different value elements that are less "'linear" as expected, meaning more is not always better. The composition of the relationship value elements across members in the same system may be fundamentally different and some value elements can even become negative resulting potentially in avoidance behaviors.
Finally, beyond the context of membership programs of non-profit cultural institutions our findings build on Hager (2014), who studied direct benefits from members in the form of donations and voluntary work, by including recommending membership to friends and colleagues. He found these behaviors to be twice as common than members either donating or volunteering. By taking a relationship value approach we show that it makes sense to distinguish recommendation behavior from referral behavior and make distinctions between recommending the museum (organization referral), joint visits to the museum with non-members (product referral) and recruiting new members (membership referral).
This study has a number of practical or managerial implications. The fact that this study was supported by the management of a leading museum shows that there is a need for more knowledge about the benefits and costs of running membership programs. The finding that the hierarchical nature of membership programs can have positive as well as negative effects has implications both for the way membership programs are designed and how its individual members are managed and incentivized. First, while museums might benefit from stimulating members in higher levels to recommend the museum, when stimulating the recruitment of new members, they may better focus their attention on members in lower levels. Second, the fact that the relationship between membership level and performance outcomes of membership programs are mediated by the perceived prestige of the focal organization, suggests that in the design of membership programs one should take into account the degree of perceived prestige of the museum. To facilitate prestige leveraging, the museum management may look for ways to increase the (perceived) prestige of the museum through showcasing famous collections and exhibitions or building affiliations with high status external actors.
This study has limitations that also point to avenues for future research. First, one has to be careful in generalizing the findings to other (non-profit) cultural institutions. For instance, whereas museums are generally non-rivalrous in consumption, in the case of theatre, ballet, and other performing arts, offering unlimited free entrance for members may not be possible due to the limited number of seats. Second, the fact that the Hermitage Museum hosts many changing exhibitions might make it more attractive for membership compared to museums that can only host (small) permanent exhibitions. Third, individuals in higher membership levels could be wealthier and have a larger social network, which might be an alternative explanation for their higher cross-buying and recommendation behavior. Fourth, since running a membership program requires resources, the costs and potential downsides involved in running these programs should not be ignored. Especially highly involved individuals demand a personal approach, which can be costly. Fifth, the data used in the study only allows for the investigation of associations that are driven by theory, but future research may also involve experiments and longitudinal studies to investigate causal relationships and use SEM and other approaches for rigorous testing of the relationships.
Finally, apart from positive and negative outcomes of membership programs, their complexity and stakeholder network impact need to be considered. Membership programs complicate stakeholder management practices (Della Torre et al., 2018) by adding a new and potentially influential group of external funders-besides government agencies, corporate sponsors and individual philanthropists-that may want to influence artistic choices (Alexander, 1996). Future studies could therefore focus on the extent to which membership programs affect the balance between the logics of art and commerce in cultural organizations (Caves, 2002;Delmestri, Montanari, & Usai, 2005;Eikhof & Haunschild, 2007). In particular, since prior research shows that corporate sponsors tend to push for more accessible content while individual patrons for less accessible content (Alexander, 1996), it would be interesting to see whether members, and particularly those in higher levels who are expected to be similar to individual patrons, shift the balance in cultural organizations towards the logic of art. This might be explained by prestige leveraging by members being easier for less accessible or unique content than for more accessible or blockbuster content.