THE IMPACT OF NEW ATTRACTIONS ON THEME PARK ATTENDANCE
January 20, 2009
Rutger D. van Oest1 Harald J. van Heerde Marnik G. Dekimpe
1 Rutger D. van Oest is Assistant Professor of Marketing, Tilburg University, The Netherlands, Email:
[email protected]. Harald J. van Heerde is Professor of Marketing at the Waikato Management School, University of Waikato, New Zealand, Email:
[email protected]. Marnik G. Dekimpe is Research Professor of Marketing & CentER Fellow, Tilburg University, The Netherlands & Professor of Marketing, Catholic University Leuven , Belgium, Email:
[email protected]. Acknowledgments: We are indebted to Olaf Vugts (Director Marketing & Development) and Rosella van Haver (Market Research Division) from the Efteling for granting us access to the data, and for their insights on the theme-park industry. We also thank Didi Lin for help with the data preparation.
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THE IMPACT OF NEW ATTRACTIONS ON THEME PARK ATTENDANCE Abstract Theme parks invest extraordinary amounts in new attractions to boost visitor numbers. However, little is known about how long such effects, if any, last, nor about how a new attraction interacts with other attractions, precluding an effective cost-benefit analysis. Therefore, we present a new model that estimates for each attraction the number of additional park visitors it generates. Using a longitudinal mixture of shifted gamma densities, it assesses how the contribution of an attraction is distributed both within a given year and across years. Interactions between the different attractions are captured through both a saturation and a reinforcement effect. The model is calibrated on twenty-five years of weekly attendance data from the Efteling, a leading European theme park. We find a saturation effect: the impact of the new attraction is smaller if similar attractions are already present in the park. New attractions also have an indirect effect by reinforcing the drawing power of similar extant attractions, especially when these were introduced recently. The overall Return on Investment (subsequent revenues divided by initial investment) across 14 major attractions is 1.21, and it becomes 1.57 when indirect effects are included. The model allows management to assess the expected ROI of future attractions. Key words: Gamma mixture modeling, Entertainment industry, Theme parks, Return on Investment.
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1. INTRODUCTION Over the last decade, the marketing-science literature has become increasingly interested in the entertainment industry. This interest, however, has mostly centered on the motion-picture industry (see e.g., Eliashberg et al. 2006 for a comprehensive review). Much less attention has been devoted to the theme- and amusement-park industry. Theme (or amusement) parks are generally outdoor venues with rides as the primary attraction. Theme parks require high capital investments, and typically charge a single entry price. They often emphasize one dominant theme around which the landscaping, rides, shows, food and personnel costumes are centered (Kemperman 2000). Well-known examples include Disney World, Disneyland, Universal Studios and Six Flags in the United States, and Disneyland Paris, Tivoli Gardens (Denmark) and the Efteling (The Netherlands) in Europe. Table 1 gives a more extensive overview. Table 1: Key Players in the Amusement Park Industry Europe Rank Park & Location
1 2 3 4 5 6 7 8 9 10
Disneyland Paris (France) Blackpool Pleasure Beach (UK) Tivoli Gardens (Denmark) Europa Park (Germany) Port Aventura (Spain) Efteling (Netherlands) Gardaland (Italy) Liseberg (Sweden) Bakken (Denmark) Alton Towers (UK)
United States 2006 Attendance (000) 10,600 6,000 4,396 3,950 3,500 3,200 3,100 2,950 2,700 2,400
Park & Location
Magic Kingdom at Walt Disney World (FL) Disneyland (CA) Epcot at Walt Disney World (FL) MGM Studios at Walt Disney World (FL) Disney’s Animal Kingdom at Walt Disney World (FL) Universal Studios (FL) Disney’s California Adventure (CA) Seaworld Florida (Florida) Island of Adventure (Florida) Universal Studios Hollywood (CA)
2006 Attendance (000) 16,640 14,730 10,460 9,100 8,910 6,000 5,950 5,740 5,300 4,700
Source: TEA & Economics Research Associates (www.parkworld-online.com)
In 2006, total attendance at the world’s Top 25 parks (each of which had an attendance of over 3.9 million) amounted to 186.5 million visitors, an increase of 2.2% relative to the previous year (Rubin 2007). Worldwide revenues in 2003 were $19.78 billion, which were estimated to increase to $24.71 billion by 2008 (PriceWaterhouseCoopers 2004). The theme park industry requires considerable capital investments. First, huge outlays are needed to enter the market with a new park. Disneyland Paris, for example, cost almost $4 3
billion to build (Spencer 2001). Once in business, considerable additional funds are needed to regularly update the available attractions, and to implement new rides to attract visitors to the park. An often-heard industry rule is that one has to expand the theme park every year with one new attraction (Dietvorst 1995). On average, close to 20% of the turnover is spent on new and better rides or activities (Kemperman 2000). Quite some anecdotal evidence exists on the incremental drawing power of such new attractions. In 1991, Universal Studios reported an attendance increase of 52%, which it attributed to its new ride inspired by the popular movie Back to the Future (Formica and Olsen 1998). Similarly, the leading Dutch theme park the Efteling witnessed a 30% increase in number of visitors during the opening year of its first rollercoaster attraction in 1981, the Python. Still, the industry is increasingly concerned with the escalating scale of the investments required to add new rides. New attractions with price tags in excess of $100 million are no exception. The Test-Track ride in Epcot, Orlando, is estimated to have cost $130 million, Disney World’s Expedition Everest cost $110 million, and Universal Studios’ Adventures of Spider-Man was $105 million (Hyman 2006). Not only are new rides becoming more and more expensive, managers also fear they no longer give a similar boost to visitor numbers, and thereby start to question their Return on Investment (Vugts and van Haver 2008). The objective of this paper is to develop and test a new model for the impact of new attractions on theme park attendance, catered to the specificities of the theme-park industry. This model (i) proposes a longitudinal mixture of shifted gamma densities to describe the over-time variation in visitor numbers, and (ii) captures in a parsimonious way the interaction (saturation and reinforcement) between different attractions. Why do we need a new model? First, the actual contribution of a new attraction to a park’s attendance is not a priori clear. Unlike motion
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pictures which are characterized by short life cycles, theme-park attractions last for multiple years, and may have a drawing power that extends well beyond their year of introduction. Still, as the attraction grows older, its novelty is likely to gradually wear out. The drawing power of a given attraction varies not only across years but also within a given year, as visitor numbers are quite sensitive to seasonal fluctuations. Because both effects operate simultaneously, the timevariation in the impact of a new attraction is unlikely to be captured through conventional decay patterns. We capture this dual (i.e. across and within years) variability through a longitudinal mixture of shifted gamma densities. To complicate matters, there is typically a single admission charge to the park which gives visitors access to all attractions. Therefore, the only data that are observed are the number of people that bought access to the combined “bundle” of attractions rather than to just the new attraction. We adopt the aforementioned mixture specification to describe a latent process, as the extra attendance due to a new attraction is not directly observed. Second, theme-park attractions are part of a larger bundle of attractions, whose life cycles may (partially) overlap in time. As a consequence, the direct impact of the new attraction may be smaller if similar attractions are already present, reflecting a saturation effect. On the other hand, existing attractions may receive a boost from the new attraction, reflecting an indirect reinforcement effect. For example, a new roller-coaster ride may rejuvenate the drawing power of the extant thrill rides. We propose a parsimonious model specification to capture both effects. We distinguish between different types of attractions (e.g., thrill attractions, as opposed to more placid attractions targeted to an older and/or family-oriented audience and designed to emphasize the park’s general theme), and assess to what extent the aforementioned saturation and reinforcement effects are present mostly (or even only) between attractions of the same type.
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To sum up, from a substantive point of view, we contribute to the growing literature of marketing-science applications in the entertainment industry. Specific features of the theme-park industry require other modeling approaches than previous applications, which typically focused on the motion-picture industry. From a methodological point of view, we (i) introduce the idea of using a longitudinal mixture of shifted gammas to reflect the over-time variation in effects, both within and across years, and (ii) develop a parsimonious way to capture the interaction between different attractions through saturation and reinforcement effects. We apply the model to a unique data set of 25 years of weekly visitor data to the Efteling, one of Europe’s leading theme parks, allowing us to disentangle the relative contribution of each of its major attractions, and derive their associated Return on Investment. By explicitly modeling the interactions among these attractions, we are able to decompose the total contribution into a direct effect and an indirect effect through a revitalization of the drawing power of extant attractions. In our application, we find that, on average, 35% of the impact of new attractions occurs in the year of introduction, while 90% materializes within the first five years. The impact within a year varies considerably, with the biggest bump occurring in the high season. Thrill rides draw more additional visitors to the park than themed attractions do. However, too many thrill rides (or too many themed ones) may not be beneficial, as there is a substantial saturation effect. On the other hand, new attractions also have an indirect effect by reinforcing the drawing power of extant attractions of the same type. 2. LITERATURE REVIEW Our work can be situated in three literature streams. First, it adds to the growing literature on how marketing science can be applied to the entertainment industry. While much recent research has looked at the movie industry (see Eliashberg et al. 2006 for a review), we could not find any study published in Marketing Science (for which we systematically checked 6
all issues since 1982), Management Science, the Journal of Marketing, and the Journal of Marketing Research (all considered over the same time) on the theme park industry.2 This is surprising, as the industry has great economic importance, and characteristics that differ considerably from the movie industry. Indeed, the “bundled” nature of the theme parks’ attractions, in combination with their much more extended life cycle characterized by timevariation both within and across years, adds a dimension not encountered in the movie industry. Within the leisure sciences, prior research has primarily looked at what drives tourist choice behavior, not only when they have to choose their destination, but also once they are at their destination. Kemperman et al. (2000) used conjoint choice models to assess the impact of seasonality and variety seeking when choosing between a theme park, the zoo, and cultural/educational parks, while Stemerding et al. (1999) developed a conjoint experiment to study the impact of various aspects (weather, time availability, presence of kids) on the preferences underlying the choice for a specific destination. Other studies have focused on tourists’ behavior once they are at a given park, such as the timing and sequencing of their activities within the park (Kemperman et al. 2002), or the duration of these activities (Darnell and Johnson 2001). None of these studies focused, however, on quantifying the contribution of individual attractions to the aggregate number of visitors, how various attractions interact, nor on how their contribution varies within and across years. Second, there is a growing recognition that marketing should be able to demonstrate the Financial Returns of its Investments (see e.g., Ambler 2003). This has been one of the recent research priorities of the Marketing Science Institute (2006, 2008). Even though numerous approaches have been developed to evaluate the financial return from a specific marketing
2
Some studies (often on the fate of Disneyland Paris) have appeared in marketing outlets (see e.g. Spencer 1995), but have been mostly descriptive in nature.
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expenditure (see e.g., Rust et al. 2004), the features of our setting require a new modeling approach, as discussed in more detail in Section 3. Finally, theme parks are “bundles” consisting of multiple attractions. The practice of product bundling has received ample attention from both microeconomists (e.g., McAfee et al. 1989) and marketing researchers (e.g., Stremersch and Tellis 2002; Foubert and Gijsbrechts 2007). In the terminology of Adams and Yellen (1976), theme parks reflect pure bundling, as only the bundle (i.e., access to all attractions) can be bought, while the separate components of the bundle (i.e., access to only one of the attractions) cannot in general.3 Prior research has established that the composition of the bundle is important, as the perceptions of the different components not only interact with each other, but also integrate into an overall bundle perception (Venkatesh and Mahajan 1997). This overall perception drives the reservation price of potential visitors, and hence their purchase intent (Harlam et al. 1995). However, prior empirical research has mostly considered bundles whose composition does not change over time, and which consists of a limited number of components. Harlam et al. (1995, p. 60), for example, opted for two-item bundles in their interactive computer experiments “because: (a) they are most common in the marketplace, and (b) it simplifies the respondent and analysts tasks”. Also Venkatesh and Mahajan (1997) considered two-item bundles. Theme parks, in contrast, consist of multiple attractions.4 Moreover, while previous studies considered static bundle compositions, we consider a setting where existing bundles are regularly augmented with new attractions, and study not only how the new attraction’s effect is affected by the bundle composition at that time, but also how the drawing power of existing attractions may be altered because of this addition.
3 4
Some of the exceptions include Blackpool Pleasure Beach (UK) and Tivoli Gardens (Denmark). In our empirical application, for example, we consider 14 attractions.
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3. MODELLING CHALLENGES The objective of this paper is to develop and test a model for the impact of new attractions on theme park attendance. In so doing, we face two key challenges. First, we need to capture the time-varying impact of new attractions, where this impact may vary along two dimensions: within the same year and across different years. Second, we need to account for interactions with other attractions. These interactions are two-dimensional as well: (i) potential saturation effects, as more existing attractions of the same type may lead to a lower number of marginal visitors, and (ii) potential reinforcement effects, as a new attraction may boost the attractiveness of extant attractions of the same type. 3.1 Time-Varying Impact of New Attractions: Within and Across Years The impact of new attractions may vary both within and across years. Within a year, the impact could be most prominent in the first weeks of introduction (as in the upper left panel of Figure 1), if only because of the press coverage such a new attraction typically receives. On the other hand, theme park attendance tends to be highly seasonal. For example, attendance tends to go up in the summer holiday period. Accordingly, the impact of new attractions on theme park attendance is also likely to be higher during this period (as shown in the upper right panel of Fig. 1), as there is a larger pool of potential visitors. The impact may also vary across years. Indeed, the impact of a new attraction may not only manifest itself in the weeks and months directly following its opening (as in the top row of Figure 1), but may be spread over time, possibly for a period of several years. Over time, the novelty of the attraction may wear out, and we expect a downward trend in the impact on attendance over a time period of multiple years. Obviously, the speed of this wear-out may be fast (row 2 of Figure 1) or gradual (row 3 of Figure 1).
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Figure 1: Potential shapes of the over-time impact, within and across years
3.2 Interactions with Other Attractions: Saturation and Reinforcement Attractions do not operate in isolation, but are part of a larger bundle. As such, our model needs to take into account the interactions between attractions. First, there may be a saturation effect, that is, the more attractions of a certain type (e.g., a thrill ride) are available in the park, the less effective the next attraction of the same type will be. This is consistent with the assortment literature, which finds that adding items that are similar to existing ones does not necessarily improve consumer perceptions or sales much (Broniarczyk et al. 1998). The underlying principle is that by offering more of the same, the target group reaches a limit on how much it can or is willing to consume. Consequently, we need to model the effect of investments in extant (earlier) attractions of a certain type on the ability of a new attraction of that same type to attract additional visitors to the theme park. Consistent with a saturation effect, we expect this
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impact to be negative. Figure 2 illustrates the direction of such saturation effects: extant attractions affect the effectiveness of the new (focal) attraction. Figure 2 Direction of saturation and reinforcement effects for the focal attraction and an extant attraction saturation
•
× extant attraction
reinforcement
time
focal attraction
Second, new attractions of a certain type may give a boost to (reinforce) the effectiveness of extant attractions of the same type (see also Fig. 2). Memory research suggests that a new attraction of a certain type may activate extant attractions of the same type in consumers’ memory (Solomon 2006, p. 102-104). For example, a new thrill ride may reactivate a consumer’s memory of the park’s extant thrill rides. Studies on attribute alignability support the idea that consumers make attributes which are common/consistent across options more salient (Van Ittersum et al. 2007), and base their preferences more on these common aspects (Zhang and Markman 2001). According to Brown and Krishna (2004), consumers search for alignable attributes in choice situations, and are more satisfied when choosing alternatives according to these attributes. This suggests that the new attraction may not only activate the memory of existing similar attractions, but may also increase their appeal. Consequently, we need to model the impact of a new attraction of a certain type on the ability of extant attractions of that type to attract additional visitors to the park. We expect this effect to be positive, consistent with a reinforcement effect. The interplay between the different factors is illustrated in Fig. 3.
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Figure 3: Saturation, reinforcement, direct and indirect effects
In the top panel, the black area depicts the direct impact of Attraction A, which clearly varies both within each year and across years. With a two-year lag, Attraction B is introduced, which is of the same type and as expensive as Attraction A. A similar over-time pattern is obtained (grey area in the middle panel). However, because of the saturation effect, the peaks for Attraction B are lower than for A, even though the initial investment is the same. Moreover, the introduction of B gives a boost to (reinforces) the drawing power of A. This indirect effect is depicted in the top panel through the white areas (on top of the black ones). Combined across both attractions, the total impact for the theme park becomes the sum of three components (bottom panel): the direct impact of Attraction A (black area), the direct impact of Attraction B (grey area), and the indirect effect of B on A (white area). The latter two only come into play once Attraction B is introduced.
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3.3 Modeling Approach to Address the Challenges Our model is based on the assumption that the researcher has access to aggregate data on theme park attendance per time period (e.g., week). Due to their high costs, new attractions tend to be introduced quite infrequently (e.g., one per one or two years), and stay in the park for many years. To cover multiple attractions, an extended time span is needed,5 especially when assessing the long-term effects of their presence on attendance. Given this requirement, it is far more likely that aggregate-level data are available than individual-level data. Indeed, neither the theme parks themselves nor specialized data providers have, to the best of our knowledge, individual-level data available that describe a panel’s theme-park visits over a time span of multiple decades. Our modeling goal is to disentangle the (latent) contributions of extant and new attractions to park attendance. We achieve this by imposing a certain structure on their contributions (see the next section for details). We refrain from imposing additional assumptions on how these contributions might come from, respectively, repeat visitors and first-time visitors, for the following reasons. A simulation study by Bodapati and Gupta (2004) shows that it is very difficult to recover heterogeneity patterns from aggregate data, even for frequently-bought consumer goods with many repeat purchases. These problems are likely to be amplified in a theme-park setting, since there is an extreme amount of variability in visit frequency . Some theme park aficionados go almost weekly, whereas many others visit a theme park only once in their life. This results in a long-tailed distribution for the inter-purchase times, with an average repeat cycle of more than two years for most parks (www.entrepreneur.com). In line with our modeling goals and to keep the model tractable, we impose model structure to unravel the latent
5
In our empirical application, we use 25 years of weekly data covering 14 new attractions.
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contributions of attractions to attendance, but do not overlay this with additional assumptions to also infer the relative contributions of first-time versus repeat visitors. A natural starting point for our modeling approach could be a regression-type model with theme park attendance as the dependent variable. In a simplistic approach, we could use as key independent variables step dummies for each attraction: zero before introduction, and one afterwards. The coefficient for each step dummy is the extra number of visitors due to the corresponding attraction. In a second stage regression, we could then explain the coefficients through saturation and reinforcement effects. However, such an approach is problematic for several reasons. First, this step-dummy approach assumes that the effect of the new attraction is the same every week of the year, which is unlikely in a highly seasonal industry such as theme parks. Second, once the attraction is introduced, the step dummies remain one. The implied time-invariant impact of the attraction on attendance is inconsistent with the likely wear-out effect of any attraction. Third, a two-stage regression is less efficient than a one-step approach. Finally, multiple step dummies are likely to create considerable multicollinearity problems. Instead of a regression model, we could consider more advanced time-series models. For example, an intervention model with step dummies (see e.g., Hanssens et al. 2001, p. 293) could be used to capture the time variation in the periods following the introduction. While such a model is well suited to capture the patterns in the upper row of Figure 1, it does not extend easily to the patterns in the subsequent rows. Moreover, when dealing with multiple introductions, a highly parameterized specification would result. Studies which allow for multiple interventions (e.g., Kornelis et al. 2008) therefore allow only for a shift in the intercept and/or slope of a deterministic trend line, and do not allow for the extent of variation within and across years
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required in our setting. Besides, such structural-break models would still require a two-step regression approach to understand the drivers of the effects of new attractions. Approaches that overcome the latter problem are Kalman Filters (e.g., Naik et al. 1998) and Dynamic Linear Models (e.g., Van Heerde et al. 2004). However, these models would still have to use step dummies for new attractions, and hence, share the other problems. 4. MODEL 4.1. Saturation and reinforcement effects In the tradition of many aggregate response models (see e.g., Hanssens et al. 2001), our dependent variable is the logarithm of weekly attendance: (1)
ln(ATTs ,t ) = X s′,t β + AllAttrContrs ,t + u s ,t ,
where the index s indicates the year,6 and the index t denotes the week within a specific year. The reason we use weekly attendance rather than a higher temporal aggregation level (e.g., year) is that this allows for a more precise measurement of the effect of an attraction. For example, we we can track attendance effects from the week the new attraction is opened, which is not necessarily the first week of the year. AllAttrContrs,t is a stock variable representing the joint contribution to attendance of all attractions in the theme park in year s and week t. Through the specification in equations (2) and (3) below, attractions may have an impact over multiple years.
X s ,t is a vector containing an intercept and other variables influencing theme park attendance (e.g., weather conditions, holiday dummies, …), and u s ,t is a disturbance term. The disturbance term u s ,t captures autocorrelation between consecutive weeks within the same year (see also footnote 5): u s ,t = ρ u s ,t −1 + ε s ,t , ε s ,t ~ i.i.d. N (0, σ 2 ).
6
A “year” is defined as the period in which the theme park is open, e.g., from April till October.
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The overall contribution of attractions in week ( s, t ) is the sum of the latent contributions
of all individual attractions in that week: K s ,t
(2)
AllAttrContrs ,t = ∑ AttrContr j ,s ,t , j =1
where K s ,t is the number of attractions available in the park in year s and week t.7 AttrContr j ,s ,t of attraction j in week ( s, t ) is operationalized as the product of (i) the attraction's impact aggregated over its lifespan, denoted AttrContrLifespan j ,s ,t , and (ii) g j ( s, t ) , the share of this
total impact materializing in week ( s, t ) . This yields (3)
AttrContr j ,s ,t = AttrContrLifespan j ,s ,t ⋅ g j ( s, t ),
The decomposition of AttrContr j ,s ,t into an aggregate and a share component is conceptually similar to a distributed-lag modeling approach in which both the cumulative long-run impact and the associated decay coefficients are estimated (Van Heerde et al. 2000). We adopt a multiplicative specification to link the attraction's total impact with the size of its investment8 (see in this respect also Cohen et al. 1997): (4)
AttrContrLifespan j ,s ,t = λ ⋅ INVESTMENT j j,s,t , η
where INVESTMENT j is the amount invested in attraction j and parameter λ an intercept. Parameter η j , s ,t is the elasticity of an attraction's contribution to its investment, and it may be driven by the type of the attraction, saturation-, and reinforcement effects. We use a parameter process function (Foekens et al. 1999), specified as
(
)
(5) η j , s ,t = exp α 1 + ∑i =1 α 2i TYPE ij + α 3SATURATION j + α 4 REINFORCEMENT j , s ,t + ξ j , s ,t , M −1
7
At first sight, AllAttrContr resembles an advertising stock variable. However, whereas an advertising stock variable is a summary of the inherently ephemeral variable advertising, AllAttrContr is a summary of the inherently permanently available attractions. 8 All monetary variables have been corrected for inflation, and are expressed relative to the base year 2000.
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where the dummy variable TYPE ij equals 1 if attraction j is of type i ∈ {1, K, M } , SATURATION j accounts for potential saturation effects due to extant attractions of the same type as attraction j, and REINFORCEMENT j , s ,t allows for potential reinforcement effects of later introductions of the same type as attraction j on attraction j itself. While we expect that
α 3 < 0 and α 4 > 0 , no sign constraints are imposed in the estimation. The error term ξ j , s ,t ~ i.i.d. N (0, σ ξ2 ) captures random effects for attraction j in year s and week t. These may arise both because of (i) unobserved, time-invariant, characteristics of the attraction, or due to (ii) unobserved time-varying conditions like (positive or negative) media attention which may affect the appeal of specific attractions in a given week. To explicitly account for the presence of the former, we added in unreported analyses an additional random term w j ~ i.i.d. N (0, σ w2 ) . However, the associated variance turned out to be extremely small, and much smaller than the variance σ ξ2 . Hence, the unobserved time-varying conditions tend to dominate the unobserved time-invariant attraction characteristics. We therefore use the more parsimonious specification described in Equation (5) as the focal model. The saturation variable captures the influence of all prior attractions of the same type as the focal attraction j, and is defined as the sum of all previous investments in the same type: (6)
SATURATION j =
∑ INVESTMENT
k∈{1,..., j −1: TYPE ik =1 if TYPE ij =1}
k
.
Similarly, the reinforcement variable is the sum of all investments in subsequent attractions of the same type as attraction j up to year s and week t: (7)
REINFORCEMENT j , s ,t =
∑ INVESTMENT ,
k∈{ j +1,..., K s , t : TYPE ik =1 if TYPE ij =1}
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k
where, as before, K s ,t is the number of attractions in the park in year s and week t. Since the REINFORCEMENT variable is time-varying (it increases every time there is a new investment of the same type as attraction j), AttrContrLifespan is time-varying as well. 4.2 Distribution of the Attraction's Total Impact over Time
To capture the within-year and across-year variation (section 3.1), we specify g j ( s, t ) in Eq. (3) as a mixture of shifted gamma densities. This describes how attraction j’s impact materializes in year s and week t: ∞
(8)
g j ( s, t ) = ∑ s =0
π j ,s
{
across − year variation
δ γ t γ −1 exp(−δ t ) . Γ(γ ) 1442443 within − year variation
The within-year variation is captured by a gamma density with shape parameter
γ > 0 and scale parameter δ > 0 . The density allows for non-monotonic and asymmetric patterns determined by γ and δ (Law and Kelton 1991). The graphs in the upper left (and right) panels of Figure 1, for example, correspond to values for γ and δ of 1 (11) and 0.20 (0.75), respectively. We capture the across-year variation by
(9)
π j,s
⎧ exp(κ ( s − S j )) ⎪⎪ ∞ ~ = ⎨ ∑~s = S j exp(κ ( s − S j )) ⎪ 0 ⎪⎩
if s ≥ S j , if s < S j
where S j is the year in which attraction j is introduced. The parameter κ determines how the mixture weights evolve over the different years after introduction. We expect that κ < 0 , i.e. that the impact of the attraction decays monotonically over time due to the wear-out effects alluded to in section 3.1. In the second and third rows of Figure 1, κ was set at -0.50 and -0.05, respectively. If κ > 0 the impact of the attraction increases monotonically over time. We impose
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no sign constraints when estimating the parameter. We have tested Eq. (9) against nonmonotonic alternatives, but these were inferior; see the empirical section for more details. Equation (8) represents a longitudinal mixture of shifted gamma densities, where each mixture component captures the dynamics in a different year after introduction. The year of introduction is covered by the first gamma component, the first year after introduction is captured by the second gamma component which has been shifted by one year, and so on. Working with shifted densities limits the number of parameters one has to estimate (as each has the same shape and scale parameters). Mixture specifications are common in the literature (see e.g., Wedel and Kamakura 2000). Cross-sectional mixtures of gamma densities, for example, have been used to describe the shape of income distributions (Chotikapanich and Griffiths 2003) and heterogeneity in a Poisson count model (Van Duijn and Böckenholt 1995). Hanson (2006), in contrast, used a longitudinal mixture of (un-shifted) gammas to allow for a multi-modal baseline in accelerated failure time models. As such, he starts from multiple observed durations, and uses the mixture specification to derive a flexible base hazard specification. In contrast, we start from a single, aggregate time series, and use the structure implied by the mixture distribution to infer unobserved (latent) contributions of individual attractions. Our specification (8) has some similarities with Functional Data Analysis (FDA). FDA is a technique to approximate discrete-measured longitudinal data by smooth curves that are linear combinations of basis functions (Ramsay and Silverman 2000, p.56). For example, Sood, James and Tellis (2008) start from multiple observed diffusion curves, and use FDA as a data reduction technique to infer common patterns. Our approach resembles FDA in the sense that equation (8) uses a linear combination of basis functions (shifted gamma densities). The extension we allow for is that in equation (8) the weights π j,s of the basis functions are time-varying (if κ ≠ 0 ), as
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opposed to the time-invariant weights in earlier FDA applications, such as Ramsay and Silverman (2000, p. 44) and Sood, James and Tellis (2008). 4.3 Parameter Estimation
Our final model is obtained by substituting equations (2)-(9) into (1). Parameter estimates are obtained via the method of simulated maximum likelihood (Train 2003) in combination with the BFGS algorithm (Greene 1997, p. 205). The log-likelihood function is given by
∑ L=− (10)
S s =1
Ts
2
(ln(2π ) + ln(σ )) + S2 ln(1 − ρ 2
⎡ ⎛ 1 + ln ⎢ ∫ exp⎜⎜ − 2 ⎢⎣ ξ ⎝ 2σ
S
Ts
∑ ∑ ( f (ln(ATT s =1 t =1
s ,t
2
)
⎤ 2 ⎞ )) − f ( X s ,t )' β − f (AllAttrContrs,t (ξ )) ) ⎟⎟ h(ξ ) dξ ⎥ ⎥⎦ ⎠
where the vector ξ contains all random shocks of existing attractions, with normal density h(ξ ) centered around zero and having variance σ ξ2 , S is the number of years (seasons) in the data, Ts is the number of weeks in year s, and f is the appropriate transformation function for a model with first-order autocorrelated disturbances (Greene 1997, p. 597): ⎧⎪ 1 − ρ 2 x s ,t f ( x s ,t ) = ⎨ ⎪⎩ x s ,t − ρ x s ,t −1
(11)
if t = 1 if t = 2, 3, ...
In the simulated maximum likelihood approach, the integral in (10) is approximated by the Monte Carlo estimate
(12)
∫ξ
⎛ 1 exp⎜⎜ − 2 ⎝ 2σ
≅
1 N
S
Ts
∑∑ ( f (ln(ATT s =1 t =1
⎛ 1 exp⎜⎜ − ∑ 2 n =1 ⎝ 2σ N
s ,t
2 ⎞ )) − f ( X s ,t )' β − f (AllAttrContrs,t (ξ )) ) ⎟⎟ h(ξ ) dξ ⎠
∑∑ ( f (ln(ATT S
Ts
s =1 t =1
s ,t
)
2 ⎞ )) − f ( X s ,t )' β − f (AllAttrContrs,t (ξˆ n )) ⎟⎟ ⎠
where ξˆ n is the n-th simulated draw from h(ξ ) . The estimation results in the empirical section are computed from N = 200 randomized Halton draws (Train 2003, p. 234).
20
4.4 Predictions
For given random components ξ , weekly attendance (not in logarithms) follows a lognormal distribution (Law and Kelton 1991, p. 337). Accounting for the uncertainty in ξ , expected weekly attendance is approximated by its Monte Carlo estimate:
(13)
(
1 N Eˆ ( ATTs ,t ) ≅ ∑ exp X s′,t βˆ + AllAttrContrs ,t (ξˆ n ) + ρˆ uˆ s ,t −1 (ξˆ n ) + σˆ 2 / 2 N n =1 n uˆ (ξˆ ) = ln( ATT ) − X ' βˆ − AllAttrContr (ξˆ n ). s ,t −1
s ,t −1
s ,t −1
)
s ,t −1
In the empirical section, we set N = 2000 when generating predictions. It is feasible to use a substantially larger N in the predictions than in the computationally more intensive estimation procedure where the simulated likelihood needs to be evaluated iteratively. 5. DATA DESCRIPTION 5.1. Description of the Research Setting
We apply our model to data from the Efteling, a major theme park situated in the south of the Netherlands, currently attracting over three million visitors per year (Table 1). In 1972, the Efteling received the Pomme d'Or (Golden Apple) for best European theme park. In 1992, the IAAPA Applause Award was awarded for the best theme park in the world. In 2005, the Efteling received the THEA Classic Award for its entire oeuvre. The Efteling not only attracts visitors from the Netherlands, but also from Belgium, Germany and other countries. The set-up of the Efteling is similar to US counterparts such as Disneyland and Universal Studios: an entrant pays one admission fee that allows him/her to visit all attractions as many times as he/she likes. The park is open from April till October. Our data set covers the period 1981-2005, and includes all weeks the park is open, yielding a total of 732 weekly observations.9
9
Over the last few years, the Efteling is open a few weeks in winter. We decided to omit the attendance data for these weeks from model estimation since these observations are a-typical, in that only part of the park is open.
21
The overarching theme of the Efteling is based on fairy tales. In 1952, the Efteling officially opened its fairy tales forest with three-dimensional and motioned characters of famous fairy tales. This forest is the heart of the theme park. Even though several smaller attractions were added in the next few decades, the forest remained the main attraction until the eighties. In the eighties, the Efteling started investing in thrill attractions to also attract consumers outside its traditional target group of families with young children. The first in the series of thrill attractions was the Python, a roller coaster inaugurated in 1981 that was unrivalled in Europe at that time. Although the attraction did not fit the fairy tales character of the Efteling, the number of visitors increased by 30% in its opening year. In the subsequent 25 years, the Efteling has invested heavily in both types of attractions (“theme” and “thrill”), as evidenced by Table 2.10 Our categorization into “thrill” or “theme” has been closely coordinated with the park’s management.
Table 2: Attractions introduced in the observation period 1981-2005, plus the Haunted Castle Name
Year of introduction Haunted Castle 1978 Python 1981 Half Moon Ship 1982 Pirana 1983 Carnaval Festival 1984 Bobsleigh Run 1985 Fata Morgana 1986 Pagoda 1987 Monsieur Cannibale 1988 Laaf People 1990 Pegasus 1991 Dream Flight 1993 Villa Volta 1996 Bird Rok 1998 Panda Vision 2002
Description
Type
Large ghost castle Roller coaster with four loops Swinging pirate ship Wild water rafting in a circular boat Show of figures that shows how people party in different countries Roller coaster shaped as a bobsleigh run Boat ride through the fairy tales of 1001 nights Gently flying temple in Thai style Quick merry-go-ride with turning boiling pots Ride on monorail to watch houses with dwarves Timber old-style rollercoaster Ride through fantasy world with elves and dwarves Seemingly rotating house with bandit storyline Indoor rollercoaster with bird theme 3D movie with World Life Fund theme
10
Theme Thrill Thrill Thrill Theme Thrill Theme Theme Thrill Theme Thrill Theme Theme Thrill Theme
We focus on the main attractions in the park, and not on minor extensions (e.g., a new drink stand). We include the Haunted Castle in Table 2, as it was the last major attraction introduced before the start of our data.
22
This categorization into M = 2 attraction types and the inflation-corrected investment amounts are used to operationalize the TYPE (0 = thrill, 1 = theme) and INVESTMENT variables from equations (4) and (5). For confidentiality reasons, we cannot reveal the exact investment of each individual attraction, but the amounts varied between, approximately, 1.5 and 15 million euro. On average, attractions opened in the nineties and in the new millennium were more expensive than introductions in the eighties. Also the introduction frequency changed over time from once a year between 1981 and 1988 to once every two to four years after that. Even though we have 25 years of weekly attendance data, our data are left-truncated as they do not go back to the opening of the park. We do not believe this will have a large impact on our findings, however. First, the drawing power of (and saturation effects due to) the Haunted Castle and other attractions available prior to the observation period should be largely captured by the intercepts in equations (1) and (5). Second, unless the decay of the impact of attractions is extremely slow, the Haunted Castle is the only prior attraction which could be expected to still be “active” at the start of the observation period. However, as the next themed attraction was only introduced six years after the opening of the Haunted Castle, the omitted reinforcement of this attraction on the Haunted Castle should also be very small.
5.2 Covariates
While estimating the effects of new attractions on theme park attendance, we need to control for covariates that may also affect theme park attendance, as shown in Table 3. These covariates, together with an intercept, are captured by the vector X s ,t in equation (1). We include seasonality dummies, holiday dummies, weather variables, dummies indicating the entry of three potential competitors within a radius of 500 kilometers in France (Disneyland Paris), the
23
Table 3: Covariates in the model to explain theme park attendance Variable Season Low season
High season
Std
Min
Max
− [Note that we omit from the model the dummy for the middle, or shoulder season (May, June, first half of July)] + [Note that we omit from the model the dummy for the middle, or shoulder season (May, June, first half of July)]
0.39
0.49
0.00
1.00
0.24
0.43
0.00
1.00
+: school children (and their parents) are one of the primary target groups of the Efteling. +: a national holiday is often used for a one-day visit to a theme park.
0.07
0.25
0.00
1.00
0.20
0.40
0.00
1.00
Expected sign
Dummy: 1 in weeks that the Efteling management categorizes as low season (April, September, October), 0 otherwise. Dummy: 1 in weeks that the Efteling management categorizes as high season (second half of July, August), 0 otherwise.
Holidays School Holiday Dummy: 1 in weeks coinciding with a school holiday outside the high season, 0 otherwise. National Dummy: 1 in weeks containing a national Holiday holiday [Easter, Queen's Day, Ascension Day, Whit], 0 otherwise. Weather Precipitation Weekly millimeters of precipitation reported by the Royal Netherlands Meteorological Institute. Temperature Temperature = Average weekly and temperature (in centigrades) reported by Temperature2 the Royal Netherlands Meteorological Institute.
Other parks Disneyland
Mean1
Definition
Dummy: 1 after opening of Disneyland Paris in 1992, 0 otherwise. Walibi-Sixflags Dummy: 1 after opening of WalibiSixflags in 1994, 0 otherwise. Movie World Dummy: 1 after opening of Warner Bros. Movie World in 1996, 0 otherwise. Miscellaneous Trend, Trend2 Trend = Counter for the number of years and ln Trend. since 1980.
−: it becomes less appealing to be in a primarily outdoor theme park when it rains. + for main effect: warmer weather makes it more pleasant to be in an outdoor theme park. − for quadratic effect: it becomes less attractive to be outside when it is too warm. −: the entry of a potential competitor in France may result in less visitors. −: the entry of a potential competitor in the Netherlands may result in less visitors. −: the entry of a potential competitor in Germany may result in less visitors.
16.16 16.86
0.00 97.40
18.81
4.40
7.00 31.70
0.57
0.49
0.00
1.00
0.50
0.50
0.00
1.00
0.41
0.49
0.00
1.00
We in general expect an upward trend in 13.28 7.16 1.00 25.00 the number of visitors due to population growth and increasing wealth. We include Trend2 and ln Trend to allow for more flexibility than just linear trend patterns (similar to Jain and Vilcassim 1991). Last week Dummy: 1 in the last week of the season, 0 +: Efteling management anticipates that 0.03 0.18 0.00 1.00 otherwise. many theme park aficionados visit the theme park one more time before the parks closes for winter. 1 The descriptives are based on the sample used for model estimation. This covers all weeks the theme park is open in the period 1981-2005. In total there are 732 weekly observations.
Netherlands (Walibi-Sixflags) and Germany (Warner Bros. Movie World) and a general trend. For reasons explained next, we exclude ticket price, (annual) advertising expenditure, and dummy variables indicating the years in which the Efteling received international awards. Ticket 24
price went up almost linearly and hence was too collinear with the trend variable (correlation = 0.93). Advertising information was only available from 1986 onwards (as opposed to 1981 for the other variables) and at an annual level of aggregation (while the attendance data are available at the weekly level). Moreover, these twenty observations were again very collinear with the trend terms (correlation = 0.92).11 Finally, preliminary testing revealed that the award dummies for the years 1992 and 2005 were both insignificant. We believe that one of the key reasons is that these awards are signs of peer esteem rather than consumer esteem. As such, they did not receive much media coverage, nor were they featured prominently in the national promotional campaigns of the Efteling. In- or excluding the omitted variables does not affect our substantive results. 6. RESULTS We first present the parameter estimates, followed by a comparison of our proposed
model with several alternative specifications. Next, we provide estimates of the additional number of visitors attributable to the attractions, and their associated Returns on Investment. 6.1. Parameter Estimates
The proposed model provides a good fit to the data, as the R 2 of the base equation (1) for log-attendance is 0.75. The parameter estimates are given in Table 4. In the equation for logattendance, all coefficients of the covariates - except for the coefficients regarding competing theme parks - are significant at 1% with the expected signs. The high season period ( β 3 = 0.378) correlates with increased theme park attendance, as do holiday weeks ( β 4 = 0.313), national holidays ( β 5 = 0.212), the season’s last week the park is open ( β15 = 0.183), and warmer weather 11
To get some insight into the potential omitted-variable bias in attraction effects, we computed the correlation between the annual advertising expenditures and the annual attraction investments for the 20 years where advertising data were available. This correlation was very low (-0.18) and insignificant (p = 0.45), which should attenuate potential omitted-variable-bias concerns.
25
( β 7 = 1.197). At the same time, very warm weather results in less attendance ( β 8 = -0.267). As
the temperature variable was expressed in tens of centigrades, it follows from the estimated coefficients that the most preferred temperature for visiting the park is 22 centigrades (= 72 degrees Fahrenheit). Attendance is also lower in rainy weather ( β 6 = -0.032) and in the low season ( β 2 = -0.102). For the three competing theme parks, only the closest park, i.e. the Dutch Walibi-Sixflags park, has a marginally significant negative effect on the Efteling ( β10 = -0.106). The coefficient for type of attraction indicates that, all else equal, a thrill attraction is more effective in drawing additional visitors than an equally-expensive themed attraction ( α 2 = -0.719 for the TYPE = Theme dummy). However, as we expected, the attraction's impact does not only depend on the type and the amount invested, but also on its interaction with other attractions. The presence of extant attractions of the same type makes the new introduction less effective, as the saturation coefficient ( α 3 = -0.096) is negative and significant at 1%. On the other hand, a new attraction boosts the effectiveness of previous introductions of the same type: the reinforcement coefficient ( α 4 = 0.025) is positive and significant at the 5% level. The decay pattern of the impact of new introductions, displayed in Figure 4, is as follows. First, the scale and shape parameters γ and δ imply that attractions are most effective in drawing additional visitors to the park in the high season, as the mean of the underlying within-year gamma density is γ / δ = 15.44 weeks after opening, and the Efteling opens in April. Second, the decay coefficient κ implies that on average 35% of the total impact of a new attraction occurs in its year of introduction, while 90% has materialized within the first five years
26
after the introduction.12, 13 Hence, new attractions not only increase attendance in the year of introduction, but also in a number of subsequent years.
Table 4: Parameter estimates and associated standard errors Model Component Attendance equation
Description Intercept
[Equation 1]
Low season
Symbol
High season Holiday National Precipitation Temperature Temperature^2 Disneyland Walibi-Sixflags Movie World
β 12
Trend Trend^2 ln Trend Last week Attraction equation [Equations 4 & 5]
Intercept Intercept of process function Type Saturation Reinforcement
Decay pattern
Shape-within
[Equations 8 & 9]
Scale-within
β1 β2 β3 β4 β5 β6 β7 β8 β9 β10 β11
Decay-across Std. deviation Autocorrelation Std. dev. attraction
β13 β14 β15 λ
Estimate
− 1.112
***
(Std. Error) (0.331)
− 0.102 ***
(0.033)
***
(0.035)
***
(0.034)
0.212 ***
(0.025)
0.378 0.313 − 0.032
***
(0.005)
1.197 ***
(0.133)
− 0.267 0.071 − 0.106
***
(0.035) (0.061)
*
(0.058)
− 0.077 2.188***
(0.054)
− 0.500
***
(0.081)
− 0.408
***
(0.130)
0.183***
(0.048)
+
(0.388)
3.461
(1.826)
α1
0.416 *
(0.242)
α2 α3 α4 γ δ κ
− 0.719 ***
(0.228)
− 0.096 ***
(0.027)
σ ρ σξ
**
0.025 6.516 *** 0.422 *** − 0.437 *** 0.209 0.288 0.022
(0.012) (0.946) (0.068) (0.101)
* significant at 10% (two-sided); **significant at 5% (two-sided); *** significant at 1% (twosided); + standard test not valid, as asymptotic normal distribution does not hold; Davies problem. 12
This supports our earlier contention that the impact of any left-truncation issues should be minimal. Although some gaps between two new attractions are just one year, our model is able to disentangle the overlapping effects of different attractions quite well. This is evident from a simulation exercise (available on request) showing that based on the historical introduction schedule, we can retrieve imposed model parameters well.
13
27
Figure 4: The estimated time-varying impact of a new attraction on theme park attendance
6.2 Comparison of Model Specifications
In order to test the proposed model, we compare it with several alternatives. In-sample, we report the log-likelihood value and the BIC and AIC3 information criteria. For out-of-sample validation, we re-estimated all models up to 1998, when the Bird Rok was introduced, and predict attendance levels in 2002, the year in which the last attraction (Panda Vision) was added.14 We report the Mean Absolute Error (MAE) and the Root Mean Squared Error (RMSE). In the first alternative model, the parameter λ is set equal to 0, in which case new attractions have no impact on attendance. We note that the significance of λ cannot be tested via a regular z-test statistic with asymptotic normal distribution. The reason is that all parameters related to the size and decay of the impact of attractions ( α 1 , α 2 , α 3 , α 4 , γ , δ , κ ) would disappear from the model under the null hypothesis λ = 0 . This is the so-called Davies problem (Davies 1987). However, the information criteria are still valid. The second alternative model replaces the within-year gamma densities in (8) by uniform densities, implying a stepwise decay pattern without within-season variation. The third model relaxes the assumption that saturation and reinforcement effects are only present for same-type attractions. Hence, attractions can now 14
We are indebted to an anonymous reviewer who suggested this out-of-sample validation.
28
interact with all other attractions, and the amount of interaction does not depend on the theme or thrill type. For this model, the expressions (6) and (7) are replaced by (14) (15)
SATURATION j =
∑ INVESTMENT
k
k∈{1,..., j −1}
REINFORCEMENT j , s ,t =
,
∑ INVESTMENT
k∈{ j +1,..., K s , t }
k
.
The fourth model extends the model by allowing for between-type (besides within-type) reinforcement and saturation effects. Hence, equation (5) is extended with two variables: (16) (17)
SATURATION_OTHER j =
∑ INVESTMENT
k∈{1,..., j −1: TYPE ik = 0 if TYPE ij =1}
REINFORCEMENT_OTHER j , s ,t =
k
,
∑ INVESTMENT
k∈{ j +1,..., K s , t : TYPE ik = 0 if TYPE ij =1}
k
,
with coefficients α 5 and α 6 . The fifth alternative generalizes the saturation and reinforcement specifications (6) and (7) by replacing the unweighted sums of investments by geometrically-
weighted sums. This reflects the idea that attractions that have been introduced closer in time to the focal attraction may carry more weight in determining saturation and reinforcement effects than attractions that were introduced at a more distant point in time. The last two models capture the across-year variation by non-monotonic decay patterns. The procedure we adopt to do so is conceptually similar to the semi-parametric base-hazard specification adopted in Dekimpe et al. (1998). The across-year variation described in (9) is replaced by dummy variables for each year since introduction of the attraction up to a cut-off year after which the impact of the attraction is assumed zero. The cut-off year was varied from 1 to 15. Preliminary testing showed that a cutoff of three years provides the best BIC (alternative model 6), while a cutoff value of 11 years gives the best AIC3 (alternative model 7). We report the performance for these two model specifications.
29
Table 5: Performance of proposed model and alternative models In-sample Model
Description
0
Proposed model: only saturation and interaction effects within the same type (theme or thrill)
1
Out-of-sample
LL
BIC
AIC3
MAE
RMSE
105.13
-38.78
-132.27
1.426
1.950
No effect of attractions
36.70
38.74
-22.39
1.710
2.346
2
Stepwise decay pattern, constant within years
49.52
59.25
-27.05
1.604
2.213
3
Saturation and reinforcement effects within and across types yet with same parameters
102.39
-33.29
-126.78
1.514
2.099
4
Saturation and reinforcement effects within and across types with different parameters
106.96
-29.25
-129.93
1.435
2.002
5
Geometrically weighted saturation and reinforcement variables
106.92
-29.16
-129.84
1.505
2.093
6
Non-monotonic 3-year pattern
101.27
-24.46
-121.55
1.693
2.129
7
Non-monotonic 11-year pattern
113.77
3.30
-122.55
1.441
2.070
Note: the best value in each column is underlined. Within the class of nonmonotonic patterns, the 3-year model provides the best BIC, while the 11-year model provides the best AIC3 value.
Table 5 contains the model comparison results. Most importantly, the proposed model performs better than all other models in terms of both in-sample information criteria and out-ofsample prediction. In addition, all models accounting for the incremental effects of new attractions on attendance (model 0 and models 2-7) outperform model 1 without these effects (though model 1 has a lower BIC than model 2). This indicates that new attractions do influence theme park attendance. Furthermore, all models with gamma pulses describing the within-year effect of an attraction’s impact (all but model 2) outperform model 2 with a constant within-year pattern (model 2 only beats model 6 in terms of MAE), indicating we need to capture the withinyear effect by a pulsing pattern.
30
In Figure 5, we show the actual weekly figures, as well as the predicted values from our proposed model (which allows for a pulsing within-year effect and a decay over years) and from model 2 from Table 5 which assumes constant within-year effects, while allowing for a decay over years. The figure illustrates that the spikes in actual attendance are tracked well by both models (top panel). However, the proposed model has (as indicated before) a better fit based both on BIC and AIC3 and on predictive validity. The bottom panel gives a more detailed picture, and illustrates for 1984 and 1985 how the bumps in the high season (July and August) are better predicted by the proposed pulsing model than by the constant- within-year-effect model 2. In the latter model, these bumps can only be captured by seasonal factors (e.g., weather conditions, holiday dummies) explicitly included in the X s ,t -matrix of Equation (1), while in the proposed model we allow, apart from these variables, also for within-year variation through the gamma density. 6.3 Impact of Individual Attractions on Theme Park Attendance
From the parameter estimates, we derive the number of additional park visitors for each attraction in the park accumulated from its introduction till 30 years later to capture the full reach of the attraction's impact. Next, we translate these estimates into Return-on-Investment values to assess the financial performance of individual attractions. As the model’s parameter estimates are inherently uncertain, the implied estimates of extra attendance and ROI are uncertain as well. To account for this, the reported metrics are accompanied by their standard errors. To this end, we rely on the asymptotic properties of maximum likelihood estimators. The model parameters are sampled from their asymptotic multivariate normal distribution, and the 2000 draws are used to derive the distribution of the metric of interest.
31
Figure 5: Actual versus predicted attendance numbers
32
Table 6: Impact of attractions on attendance, aggregated over all weeks/years since introduction (standard errors in parentheses) Year
Python
1981
Half Moon Ship
1982
Pirana
1983
Carnaval Festival
1984
Bobsleigh Run
1985
Fata Morgana
1986
Pagoda
1987
Monsieur Cannibale
1988
Laaf People
1990
Pegasus
1991
Dream Flight
1993
Villa Volta
1996
Bird Rok
1998
Panda Vision
2002
Direct Effect (000) 2050 (527) 253 (17) 993 (236) 842 (218) 401 (60) 647 (159) 280 (24) 239 (14) 289 (22) 319 (30) 297 (24) 261 (15) 399 (69) 251 (14)
Combined Effect: direct+indirect (000) 2050 (527) 379 (38) 1749 (306) 842 (218) 872 (221) 857 (229) 426 (103) 280 (32) 372 (58) 361 (47) 439 (184) 287 (54) 434 (80) 261 (44)
Indirect as % of Combined 0 (0) 33 (8) 42 (12) 0 (0) 54 (15) 24 (8) 35 (12) 15 (7) 22 (9) 10 (8) 32 (16) 8 (10) 5 (8) 3 (8)
Table 6 reports the additional number of visitors attributable to each attraction, both in terms of its direct effect (i.e., without reinforcement of extant attractions of the same type), and in terms of its combined effect, which includes the reinforcement effect (see also Figure 3). There are clear saturation effects: while new attractions tend to be increasingly expensive, they become less effective over time. In some instances, strong reinforcement effects are present. For example, the direct impact of the Bobsleigh Run on park attendance is estimated at 401,000 visitors. This extra attendance is more than doubled to 872,000 visitors when accounting for the boost that the Bobsleigh Run provides to other, previously introduced, thrill rides. In the four years preceding the opening of the Bobsleigh Run, three thrill attractions had been added to the
33
park, providing the Bobsleigh Run with ample opportunities to double its effectiveness. On the other hand, the Pegasus and the Panda Vision generated hardly any reinforcement effects. Their overall impact is almost completely determined by their direct effects: in the 5-year periods preceding their introduction, no major attractions of the same type had been opened in the park, resulting in few opportunities for reinforcement. 6.4 Return on Investment Analysis
The ROI of an attraction can be defined as the discounted revenue expressed as a percentage of the underlying investment, ROI =
DISCOUNTED REVENUE × 100% . A value INVESTMENT
smaller than 100% implies a loss, while a number exceeding 100% means that the investment has been more than recovered. In our analyses, we assume an annual discount rate of 12% (in line with Gupta et al. 2004), and assume that each visitor is worth the park entrance fee times a factor (100/60), reflecting an industry rule of thumb that 60% of the total revenues comes from entrance fees, and 40% from catering and merchandising (Kemperman 2000). For illustrative purposes, we focus on three attractions: the Bobsleigh Run, the Pegasus and the Panda Vision, for which the results are summarized in Table 7. The first two have very attractive ROIs of 264% and 240%, respectively. However, the underlying sources of these excellent financial results are very different. The Pegasus has been very profitable, even in the absence of good opportunities to boost extant thrills. Even when only its direct effect is considered, the ROI is still an impressive 211%. On the other hand, the ROI for the Bobsleigh Run, based on its direct effect only, would have been a reasonable 121%, just one standard error above the break-even ROI of 100% and much less than its combined ROI of 264%. Finally, the Panda Vision does not recover its costs, as its ROI is less than 100%. It is a relatively expensive theme attraction, and at the time of introduction many other theme attractions were already
34
present in the park. This saturation effect has hampered its profitability. The estimated 261,000 additional visitors are not enough to offset the high investment cost resulting in an ROI of 85%, one standard error below the break-even ROI. Across all attractions introduced in the observation period 1981-2005, the average ROI is 121% (direct effects only), and 157% when the indirect effects due to reinforcement are included. Table 7: Return-on-Investment of Attractions (standard errors in parentheses) Year of introduction Type of attraction ROI - direct ROI - combined
Bobsleigh Run 1985 Thrill 121% (17%) 264% (66%)
Pegasus 1991 Thrill 211% (20%) 240% (28%)
Panda Vision 2002 Theme 77% (13%) 85% (15%)
Overall 1981 - 2005 Theme & thrill 121% (12%) 157% (19%)
While Table 7 gives the combined performance of all attractions at the end of 2005, it is also informative to consider how this overall ROI has developed towards its final outcome of 157%, as shown in Figure 6. At each point in time, the displayed ROI level is based on all investments in new attractions up to that time period, and on the extra attendance generated in all preceding periods. The ROI graph starts at value zero in 1981, when the Python was introduced. In this first week of the observation period the Python investment was made, but no additional visitors had been drawn to the park yet. However, by the end of 1981, the investment was already recovered (ROI in excess of 100%). Every time a new attraction is introduced, the ROI curve drops because of the investment made, and gradually increases as additional visitors are generated. A lot of turbulence is present in the eighties. This is partly due to the evolving ROI metric which requires some time to settle, but is also caused by the frequency of the investments. Saturation effects and reduced reinforcement opportunities result in less volatility in later stages.
35
Figure 6: The Evolution of the Cumulative ROI over Time (with 95% conf. interval)
6.5 Simulating the ROI of Hypothetical Attractions
In the previous analysis, we investigated the ROIs of historically-available attractions in the data set. However, our results can also be used to assess the expected effectiveness of
hypothetical introductions. We consider the following simulation experiment in order to extract some general guidelines for profitable investments. We assume that the theme park has a budget of €12 million (M) available for investments in a planning period of four years, labeled year 1 to year 4. This budget can be used in ten different strategies (a-j): one expensive attraction of 12M (either theme (a) or thrill (b)), two medium-priced attractions of 6M each (either both theme (c), both thrill (d), first theme and next thrill (e), or vice versa (f)), or four consecutive inexpensive attractions of 3M each (either all theme (g), all thrill (h), or first two theme and next two thrill attractions (i), or vice versa (j)). Each year that the theme park does not spend the available budget, it earns 12% over the remaining amount, consistent with the adopted discount rate. Even though investments can only be made within the considered planning horizon, we consider a sufficiently long future period of 30 years to capture the full reach. Note that the investment 36
strategies may involve multiple attractions in multiple years, and hence go beyond singleattraction investment options. The ten strategies are investigated for three hypothetical scenarios, described by the attractions already available in the park. Scenario A is the “plain” scenario in which the two types theme and thrill are equally saturated (past investment in both types is 18M) and in which there are no opportunities to take advantage of reinforcement effects (as all previous introductions occurred very long ago and are therefore “sunk”). Scenario B also eliminates reinforcement potential, but now theme attractions are less saturated than thrills (past investments of 12M vs. 24M). In scenario C, theme and thrill are equally saturated (for both types the total past investments amount to 18M), but theme now has reinforcement potential. For theme, only 6M (from the total of 18M) was invested long ago (“sunk”), while 12M was invested one year ago, in year 0, and can therefore be reinforced by new theme attractions. Table 8 shows the ROI estimates for the ten investment options in each of the three scenarios.15 The reported numbers account for parameter uncertainty. For each scenario, the strategy with the highest (average) ROI has been underlined, and the percentages indicate how often each of the strategies yields the highest ROI in the 2000 simulation runs. All three scenarios indicate that it is more efficient to invest in multiple smaller attractions than in one big attraction. In addition, scenario A illustrates that, all else equal, investing in thrill attractions is more effective than investing in themed ones. However, under certain conditions theme attractions may become more effective than thrills. This holds if either thrill has become very saturated due to a large presence of this type (scenario B), or if theme has a lot of reinforcement potential due to recent theme introductions (scenario C). 15
For any of the scenarios we obtained the result that it is more profitable to introduce the attractions as early on as possible (e.g., better to invest in year 1 than in year 2), so these are the only scenarios we show.
37
Table 8: Return-on-Investment (in %) for ten simulated investment strategies in three hypothetical scenarios Scenario A
B
C
18M
12M
6M
-
-
12M
18M
24M
18M
-
-
-
36M
36M
36M
Saturation level for
Theme = Thrill
Theme < Thrill
Theme = Thrill
Reinforcement potential for
Theme = Thrill
Theme = Thrill
Theme > Thrill
86 (0%) 102 (0%) 151 (0%) 168 (1%) 163 (0%) 164 (0%) 251 (0%) 265 (84%) 261 (0%) 263 (16%)
103 (0%) 93 (1%) 169 (1%) 157 (1%) 167 (0%) 166 (0%) 268 (80%) 254 (7%) 265 (3%) 265 (8%)
127 (0%) 109 (0%) 190 (2%) 176 (0%) 189 (1%) 185 (0%) 284 (23%) 274 (5%) 287 (66%) 281 (3%)
Theme attractions: • sunk investments • investment in previous year Thrill attractions: • sunk investments • investment in previous year Total investment
Year 1 Investment strategies
Year 2
Year 3
Year 4
a 12M theme
-
-
-
b 12M thrill
-
-
-
c 6M theme
6M theme
-
-
d 6M thrill
6M thrill
-
-
e 6M theme
6M thrill
-
-
f 6M thrill
6M theme
-
-
g 3M theme
3M theme
3M theme
3M theme
h 3M thrill
3M thrill
3M thrill
3M thrill
i 3M theme
3M theme
3M thrill
3M thrill
j 3M thrill
3M thrill
3M theme
3M theme
Note. For each strategy, a budget of €12 million (M) is available for investments in the 4-year planning period; This budget can be spent on either one big 12M attraction, two medium-sized 6M attractions, or four consecutive small 3M attractions of either type (1 = theme, 2 = thrill). The reported numbers account for parameter uncertainty. For each scenario, the strategy with the highest average ROI has been underlined, and the percentages indicate how often each of the strategies yields the highest ROI in the 2000 simulation runs.
Interestingly, a mixed strategy is optimal in scenario C. The optimal strategy (i.e., strategy i) consists of two themes followed by two thrills. The intuition is that even though the two theme attractions allow for substantial reinforcement effects, the saturation of this type increases as well due to these introductions. This in turn makes switching towards thrill preferable in a later stage. 38
7. CONCLUSIONS
We introduced a new modeling approach to disentangle the contribution of individual attractions to total theme-park attendance. The over-time contribution is well described by a slowly extinguishing pulsing pattern, accounting for stronger effects in high (mid) seasons. On average, attractions obtain 35% of their total impact in the year of introduction, while 90% materializes in the first five years following their introduction. Hence, new attractions increase attendance in multiple years beyond the year of introduction. Our results also indicate that attractions indeed do not operate in isolation, but interact with other attractions in the park’s portfolio or “bundle”, at least when they are of the same type. When planning a new attraction, one should consider the relative size of the (negative) saturation and (positive) reinforcement effects. As such, whether it is better to add a new ride that targets families (as most theme rides do), or rather go after the thrill-seeking segment, depends not only on what rides are already in the park, but also on when those were introduced. Indeed, to fully capitalize on the potential reinforcement effects, one should not let too much time elapse between consecutive introductions of the same type. However, at some point, the negative saturation effect will dampen the direct effect to such an extent that the addition of attractions of another type becomes more appealing. We find that an even spending strategy (i.e., smaller investments in consecutive years) results in higher pay-offs than a pulsed strategy, with only a few, but bigger investments. This finding is in remarkable contrast with the “arms race” that currently takes place in the theme park industry with recent $100 million-plus investments to which we alluded in the introduction. However, our finding is consistent with the idea that also new rides that are smaller and relatively cheap can still lure visitors looking for something new (Schneider 2008). As a case in point, Legoland California was able to achieve a record growth of 16 percent in 2006 because of 39
the popularity of its Pirate Shore addition. Still, the $10 million investment for this attraction was only a fraction of the amounts invested by competing parks in some of their new rides (Rubin 2007). A similar observation was made (albeit in a different setting) by Pauwels et al. (2004, p. 154). They also concluded that “..., managers need not always incur the high development and launch costs that are associated with major product innovations, ” and may as well opt for smaller, but more frequent, innovations. As with any study, multiple areas for future research remain. First, since our model specification is generally applicable, it would be useful to replicate our study for other theme parks. These might differ in terms of their size and location (US, Asia, …), and the set of M types of attractions (e.g., a separate category of water attractions). Second, we could also adopt an attribute-based approach and model the variety of the assortment of attractions based on their attributes (Hoch et al. 1999). Third, future modeling endeavors may try to add additional assumptions to separate the latent contributions of first-time visitors and repeat visitors something we refrained from doing in this study for reasons outlined before. Fourth, it would be interesting to extend our model specification with marketing-mix variables such as price and advertising spending. Fifth, our ROI calculations could be refined by also considering maintenance costs (which may well vary across attractions), by allowing for a more intricate price (revenue) structure, and by also considering the impact that new attractions may have on related activities outside the park itself, such as lodging facilities (Vugts and van Haver 2008). We hope that our research results inspire further research on these, or other, issues in the themepark industry.
40
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