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Marketing models of entertainment products Ho, Yiu Chung 2005

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M A R K E T I N G M O D E L S OF ENTERTAINMENT PRODUCTS by Y I U C H U N G (JASON) HO M . Phil., The Chinese University of Hong Kong, 2000 B.B.A. , The Chinese University of Hong Kong, 1995 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES (BUSINESS ADMINISTRATION) THE UNIVERSITY OF BRITISH C O L U M B I A July 2005 © Y i u Chung (Jason) Ho, 2005 Abstract Television broadcasts of major events like the Super Bowl command extremely high advertising rates. It is important to evaluate the value created by this advertising tactic. The first essay develops a marketing model that illustrates a direct and an indirect effect path created by Super Bowl T V advertising in the movie industry. First, via the direct path, Super Bowl advertising directly increases initial theatrical demand for a movie. Second, through the indirect path, Super Bowl advertising first encourages more exhibitors to screen a movie, then this increased exhibition rate in turn increases initial box office revenue. Four variants of the marketing model are explored in the attempt to capture the non-linearity of the two paths and other control variables' effects. Three main results are obtained. First, Super Bowl advertising is demonstrated to affect opening box office revenues positively. Second, this positive effect occurs mainly through the indirect path, establishing the mediating role of movie exhibitors. Third, compared to other TV advertising efforts, Super Bowl advertising appears less effective i f both efforts are evaluated at the same initial level. However, at current spending levels, Super Bowl advertising can still be justified. Many entertainment service providers serve customers according to pre-announced schedules, and the timing factor can be as important as price and service quality in determining consumer demand. The second essay develops three demand models to characterize the effects of different service start times in a multiplex movie theater context. The models address two recurring issues, namely the confounding of product quality and time preference in aggregated sales data, and the difficulty of distinguishing between cannibalization and market expansion. Meaningful results are obtained by applying the models to two data sets of admission records from a multiplex movie theater in Amsterdam. First, one of the data sets is demonstrated to exhibit confounding of unobserved movie quality and moviegoers' underlying time preference, establishing the value of the demand models in disentangling these two effects in the aggregated sales data. Second, the effectiveness of the models in comparison to previous models is demonstrated in the process of discerning between cannibalization and market expansion. (Marketing Models, Movies, Entertainment Marketing) i i i Table of Contents Abstract ii Table of Contents iv List of Tables v i i List of Figures J x Acknowledgements X 1 CHAPTER 1 Introduction 1 1. Motivation 1 1.1 Essay 1 2 1.2 Essay 2 3 2. Overview 4 2.1 Essay 1 4 2.2 Essay 2 5 3. Organization of Dissertation 6 4. References 7 CHAPTER 2 Is there a Payoff for Playoffs? Part I: Model Development 8 1. Introduction $ 2. Related Literature 11 2.1 Marketing Accountability X1 2.2 Major TV Event Advertising 15 3. Movie Industry 18 4. Model Development 20 4.1 Variable Conceptualization 22 4.2 Conceptual Model 25 iv 4.3 Estimation Models .28 4.4 Summary 35 CHAPTER 3 Is there a Payoff for Playoffs? Part II: Data Analysis 37 5. Data Description 37 6. Model Estimation and Results 44 6.1 Main Results 4 6 6.2 Other Results 5 2 7. Further Analysis 54 7.1 Marketing Metrics 54 7.2 Marginal Analysis 57 8. Concluding Remark. 60 9. References 62 Appendix-A 65 Appendix-B 70 CHAPTER 4 Good Movie or Nothing Better to Do? 107 1. Introduction 107 2. Related Literature 1 1 1 2.1 Market Response Models for Managers 111 2.2 Discrete Choice Models with Market Level Data 114 3. Model Development 123 3.1 Base Model 1 2 3 3.2 Nested Logit Model 1 3 1 3.3 Crowding Model 1 3 5 4. Data Description * 3 ^ 5. Estimation Results 145 6. Concluding Remark 156 7. References 158 CHAPTER 5 Conclusion 192 1. Contributions 192 1.1 Essay 1 192 1.2 Essay 2 194 2. Managerial Implications 196 2.1 Essay 1 197 2.2 Essay 2 197 3. Further Analysis 198 3.1 Essay 1 1 9 8 3.2 Essay 2 199 4. References 201 vi List of Tables Essay 1: Is there a Payoff for Playoffs? Table-1: Summary of Variables 73 Table-2: MPAA Member Company Distribution of Advertising Costs by Media 74 Table-3: List of Super Bowl Movies 75 Table-4: Classification of Entertainment Weekly Articles for PUBj Operationalization ...77 Table-5: Pearson Correlation Matrix of continuous variables .78 Table-6: Summary Statistics of non-Super Bowl vs. Super Bowl advertised movies 79 Table-7: Frequency of non-Super Bowl vs. Super Bowl advertised movies 80 Table-8: Pairwise tests for non-nested model 82 Table-9a: Parameter Estimates of M l : Log-linear Model 83 Table-9b: Parameter Estimates of M2: Log-Log Model 84 Table-9c: Parameter Estimates of M3: Log-Quadratic-a Model 85 Table-9d: Parameter Estimates of M4: Log-Quadratic-b Model 86 Table-10: Comparison of the effectiveness of Super Bowl and Other Launch TV advertising 87 Table-11: Elasticity Measures on the basis of M3, the Log-quadratic-a Model 88 Table-Al: Regression Results for IMDb_ALEXAd 89 Essay 2: Good Movie or Nothing Better to Do? Table-1: Admission per Showing (Jan 4, 2001 - Apr 18, 2001) 160 Table-2: Admission per Showing in Different Time of Day (Jan 4, 2001 -Apr 18, 2001) 161 Table-3: Admission per Showing (May 29, 2003 - May 26, 2004) 165 Table-4: Admission per Showing in Different Time of Day (May 29, 2003 -May 26, 2004) 168 Table-5: Summary of Weather Variables 172 Table-6: Models with Holiday variables (Jan 4, 2001'- Apr 18, 2001) 173 Table-7: Models with Weekly variables (Jan 4, 2001 - Apr 18, 2001) 174 Table-8: Nested Logit Models with Holiday variables (Jan 4, 2001 - Apr 18, 2001) 176 Table-9: Models with Holiday variables (May 29, 2003 - May 26, 2004) 177 Table-10: Models with Weekly variables (May 29, 2003 - May 26, 2004) 178 Table-11: Nested Logit Models with Holiday variables (May 29, 2003 - May 26, 2004).. 181 Table-12: Predicted Shares of a Base Case Movie on the basis of Data Set 2 182 Table-13: Predictive Performance in the validation sample (May 27, 2004 -June 9,2004) 183 List of Figures Essay 1: Is there a Payoff for Playoffs? Figure-1: Survey Results for Difficulties in Marketing Metrics 90 Figure-2: Survey Results for Definition of Marketing Metrics 91 Figure-3: A Research Framework proposed by Rust et al. (2004) 92 Figure-4: A Marketing-Shareholder Value Framework proposed by Srivastava etal (1998) 93 Figure-5: Cross-sectional relationships between brand share and retail distribution in packaged goods 94 Figure-6: Conceptual model of Super Bowl and other launch TV advertising 95 Figure-7: Distribution of Theater Numbers in the Release Week by Individual Movies____96 Figure-8: An example to show the definitions of six Duration-based Variables 97 Figure-9: Box Plots of Continuous Variables: Non-Super Bowl vs. Super Bowl advertised Movies 98 Figure-10: Simulation by Individual Scenarios 101 Figure-11: Response Functions 103 Figure-Al:Number of Visitors to IMDb.com per Million Alexa Tool Bar users 106 Essay 2: Good Movie or Nothing Better to Do? Figure-1: Weekly Number of Showings from Jan to April 2001 184 Figure-2: Weekly Number of Showings from May 2003 to May 2004 185 Figure-3: Daily Mean Temperature from January 4 to April 18, 2001 186 Figure-4: Daily Precipitation Duration from January 4 to April 18, 2001 187 Figure-5: Daily Mean Temperature from May 29, 2003 to May 26, 2004 188 Figure-6: Daily Precipitation Duration from May 29, 2003 to May 26, 2004 189 ix Figure-7: Predicted Share of a Base Case Movie on the basis of Data Set 2 190 Figure-8: Total Predicted Share of all showings of the Base Case Movie in an hour on the basis of Data Set 2 191 x Acknowledgments Many people contributed to the development of the two essays in this dissertation. First, I wish to thank my thesis committee, Professor Charles (Chuck) Weinberg, Professor Tirtha Dhar and Professor Ralph Winter, for their guidance and support. I am particularly indebted to Chuck. I could not have survived the first year of my doctoral program, let alone have reached this final stage, without his support and faith in me. I would also like to thank Professor Jehoshua Eliashberg, Professor Berend Wierenga, Professor Daniel Putler, Professor Dale Griffin, Professor Darren Dahl, Professor Srabana Dasqupta, Professor Peter Darke and many other wonderful people at U B C for giving me advice, and more importantly, for sharing their enthusiasm and vision. I am also lucky to have research assistance from Denise Yan, Jennifer Nugent, Charmaine So, Peter Sabourin, Kingston Zhu, Eric Lai, Kellie Cottick, Eungjin Park and Mitchell Gray. Last, but not least, I would not have even dared to pursue my Ph.D. dream, or would have given up long before this point i f not for the support of my family and especially my wife, Sally. xi Chapter 1: Introduction 1. Motivation This dissertation is comprised of two essays. Both essays address marketing problems in entertainment industries, the movie industry in particular. Entertainment products are crucial to our quality of life and vital to the economy. For example, Americans annually spend at least 130 billion hours and more than $260 billion enjoying entertainment products. More importantly, the economic significance of entertainment industries is growing rapidly: together, the industries demonstrated an annual revenue growth rate averaged at 7.5% from 1998 to 2002 (Vogel 2004). Parallel to their growing significance for the economy, entertainment industries in general, and the movie industry in particular, are also receiving increasing attention from academics. Observing the trend that an increasing number of academic studies are conducted in relation to the movie industry, Eliashberg, Elberse and Leenders (2005) and Weinberg (2005) suggest several reasons for such growth. The main three reasons are summarized here: 1) The movie industry highlights several important dimensions of marketing problems common to both other entertainment and non-entertainment industries, such as channel relationships and timing decisions. For example, the profitability of a movie depends greatly on the timing decision. As shown by Krider and Weinberg (1998), releasing a movie head-to-head against a similar movie is usually an inferior strategy compared to releasing such competing movies at different times in the same season. 2) The rich data available in the movie industry not only provide high quality measurement of hard-to-measure marketing variables and phenomena, but also enable researchers to sort out complex causal structures, which are difficult to assess in other settings. Some researchers, such as Weinberg (2005), even refer to the movie industry as a "natural experimental 1 laboratory" with which to study complex relationships, which can potentially be generalized beyond the entertainment industries. 3) As one of the key industries in the entertainment business sector, the movie industry is crucial to the U.S. and global economies. For example, in the theatrical market alone, the U.S. movie industry generated $11 billion internationally in 2004. Therefore, the substantive findings of any movie research have high managerial relevance. While the two essays in this dissertation seek to shed light on marketing practices beyond the movie industry, their empirical studies are based in the movie industry. In the following, we first describe the specific marketing problem addressed by each essay and then discuss why the movie industry is an excellent setting for the corresponding empirical study in light of the three reasons highlighted above. 1.1 Essay 1: Is There a Payoff for Playoffs? The launch of new products is a frequently encountered marketing problem in many entertainment industries. For example, according to the Funworld data from NDP, more than 200 new video game titles were released in the three-month window from October to December, 2003. However, movie marketers are among the most sophisticated in terms of the management of new product launches. One of the launch tactics used by movie marketers is airing television commercials during major TV events like the Super Bowl and the Oscars. However, such a tactic is not cheap: a 30-second time slot during Super Bowl 2005 cost $2.4 million, almost twenty times the cost of airing the same advertisement on prime-time network TV. This is a dramatic marketing choice, but does it pay off? The objective of the first essay, "Is There a Payoff for Playoffs? Effects of Major TV Event Advertising" is to answer this question. 2 Why study the effects of major T V event advertising in relation to the movie industry? First, new product launches are common to a variety of product categories in both entertainment and non-entertainment industries. This issue is particularly important to the movie industry, because each movie title has a very short product life cycle and the overall profitability depends greatly on the box office performance during the release week. For 402 movies released widely in the U.S. theatrical market from 2000 to 2002, each movie on average received 45% of its total box office revenue in the opening week alone. Afterward, the percentages decreased very rapidly: 25% in the second week, 13% in the third, 7% in the fourth, and 4% in the fifth week. In fact, not all movies lasted for f i ve weeks. Therefore, the importance of evaluating new product launch tactics such as those related to major T V advertising is highlighted in the movie industry. Second, unlike their counterparts in other industries, movie marketers air their movie commercials during major T V events before the movies are released. The causal order between the major T V event advertising and the outcomes, for example box office revenues, is therefore more apparent in the movie industry. Third, the movie industry is an inherently critical industry due to its size. In addition to providing substantive findings, the marketing models developed in this essay can be used directly by managers within the industry. 1.2 Essay 2: Good Movie or Nothing Better to Do? Many entertainment products are delivered according to a pre-announced schedule. For example, music concerts advertise their schedule in advance in magazines and newspapers. Because consumers decide whether they wish to purchase certain entertainment products on the basis of these pre-announced schedules, the time schedule factor is as important as advertising and product quality in determining consumer demand. It is therefore important to capture consumer time preferences in the demand models for entertainment service providers. However, 3 there are two difficulties in building the type of demand models studied here. First, underlying consumer time preferences must be disentangled from unobserved product quality in aggregate demand data. Second, the cannibalization and market expansion effects must be distinguished when new choice alternatives are added to a schedule. The objective of the second essay, "Good Movie or Nothing Better to Do? Time of Day Demand Models for Multiplex Movie Theaters", is to develop demand models that can address these two issues. Again, there are several reasons this problem warrants study in the context of the movie industry. First, pre-announcing a service time schedule is a common practice among some service providers such as transportation companies. However, since movies are experience goods, the relative attractiveness of individual movies is typically unobservable to researchers, and such unobservability makes it more important to disentangle underlying consumer time preferences from unobserved product quality in aggregate demand data. Second, multiplex movie theaters typically do not charge differential prices for different movie titles. This eliminates any possible confounding of quality and price effects from the sales data. Our demand models therefore demonstrate the two major issues more clearly. Third, the movie exhibition industry generated tens of billions of dollars in 2004. The substantive findings generated and marketing models developed in this essay are of clear benefit to this important industry. 2. Overview 2.1 Essay 1: Is There a Payoff for Playoffs? This essay argues that there are two potential effects of major T V event advertising, namely a direct effect on consumer demand and an indirect effect on consumer demand mediated through the attraction of more downstream channel members or retailers. Focusing on the U.S. 4 movie industry from 2000 to 2002, we empirically test these two potential causal paths in the case of T V advertising during the Super Bowl, which is the largest major T V event each year. We demonstrate that Super Bowl T V advertising by a movie affects opening week box office revenue mainly by indirectly attracting more movie exhibitors and thereby increasing product availability, which in turn increases initial box office revenues. More importantly, we also compare the effects of Super Bowl T V advertising to those of other TV advertising expenditures on potential exhibitors and ultimately initial box office demand. Our results demonstrate that Super Bowl T V advertising is not as effective as other T V advertising efforts, i f both are evaluated at the same initial levels. However, using a counterfactual simulation, we highlight the fact that the Super Bowl could still be an attractive advertising opportunity when a movie also commits to substantial spending on other advertising efforts. 2.2 Essay 2: Good Movie or Nothing Better to Do? Focusing on multiplex movie theaters, this essay develops three models to address two critical issues related to multiplex movie theaters and similar service providers, namely the confounding of product quality and time preference in the aggregated sales data, and the difficulty of distinguishing between cannibalization and market expansion. First, we extend Einav's (2003) yearly seasonality model to build a base model. Second, we further extend the base model in accordance with two approaches in the literature, the nested logit model and Ackerberg and Rysman's [AR] (2002) congestion model, which can better distinguish between cannibalization and market expansion effects when there is choice set variation. In applying the three models to two data sets from a multiplex movie theater in Amsterdam, we obtain two main results. First, one of the two data sets does exhibit the confounding of unobserved movie quality and moviegoers' underlying time preference, demonstrating the value of our demand models in disentangling these two effects in the aggregated sales data. Second, the nested logit and AR ' s models both indicate that the two data sets exhibit slightly more cannibalization than the magnitude suggested by the standard logit when new movie choices are added to a particular one-hour viewing time slot. 3. Organization of Dissertation The rest of the dissertation is organized as follows. The first essay is presented in two chapters. The marketing models used to test the effects of major T V event advertising are developed in Chapter 2, and the data and the model estimation results are discussed in Chapter 2 For ease of reference, the first essay's figures, tables, appendices and bibliographies are all placed at the end of Chapter 3. We present the second essay in Chapter 4. Finally, in Chapter 5 we conclude the dissertation with a summary of the contributions, managerial implications and future research directions of the two essays. 4. References: Ackerberg, Daniel A . and Marc Rysman (2002), "Unobserved Product Differentiation in Discrete Choice Models: Estimating Price Elasticities and Welfare Effects," working paper, U C L A Einav, Liran (2003), "Gross Seasonality and Underlying Seasonality: Evidence from the U.S. Motion Picture Industry," working paper, Stanford University Eliashberg, Johoshua, Anita Elberse, and Mark A . A . M . Leenders (2005), "The Motion Picture Industry: Critical Issues in Practice, Current Research and New Research Directions," Marketing Science, forthcoming Krider, Robert E. and Charles B. Weinberg (1998), "Competitive Dynamics and the Introduction of New Products: The Motion Picture Timing Game," Journal of Marketing Research, 35(1), 1-15 Vogel, Harold L. (2004), Entertainment Industry Economics, 6th ed., Cambridge University Press Weinberg, Charles B. (2005), "Research and the Motion Picture Industry," Marketing Science, forthcoming 7 Chapter 2: Is there a Payoff for Playoffs? Effects of Major TV Event Advertising Part I: Model Development 1. Introduction Television broadcasts of major events like the Super Bowl, Olymics or Oscars are commanding record-high advertising rates: a 30-second commercial cost an estimated average of $2.4 million during Super Bowl 2005' and $1.6 million during the 2005 Oscars (New York Times February 10, 2005). As a recurring theme in Corporate America at present is to make marketing more accountable (Businessweek December 13, 2004), it is important for both academics and practitioners to know if such a 30-second spot in a sports playoff game or an award show is worth the high cost. Consider the National Football League's Super Bowl in particular. As a 30-second prime time network T V commercial in February 2004 cost around $120,500 and had a cost per million audience of $19.85, the 2-million-dollar price tag of an advertisement during that year's Super Bowl, which had a cost per million audience of $51.26, simply cannot be justified on the basis of a cost efficiency argument. In fact, Starcom, a Chicago-based media agency, has shown that their TV-reach optimizer could use $2.3 million, the average Super Bowl rate in 2004, to build a schedule of commercials running on the other broadcast networks to achieve 60% more reach than the 30-second commercial during the Super Bowl period (Broadcasting & Cable January 31, 2005). A l l these facts lead to one important question: What additional value would a 30-second spot during a major T V event create compared to a mere prime time T V spot? 1 A B C is reported to be asking for an estimated $2.6 million for each 30-second commercial during Super Bowl 2006 (New York Times April 20, 2005) 8 This essay argues that there are two potential effects specific to advertisements during major T V events, namely a direct effect on consumer demand and an indirect effect on consumer demand through the attraction of more downstream channel members or retailers. Focusing on the U.S. movie industry from 2000 to 2002, we empirically test these two potential causal paths in the case of T V advertising during the Super Bowl, which is the largest major T V event each year and therefore serves as an excellent illustration of the issue. In particular, we show that Super Bowl T V advertising for a movie affects the opening week box office revenues mainly by indirectly attracting more movie exhibitors so as to increase the product availability, which in turn increases the initial box office revenues. Moreover, we also compare the effects of Super Bowl T V advertising to those of other T V advertising expenditures on exhibitors and ultimately the initial box office demand. Our results indicate that Super Bowl T V advertising is not as effective as other T V advertising efforts, i f we consider marginal returns at the same initial level. However, the Super Bowl is still an attractive advertising opportunity when movie advertisers also commit to substantial spending on other advertising efforts, which start generating responses in a saturation manner. A broader purpose of the present essay is to highlight the role of downstream channel members in mediating the effects of marketing tactics such as major T V event advertising. As mentioned earlier, marketing practitioners are now under enormous pressure to be more responsible for their marketing spending. Specifically, before (and after) allocating resources in a marketing action, marketing practitioners have to know what effects the marketing action will create (and will have created). Tracking such causal effects and measuring the outcomes is now one of the top priorities among marketing practitioners. Unfortunately, as illustrated in a recent survey of the members of the Association of National Advertisers (Nail 2005), marketing practitioners are still having difficulty agreeing on the right metrics to measure marketing 9 performance in general. As shown in Figure-1, 69% of the marketing executives surveyed think "agreeing on the right definition of marketing metrics" is one of the difficulties in their marketing accountability efforts, making it the second most cited difficulty. More alarming is the fact that among the metrics marketing practitioners are currently using and/or will adopt (as shown in Figure-2), there is none explicitly tracking the effects of marketing initiatives on retailers in particular or downstream channel members in general. Such a lack of attention to the metrics of the distribution channel is somewhat mirrored in academic research on marketing accountability. Rust et al. (2004) propose a chain of marketing productivity framework to help academic researchers put various research literatures and potential research directions into a marketing accountability perspective. Their framework is shown in Figure-3. While the framework covers many aspects of the chain from marketing expenditures to shareholder values, one crucial element is apparently absent. That is the mediating role of downstream channel members. We argue that in addition to customer impact, tactical actions would also create impacts on the downstream channel members, which in turn affects consumer demand. Major T V event advertising like Super Bowl advertising provides an abundance of anecdotal examples to illustrate this mechanism. When Master Lock ran its first commercial during the Super Bowl in 1974, the primary target was not consumers but distributors (Kanner 2004, p. 127-128). In the subsequent twenty years, when Master Lock committed a large portion of its yearly marketing budget to Super Bowl advertising, the company reminded the hardware wholesalers that their premium pricing was well justified by the strong brand equity. In other words, distributor response is a potentially crucial factor mediating the effect of Master Lock's Super Bowl advertising effort. If one attempts to use the extant consumer-based marketing metrics to measure the effect of Master Lock's Super Bowl advertising, an incomplete understanding would result. 10 In a nutshell, the present essay intends to make two levels of contribution. First, we study the worth of major T V event advertising by focusing on the U.S. movie industry's use of Super Bowl T V advertising to launch new movies. Second, we highlight the mediating role of downstream channel members in a broader perspective of marketing accountability. This essay consists of two chapters, namely "Model Development" and "Data Analysis." The next section of this chapter more specifically discusses how this essay advances the marketing literature. We then discuss in section 3 the rationale for using the movie industry for our empirical investigation. Section 4 introduces our models. The next chapter continues with section 5 and section 6, which describe the data variables and discuss the estimation results. Section 7 presents further analysis on the basis of the estimation results. The limitations of this research, and further research directions, are discussed in section 8. 2. Related Literature As stated in the previous section, this essay intends to contribute at two levels, examining the effects of the tactic of major T V event advertising, and demonstrating the mediating role of downstream channel members in the broader perspective of the marketing productivity chain. We first review the literature from the broader perspective and then use a previous major T V event advertising study to motivate our main research questions. 2.1 Marketing Accountability In their widely cited papers in the marketing metrics literature, Srivastava, Shervani and Fahey (1998, 1999) introduce a conceptual framework outlining the chain from tactical marketing activities to ultimate shareholder value. Figure-4 reproduces their marketing-shareholder value framework. The main tenet in their framework is that in managing market-11 based assets, marketers should aim at four shareholder value drivers, namely accelerating cash flows, enhancing cash flows, reducing risk (vulnerability and volatility of cash flows), and enhancing the residual value of cash flows. An important insight from the framework is the importance of measuring market-based assets. Marketers must have some measures of market-based assets before being able to manage them. While Srivastava et al. discuss two types of relational market-based assets - customer relationship and partner relationship - subsequent market metrics studies primarily focus on customer relationships. In particular, a growing amount of research effort is devoted to measuring the lifetime values of customers (e.g., Werner and Kumar 2000; Niraj, Gupta and Narasimhan 2001) and modeling how customer behaviors would be influenced by different tactical marketing activities (e.g., Rust, Lemon and Zeithaml 2004). In contrast, partner relationship in general and channel relationship in particular are other important relational market-based assets in Srivastava et al's framework, but are apparently absent in the extant marketing metrics literature. An intended contribution of this essay is to highlight the importance of distribution channel in this literature stream. A major challenge related to measuring distribution channels is that downstream channel members are independent decision makers, just like consumers, but their behaviors only facilitate (as opposed to directly generate) cash flows from consumer purchases. From a marketing productivity chain perspective, we have to understand a two-part causal path, namely how a tactical marketing action would influence the downstream channel members' behaviors and how the resultant downstream channel members' behaviors would influence consumer purchases. Relatively little academic attention has focused on examining the first part of the path or investigating both parts simultaneously. However, the second part is relatively well established in the marketing literature. Specifically, as reviewed by Reibstein and Farris (1995), there is a robust finding in the literature that the cross-sectional relationships between brand share and 12 retail distribution in the packaged goods industry show a convex pattern. In other words, brands with greater distribution coverage tend to achieve higher sales revenues per point of distribution. Figure-5 illustrates this typical pattern. As argued by Farris, Olver and De Kluyer (1989), the convex line is due to the fact that retailers do not stock all the competing brands. Some consumers therefore cannot find their preferred brands at retail outlets within their sphere of convenient access, and are forced to switch to the brands carried by most retailers.2 While not explicitly studying the shape of the sales responses with respect to distribution, previous research work has shown the presence of a relation between sales and distribution in the movie industry. For example, Jones and Ritz (1991) show that a diffusion model incorporating retailer actions without the contagion effect among consumers can still fit the weekly box office revenues of a sample of movies as well as the more sophisticated Bass models do. Despite the fact that the small degree of freedom in their model estimation may limit the generalizability of their results, Jones and Ritz's study successfully sheds light on the potential role of distribution channels in movie launches and attracts more academic attention in this area. Sawhney and Eliashberg (1996), for example, explicitly model the effect of product availability in a diffusion model for new movies. They divide a consumer's movie viewing behavior into a time to decide and a time to act. Even i f a consumer decides to see a movie after being influenced by word-of-mouth or other communication campaigns, unless the movie is available, the consumer may still not see the movie (at least not in a theater). When modeling the international diffusion of U.S. movies, Neelamegham and Chintagunta (1999) found that the number of screens is a significant predictor of box office sales in various countries. It is clear that, similar to packaged goods industries, product availability is also a significant factor in the consumer purchase of movies. 2 In the hypothetical case where all retailers carry all competing brands of a category and all consumers' tastes are similar across different geographical locations, all consumers should be able to find their preferred brands at every retailer and the sales should be simply proportional to the distribution coverage. The dotted straight line in Figure-5 represents this hypothetical case. 13 On the other hand, to the best of our knowledge there are no studies examining the effect of tactical marketing activities on distribution channels.3 In particular, although studies like Parson (1974) and Elberse and Eliashberg (2003) shed light on how advertising expenditures in general influence distribution intensity, it is still not clear whether the advertising expenditures should be allocated to a specific marketing tactic like major T V event advertising or not. As shown by Mantrala, Sinha and Zoltners (1992), the allocation of marketing resources to various marketing tactics is as important as determining the total resource level. Therefore, it is non-trivial to understand the effects of specific advertising tactics. This essay extends Parson (1974) and Elberse and Eliashberg (2003) by focusing on a specific tactical action, namely major T V event advertising. First, we focus on the advertising expenditure in the pre-launch period. This variable is more specific than the total advertising expenditures used by Elberse and Eliashberg, which cover advertising efforts in both pre-launch and post-launch periods, and different from the post-launch advertising expenditures used by Parson. Furthermore, we separate the pre-launch advertising expenditure into the allocation to Super Bowl advertising and other T V advertising efforts. By allowing these two tactics to have differential effects on the downstream channel members and in turn consumer demand, we go beyond considerations of what level of advertising expenditure a new product should invest to how the advertising expenditure should be allocated. 3 However, there are theoretical studies arguing that launch advertising in general can attract more distribution points. For example, some game theorists have formalized launch advertising expenditure as a product quality signaling game between upstream channel members and their downstream partners (e.g., Chu 1992, Desai 2000). The separating equilibrium is usually that the manufacturers of the low demand products finding it too costly to imitate those of the high demand products to spend a large sum of launch advertising. 2.2 Major TV Event Advertising Being an important marketing tactic, it is surprising that major T V event advertising has not received much academic attention. Studies like Newell and Henderson (1998); Newell, Henderson and Wu (2001); or Tomkovick, Yelkur and Christians (2001) only use the Super Bowl as a field setting to examine the effects of various design and media factors. Their studies explain only variations in commercials placed in the Super Bowl, but not the more interesting variations, such as the differences between commercials placed in the Super Bowl and those not in it. A notable exception is an exploratory study by Yelkur, Tomkovick, and Traczyck [YTT] (2004). They found that movies that advertised during the Super Bowl achieved around 40% greater box office revenues than a matched sample of mass-market movies. However, this finding is weakened by their methodology and several potential confounding variables, for which they did not control. First, the main method used by Y T T was to compare the mean box office revenues of two groups, Super Bowl-advertised movies and non-Super Bowl-advertised movies. When they attempted to control for the factors of release date and production budget, they simply cut out movies released between September and January and/or movies with production budgets lower than US$35M. We argue here that this may not be the most desirable method of controlling for these two factors, and suggest an alternative method. Specifically, YTT ' s way of dropping movies released between September and January is potentially equivalent to dropping movies with a gross as big as the Super Bowl movies. In fact, as suggested by Krider and Weinberg (1998), movies with similar appeal would avoid head-on competition by releasing in a different time of year. By dropping movies released in periods different from those of the Super Bowl-advertised movies, Y T T are essentially excluding movies that are more similar to Super Bowl-advertised movies from their matched sample (non-Super Bowl-advertised movies), and keeping the more dissimilar ones, artificially making the two groups more dissimilar. In other 15 words, YTT's attempt to control for one confounding factor is potentially creating another confounding problem. To improve on this method, the present study will control for the differences in release dates by explicitly capturing the potential effect of movies released in different Hollywood seasons. Instead of dropping some observations, we include all observations but statistically control for their different release dates by including some Hollywood seasons variables in our econometric models. On the other hand, another exclusion in YTT's sample is movies with production budgets lower than $35M. While this exclusion may not make the matched samples more dissimilar, as above, the rich information provided by the continuous variable of production budget is somewhat lost by making the production budget a binary variable. Instead, this study will keep production budget as a continuous variable and statistically control for its potential confounding with Super Bowl T V advertising tactic by explicitly capturing its effect in our models. Moreover, there are two factors for which Y T T have not controlled in their study, but which are potentially confounding with the factor of Super Bowl T V advertising. First, as shown in Table-6, Super Bowl-advertised movies tend to have higher total expenditure related to other T V advertising opportunities (TVAD) than non-Super Bowl-advertised movies in the launch period. It is possible that the higher box office performance of Super Bowl-advertised movies is due to such high total T V advertising expenditure, rather than the specific commercials during the Super Bowl. In other words, only how much a movie studio spends matters. Where it spends (Super Bowl or other prime time network T V programs) does not. It is therefore important for the current study to measure both Super Bowl and other T V advertising expenditure in the pre-launch period. In fact, by including both expenditures, we can answer a very important question: "Is Super Bowl T V advertising more effective than other launch T V advertising opportunities?" Y T T only attempt to determine whether Super Bowl T V advertising generates a non-zero effect 16 on box office revenues. However, the null effect is not a sufficient benchmark to examine the true worth of Super Bowl T V advertising. For marketing practitioners, it is more important to know if Super Bowl T V advertising can generate more impact than other alternative launch tactics. Even i f commercials during the Super Bowl can generate a non-zero effect, as long as there are other alternatives which can generate more effects, marketing practitioners would not allocate any resources on Super Bowl T V advertising. In other words, the benchmark to which Super Bowl T V advertising should be compared is the effect of other tactical alternatives, rather than the null effect. Therefore, we will use other launch T V advertising as the more meaningful benchmark in the present study. Second, as we can see from Table-6, Super Bowl-advertised movies tend to start their T V campaign much more ahead of their release dates (LEAD) than non-Super Bowl-advertised movies. Therefore, it is possible that the superior box office performance of Super Bowl-advertised movies is caused by the earlier T V campaign start date. In other words, it is when a movie studio starts spending, as opposed to where it spends, that makes the difference. Therefore, the time lag between a movie's launch T V campaign start date and its release date must be controlled for so as to disentangle the true effect of Super Bowl advertising from this confounding factor. More importantly, Y T T do not look at the detailed mechanism of how Super Bowl advertising works. In particular, the mediating role of downstream channel members and exhibitors in the movie context is overlooked. As argued in Section 1, the 2-million-dollar price tag of Super Bowl advertising cannot be justified on the basis of cost efficiency. What makes Super Bowl advertising worth such a high cost? Marketers and advertising agents have cited various factors ranging from corporate esteem, employee morale, trade support, and public relations, to plenty of water-cooler talk. For example, InsightExpress found through an online 17 survey in 2004 that 50% of the 500 respondents were watching the game for the commercials and 58% said they pay closer attention to the ads during the Super Bowl than those they see every day (Advertising Age Jan 31, 2005). This suggests that Super Bowl T V advertising is reaching more "engaged" consumers, who probably devote more mental resources to processing the advertising information. Therefore, research companies generally found the week-later recall of Super Bowl advertising better than recall of other prime-time advertising (Advertising Age Jan 31, 2005). This essay focuses on the generally overlooked trade support factor. As discussed earlier, we hypothesize that Super Bowl TV advertising has two paths to influencing opening week box office revenues. First, there is a direct path, in which Super Bowl T V advertising directly increases the demand of moviegoers. Second, there is an indirect path, which consists of two parts. First, Super Bowl T V advertising attracts more movie exhibitors to show the movies. Then, increased product availability enhances final sales revenues. In summary, there are three research questions central to this essay. First, we re-examine the effect of Super Bowl T V advertising using a method improved from YTT. Second, by introducing the mediating role of movie exhibitors, we decompose the effect of Super Bowl T V advertising into two potential causal paths. Third, we compare the effect of Super Bowl T V advertising to a more meaningful benchmark, namely the effect of other launch T V advertising. 3. Mov ie Industry Among the many U.S. industries adopting the popular tactic of Super Bowl T V advertising, why is it so interesting to focus on the movie industry? There are four factors making the movie industry a powerful setting in which to study the effects of advertising: 1) an 18 inherently interesting question, 2) minimal advertising development cost, 3) temporal order, and 4) large sample size. First and foremost, the role of the distribution channel in mediating the effects of Super Bowl commercials is inherently interesting. With the cost of a 30-second spot during the Super Bowl exceeding $2 million, it is unclear why more than half of the movies that are advertised during the Super Bowl are not released to the market until three or more months after the Super Bowl is played (as shown by the long time lag from Super Bowl to the release week in Table-3). It would be surprising i f consumers remembered advertising that they had seen more than three months earlier. This is especially surprising given that in a typical week, the Hollywood studios release between two and four movies, with an average advertising budget in 2003 of $35 million (MPA Market Statistics 2003). In other words, more than 24 new movies are likely to be introduced into the market before the movies seen during the Super Bowl are released in movie theaters in the United States. Second, almost all commercials for movies are made by cutting and pasting scenes from the actual films. On the other hand, developing a T V commercial in other product categories can be expensive, and more importantly, the effectiveness of the T V commercial may vary greatly from one campaign to another. For example, in addition to paying for the Super Bowl time slots to air their commercials, Budweiser each year also hires several advertising agents to develop different commercials specifically for the Super Bowl. This practice does not only confound the advertising media cost with development costs but also entails variations in different advertising campaigns' effectiveness. In contrast, a movie's T V commercials involve primarily the media costs only. This allows us to study the net effect of our focal media buying decision: Super Bowl or not. Moreover, even i f there is more than one version of commercials for a movie, all versions are highly correlated with the perceived quality of the movie. In other words, the 19 effectiveness of different versions is relatively consistent, which allows us to focus on Super Bowl advertising versus other T V advertising opportunities by summing all other T V advertising expenditures. Third, the response of retailers in the movie industry is more causally apparent than in other industries. Exhibitors have to allocate their scarce "shelf space" to movies (particularly during the peak summer season which starts in May) and base their judgments on the expected sales of movies. Super Bowl advertising may act both as a signal to exhibitors of the expected performance of a movie and also have a direct impact on their decisions to book a movie. In fact, a major trade show in which exhibitors make commitments to showing movies, Showest, occurs every year in Las Vegas in March. Thus, the Super Bowl may be well timed to stimulate exhibitor awareness and interest in a movie. On the other hand, much of the advertising expenditure, and certainly the Super Bowl T V advertising, are spent before the movie is released. For example, in a sample of 398 mass-market movies released between 2000 and 2002, more than 95% of the movies allocated more than 70% of their total T V advertising expenditures before and during the opening week. Thus, the effect of Super Bowl advertising on opening week sales can be measured without the need to consider purchase feedback effects. Last but not least, there are a sufficient number of movies released each year for us to conduct a statistical analysis of these effects without needing to rely on a small set of case studies. In our sample of movies released between 2000 and 2003, there were 19 that advertised during the Super Bowl. 4. Model Development We limit the scope of the present essay to the opening week box office revenues. There are two reasons. First, as the consumers' and retailers' decisions in the second week and 20 onwards would usually be influenced by additional factors such as the movie's ranking in the previous weeks (e.g., De Vany and Walls 1997) and "sliding scale" revenue sharing contracts between movie studios and individual theaters (e.g., Swami, Eliashberg and Weinberg 1999), which are not antecedents to the launch advertising decision, we believe the complexity of adding these factors to our study would not generate much additional insight for our main focus, namely using major T V event advertising as a new product launch marketing tactic. Second, as noted by Neelamegham and Chintagunta (1999), the mean first week viewership of their U.S. movie sample is almost double the mean weekly viewership in the U.S. and 13 other countries. This suggests that the first week box office sales are very critical to a movie's ultimate profitability. Therefore, it is non-trivial to study whether a specific launch marketing tactic is more effective than others in influencing the first week box office sales. We formalize the research questions discussed in the literature section into three hypotheses: HI: Replication of Super Bowl T V Advertising Effect: Super Bowl T V advertising increases the opening week box office revenues. H2: Mediation of Movie Exhibitors: Through the mediation of movie exhibitors, Super Bowl T V advertising increases the opening week box office revenues along two paths. A) Super Bowl T V advertising first increases the number of movie exhibitors. Then, the increased number of movie exhibitors increases opening.week box office revenues. B) Super Bowl T V advertising directly increases opening week box office revenues. H 3 : Effectiveness of Super Bowl and other T V Advertising opportunities: Super Bowl T V advertising is as effective as other T V advertising opportunities. 21 4.1 Variable Conceptualization In order to test these hypotheses, we use three groups of variables, namely endogenous variables, main exogenous variables and other exogenous variables. Table-1 lists the specific definitions of these variables. We will discuss the conceptualization of the variables here and the detailed operationalization in next chapter. Endogenous Variables: There are two endogenous variables in our model: opening week box office revenues (denoted as BO/), and opening week number of theaters engaged for the movie (denoted as THEATERj). These essentially represent the decision outcomes of two market participants, namely moviegoers and movie exhibitors. Main Exogenous Variables: According to 2003 M P A A market statistics (Table-2), T V advertising was the major medium used by movie distributors from 2000-2002. We therefore use T V advertising expenditure as a proxy for total advertising expenditure in the pre-launch period. Specifically, our two main exogenous variables are Super Bowl T V advertising expenditures (SUPERBOWLj) and total expenditures on other T V advertising opportunities prior to movie release (TVADj). In order to identify the true effect of Super Bowl T V advertising, among other factors, we have to control for the total launch T V advertising expenditure, which is one of the potential confounding factors in Y T T as discussed earlier. TVADj is therefore used to distinguish the effect of Super Bowl T V advertising from the effect of "high" advertising expenditure in the pre-launch period. In particular, i f SUPERBOWLj is found to be an insignificant factor when the total launch T V advertising expenditure is controlled for, it suggests that a new product launch's 22 sales only depend on how much advertising expenditure is behind the launch, and it does not matter where such advertising expenditures go (either Super Bowl or other network T V programs). Note that TVADj does not double-count SUPERBOWLj. This allows us to compare the effectiveness of the two types of advertising opportunities as in H3. Furthermore, as discussed in the movie industry section, these two expenditures are made prior to the realization of the endogenous variable of box office revenue and theater numbers, therefore establishing a relatively clear causation order. Other Exogenous Variables: In addition to total launch T V advertising expenditures, T V campaign start date is the other potential confounding variable with Super Bowl T V advertising. We therefore include the duration between a movie's major T V campaign start date and its release date (LEAD/) in our model. If the success of Super Bowl-advertised movies actually does not depend on where they advertise, but when they start advertising, LEADj should remove the effect of Super Bowl T V advertising. Similarly, eight more exogenous variables will be used to control for other potential confounding effects with our main exogenous variables. In particular, four exogenous variables are related to the unobserved expected quality of individual movies. The expected movie quality is important because moviegoers' decisions whether to purchase tickets for a movie in its opening week are primarily based on the expected movie quality. Similarly, theater managers decide i f they will show the movie in their movie theaters based primarily on the expected number of tickets sold. In other words, expected movie quality is a main factor determining the two endogenous variables, namely BOj and THEATERj. While our two T V advertising 23 expenditure variables are treated as exogenous here, one may argue that these advertising decisions are in fact determined endogenously by the movie studios. Specifically, when a movie studio has a movie with high expected quality, the studio is likely to increase total launch advertising expenditure to make more potential moviegoers aware of the movie. If we as researchers do not have any measures for expected movie quality in our model, we would only observe that larger launch advertising expenditures always lead to higher theater numbers and higher box office grosses, and would be misled in conclusions related to the effect of advertising expenditures, which is potentially confounded with the expected quality. Therefore, it is very important to control for expected movie quality. As movie is an experience good (Nelson 1970), moviegoers and even theater managers can only use cues to infer the expected quality. Our model includes four cues available to theater managers and moviegoers, namely production budget (BUDGET/), pre-release buzz (BUZZ/), publicity generated (PUB/) and critic reviews (CRITICS/). While we argue these four cues are reasonable proxy variables for expected movie quality, we acknowledge that they do not completely represent expected movie quality and it is possible that some dimensions of the expected movie quality, which are not captured by these proxy variables, have potential influences on the parameter estimates of Super Bowl advertising effect. Moreover, to control for the possibility that Super Bowl-advertised movies tend to be a particular type of movies, and that this particular type of movie would usually do better than others in terms of box office revenues, we include two sets of variables to characterize the genre (GENRE/. Action, Comedy, Drama or Family) and M P A A rating (MPAAf. G, PG, PG-13 or R) of the movies. As discussed earlier, we control for the potential confounding of Super Bowl-advertised movies and their tendency to release before the end of the summer season using a set of binary 24 variables to indicate in which Hollywood seasons the movies open (SEASON/. January-April, May-August, September-October, or November-December). Moreover, as moviegoers have more free time to visit movie theaters during holidays, we capture this possibility with a binary variable, HOLIDAYj, to indicate whether the opening week covers any of the eight major U.S. holidays (New Year, Martin Luther King Day, Presidents Day, Memorial Day, Independence Day, Labor Day, Thanksgiving, and Christmas). Finally, different movie distributors may have differential powers in signing up movie theaters. To capture this possibility, a set of variables is used to indicate different major distributors (DISTRIBUTOR/. Buena Vista/Miramax, Warner Brothers/New Line, Paramount, Sony, Fox, and Universal). 4.2 Conceptual Model Corresponding to HI and H2, the relations among the endogenous and main exogenous variables are hypothesized as in Figure-6a and Figure-6b. Figure-6a is a diagram showing the two paths of Super Bowl T V advertising effect and other launch T V advertising effect on box office revenues. The first path is a direct effect from the two T V advertising efforts. The second path is an indirect effect mediated by the movie exhibitors, as discussed previously. We can test H2 using this model. Figure-6b is an alternative model, in which the two types of T V advertising efforts only have direct effects on box office revenues and the movie exhibitors. Unlike the two-path model, the single-path model does not allow movie theaters to influence the box office revenues, essentially omitting the second part of the indirect path of the two-path model. Such an omission allows us to test a replicated model of YTT, as hypothesized in HI , with several key potentially confounding factors now being controlled for. More importantly, by comparing the two-path model with the single-path model, we can examine whether the direct 25 effect from T V advertising on box office revenues would be reduced once the mediating role of movie exhibitors is allowed. Note that this testing approach is similar to Baron and Kenny's (1986) mediation analysis, which uses three regression models, namely 1) regressing the mediator on the independent variable, 2) regressing the dependent variable on the independent variable, and 3) regressing the dependent variable on both the independent variable and the mediator. As we discuss the estimation in more detail later, rather than estimating their regression models 1 and 2 separately, our single-path model estimates the two models as a seemingly unrelated regression (SUR) model, also allowing us to test whether our independent variable, SUPERBOWLj, affects the mediator, THEATER,-, and the dependent variable, BOj, separately. On the other hand, our two-path model is in fact a more sophisticated version of Baron and Kenny's third regression model. Note that Figure-6a and Figure-6b also characterize the temporal order of the movie theater managers' and moviegoers' decisions. In particular, movie exhibitors may begin to . consider whether or not to screen a specific movie as early as during exhibitor trade shows like Showest, but they have to finalize their screening decision on the Monday preceding the release date (Swami, Eliashberg and Weinberg 1999). On the other hand, potential moviegoers may make up their mind about going to watch a specific movie very early on, but they do not need to make any commitment until the moment they show up in front of the box offices. In brief, the variable THEATER is determined a week before the realization of BO in the opening week. The temporal order of our two endogenous variables leads to two implications. First, variables like TVADj, BUZZj and PUBj need to be defined differently for BO and for THEATER. Specifically, T V advertising efforts in the release week are not observed nor considered by movie exhibitors when making their screening decisions. In contrast, potential moviegoers can observe, and would be influenced by, the release week's T V advertising efforts. Denote 26 TVAD-ij as the total T V advertising expenditure prior to the release week and TVADQJ as the total T V advertising expenditure prior to and including the release week. TVAD-ij influences movie exhibitors' screening decisions (THEATERj), while TVADQJ influences release week box office sales (BOj). Similarly, we denote BUZZ-ij, BUZZoj, PUB.jj and PUBoj as the buzz in the week prior to the release week, the buzz in the release week, the total amount of publicity up to but not including the release week, and the total amount of publicity up to and including the release week. While BUZZ.,j and PUB.ij influence THEATERj, BUZZ0J and PUB0J influence BOj. Also note that the cumulative T V advertising expenditures (TVAD-ij and TVADoJ) and the total amount of publicity (PUB.ij and PUBoj) are stock variables, while BUZZ-IJ and BUZZoj are flow variables. By definition, the relations between TVAD-ij and TVADQJ and between PUB.jj and PUBoj are: TVADQJ = TVAD-ij + T V advertising expenditure in the release week (la) PUBoj• = PUB.ij• + Publicity received in the release week (lb) On the other hand, the relationship between BUZZ-ij and BUZZoj is less clear. Future research efforts may explicitly model this relation. Another implication from the temporal order of BO and THEATER is that the other exogenous variable, CRITICSj, is only relevant to BO. In particular, as critic reviews are only available in the release week, CRITICSj can affect only BO. However, one should note that some variables are specified to influence either THEATERj or BO, not because of the temporal order but due to other reasons. First, SEASONj and HOLIDAY j influence BO only, not because of the temporal order, but rather due to the fact that most theater managers do not increase or decrease the total number of movie theaters according to different times of year. Similarly, the specification that DISTRIBUTOR would influence only THEATERj is due to the previous 27 discussion that DISTRIBUTOR] variables are used to capture the differential "pushing" abilities of different distributors on movie exhibitors. 4.3 Estimation Models We are now ready to discuss the econometric model corresponding to the two-path and single-path models (Figure-6a and Figure-6b). First, we use a system of two simultaneous equations to capture the relations in the two-path model: THEA TERj = f, (SUPERBO WLj, TVAD.,,j, BUDGETj, LEADj, BUZZ.,j, PUB.,j,GENREj,MPAAj, DISTRIBUTOR], £,) (2) BOj = UTHEATERj, SUPERBOWLj, TVAD0J, BUDGETj, LEADh BUZZoj, PUB0J, GENREj, MPAAj, SEASONj, HOLIDAYj, CRITICSj, s2) (3) Here, f i ( . ) and f2(.) are the functions and s, and e2 are the error terms for THEATER and BO respectively. As the two-path and single-path models are nested, the system corresponding to the single-path model can be obtained by omitting THEATERj in equation (3). For brevity, we will discuss only the two-path model in the rest of this section. We explore four models with different functional forms, f|(.) and f2(.) . There are two reasons for this approach. First, it is important for our comparison of the effectiveness of Super Bowl and other T V advertising as these functional forms determine the shapes of responses of THEATER and BO with respect to various variables and the diminishing or increasing rate of the marginal returns. Different functional forms may give different comparison results. It is very important to find the appropriate functional forms. Moreover, we can get a better sense of the 28 robustness of our results by comparing the estimation results of different functional forms. The first two functional forms explored are the commonly used log-linear and log-log models: M l : Log-linear \n(THEATERj) = Bl0 +B, ^ SUPERBOWLj + BUD-TVAD.,j . + PI.BUDGETBUDGETJ + BUEAD-LEADj + BliBUZZ-BUZZ.ij + BliPUB-PUB.Ij + GENREj-B, GENRE + MPAAj-BLMPAA + DISTRIBUTORJ-B,,DISTRIBUTOR + e, (2a) \n(BOj) = B2J)+ BTHR-THEATERj + BlSB-SUPERBOWLj + B2,AD-TVAD0j + PLBUDGETB UDGETJ + BlLEADEEADj + BLBUZZ-BUZZ0J + B2,PUB PUBoj + GENRE j -B2 GENRE + MPAAj-B2MPAA + SEASONj REASON + HOLIDAYj-B2 .HDY + BlCRITIC.CRITICSj + s2 (3a) M2: Log-log MTHEATERj) = B10 +B,,SB-ln(S+SUPERBOWLj) + BiAD-ln(5+TVAD.,j) + B iTBUDGET'ln(BUDGETj) + BUEAD-ln(S+LEADj) + B!tBUZZ-ln(BUZZ.!,j) + B1,PUB-ln(S+PUB.!J) + GENREj -Bj GENRE + MPAAj-PwPAA + DISTRIBUTORj-BliDISTR1BUTOR + e, (2b) \n(BOj) = Bl0 + BTHR-ln(THEATERj) + B2SB-ln(5+SUPERBOWLj) + BlAD-ln(5+TVAD()j) + PIBUDGETWBUDGETJ) + B2,LEAD -ln(5+LEADj) + B2 ln(BUZZ0,j) + BlPUB-ln(S+PUB0,j) 29 + GENRE j y5? GENRE + MPAAjfr.MPAA + SEASONjfcsEASON + HOLIDAYjfo.HDY + ft7, CRITIC In(CRITICSj) + E2 (3b) As the continuous variables - SUPERBOWLj, LEADj, CRITICSj, and PUBj - have zero values for some observations in our data set, taking the natural log of the variables would result in undefined values. In order to allow the use of the log-log model, 8, a very small pre-set numerical value, is added to each of these continuous variables before taking the logarithm. In estimation, we set 8 at 0.000001.4 Note that, in order to ensure compatibility between the two T V advertising expenditures, 8 is also added to T V AD, before the logarithm is taken. As mentioned earlier, to compare the effectiveness of Super Bowl and other launch T V advertising (H3), the functional forms of the relations among THEATERj, BOj, SUPERBOWLj, and TVADj are very important. In particular, the log-linear model (Ml ) implies an increasing marginal return for the left-hand side variable as compared to the right-hand side variables in an equation. Denote Fas the left-hand side variable, which is THEATERj or BOj] and denoteXas a right-hand side variable, which is THEATERj, SUPERBOWLj, or TVADj. From (2a) or (3a), we can express the relation between Y and Xas: Y=exp(BxX)-k where A; is a constant invariant to X. As Y (THEATERj or BOj) is always positive in our context, we assume k is positive for the subsequent discussion. The first- and second-order derivatives are: ?L = Rx.exp(RxX)-k Other values of 8 have been tried and the estimation results are relatively robust to d. 30 | ^ = px2 -exp(RxX) -k > 0 i f Rx * 0 oX dY As we hypothesize that — is positive for all X in our context, [ix is expected to be positive. dX d2Y Together with the positive , the log-linear model assumes that Y increases with X at an dX increasing rate. In the case that Xis THEATERj, an increasing marginal return relation may make sense, as discussed in the literature section. However, in the case that X is either of the two T V advertising variables, the increasing marginal return is counterintuitive and contradictory to the results in previous advertising studies (e.g., Vakratsas, Feinberg, Bass and Kalyanaram 2004). On the other hand, the log-log model (M2) allows the marginal return to be diminishing or increasing but in a restrictive manner. Similar to the above, we can write the relation characterized by (2b) or (3b) between each pair of our focal variables, TandXas: Y = XPx-h where A is a constant invariant to X and we assume it to be positive. The first- and second-order derivatives are: — =Rx^,-h dx ^-Bx<Px-l)-^-2-h >QifRx>\ < 0 i f l>px>0 d2Y Even under our hypothesis that Rx is positive, — - can be positive or negative, depending on dX whether Rx is larger than one or not. That means the log-log model allows Y to increase with X at either an increasing rate or a diminishing rate. However, this is still a very restrictive functional 31 form. The log-log model essentially implies a constant elasticity of Y to X, restricting the percentage change of Y due to one percentage change ofXto be constant over all range o f X While we will apply both log-linear and log-log models to the data, we also explore a more flexible form for f](.) and f2(.). First, we no longer restrict all continuous variables on the right-hand side of an equation to the same functional form. While the log-linear and log-log models are common model specifications in econometrics, their assumption that all continuous variables on the right-hand side influence the left-hand side variables in the "same" manner is arbitrarily restrictive. For example, there is no a priori reason why THEATERj and BUZZj have to follow SUPERBOWLj and TVADj in exhibiting constant elasticity in the log-log model, or why managerial decision variables like BUDGETj must give an increasing marginal return just like CRITICSj. Therefore, while we keep the three managerial decision variables, SUPERBOWLj, TVADj, and BUDGETj in the log form, we test the functional forms of other continuous exogenous variables like BUZZj using two models, one incorporating the linear form and the other using the log form. More importantly, since the mediating role of THEATERj is the main thesis in this essay, we use a quadratic form for THEATERj in the box office revenues equation. In other words, we regress BOj against a linear and a squared term of THEATERj. Two parameters, rather than one, are used to characterize the relation between BOj and THEATERj. We call this a log-quadratic model. By using two parameters, the log-quadratic model is more flexible than a constant elasticity model, while allowing increasing and/or diminished marginal return: BOj = exp(pTHRi -THEATERj + RTHRI -THEATERJ2) -m where m is a constant invariant to THEATERj and is assumed to be positive. d B ° J • = exp0THRi -THEATERJ+RTHR2 -THEATER2) -(PTHRI + 2 -RTHR2 -THEATERJ) m dTHEATERj 32 9 B ° j 2 = exp(BTHRi-THEATERj + BTHR2.THEATER?) dTHEATER/ •((PTHRI + 2-BTHR2.THEATER/ + 2 PTHEATERI) -m d2BOj dTHEATER/ Despite the complex form, 2 i s n ° t restricted to being either positive or negative. For example, i f BTHRl = 0.02 and BTHR2 = -0.000009, AJ„n2 i s negative (= -0.000014) at d2BOj dTHEATER/ THEATERj = 1000. If BTHR1 = 0.02 and BTHR2 = 0.000001, 3 B ° J 2 is positive (= 0.000486) dTHEA TERj at THEATERj = 1000. As discussed earlier, we also allow the functional forms of other continuous exogenous variables to be different from those of the three managerial variables, SUPERBOWL, TVAD and BUDGET. Therefore, there are two variants of the log-quadratic model: M3 and M4. In both M3 and M4, the three managerial variables are related to THEATERj or BOj in log-log form and THEATER influences BOj in log^quadratic form. The difference lies in the functional forms of the other continuous exogenous variables, LEADj, BUZZj, CRITICSj and PUBj. While M3 assumes that the continuous variables are in linear form, M4 assumes they are in log form. M3: Log-Quadratic-a \n(THEATERj) = BI0 +BISB-ln(S+SUPERBOWLj) + BIAD-ln(5+TVAD.tj) + Pi,BUDGEJ-ln(BUDGETj) + PUEAD EEADJ + PI.BUZZBUZZ-U + p l i P m -PUB.,j + GENREj -fii} GENRE + MPAAjP,,MPAA + DISTRIBUTOR p i,DISTRIBUTOR + s, (2c) \n{BOj) = p2,o + PTHRI -THEATERj + pTHR2 -THEATERj2 + P2,SB-ln(8+SUPERBOWLj) + p2,AD-ln('S+TVADQJ) 33 + p2.BUDGET-ln(BUDGETj) + p2,LEAD-LEADj + PIBUZZ-BUZZOJ + PIPUB -PUBoj + GENREj p2r GENRE + MPAAjP2,MPAA + SEASONJP2,SEASON + HOLIDAYyp2,HDY + pi.CRiTic-CRITICSj + s2 (3c) M4: Log-Quadratic-b MTHEATERj) = pU) +p,iSB-ln(S+ SUPERBOWLj) + pLAD-ln(S+TVAD.,j) + PIBUDGETMBUDGETJ) + pUEAD -ln(S+LEADj) + Pi.Buzz-ln(BUZZ.ij) + P,,PUB-ln(S+PUB.,j) + GENREj pi, GENRE + MPAAjpiTMPAA + DISTRIBUTORj P,,DISTRIBUTOR + e, (2d) ln(BO) = p2,0 + PTHRI -THEATERj + pTHR2-THEATER/ + PISBMS+SUPERBOWLJ) + plAD-ln(S+TVAD0J) + PI.BVDGETMB UDGETJ) + plLEAD -ln(S+LEADj) + P2,Buzz-ln(BUZZ0j) + p2,PUB-ln(S+PUB0j) + GENREj p2, GENRE + MPAAj-p2MPAA + SEASONJP2.SEASON + HOLIDAYj-pulDY + p2,CRiTic-ln(CRITICSj) + s2 (3d) Despite assuming different functional forms for the relation among our key variables of THEATERj, BOj, SUPERBOWLj and TVADj, the above four models test the three hypotheses H l -H3 in a similar fashion. First, with respect to replicating YTT's result (HI), by estimating the "single-path" versions of the four models (i.e. omitting THEATERj from the BOj equation), we would expect P2,SB, the coefficient for SUPERBOWLj on BOj, to be positive, suggesting Super 34 Bowl T V advertising would have a positive effect on the box office before taking the mediating role of movie exhibitors into consideration. Second, we test the mediating role of movie exhibitors (H2) by estimating the two-path versions of the four models, M1-M4. In addition to the direct causal path, we hypothesize that there is also an indirect casual path between Super Bowl T V advertising and box office revenues, through movie exhibitors. In particular, we expect that J3, SB, the coefficient of SUPERBOWLj on THEATER,, to be positive, supporting the first part of the indirect path of the Super Bowl T V advertising effect. Then, for the log-linear (Ml ) and log-log (M2) models, which use one parameter to capture the relation between THEATERj and BOj, we would expect BTHR to be positive, supporting the second part of the indirect path. For the log-quadratic models (M3 and M4), we would expect the net effect of the two parameters, BTHR/ and BTHR2 would create a positive effect at the mean theater engagement level. Note that we also expect the inclusion of movie exhibitors as a mediator to reduce the magnitude of the direct causal path. Finally, we compare the effectiveness of the Super Bowl and other T V advertising opportunities (H3). We could make the comparison on two bases. On the one hand, conditional on one specific functional form ( M l , M2, M3 or M4), we test the constraints, B, SB = B] A D and P2,SB = fii.AD- If both of the constraints are satisfied, it suggests that Super Bowl T V advertising is as effective as other T V advertising when both expenditure levels are equal (e.g., both SUPERBOWL and TV AD are zero). On the other hand, we can compare the effects of the two advertising tactics at their median expenditure levels, which are typically not equal. 4.4 Summary A series of models has been formulated to test the comparative effects of launch T V advertising in general and Super Bowl T V advertising in particular on theater engagements and 35 audience size in the first week of a movie's release. The next chapter discusses the data to be used, estimation methods, and results. 36. Chapter 3: Is there a Payoff for Playoffs? Effects of Major TV Event Advertising Part II: Data Analysis 5. Data Description As our objective is to study Super Bowl-advertised movies, all of which are wide-release movies, our sample consists of wide-release movies from 2000 to 2002. In particular, similar to other empirical studies in the movie industry (e.g. Einav 2003), we use the number of theaters engaged in the opening week as our sampling criterion. There were 1445 movies released in the U.S. between 2000 and 2002. Figure-7 shows the distribution of the opening week theater numbers of these 1445 movies. As we can see, the distribution is bi-modal, with one mode at zero (67% of movies with smaller than 50 theater engagement in their opening week) and another mode at 2,500. This suggests there are two groups of movies5: one with the opening week theater engagement figure equal to 600 or above, and another with numbers under 600. As it is more likely for movies with high opening week theater engagement numbers to invest in launch T V advertising, we choose this group of movies as our sample6. Note that there is still high variability in first week engagement within this group. From 2000 to 2002, there were 402 movies with a first week engagement total equaling 600 or above. Of these 402 movies, we deleted four, which have missing values for production budget, forming a sample of 398 movies. The resultant 398 movies contribute 88% of US$25 billion, the total box office revenues for all movies released from 2000 to 2002. 5 600 is chosen as the cut-off point because it appears to be the inflection point of the slops of the distribution surface. 6 Hollywood Stock Exchange also uses a similar criterion (theater engagement > 650) to define wide-release movies. 37 There were 19 movies advertised during the Super Bowls in our sample from 2000-2002. Table-3 lists these movies with the variables such as BOj, THEATER,, SUPERBOWLj, TVADj and BUDGETj. While all the Super Bowl-advertised movies, except Mission to Mars, placed only one 30-second commercial during the Super Bowl events, there are non-trivial variances in other variables such as production budget and launch T V advertising spending. Also note that these Super Bowl-advertised movies were released on average 13 weeks after the Super Bowl events and, with the exception of four movies, their commercials during the Super Bowls were their first major T V advertising efforts. The time lags from Super Bowl and from the major T V advertising efforts to the release week are therefore identical. Our exogenous and endogenous variables are constructed from several different data sources. The major sources are: 1) Variety.com, the website of the authoritative trade magazine in the entertainment industry; 2) IMDb.com, the popular interactive movie database website established in 1996 and visited by more than 25 million visitors each month; 3) TNS/CMR, the research company tracking T V commercials on over 425 network and cable channels in more than 75 T V markets in the United States, 4) Entertainment Weekly, the popular consumer magazine for entertainment, 5) Rottomtomato.com, a comprehensive website archiving reviews by movie critics, and 6) Alexa, a company tracking the web traffic created by their Alexa tool bar users, who have made 10 million tool bar downloads since 1997. The operationalization of our variables from these different sources is as follows: Opening week box office revenues, BOf. We obtained the opening week box office revenue numbers from Variety.com. As it is an industry practice to release new movies to theaters on Friday, an opening week's box office revenue is defined as the total box office receipts from Friday to Thursday. However, there are 52 movies in our sample that were released on a day different from Friday. For example, Lord of the Rings: The Two Towers started its theatrical run 38 on December 12, 2002, which was a Thursday. The opening week box office totals for these movies are actually cumulative revenues from an "eight-day" or "nine-day" week. In order to ensure the consistent definition of opening week, we include only the box office revenues from Friday to the following Thursday for these movies. Note that we also run all models with the opening week box office revenues including the additional receipts from the earlier releases. As the results are similar to those with a seven-day week definition of BOj, we only report the results of the seven-day week definition. Opening week theater engaged, THEATERf. The numbers of movie theaters engaged for individual movies in the opening week were also obtained from Variety.com. Note that these numbers only represent the numbers of sites showing individual movies, rather than the precise measure of the movies' availability. This is because many movie theaters in the U.S. have multiple screens and show multiple movies at the site. For example, a movie exhibitor may have two movies sharing one screen or have two screens showing the same movie. We acknowledge this as one of our data limitations. Super Bowl T V advertising expenditures, SUPERBOWLj. We identified the T V commercials for individual movies placed in the Super Bowls of years 2000, 2001 and 2002 from the T V recordings of the Super Bowl games from kick-off to the end of the game. While there were T V commercials for other films appearing before and after the games (e.g., during the pre-game and post-game shows), we include only the commercials appearing in the commercial breaks during the games. We then assigned the Super Bowl T V advertising expenditures to individual commercials on the basis of the average costs charged by the T V stations and the length of the T V commercials. These expenditure numbers were then verified by the data source from TNS/CMR. 39 Other TV advertising expenditures, TVAD.JJ and TVAD0/. We obtained the T V advertising expenditure data from TNS/CMR. Note that TNS/CMR defines a week from Monday to the following Sunday. As this definition differs from the Friday-Thursday definition for box office revenue, we set a "TNS/CMR week" to be the release week of a movie i f this TNS/CMR week covers the Friday (and also the weekend) of the movie's release week. Therefore, the non-Super Bowl T V advertising expenditure before and including the release week, TVADoj is defined as all expenditures up to the first Sunday of the movie's theatrical run. Similarly, the non-Super Bowl T V advertising expenditure before but not including the release week, TVAD.ij, is defined as all expenditures up to the last Sunday before the movie's theatrical run. Note that the next day, a Monday, is when theater managers finalize their screening decisions. TVAD./j is therefore specified to affect THEATER], while TVAD0J is used to explain BOj. Time lag from the first major TV advertising efforts to the release week, LEAD/. We define the start week of a major T V campaign as the first week in which a movie's T V advertising expenditure exceeds the average cost of a network T V spot (US$61,063 in 2000-2002). The time lag between the first major T V advertising efforts and the release week is therefore defined as the number of TNS/CMR Monday-Sunday weeks between the campaign start week and the release week. Production Budget, BUDGET/. We obtained the estimated production budgets for 392 movies in our original 402-movie sample from IMDb.com. We then filled in the missing values for six more movies using information from BoxOfficeMojo.com and the-numbers.com. In the end, we are unable to find the production budgets for four movies, namely Adam Sandler's 8 Crazy Nights, Simone, The Hot Chick, and The Truth about Charlie. As there is no systematic pattern shared by these four movies and the other 398 movies, we decided to drop these four movies from our sample. 40 Buzz generated, BUZZ.ij and BUZZoj. We assume that strong interest in a specific movie, or a high level of buzz among the general public, manifests as two behaviors, namely word-of-mouth and click-of-mouse. While we do not observe word-of-mouth behavior in the present study, we are able to track online activities on a popular movie website, IMDb.com. Specifically, by assuming that a high level of buzz for a specific movie would lead to more related search attempts and newsgroup messages posted for the movie on IMDb.com, we argue that the amount of online activity related to individual movies is a reasonable proxy measure of buzz. We constructed our click-of-mouse buzz proxy measure from a data series called MOVIEmeter™ available from IMDb.com. Based on which specific movie pages its four to five million weekly visitors view, IMDb.com produces the weekly MOVIEmeter™ ranking for more than 290,000 movie titles in its database. We believe online activities at IMDb.com are a good representation of all online activity on the world-wide web, for two reasons. First, many potential moviegoers enjoy visiting IMDb.com for movie information such as theatrical release dates, or to share opinions by posting and/or reading newsgroup messages for specific movies. Second, IMDb.com usually appears as one of the choices when people search for a specific movie using google.com oryahoo.com. MOVIEmeter™ is therefore a good click-of-mouse buzz proxy measure. Appendix-A describes the detailed procedure used to transform the MOVIEmeter™ ranking into our continuous variables, BUZZ.ij and BUZZoj. Average ratings given by movie critics, CRITICS/. Average critic ratings for individual movies were collected from RottenTomatoes.com. RottonTomatoes.com considers only accredited film critics (members of critics associations and/or those currently employed by an accredited print publication) when calculating average critic ratings. Each critic's original rating scale (e.g., star, letter grade, numeric) is first converted to a one-to-ten scale. Critic reviews without original ratings are then discarded. The average is computed on the converted rating scale. 41 Publicity received, PUB.ij and PUBoj. We measure the publicity for a movie by determining the total amount of coverage the movie received in Entertainment Weekly, which has a circulation of 1.79 million, the largest after the number one publication, TV Guide, in the entertainment magazine category (Audit Bureau of Circulations). We first identified articles related to specific movies by coding the table of contents of each issue of Entertainment Weekly. We then classified each article into one of ten categories, e.g., Departments, News & Notes Category I, or Movie Review. We determined the amount of publicity generated by each article using the average number of pages of the category to which it belongs. Table-4 lists the ten categories and their average page number totals. For example, an article in the News & Notes Category I will be assigned a value of six, as articles in this category on average have six-page coverage. We therefore define PUBoj as the sum of coverage values of all articles for movie j before and including its release week, and PUB.ij as the sum up to but not including the release week. Note that each new issue of Entertainment Weekly is usually displayed until Friday. Therefore, we define the week of Entertainment Weekly from Saturday to Friday. Recall that new movies typically open on Friday. When an "Entertainment Weekly % Saturday-Friday week" includes the first Saturday of a movie's theatrical run, we set this week as the release week for the movie. Categorical variables, GENREj, MPAAj, DISTRIBUTOR], SEASON] and HOLIDAY/. We obtained the distributor name, M P A A rating and release date of each movie from Variety.com and IMDb.com. Starting from the twelve genre categories used by Variety.com, we simplify the categories into four main types, namely Action, Comedy, Drama and Family. An Example: As the definition of a week varies slightly across different variables, especially those defined over a duration of multiple weeks, it would be useful to compare these various definitions using an example. Consider Bridget Jones's Diary, which was released on April 13, 42 2001 (Friday). Figure-8 shows how seven "duration-based variables" are defined. Opening in theaters on Friday, Bridget Jones's Diary's BOj is the box office receipt total from Friday to the next Thursday. Including the issue of Entertainment Weekly displayed until April 20, 2001 (Friday), PUBQJ for Bridget Jones's Diary is the sum of coverage in Entertainment Weekly until April 20, 2001, while PUB.ij is the sum up to April 13, 2001. TVAD.ij and TVADQJ for Bridget Jones's Diary are the cumulative T V advertising expenditures up to April 8, 2001 (Friday) and April 15, 2001 (Friday) respectively (there is no need to subtract SUPERBOWLj because Bridget Jones's Diary did not use Super Bowl T V advertising). BUZZ.ij and BUZZoj for Bridget Jones's Diary represent the estimated traffic to the movie's page at IMDb.com during the week of April 2 - April 8, 2001 and for the week of April 9 - April 15, 2001. Note that BOj is led temporally by the main exogenous variables, TVAD.ij and TVADQJ. The Pearson correlation matrix of the continuous variables is shown in Table-5. Excluding the pairs of TVAD.IJ and TVADQJ, BUZZ.IJ and BUZZ0J, and PUB.ij and PUB0J, which do not appear in the same equations, we can see there is no severe multicolinearity problem among the variables (correlation ranges from 0.029 to 0.485), except for the correlation between BUDGETj and TVADj, which is 0.690.7 Table-6 shows the summary statistics for the continuous variables for the Super Bowl-advertised (SB) and non-Super Bowl-advertised (NSB) movies. Figure-9a and Figure-9b are the box plots of BOj and THEATERj by SB and NSB. As expected, SB movies tend to have higher box office revenues and theater engagement in the opening week as compared to NSB, even though our sample consists of only wide-release movies. These differences may be caused by Super Bowl T V advertising or other differences between NSB and SB. Figure-9c, 9d, 9e, 9f, 9g, 9h, 9i, 9j, and 9k are the box plots for the 7 However, as we will see in the results section, both BUDGETj and TVADj give significant coefficients in most models, suggesting the estimation efficiency is not affected substantially by the multicolinearity of these two variables. 43 continuous exogenous variables, TVAD.JJ, TVAD0J, LEADj, BUDGET], BUZZ.,j, BUZZ0J, PUB. IJ, PUBoj, and CRITICS] by NSB and SB. As we can see, the distributions of SB tend to have higher means and medians than those of NSB, with the exception of CRITICSj. In particular, SB movies typically have larger launch T V advertising expenditures {TVADj), higher production budgets {BUDGETj), a longer lead time from the first major T V advertising effort to release week {LEADj), a higher level of pre-launch buzz {BUZZ]), and more publicity {PUBj), suggesting that they are potential confounding factors with the tactic of Super Bowl T V advertising. On the other hand, Table-7 shows the frequencies of the categorical variables by SB and NSB. While there is no apparent pattern in distributors and holidays, SB movies tend to be PG13 and R-rated Action movies released between January and August. Therefore, our models must control for the continuous and categorical variables so as to identify the true effects of Super Bowl T V advertising. 6. Model Estimation and Results For each of our four models M1-M4, there are two versions, single-path and two-path. Each model was estimated as a system of simultaneous equations using the full information maximum likelihood method, in which £7 and £2 are assumed to be bivariate-normally distributed. We estimate the single-path models as seemingly unrelated regression (SUR) models. On the ' other hand, while each of the two-path models appears to be a triangular structural system and thus can be estimated as a recursive model, we still allow £7 and £2 to be correlated so as to increase the efficiency of the model estimation. Both endogeneity and simultaneity are therefore considered in the estimation of the two-path models. As we have SEASON], HOLIDAY], CRITICS], or DISTRIBUTOR] as the excluded exogenous variables to either THEATER] or BOj, 44 the rank order condition is fulfilled for each of the models. In other words, all parameters can be identified in the four models, M1-M4. One binary variable of each set of categorical variables, GENRE, MPAA, DISTRIBUTOR and SEASON, is dropped for identification purposes. In particular, we drop the binary variables to indicate: 1) the movie is a family movie, 2) it is rated as G by the M P A A , 3) it is distributed by Disney, and 4) it is released in the Sept.-Oct. season. The effect of Disney's G-rated family movie is then indistinguishable from the intercept in the THEATERj equation (2a, 2b, 2c or 2d) while the effect of G-rated family movie released in the season of September and October is captured by the intercept in the BOj equation (3a, 3b, 3c or 3d). When interpreting the effect of other binary variables, such as an R-rated movie, we should note that the estimated parameter associated with MPAA-Rj captures the effects of MPAA-Rj relative to the base case, a G-rated family movie released in Sept.-Oct. (by Disney i f in THEATERj equation). Since the single-path versions are nested by their two-path counterparts, we can compare each pair using a likelihood ratio statistic. The bottoms of Table-9a, 9b, 9c and 9d show such statistics. As indicated by the small p-values, the two-path version indeed has a better fit to the data than the single-path version across all models, M1-M4. We can therefore focus on comparing the two-path versions. As our models are similar to the seemingly unrelated regression (SUR) models (e.g., Green 2000, ch.5), we can assess the goodness of fit of individual models with a system-wide measure suggested by McElroy (1977). The basic notion of McElroy's measure is in line with the R measure in the standard regression context. In particular, McElroy's measure evaluates the degree to which variability in the endogenous variables (THEATERj and BOj in our case) can be explained by the model. The McElroy measures for the two-path versions of M l , M2, M3 and M4 are 0.700, 0.666, 0.706 and 0.712, respectively. In other words, M l , M3 & M4 are able to explain relatively more variability in 45 THEATERj and BOj than the log-log model, M2. On the other hand, we can compare the four models by a model selection test. Specifically, the two-path versions of the four models are not nested with one another. We use a simple likelihood ratio-based statistic proposed by Vuong (1989) for each pair of models to test the null hypothesis that the two models are equally close to the true data generating process against the alternative hypothesis that one model is closer. Table-8 presents the statistics for each pair of models. As we can see, the two log-quadratic models significantly fit the data better than the log-linear and log-log models. Particularly, M3, the log-quadratic-a model has the best fit to the data. In the remaining portion of this section, the results of all four models will be compared. The objective is to evaluate the robustness of the findings. If a certain finding is supported by all four models, we know the findings are robust to model specification. On the other hand, in the next section, we will illustrate how marketing practitioners can use our models to evaluate marketing tactics and improve decisions by focusing on M3, the log-quadratic-a model. 6.1 M a i n Results Table-9a, 9b, 9c and 9d present the parameter estimates of M l , M2, M3 and M4. The standard errors reported are robustness standard errors. In each table, we also compare our two-path model to the single-path model (which has THEATERj omitted from the BOj equation). In HI , we hypothesize that Super Bowl T V advertising will have an effect on opening week box office revenue. Across the various functional forms, the single-path versions of M l , M2, M3 and M4 all give a significantly positive estimate for fo.SB, the effect of SUPERBOWLj on BOj. Note that this effect is obtained after we control for other potentially confounding variables, which are overlooked by YTT. We can therefore rule out some alternative explanations such as the idea that the higher box office revenue is due to the large launch T V advertising expenditures 46 or an earlier T V advertising campaign, conditions which are usually associated with Super Bowl-advertised movies. Although not posited as our main hypothesis, the effect of SUPERBOWLj on THEATERj is also found to be significantly positive in each of the four single-path model variants. In other words, Super Bowl T V advertising usually results in a higher number of movie exhibitors and higher box office revenues in the opening week. This finding naturally leads to the questions underlying our second hypothesis, H2: Does Super Bowl T V advertising attract more movie theaters, which in turn increases box office revenues? When we allow this indirect causal path, does Super Bowl T V advertising still have a direct effect on box office revenues? The two-path versions of M1-M4 hold these answers. In particular, in all four models, the effect of SUPERBOWLj on THEATERj (J3I,SB) is found to be significantly positive, establishing the first part of the indirect path. Then, the second part of the indirect path is also supported by the significant positive effect of THEATERj on BOj, found in all four models. In particular, estimates of RTHR are statistically positive in M l and M2. For the more flexible models, M3 and M4, the net effects of PTHRI and BTHR2 are positive when THEATERj is larger than 1,041 in M3 and 754 in M4, both of which are lower than 1,892, the 25% percentile of THEATERj in our o sample. In brief, our model estimation results support the postulate that movie exhibitors are playing a mediating role in the causal chain from Super Bowl T V advertising to opening week • box office revenues. Next, is the direct effect of SUPERBOWLj on BOj affected once we introduce the mediator, movie exhibitors? While the two-path versions of M2 and M4 no longer show any significant direct effect {P2,SB is not statistically different from zero), the two-path versions of M l and M3 have a smaller direct effect than their single-path counterparts. In other 8 For M3, SBOs > Q w hen THEATERj > 1.041 thousands. For M4, SBOj > Q w hen THEATERj > 0.754 dTHEATERj dTHEATERj thousands. 47 words, our movie sample shows that the main effect of Super Bowl T V advertising is an indirect effect through the mediation of movie exhibitors. In addition to demonstrating the presence of the mediating role of movie exhibitors, it is also interesting to note the form of the mediation. Except for M l : log-linear model, which restricts a priori the positive effect of THEATERj on BOj to exhibit increasing marginal return, the log-log and log-quadratic models allow more flexibility for the relation between THEATERj and BOj. In M2: log-log model, although PTHR is not statistically larger than one at the 5% level, the estimate for ft THR at 1.651 still suggests that there is a high chance of THEATERj exhibiting an increasing marginal return of BOj. In the log-quadratic models, M3 and M4, the net effects of PTHRI and PTHRI exhibit increasing positive marginal returns after the critical points, 1,041 theaters in M3 and 754 theaters in M4. Both of the more flexible models suggest that movie exhibitors influence box office revenue in the opening week in a manner of increasing marginal return. In brief, all four models suggest a convex relation between THEATERj and BOj. This pattern is consistent with the convex relation found in the packaged goods studies reviewed earlier. One may wonder why we obtain such a convex relation in the movie industry. While our current data set does not allow further study of the underlying mechanism, we speculate that when a movie can attract a major share of movie exhibitors, two additional effects may occur. First, the movies become an "event", which people enjoy discussing in social conversation. Examples are Spider-man and Lord of the Rings. Second, movie exhibitors start increasing the "availability" of the movies beyond normal movie scheduling by offering multiple screens, a factor which is beyond our unit of observation. Similar to Super Bowl T V advertising, other T V advertising expenditures in the pre-launch period influence box office revenues mainly through the theater engagement factor. In particular, we found that TVADj has direct positive effects on both THEATERj and BOj in the 48 single-path versions of M1-M4. On the other hand, once we introduce the mediation of movie exhibitors in the two-path versions of M1-M4, we find that TVAD/s effect on BOj works only through THEATERj (significant positive Pi,AD but insignificant PUD)- As discussed earlier, Elberse and Eliashberg (2003) also studied the mediating role of movie exhibitors and the advertising effect on box office sales. Although we cannot directly compare our findings to their results, because they define advertising as the total advertising expenditure over the whole theatrical run, we can still see the similarity between their findings and ours: advertising influences box office revenue mainly through the mediation of movie exhibitors. Our third hypothesis, H3, requires us to compare the effectiveness of Super Bowl and other T V advertising expenditures. From this point forward, we discuss only the two-path models. As the indirect effects of SUPERBOWLj and TVADj on BOj function through the same mediator, THEATERj, we focus on comparing their differential effects on this mediator as well as their direct effects on BOj. Using the delta method, we specifically test two sub-hypotheses for each of M1-M4: H3a: P,,SB = PI,AD H3b: p2,SB = p2,AD Table-10 presents the test results. As we can see, M l tends to generate results different from the others. In M l , we can reject H3b but not H3a. However, in M2, M3 and M4, we can reject H3a but not H3b. We focus on the group of M2, M3 and M4 first. Our failure to reject H3b is consistent with our previous finding that the direct effect of advertising is greatly reduced (to zero in most cases) once the indirect path is introduced: both p2iSB and p2jD tend to be statistically not different from zero. On the other hand, our rejection of H3a suggests that Super Bowl T V advertising does not generate the same effect as other T V advertising opportunities. In fact, as indicated by the signs of the t-statistics, PUB is statistically smaller than PUD- This implies that 49 Super Bowl T V advertising is not as effective as other T V advertising, i f evaluated at the same initial levels. For M l , since we fail to reject H3a, this suggests that Super Bowl and other launch T V advertising opportunities are equally effective on the indirect path. Moreover, the rejection of H3b is consistent with the above finding that there is a direct effect from Super Bowl but not other T V advertising on box office revenues. The fact that M l has implications opposite to those of the other models is troubling. To shed light on both sides, we need to first identify the difference between M l and the group of M2, M3 & M4. Specifically, recall that M2-M4 all assume that the effects of T V advertising (SUPERBOWLj and TVADj) on THEATERj are in log-log form. As the estimates ofB,SB and Pi,AD in M2-M4 are statistically smaller than one, the log-log form actually suggests a pattern of diminishing marginal return to T V advertising, which contrasts with the pattern of increasing marginal return implied by M l . In other words, the main difference between M l and the group of M2-M4 lies in the shape of the relation between advertising and the two endogenous variables. If we restrict the relation between T V advertising and THEATERj and BOj to exhibit only increasing marginal return, as in M l , we find that Super Bowl T V advertising is as effective as other T V advertising expenditures in the pre-launch period. On the other hand, i f we allow more flexibility by assuming a log-log form between T V advertising and THEATERj, the effect of Super Bowl T V advertising is found to be not as effective as other T V advertising expenditures when both types of expenditure are evaluated at the same initial values. Upon which models should we base our conclusion? Although our model comparison criteria do not provide any conclusive support for any specific model, M l relatively lacks face validity. Specifically, the increasing marginal return to advertising implied by M l , the log-linear model, is contradictory to previous advertising literature and intuition (e.g., Vakratsas, Feinberg, Bass and Kalyanaram 50 2004). We therefore argue that a log-log relation between T V advertising and THEATERj (M2-M4) is a preferred specification. In summary, based on M2-M4, we find that Super Bowl T V advertising is not as effective as other T V advertising expenditures in the pre-launch period, when both are evaluated at the same initial values. Note that we have to qualify the statement that Super Bowl T V advertising is not as effective as other T V advertising with the condition that both expenditures are evaluated at the same initial values. This is because the diminishing marginal return could make the marginal effect of Super Bowl T V advertising higher than that of other T V advertising expenditures when the two expenditures are evaluated at two levels. Consider M3 as an example. The medians of TVAD-ij and SUPERBOWLj in our sample are 8.04 and 0.00 (i.e. no Super Bowl advertising), respectively. If we evaluate a movie at these medians, the estimates of M3 would suggest that adding an extra US$1 million to SUPERBOWLj would result in a larger marginal gain than adding the same amount to TV AD.if. Scenario 1: Increase SUPERBOWLj from US$0 to US$1 M THEATERNEW _ (S + 0 + l)'ilSB _ l Q ( ) THE A TERORIGINAL (S + 0)PISB Scenario 2: Increase TVAD_,j from US$8.04M to US$9.04M THEATERNEW (g + 8.04 + l / u o _ 1 Q 3 THEATERORIGINAL (S + S.04)pud In other words, i f M3 is an adequate representation of moviegoers' and theater managers' behaviors, 50% of the movies in our sample, which have spent US$8.04M or more on TVAD.ij but have not considered Super Bowl T V advertising, should recognize that Super Bowl T V advertising is indeed a very attractive advertising opportunity. We will illustrate this point further with a counterfactual simulation in the next section. 51 6.2 Other Results Apart from our three main hypotheses, there are also some interesting results from the estimation of M1-M4: 1) LEAD/. The duration between the major campaign start date and the release date does not have any significant effects on either theater engagement or box office revenues. As T V advertising expenditures are significant, however, it suggests that only the level of T V advertising expenditure by a movie studio in the launch period matters. On the other hand, LEADj is only one of the dimensions characterizing a pre-launch advertising campaign for new products. For example, the detailed allocation of the pre-launch advertising budget in individual weeks may demonstrate that how (or when) the money is spent still matters. Future research is required on this area. 2) BUDGETj and BUZZ/ Both production budget and pre-launch buzz influence the opening week box office only by encouraging more movie exhibitors to show the movie, i f there is an effect (buzz has no effect at all in M2 and M4). Intuitively, as movie exhibitors must make their screening decisions for wide-release movies before the critics' reviews are available, they must use production budget, pre-launch advertising expenditure and buzz as "cues" to infer the movie's quality. 3) CRITICS/ The significant positive effect of critics' reviews on opening week box office revenue suggests that moviegoers may infer a movie's quality in a way that differs from the movie exhibitors: once the reviews are available in the opening week, moviegoers then rely on the reviews, rather than buzz or budget, to infer movie quality and make their ticket purchase decision. 4) PUB/ The significant positive effects of PUBj on BOj suggest that moviegoers are influenced by the degree of media attention surrounding individual movies. On the other hand, except for 52 M3, there is no significant effect of PUBj on THEATERj, suggesting theater managers are less influenced by publicity. This is an unexpected result. As PUBj is a new measure in the movie literature, we cannot compare this to other studies using the same variable. Future movie research should attempt to replicate such a null effect on theater managers. 5) GENREJ: Recall that family movies are used as the base case. The magnitude order of the three genre binaries in the THEATERj equation suggests that family and action movies tend to attract the largest number of movie exhibitors while comedies and dramas usually prompt the lowest theater engagement numbers. As the increased number of movie exhibitors in turn increases opening week box office revenue, family and action movies also tend to do better in the opening week. 6) MPAAf. G-rated movies are used as the base case. Similar to genre binaries, we can use the relative magnitude of the estimates to infer that G-rated movies are the best movies to attract movie exhibitors, PG-rated movies are second, and PG 13-rated and R-rated are relatively weak. Once again, as movie exhibitors play a mediating role, more movie exhibitors showing G-rated movies translates into higher opening week box office revenue. This finding is consistent with the results of previous studies such as Ravid (1999), which shows that G-rated movies on average generate better box office sales than other movies. 7) DISTRIBUTORj-. Apparently, some distributors are doing a better job in attracting theaters than the base case, Disney. However, except for the fact that 20th century Fox and Warner Brothers/New Line are consistently the most effective distributors in managing their "push" strategy, the effects of other major or non-major distributors (including Disney) are not statistically different from one another. 8) SEASONj and HOLIDAYf. As expected, movies released in the summer season of May -August and the holiday season of November - December fared robustly better in opening week 53 box office revenue than the base case of movies released in the September - October season. Moreover, across all four models, movies opening in a week covering a major U.S. holiday generate higher opening week box office revenues. This is consistent with the notion that the opportunity cost of movie watching is lower during holidays. 7. Further Analysis It is apparent from the above results that distribution channels play an important role in mediating the productivity of major T V event advertising in general and Super Bowl advertising in particular. What are the implications for marketers? In this section, we discuss two implications using the illustration of the best fit model, M3: log-quadratic-a. 7.1 Marketing Metrics First, from a marketing accountability perspective, we argue that marketers should measure the effects of major T V event advertising on both distribution channels and consumer demand. In particular, the use of models like M3 would allow marketers to decompose the total effect on sales into the direct and indirect paths. We use M3 to illustrate this decomposition here. Appendix-B contains the elasticity derivation of the other models. We first identify the two parts of the indirect path, the effect of Super Bowl T V advertising on movie exhibitors and the effect of movie exhibitors on opening week box office revenues, using two measures: esB -THR, the elasticity of THEATER with respect to SUPERBOWL and e T H R - B O , the elasticity of BO with respect to THEATER. SUPERBOWL dTHEATER eSB-THR -THEATER dSUPERBOWL - Pi,SB' — SUPERBOWL (4) S + SUPERBOWL 54 _ THEATER dBO < ? T H R - B O -BO dTHEATER = BTHRI -THEATER + 2 -BTHR2 -THEATER2 (5) We now summarize the total effect of Super Bowl T V advertising on the opening week box office by e S B-Bo, the elasticity of BO with respect to SUPERBOWL: SUPERBOWL dBO e s B - B O ~ BO dSUPERBOWL (PTHRI -THEATER + 2-BTHR2-THEATERz)-BLSB 2. n SUPERBOWL S + SUPERBOWL SUPERBOWL + PISB (6) ' S + SUPERBOWL Note that expression (6) can be re-written as: „ SUPERBOWL . S B - B O " ^ T H R - B O ^ B - T H R + / W g + s u p E R B O W L ^ While the first term of (7) is the product of the two components of the indirect path, the second term captures the direct path. As an elasticity is interpreted as the percentage change of an endogenous variable when the corresponding exogenous variable changes by one percent, the decomposition of the total effect using (7) would be very intuitive to marketing practitioners. Similarly, we can also decompose the total effect of another advertising variable, T V advertising expenditure other than Super Bowl up to but not including the release week, TVAD./t using M3. First, we define the elasticity of THEATER with respect to TVAD.i, C A D - T H R : TVADA dTHEATER THEATER dTVAD_x - p TVAD-> m 55 As stated in (la), the relation between TVAD.i and TVADQ is additive. We can therefore express the total effect of TVAD.i on BO by e A D - B O , the elasticity of BO with respect to TVAD.r. _ TVAD, 8BO 6 AD-BO " BO dTVAD_x (BTHRI -THEATER + 2-pTHR2-THEATER2)-RLAD- T V A E > A 3 + TVADA TVAD. ' 0 Once again, by (5) and (8), we can decompose (9) into the direct and indirect effects: _ TVAD, .... CAD-BO - ^THR-BC^AD-THR + P2,AD- ——=77— (It)) 8 + TVAD0 Table-11 reports the above elasticity measures obtained from our movie sample. Note that the above elasticity measures depend primarily on the value of THEATER. We therefore compute the elasticity measures at four values of THEATER (its mean, 1st quartile, median, and 3rd quartile) and use only means for SUPERBOWL and TVAD. One may question the robustness of the elasticity measures in relation to the values of SUPERBOWL and/or TVAD. The answer is: they do not play an important role. As S is a very small value (we set it at 0.000001), both TVAD, , SUPERBOWL . . . _._~ — and are very close to one in computation. Although TVAD./ and S + TVAD \ 5 +SUPERBOWL TVAD TVADn are not identical, they are not very different and — is typically close to one as y S + TVAD0 y V well. When the above fractions are approximately one, the elasticity measures do not depend on SUPERBOWL or TVAD. In fact, this is a feature of our M3 model, which assumes log-log forms for the effects of the two T V advertising expenditures. 56 As we can see from Table-11, the elasticity measures of the total effects, S S B - B O and eAD-BO, can be decomposed into direct and indirect effects. The indirect effects can be further decomposed as 6 S B - T H R and e raR -Bo or C A D - T H R and C T H R - B O - One can see that these elasticity measures summarize well the findings in our model. First, as discussed in the previous section, while the direct effect of Super Bowl T V advertising is statistically different from zero, the direct effect of other T V advertising expenditures is insignificant. Their corresponding elasticity measures decomposed from C S B - B O and 6 A D - B O therefore maintain this result: C S B - B O but not C A D - B O is statistically different from zero. Second, essentially equal to B/ SB and B/iAD, £ S B - T H R and C A D - T H R preserve the finding that a one percent change of Super Bowl T V advertising cannot generate as large a percentage change on THEATER as one percent of other T V advertising expenditures in the launch period. Third, the increasing marginal return of BO to THEATER can also be seen in <?THR-BO when we evaluate it at different levels of THEATER: the higher value of THEATER at which we evaluate C T H R - B O ; the more elastic the response given by BO. Furthermore, this increasing marginal return to THEATER is very dominant and this effect pattern is preserved in esB-Bo and eAo-Bo- By decomposing the effects into several components, marketing practitioners can thereby understand which causal path is underperforming and which causal path is the critical one driving end results. 7.2 Marginal Analysis: a Counterfactual Illustration The second implication for marketing practitioners is that they can use models like M3 to improve their decisions. In particular, subject to marketing budget constraints, they can evaluate the marginal effect of each additional dollar spent on one marketing tactic as opposed to the other. To illustrate this idea, we conducted a counterfactual simulation by giving each movie in our sample an additional $2.2M, which is equal to one spot during the Super Bowl, to spend on 57 either Super Bowl or other T V advertising opportunities. In particular, we use M3 to simulate opening week theater engagement and box office revenue under three scenarios: Scenario 0: Each movie does not spent the additional $2.2M on either Super Bowl or other T V advertising. (This is used as the benchmark for comparison). Scenario 1: Each movie spends its additional $2.2M on Super Bowl advertising Scenario 2: Each movie spends its additional $2.2M on other T V advertising opportunities. When using M3 to obtain the predicted values of THEATER and BO for each movie, we insert the point estimates of individual parameters for the observed exogenous variables. More importantly, we also add the estimates of e\ and s2 to the simulated values such that the values are identical to the observed values under the benchmark case. Figure-lOa and 10b show the simulated values of the two endogenous variables, THEATER and BO, under different scenarios. While the averages of the simulated values of THEATER and BO across 398 movies, under Scenarios 1 and 2 are higher than the benchmark case, the values under Scenario 1 are highest. At first glance, this simulation result may look inconsistent with our previous finding that Super Bowl T V advertising is not as effective as other T V advertising opportunities. However, as the $2.2M is added on top of each movie's original advertising plan, which spends on average US$8M on TVAD.i but zero on SUPERBOWL, the marginal effect of SUPERBOWL is indeed larger than the marginal effect of TVAD.i in most cases. Therefore, when TVAD.i is in the more saturated region, an additional $2.2M spent during the Super Bowl event could give more bang than other T V advertising opportunities. This reinforces our earlier argument that Super Bowl advertising presents a good advertising opportunity. Figure-10c and lOd show a breakdown of the overall means by the groups of Super Bowl-advertised (SB) movies and non-Super Bowl-advertised (NSB) movies. We can see that NSB movies, which have not used Super Bowl T V advertising, can get more impact on 58 THEATER and BO by adopting the Super Bowl T V advertising tactic. On the other hand, as SB movies have already placed at least one spot in the Super Bowl T V event, they receive only a positive but much diminished response i f purchasing another spot. SB movies would therefore find spending on other T V advertising opportunities more attractive. In practice, marketing practitioners evaluate the marginal effects of spending on Super Bowl and other T V advertising opportunities by directly using our models as the market response functions. Figure-11 a and l i b plot the response functions of THEATER with respect to SUPERBOWL and TVAD.i for a base case movie (G-rated family movies distributed by Disney) with LEAD, BUDGET, BUZZ and PUB at their means as they appear in our sample. TVAD.i in Figure-1 l a and SUPERBOWL in Figure-1 lb were kept at their mean values respectively. As we can see, the slope of the response function to SUPERBOWL is relatively flat after the jump from zero to one million. 9 On the other hand, the slope of the response function to TVAD.i tends to be larger, although decreasing as TVAD.i increases. We now consider the overall effect of the two advertising tactics. Figure-1 l c and 1 Id plot the overall response functions of BO with respect to SUPERBOWL and TVAD., for a base case movie at mean LEAD, BUDGET, BUZZ, PUB and CRITICS. TVAD., in Figure-11 c and SUPERBOWL in Figure-1 Id were kept at their mean values respectively. Note that these response functions contain both direct and indirect effects. As the second part of the indirect path is the response of BO to THEATER, the overall effect is highly influenced by this mediating factor. Figure-1 le plots the response of BO to this mediating factor when SUPERBOWL and TVAD., are kept at their mean values. The increasing marginal return pattern after the critical point of 1,041 exhibitors is apparent in the figure. Although the response of THEATER to SUPERBOWL is rather modest (Figure-1 la), the increasing marginal return of THEATER clearly magnifies this indirect effect and demonstrates a more apparent 9 Note that there is little variation of SUPERBOWL in our data set. The response function to SUPERBOWL is therefore for illustration purposes only. 59 effect on BO (Figure-1 lc). On the other hand, THEATER is already very responsive to TVAD.i (Figure-1 lb). Combining the increasing marginal return pattern of THEATER with this variable actually makes the overall effect of TVAD.i on BO exhibit the same increasing marginal return pattern. 8. Concluding Remark Using a movie sample from the years 2000-2002, this essay demonstrates that Super Bowl T V advertising influences opening week box office revenue through increasing the number of movie exhibitors. This finding is robust to various model specifications. Although Super Bowl T V advertising is not as effective as other launch T V advertising opportunities when both are evaluated at the same levels, Super Bowl T V advertising is still an attractive advertising opportunity in most cases. We hope the essay can attract more attention to the important mediating role of distribution channels in the marketing productivity literature and demonstrate to marketing practitioners how such a crucial mediating factor can be summarized as elasticity measures and used in their marginal analysis. We acknowledge several limitations in the essay and believe these limitations open interesting research opportunities. First, our study is essentially a cross-sectional analysis. While we can demonstrate how movie exhibitors and potential moviegoers respond to movies that use different advertising tactics, it is not clear whether the response patterns would hold i f a movie varied its advertising tactics. Future studies of distribution channels' mediating role may consider panel data, which allows researchers to identify both cross-sectional and longitudinal effects. Second, there is little variation in terms of Super Bowl T V advertising expenditures within the Super Bowl-advertised movies. We are therefore limited in the ability to distinguish 60 different functional forms of the variables using the data. Future research on Super Bowl T V advertising may consider other product categories, in which one company may place multiple units of T V commercials in the Super Bowl time slot. However, we can foresee that those industries would be faced with the problem of insufficient number of observations, over which the movie industry actually has an advantage. Third, focusing on the behaviors of movie exhibitors and moviegoers in the opening week, this essay essentially assumes away the dynamic aspect of the advertising decisions. In particular, the feedback mechanism of box office revenues on both exhibitors and moviegoers creates a very challenging future research problem. Fourth, we may study in detail the relation between pre-launch advertising efforts and pre-launch buzz and/or study the evolution of buzz over time. Fifth, our research assumes that there are no strategic behaviors at the level of movie studios (would they increase advertising expenditures i f a strong movie is going to open in the same week?) or at the levels of exhibitors (when would movie exhibitors allow double booking of a movie?). 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For example, there are more than a dozen movie titles in our sample having the number one MOVIEmeter™ rank in their release weeks. However, the underlying numbers of visits responsible for these twelve number one ranks are not likely to be the same and therefore these number one ranks may represent different levels of buzz. To make MOVIEmeter™ ranks more compatible across different calendar weeks, we use additional assumptions and data sources to convert the rank measure into a traffic-based measure, BUZZW/. BUZZW,= IMDb TRAFFICW (Al) J MM_Rankwj + C where MM_Rankwj = MOVIEmeter™ rank for movie j in the calendar week w IMDb_TRAFFICw = Number of visits to IMDb.com in the calendar week w As we do not observe the underlying distribution of the number of visits to a specific movie's page within IMDb.com, we have to develop a model to estimate the relation between the rank of a movie and its share of total visitors within week w. The first part of expression (Al ) is our assumption for such a relation. C is set at 210 in our data sample, which ensures the sum of from the movie of rank 1 to the movie of rank 100, which is the 90 MM_Rankwj + C percentile in 398-movie sample, to be bound by one.1 0 Intuitively, i f two movies have two consecutive ranks in MOVIEmeter™, say m and m+l, we assume the ratio of their numbers of m + C + 1 visits to be . This ratio will become very close to one i f the movies have a very low m + C rank (i.e. large m; relatively few "hits"). This means that when two movies are high in rank, 1 0 We have estimated the models with C equal to other values, e.g., C = 60, and the results are qualitatively similar to those of C = 210. 65 their difference in numbers of visits could be large. However, when two movies are very low in rank, there is not a large difference between the numbers of visits. As stated in (Al ) , i f we observe the actual total number of visits to IMDb.com, IMDb_TRAFFICw, multiplying the above share expression to it would give us the estimated number of visits to a specific movie's page within IMDb.com. However, the weekly number of visits to IMDb.com is not available. To estimate IMDb_TRAFFICw, we use the web behaviors of Alexa tool bar users. In particular, we proceed in two steps. First, we estimate the total number of Alexa tool bar users in each month, ALEXAm. This is because Alexa provides only the daily number of visitors to IMDb.com per one million Alexa tool bar users (as opposed to the absolute daily number), and the total number of Alexa tool bar users is also unavailable. Second, with estimated ALEXAm, we construct a time series of the daily numbers of Alexa tool bar users visiting IMDb.com from September 2001 to August 2004. This time series then allows us to extrapolate backwards and estimate IMDb_TRAFFICw for the time frame of our data sample. We now describe the first step in detail. From internetworldstats.com, a website archiving internet usage data, we obtained monthly numbers of internet users for some of the months from 2001 to December 2004. As the monthly numbers are available only for some months, we use a regression model to identify the underlying structure of the monthly internet user numbers, USERm: USERm = a0 + a, -TRENDm + em, (A2) where TRENDm is a monthly trend variable With 12 observations, we estimated (A2) by OLS and the estimates for CCQ and ai are 519.51 (std. error = 9.03) and 8.12 (std. error = 0.41). Inserting these estimates to (A2), we estimated the number of internet users in each month from September 2001 to August 2004, the time frame of Alexa's per million user data. To use a monthly series of USERm to estimate ALEXAm, we 66 assume that the proportion of Alexa users to total number of internet users is fixed over time. As the fixed proportion is just a linear scaling to our final variable, BUZZwj, we simply set ALEXAm = USERm. While the public can access graphs plotting the daily number of visitors to popular websites, like IMDb.com, per million Alexa tool bar users from September 2001 to August 2004, Alexa does not provide the actual numerical values of the data points. Therefore, the second step starts with converting a graph of daily number of IMDb.com visitors per million Alexa tool bar users to a time series of numerical values. Note that this graph-number conversion procedure makes us unable to obtain all the numerical values from September 2001 to August 2004. In other words, daily values for some dates are missing. Figure-A1 is a graph based on the "reconstructed" daily values. By assuming that the daily number of Alexa users is equal to ALEXAm i f the date falls in month m, we multiply the estimated ALEXAm by the reconstructed daily values to obtain the daily number of Alexa tool bar users visiting IMDb. com, IMDb_ALEXAd- In order to interpolate and extrapolate IMDb_ALEXAd for all weeks in our sampling frame of 2000-2002, we identify the underlying seasonality and time trend using the regression model: \n(IMDb_ALEXAd) = y„ + ys -TRENDW + y2EEB + 75 -MAR + ... + y,3DEC + ylrNEWYEAR + ... + y23-XMAS + sm, (A3) where TRENDW is a weekly trend variable FEB, MAR, DEC are 11 binary variables to indicate i f date d is in the week of February, March, ... or December (January is used as the base case) NEWYEAR, XMAS are 10 binary variables to indicate i f date d is in the week containing the holiday of New Year, Martin Luther King Day, Presidents Day, Memorial 67 Day, Independence Day, Labor Day, Columbia Day, Veterans Day, Thanksgiving or Christmas. Model (A3) is estimated with 180 observations. Table-Al presents the estimation results. While the trend and several monthly binaries are significant, the holiday binary variables turn out to have large standard errors. We speculate that this is due to the limited number of observations with the specific holidays (only three years of data) and believe the holiday binaries still capture some seasonality of IMDb.com traffic. We therefore use (A3) to estimate the number of Alexa users visiting IMDb.com for 2000-2002. In particular, two adjustments are made when interpolating/extrapolating IMDb_ALEXAci. First, as (A3) is a log-linear model, a correction factor for the downward bias is used. The details of the correction factor can be found in Hanssens, Parsons and Schultz (2003), p.395. Second, TRENDW is set to zero, essentially de-trending the traffic of IMDb.com while keeping the seasonality across weeks. Note that MM_Rankwj, from which we are deriving BUZZwj, is a weekly measure. We therefore only need to generate weekly, rather than daily, numbers of Alexa users visiting IMDb.com. By assuming the daily number of Alexa users to be constant across different days of a week, the weekly number of Alexa users visiting IMDb.com, IMDb_ALEXAw = l*IMDb_ALEXAct, i f date d falls into week w. As seven is just a linear scaling to our ultimate variable of interest, BUZZwj, we can simply set IMDb_ALEXAw equal to IMDb_ALEXAd, for date d falls into week w. Also note that our definition of "week" here is consistent with the definition of "week" used by IMDb.com for their MOVIEmeter™, which starts Monday and ends on the following Sunday. The last assumption we must make concerns the relation between IMDb_ALEXAw and IMDb_TRAFFICw. By assuming that the proportion of Alexa users visiting IMDb.com to all visitors of IMDb.com is constant over time and that each visitor makes the same number of visits 68 to IMDb.com in each week, we can argue that IMDb_ALEXAw is related to IMDb_TRAFFICw by a fixed proportion and we can therefore set IMDb_TRAFFICw = IMDb_ALEXAw. Finally, we use expression (Al ) to generate BUZZwj for movie j in its release week and a week before the release. For ease of estimation, we scaled BUZZWJ- by million. In addition to the above formulation of BUZZwj, we have also tried 1/ (MOVIEmeter™ rank) as an alternative formulation of BUZZwj. As the main results are similar to those obtained from the above procedure, we report only the latter. 69 Appendix-B: Elasticity Measures based on M1-M4 Five elasticity measures can be derived from each of M1-M4: Elasticity of THEATER w.r.t. SUPERBOWL, 6 S B - T H R = S U P E R B O W L . THEATER THEATER dSUPERBOWL c ] r ^ A , dTHEATER Elasticity of THEATER w.r.t. TVAD.i, C A D - T H R = 1 (B2) THEATER dTVAD_x Elasticity of BO w.r.t. THEATER, C T H R - B O = T H E A T E R ^ (B3) BO dTHEATER T J I • • f D n f C T " T r > i 7 D n / ~ n x / T SUPERBOWL dBO Elasticity of 5 0 w.r.t. SUPERBOWL, esB-BO = (B4) BO dSUPERBOWL Elasticity of BO w.r.t. TVAD.,, eA D-BO = T V A E > A - d B O (B5) 5 0 dTVAD_v M l : Log-linear Model By the first order derivatives of (2a) and (3a) with respect to SUPERBOWL and TVAD.i, we can obtain the following elasticity measures: esB-THR =P,,SB-SUPERBOWL S A D - T H R = P i,AD-TV AD.i £ T H R - B O = ft THR-THEATER esB-BO = PTHR-THEATER -Bisb -SUPERBOWL + B2SB-SUPERB OWL = STHR-BO-esB-THR + B2SB-SUPERB OWL e AD-BO =BTHR-THEATER-BUD-TVAD.I + B2AD-TVAD.1 = ^ T H R - B O ^ A D - T H R + ^.AD'TVAD./ M2: Log-Log Model By the first order derivatives of (2b) and (3b) with respect to SUPERBOWL and TVAD.i, we can obtain the following elasticity measures: 70 _ _ SUPERBOWL 6SB -THR -pi,SB-~ 3 + SUPERBOWL TV AD, e AD-THR = / W ^ ^ 6 T H R-BO - ft THR ^SB-BO _ a a SUPERBOWL SUPERBOWL = M l S B ' 3 +SUPERBOWL + 5 (5 + SUPERBOWL 0 SUPERBOWL — ^THR-BO'^SB-THR + P2.SB' 3 + SUPERBOWL _ TV AD, . TVAD, eAD-BO - PTHR-PI.AD'- =-—— + />. - ^THR-BO' e AD-THR + M3 •& M4: Log-Quadratic SUPERBOWL 3 + TVAD_, ' 3 + TVAD0 TVAD, -i 3 + TVAD0 6SB-THR - Pi,SB' — ^AD-THR - PLAD-S'^ SUPERBOWL TVAD, 8 + TVADA eraR-BO = PTHRI -THEATER + 2 -BTHR2 -THEATER ess-Bo = (PTHRI -THEATER + 2 -8THR2 -THEATER') S,iSB 2. n SUPERBOWL 3 +SUPERBOWL SUPERBOWL SB' ^THR-BO'^SB-THR + P2,SB 3 + SUPERBOWL SUPERBOWL 3 +SUPERBOWL eAD-BO = (BTHR]-THEATER + 2-BTHR2 -THEATER')-BUD-TVAD_{ 5 + TVADA 71 TVAD ISB + 02.- 8 + TVAD0 a T V A D i 3 + TVADQ 72 Table-1: Summary of Variables BOj THEATERJ SUPERBOWLj TVAD-IJ TVADoj LEAD, BUDGETj BUZZ-ij BUZZ, <>J PUB.,j PUBoj CRITICSJ DISTRIBUTOR, GENRE, MPAA, SEASON HOLIDAY j Opening week box office revenues by movie j Number of movie theaters engaged for movie j in the release week Super Bowl T V advertising expenditure by movie j Total T V advertising expenditure other than SUPERBOWLj, up to and including the week before the release week of movie j (i.e. Total launch T V Ad effort, observed by theater managers before their final screening decisions) Total T V advertising expenditure other than SUPERBOWLj, up to and including the release week of movie j (i.e. Total launch T V A d effort, observed by potential moviegoers before their moviegoing decisions) No. of weeks between the first major T V advertising effort and the release week of movie j Production budget (US$) of movie j Buzz for movie j in the week before its release week (i.e. The buzz observed by theater managers when making their final screening decisions) Buzz for movie j in its release week (i.e. The buzz generated and observed by the potential moviegoers when making their moviegoing decisions) Cumulative Publicity received by movie j, up to the release week Cumulative Publicity received by movie j, up to and including the release week Average critics rating given for movie j A set of binary variables to indicate if movie j is distributed by one of the following distributor groups: 1) Buena Vista or Miramax, 2) Warner Brothers or New Line, 3) Paramount, 4) Sony, 5) 20th Century Fox, 6) Universal, and 7) Other movie distributors A set of binary variables to indicate if movie j is of one of the genre categories: 1) action, 2) comedy, 3) drama, and 4) family A set of binary variables to indicate i f movie j is rated by M P A A into one of the following categories: 1) G, 2) PG, 3) PG-13, and 4) R A set of binary variables to indicate if movie j is released in one of the following four Hollywood seasons: 1) January - April, 2) May - August, 3) September - October, and 4) November -December A binary variable to indicate i f movie j is released in the week covering any of the following major U.S. holidays: New Year, Martin Luther King Day, Presidents Day, Memorial Day, Independence Day, Labor Day, Thanksgiving, Christmas 73 Table-2: MPAA Member Company Distribution of Advertising Costs by Media Year Newspaper TV Internet /Online Trailers Other Media 2003 17.29% 48.38% 1.62% 5.47% 27.24% 2002 16.69% 50.19% 1.11% 5.56% 26.45% 2001 15.98% 51.59% 1.59% 6.22% 24.63% 2000 18.66% 50.36% 0.84% 7.66% 22.49% 1999 20.80% 51.18% 0.59% 9.22% 18.20% 74 Table-3: List of Super Bowl Movies Movie Title Release Week Total Box Office Revenues (US$ in Million) Opening week Box Office Revenues (US$ in Million) Number of Theaters engaged in the opening week (in Thousand) Super Bowl TV advertising Expenditure (US$ in Million) Other TV advertising Expenditure before the opening week (US$ in Million) Other TV advertising Expenditure before and including the opening week (US$ in Million) Gladiator (Dreamworks) 5/5/2000 187.7 49.0 2.938 2.1 12.8 17.6 Mission to Mars (Buena Vista) 3/10/2000 60.9 29.2 3.054 4.2 10.2 13.1 Nutty Professor 2: The Klumps (Universal) 7/28/2000 123.3 58.5 3.242 2.1 9.0 12.9 Titan A . E . (20th C Fox) 6/16/2000 22.8 13.2 2.734 2.1 11.8 14.6 U-571 (Universal) 4/21/2000 77.1 25.9 2.583 2.1 7.9 12.0 A Knight's Tale (Sony) 5/11/2001 56.1 21.5 2.980 2.2 11.6 15.3 Exit Wounds (WB) 3/16/2001 51.8 23.4 2.830 2.2 6.5 9.3 Hannibal (MGM/UA) 2/9/2001 165.1 73.9 3.230 2.2 10.0 14.0 Swordfish (WB) 6/8/2001 69.8 27.1 2.678 2.2 13.3 17.1 The Mummy Returns (Universal) 5/4/2001 202.1 84.3 3.401 2.2 12.2 19.9 40 Days and 40 Nights (Mira Max) 3/1/2002 38.0 15.8 2.225 2.2 8.0 10.6 Austin Powers in Goldmember (New Line) 7/26/2002 213.1 110.6 3.613 2.2 9.4 14.5 Bad Company (Buena Vista) 6/7/2002 30.2 15.7 2.944 2.2 13.2 17.0 Blade 2 (New Line) 3/22/2002 81.7 41.9 2.707 2.2 5.7 8.5 Collateral Damage (WB) 2/8/2002 40.1 19.5 2.824 2.2 13.5 16.4 Hart's War (MGM/UA) 2/15/2002 19.1 10.5 2.459 2.2 11.3 17.0 Signs (Buena Vista) 8/2/2002 228.0 88.3 3.264 2.2 7.8 10.4 The Scorpion King (Universal) 4/19/2002 90.5 43.3 3.444 2.2 9.4 13.4 X X X (Sony) 8/9/2002 141.2 61.9 3.374 2.2 15.7 20.5 Table-3 (Continued): List of Super Bowl Movies Time Lag from Super Bowl to the Release Week Time Lag from the Buzz in Buzz in Publicity received Movie Title first major TV advertising effort and Production Budget (US$ in Million) the week before the Release the week during the Release before and including the Average Critics Rating Genre MPAA Rating the Release week week Release Week week Gladiator (Dreamworks) 14 14 103 0.0278 0.0281 7.2 7 Drama R Mission to Mars (Buena Vista) 6 6 90 0.0276 0.0276 1.2 4.1 Action P G Nutty Professor 2: The Klumps (Universal) 26 26 84 0.0279 0.0279 4.0 4.4 Comedy PG13 Titan A .E . (20th C Fox) 20 20 75 0.0268 0.0269 1.2 5.7 Family PG. U-571 (Universal) 12 12 62 0.0278 0.0278 5.2 6.3 Action PG13 A Knight's Tale (Sony) 15 15 41 0.0022 0.0063 5.2 5.7 Action PG13 Exit Wounds (WB) 7 7 33 0.0266 0.0273 0.0 4.3 Action R Hannibal ( M G M / U A ) 2 4 87 0.0296 0.0296 21.7 5 Drama R Swordfish (WB) 19 19 80 0.0267 0.0272 1.2 4.4 Action R The Mummy Returns (Universal) 14 14 98 0.0278 0.0281 9.2 5.2 Action PG13 40 Days and 40 Nights (Mira Max) 4 4 17 0.0251 0.0272 1.2 4.9 Comedy R Austin Powers in Goldmember (New Line) 25 25 63 0.0279 0.0287 13.5 5.8 Comedy PG13 Bad Company (Buena Vista) 18 39 70 0.0227 0.0262 0.0 3.9 Action PG13 Blade 2 (New Line) 7 7 55 0.0262 0.0273 1.2 5.8 Action R Collateral Damage (WB) 1 22 85 0.0254 0.0291 0.5 4 Action R Hart's War ( M G M / U A ) 2 3 70 0.0269 0.0287 1.2 5.9 Drama R Signs (Buena Vista) 26 26 72 0.0282 0.0275 3.2 6.9 Drama PG13 The Scorpion King (Universal) 11 11 60 0.0259 0.0276 3.2 4.8. Action PG13 X X X (Sony) 27 27 85 0.0264 0.0273 10.0 5.6 Action PG13 76 Table-4: Classification of Entertainment Weekly Articles for PUBj operationalization Article Type Average page number News & Notes Category I 6 News & Notes Category II 4 News & Notes Category III 2 News & Notes Category IV 1 News & Notes Category V 0.8 Special Preview Feature 2 Departments 1.25 Movie Review 1.2 Internet Page 0.5 Mail Page 0.25 Table-5: Pearson Correlation Matrix of continuous variables (Sample Size = 398) B O , THEATER, SUPER BOWL, TVAD.u TVAD„, LEAD, BUDGET, CRITICS, BUZZ.,, BUZZ„, PUB.,., P U B 0 , BO, 1.000 0.637 0.209 0.498 0.514 0.364 0.631 0.405 0.135 0.134 0.608 0.688 THEATER/ 0.637 1.000 0.204 0.675 0.705 0.379 0.631 0.190 0.186 0.234 0.320 0.396 SUPERBOWL/ 0.209 0.204 1.000 0.108 0.120 0.419 0.201 0.029 0.052 0.054 0.091 0.116 TVAD.,, 0.498 0.675 0.108 1.000 0.974 0.370 0.690 0.331 0.160 0.234 0.268 0.337 TVAD/i; 0.514 0.705 0.120 0.974 1.000 0.358 0.689 0.356 0.167 0.238 0.264 0.338 LEAD, 0.364 0.379 0.419 0.370 0.358 1.000 0.317 0.120 -0.001 0.063 0.135 0.182 BUDGET, 0.631 0.631 0.201 0.690 0.689 0.317 1.000 0.294 0.160 0.174 0.404 0.485 CRITICSj 0.405 0.190 0.029 0.331 0.356 0.120 0.294 1.000 0.010 0.048 0.288 0.350 BUZZ.,, 0.135 0.186 0.052 0.160 0.167 -0.001 0.160 0.010 1.000 0.883 0.100 0.109 BUZZ„, 0.134 0.234 0.054 0.234 0.238 0.063 0.174 0.048 0.883 1.000 0.079 0.087 PUB.,, 0.608 0.320 0.091 0.268 0.264 0.135 0.404 0.288 0.100 0.079 1.000 0.908 PUB„, 0.688 0.396 0.116 0.337 0.338 0.182 0.485 0.350 0.109 0.087 0.908 1.000 78 Table-6: Summary Statistics of non-Super Bowl vs. Super Bowl advertised movies Variables Group Mean Std. Deviation Minimum Maximum BOj ($ in Millions) Non-Super bowl Super bowl 20.17 42.81 21.13 28.54 0.76 10.54 151.62 110.56 THEATERj (in Thousands) Non-Super bowl Super bowl 2.30 2.97 0.69 0.36 0.60 2.23 3.68 3.61 TVAD.JJ ($ in Millions) Non-Super bowl Super bowl 8.32 10.48 4.19 2.60 0.06 5.69 20.80 15.75 TVADoj ($ in Millions) Non-Super bowl Super bowl 11.52 14.44 5.03 3.29 0.21 8.53 23.98 20.53 LEADj Non-Super bowl Super bowl 5.03 15.84 4.19 9.63 0.00 3.00 34.00 39.00 BUDGETj ($ in Millions) Non-Super bowl Super bowl 40.70 70.00 31.15 21.51 1.00 17.00 142.00 103.00 BUZZ.,j Non-Super bowl Super bowl 0.024 0.026 0.006 0.006 0.000 0.002 0.034 0.030 BUZZoj Non-Super bowl Super bowl 0.025 0.027 0.006 0.005 0.000 0.006 0.035 0.030 PUB.jj Non-Super bowl Super bowl 1.34 2.84 3.02 5.07 0.00 0.00 30.60 20.50 PUBoj Non-Super bowl Super bowl 2.43 4.74 3.73 5.43 0.00 0.00 31.55 21.70 CRITICSj Non-Super bowl Super bowl 5.00 5.25 1.36 0.91 2.20 3.90 9.20 7.00 79 Table-7: Frequency of non-Super Bowl vs. Super Bowl advertised movies Percentage Frequency in the sample By Studio Buena Vista/Miramax Non-Super bowl Super bowl 65 4 16% 1% WB/New Line Non-Super bowl Super bowl 86 5 22% 1% Paramount Non-Super bowl Super bowl 43 0 11% 0% Sony Non-Super bowl 50 13% Super bowl 2 1% 20th Century Fox Non-Super bowl Super bowl 43 1 11% 0%. Universal Non-Super bowl Super bowl 32 4 8% 1% Rest of the Studios Non-Super bowl Super bowl 60 3 15% 1% By Ratings Rating: G Non-Super bowl Super bowl 19 0 5% •o% Rating: PG Non-Super bowl Super bowl 48 2 . 12% 1% Rating: PG13 Non-Super bowl Super bowl 173 9 43% 2% Rating: R Non-Super bowl Super bowl 139 8 35% 2% By Genre Genre: Action Non-Super bowl Super bowl 79 11 20% 3% Genre: Comedy Non-Super bowl Super bowl 146 3 37% 1% Genre: Drama Non-Super bowl Super bowl 122 4 31% 1% Genre: Family Non-Super bowl Super bowl 32 1 8% 0% Table-7 (Continued): Frequency of non-Super Bowl vs. Super Bowl advertised movies Frequency Percentage in the sample By Hollywood Seasons T . . . Non-Super bowl January - April r Super bowl 120 9 3 0 % 2 % A , . Non-Super bowl May - August r Super bowl 118 10 3 0 % 3 % c * u rs * t. Non-Super bowl September - October ^ Super bowl 72 0 1 8 % 0 % X T , „ . Non-Super bowl November - December r Super bowl 69 0 1 7 % 0 % By Major U.S. Holidays Release week covering Non-Super bowl a maj or holiday Super bowl 66 1 1 7 % ' 0 % Release week NOT covering Non-Super bowl any major holiday Super bowl 313 18 7 9 % 5 % 81 Table-8: Pairwise tests11 for non-nested model (Vuong 1989) Weighted Likelihood Ratio Statistic M2: log-log M3: Log-Quadratic-a M4: Log-Quadratic-b M l : Log-linear -0.708 -4.487 -3.197 M2: log-log -3.743 -3.733 M3: Log-Quadratic-a 1.200 Critical value for 2-tail 5% significance level: 1.960 Critical value for 2-tail 10% significance level: 1.645 ' 1 Please refer to Gasmi, Laffont and Vuong (1992) for the detailed calculation of the statistics Table-9a: Parameter Estimates of M l : Log-linear Model Two-path Model Singl e-path Model Variable Coefficient Estimate Standard Error P -value for H: ^=0 Coefficient Estimate Standard P-value Error for H : P=Q Equation: \n(THEATER,) Equation: ^{THEATER,) Intercept 0.392 0.093 0.000 0.368 0.098 0.000 SUPERBOWL, 0.051 0.019 0.007 0.051 0.019 0.006 TVAD.,j 0.043 0.005 0.000 0.043 0.005 0.000 BUDGETj 0.002 0.001 0.010 0.001 0.001 0.008 LEAD, 0.002 0.002 0.347 0.003 0.002 0.261 BUZZwj 6.344 2.585 0.014 6.778 2.683 0.012 0.006 0.003 0.061 0.007 0.003 0.023 GENRE: Action -0.050 0.056 0.374 -0.044 0.056 0.434 GENRE: Comedy -0.115 0.053 0.031 -0.108 0.053 0.040 GENRE: Drama -0.143 0.058 0.013 -0.135 0.057 0.019 MPAA: PG -0.132 0.070 0.058 -0.122 0.068 0.072 MPAA: PG13 -0.160 0.071 0.024 -0.157 0.067 0.019 MPAA: R -0.180 0.075 0.016 -0.181 0.070 0.010 WB/New Line 0.099 0.044 0.026 0.086 0.031 0.005 Paramount 0.081 0.051 0.108 0.074 0.040 0.066 Sony 0.061 0.047 0.196 0.084 0.032 0.008 20th Century Fox 0.129 0.047 0.006 0.107 0.034 0.002 Universal 0.096 0.059 0.102 0.046 0.049 0.342 Other Distributors -0.051 0.056 0.370 0.007 0.038 0.849 Equation: ln(j50,) Equation: \n(BO.) Intercept -0.913 0.334 0.006 0.608 0.241 0.012 THEATERj 0.914 0.172 0.000 SUPERBOWLj 0.090 0.045 0.045 0.162 0.060 0.007 TVADoj 0.000 0.013 0.978 0.054 0.009 0.000 BUDGETj -0.002 0.002 0.303 0.003 0.002 0.097 LEADj -0.001 0.005 0.814 0.007 0.007 0.342 BUZZ„j 5.657 4.775 0.236 14.769 5.294 0.005 PUB0j 0.043 0.007 0.000 0.062 0.007 0.000 GENRE: Action 0.271 0.140 0.052 0,116 0.113 0.303 GENRE: Comedy 0.281 0.139 0.043 0.019 0.102 0.855 GENRE: Drama 0.257 0.147 0.080 -0.074 0.111 0.506 MPAA: PG -0.157 0.150 0.296 -0.290 0.155 0.062 MPAA: PG13 -0.057 0.162 0.726 -0.233 0.148 0.115 MPAA:R -0.040 0.172 0.817 -0.260 0.153 0.089 SEASON: Jan-Apr 0.034 0.065 0.603 0.020 0.070 0.780 SEASON: May-Aug 0.259 0.070 0.000 0.270 0.072 0.000 SEASON: Nov-Dec 0.166 0.083 0.046 0.152 0.085 0.072 HOLID AY j 0.188 0.068 0.006 0.173 0.069 0.012 CRITICS, 0.179 0.020 0.000 0.161 0.021 0.000 McElroy's R 2 Log-likelihood Likelihood Ratio 0.700 -1624.318 0.569 -1645.189 41.745 (P-value = 0.000) Table-9b: Parameter Estimates of M 2 : Log-Log Model Two-path Model Singh ;-path Model Coefficient Variable Estimate Standard Error P-value for H : ^=0 Coefficient Estimate Standard P-value Error for H: B=0 Equation : \n(THEATERj) Equation: \n(THEATERi) Intercept 0.495 0.149 0.001 0.422 0.151 0.005 H8+SUPERBOWL,) 0.010 0.003 0.001 0.009 0.003 0.002 \n{8+TVAD.,j) 0.320 0.038 0.000 0.316 0.037 0.000 \n(BUDGETj) 0.069 0.022 0.002 0.081 0.022 0.000 ln(S+LEADj) -0.032 0.020 0.107 -0.025 0.021 0.233 ln(BUZZ.,j) 0.036 0.021 0.087 0.041 0.021 0.053 ln(8+PUB.LJ) 0.004 0.002 0.140 0.000 0.002 0.979 GENRE: Action -0.069 0.054 0.196 -0.067 0.049 0.178 GENRE: Comedy -0.150 0.050 0.003 -0.144 0.044 0.001 GENRE: Drama -0.177 0.055 0.001 -0.165 0.050 0.001 MPAA: PG -0.136 0.064 0.034 -0.120 0.068 0.076 MPAA:?G\3 -0.180 0.065 0.006 -0.167 0.066 0.012 MPAA: R -0.199 0.070 0.004 -0.185 0.071 0.009 WB/New Line 0.124 0.048 0.009 0.111 0.029 0.000 Paramount 0.085 0.045 0.057 0.069 0.034 0.044 Sony 0.105 0.047 0.025 0.099 0.029 0.001 20th Century Fox 0.147 0.046 0.001 0.117 0.032 0.000 Universal 0.097 0.059 0.099 0.062 0.048 0.190 Other Distributors 0.007 0.064 0.911 0.047 0.037 0.203 Equation: \n(BO,) Equation: \n(BO,) Intercept 0.330 0.384 0.391 0.711 0.394 0.071 XnCTHEATERj) 1.651 0.756 0.029 ln(<S+SUPERBOWLj) 0.018 0.011 0.090 0.030 0.011 0.008 \n(d+TVAD0J) -0.189 0.274 0.491 0.362 0.093 0.000 \n(BUDGETj) 0.006 0.080 0.938 0.160 0.055 0.004 \n(8+LEADj) 0.029 0.027 0.295 0.016 0.051 0.750 \n(BUZZ0j) 0.052 0.043 0.230 0.121 0.051 0.019 IniS+PUBo.j) 0.021 0.004 0.000 0.021 0.005 0.000 GENRE: Action 0.289 0.183 0.114 0.165 0.104 0.112 GENRE: Comedy 0.253 0.203 0.212 -0.005 0.071 0.943 GENRE: Drama 0.210 0.224 0.348 -0.080 0.093 0.391 MPAA: PG -0.072 0.109 0.508 -0.193 0.167 0.248 MPAA: PG13 -0.008 0.119 0.949 -0.187 0.149 0.211 MPAA: R -0.036 0.132 0.787 -0.230 0.156 0.142 SEASON: Jan-Apr -0.023 0.083 0.781 -0.013 0.082 0.878 SEASON: May-Aug 0.326 0.083 0.000 0.348 0.081 0.000 SEASON: Nov-Dec 0.252 0.099 0.011 0.289 0.094 0.002 HOLIDAYj 0.197 0.074 0.008 0.181 0.075 0.016 \n(CRITICS,) 0.975 0.102 0.000 0.927 0.103 0.000 McElroy's R 2 Log-likelihood Likelihood Ratio 0.666 -1613.544 0.519 -1617.683 8.283 (P-value = 0.004) S is set to be 0.000001 Table-9c: Parameter Estimates of M 3 : Log-Quadra t ic -a M o d e l Two-path Model Singh :-path Model Coefficient Standard P-value Coefficient Standard P-value Variable Estimate Error for H: B=0 Estimate Error for H: B=0 Equation: \n(THEATER,) Equation: MTHEATERj) Intercept 0.077 0.114 0.499 0.073 0.121 0.544 \n(S+SUPERBOWLj) 0.006 0.003 0.019 0.006 0.003 0.028 \n(8+TVAD_,j) 0.292 0.040 0.000 0.288 0.039 0.000 MBUDGETj) 0.076 0.024 0.002 0.078 0.024 0.001 LEADj 0.002 0.002 0.389 0.002 0.002 0.317 BUZZ.,j 6.516 2.354 0.006 6.440 2.347 0.006 PUB.,j 0.007 0.003 0.017 0.007 0.003 0.009 GENRE: Action -0.061 0.053 0.254 -0.059 0.053 0.263 GENRE: Comedy -0.131 0.050 0.008 -0.130 0.051 0.010 GENRE: Drama -0.155 0.054 0.004 -0.154 0.055 0.005 MPAA: PG -0.140 0.066 0.036 -0.130 0.067 0.054 MPAA: PG13 -0.181 0.066 0.006 -0.172 0.066 0.009 MPAA: R -0.202 0.070 0.004 -0.192 0.070 0.006 WB/New Line 0.122 0.036 0.001 0.099 0.029 0.001 Paramount 0.079 0.041 0.052 0.066 0.035 0.061 Sony 0.115 0.033 0.001 0.102 0.029 0.000 20th Century Fox 0.135 0.045 0.003 0.118 0.031 0.000 Universal 0.075 0.061 0.222 0.049 0.048 0.303 Other Distributors 0.037 0.049 0.447 0.040 0.035 0.244 Equation: ln(J50,) Equation: \n(BO.) Intercept 0.590 0.638 0.355 0.208 0.326 0.523 THEATERj -0.452 0.743 0.543 THEATER^ 0.217 0.101 0.032 \n{8+SUPERBOWLj) 0.017 0.008 0.034 0.024 0.010 0.020 Md+TVAD()j) 0.319 0.220 0.147 0.421 0.078 0.000 MBUDGETj) -0.015 0.068 0.831 0.109 0.051 0.033 LEADj 0.000 0.006 0.959 0.008 0.007 0.299 BUZZ0j 11.622 6.160 0.059 15.684 5.227 0.003 PUBgj 0.043 0.007 0.000 0.064 0.007 0.000 GENRE: Action 0.245 0.138 0.076 0.120 0.151 0.429 GENRE: Comedy 0.183 0.154 0.235 -0.005 0.154 0.975 GENRE: Drama 0.169 0.168 0.314 -0.095 0.152 0.531 MPAA: PG -0.263 0.149 0.077 -0.268 0.164 0.102 MPAA: PG13 -0.191 0.161 0.236 -0.218 0.164 0.183 MPAA:R -0.189 0.169 0.266 -0.253 0.169 0.135 SEASON: Jan-Apr 0.055 0.066 0.410 0.016 0.064 0.801 SEASON: May-Aug 0.270 0.071 0.000 0.293 0.070 0.000 SEASON: Nov-Dec 0.196 0.082 0.017 0.215 0.082 0.009 HOLIDAYj 0.163 0.068 0.017 0.172 0.071 0.015 CRITICS; 0.162 0.022 0.000 0.174 0.022 0.000 McElroy's R 2 0.706 0.576 Log-likelihood -1567.853 -1594.308 Likelihood Ratio 52.913 (P-value = 0.000) Table-9d: Parameter Estimates of M4: Log-Quadratic-b Model Two-path Model Single-path Model Coefficient Standard P-value Coefficient Standard P-value Variable Estimate Error for H : (3=0 Estimate Error for H : P=0 Equation: \n(THEATERj) Equation: \n(THEATER.) Intercept 0.482 0.151 0.001 0.422 0.151 0.005 ln(<5+SUPERBOWLj) 0.010 0.003 0.001 0.009 0.003 0.002 \n(d+TVAD.,j) 0.322 0.036 0.000 0.316 0.037 0.000 \n(BUDGETj) 0.070 0.022 0.001 0.081 0.022 0.000 \n{8+LEADj) -0.031 0.020 0.128 -0.025 0.021 0.233 \n(BUZZ_,j) 0.038 0.021 0.070 0.041 0.021 0.053 \n(5+PUB.Lj) 0.003 0.002 0.166 0.000 0.002 0.979 GENRE: Action -0.068 0.054 0.205 -0.067 0.049 0.178 GENRE: Comedy -0.147 0.050 0.003 -0.144 0.044 0.001 GENRE: Drama -0.172 0.055 0.002 -0.165 0.050 0.001 MPAA: PG -0.137 0.065 0.037 -0.120 0.068 0.076 MPAA: PG13 -0.183 0.065 0.005 -0.167 0.066 0.012 MPAA: R -0.203 0.069 0.003 -0.185 0.071 0.009 WB/New Line 0.134 0.036 0.000 0.111 0.029 0.000 Paramount 0.087 0.042 0.041 0.069 0.034 0.044 Sony 0.118 0.036 0.001 0.099 0.029 0.001 20th Century Fox 0.147 0.043 0.001 0.117 0.032 0.000 Universal 0.092 0.060 0.124 0.062 0.048 0.190 Other Distributors 0.030 0.062 0.627 0.047 0.037 0.203 Equation: \n(BO,) Equation: ln(BOj) Intercept 0.686 0.926 0.459 0.711 0.394 0.071 THEATERj -0.362 0.804 0.652 THEATER/ 0.240 0.110 0.029 \n(5+SUPERBOWLj) 0.014 0.009 0.100 0.030 0.011 0.008 \n(5+TVAD0j) 0.207 0.254 0.416 0.362 0.093 0.000 \n(BUDGETj) -0.041 0.074 0.578 0.160 0.055 0.004 ln(8+LEADj) -0.008 0.026 0.761 0.016 0.051 0.750 \n(BUZZUj) 0.066 0.049 0.176 0.121 0.051 0.019 \n(d+PUB0J) 0.017 0.004 0.000 0.021 0.005 0.000 GENRE: Action 0.322 0.150 0.032 0.165 0.104 0.112 GENRE: Comedy 0.258 0.168 0.124 -0.005 0.071 0.943 GENRE: Drama 0.267 0.182 0.144 -0.080 0.093 0.391 MPAA: PG -0.207 0.139 0.138 -0.193 0.167 0.248 MPAA: PG13 -0.150 0.145 0.300 -0.187 0.149 0.211 MPAA: R -0.143 0.153 0.350 -0.230 0.156 0.142 SEASON: Jan-Apr 0.036 0.068 0.595 -0.013 0.082 0.878 SEASON: May-Aug 0.289 0.073 0.000 0.348 0.081 0.000 SEASON: Nov-Dec 0.225 0.089 0.011 0.289 0.094 0.002 HOLIDAY j 0.171 0.069 0.013 0.181 0.075 0.016 ln(CRITICS,) 0.815 0.102 0.000 0.927 0.103 0.000 McElroy's R 2 0.712 0.519 Log-likelihood -1576.426 -1617.683 Likelihood Ratio 82.515 (P-value = 0.000) Table-10: Comparison of the effectiveness of Super Bowl and Other Launch T V advertising Effects on THEATERj Effects on BOj H3a: PI,SB=PLAD H3b: B2.sB=P2.AD t-statistic P-value t-statistic P-value M l : Log-linear 0.459 0.647 2.137 0.033 M2: Log-Log -8.313 0.000 0.774 0.439 M3: Log-Quadratic-a -7.222 0.000 -1.386 0.167 M4: Log-Quadratic-b -8.768 0.000 -0.772 0.441. 87 Table-11: Elasticity Measures on the basis of M3, the Log-quadratic-a Model THEATER Two Causal Paths from Super Bowl TV advertising to Opening Week B >ox Office Revenues Indirect Effect Direct Effect Total Effect ^ S B - T H R ^ T H R - B O ^ S B - B O Estimate Std. Err. p-value Estimate Std. Err. p-value Estimate Std. Err. p-value Estimate Std. Err. p-value Mean: 2.336 0.006 0.003 0.019 1.309 0.695 0.060 0.017 0.008 0.034 0.026 0.010 0.011 1st quartile 1.892 0.696 0.713 0.330 0.022 0.009 0.016 Median 2.491 1.563 0.675 0.021 0.027 0.010 0.010 3rd.quartile 2.783 2.099 0.626 0.001 0.031 0.011 0.008 THEATER Two Causal Paths from Other Launch TV advertising to Opening Week Box Office Revenues Indirect Effect Direct Effect Total Effect ^ A D - T H R ^ T H R - B O £ A D - B O Estimate Std. Err. p-value Estimate Std. Err. p-value Estimate Std. Err. p-value Estimate Std. Err. p-value Mean: 2.336 0.292 0.040 0.000 1.309 0.695 0.060 0.231 0.159 0.148 0.613 0.107 0.000 1 st quartile 1.892 0.696 0.713 0.330 0.434 0.088 0.000 Median 2.491 1.563 0.675 0.021 0.687 0.115 0.000 3rd quartile 2.783 2.099 0.626 0.001 0.843 0.136 0.000 88 Table-Al: Regression Results for IMDbALEXAj Variables Parameter Estimates Standard Errors P-values \n{IMDb_ALEXAd) Intercept 12.67 0.06 0.00 Trendw 0.01 0.00 0.00 FEB -0.03 0.05 0.59 MAR -0.10 0.05 0.05 APR -0.09 0.05 0.06 MAY -0.08 0.05 0.08 JUN -0.10 0.05 0.03 JUL -0.06 0.05 0.25 AUG -0.09 0.05 0.04 SEP -0.04 0.05 0.46 OCT -0.12 0.05 0.01 NOV -0.14 0.06 0.03 DEC -0.12 0.04 0.01 NEW YEAR 0.15 0.05 0.01 MAR TIN L UTHER KING DA Y 0.05 0.07 0.47 PRESIDENTS DAY -0.10 0.09 0.25 MEMORIAL DAY -0.02 0.06 0.79 INDEPENDENCE DA Y 0.02 0.08 0.79 LABOR DAY -0.03 0.08 0.69 COLUMBIA DAY -0.08 0.07 0.25 VETERANS DAY -0.05 0.09 0.56 THANKSGIVING DAY -0.04 0.08 0.65 XMAS 0.11 0.06 0.07 N R 2 180 0.94 Figure-1: Survey Results for Difficulties in Marketing Metrics In Improving marketing ROI, how difficult are each of these tasks?"* Acting quickly to improve results Agreeing on a definition of marketing ROI Improving reporting systems Improving comprehensiveness of sales data Changing established practices Improving timeliness of sates data Improving accuracy of sales data Improving granularity of sales data Improving granularity of marketing spending data Improving comprehensiveness of 64% 64% 63% 57% 51% 46% 40\. 42% 81% marketing spending data , Base: 111 marketing executives *Percentages represent those who responded "somewhat difficult"or*very difficult" (Reproduced from Nail 2005) Figure-2: Survey Results for Definition of Marketing Metrics "What is your company's current definition of marketing ROI?" "Which new definitions are you developing?" Incremental sales from marketing Changes In brand awareness Total sales from marketing Attitudinal changes Changes in market share j Changes In purchase intent | Ratio of ad cost to revenue I Number of leads | Current definition New definition Cost per sate jggggmmmm Cost per lead GRPs delivered mm Increase in customer lifetime value n Changes in the financial value I of brand equity J. 0 % 1 0 % 2 0 % 3 0 % 6 0 % 7 0 % 8 0 % 9 0 % 1 0 0 % 4 0 % 5 0 % Base: 111 marketing executives (multiple responses accepted) Source The 2 0 0 4 Forrester/Association of National Advertisers Survey on Marketing Accountability (Reproduced from Nail 2005) Figure-3: A Research Framework proposed by Rust et al. (2004) The Chain of Marketing Productivity Marketing Actions The Firm Tactical Actions Advertising, service improvements, etc. Customer Impact Impact on attitudes, impact on satisfaction, etc. Market Impact Market share impact, sales impact, etc. Financial Impact ROI. EVA, etc. Impact on Firm Value MVA Strategies Promotion strategy, product strategy, channel strategy, etc. Marketing Assets Brand equity, customer equity, etc. Market Position Market share, sates, etc: Financial Position Profits, cash flow, etc. Value of the Firm Market capitalization. Tobin's q (Reproduced from Rust et al. 2004) Figure-4: A Marketing-Shareholder Value Framework proposed by Srivastava et al (1998) Linking Market-Based Assets to Shareholder Value Market-Based Market Shareholder Assets Performance a * Value Customer Faster Marke t Accelerate Cash Flows Relationships: Penetration •Brands •Faster Tr ia ls Enhance Cash Flows •Installed Base •Faster Referrals Reduce Volat i l i ty and Partner Relationships: •Channels •Cobranding •Faster Adopt ion Price Premium Share Premium Extensions Vulnerabi l i ty of Cash Flows Enhance Residual Value of Cash Flows •Network Sales/Service Costs Loyalty/Retention (Reproduced from Srivastava et al. 1998) 93 Figure-5: Cross-sectional relationships between brand share and retail distribution in packaged goods show a convex pattern % A C V is the percentage of total outlet sales in "all commodity groups" made by stores that stock the product category (Reproduced from Reibstein and Farris 1995) 94 Figure-6a: A two-path model of Super Bowl and other launch T V advertising Figure-6b: A single-path model of Super Bowl and other launch T V advertising Figure-7: Distribution of Theater Numbers in the Release Week by Individual Movies Release Week's Theater Engagement Distribution 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% FI m , B , m , n , B , B , l , B , H , H , f f l , n , r i , l » l , CD OO Number of Theater Engagement in Release Week 96 Figure-8: An example to show the definitions of six Duration-based Variables BUZZ. LL BUZZ,,,, TVAD.IJ TVAD, (LL PUB. 11 PUB, Hi, BOi S U N M O N TUE W E D T H U FRI SAT SUN M O N T U E W E D T H U FRI SAT April 9, 2001 April 13.2001 April 15,2001 Release Date of Bridget Jones's Diary April 20, 2001 Figure-9a: Box Plot of BOj Non-Super Bowl advertised Movies (NSB) vs. Super Bowl advertised Movies (SB) 200 H 150' 100 50 NSB SB Figure-9b: Box Plot of THEATERj Non-Super Bowl advertised Movies (NSB) vs. Super Bowl advertised Movies (SB) SB NSB Figure-9c: Box Plot of TVAD.ld Non-Super Bowl advertised Movies (NSB) vs. Super Bowl advertised Movies (SB) NSB SB Figure-9d: Box Plot of TVAD0J Non-Super Bowl advertised Movies (NSB) vs. Super Bowl advertised Movies (SB) io H o -t NSB SB 98 Figure-9e: Box Plot of LEADj Non-Super Bowl advertised Movies (NSB) vs. Super Bowl advertised Movies (SB) 40 1 30 tjq 20 o -i N S B S B Figure-9f: Box Plot of BUDGETj Non-Super Bowl advertised Movies (NSB) vs. Super Bowl advertised Movies (SB) N S B S B Figure-9g: Box Plot of BUZZ.jj Non-Super Bowl advertised Movies (NSB) vs. Super Bowl advertised Movies (SB) N S B S B Figure-9h: Box Plot of BUZZ0J Non-Super Bowl advertised Movies (NSB) vs. Super Bowl advertised Movies (SB) N S B S B 99 Figure-9i: Box Plot of PUB.ij Non-Super Bowl advertised Movies (NSB) vs. Super Bowl advertised Movies (SB) 30 69 b 20 10 NSB SB Figure-9j: Box Plot of PUB0j Non-Super Bowl advertised Movies (NSB) vs. Super Bowl advertised Movies (SB) 30 O 20 O H NSB SB Figure-9k: Box Plot of CRITICSj Non-Super Bowl advertised Movies (NSB) vs. Super Bowl advertised Movies (SB) NSB SB Figure-lOa: Simulated THEATER by Individual Scenarios Overall Average THEATER by Individual Scenarios 2.60 2.55 2.50 2.40 ¥ 2.35 2.30 2.20 "2 :34" 2.55 2.53 Scenario 2 Figure-10b: Simulated BO by Individual Scenarios Overall Average BO by Individual Scenarios 40.00 30.00 25.00 s £ 20.00 o m 15.00 10.00 0.00 33.42 25.89 21.25 ^^^^^^^^^ • H p Scenario 0 Scenario 1 Scenario 2 Figure-lOc: Simulated THEATER by Individual Scenarios: SB vs. NSB Average THEATER by Individual Scenarios Super Bowl advertised Movies (SB) and non-Super Bowl advertised Movies (NSB) 3.50 3.00 2.50 a. w 1.50 < 1.00 0.50 0.00 2.97 2.99 2.53 3.15 2.50 • SB B N S B Scenario 1 Scenario 2 Figure-10d: Simulated BO by Individual Scenarios: SB vs. NSB Average BO by Individual Scenarios Super Bowl advertised Movies (SB) and non-Super Bowl advertised Movies (NSB) 60.00 50.00 40.00 .= 30.00 O CO 20.00 10.00 0.00 20.17 43.88 32 90 54.23 24.47 • SB • NSB Scenario 0 Scenario 1 Scenario 2 102 F i g u r e - l l a : THEATER Response Funct ion w.r.t. SUPERBOWL Response of THEATER w.r.t. SUPERBOWL (95% Confidence Interval) A o.ooo 4-9 10 11 12 13 14 15 16 SUPERBOWL (US$ in Millions) 19 20 21 22 23 24 25 F i g u r e - l i b : THEATER Response Funct ion w.r.t. TVAD.j Response of THEATER w.r.t. TVAD., (95% Confidence Interval) 6.000 5.000 -1.000 1 TVAD., (US$ in Millions) F i g u r e - l l c : BO Response Funct ion w.r.t. SUPERBOWL Response of BO w.r.t. SUPERBOWL (95% Confidence Interval) 60.000 -10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 SUPERBOWL (US$ in Millions) F i g u r e - l i d : BO Response Funct ion w.r.t. TVAD. Response of BO w.r.t. TVAD., (95% Confidence Interval) 1 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 TVAD., (US$ in Millions) Figure-lie: BO Response Function w.r.t. THEATER Response of BO w.r.t. THEATER (95% Confidence Interval) -/—y X 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 THEATER (in Thousands) 3 3.2 3.4 3.6 3.8 4 105 Figure-Al: Number of Visitors to IMDb.com per Million Alexa Tool Bar users Chapter 4: Good Mov ie or Noth ing Better to Do? T ime of Day Demand Models for Mu l t ip lex Mov ie Theaters 1. Introduct ion Many service providers, such as movie theaters and airlines, serve a cohort of customers according to pre-announced time schedules, rather than serving individual customers as they arrive or order. For these pre-announced time schedule service providers, choosing the optimal service time schedule is crucial to profit maximization. On the one hand, the time schedule is an operation plan, which aligns different cost centers, like human resources and capacity management, to achieve the most cost-efficient operation. On the other hand, customers decide i f they want to purchase services from a service provider on the basis of its pre-announced time schedule. If a customer cannot find any services scheduled by a service provider that match her preferred start/end time, she may switch to a competing service provider or pursue an outside alternative. In other words, like price and service quality, the start/end time of a service is potentially an important choice attribute in determining consumer demand. Focusing on multiplex movie theaters, this essay develops demand models, which disentangle consumer preferences for different start times from aggregate historical sales data1. In particular, the demand models address two recurring issues in multiplex movie theaters and similar service providers, namely the confounding of product quality and time preferences, and the difficulty of distinguishing between cannibalization and market expansion. The demand models are intended to be used by multiplex movie managers and other service providers, which need to pre-announce their service schedules, to optimize their service schedules. 1 A n alternative approach to understanding customer time preference is to conduct a market survey, asking the customers explicitly their preferred start/end times for various service offerings. However, this approach is usually very costly and subject to various sampling biases. 107 Let us take a closer look at the first issue. We, as researchers and analysts, cannot observe moviegoers' perceptions concerning the quality of each movie. If a theater manager, however, had some idea of moviegoers' perceptions of quality, and had a tendency to schedule high-perceived-quality movies in a particular time slot, say 9 pm, it is unclear whether high attendance at 9 pm in the historical sales data was due to moviegoers' underlying time preferences or higher movie quality perceptions. Moviegoers' time preference and their preference for movies are essentially confounded. To put it lightly, we cannot distinguish whether moviegoers choose to watch a movie because it is a good film, or because they have nothing better to do at that time. While this problem is particularly apparent in multiplex movie theaters, other service providers who schedule differentiated services at different times of day may encounter the same problem. To address this issue, we characterize the choice set of potential moviegoers in a particular hour as one consisting of the movie showings starting in the hour and an option to not watch any movie. The not-watching option includes all other alternatives such as going to movies starting at another time, going to another multiplex movie theater, going to museums, spending time with friends in coffee shops, working in the office, studying, and so on. Referring to these other options (outside the choice of watching a movie in a specific hour at the focal movie theater) the "outside option", we assume that the attractiveness of the outside option varies over time of day, day of week and time of year, while the appeal of watching a movie title at a theater decays over weeks but stays constant within a week. By capturing the time variations of the outside option, relative to the systematic decay of unobserved movie quality in a utility model, we disentangle moviegoers' underlying time preference and their preference for movie titles in the aggregated sales data. Our approach is similar to Einav's (2003), through which he identifies the weekly seasonality over a year at the total U.S. market level. However, the present research differs from his work in three aspects. First, we go beyond 108 weekly seasonality to examine all three layers of seasonality, namely time of day, day of week, and day of year. And we do it at a more micro level, that of multiplex theaters, as opposed to the whole U.S. market. Second, we improve on his specification by allowing a more flexible weekly decay of the unobserved movie quality. Finally, we extend the model to address the second issue common to pre-announced time schedule service providers: the difficulty of distinguishing between cannibalization and market expansion. Let us examine the second issue in more detail. This issue is a mainstay concern in the discrete choice literature, but is especially apparent in our context. When modeling consumer demand for different services within an hour as discrete choice occasions, we must assume the manner in which the unobserved utility components in individual alternatives are correlated. Two commonly used models, which assume different structures of such correlation, are probit and nested logit models.2 While these models have been shown to be satisfactory solutions in situations where the choice sets are relatively constant across choice occasions, it is not clear i f they are as effective when there is non-trivial variation in the choice set. Specifically, in the context of demands for service scheduling, the choice set in general and the number of choice alternatives in particular varies from one choice occasion to another. For example, there were two movies, say Batman Begins and The Interpreter, starting within the hour beginning at 7pm on a specific Monday, but Star Wars Episode III was added to this choice set within the hour of 7pm the next Tuesday. Beside accounting for the different time preferences between Monday and Tuesday, it is necessary for our demand model to identify two effects triggered by the addition of Star Wars Episode III: 1) overall demand expansion effect (the additional title is attracting new moviegoers, who would not go to the theater otherwise), and 2) cannibalization effect (the additional title is prompting "decided" moviegoers to switch from the other titles). 2 Refer to Train 2001 for an overview. 109 Due to the well-known property of Independence of Irrelevant Alternatives (IIA), the standard logit model is unable to distinguish these two effects. We therefore need discrete choice models, which relax the IIA property. Explicitly modeling the correlation of individual choice alternatives, the multinomial probit model usually faces increasing challenges in estimation as the number of unique choice alternatives increases. As the aggregated sales data of a multiplex movie theater typically contain a large number of unique movie titles, the probit model is almost infeasible to implement, or at least incurs a high cost of implementation. Another approach to overcoming IIA is the mixed logit model. However, as there is no apparent demographic or other cross-sectional variation of moviegoers across our units of observation, which are different time slots for a focal movie theater, the random coefficient specification in the mixed logit model is not very useful to our context. Therefore, this essay focuses on the nested logit model and a model suggested by Ackerberg and Rysman (2002). Both models will be applied to our context of multiplex movie theaters and their relative merits in identifying the cannibalization and market expansion effects will be discussed. In summary, this essay develops a model addressing two issues, namely the confounding of underlying seasonality and unobserved product quality, and the difficulty of distinguishing between cannibalization and market expansion effects. These two issues are recurring but relatively under-researched issues in marketing practice. The multiplex movie theater context provides a unique opportunity and data set for addressing these problems in an integrated manner. To the best of our knowledge, this is the first attempt to address the two problems together. This research advances our methodology for helping companies frequently facing both problems. The next section reviews the literature streams related to this essay. Section 3 discusses three models. First, we present the base model to illustrate how the underlying time preferences of moviegoers are disentangled from the unobserved movie qualities. To identify the 110 cannibalization and market expansion/subtraction effects of varying choice sets, we then extend the base model in two directions, using the nested logit approach and Ackerberg and Rysman's approach. The demand models are estimated with two data sets from a multiplex movie theater in the Netherlands. Section 4 describes the data sets and section 5 discusses the estimation results. Section 6 concludes the essay with a discussion of the limitations of our study and future research directions. 2. Related Literature This essay is related to two literature streams. First, our demand model adds to the broad literature of market response models for managers. Second, we advance the literature related to discrete choice models with market-level data. 2.1 Market Response Models for Managers Similar to their counterparts for the use of policy makers, market response models for managers attempt to represent reality using parsimonious mathematical models. These models may stand alone as predictive or diagnostic models (refer to Hanssens, Parsons and Schultz 2003 for a comprehensive review) or be incorporated into the decision optimization procedure in marketing management support systems (MMSS) (see Wierenga and Bruggen 2000 for a review of MMSS). Our demand model extends the literature by focusing on an under-researched marketing decision variable, namely "what to offer in a choice occasion". As reviewed by Hanssens, Parsons and Schultz (2003), extant market response models are primarily concerned with advertising, pricing or other decisions in which the decision alternatives are at least ordinal in nature. For example, to distinguish between the carryover effect of advertising and the effect of purchase feedback, Givon and Horsky (1990) built a 111 response model relating sales levels in a current period to current and previous advertising levels and the last period's sales level. Regarding the focal decision in their study - advertising level -we can readily rank one decision alternative over the other (e.g., $25,000 is higher than $10,000). In contrast, our demand model concerns the type of decisions in which decision alternatives cannot be readily ordered. Specifically, our focal decision is different pre-announced service schedules. In a specific hour, say 7pm on Tuesday, we have decision alternatives such as 1) showing Batman Begins and The Interpreters, 2) showing Star Wars Episode III and The Interpreters, and 3) showing Batman Begins only. While we may still be able to rank different decision alternatives by the numbers of titles in the choice sets, the order among decision alternatives involving the same number of titles is not readily apparent. For example, before applying a model to the data, we do not know if the decision alternative of showing Batman Begins and The Interpreters within the hour of 7pm is better than the decision alternative of showing Star Wars Episode III and The Interpreters. In summary, the decision of choice set is an important but under-researched area for marketing response models. We believe our demand model can shed light on difficulties usually associated with models handling these unique types of marketing decision variables. As mentioned, there are relatively few demand models for service scheduling in particular and models for choice set decision in general. A notable exception is the market response model in SilverScreener (Swami, Eliashberg and Weinberg 1999; Eliashberg, Swami, Weinberg and Wierenga 2001), a marketing decision support system used by multiplex movie theater managers in the Netherlands to both select and assign movies to specific screens each week. By the afternoon of each Monday, theater managers must finalize their decision concerning movies to be shown for the week starting on the next Thursday (or next Friday for the U.S. exhibitors), and must assign the chosen movies to different screens. SilverScreener 112 helps make these decisions in two steps. First it uses a market response model to project the total weekly box office revenue for each movie i f the movie is shown in a particular theater. These projected weekly revenues are then used in an optimization algorithm to choose the movies with the highest projected gross profits and assign the chosen movies to the screens, minimizing the possibility of capacity constraint. Note that SilverScreener abstracts away from the micro-scheduling issue, namely when and how frequently the theater should actually show the selected movies on a chosen day of the week. This micro-scheduling issue is essentially the choice set decision, upon which our demand model focuses. As micro-scheduling is not the purpose of SilverScreener, its market response model does not capture the underlying time preferences of moviegoers and does not consider the possible cannibalization and market expansion effects of adding or subtracting movie titles to a specific choice occasion. Our demand model therefore extends the market response model of SilverScreener to capture a richer set of moviegoer behaviors. Beyond marketing, our demand model for service scheduling is also related to the literature of yield management and revenue management (see McGi l l and Van Ryzin 1999 for a literature review of both operation management and economics). Studied extensively in the airline reservation context, revenue management is the practice of controlling the availability and pricing of travel seats in different booking classes with the goal of maximizing expected revenues or profits. However, the present essay will not incorporate retail prices in its demand model nor model explicitly the truncation by capacity constraints, because our empirical application - that of multiplex movie theaters - does not change retail prices across alternatives of different qualities, and rarely encounters excess demand. We leave the incorporation of both retail pricing decision variables and service time scheduling in an integrated demand model for future research. 113 2.2 Discrete Choice Models with Market Level Data Another literature stream to which our demand model relates is that of discrete choice demand models using aggregate market level data. As will be discussed in the next section, our demand model assumes that individual moviegoers' choice outcomes can be aggregated as the market shares of individual movie screenings. In marketing, there is a long tradition of using market share models to study various marketing problems (see Cooper and Nakanishi 1988). While these market share models work very well in cases characterized by stable market sizes, they cannot handle possible substitutions consumers make between a product and an alternative solution, one which is totally outside the defined product market. In other words, the primary demand expansion is assumed away. In order to capture such a potential demand expansion effect, this essay therefore adopts a setup used widely in demand models of empirical industrial organization and more recent marketing literature: specifying an outside option for each choice occasion. This specification not only captures both primary demand and substitution among different choice alternatives under a single utility maximization framework, but also greatly simplifies the estimation complexity of demand models. Specifically, as demonstrated by Berry (1994), we can invert the market shares to linearize the utility of individual choice alternatives. As mentioned in the previous section, our demand model is similar to Einav's (2003) study of weekly seasonality in U.S. box office revenues. Also using Berry's inversion method, Einav's model specifies that the outside option should vary across different weeks of a year. Specifically, Einav hypothesizes that movie studios actually release their highest quality movies in certain weeks, which do not necessarily overlap with the weeks with highest seasonality. To distinguish empirically the weekly seasonality from the movie set variation confounded with unobserved quality perception, he specifies two structures in his discrete choice model. First, he 114 assumes that the unobserved quality perception of each movie can be completely characterized by a movie-specific fixed effect parameter and a weekly decay factor that is constant across all movies. As these two parameters stay constant across different weeks for a movie, Einav can then pool observations of different weeks to estimate these two observation-invariant parameters and attribute the remaining weekly variability to weekly seasonality. Second, he assumes that each week of a year has its own base demand level and therefore uses 56 parameters to completely characterize the weekly seasonality and several holiday effects. Our demand model improves on Einav's model in three aspects. First, we broaden our focus from weekly seasonality to two additional layers of seasonality, time of day and day of week. And we do this at the level of one multiplex movie theater, which is more micro than the level of the whole U.S. market. Second, in order to identify the 56 parameters for weekly seasonality, Einav must restrict all movies to having the same weekly decay rate. As our data are at a more micro level, we can allow each movie title to retain its unique weekly decay rate. We will return to this point when we discuss model specification. Third, in order to distinguish between cannibalization and market expansion, we relax Einav's assumption of IIA by exploring two model specifications, namely the nested logit and Ackerberg and Rysman's (2002) congestion specification. To facilitate the discussion of the nested logit and Ackerberg and Rysman's (2002) specifications, we first review the notion of IIA and its implication for situations where the choice sets vary across choice occasions. In a choice set, C, which consists of alternative 1, j, ... J, define the utility for alternative j as: Uj=Vj + ej, (1) where Vj is the deterministic component and ey is the random component. 115 By assuming e7 i.i.d. Gumbel (0, JU) for all j, we can derive the logit model. (Refer to Ben-Akiva and Lerman 1985, pl04-107 for detailed derivation): hsC If we compare the choice probabilities of two alternatives, say j and /, we can see the ratio of the two probabilities is entirely unaffected by any other alternatives: This property of logit models is called Independence of Irrelevant Alternatives (IIA). Note that this property is mainly driven by the assumption that Sj is independently distributed across all j. Using an example from our multiplex movie theater context, we now illustrate the implication of IIA when there is variation in choice sets across different choice occasions. Suppose there are two movies, a and b, plus an outside option. The utilities of these three alternatives are defined as: Movie a: Ua — Va + ea Movie b: Ub = Vb + sb Outside option: U0 = V0 + e0 While Va, Vb, and V0 are the systematic components, ea, eb, and e0 are the random components. For convenience of illustration, suppose Va=Vb = V0. To derive a logit model, we assume Sj is i.i.d. Gumbel (0, ft) across j, for j = a, b, o. Consider two choice occasions: Occasion 1: Only Movie a starts within the time slot The probability of choosing alternative j, P(j) (2) PU) _ e-P(l) e P(a) = P(o) = 1/2 (3) 116 Occasion 2: Movie a and b start within the time slot P(a) = P(b) = P(o) = 1/3 (4) As the difference between these two choice occasions is the addition/sub traction of movie b to/from the choice set, (3) and (4) together imply that the addition/subtraction of movie b affects movie a and the outside option equally. This is rather counterintuitive, as we would expect movie b to substitute more toward another movie than to the outside option. Note that under occasion (2), the substitution of movie b to the outside option essentially captures the demand expansion effect (attracting new moviegoers), while the substitution of movie b to movie a is the cannibalization effect: (prompting moviegoers to switch from movie a). To restate the implication, the addition/subtraction of a movie to/from a choice set generates equal levels of demand expansion and cannibalization effects. This implication is indeed more general than our example: one can show that, in accordance with IIA, the addition/subtraction of a movie to/from a choice set affects all existing movies and the outside option equally. In other words, IIA a priori assumes the demand expansion and cannibalization effects indistinguishable. To gain more insight into the implications of IIA on choice set variation, we follow Ben-Akiva and Lerman's (1985, p.300-304) discussion of inclusive values in re-examining occasion (2) of our example. We define the expected utility from choosing either movie a or b as: U* = max(Ua,Ub)=V* + e* With the assumption that £, is i.i.d. Gumbel (0, /u) across movie a, b and outside option and the properties of Gumbel distribution, we can show that the systematic component of U*, P = - l n ( / ' + / " ) (5) M and the random component, e*, is Gumbel distributed with parameters (0, pi). The discrete choice literature (e.g., McFadden 1978) typically calls V* the "inclusive value" as it is essentially 117 a scalar summary of the expected "worth" of all choice alternatives included in a subset of the choice set (movie a and b in our example). Examining (5), we can see that V* of the logit model contains an overestimate. As Va = Vt, = V0 in our example, (5) can be re-written as: V*=-ln2+Va (5a) If movies a and b are perfectly correlated (e.g., different showings of the same movie title), the utility of watching either movie should be equal to Ua = Va + ea by intuition. Comparing this intuitive expression to U*, which is defined as the expected utility of watching either movie, we see that our i.i.d. assumption for e, makes V* too high by an amount equal to (l///)-ln(2). In fact, i f we correct this overestimate in V*, we obtain more intuitive probabilities for occasion (2) than (4): P(a or b) = P(o) = 1/2 (6) In other words, when movies a and b are perfectly correlated, the addition of movie b in occasion (2) would completely substitute toward movie a and not affect the outside option at all. To restate this in terms of cannibalization and demand expansion, when a and b are perfectly correlated, the addition of movie b in occasion (2) would only cannibalize movie a, without gaining any demand expansion. What i f the "inside" choice alternatives (those other than the outside option) are not perfectly correlated but only somewhat correlated? When the inside choices are correlated, we expect adding a new inside choice alternative to generate more cannibalization than market expansion. As standard logit models are restricted to equal cannibalization and demand expansion effects, they are not appropriate for this situation. Essentially, we must correct the overestimate in V* discussed above. However, as the inside choice alternatives are not perfectly 118 correlated, the overestimate is no longer precisely (l///;)-ln(2) and we cannot correct it by simply subtracting (l///)-ln(2) from V*. We evaluate two approaches to correct for the overestimate in this situation: nested logit models and Ackerberg and Rysman's (2002) congestion model. While both approaches essentially perform the same function of correcting the overestimate in the inclusive values over all inside alternatives, they extend logit models by introducing different model structures. As discussed in Ben-Akiva and Lerman (1985, ch.10), nested logit models differ from logit models in their distributional assumption for ey, the random component in the utility. Specifically, nested logit models assume that e7 for each choice alternative can be decomposed into subcomponents, and that similar choice alternatives share one or two subcomponents. By assuming each subcomponent to be Gumbel distributed with a unique scale parameter, ft, nested logit models use these different Gumbel scale parameters to correct for the overestimate in the inclusive values. Specifically, i f we model our earlier example as a nested logit, we decompose sa and e& into: £b Em &b' where em is the random component common to all choice alternatives in a subset, Cm (i.e. "watching movies" in our example), and ea- and e/y are the random components unique to specific movies. We essentially group all movies into a subset of "watching movies". As the outside option forms its own subset, we do not need to decompose its random component, e0. To derive a nested logit model, we assume: 1) em, ea - and are independent; 2) ea - and i.i.d. Gumbel (0, fi'); and 3) em and e0 are distributed so that e0 and em + Sj for j - a' and b' are independently Gumbel distributed with scale parameter fT. The choice probabilities in occasion (2) are then: PG) = — forj = aoxb (7) u / efm(Vo) + y ^"(c™*) j v ' he Cm 119 where Vm * = — ln( e"'Va + e"'Vh) (8) P(o) = ef'"'{Vl>) (9) ef,m(r') ,;/"(Cm*) he Cm Note that F"m* is essentially the inclusive value for the alternatives in the subset Cm or the expected utility of choosing either movie a or b. At first glance, the inclusive value in the nested logit, (8), is identical to its counterpart in the standard logit, (5), only with a different scale parameter, pi or pi', suggesting that nested logit models may suffer from the same type of overestimate as logit models. However, note that pi in logit models is empirically non-identifiable and therefore is usually set to one during estimation. On the other hand, while pim in nested logit models is also empirically non-identifiable, pi' is actually identifiable. In other words, pu' serves as the parameter to rescale the inclusive value such that the overestimate in the logit model can be somewhat corrected. We illustrate how the rescaling works in our example. In the case in which movies a and b are highly correlated, the variance for the Gumbel distribution of ea • and eb • should be very small, and the scale parameter, pi', which is inversely related to the variance, is therefore very large. In the extreme case that pi' tends to infinity, according to the line of proof in Ben-Akiva and Lerman (1985, p.309-310), the inclusive value, Vm*, would tend to max(Va, Vb). As Va = Vb = V0 in our example, when movies a and b are almost identical, Vm* will tend to Va, and both P(a or b) and P(o) therefore tend to 1/2, which is in line with our intuition that the addition of movie b completely cannibalizes movie a but does not attract new customers from the outside option. We now consider the second approach for distinguishing cannibalization and demand expansion when there is choice set variation. While Ackerberg and Rysman (2002) do not interpret their congestion model with the notion of inclusive values, we illustrate here that their 120 basic tenet is also to correct for the overestimate in the inclusive value of the standard logit model. In fact, by considering Ackerberg and Rysman's [AR] model from such a perspective, we can easily compare their model structures to the nested logit's. More specifically, unlike nested logit models, which focus on modifying the random utility component of standard logit models, e,-, A R model essentially introduces a correction factor to the systematic component, Vj. In our earlier example, i f movies a and b are perfectly correlated, (l///;)-ln(2) is precisely the overestimate in the inclusive value, V*, and we therefore should add a correction factor equal to - (l/^)-ln(2) to each of Va and V/,. In a more general case in which there are /perfectly correlated movies, the corresponding inclusive value, denoted as P"*', is: For convenience of illustration, suppose the systematic component, J7} for ally = 1, Jare equal. J 7*' can be rewritten as: Similar to the argument in the two-movie case, the more intuitive value of the inclusive value or the expected utility of choosing one of the perfectly correlated movies is simply Vj. In other words, the independent random component assumption in standard logit models makes J 7*' too large by the amount equal to (l/ju)-ln(J). If we want to correct for this overestimate, we should add a correction factor equal to - (l/ju)-\n(J) to each of the systematic component, Vj for all j = In an even more general case in which the J movies are not perfectly correlated, we no longer know precisely what the correction factor should be. However, from the perfect correlation case, we know that the correction factor is related to the number of inside choice (10) F*' = - \n(J)+Vj M (10a) 121 alternatives, J. We therefore can let the data tell us how much to correct by specifying the correction factor as a function of J, f(/;y), where y is a vector of parameters to be estimated from the data. This is precisely the specification of A R additive model. Note that with the exception of adding the correction factor to the systematic utility component, A R model is a standard logit model. Consider one of the specifications of f(J;y) proposed by A R model: yln(7). Back to our two-movie example, the correction factor is then equal to yln(2). Given that we set the non-identifiable ju at one during estimation, i f movies a and b are perfectly correlated, the data would estimate y to be -1 , which makes yln(2) equal to the required correction. In summary, both the nested logit model and A R congestion model share the same conceptual underpinning: to correct the overestimate in the inclusive value of standard logit models. However, there are two main differences between the two. First, they use different model structures to correct for the overestimate. While the nested logit model focuses on the random utility component, A R model works with the systematic utility component3. Second, A R model allows more flexibility to approximate the required correction by specifying a different functional form for f(J;y). For example, a quadratic form for f(J;y) is more flexible. Compared to the single parameter (ju in nested logit models), the two parameters of the quadratic form provide more flexibility in characterizing the required correction. On the other hand, as stated as the property of "monotonicity with respect to choice set size" by Ben-Akiva and Lerman (1985, p.301), nested logit model does not allow total shares of all inside alternatives to decrease as more choice alternatives are added. However, A R model has enough flexibility to allow the data to exhibit this pattern. 3 Note that in Ackerberg and Rysman (2002) and our later model development section, the congestion models are in fact motivated by making an additional assumption for the random utility component. However, this additional assumption does not change any underlying distributional assumptions for the random component and in effect affects only the systematic utility component. 122 3. Model Development We now develop three demand models for multiplex movie theaters. The first is a base model used to illustrate how moviegoers' underlying time preferences can be disentangled from unobserved product quality. Next, to distinguish between the cannibalization and market expansion effects when there is choice set variation across choice occasions, we develop a nested logit model and a variant of A R congestion model. 3.1 Base Model We seek to identify three layers of time preference from the aggregate attendance data: systematic variations across different times of day, different days of the week and different times of year. We call these three layers of systematic variations time of day, day of week and time of year seasonality, respectively. At first glance, these three seasonality layers appear to be easily identifiable through a simple examination of the hourly pattern of historical attendance data. For example, we can generate cross-tables of admission per showing by each hour, by each day of the week and by each week. Table-la, lb and l c show such cross-tables for one of our samples, which contains the admission records of all movie screenings at a multiplex movie theater in Amsterdam, the Netherlands from January 4, 2001 to April 18, 2001. Let us start with time of day seasonality. We can see from Table-la that movie showings starting in the hour beginning at 9pm tend to attract the highest admission numbers. One may therefore assume that the hour of 9pm is the most preferable time slot in which to watch movies at the focal multiplex movie theater. However, one should also note that the number of showings is unevenly distributed across different hours. For example, there were 820 movie showings starting in the hour of 9pm, but only 252 movie showings starting in the hour of 8pm. This 123 uneven distribution suggests that the same set of movies does not start in each hour. In other words, one movie title may start in one hour but not the other. If there is a systematic relationship between a specific hour and perceived quality of movies, the seasonality pattern revealed by Table-la may be susceptible to substantial bias. For example, due to habit or a belief in a certain myth, suppose that a theater manager has a tendency to select the highest quality movies for the 9 pm time slot. The movie choice set variation across hours will then be confounded with the perceived quality variation. When we observe from a historical data set that movie showings starting in the hour of 9 pm generate the highest average attendance, as suggested by Table-la, it is difficult to determine whether this is due to the fact that moviegoers had the strongest preference for the 9 pm time slot, or due to a confounding between movie set variation and perceived quality. To complicate things further, the ways in which moviegoers perceive the quality of each movie are unobservable to us researchers and analysts (but may have been observable to theater managers at the time they scheduled the movies), and it is likely that these unobserved qualities change over time and therefore vary across observations. In other words, each observation has a unique unobservable component, which may be confounded with the seasonality in which we are interested. Our solution to this problem is to impose a parsimonious specification on how unobserved movie quality varies over time. We then assume that all remaining variability across time and across observations is the result of seasonality and white noise. In fact, after controlling for such a confounding issue, our demand model suggests 8pm, rather than 9pm, is the most preferred start time for moviegoers at the multiplex movie theater in Amsterdam. Table-lb suggests that movie screenings on Saturday and Sunday tend to attract the largest admission figures. Unlike the circumstance related to time of day seasonality, it is 124 unlikely that the set of movies would vary greatly across different days of the week.4 In fact, the rather stable numbers of showings across different days of a week in Table-lb are consistent with the industry practice that theater managers have a fixed set of movies to be shown for the whole week, while the set may vary greatly across weeks. In other words, we expect the day of week pattern revealed by a simple cross-table to remain unchanged in our demand model. Finally, Table-lc demonstrates time of year seasonality. Specifically, movie showings during the week of March 1-7, 2001 tend to attract most moviegoers. Note that this week overlaps with the spring vacation for secondary schools in Amsterdam (March 3-11, 2001), therefore suggesting a school holiday effect. As the sets of movies shown vary greatly across weeks, it is possible that the holiday effect is confounded with movies of higher perceived quality. Therefore, after controlling for the unobserved movie quality, our demand model may estimate insignificant holiday effects. Our modeling approach is to model demand as an aggregation of individuals' discrete choices. In line with other discrete choice models using aggregate level data, we assume that there are a finite number of potential moviegoers, N, for our multiplex movie theater, and that each of the potential moviegoers consumes at most one movie showing within a chosen time frame. To simplify our three models, and for ease of exposition, the present essay assumes that the time frame for the unit demand restriction is one hour. We recognize that it is unlikely that an individual moviegoer would consume in the next hour with the same probability another unit of the same movie. However, while we may not capture the richer details of moviegoer behaviors, the setting is certainly sufficient for studying the three layers of seasonality in which we are interested and to serve as a clean platform for comparison of the nested logit and A R models. We therefore leave the exploration of other time frame assumptions for future research. 4 In our data sets, for every week the same set of movies was shown every day from a Thursday to the following Wednesday. The only exception was that few children's movie titles were shown only as the matinees on weekdays. 125 To derive our base model, we first introduce the notations: d = Date a movie is shown h = Hour a movie starts (e.g. 10 am - 10 pm) TPd = Average temperature on date d DRd = Precipitation duration on date d HDld = Indicator variable for the event that date d falls during the spring vacation HD2d = Indicator variable for the event that date d falls during the May vacation HD3d = Indicator variable for the event that date d is Ascension Day HD4d = Indicator variable for the event that date d is Whit Sunday or Whit Monday HD5d = Indicator variable for the event that date d falls on the Easter weekend HD6d = Indicator variable for the event that date d falls during the summer vacation HD7d = Indicator variable for the event that date d falls during the fall vacation HD8d = Indicator variable for the event that date d falls during the Christmas vacation MONd = Indicator variable for the event that date d is Monday TUEd = Indicator variable for the event that date d is Tuesday WEDd = Indicator variable for the event that date d is Wednesday THUd = Indicator variable for the event that date d is Thursday FRId = Indicator variable for the event that date d is Friday SATd = Indicator variable for the event that date d is Saturday SUNd = Indicator variable for the event that date d is Sunday Ifjj = Indicator variable for the event that movie j is being shown I{h} = Indicator variable for the event that the movie starts within hour h SUNPM = Indicator variable for the event that the movie starts on Sunday between the hour of 2pm to 6pm 126 Ajd = Age of movie j on date d (number of weeks since movie fs release week) We now specify potential moviegoer fs utility for the outside good in hour h on date d: Uwhd — - Vid + £iOhd = -(co()+ coTp-TPd + (OoR-DRd + coHD,-HDld + coHD2-HD2d + ... + coHD8-HD8d + coMo-MONd + ... + cosu-SUNd + £ / ? A • Iih) + o)SUNpM-SUNPM) + emd (11) V// where -T/,d is the systematic utility component of the outside option in hour h on date d and Smd is the unobserved utility component facing individual / in hour h on date d. Potential moviegoer z's utility for movie j starting in hour h on date d:5 Ui/hd = (>jd +%jhd +£ijhd = "Lej •I^> + XrAJd +%hd +eijhd (12) Y/ where Sjd is the systematic utility component of movie j on date d, Sij/,d is the unobserved utility component of movie j starting in hour h on date d, specific to individual i; and ^d is the unobserved utility components of movie j starting in hour h on date d, common to all individuals. We may interpret and Smd as taste variation across individuals. However, unlike Hotelling's horizontal differentiation framework, we actually do not observe the ways in which different choice alternative fs are differentiated from one another (i.e. their location on the unobserved product space is unobservable). Such unobservablility keeps us from capturing precisely the notion that an individual's address will lead her to prefer a choice alternative located in her neighborhood and to dislike a remotely located alternative. In other words, the negative correlation of an individual's preferences towards different products cannot be characterized here. 5 Note that we cannot identify all the parameters in (11) and (12) at the model estimation stage. For example, we need to drop Saturday in order to estimate the "parameter differences" between other weekdays and Saturday. Also note that by normalization, we can move all variables in Um<j, (11), including the intercept co0, to U^d, (12). 127 The three layers of seasonality are captured by three sets of parameters in (11). First, COHDI, ®HD2, G>mi, •••> G>HD7 and a>HD8 capture the time of year effect. In particular, as people tend to have more free time for leisure activities such as going to movie theaters during holidays or school vacations, as compared to normal work or school days, we expect all of these parameters to be positive and therefore to make the outside option less attractive (due to the negative sign of Uiohd)- The eight holiday indicator variables are chosen to primarily represent the holidays and vacations taken by secondary school students in Amsterdam, as they represent the main target market for the focal multiplex movie theater, according to the theater managers. Five school vacation periods, namely spring, May, summer, fall and Christmas vacations are therefore identified first. Three public holidays outside these vacation periods, namely Ascension Day, Whit weekend and Easter weekend are then added to capture the other potential holiday effects. The second layer of seasonality is the day of week effect. Seven parameters COMO, (OTU, (OWE. G>TH. G>ER, (OSA and a>su capture such seasonality. As students and adults must skip work or school to watch a movie on a normal weekday, we expect a>M0, G>TU, (OWE, ($TH and coFR, the parameters for the five weekdays, to be smaller than &SA and a>su, the parameters of the weekends, so as to reflect the higher opportunity costs on a weekday. Finally, /J/,'s capture the time of day effect. Similar to the above argument, students and adults on a normal weekday tend to have higher opportunity costs (learning or wage) during the daytime and prefer to watch movies in the evening. Moreover, even during weekends, people tend to have more activities other than movie-watching during the daytime than in the evening (e.g., outdoor activities). We therefore expect the /J/,'s corresponding to the daytime to be smaller than those for the evening. The present essay also explores a potential interaction effect among different layers of seasonality, namely the Sunday afternoon effect. Table-2a, 2b, 2c, 2d, 2e, 2f and 2g are cross-tables of the admission figures per showing by each hour across all Sundays, all Mondays, all 128 Tuesdays, all Wednesdays, all Thursdays, all Fridays and all Saturdays of our 2001 sample discussed earlier. Examining these tables carefully, we can see roughly the same time of day pattern across different days of a week, with the exception of Sunday (Table-2a). Unlike other days, movie screenings starting Sunday afternoon (between the hours of 2pm and 6pm) tend to attract more admission than those in the evening, suggesting a deviation from the time of day pattern of other days, OJSUNPM, the parameter associated with SUNPM, is intended to capture this deviation. We expect COSUNPM to be positive. Note that in addition to capturing two more layers of seasonality, our model also differs from Einav's (2003) in the way the time of year is characterized. As discussed earlier, Einav assumes each week of a year has a unique base demand, and therefore characterizes the time of year seasonality with 56 parameters (52 weekly parameters plus 4 major holidays, which move around in the calendar). We decided not to follow Einav's specification for two reasons. First, as we will discuss in the data description section, both of our data samples are shorter than one year. In other words, for any of the 52 weeks, we do not have any replication of the same week of another year. It is therefore difficult to estimate reliably the average effect of each of the 52 weeks. On the other hand, i f we assume the base demand level would deviate from other times of year only on holidays or school vacations (some of which span longer than a week), we would have more movie showings in the base group as well as in different holiday groups, and the estimated time of year pattern would therefore be relatively more reliable. Second, as argued by Pierce, Grupe and Cleveland (1984), the use of weekly fixed effect parameters to capture time of year seasonality is not very satisfactory, for two main reasons. First, many holidays occur in different weeks of different years. Although Einav attempts to address the second concern by allowing additional parameters to capture the "moving" holidays, this specification essentially increases more parameters, which are even harder to estimate reliably with our "less-than-a-129 year-long data sets". Second, there is not an integral or even a constant number of weeks in the year: 52 \C weeks in most years and 52 ^ vC weeks in leap year. In addition to the variation across time, we also assume the outside option to vary with two weather variables, namely average daily temperature, TP^ and total daily precipitation (rain or snow) duration, DRj. Unlike the seasonality parameters, we do not offer an a priori prediction on how the weather may affect the attractiveness of the outside option. As discussed in the beginning of the section, in order to identify the underlying time preferences of moviegoers, we must control for the unobserved movie quality. The unobserved quality of individual movies is captured with a movie-specific parameter, 0Jt and a movie-specific weekly decay factor, Xj. As shown in (12), we structurally restrict Uijhd to vary across time only through Xj> and the unobserved quality of each movie is assumed to be characterized completely by Xj and Oj. Under this model specification, all remaining variation in the aggregated demand is due to white noise and seasonality only. Choice outcomes across different weeks can therefore be pooled together to increase the number of observations and identify all parameters in the model. Einav (2003) actually imposes an identification restriction stronger than ours. In particular, he restricts the weekly decay parameter, X, to be common to all movies, or at best to be specific to a particular movie genre. The reason we can estimate a movie-specific decay parameter, Xj, lies in the fact that our unit of observation- admission for each movie showing- is more micro than Einav's. While Einav relies only on one observation per week per movie title to identify both X and his 56 weekly seasonality parameters, we have by and large 30 observations per week per movie title. Moreover, our simpler specification of time of year seasonality also 130 gives us more degrees of freedom to identify the movie-specific decay parameters and the holiday parameters. By assuming that moviegoer heterogeneity in taste, s^d and smd, are independently and identically distributed Gumbel (0,1), we can derive the multinomial logit hourly shares for individual movies and the outside option: For movie j e C/,d, where Q,d is the set of movies starting within hour h on date d, the share of movie j starting in hour h on date d, f S X Q { S J d + £ J M ) • Sji,d= =^= (13) e * P ( - ^ ) + 2. e x P ( ^ / + Zu,d ) ks CM The share of the outside option, . exp(-r M ) sohd =s — —— (14) e x P(- r / , r f ) + 2. e x P(3w + tad ) keClid Following Berry's (1994) inversion method, we transform and rearrange (13) and (14) to obtain: \n(sjhd) - \n(s0hd) = rhd + Sjd + &,d (15) By assuming that is normally distributed and i.i.d. across j, h and d, we can estimate (15) by OLS. 6 3.2 Nested Logi t M o d e l Essentially a standard logit model, the base model always predicts that a new movie title added to an existing choice set will substitute the outside option and other movie titles equally, making the cannibalization and market expansion effects indistinguishable. As discussed earlier, 6 One may compare (15) to a model regressing ln(attendance of movie j in hour h on date d) against the same right-hand side variables of (15). As the right-hand side specification is the same, such a regression model will also allow us to identify both the unobserved movie quality and seasonality. The problem is that it abstracts away from the substitution among different showings and the outside option. As another objective of our demand model is to characterize cannibalization among different movie choices and market expansion, the underlying discrete choice notion of (15) serves as a better foundation from which to extend the base model. 131 the nested logit model and A R model are the two specifications that can address this issue. We therefore develop a nested logit model from the base model in this subsection. Following the specification of the base model, we define the utilities for the outside option and for movie j starting in hour h on date d as below: Potential moviegoer fs utility for the outside good within hour h on date d: UiOhd = - Thd+ S'iOhd = -(coo+ coTP-TPd + coDR-DRd + coHDI-HDld + coHD2-HD2d + ... + coHD8-HD8d + 6)MC-MONd + ... + cosu-SUNd + £ / ? A -Im + coSUNPM-SUNPM ) + e'md (16) V/i where e'md is the unobserved utility component of the outside option facing individual / in hour h on date d. Potential moviegoer fs utility for movie j starting in hour h on date d: Ujhd = $jd +%ji,d + vm + (1 - o)-e'ijhd = YJ0J'1 [ J ) + X J ' A J ' D + §>>d +vihd + (\- cj)-e'iJhd (17) where vuld is the unobserved utility component common to all movies in hour h on date d, specific to individual i, while e'ij/ld is the unobserved utility component specific to movie j in hour h on date d, specific to individual i. Note that the systematic components of Umd and Uyhd in the nested logit model, (16) & (17), are identical to those in the standard logit model, (11) & (12). We therefore maintain the feature of disentangling the underlying time preference and unobserved movie quality in the nested logit model. The point of departure is the specification of random components. Specifically, we decompose the random component of Uyhd into two subcomponents, vihd and s'ijhd- While VM is common to all movie titles in hour h on date d, e'yhd is unique to each movie 132 title. In the terminology of the nested logit model literature, we essentially define two nests in the choice set of each hour. One is a nest of movie choices and the other is the outside option, which is the sole element in its nest. Therefore, VM, together with s'md, represent the randomness at the level of choosing which nest, and s'ijhd represents the randomness of each movie choice within the nest of movie-watching. We can interpret this specification intuitively. Individual i incurs the same amount of random utility i f choosing any movie available at the focal multiplex movie theater at the time, and by choosing a specific movie j , s/he then also obtains s'ijhd, an additional amount of utility unique to movie j. Although we followed Ben-Akiva and Lerman's (1985) notation when reviewing the distributional assumptions of nested logit models earlier, we now switch to Cardell's (1997) notations, as these can simplify the exposition when we use Berry's (1994) inversion method later. Specifically, we assume: 1) vu,d and s'-^d are independently distributed; 2) s'ijhd i.i.d. Gumbel (0, 1); and 3) vihd and s'md are distributed so that s'md and [vihd + (1-cr)-s'yhd ] are independently Gumbel (0,1). Note that (1-cr) is the variance component within the nest of movie-watching and 0 < cr< 1. As cr approaches one, the within-nest correlation of different choice utilities goes to one. Intuitively, when a is close to one, individual i essentially perceives all available movies in the same way (all movies are perfectly correlated). On the other hand, i f cr is smaller than one, individual / exhibits some unobserved taste variation across different movie titles. For movie j e C/,d, we can integrate vihd, s'ijhd and s'md over all individuals / in hour h on date d to obtain the following share expressions: 7 One can reconcile this notation with the notation we used in our earlier example: (1-cr) is the inverse of the scale parameter, ju', and we set //" to be one. 133 The share of movie j starting in hour h on date d, on the condition that a movie from Chd is chosen, e x p ( ( ^ + ^ M ) / ( l - < 7 ) ) The total share of all movie titles in Chd, [Xexp((^/+^)/(l-cT))f-CT) scn= * e C"' • (19) expC-r.J + C ^exp((^+4 , r f ) / ( l -cr) ) ] ( , - C T > keClul The share of moviesy starting in hour h on date d, e x p ( ( ^ + ^ ) / ( l - c x ) ) Sjhd - Sjhd\Ci«rSo.,i : keClul keCu [ S e x P ( ( ^ +4kMV(\-<T))T - [ exp ( -T w ) + [ £exp((c>A, + ^ ) / ( l - ^ ) ) ] ( 1 " a ) ] (20) The share of the outside option in hour h on date d, exp(-r M ) exp(-r M ) + [ 2>p((<Jw + -„ = ( - r M ) Following Berry's (1994) inversion method, we can obtain the following two expressions: \n(sjhd) - \n{s0hd) = {Sjd + %hd)K 1 -o) + V,d - &]n( £ e x p ( ( £ w + ^ ) /(l - cr)) ) (22) ksOul \n(scJ) - Hsohd) = (l-cr)-ln( ]>>xp((c?w + )/(I " <>•))) + ^ (23) keClul Using (23) to substitute ln( ^ e x p ( ( c ) M + cf w , r f)/(l - cr))) out in (22) and using the fact that sp, hd\Cu keClul = s/hd I s0:,,, we get: \n(sjhd) - \n{s()hd) = 8jd + rhd + or-\n(sjhd\o«i) + gjhd (24) 134 As Sjhd\o„i is an endogenous variable to \xi(sjkd) - \n(soi,d), we need to estimate (24) by the two-stage least square method with instruments for SJ/UI\O„I. The details of the estimation will be discussed in a later section. 3.3 Crowding Model In addition to the nested logit model, we now develop an alternative model, Ackerberg and Rysman's (2002) additive congestion model, which also can distinguish the cannibalization and market expansion effects when a new movie title is added to an existing choice set. To better understand the linkage between A R model and the logit model, we will motivate the model differently from that of Ackerberg and Rysman. In the base model, moviegoers are assumed to have their unobserved preferences distributed over the available movie choices. Our crowding model departs from this by assuming that moviegoers have their unobserved preferences distributed over an unobserved product space, which is the building block for the available movie choices and the outside option. In particular, we assume that when a new movie choice is added to the choice set, the new choice would make such a product space more crowded and would cause the attractiveness of the existing movie choices, relative to the outside option, to decrease. Therefore, by modeling the degree of crowding of the unobserved product space, we can characterize the cannibalization relative to the market expansion effect. To fix the idea, we denote the volume of the unobserved product space in hour h on date d to be Ri,d- We also assume that the unobserved product space is filled with very small dots and that each dot is "owned" by either the outside option or one available movie choice. By normalization, we can set the total number of dots equal to Rhd- Note that our assumption does not allow any dot to be "not owned". Thus, i f we denote Rohd and Rji,d as the number of dots (or 135 the volume of the unobserved product space), the outside option and choice alternative j occupy respectively, ^Rjhd + Rohd = Rkd- As a new movie choice is expected to crowd out more toward y/ other movie choices than toward the outside option, we characterize the degree of crowding Rjhd among movie choices by specifying that the normalized product space, , varies with Jj,d, the Rohd Rjhd number of movie choices available in hour h on date d. In particular, we expect to decrease Rohd with JM. Denote QQM and Qjhd as the sets of product space dots owned by the outside option and movie j in the choice occasion of hour h on date d, respectively. As mentioned earlier, moviegoer preferences are now distributed over the unobserved product space. We can express moviegoer fs utility for a dot r e Qohd a s: Uir =~ Thd + Sir = -((Do + atTP-TPd + coDR-DRd + a>HDrHDld + 6}HD2-HD2d + ... + coHD8-HD8d + 0)Mo-MONd + ... + cosu-SUNd + Y J n „ • Tj,) +o)SUNPM-SUNPM) + sir (25) Note that (25) is almost identical to (11), the utility for the outside option in the base model. Although the random component is sir, the systematic component still varies with time of day, day of week, time of year and two weather variables. Similarly, we can express moviegoer i's utility for a dot r e Qjhd as: Uir . = Sjd +4jhd +£ir = Ya6J-1 W + AJ -AJd + §hd +£ir (26) V/ 136 By assuming sir to be i.i.d. Gumbel (0,1), we obtain the share for dot r e Qohd-exp(-rA r f). reQow keCiul r E 0 i H (27) exp(-r w ) flow • exp(-r / i r f) + • exp(£ w + £ m ) Similarly, the share for dot r e Qji,d is: / • e f i o w keC/ui reChiul l & lkhd Rohd • exp(-rA r f) + £ • exp(£ w + £ m ) (28) By assuming that all the product space dots owned by a choice alternative are identical, we can aggregate the share of dot r up to the share of the choice alternative by multiplying sr by the number of dots owned by the choice alternative. For r e Q0hd, SOhd - Rohd'Sr Rohd • exp(-r / i r f) ROM • exp(-r M ) + Y,Rk,'d ' e x P(^w + 4m) keCiul exp(-rA r f) For r e QJhd, Sjhd Rjhd'Sr ~ exp(-r M ) + Z ^ • e x P(<^ + 4,/) keCu K o l l d ROM • exp(-r M ) + ^Ru,d • exp(Skcl + %m) keCiul (29) 137 (30) Similar to the derivation of the base model, we combine and rearrange (29) and (30) to obtain: Note that (31) is almost identical to (15) from the base model, except for the Rjhd/Rohd term. Upon the specification of \n(Rji,d/Roi,d), we can estimate (31) by OLS. \n(Rjhd/Roi,ti ) is essentially a correction factor for the overestimate of the expected utility for all available movie choices relative to the outside option. As discussed in section 2.2, an overestimate in the inclusive value over the movie choices is causing difficulty in distinguishing between cannibalization and market expansion. We also argued that the basic tenet of A R model is to introduce a correction factor into the systematic component of the utility. However, one should distinguish this basic tenet from the actual model derivation of our crowding model. In particular, note that the correction factor does not enter the systematic component directly. Instead, \n( RJM / ROM ) is derived from aggregating Uir over all product space dots for a specific choice alternative. In fact, i f we work backward from (30), we can deduce the utility for movie j starting in hour h on date d under our crowding model: Uijhd = 5jd + ln( Rjhd/Rohd ) +%jhd +£ijhd (32) Absent in Uyhd of the standard logit model (12), \n(Rji,d/Roi,d ) serves as a correction factor in the systematic utility component, which can correct for the overestimate when the inclusive value for all available movie choices is computed. We now discuss the specification of \n(Rji,d/Roi,d ). As mentioned earlier, to characterize the degree of crowding in the unobserved product space, we expect Rji,d/Roi,d will decrease with \n(sjhd) - \n(s0hd) = Thd + Sjd +ln( Rjl'd ) + %hd (31) Roiid 138 Jhd, the number of movie choices available in hour h on date d. We explore three different functional forms for this relation: Rjhd/Rohd = (Jhdy" (33a) Rji,d/Roi,ri = exp(ybl-Jhll) (33b) Rjhd/Rohd = exp(y c rJ/, r f + yc2- J/J) (33c) As Jhd is non-negative, the above three specifications can ensure that the logarithm of Rjhd/Rohd is well defined. Note that all three specifications incorporate the standard logit model as a special case. For (33a), when ya is zero, \n(Rji,d/Roi,d ) will become zero, reducing the model to a standard logit. Similarly, when ybi is zero or when y c / and yc2 are both zero, ln( Rji,d/Ro/,d ) will become zero for (33b) or (33c). By determining i f \n(Rji,d/Roi,d ) is zero, we can tell i f the addition of new movie choices will substitute the existing movie choices and the outside option equally. In other words, instead of a priori assuming equal cannibalization and market expansion, the crowding model can tell us i f this is an appropriate description of the data. 4. Data Description We calibrate the three demand models with two data sets from a multiplex movie theater in the Netherlands. The first data set records the admissions for 5,906 movie screenings during the first 15 weeks of 2001, from January 4 to April 18.8 The second data set spans from May 29, 2003 to June 9, 2004 (54 weeks) and records the admissions for 22,121 movie showings. As the second data set covers more than a whole year and contains a relatively large number of 8 We define admissions here as paid admissions only; because free admissions represent a totally different moviegoer behavior and free admissions are not substantial in our two data sets: free admissions for each movie showing on average comprise only 3.15% and 4.09% of total admissions in the first and second data sets. In fact, in both data sets, only around 20% of movie showings had free admissions at a level of more than 5% of the total admissions. 139 observations, we can afford reserving the last two weeks of observations for validation purposes. The second data set is therefore split into two: a 52-week calibration sample of 21,341 movie showings from May 29, 2003 to May 26, 2004; and a two-week validation sample of 780 movie showings from May 27 to June 9, 2004. Capacity constraint for each service offering and price variation across different offerings are two issues commonly encountered by pre-announced time schedule service providers when they optimize their time schedules. While critical to most service providers, these issues are relatively less important to the demand models of multiplex movie theaters. First, our multiplex movie theater in the Netherlands did not have many capacity-censored observations during the two observation windows for our data sets. Only 4.03% and 3.60% of movie showings in the first and second data sets had more than 90% utilization of their seating capacities.9 In fact, the mean utilization per movie showings is just 26.74% for the first data set and 25.71% for the second. Therefore, handling the factor of capacity-constrained attendance is not a priority concern in our demand models. Another issue common among other pre-announced time schedule service providers, but less so in multiplex movie theaters, is the price variation across different services offered. Similar to their counterparts in the U.S., our focal multiplex movie theater charges differential prices for showings starting in different time slots (e.g., matinees) and for moviegoers of different ages (e.g., senior discounts), but there is no differentiation of prices across different movie titles. As a result, the price variation is perfectly correlated with the outside option's time of day variation. Therefore, the price effect will be completely absorbed by the time of day effects in our demand models and there is no need to include any price variables. Note that this 9 Utilization is defined as the ratio of total admissions (i.e. sum of free and paid admission) to the total number of seats available. 140 is unique to the movie exhibitors. Demand models for other pre-announced schedule service providers typically must capture the pricing decision variables separately. As our three models are essentially share models, we need to transform the admissions totals to shares. The transformation takes two steps. First, we group movie showings by their starting hours. Each hour is defined as a choice occasion. Note that around 1 % of movie showings face another showing of the same title within one choice occasion (hourly period). Assuming multiple showings of the same titles are equivalent to perfectly correlated choice alternatives within a choice occasion, we therefore combine the admissions of the multiple showings into the admission of one choice alternative. After this combination, there are 5,856 "unique" movie showings in the first data set and 20,970 "unique" movie screenings in the second data set. Second, we obtain the shares of individual showings by dividing the admissions by the total number of potential moviegoers. We set the total potential market size equal to the average monthly admissions in our first sample, 73,962. The rationale is as follows. According to 2003 market statistics released by the Motion Picture Association in the U.S., 25% of the U.S. population aged 12 and over (accounting for 78% of total admissions) are frequent moviegoers, who visit theaters at least once per month. If we assume that the moviegoer behaviors in Amsterdam, where our focal movie theater is located, are similar to those in the U.S., the monthly total attendance in our multiplex theater should be a rough approximation for the "maximum" number of potential customers at any snapshot of time. To put this assumption into perspective, note that the population of Amsterdam over age ten in 2001 was 652,270, which is roughly nine times 73,962.10 Also note that there were movie showings in our two data sets with zero admissions, resulting in zero shares. As our three models require taking logarithm of the Different total market sizes have been tried and the estimation results are qualitatively similar. 141 shares, we replace these zeros with 1/73,962, which is equivalent to only one admission for the showing.11 Before discussing the estimation results of the three models, we first examine some patterns in our two data sets. Table-la, lb and lc show the admission per showing in the first data set by different hours of day, different days of week, and by different weeks. Table-2a-2g show the admission per showing by different hours of Sundays, Mondays, etc. As discussed in the model development section, these tables suggest the following patterns in the first data set: 1) 9pm appears to be the best time slot in which to start a movie. 2) Saturday and Sunday appear to be the best and second best days of the week. 3) The weeks covering spring vacation (Mar 3-Mar 11, 2001) and Easter weekend (Aprl3-16, 2001) appear to attract more people than other weeks. 4) As shown in Table-2a-2g, the time of day pattern (admission per showing increases as showings get closer to 9pm) is quite robust across different days of the week, except Sunday. In particular, Sunday afternoon appears to do better than Sunday evening. We therefore include a Sunday afternoon effect in the three models. For the calibration part of the second data set, Table-3a, 3b and 3c show the admission figures per showing by different hours of day, different days of week, and by different weeks; and Table-4a-4g show the admission per showing by different hours of Sundays, Mondays, etc. The following observations can be made: 1) Unlike in the first data set, 8pm appears to be the best time slot in which to start a movie. This inconsistency leads to an interesting question: Does the time of day preference shift from 2001 to 2004 or does the confounding between movie qualities and time preferences 1 1 We have tried replacing those zeros with other values and obtained similar estimation results. 142 appear more prevalent in one data set than the other? Our three models should be able to address this question. 2) Saturday and Sunday appear to be equally good. 3) The weeks covering Christmas vacation (Dec 20, 2003-Jan 4, 2004) appear to be the most preferred time to watch movies. On the other hand, some of the weeks covering summer vacation (June 28-Aug 31, 2003) appear to draw the lowest number of admissions. The holiday effects in the second data set are less apparent than those in the first data set. 4) Similar to the first data set, the time of day pattern (admission per showing increases as showings get closer to 8pm) is quite robust across different days of a week, except Sunday, in which the afternoon did as well as the evening. Once again, it suggests that a Sunday afternoon effect is very plausible. Examining Table-2a-2g or Table-4a-4g, one may wonder i f there is any variation in the number of movie choices in each hour across different days, since the numbers of showings in individual hours appear to be relatively constant across different days of the week. For example, Table-2a-2g show that 10pm appears to have the same number of showings on Sundays, Mondays, etc. This is an important concern, as the number of movie choices enters our crowding model as one of the explanatory variables. However, one should note from Table-lc or Table-3c that while the pattern of numbers of showings across different hours is relatively stable across different days of a week, the number of showings varies greatly across different weeks. Figure-1 and 2 show the weekly number of showings across different weeks in the two samples. As we can see, there is non-trivial variation in the number of showings across different weeks, and this weekly variation should help identify the parameters associated with the time of day effect and the crowding effect (i.e. numbers of movie choices in individual choice occasions). In fact, we may get a sense of how the admissions per showings vary with the number of movie 143 choices by examining the Pearson correlation between the admission per showings and the number of movie choices in individual hours. Such a correlation is 0.30 in the first data set and -0.10 in the second data set. While the second data set's correlation is in line with our expectation (more movie choices results in more cannibalization, resulting in lower admissions to each movie), the first data set suggests an opposite effect. This inconsistency further reinforces the need to study discrete choices using structural models like our three models, which control for the three layers of seasonality and the unobserved quality. Our three models control for unobserved movie quality with a pair of movie-specific parameters. In particular, i f we have more than a one-week observation for a movie, we estimate a movie-specific intercept, 6jt and a movie-specific weekly decay factor, A,/, otherwise we estimate only 9j. Note that some movie titles have versions in different languages. For example, 102 Dalmatians and 102 Dalmatiers are the same movie, but the first is in English and the second is in Dutch. To capture any subtle differences between these versions, we treat different versions of the same movie title as separate movies. Therefore, the first data set has 48 movie titles. Moreover, in the second data set, 64 movie showings (0.3% of all movie showings) are non-first run movie titles, and each of these movie titles were shown only once. As each of these "classic" movies essentially has only one observation, we cannot estimate the pair of movie-specific parameters. Assuming that these classic movies have by and large the same mean appeal to potential moviegoers, we group these movies as one unique movie title called "classics" and estimate one group-specific intercept, 6. As a result, for the second data set, the calibration part includes 147 movie titles plus a group of classics and the validation part adds three more titles. Two weather variables are hypothesized to affect the outside option. The first weather variable is the daily average temperature (in degrees Celsius) measured in De Bilt, the weather 144 station closest to Amsterdam. Another weather variable is the daily precipitation duration (in 0.1 hour) measured in De Bilt. Table-5 shows the summary statistics of these two variables in the first and second data sets. Figure-3, 4, 5 and 6 are the plots of these weather variables over the observation windows of the two data sets. Comparing the plots of the two data sets, we can see that the longer duration of the second data set allows more apparent weather trends, daily temperature in particular, to emerge. It suggests that the second data set should give a better sense of how the daily temperature affects the outside option. 5. Estimation Results We now discuss the estimation results of the three models developed in section 3. For comparison purposes, we also estimate some variants, which adopt Einav's (2003) specifications instead. First, in addition to allowing each movie title to have its own weekly decay rate, Aj, we follow Einav to develop some model variants by restricting all movie titles to have the same weekly decay rate. Second, as Einav captures the time of year seasonality using weekly parameters, we also estimate model variants that use weekly parameters instead of holiday parameters. Furthermore, to further explore the approaches used to distinguish cannibalization and market expansion effects, we also estimate a hybrid model that combines the features of both the nested logit and crowding models. Specifically, similar to the derivation of the crowding model, we assume that the choice probabilities of the hybrid model also depend on the degree of crowding in the unobserved product space, while the unobserved utility components are assumed to be distributed as in the nested logit model. Using Berry's (1994) inversion method, we can express the exploratory hybrid model as : 1 2 We set Rjhd I Rohd = (Jhljf as this is equal to the original specification used in Ackerberg and Rysman's (2002) additive model. 145 ln(s//w) - ln(j 0 M ) = T W + djd + (J-yAr\(Jhd) + a-\v\(sjhd\o») +£jM (34) As discussed in the previous section, we estimate different versions of the base and crowding models, (15) and (31), by OLS. This estimation approach is similar to the least square . estimation method put forward by Theil (1969). For the nested logit model as well as the hybrid model, as the conditional share, SJM\CM , is an endogenous variable to \n(sjhd) - \n(sohd), w e cannot estimate (24) or (34) by OLS. Instead, we introduce instrumental variables for spld\o«i and estimate (24) and (34) using the two-stage least square method. For movie fs observation in the choice occasion of hour h on date d, the instruments for Sj/,d\o„, are the percentages of competing I{k] movies in the choice occasion, —=^ , VA: These instruments are chosen because the percentages of competing movies in a choice occasion are certainly correlated with the conditional shares, sjhd\o..i, but should be independent of ^pld, the error specific to movie j. In fact, the instruments are statistically significant in the first stage of the two-stage least square estimation of (24) and (34), and Hausman's tests of exogeneity show that the conditional shares, Sjhd\a,i, are endogenous with these instruments.13 Note that when estimating the models, we set some parameters at zero for identification purposes. In the first data set, we chose Cast Away starting in the hour of 9pm on Saturday as the base case and set the corresponding parameters, OcasiAway, ®SA, and p9pm equal to zero. The intercept in (15), (31), (24) and (34) therefore becomes o)0 + <X>SA + P'jPm + &castAway and the estimates for other time of day, day of week and movie-specific parameters are indeed the differences between the corresponding weekdays, hours or titles and the base case. Similarly, in 1 3 We conducted a simpler version of Hausman's test of exogeneity (Greene 2002, p.385): we first regress sp^o-i on all the exogenous variables including the instruments and then regress \n(sJhd) - \n(snhd) on its explanatory variables (except the instruments) as well as the residual of the first regression. Testing i f the coefficient of the residual is significantly different from zero is equivalent to testing if SJ^CM is exogenous. In all of our nested logit and hybrid models, the coefficients of the residuals are statistically different from zero. 146 the second data set, we set the parameters associated with Classics starting in the hour of 8pm on Saturday as the base case. Table-6 reports the estimation results of six models using our first data set, January 4 -April 18, 2001. These six models are variants of the base and crowding models, which capture the time of year effect by holiday effects: Mil: The base model without the Sunday afternoon effect Ml2: The base model with the Sunday afternoon effect, which is exactly (15) Ml3: The crowding model with RJM/'ROM specified as (33a), (Ji,d)y" Ml4: The crowding model with RJM/ROM specified as (33b), Qxp(ybrJM) Ml5: The crowding model with Rjhd/Rohd specified as (33b), exp(ycj-Ji,d + ycj- Jhl) Ml6: The base model restricting the weekly decay rate to be the same for all movie titles, which is one of the features in Einav's (2003) specification We also test another feature of Eianv's specification, which is the capture of the time of year effect by weekly parameters. We replace the holiday effects in the above six models with the weekly parameters. Table-7 reports the estimation of these models using the first data set: M21: The base model without the Sunday afternoon effect M22: The base model with the Sunday afternoon effect M23: The crowding model with Rji,d/Roi,d specified as (33a), (JhdY" M24: The crowding model with Rji,d/Roi,d specified as (33b), exp(ybi-Ji,d) M25: The crowding model with Rjhd/Rohd specified as (33b), exp(yci-Ji,d + Id- Jhd1) M26: The base model with a movie-average weekly decay rate Finally, Table-8 reports the estimation results of the nested logit (IV!) and hybrid models (JV2) using the first data set. There are a total of 14 models for the first data set. Similarly, the same 147 14 models are estimated with the calibration part of the second data set, May29, 2003 - May 26, 2004. Table-9 and Table-10 report the estimation results of M11-M16 and M21-M26, respectively. Table-11 contains the results of IV 1 and IV2. Movie-specific Weekly Decay Rate For brevity of presentation, we do not report the estimation results of the movie-specific parameters. However, almost all of Xj estimates are negative i f they are significantly different from zero. Across M11-M16, IV1 and IV2, there is only one movie in the first data set and around ten movies in the second that have statistically positive weekly decay rates. However, all these movies are either left-censored.(the opening weeks are before the left end of our observation window, May 29, 2003) or family-oriented movies (e.g., Cheaper by the Dozen or Pokemon 4). As the targeted moviegoers for the family-oriented movies probably did not have an urgent need to see the movies during the release weeks, the corresponding decay rates may behave differently. We therefore argue that Mil-Ml 6, IV 1 and IV2 all give reasonable Xj estimates. On the other hand, as we will discuss later, the weekly effects in M21-M26 are likely to be confounded with the weekly decay rates, and therefore some estimated Xj have unexplainable positive signs. Time of Day effects: Good Movie or Nothing Better to Do? Our earlier examination of the raw data pattern suggests that the first and second data sets have two different best hours to start a movie. In particular, Table-1 shows that 9pm is the best hour from January to April 2001, while Table-3 shows that 8pm is the best hour from May 2003 to May 2004. However, these observations have not accounted for the possible uneven movie quality across different hours. It is not clear whether 9pm is an hour with many good movies or 148 i f 9pm has a low utility of outside option. As shown in Table-6-8, all models estimated with the first data set give a very consistent result, namely that 8pm is the most preferred hour for moviegoers to watch movies, a finding which is contradictory to the raw data pattern. In other words, by structurally disentangling the underlying time preference from unobserved varying movie quality, we now know that the high average admission per showing in the hour of 9pm is not due to the lowest outside option utility, but to better movies. Moreover, all structural models also show that the time of day effect increases as showings move towards the evening. On the other hand, consistent with the raw data pattern, all models in the second data set give a consistent result: 8pm is the best time slot and movie-watching becomes more attractive than the outside option as screenings move closer to the evening. Day of Week Effects A l l models in the first and second data sets give a very consistent result: Saturday is the best day of the week to watch movies and Sunday is usually as good as Saturday. This result is consistent with our earlier explanation that the opportunity cost of watching movies on the weekend is lower than that on weekdays. Sunday Afternoon Effect Also consistent with our earlier argument, all models in both data sets consistently demonstrate a Sunday afternoon effect. In fact, when we do not have S U N P M in both data sets (i.e. M l 1), Sunday appears to be statistically stronger than Saturday, which is not in line with the raw data pattern (Table-la and 3a). 149 Time of Year Effect There are two ways to capture the time of year effect, namely the holiday effects and the weekly effects. First, for the holiday effect approach (Ml 1-M16), models with the first data set give a very consistent result, namely positive effects from Christmas vacation, spring vacation and Easter weekend. While the spring vacation and Easter weekend results are as expected from the raw data pattern (Table-1 c), the Christmas vacation result is an effect uncovered only after controlling for the unobserved movie quality. In the second data set, all holidays are significantly positive, which is once again consistent with the raw data pattern (Table-3c). For the weekly effect approach (M21-M26), models with the first data set give some very unintuitive estimates of the weekly effects, namely a monotonically increasing time trend. The result may be due to the fact that we do not have replication of each week of a year (i.e. we do not observe the same holidays for several years in one continuous data set). Therefore, our weekly binaries are likely to confound somewhat with the weekly variation of unobserved movie quality. In particular, when we compare the estimated Xj of the holiday effect and weekly effect approaches in the first data set, we observe that the latter tends to be more negative than the former. Together with the increasing time trend associated with the weekly effect, the weekly effect approach may allow the models to have a more flexible pattern of decay, namely an up and down trend within a specific movie's theatrical run. Similarly, the weekly effects estimated with the second data set also lack face validity. For example, while the raw data pattern indicates that Christmas vacation (Week 30-32) should include the best weeks and the weeks of June 2003 (Week 3-4) should be relatively average weeks, the estimated weekly effects for the former turn out to be smaller than those for the 150 latter. While one may argue that this is the true seasonality, revealed after controlling for unobserved movie quality, there is no obvious way to test this conjecture. To evaluate another specification made by Einav (2003), we estimate models using a movie-average decay rate, Ml 6 and M26. While the models with holiday effects (Ml6) in both samples give a significantly negative AGE effect, the models with weekly effects (M26) give an insignificant AGE effect in the first data set and a significantly "positive" AGE effect in the second data set. As M26 is essentially Einav's specification with time of day and day of week effects added, it appears that Einav's specification is not appropriate to our data set.15 One reason may be that our data sets are not long enough to provide replication of individual weeks of a year. Weather Effects While daily precipitation duration consistently gives a significant positive effect in both samples, daily temperature is only significant in the second data set. The insignificance of daily temperature in the first data set may be due to our earlier postulation that the temperature pattern in the first data set is not as apparent as that of the second, which essentially covers the whole year of weather variation. Cannibalization vs. Market Expansion We now discuss the two approaches used to distinguish between the cannibalization and market expansion effects when a new movie choice is added to a choice occasion. As the weekly effect approach relatively lacks face validity, we focus hereafter on the holiday effect approach 1 4 Unlike the first data set, the,second data set does not demonstrate a clear monotonic trend in the weekly effect estimates, and there is no apparent pattern in the estimated Xj. 1 5 Of course, to begin with, the specification of constant decay is overly strong and counterintuitive. 151 (M13-M15, IV! and IV2). The crowding models can be discussed (M13-M15) first. For the first data set, the number of movie choices is insignificant in all three specifications of the crowding models, Ml 3- Ml 5. For the second data set, while the number of movie choices is insignificant in the log form (Ml3), it has a significant negative sign in the linear form (Ml4). Probably due to increased multicolinearity, when the number of movie choices is in quadratic form (Ml5), only the squared term is significantly negative at the 10% level. As discussed earlier, when \n(Rjii(i/Roiid ) is close to zero, the crowding model is close to a standard logit model, suggesting that a new movie choice added to a choice occasion would substitute toward other movie choices and the outside option equally. Apparently, our first data set is more in line with the IIA implied by a standard logit model. On the other hand, while still relatively close to zero, the significant negative ln( Rjiid/Roiui) for some specifications in the second data set suggests that when a new movie choice is added, cannibalization tends to be slightly greater than the magnitude suggested by a standard logit model. Do the nested logit models suggest a similar pattern? Examining IV 1 of Table-8 and Table-11, we can see that the estimated nesting parameters, cr, are statistically larger than zero in both data sets, but still not very large. As discussed earlier, when cr is close to zero, the nested logit model is similar to a standard logit model. Somewhat in line with the results of the crowding models, the relatively small cr estimates in both data sets suggest that new movie showings would substitute more towards other movie showings than towards the outside option, but the effect is not very large. Finally, we examine the hybrid models (IV2 in Table-8 & Table-11). In both data sets, the sign of ln(no. of movie choices) now becomes positive. At first glance, it appears to suggest a "variety effect" (new choice alternatives increase the utility of existing choice alternatives), rather than cannibalization. However, we also need to consider cr. In fact, the estimated cr in IV2 152 are larger than the estimated cr in the pure nested Logit model IV 1, suggesting more cannibalization within the movie choice nest in IV2. Apparently, the positive coefficient of ln(no. of movie choices) compensates for this larger estimated cr. Figure-7 shows the predicted share of a base case movie showing when the same base case movie continues to be added to the choice occasion. The predictions are made by four models, namely the base model, Ml2; the nested logit, IV 1; the crowding model, Ml3; and the hybrid model, IV2; on the basis of the second data set estimation results. As the base model is a standard logit, which cannot distinguish the cannibalization and market expansion effect, it is not surprising to see that it gives approximately a horizontal straight line. Moreover, as expected, the nested logit and crowding models predict the share of admissions for a movie showing to decrease as more choice alternatives are added. However, it is interesting to note that the hybrid model also has a downward-sloping curve in Figure-7, suggesting that the larger estimated cr dominates the effect of positive coefficient of ln(no. of movie choices). In fact, i f we compare the curves of the three non-standard logit models, we can see that, 1) the crowding model's curve is relatively flat; 2) the nested logit has the largest slope, especially moving from one to two showings; and 3) the hybrid model has both of the above features, namely a large slope when the choice set is small and a trend toward relative flatness afterward (essentially overlapping with the crowding model's curve, beyond seven showings). This suggests that the positive coefficient of ln(no. of movie choices) in IV2 is more likely to increase the flexibility of the model in terms of characterizing the data pattern than to result in a variety effect. Let us further examine how our four models (Ml 2, IV 1, Ml 3 and IV2) respond to the variation in choice set size. Figure-8 shows individual models' predicted total share of all showings of the base case movie when the choice set size increases. As we can see, all four models predict that the total share of all movie showings will increase as the number of movie 153 showings in an hour increases. As expected, the standard logit (Ml2) predicts a larger market expansion effect than the other three models, which are designed to better distinguish between the cannibalization and market expansion effects. Another observation from Figure-8 is that the market expansion effect predicted by the standard logit does not diminish as fast as that in other models when the choice set size increases. We can see this more clearly from Table-12, which shows the four models' predicted incremental share changes in situations with an additional showing. As we can see, the standard logit model predicts very similar incremental gains in the group share, regardless of choice set size. Moreover, i f we compare the models' predicted incremental gains of group shares from one to two showings and those from seven to eight showings, we can see that the incremental gains predicted by the other three models are diminishing at a faster rate than those of the standard logit model. This suggests that the standard logit tends to overestimate the gain resulting from the addition of extra showings, especially when the choice set is already large. On the other hand, we observe a similar pattern when examining the changes in individual shares: the standard logit model does not predict as much diminishment of individual share losses as the other three models when the choice set size increases. If we combine the patterns of both individual shares and group shares, we see the following: 1) the standard logit model predicts that the marginal effect of adding a new movie choice to a choice set is rather insensitive to the total choice set size; and 2) the other three models predict that as a choice set increases, each extra showing will create less impact on the outside option and individual movie choices. Predictive Performance Given that the base model has such a good fit to the data (as indicated by the high R ), there is a limit as to how much model discrimination we can obtain. In fact, when examining the 154 model fitness criteria such as AIC and BIC, it appears that the models are similar in terms of fit. Following the tradition established by Guadagni and Little (1983), we therefore examine how these models perform in the validation part of the second data set, May 27, 2004-June 9, 2004. In order to obtain the movie-specific parameters for movies that were newly released or had just entered their second week in the validation sample, the models were first estimated in a sample combining both the calibration and validation parts. The new movies' parameters were then inserted into the models calibrated with only the calibration sample to generate predictions for the validation period. Note that the results using such a combined sample are in line with the results of only the calibration sample. Except for the movie-specific parameters of movies new to the validation data set, all models use the estimates reported earlier to generate predictions. For M21-M26, because the validation sample approximately covers the same time of year as the first two weeks of the calibration sample, we use the first two of the 52 weekly parameter estimates to generate the predictions. Table-13 reports the mean absolute error (MAE), mean absolute percentage error (MAPE) and root mean squared error (RMSE) of the 14 models in the validation sample. As noted earlier, the models using weekly parameters (M21-M26) do not give parameter estimates with high face validity. In fact, as shown in Table-13, they also give very large errors, relative to the models using holiday effects. Therefore, models with weekly parameters are not the preferred approach for capturing time of year seasonality in our context. Among models using holiday effects, the models with the nesting parameter, <r(i.e. nested logit and hybrid), tend to have the lowest error levels, but the results are generally close. This is probably due to the fact that the cannibalization-correction parameters in the crowding model and the nested logit model, y and cr, are not very different from zero, meaning all these models are largely similar to the base model. 155 6. Concluding Remark We have successfully disentangled the time of day and day of week effects from the unobserved movie quality. In particular, simply by examining average admission per showing starting in different hours, we find that our two samples give different answers regarding the best time slot in which to start a movie: 9pm in the first data set vs. 8pm in the second data set. However, once we control for the unobserved movie quality using our models, 8pm is revealed as the best hour in both data sets. More importantly, at least from a substantive viewpoint, the time effects are relatively consistent across the two data sets, although magnitude may vary. This essay extends Einav's work in three ways. First, our focus is studying two more micro levels of seasonality, time of day and day of week, while shedding light on yearly seasonality. Second, allowing a more flexible weekly decay for the unobserved movie quality improves the seasonality estimates. Third, we begin to examine the issue of choice set variation by comparing two approaches, namely the nested logit and Ackerberg & Rysman's specification. We provide a unifying framework for examining those two approaches, while Ackerberg and Rysman motivated their model in an independent manner. Both approaches suggest that our two data sets should have slightly more cannibalization than those suggested by the standard logit when new movie choices are added to an hour. Although the effects are relatively small in magnitude, they suggest that a standard logit model is insufficient for both data sets. Further research could examine both the absolute and relative importance of expansion and cannibalization at other time intervals. In fact, one should note that this pattern may be limited by our assumption of choice occasion. For clean demonstration of our models, the present study simply defines a choice occasion as one hour. Further research efforts should relax this assumption. For example, by defining a choice occasion as a day or a week, the demand models need to be extended to capture another aspect of moviegoers' behaviors, for example substitution 156 between a screening of Star Wars Episode III on Monday at 7pm and a showing on Saturday at 11am. The demand models developed in this essay can be used by managers. They can serve as a diagnostic tool to help managers understand the time preferences of potential moviegoers. Further research can take one further step by modifying the demand models for decision optimization purposes like MMSS. In particular, new models should address the challenges of generating movie-specific parameters for forthcoming or new movies. Moreover, further research should go beyond data sets from multiplex movie theaters. 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Cleveland (1984), "Seasonal Adjustment of the Weekly Monetary Aggregates: A Model-based Approach," Journal of Business and Economic Statistics, 2(3), 260-270 158 Sawhney, Mohanbir S., and Jehoshua Eliashberg (1996), " A parsimonious model for forecasting gross box-office revenues of motion pictures," Marketing Science, 15(2), 113-131 Swami, Sanjeev, Jehoshua Eliashberg and Charles B. Weinberg (1999), "SilverScreener: A Modeling Approach to Movie Screens Management," Marketing Science, 18(3), 352-372 Train, Kenneth (2001), Discrete Choice Methods with Simulation, Cambridge University Press Wierenga, Berend and Gerrit van Bruggen (2000), Marketing Management Support Systems, Kluwer Academic Publishers 159 Table-la: Admission per Showing in Different Time of Day (Jan 4, 2001-Apr 18, 2001) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 11am 311 3301 10.61 12pm 619 7560 12.21 1pm 465 10788 23.20 2pm 512 19048 37.20 3pm 534 20810 38.97 4pm 472 18618 39.44 5pm 261 5952 22.80 6pm 763 50469 66.15 7pm 518 31313 60.45 8pm 252 18232 72.35 9pm 820 93045 113.47 10pm 329 16857 51.24 Table-lb: Admission per Showing in Different Day s of Week (Jan 4, 2001 - Apr 18 No. of Total Admission Showings available on: Showings Admission per Showing SUN 840 56893 67.73 M O N 835 27968 33.49 TUE 831 26776 32.22 WED 841 32428 38.56 T H U 835 39652 47.49 FRI 834 48146 57.73 SAT 840 64130 76.35 Table-lc: Admission per Showing in Different Weeks (Jan 4, 2001 --Apr 18, 2001) No. of Total Admission Showings available between: Showings Admission per Showing 4-Jan-01 10-Jan-01 410 18463 45.03 ll-Jan-01 17-Jan-01 378 17716 46.87 18-Jan-01 24-Jan-01 388 18814 48.49 25-Jan-01 31-Jan-01 385 17426 45.26 l-Feb-01 7-Feb-01 378 15915 42.10 8-Feb-01 14-Feb-01 393 19641 49.98 15-Feb-01 2l-Feb-01 400 19986 49.97 22-Feb-01 28-Feb-01 397 25258 63.62 l-Mar-01 • 7-Mar-01 392 26613 67.89 8-Mar-01 14-Mar-01 376 21433 57.00 15-Mar-01 2 l-Mar-01 399 17531 43.94 22-Mar-01 28-Mar-01 397 19310 48.64 29-Mar-01 4-Apr-01 395 18887 47.82 5-Apr-01 ll-Apr-01 385 17042 44.26 12-Apr-01 18-Apr-01 383 21958 57.33 , 2001) 160 Table-2a: Admission per Showing in Different Time of Day on Sunday (Jan 4, 2001 -18, 2001) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 1 lam 46 716 15.57 12pm 89 1678 18.85 1pm 65 2740 42.15 2pm 73 5782 79.21 3pm 78 6605 84.68 4pm 68 6180 90.88 5pm 38 1774 46.68 6pm 109 11340 104.04 7pm 74 5106 69.00 8pm 36 2313 64.25 9pm 117 11337 96.90 10pm 47 1322 28.13 Table-2b: Admission per Showing in Different Time of Day on Monday (Jan 4, 2001 18, 2001) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 1 lam 43 357 8.30 12pm 89 836 9.39 1pm 67 1118 16.69 2pm 74 1924 26.00 3pm 75 2011 26.81 4pm 67 1566 23.37 5pm 37 536 14.49 6pm 109 5140 47.16 7pm 74 3019 40.80 8pm 36 1733 48.14 9pm 117 8568 73.23 10pm 47 1160 24.68 Table-2c: Admiss ion per Showing in Different T ime of Day on Tuesday (Jan 4, 2001 - A p r 18, 2001) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 1 lam 43 451 10.49 12pm 87 794 9.13 1pm 68 999 14.69 2pm 72 1418 19.69 3pm 75 1572 20.96 4pm 67 1161 17.33 5pm 36 382 10.61 6pm 109 4651 42.67 7pm 74 3189 43.09 8pm 36 2063 57.31 9pm 117 8869 75.80 10pm 47 1227 26.11 Table-2d: Admiss ion per Showing in Different T ime of Day on Wednesday (Jan 4, 2001 -A p r 18, 2001) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 1 lam 46 459 9.98 12pm 90 819 9.10 1pm 63 1242 19.71 2pm 74 2412 32.59 3 pm 78 2036 26.10 4pm 68 1577 23.19 5pm 38 539 14.18 6pm 109 5482 50.29 7pm 74 3715 50.20 8pm 36 2318 64.39 9pm 118 10359 87.79 10pm 47 1470 31.28 162 Table-2e: Admiss ion per Showing in Different T ime of Day on Thursday (Jan 4, 2001 -A p r 18, 2001) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 11am 44 461 10.48 12pm 87 1138 13.08 1pm 69 1650 23.91 2pm 73 2107 28.86 3 pm 75 2268 30.24 4pm 67 1901 28.37 5pm 37 559 15.11 6pm 109 6489 59.53 7pm 74 4697 63.47 8pm 36 2648 73.56 9pm 117 13400 114.53 10pm 47 2334 49.66 Table-2f: Admiss ion per Showing in Different T ime of Day on F r iday (Jan 4, 2001 2001) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 1 lam 43 548 12.74 12pm 88 1291 14.67 1pm 68 1674 24.62 2pm 73 2523 34.56 3 pm 75 2606 34.75 4pm 67 2231 33.30 5pm 37 707 19.11 6pm 109 6601 60.56 7pm 74 4727 63.88 8pm 36 3093 85.92 9pm 117 18388 157.16 10pm 47 3757 79.94 Table-2g: Admission per Showing in Different Time of Day on Saturday (Jan 4, 2001 18, 2001) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 11 am 46 309 6.72 12pm 89 1004 11.28 1pm 65 1365 21.00 2pm 73 2882 39.48 3pm 78 3712 47.59 4pm 68 4002 58.85 5pm 38 1455 38.29 6pm 109 10766 98.77 7pm 74 6860 92.70 8pm 36 4064 112.89 9pm 117 22124 189.09 10pm 47 5587 118.87 Table-3a: Admission per Showing in Different Time of Day (May 29, 2003 - May 26, 2004) Showings starting in the hour of: No. of Showings Total Admission Admission per Showing 10am 738 9848 13.34 1 lam 914 15439 16.89 12pm 1944 34006 17.49 1pm 1943 52755 . 27.15 2pm 1677 58236 34.73 3 pm 1883 77134 40.96 4pm 1899 67949 35.78 5pm 1309 46004 35.14 6pm 2203 103620 47.04 7pm 1751 102590 58.59 8pm 1133 108128 95.44 9pm 2715 223844 82.45 10pm 861 43976 51.08 Table-3b: Admission per Showing in Different Days of Week (May 29, 2003 - May Showings available on: No. of Showings Total Admission Admission per Showing SUN 3240 184928 57.08 M O N 2903 93878 32.34 T U E 2887 102036 35.34 WED 2888 98381 34.07 T H U 2904 124309 42.81 FRI 2891 148851 51.49 SAT 3257 191146 58.69 26, 2004) 165 Table-3c: Admission per Showing in Different Weeks (May 29, 2003 - May 26, 2004) No. of Total Admission Showings available between: Showings Admission per Showing 29-May-03 4-Jun-03 410 9995 24.38 5-Jun-03 ll-Jun-03 400 13804 34.51 12-Jun-03 18-Jun-03 404 11506 28.48 19-Jun-03 25-Jun-03 410 16028 39.09 26-Jun-03 2-M-03 424 15699 37.03 3-Jul-03 9-M-03 460 17119 37.22 10-Jul-03 16-M-03 434 10983 25.31 17-Jul-03 23-M-03 463 14036 30.32 24-Jul-03 30-M-03 440 18123 41.19 31-Jul-03 6-Aug-03 469 11052 23.57 7-Aug-03 13-Aug-03 465 11348 24.40 14-Aug-03 20-Aug-03 437 17193 39.34 21-Aug-03 27-Aug-03 406 22668 55.83 28-Aug-03 3-Sep-03 415 18661 44.97 4-Sep-03 10-Sep-03 394 14330 36.37 ll-Sep-03 17-Sep-03 396 17625 44.51 18-Sep-03 24-Sep-03 402 12969 32.26 25-Sep-03 l-Oct-03 399 15471 38.77 2-Oct-03 8-Oct-03 390 14904 38.22 9-Oct-03 15-Oct-03 453 25577 56.46 16-Oct-03 22-Oct-03 430 18937 44.04 23-Oct-03 29-Oct-03 394 14674 37.24 30-Oct-03 5-Nov-03 415 13870 33.42 6-Nov-03 12-Nov-03 373 18687 50.10 13-Nov-03 19-Nov-03 379 13624 35.95 20-Nov-03 26-Nov-03 332 25638 77.22 27-Nov-03 3-Dec-03 369 26497 71.81 4-Dec-03 10-Dec-03 356 20964 58.89 ll-Dec-03 17-Dec-03 364 19256 52.90 18-Dec-03 24-Dec-03 400 33496 83.74 25-Dec-03 31-Dec-03 398 36273 91.14 l-Jan-04 7-Jan-04 364 26801 73.63 8-Jan-04 14-Jan-04 340 21422 63.01 15-Jan-04 21-Jan-04 351 19921 56.75 22-Jan-04 28-Jan-04 361 18691 51.78 29-Jan-04 4-Feb-04 385 22957 59.63 5-Feb-04 ll-Feb-04 370 21031 56.84 12-Feb-04 18-Feb-04 388 19893 51.27 19-Feb-04 25-Feb-04 391 19258 49.25 26-Feb-04 3-Mar-04 389 23663 60.83 4-Mar-04 10-Mar-04 403 19451 48.27 ll-Mar-04 17-Mar-04 388 14765 38.05 18-Mar-04 24-Mar-04 410 15031 36.66 Table-3c (continued): Admission per Showing in Different Weeks (May 29, 2003 - May 2004) No. of Total Admission Showings available between: Showings Admission per Showing 25-Mar-04 31-Mar-04 409 14587 35.67 l-Apr-04 7-Apr-04 405 16802 41.49 8-Apr-04 14-Apr-04 428 18654 43.58 15-Apr-04 21-Apr-04 419 11517 27.49 22-Apr-04 28-Apr-04 412 13762 33.40 29-Apr-04 5-May-04 430 19201 44.65 6-May-04 12-May-04 448 20265 45.23 13-May-04 19-May-04 387 16391 42.35 20-May-04 26-May-04 411 18459 44.91 Table-4a: Admission per Showing in Different Time of Day on Sunday (May 29, 2003 -May 26, 2004) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 10am 216 4267 19.75 1 lam 269 7215 26.82 12pm 269 7984 29.68 1pm 279 11968 42.90 2pm 244 14854 60.88 3 pm 267 21944 82.19 4pm 273 20189 73.95 5pm 191 12939 67.74 6pm 311 22124 71.14 7pm 251 17716 70.58 8pm 165 14529 88.05 9pm 382 24578 64.34 10pm 123 4621 37.57 Table-4b: Admission per Showing in Different Time of Day on Monday (May 29, 2003 -May 26, 2004) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 10am 65 750 11.54 1 lam 76 855 11.25 12pm 285 3819 13.40 1pm 274 5653 20.63 2pm 237 5572 23.51 3 pm 271 7152 26.39 4pm 271 6106 22.53 5pm 185 3850 20.81 6pm 318 10695 33.63 7pm 249 11160 44.82 8pm 132 10695 81.02 9pm 420 23761 56.57 10pm 120 3810 31.75 168 Table-4c: Admission per Showing in Different Time of Day on Tuesday (May 29, 2003 -May 26, 2004) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 10am 57 • 774 13.58 11am 66 982 14.88 12pm 286 4134 14.45 1pm 272 6335 23.29 2pm 240 6619 27.58 3 pm • 268 7207 26.89 4pm 270 6092 22.56 5pm 187 4222 22.58 6pm 314 11617 37.00 7pm 252 12554 49.82 8pm 168 13920 82.86 9pm 384 23699 61.72 10pm 123 3881 31.55 Table-4d: Admission per Showing in Different Time of Day on Wednesday (May 2i May 26, 2004) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 10am 58 748 12.90 1 lam 63 719 11.41 12pm 287 4157 14.48 1pm 279 6562 23.52 2pm 246 7452 30.29 3pm 271 8162 30.12 4pm 277 5747 20.75 5pm 186 4038 21.71 6pm 315 10725 34.05 7pm 245 11294 46.10 8pm 167 13217 79.14, 9pm 377 22284 59.11 10pm 117 3276 28.00 Table-4e: Admission per Showing in Different Time of Day on Thursday (May 29, 2003 -May 26, 2004) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 10am 59 539 9.14 1 lam 77 987 12.82 12pm 277 4534 16.37 1pm 280 6816 24.34 2pm 237 7199 30.38 3 pm 270 8385 31.06 4pm 273 7436 27.24 5pm 186 5319 28.60 6pm 315 13526 42.94 7pm 251 14836 59.11 8pm 169 16175 95.71 9pm 384 32907 85.70 10pm 126 5650 44.84 Table-4f: Admission per Showing in Different Time of Day on Friday (May 29, 2003 - May 26, 2004) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 10am 65 763 11.74 11am 81 1095 13.52 12pm 271 5155 19.02 1pm 279 8327 29.85 2pm 231 7826 33.88 3 pm 266 10019 37.67 4pm 265 8765 33.08 5pm 184 5856 31.83 6pm 318 14772 46.45 7pm 252 15515 61.57 8pm 167 18518 110.89 9pm 386 42936 111.23 10pm 126 9304 73.84 170 Table-4g: Admission per Showing in Different Time of Day on Saturday (May 29, 2003 May 26, 2004) No. of Total Admission Showings starting in the hour of: Showings Admission per Showing 10am 218 2007 9.21 1 lam 282 3586 12.72 12pm 269 4223 15.70 1pm 280 7094 25.34 2pm 242 8714 36.01 3pm 270 14265 52.83 4pm 270 13614 50.42 5pm 190 9780 51.47 6pm 312 20161 64.62 7pm 251 19515 77.75 8pm 165 21074 127.72 9pm 382 53679 140.52 10pm 126 13434 106.62 Table-5: Summary of Weather Variables Data Set 1: January 4, 2001 - April 18, 2001 Daily Average Temperature (Degree Celsius) Daily Precipitation Duration (0.1 Hour) Mean 4.61 25.84 Standard Deviation 3.75 35.56 Maximum 14.40 174.00 Minimum -4.80 00.00 Data Set 2: May 29, 2003 - May 26, 2004 Daily Average Temperature (Degree Celsius) Daily Precipitation Duration (0.1 Hour) Mean 10.57 15.00 Standard Deviation 6.46 29.00 Maximum 25.70 228.00 Minimum -3.80 0.00 172 Table-6: Models with Holiday variables (Jan 4,2001 Apr 18, 2001) Model Mil M12 M13 Ml 4 M15 Ml 6 R-Square 0.7593 0.7717 0.7717 0.7718 0.7718 0.7407 Adj R-Sq 0.7547 . 0.7673 0.7673 0.7673 0.7673 0.7376 N 5856 5856 5856 5856 5856 5856 AIC -0.8853 -0.9379 -0.9375 -0.9377 -0.9375 -0.8242 BIC -0.7588 -0.8102 -0.8087 -0.8089 -0.8076 -0.7421 Parameter Parameter Parameter Parameter Parameter Parameter Variable Estimate Pr>|t| Estimate Pr> |t| Estimate Pr> |t| Estimate Pr>|t| Estimate Pr>|t| Estimate Pr>|t| Intercept -5.22 <.0001 -5.17 <0001 -5.15 <.0001 -5.10 <.0001 -5.16 <.0001 -5.40 <.0001 1 lam -2.71 <.0001 -2.71 <0001 -2.72 < 0001 -2.75 <.0001 -2.76 <0001 -2.65 <.0001 12pm -2.13 <.0001 -2.13 <.0001 -2.13 <.0001 -2.15 <.0001 -2.17 <.0001 -2.20 <0001 1pm -1.54 <0001 -1.54 <0001 -1.54 <0001 -1.57 <0001 -1.59 <.0001 . -1.52 <0001 2pm -1.13 <0001 -1.24 <.0001 -1.25 <.0001 -1.27 <.0001 -1.29 <0001 -1.28 <.0001 3 pm -1.03 <0001 -1.14 <.0001 -1.15 < 0001 -1.17 <0001 -1.19 <.0001 -1.20 <0001 4pm -1.11 <0001 -1.23 <.0001 -1.24 <.0001 -1.26 <0001 -1.28 <.0001 -1.24 <0001 5 pm -1.14 < 0001 -1.26 <.0001 -1.27 <.0001 -1.31 <0001 -1.31 <.0001 -1.32 <0001 6pm -0.54 <.0001 -0.66 <.0001 -0.66 < 0001 -0.66 <.0001 -0.67 <0001 -0.72 < 0001 7pm -0.27 <.0001 -0.27 <0001 -0.28 < 0001 -0.30 <.0001 -0.32 < 0001 -0.31 <0001 8pm 0.25 <.0001 0.25 <.0001 0.23 0.0008 0.20 0.0070 0.20 0.0071 0.13 0.0128 10pm -0.36 <0001 -0.36 <.0001 -0.38 <.0001 -0.41 <0001 -0.42 <.0001 -0.45 <0001 SUNPM 0.82 <0001 0.82 < 0001 0.82 <.0001 0.82 <0001 0.82 <.0001 M O N -0.78 <0001 -0.78 <0001 -0.78 <.0001 -0.78 <.0001 -0.78 <0001 -0.79 <.0001 TUE -0.75 <0001 -0.75 <.0001 -0.75 <.0001 -0.75 <.0001 -0.75 <.0001 -0.77 <0001 W E D -0.52 <.0001 -0.52 <.0001 -0.52 <.0001 -0.52 < 0001 -0.52 <0001 -0.53 <.0001 T H U -0.47 • <.0001 -0.47 <.0001 -0.47 <.0001 -0.47 < 0001 -0.47 <0001 -0.47 <.0001 FRI -0.25 <.0001 -0.25 <0001 -0.25 <.0001 -0.25 <0001 -0.25 <0001 -0.25 <.0001 SUN 0.07 0.0187 -0.29 <.0001 -0.29 <0001 -0.29 < 0001 -0.29 <0001 -0.29 <0001 Temperature 0.00 0.2378 0.00 0.2385 0.00 0.2378 0.00 0.2368 0.00 0.2321 0.00 0.1143 Precip. Duration 0.00 <.0001 0.00 <.0001 0.00 . <0001 0.00 <0001 0.00 <.0001 0.00 <.0001 Easter Weekend 0.57 <0001 0.57 <.0001 0.57 <.0001 0.57 <.0001 0.57 < 0001 0.41 <0001 Spring Vacation 0.31 <0001 0.32 <0001 0.32 <.0001 0.31 <.0001 0.31 <.0001 0.44 < 0001 Xmas Vacation 0.77 <.0001 0.77 <.0001 0.77 <.0001 0.77 < 0001 0.77 <.0001 0.53 <.0001 ln(N MOVIE) -0.01 0.7330 N MOVIE -0.01 0.3113 0.02 0.5268 N M O V I E 2 0.00 0.3263 A G E -0.17 <.0001 173 Table-7: Models with Weekly variables (Jan 4, 2001 Apr 18, 2001) Model M21 M22 M23 M24 M25 M26 R-Square 0.7616 0.7740 0.7740 0.7740 0.7740 0.7398 Adj R-Sq 0.7566 0.7692 0.7691 0.7691 0.7691 0.7361 N 5856 5856 5856 5856 5856 5856 AIC -0.8910 -0.9440 -0.9436 -0.9437 -0.9434 -0.8168 BIC -0.7520 -0.8038 -0.8023 -0.8024 -0.8010 -0.7222 Parameter Parameter Parameter Parameter Parameter Parameter Variable Estimate Pr> |t| Estimate Pr>|t| Estimate Pr> |t| Estimate Pr> |t| Estimate Pr> |t| Estimate Pr> |t| Intercept -4.23 <0001 -4.16 <.0001 -4.15 <.0001 -4.11 <.0001 -4.16 <0001 -5.00 <0001 1 lam -2.70 <0001 -2.69 <0001 -2.70 <.0001 -2.73 <.0001 -2.73 <0001 -2.65 <.0001 12pm -2.11 <.0001 -2.11 <.0001 -2.11 <0001 -2.12 <.0001 -2.13 <0001 -2.20 <.0001 1pm -1.54 <0001 -1.54 <.0001 -1.55 <.0001 -1.57 <.0001 -1.58 <0001 -1.51 <.0001 2pm -1.10 <0001 -1.21 <.0001 -1.22 <.0001 -1.23 <.0001 -1.25 <0001 -1.28 <.0001 3pm -1.01 <.0001 -1.13 <.0001 -1.13 <0001 -1.15 <0001 -1.17 <.0001 -1.20 <0001 4pm -1.11 < 0001 -1.23 <0001 -1.23 <0001 -1.25 <.0001 -1.26 <.0001 -1.23 <.0001 5pm -1,10 <0001 -1.22 <0001 -1.23 <0001 -1.26 <.0001 -1.26 <.0001 -1.32 <.0001 6pm -0.55 <.0001 -0.67 <.0001 -0.67 <.0001 -0.67 <.0001 -0.68 <0001 -0.72 <.0001 7pm -0.23 <.0001 -0.23 <.0001 -0.24 <0001 -0.25 <0001 -0.27 <0001 -0.31 <0001 8pm 0.23 <.0001 0.23 <.0001 0.22 0.0013 0.19 0.0079 0.19 0.0080 0.12 0.0188 10pm -0.31 <0001 -0.31 <0001 -0.32 <,0001 -0.34 <.0001 -0.35 <.0001 -0.45 <.000i S U N P M 0.82 <.0001 0.82 <.0001 0.82 <.0001 0.82 <0001 0.82 <.0001 M O N -0.87 <0001 -0.87 <0001 -0.87 < 0001 -0.87 <.0001 -0.87 <.0001 -0.88 <.0001 T U E -0.86 <.0001 -0.86 <.0001 -0.86 <.0001 -0.86 <0001 -0.86 <0001 -0.87 <0001 W E D -0.64 <.0001 -0.64 <.0001 -0.64 <.0001 -0.64 <.0001 -0.64 <0001 -0.64 <0001 T H U -0.54 <0001 -0.54 <0001 -0.54 <0001 -0.54 <.0001 -0.54 <0001 -0.54 <.0001 FRI -0.28 <.0001 -0.28 <.0001 -0.28 <.0001 -0.28 <.0001 -0.28 <0001 -0.29 <0001 SUN 0.05 0.0818 -0.30 <.0001 -0.30 <.0001 -0.30 <.0001 -0.30 <.0001 -0.30 <0001 Temperature 0.00 <0001 0.00 <0001 0.00 <0001 0.00 <.0001 0.00 <0001 0.00 <.0001 Precip. Duration 0.00 <0001 0.00 <,0001 0.00 <.0001 0.00 <.0001 0.00 <0001 0.00 <0001 Week 1 -1.31 0.3846 -1.34 0.3608 -1.34 0.3616 -1.33 0.3668 -1.31 0.3715 -0.76 0.6250 Week 2 -1.26 0.2655 -1.28 0.2443 -1.28 0.2448 -1.27 0.2482 -1.26 0.2515 -0.74 0.5229 Week 3 -0.86 0.2565 -0.87 0.2346 -0.87 0.2352 -0.87 0.2385 -0.86 0.2417 -0.50 0.5167 Week 4 -0.25 0.5085 -0.26 0.4823 -0.26 0.4831 -0.26 0.4869 -0.26 0.4888 -0.10 0.8030 Week 6 0.45 0.2415 0.45 0.2205 0.45 0.2208 0.45 0.2251 0.44 0.2330 0.28 0.4811 Week 7 1.04 0.1695 1.06 0.1516 1.06 0.1518 1.05 0.1546 1.04 0.1600 0.67 0.3910 Week 8 1.76 0.1197 1.78 0.1053 1.78 0.1054 1.77 0.1074 1.76 0.1110 1.04 0.3674 Week 9 2.51 0.0956 2.55 0.0828 2.54 0.0829 2.53 0.0846 2.51 0.0875 1.48 0.3375 Week 10 2.82 0.1351 2.86 0.1194 2.86 0.1196 2.84 0.1220 2.81 0.1257 1.31 0.4958 Week 11 3.51 0.1205 3.56 0.1057 3.56 0.1059 3.54 0.1077 3.52 0.1104 1.47 0.5254 Week 12 4.28 0.1046 4.34 0.0911 4.34 0.0913 4.32 0.0929 4.29 0.0954 1.62 0.5485 Week 13 5.05 0.0945 5.11 0.0819 5.11 0.0820 5.09 0.0834 5.05 0.0856 1.77 0.5664 174 Table-7 (Continued): Models with Weekly variables (Jan 4, 2001 - Apr 18, 2001) Model M21 M22 M23 M24 M25 M26 Parameter Parameter Parameter Parameter Parameter Parameter Variable Estimate Pr> |t| Estimate Pr> |t| Estimate Pr> |t| Estimate Pr>|t| Estimate Pr> |t| Estimate Pr> |t| Week 14 6.03 0.0761 6.10 0.0651 6.10 0.0653 6.07 0.0666 6.03 0.0685 2.12 0.5413 Week 15 7.26 0.0547 7.34 0.0459 7.34 0.0460 7.31 0.0470 7.26 0.0484 2.65 0.4932 ln(N MOVIE) -0.01 0.8877 N MOVIE -0.01 0.4943 0.01 0.6606 N M0VIE2 0.00 0.4997 AGE -0.42 0.2823 175 Table-8: Nested Logi t Models wii th Hol iday variables Model IV1 IV2 R-Square 0,7969 0.8061 Adj R-Sq 0.7930 0.8023 N 5856 5856 AIC -1.0859 -1.1429 BIC -0.9571 -1.0130 Variable Parameter Estimate Pr > |t| Parameter Estimate Pr > |t| Intercept -5.05 <.0001 -5.31 <0001 1 lam -2.80 <0001 -2.69 <.0001 12pm -2.18 <.0001 -2.16 <.0001 1pm -1.61 <.0001 -1.55 <0001 2pm -1.31 <.0001 -1.27 <0001 3pm -1.21 <0001 -1.17 <.0001 4pm -1.30 < 0001 -1.24 <.0001 5pm -1.44 <0001 -1.34 <.0001 6pm -0.66 <.0001 -0.65 <.0001 7pm -0.36 <0001 -0.32 <.0001 8pm 0.06 0.3936 0.16 0.0112 10pm -0.52 <.0001 -0.43 <0001 SUNPM 0.82 <.0001 0.82 <.0001 MON -0.77 <.0001 -0.77 <.0001 TUE -0.74 <.0001 -0.74 <0001 WED -0.51 <.0001 -0.51 <.0001 THU -0.46 <:oooi -0.45 <.0001 FRI -0.25 <0001 -0.25 <.0001 SUN -0.28 <.0001 -0.28 <.0001 Temperature 0.00 0.1039 0.00 0.0735 Precip. Duration 0.00 <.0001 0.00 <.0001 Easter Weekend 0.56 <.0001 0.55 <.0001 Spring Vacation 0.32 <.0001 0.33 <0001 Xmas Vacation 0.76 <.0001 0.74 <.0001 a 0.11 <0001 0.15 <0001 ln(N MOVIE) 1 6 0.16 0.0029 6 The parameter is y, which is obtained from estimates of cry and crby the Delta method 176 Table-9: Mod els with Holiday variables (May 29, 20( [)3 - May 26, 2004) Model Mil M12 M13 M14 Ml 5 Ml 6 R-Square 0.6560 0.6617 0.6618 0.6618 0.6619 0.6151 Adj R-Sq 0.6508 0.6566 0.6566 0.6567 0.6567 0.6119 N 20970 20970 20970 20970 20970 20970 AIC -0.7515 -0.7681 -0.7681 -0.7682 -0.7683 -0.6520 BIC -0.6328 • -0.6491 -0.6487 -0.6488 • -0.6485 -0.5846 Variable Parameter Estimate Pr > |t| Parameter Estimate Pr>|t| Parameter Estimate Pr>|t| Parameter Estimate Pr > |t| Parameter Estimate Pr > |t| Parameter Estimate Pr > |t| Intercept -7.01 <0001 -7.00 <.0001 -6.97 < 0001 -6.97 <0001 -7.03 <.0001 -4.86 <0001 10am -2.29 <.0001 -2.26 <0001 -2.25 <.0001 -2.25 <.0001 -2.26 <.0001 -2.12 <.0001 1 lam -1.95 <0001 -1.92 <0001 -1.91 <.0001 -1.90 <0001 -1.91 <.0001 -1.88 <0001 12pm -1.82 <0001 -1.83 <0001 -1.81 <.0001 -1.81 <0001 -1.82 <.0001 -1.78 <0001 1pm -1.27 <0001 -1.27 <.0001 -1.26 < 0001 -1.25 <.0001 -1.26 <.0001 -1.22 <0001 2pm -0.97 <.0001 -1.04 <0001 -1.03 <0001 -1.03 <.0001 -1.04 <0001 -1.01 <.0001 3pm -0.99 <0001 -1.06 <.0001 -1.04 <.0001 -1.04 <.0001 -1.05 <0001 -1.01 <.0001 4pm -1.09 <0001 -1.16 <.0001 -1.15 <.0001 -1.14 <.0001 -1.15 <0001 -1.13 <0001 5pm -0.97 <.0001 -1.04 <0001 -1.04 <0001 -1.04 <.0001 -1.04 <0001 -1.02 <.0001 6pm -0.65 <.0001 -0.72 <.0001 -0.70 < 0001 -0.69 <.0001 -0.70 <0001 -0.69 <.0001 7pm -0.26 <.0001 -0.26 <.0001 -0.25 < 0001 -0.25 <.0001 -0.26 <:0001 -0.27 <.0001 9pm -0.10 <.0001 -0.10 <.0001 -0.08 0.0122 -0.07 0.0420 -0.06 0.0620 -0.08 0.0053 10pm -0.45 <.0001 -0.45 <.0001 -0.45 < 0001 -0.45 <.0001 -0.44 <.0001 -0.47 <.0001 SUNPM 0.49 <.0001 0.50 <.0001 0.50 <.0001 0.50 <0001 0.49 <.0001 M O N -0.62 < 0001 -0.62 <.0001 -0.61 <.0001 -0.61 <0001 -0.61 <.0001 -0.63 <0001 TUE -0.52 <.0001 -0.51 <0001 -0.51 <0001 -0.51 <.0001 -0.51 <0001 -0.53 <.0001 WED -0.50 <.0001 -0.49 <0001 -0.49 < 0001 -0.49 <.0001 -0.49 <0001 -0.49 <.0001 THU -0.34 <0001 -0.34 <0001 -0.34 <0001 -0.34 <.0001 -0.34 <.0001 -0.34 <0001 FRI -0.17' <0001 -0.16 <.0001 -0.16 <.0001 -0.16 <0001 -0.16 <.0001 -0.18 <.0001 SUN 0.15 <0001 -0.05 0.0230 -0.05 0.0218 -0.05 0.0211. -0.05 0.0207 -0.04 0.0659 Temperature 0.00 < 0001 0.00 < 0001 0.00 <.0001 0.00 <.0001 0.00 <.0001 0.00 <0001 Precip. Duration 0.00 <0001 0.00 <.0001 0.00 <.0001 0.00 <0001 0.00 <.0001 0.00 <0001 Ascension Day 0.79 <0001 0.78 <.0001 0.78 <.0001 0.78 <0001 0.78 <0001 0.64 <.0001 Whit Day 0.79 <0001 0.78 <0001 0.78 <0001 0.78 <0001 0.79 <0001 0.68 <0001 Easter Weekend 0.52 <0001 0.51 <0001 0.51 <0001 0.51 <0001 0.51 <.0001 0.48 <0001 Summer Vacat. 0.19 <.0001 0.19 <.0001 0.19 <.0001 0.19 <0001 0.19 <.0001 0.17 <0001 Fall Vacation 0.65 <0001 0.64 <.0001 0.64 <0001 0.64 <0001 0.64 <.0001 0.66 <0001 Xmas Vacation 0.49 <0001 0.49 <.0001 0.49 <.0001 0.49 <0001 0.48 <.0001 0.57 <0001 Spring Vacation 0.59 <0001 0.59 <.0001 0.59 <.0001 0.59 <.0001 0.59 <.0001 0.61 <.0001 May Vacation 0.38 <0001 0.37 <.0001 0.37 <.0001 0.37 <0001 0.38 <.0001 0.33 <0001 ln(N MOVIE) -0.03 0.1259 N MOVIE -0.01 0.0403 0.02 0.2096 N M O V I E 2 0.00 0.0724 A G E -0.08 <.0001 177 Table-10: Models with Weekly variables (May 29, 2003 - May 26,2004) Model M21 M22 M23 M24 . M25 M26 R-Square 0.6617 0.6676 0.6677 0.6677 0.6678 0.6215 Adj R-Sq 0.6559 0.6619 0.6620 0.6620 0.6620 0.6175 N 20970 20970 20970 20970 20970 20970 A1C -0.7640 -0.7816 -0.7818 -0.7819 -0.7818 -0.6646 BIC -0.6290 -0.6463 -0.6461 -0.6461 -0.6457 -0.5808 Parameter Parameter Parameter Parameter Parameter Parameter Variable Estimate Pr > |t| Estimate Pr> |t| Estimate Pr> |t| Estimate Pr > |t| Estimate Pr > |t| Estimate Pr>|t| Intercept -7.42 <0001 -7.43 <.0001 -7.37 <.000i -7.38 <0001 -7.41 <.0001 -27.58 <0001 10am -2.27 <0001 -2.24 <.0001 -2.23 <0001 -2.23 <.0001 -2.23 <.0001 -2.12 < 0001 1 lam -1.93 <.0001 -1.89 <.0001 -1.87 <.0001 -1.87 <.0001 -1.87 <.0001 -1.85 <0001 12pm -1.85 <.0001 -1.85 <0001 -1.83 <0001 -1.83 <.0001 -1.83 <0001 -1.82 <.0001 1pm -1.28 <0001 -1.28 <.0001 -1.25 <.0001 -1.25 <.0001 -1.26 <.0001 -1.23 <.0001 2pm -0.99 <0001 -1.07 <.0001 -1.05 <.0001 -1.05 <0001 -1.05 <.0001 -1.06 <.0001 3pm -0.99 <0001 -1.07 < 0001 -1.04 <0001 -1.04 <.0001 -1.05 <.0001 -1.03 <0001 4pm -1.10 <0001 -1.17 <.0001 -1.15 <.0001 -1.15 <.0001 -1.16 <0001 -1.16 <0001 5pm -0.98 <.0001 -1.06 <.0001 -1.05 <.0001 -1.05 <0001 -1.05 <.0001 -1.05 <.0001 6pm -0.65 <.0001 -0.72 < 0001 -0.69 <0001 -0.68 <.0001 -0.69 <.0001 -0.71 <0001 7pm -0.28 <0001 -0.28 <.0001 -0.25 <.0001 -0.26 <0001 -0.26 <0001 -0.31 <.0001 9pm -0.12 < 0001 -0.12 <.0001 -0.07 0.0166 -0.06 0.0444 -0.06 0.0567 -0.10 0.0001 10pm -0.45 <.0001 -0.45 <.0001 -0.46 < 0001 -0.46 <,0001 -0.45 <0001 -0.49 <0001 S U N P M 0.50 <.0001 0.51 <0001 0.51 <0001 0.51 <.0001 0.50 <.0001 M O N -0.63 <0001 -0.63 <0001 -0.63 <0001 -0.63 <0001 -0.62 <0001 -0.64 <.0001 TUE -0.56 <0001 -0.55 <0001 -0.55 <.0001 -0.55 <0001 -0.55 <0001 -0.57 <.0001 W E D -0.54 < 0001 -0.53 <0001 -0.53 <0001 -0.53 <.0001 -0.53 <0001 -0.54 <.0001 T H U -0.35 < 0001 -0.35 <0001 -0.35 <0001 -0.35 <.0001 -0.35 <0001 -0.36 <.0001 FRI -0.20 <0001 -0.19 <.0001 -0.19 <0001 -0.19 <0001 -0.19 < 0001 -0.20 <.0001 SUN 0.16 <.0001 -0.04 0.0732 -0.04 0.0678 -0.04 0.0661 -0.04 0.0656 -0.03 0.1457 Temperature 0.00 <.0001 0.00 <.0001 0.00 <0001 0.00 <0001 0.00 <.0001 0.00 <0001 Precip. Duration 0.00 <0001 0.00 <.0001 0.00 <0001 0.00 <.0001 0.00 <0001 0.00 <.0001 Week 1 1.90 <0001 1.90 <0001 1.91 <0001 1.90 <.0001 1.89 <0001 23.06 <.0001 Week 2 1.96 <0001 1.96 <0001 1.97 <0001 1.96 <.0001 1.95 <.0001 22.71 <.0001 Week 3 1.59 <0001 1.58 <0001 1.59 <.0001 1.58 <0001 1.57 <0001 21.94 <.0001 Week 4 1.62 <.0001 1.62 <.0001 1.63 <.0001 1.62 <.0001 1.61 <0001 21.50 <.0001 Week 5 1.56 <0001 1.56 <,0001 1.56 <.000i 1.56 <.0001 1.55 <.0001 20.88 <0001 Week 6 1.24 <.000l 1.24 <.0001 1.24 <0001 1.23 <0001 1.22 <0001 20.00 < 0001 Week 7 0.73 0.0008 0.72 0.0008 0.72 0.0008 0.71 0.0009 0.71 0.0010 18.94 <.0001 Week 8 0.97 <.0001 0.96 <0001 0.96 <0001 0.96 <0001 0.95 <0001 18.63 <0001 Week 9 1.36 < 0001 1.36 <.0001 1.36 <0001 1.36 <.000i 1.35 <,0001 18.42 <0001 Week 10 0.75 0.0001 0.74 0.0001 0.74 0.0001 0.73 0.0001 0.72 0.0002 17.29 < 0001 Week 11 0.80 <.0001 0.80 <.0001 0.80 <0001 0.79 <0001 0.78 <.0001 16.73 <0001 Week 12 0.79 <0001 0.79 <0001 0.79 <.0001 0.79 <0001 0.78 <0001 16.18 <.0001 178 Table-10 (Continued): Models with Weekly variables (May 29,2003 - May 26, 2004) Model M21 M22 M23 M24 M25 M26 Variable Parameter Estimate Pr > |t| Parameter Estimate Pr > |t| Parameter Estimate Pr>|t| Parameter Estimate Pr > |t| Parameter Estimate Pr > |t| Parameter Estimate Pr > |t| Week 13 1.15 <.0001 1.15 <0001 1.16 <.0001 1.15 <.0001 1.14 <0001 15.92 <.0001 Week 14 0.84 <.0001 0.85 <0001 0.85 <.0001 0.85 <0001 0.84 <.0001 14.96 <.0001 Week 15 0.52 0.0017 0.52 0.0013 0.52 0.0014 0.51 0.0016 0.51 0.0019 14.04 <0001 Week 16 0.49 0.0023 0.49 0.0019 0.49 0.0018 0.49 0.0021 0.48 0.0025 13.51 <0001 Week 17 0.27 0.0797 0.28 0.0709 0.28 0.0687 0.27 0.0767 0.26 0.0875 12.68 <.0001 Week 18 0.38 0.0112 0.38 0.0095 0.39 0.0092 0.38 0.0105 0.37 0.0122 12.16 <.0001 Week 19 0.42 0.0037 0.43 0.0031 0.43 0.0031 0.42 0.0036 0.41 0.0042 11.50 <0001 Week 20 1.04 <.0001 1.04 <.0001 1.04 <.0001 1.03 <.0001 1.02 <.0001 11.46 <0001 Week 21 0.80 <0001 0.80 <0001 0.81 <.0001 0.80 <.0001 0.79 <0001 10.49 <.0001 Week 22 0.49 0.0005 0.49 0.0004 0.49 0.0004 0.49 0.0005 0.48 0.0006 9.50 <0001 Week 23 0.56 <.0001 0.56 <.0001 0.57 <.0001 0.56 <.0001 0.55 <.0001 8.89 <0001 Week 24 0.60 <.0001 0.60 <0001 0.60 <.0001 0.59 <.0001 0.59 <0001 8.31 <0001 Week 25 0.55 <0001 0.55 <0001 0.55 <.0001 0.54 <0001 0.53 <0001 7.57 <0001 Week 26 0.69 <0001 0.69 <0001 0.69 <0001 0.68 <.0001 0.68 <0001 7.25 <0001 Week 27 0.34 0.0051 0.35 0.0042 0.35 0.0044 0.34 0.0053 0.33 0.0064 6.46 <0001 Week 28 0.04 0.7508 0.04 0.7228 0.04 0.7478 0.03 0.7770 0.03 0.8061 5.63 <0001 Week 29 0.05 0.6478 0.05 0.6209 0.05 0.6306 0.05 0.6545 0.04 0.6797 5.02 <0001 Week 30 0.34 0.0006 0.33 0.0006 0.33 0.0006 0.33 0.0007 0.32 0.0009 4.84 <0001 Week 31 0.69 <.0001 0.68 <.0001 0.68 . <.0001 0.67 <.0001 0.67 <.0001 4.52 <0001 Week 32 0.28 0.0008 0.28 0.0008 0.28 0.0009 0.27 0.0010 0.27 0.0012 3.42 <.0001 Week 33 0.17 0.0299 0.17 0.0312 0.16 0.0354 0.16 0.0403 0.15 0.0456 2.67 <.0001 Week 34 0.10 0.1839 0.09 0.1938 0.09 0.2064 0.09 0.2128 0.09 0.2170 1.91 <0001 Week 35 0.01 0.9075 0.00 0.9528 0.00 0.9793 0.00 0.9936 0.00 0.9956 1.20 <0001 Week 36 0.32 <.0001 0.31 <.0001 0.31 <.0001 0.31 <.0001 0.31 <.0001 0.88 <0001 Week 38 -0.01 0.8709 -0.01 0.8478 -0.01 0.8408 -0.01 0.8559 -0.01 0.8739 -0.62 < 0001 Week 39 -0.03 0.6926 -0.03 0.7073 -0.02 0.7342 -0.02 0.7263 -0.02 0.7198 -1.33 <.0001 Week 40 0.53 <.0001 0.53 <.0001 0.53 <.0001 0.53 <.0001 0.53 <.0001 -1.51 <.0001 Week 41 0.34 <.0001 0.33 <.0001 0.34 <.0001 0.34 <.0001 0.34 <0001 -2.50 <.0001 Week 42 0.25 0.0084 0.26 0.0072 0.26 0.0065 0.26 0.0058 0.27 0.0050 -3.31 <0001 Week 43 0.13 0.2373 0.13 0.2181 0.13 0.2035 0.14 0.1922 0.14 0.1771 -4.11 <.0001 Week 44 0.07 0.5592 0.07 0.5236 0.08 0.5094 0.08 0.4961 0.08 0.4755 -4.81 <.0001 Week 45 • 0.14 0.2781 0.15 0.2495 0.15 0.2424 0.15 0.2323 0.16 0.2186 . -5.41 <.0001 Week 46 0.43 0.0018 0.44 0.0015 0.44 0.0014 0.44 0.0013 0.45 0.0011 -5.88 <0001 Week 47 0.04 0.7945 0.05 0.7519 0.05 0.7369 0.05 0.7199 0.06 0.6939 -7.08 <0001 Week 48 0.26 0.1013 0.27 0.0884 0.28 0.0840 0.28 0.0786 0.29 0.0717 -7.61 <.0001 Week 49 0.87 <0001 0.87 <.0001 0.88 <.0001 0.88 <.0001 0.89 <0001 -7.82 <.0001 Week 50 0.92 <.0001 0.93 < 0001 0.93 <.0001 0.93 <.0001 0.94 <.0001 -8.65 <0001 Week 51 0.78 0.0001 0.79 <.0001 0.79 <.0001 0.79 <0001 0.80 <.0001 -9.74 <.0001 Week 52 1.50 <0001 1.50 <.0001 1.50 <.0001 1.50 <.0001 1.51 <.0001 -10.07 <0001 179 Table-10 (Continued): Models with Weekly variables (May 29, 2003 - May 26, 2004) Model M21 M22 M23 M24 M25 M26 Variable Parameter Estimate Pr > |t| Parameter Estimate Pr > |t| Parameter Estimate Pr>|t| Parameter Estimate Pr > |t| Parameter Estimate Pr > |t| Parameter Estimate Pr > |t| ln(N MOVIE) -0.05 0.0145 N MOVIE -0.01 0.0064 0.01 0.7607 N MOVIE 2 0.00 0.3289 AGE 0.57 <0001 180 Table-11: Nested Logit Models with Holiday variables (May 29, 2003 - May 26, 2004) Model IV! IV2 R-Square 0.6866 . 0.7111 Adj R-Sq 0.6818 0.7067 N 20970 20970 AIC -0.8808 -0.9966 BIC -0.7614 -0.8768 Variable Parameter Estimate Pr > |t| Parameter Estimate Pr > |t| Intercept -6.87 <.0001 -6.91 <.0001 10am -2.24 <.0001 -2.26 <0001 1 lam -1.88 <.0001 -1.91 <.0001 12pm -1.78 <.0001 -1.80 <.0001 1pm -1.23 <.0001 -1.28 <.0001 2pm -1.02 <0001 -1.05 <.0001 3 pm -1.01 <0001 -1.04 <0001 4pm -1.13 <.0001 -1.16 <.0001 5pm -1.04 <.0001 -1.05 <.0001 6pm -0.66 <.0001 -0.70 <.0001 7pm -0.24 <.0001 -0.28 <.0001 9pm -0.03 0.3123 -0.08 0.0041 10pm -0.48 < 0001 -0.50 <0001 SUNPM 0.50 <.0001 0.49 <0001 M O N -0.61 <.0001 -0.61 <.0001 TUE -0.51 <0001 -0.51 <0001 WED -0.49 <.0001 -0.49 <.0001 T H U -0.33 <0001 -0.33 <0001 FRI -0.16 <0001 -0.16 <0001 S U N -0.05 0.0154 -0.04 0.0132 Temperature 0.00 <.0001 0.00 <0001 Precip. Duration 0.00 <.0001 0.00 < 0001 Ascension Day 0.76 <0001 0.75 <.0001 Whit Day 0.78 <.0001 0.77 < 0001 Easter Weekend 0.51 <.0001 0.50 <.000i Summer Vacat. 0.19 <0001 0.20 <0001 Fall Vacation 0.64 <0001 0.63 <0001 Xmas Vacation 0.49 <.0001 0.49 <.0001 Spring Vacation 0.58 <.0001 0.57 <0001 May Vacation 0.37 <.0001 0.37 <.0001 a 0.09 <.0001 0.18 <.0001 ln(N MOVIE) 0.15 <.0001 Table-12: Predicted Shares of a Base Case Movie on the basis of Data Set 2 Model The number of showings change from 1 to 2 . The number of showings change from 4 to 5 The number of showings change from • 7 to 8 Individual Share Group Share Individual Share Group Share Individual Share Group Share Standard Logit Model, Ml 2 -0.000001 0.000909 -0.000001 0.000904 -0.000001 0.000900 Nested Logit Model, IV 1 -0.000063 0.000911 -0.000019 0.000822 -0.000011 0.000782 Crowding Model, Ml 3 -0.000020 0.000898 -0.000007 0.000864 -0.000004 0.000847 Hybrid Model, IV2 -0.000039 0.000920 -0.000012 0.000862 -0.000007 0.000835 182 Table-13: Predictive Performance in the validation sample (May 27, 2004 - June 9, 2004) Model M A E M A P E R M S E Mil 26.99 72.69 52.08 M12 26.13 71.03 49.18 M13 26.14 71.07 49.09 M14 26.12 71.07 49.03 M15 26.06 70.93 48.94 M16 27.87 85.62 49.12 M21 44.02 124.65 79.08 M22 43.51 121.67 76.33 M23 44.19 124.00 77.73 M24 43.89 122.76 77.08 M25 43.06 120.10 75.30 M26 16004.53 46864.23 25247.93 IV1 26.08 70.20 48.69 IV2 26.08 69.21 48.78 183 Figure-1: Weekly Number of Showings from Jan to Apr i l 2001 ;ure-2: Weekly Number of Showings from May 2003 to May 2004 Figure-3: Daily Mean Temperature from January 4 to April 18, 2001 Daily Mean Temperature measured at De Bilt 20 -10 Date 186 0.1 hour January 4, 2001 January 11, 2001 January 18, 2001 January 25, 2001 February 1, 2001 February 8, 2001 February 15, 2001 February 22, 2001 March 1, 2001 March 8, 2001 March 15, 2001 March 22, 2001 March 29, 2001 April 5, 2001 April 12, 2001 D fi) <" Tl —< CD O fi) o' 3 D c - T fi) o" 3 3 (D fi) C/> C CD a D CD CO CfQ e a 85 Si o" O G 5" 3 e-i » 3 S SS •"J «•< -fe. o -a "I OO o o ;ure-5: Daily Mean Temperature from May 29, 2003 to May 26, 2004 Daily Mean Temperature measured at De Bilt 188 Figure-6: Daily Precipitation Duration from May 29, 2003 to May 26, 2004 Daily Precipitation Duration measured at De Bilt "I • 1 li ' ii 1 I tl 1 J UQV m o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o C N I C N C N C N I C v J C N I C N I C N J C \ I C N C N C \ | C N C ^ a CM C D o" -3-" h- t- -^ j- CO CSi CD o" CO r»- T - IT) co" CM" isi a> T£ CO T - " if) o> CO Date Figure-7: Predicted Share of a Base Case Movie on the basis of Data Set 2: Comparison among Standard Logit (Ml2), Nested Logit (IV1), Crowding (Ml3) and Hybrid Models (IV2) (Base Case: a C l a s s i c starting i n the hour o f 8pm on Saturday) Predicted Share of a base case movie showing: Comparing Standard Logit (M12), Nested Logit (IV1), Crowding (M13) and Hybrid (IV2) Models 0.00120 0.00100 0.00080 S 0.00060 03 o • ra 0.00040 0.00020 0.00000 '* m- • --M12 IV1 -M13 IV2 6 7 8 9 10 No. of Showings in the hour 11 12 13 14 15 190 Figure-8: Total Predicted Share of all showings of the Base Case Movie in an hour on the basis of Data Set 2: Comparison among Standard Logit (A/72), Nested Logit (IV1), Crowding (M13) and Hybrid Models (IV2) Total Predicted Shares of all showings of the base case movie in an hour: Comparing Standard Logit (M12), Nested Logit (IV1), Crowding (M13) and Hybrid (IV2) Models 0.01600 i 0.01400 0.00000 -I 1 1 1 1 1 1 1 1 , , , , | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 No. of Showings in the hour 191 Chapter 5: Conclusion 1. Contr ibut ions There are two levels of contribution intended to be made by each essay of this dissertation. First, using data from the movie industry, we provide substantive findings, which benefit this prominent entertainment industry. Second, the marketing models developed in each essay are intended to advance the concepts and methods used to study more general marketing phenomena. In the following, we present a summary of each essay and discuss its contributions at these two levels. 1.1 Essay 1: Is There a Payoff for Playoffs? The first essay develops four models to examine the value of Super Bowl T V advertising, and tests the models with a movie sample of 398 wide-release movies from the years 2000-2002. A l l four estimation models capture a two-path conceptual model for the effects of Super Bowl T V advertising on opening week box office revenues. Specifically, we hypothesize that there are two causal paths associated with such a marketing tactic. First, there is a direct path: Super Bowl T V advertising for a movie directly increases the demand for the movie. Second, there is an indirect path, which consists of two parts. In the first part, Super Bowl T V advertising first encourages more movie exhibitors to screen the movie and thereby increase the availability of the movie to moviegoers. In the second part, the increased product availability in turn increases box office revenues. Although all correspond to this two-path conceptual model, our four estimation models differ in how the non-linearity of the paths and other control variables' effects are captured. 192 Estimated with a data set integrated from different data sources such as IMDB.com and Entertainment Weekly, the four models give the following results: 1) Robust to various model specifications, it is found that Super Bowl T V advertising has a positive effect on opening week box office revenue. This effect is present when potential confounding factors like T V campaign start date and total launch T V advertising expenditure are controlled for. 2) Robust to various model specifications, the indirect path of Super Bowl T V advertising is significant. On the other hand, the direct path is significant only in two model specifications. <• In fact, compared to alternative models, which do not incorporate the mediation of movie exhibitors, the significance of the direct paths in the two-path models is greatly reduced. 3) Except for one model specification, which restricts the marginal effect of three managerial decision variables (Super Bowl T V advertising expenditure, other launch T V advertising expenditure, and product budget) to an increasing pattern, the other three more flexible models show Super Bowl T V advertising to be not as effective as other T V launch advertising efforts when evaluated at the same initial levels. As mentioned, the essay intends to make contributions at two levels. At the substantive level, we first reconfirmed Yelkur, Tomkovick and Traczyck's (2004) finding that Super Bowl T V advertising increases opening week box office revenues. We used an improved method and better controlling for potential confounding factors. More importantly, we know more about the mechanism of the effect: Super Bowl T V advertising mainly influences opening week box office revenues by increasing the number of movie exhibitors. Finally, while Super Bowl T V advertising creates a non-zero effect on opening week box office revenues, we showed that it is still not as effective as other T V advertising efforts when evaluated at the same initial level. That 193 being said, Super Bowl T V advertising is an attractive tactical alternative when other T V advertising starts generating diminished marginal effects. At a more conceptual level, the essay contributes to the marketing accountability literature by highlighting the mediating role of downstream channel members when evaluating the effects of marketing tactical actions. Specifically, our results demonstrate the need to evaluate marketing tactics using frameworks incorporating the responses of both downstream channel members and consumers, as in our two-path model. 1.2 Essay 2: Good Movie or Nothing Better to Do? The second essay develops three demand models for multiplex movie theaters and applies them to two data sets from a multiplex movie theater in Amsterdam. A l l three models are designed to disentangle moviegoers' three layers of time preference (time of day, day of week, and time of year seasonality) from the unobserved movie quality in the aggregated sales data. While our model specifications are similar to Einav (2003), we depart from his work in three ways: 1) we study seasonality at a more micro level, 2) we relax Einav's restriction that the unobserved quality of all movie titles decays at the same weekly rate, and 3) we address the difficulty of distinguishing cannibalization and market expansion effects when there is choice set variation by relaxing the IIA property in Einav's model. In particular, of the three models, one is a base model maintaining the IIA property. The other two models represent two approaches to relaxing the IIA property, namely the nested logit and Ackerberg and Rysman's (AR 2002) model. While Ackerberg and Rysman motivated their model in an independent manner, we provide a unifying framework to look at the similarities and differences between the two approaches. 194 Applying the three models to two data sets from the multiplex movie theater in Amsterdam, we obtain the following major findings: 1) Examining the raw patterns of the two data sets, we find that one data set suggests that the most preferred hour to watch movies is 8pm, while the other suggests it is 9pm. This data discrepancy is resolved once we apply the three models to disentangle the time preferences and unobserved movie quality: 8pm is the most preferred hour in both data sets. 2) A l l three models show that Saturday and Sunday, as well as holidays or school vacations, tend to attract more moviegoers than other days. 3) Both the nested logit and A R models suggest the two data sets have slightly more cannibalization than the magnitude suggested by the standard logit, when new movie choices are added to a choice occasion. 4) While the three models fit the two data sets equally well, nested logit models tend to give a better predictive performance in a validation sample. Similar to the first essay, the second also makes contributions at two levels. At the substantive level, we found that confounding of unobserved movie quality and underlying time preferences exist in some multiplex movie theaters' gross admission records. This suggests that in some cases, theater managers have a higher tendency to schedule higher quality movies at some time slots than at others. Moreover, we confirmed that the high gross admissions for movie showings on Saturday, Sunday, holidays or school vacations are more due to "nothing better to do" than to "good movies". Finally, we showed that multiplex movie theaters' gross admission records can exhibit more cannibalization than the magnitude suggested by the standard logit, calling for the need to apply nested logit or A R models when analyzing this type of data. 195 At a methodological level, we showed how the movie-specific parameters 0j and Xj can be used to resolve the confounding of unobserved product quality and underlying time preferences in the gross sales data. Note that this method is not limited to multiplex movie theaters, and is applicable to all other service providers that encounter such confounding in their aggregated sales data. More importantly, we demonstrated the similarities and differences of the nested logit and A R congestion models in distinguishing between cannibalization and market expansion effects when there is non-trivial choice set size variation. With our data sets, nested logit models tend to have a slightly better performance. 2. Managerial Implications The two essays in this dissertation present two types of implications for managerial practices. First, managers should benefit from the substantive findings highlighted above. For example, movie marketers now know the benefit of Super Bowl T V advertising may not be as substantial as that of other T V advertising. This is important i f they are considering spending the same amount on either type of advertising. However, they may achieve a larger marginal effect from Super Bowl T V advertising when other T V advertising starts generating diminished marginal returns. Another example is that multiplex movie theater managers now know the raw pattern of their gross sales data sometimes cannot reveal the true time of day seasonality due to the confounding of movie quality and time preferences. The second type of managerial implication is that the marketing models developed in the two essays could be useful tools for marketing practitioners. We discuss below how our marketing models could be used. 196 2.1 Essay 1: Is There a Payoff for Playoffs? In Chapter 3, we demonstrated how a two-path model like our log-quadratic-a model can be used to summarize the direct and indirect effects of such marketing tactics as Super Bowl T V advertising using several elasticity measures. Specifically, from a marketing accountability perspective, marketing practitioners can track these elasticity measures over time to evaluate the response generated by their chosen marketing tactics and whether the marketing tactics are pushing the retailers or directly influencing the end consumers. More importantly, the four marketing models developed in the first essay can be used directly as market response models to evaluate different tactical alternatives. For example, as shown in the marginal analysis illustration in Chapter 3, marketing practitioners can evaluate the marginal effect of allocating an extra $2.2 million to Super Bowl T V advertising as opposed to allocating it to other T V advertising opportunities by inserting the values corresponding to each tactical alternative into the chosen marketing model. 2.2 Essay 2: Good Movie or Nothing Better to Do? The demand models developed in the second essay can be used for both diagnosis and decision optimization purposes. For diagnosis, managers of pre-announced time schedule service providers can apply the demand models to their historical sales data and uncover the underlying three layers of seasonality. For decision optimization, the demand models can be used to generate predictions for alternative service schedules. By comparing the predicted sales of different service schedules, marketing practitioners can choose the ones that maximize revenues, subject to operational constraints. However, one should note that while the current version of the demand models is ready to be used to generate predictions for service providers 197 with a rather stable set of services, some modifications are needed for multiplex movie theaters. We will return to this point in the further research section. 3. Further Research Each of the essays in this dissertation calls for a number of further research directions. We highlight several major ones in this section. In fact, one specific direction from each essay is currently being pursued as an ongoing research project. We will also briefly describe these two ongoing projects. 3.1 Essay 1: Is There a Payoff for Playoffs? We can extend the movie launch tactic models in several challenging and yet potentially rewarding dimensions: 1) We can explore the dynamic aspect of advertising tactics by going beyond the opening week. As all three parties - movie marketers, movie exhibitors and moviegoers - would adjust their behaviors after observing the movie's box office performance during the previous week, modeling such a feedback mechanism poses some very interesting challenges. 2) We can explore the competition aspect of advertising tactics by considering the strategic behaviors of movie studios. A major challenge here is to define the boundary of a competition set. For example, are movies opening at theaters two weeks apart competing with one another? What about movies opening at theaters four weeks apart? 3) We can explore the weekly allocation of T V advertising expenditures before the movie release. In fact, this direction is currently being pursued in an ongoing project. We briefly discuss the motivation for this extension here. 198 In examining the detailed allocations for wide-release movies from 2000 to 2002, we recognize a spending pattern not consistent with two mainstay notions in the advertising literature, namely diminishing marginal return to advertising and consumers' forgetting effect. Specifically, the two notions suggest that there are two incentives a movie marketer needs to balance when allocating a movie's launch advertising budget. The diminishing marginal return suggests an incentive to spread the budget evenly across all available weeks leading to the release week, while the consumer forgetting effect implies an opposite incentive to concentrate the entire budget in the release week, when consumers can immediately act upon any aroused interest to watch the movie immediately. By trading off these two incentives, we can show that the optimal launch advertising allocation tactic is to increase the spending levels monotonically in each week as the release date gets closer. However, such a monotonically increasing spending pattern is not the only pattern observed in the movie industry. If we define a monotonically increasing spending pattern as an increasing spending trend with each period having no more than a 20% drop compared to the previous period, around 37% of wide-release movies in 2000-2002 violate this pattern in their last six weeks. To resolve this inconsistency, we are exploring different explanations under the framework involving both responses of movie exhibitors and moviegoers. We believe this project will not only advance our understanding of movie launch tactics, which are cited as an under-researched area by Eliashberg, Elberse, and Leenders (2005), but will also shed light on advertising tactics in a more general context. 3.2 Essay 2: Good Movie or Nothing Better to Do? The second essay leads to two main future research directions, namely capturing a richer movie-showing substitution pattern and adapting the models to generate predictions for multiplex movie theaters. First, in order to avoid unnecessary complexity when comparing 199 different approaches to relaxing IIA, the second essay assumes each hour is one choice occasion. After establishing the validity of the demand models, we can now explore other choice occasion definitions, e.g., each day is one choice occasion. This extension would allow us to study more complex cannibalization structures among different movie screenings. For example, a screening of Batman Begins at 7pm may substitute more toward a showing of Star Wars: Episode III at 7pm than toward a showing of Batman Begins at 10pm. Another exciting research direction illuminated by the second essay is adapting the demand models to generate predictions for multiplex movie theaters, which have new movie releases every week. In fact, as an ongoing research project, we are modifying the time of day demand models for use in a marketing management support system (MMSS), called SilverScreener II. The objective of SilverScreener II is to help multiplex movie managers decide how frequently and when a chosen set of movie titles should be shown each week. Similar to other types of MMSS, SilverScreener II consists of two components, namely the demand forecasting model and the decision optimization model. We focus here on the demand forecasting model. A major challenge in adapting the second essay's demand models for the demand forecasting model is assigning movie-specific parameters to movies for which we have not observed any data. A n approach which we are currently exploring is to build two additional regression models to predict the movie-specific parameters using some observed characteristics for individual movies. A test of such an approach is now being undertaken with a streamlined version of the estimation models presented here. We believe such research can advance the M M S S literature related to the ways in which demand forecasting and decision optimization models can be integrated on an ongoing basis. It also adds to the forecasting literature on making predictions for new products. 200 4. References: Ackerberg, Daniel A . and Marc Rysman (2002), "Unobserved Product Differentiation in Discrete Choice Models: Estimating Price Elasticities and Welfare Effects," working paper, U C L A Einav, Liran (2003), "Gross Seasonality and Underlying Seasonality: Evidence from the U.S. Motion Picture Industry," working paper, Stanford University Eliashberg, Johoshua, Anita Elberse, and Mark A . A . M . Leenders (2005), "The Motion Picture Industry: Critical Issues in Practice, Current Research and New Research Directions," Marketing Science, forthcoming Yelkur, Rama, Chuck Tomkovick and Patty Traczyk (2004), "Super Bowl Advertising Effectiveness: Hollywood Finds the Games Golden," Journal of Advertising Research, March, 143-159 201 

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