Bertrand Belvaux
email: bertrand.belvaux@u-bourgogne.fr

Rémi Mencarelli
email: remi.mencarelli@univ-smb.fr

Prevision model and empirical test of the box office results for sequels

Keywords: Movie industry, Review, Sequel, Box office, Accessibility-diagnosticity framework

As studios release an increasing number of movie sequels, scholars have begun to examine this strategic choice. Prior studies use standard models of box office performance to evaluate sequels' performance and have mainly compared the box office results of the original movie with those of its sequel. However, sequels hold a unique position in the motion picture market since they are strongly associated with the original movie. Using the accessibilitydiagnosticity framework, this research investigates the drivers behind the success of sequels and examines specifically the original movie's impact through the role of reviews. The results from 232 movies (116 original movies and 116 first sequels)demonstrate the direct impact of the original movie's reviews on the sequel's performance.

Introduction

The lifespan of movies in theaters has been steadily decreasing over the last several years. This is due to the abundant and constantly increasing number of films released, a sharp growth in distribution (through the number of screens per movie) and alternative means to access films (video-on-demand, streaming, screening rooms), which has led to studios perceiving the release of new movies as highly risky. Instead, over the past few years, they have capitalized on past successes, exploiting well-established movies with enduring reputations and strong consumer preferences [START_REF] Eliashberg | The motion picture industry: Critical issues in practice, current research, and new research directions[END_REF], and thus focusing more on motion picture sequels than on stand-alone movies [START_REF] Filson | The performance of global film franchises: installment effects and extension decisions[END_REF]. With this strategic orientation, studios have aimed at minimizing risk by capitalizing "on the success of an original movie by producing another film that reprises the same characters evolving in a new situation" [START_REF] Sood | Brand extensions of experiential goods: Movie sequel evaluations[END_REF]. In 2019, the top ten box office successes worldwide were sequels, compared to only two in 2000.

Given the enormous economic impact of sequels in the movie industry, scholars have begun to examine this strategic choice [START_REF] Filson | The performance of global film franchises: installment effects and extension decisions[END_REF]. Some studies have used sequels as a control variable in existing models of box office performance; others have evaluated and compared the box office results of sequels with those of the original movies or contemporaneous non-sequel movies [START_REF] Ravid | Information, blockbusters, and stars: A study of the film industry[END_REF][START_REF] Basuroy | Fast and frequent: investigating box office revenues of motion picture sequels[END_REF][START_REF] Hennig-Thurau | Conceptualizing and measuring the monetary value of brand extensions: the case of motion pictures[END_REF][START_REF] Moon | Dynamic effects among movie ratings, movie revenues, and viewer satisfaction[END_REF][START_REF] Dhar | The long-term box office performance of sequel movies[END_REF]. Most existing studies use standard models of box office performance to evaluate sequels' performance, even though sequels hold a unique position in the motion picture market since they are strongly associated with an original work [START_REF] Chisholm | Economics of motion pictures: the state of the art[END_REF]. Some studies equate sequels with brand extension, thereby indirectly associating the sequel with the original movie [START_REF] Moon | Dynamic effects among movie ratings, movie revenues, and viewer satisfaction[END_REF], but they have neglected to examine the role of any pre-existing signals from the original movie, especially the role of reviews. However, experiential information generated about the original movie (i.e., reviews from consumers and critics) can be used by moviegoers to make inferences and judge the sequel and, in turn, affect the box office performance of the sequel.

Hence, this research investigates what drives the success of sequels and demonstrates that over and above the usual characteristics that affect the performance of a movie (i.e., characteristics of the film, studios' actions and third-party information), the drivers of a sequel may also include the reviews associated with the original movie. Using the accessibility-diagnosticity framework, which has been recently applied to motion picture box office performance [START_REF] Joshi | Adapting to succeed? Leveraging the brand equity of best sellers to succeed at the box office[END_REF][START_REF] Knapp | The importance of reciprocal spillover effects for the valuation of bestseller brands: introducing and testing a contingency model[END_REF][START_REF] Carrillat | Debates and assumptions about motion picture performance: A meta-analysis[END_REF], we hypothesize and empirically show that these peripheral signals do not originate from the sequel itself, but impact the sequel's box office performance, specifically during the release phase. This result explains the unique position sequels hold in the movie market compared to stand-alone movies and why a specific performance model should be developed for sequels.

In addition to the indirect effect of the original movie on the sequel through a brand extension effect, we highlight the direct impact of the original movie's reviews on the sequel's performance with the accessibility-diagnosticity framework, demonstrating that reviews from an original movie can be applied to a sequel and thus have an effect over time. From a managerial perspective, our results suggest that it would be interesting for cinema executives to reactivate positive reviews of the original movie at the launch of a sequel.

In this paper, we first review the literature dedicated to the box office performance of motion pictures and, based on the accessibility-diagnosticity framework, we develop a specific model for sequels. The methodology used and the results obtained are then presented. To test the model, we use data from 232 recent movies (116 original movies and 116 first sequels).

Finally, the contributions and limitations of the study are noted, and avenues for future research are proposed.

Conceptual framework

Motion picture box office performance: original movie versus sequel

Researchers have produced a substantial number of studies analyzing the box office performance of films. Like any other product, a movie's success is based on the interaction between supply and demand. The supply strategy is developed by two key players in the motion picture industry, the producer and the distributor; the major studios usually assume these two functions internally [START_REF] Hadida | Motion picture performance: A review and research agenda[END_REF]. The producer defines the main characteristics of a movie: genre, country of origin, MPAA ratings, selection of the director and the actors.

The associated budget is also defined by the producer according to the expected performance of the film and its anticipated profits [START_REF] Dhar | The long-term box office performance of sequel movies[END_REF]. The producer entrusts the distributor with a mandate to define the marketing actions associated with the release strategy [START_REF] Prieto-Rodriguez | Theatre allocation as a distributor's strategic variable over movie runs[END_REF]. In order to maximize revenues, the distributor determines the optimal combination of resourcessuch as advertising expenditures and distribution intensity through number of screens -by estimating the movie's potential audience.

With regard to demand, a movie's attractiveness is based on its reputation and image among consumers [START_REF] Liu | Word of mouth for movies: its dynamics and impact on box office revenue[END_REF]. Even if a movie is an original experience [START_REF] Nelson | Information and consumer behavior[END_REF][START_REF] Chen | When do third-party product reviews affect firm value and what can firms do? The case of media critics and professional movie reviews[END_REF], potential moviegoers can develop preferences without consuming the film. They use signals that resonate with their past experience. For example, the genre, the actors or the director are signals that can influence a priori the consumer's preference for a movie. The audience can also use external information such as expert reviews or interpersonal communications [START_REF] Holbrook | The role of ordinary evaluations in the market for popular culture: Do consumers have "good taste[END_REF]. The influence of third-party information used by moviegoers has been demonstrated in various studies [START_REF] Liu | Word of mouth for movies: its dynamics and impact on box office revenue[END_REF][START_REF] Karniouchina | Impact of star and movie buzz on motion picture distribution and box office revenue[END_REF][START_REF] Lee | Do I Follow My Friends or the Crowd? Information Cascades in Online Movie Ratings[END_REF]. Third parties are people who share their experiences and opinions of a film with potential moviegoers. These information sources are usually perceived as credible and trustworthy [START_REF] Liu | Word of mouth for movies: its dynamics and impact on box office revenue[END_REF][START_REF] Chakravarty | The differential effects of online word-ofmouth and critics' reviews on pre-release movie evaluation[END_REF], and moviegoers view them as an indicator of quality [START_REF] Hennig-Thurau | Can good marketing carry a bad product? Evidence from the motion picture industry[END_REF]. Third-party information is all the more important for entertainment products because it sparks discussions among consumers [START_REF] Liu | Word of mouth for movies: its dynamics and impact on box office revenue[END_REF].

Consequently, a vast majority of moviegoers base their decision processes on third-party information [START_REF] Karniouchina | Impact of star and movie buzz on motion picture distribution and box office revenue[END_REF]. Many studies have analyzed the role of third parties and distinguished:

• the sources: expert-based reviews (professional critics' reviews) and non-expert reviews (consumer reviews). These third parties play the role of influencer or predictor [START_REF] Basuroy | How critical are critical reviews? The box office effects of film critics, star power, and budgets[END_REF]);

• the characteristics: volume (total number of reviews, which contributes to the reputation and awareness of a film's existence; i.e., the informative dimension) and valence (naturepositive or negativeof the reviews, which contributes to the movie's image; i.e., the persuasive dimension) are the main characteristics1 used to describe reviews [START_REF] Liu | Word of mouth for movies: its dynamics and impact on box office revenue[END_REF].

To sum up, the box office success of a movie is based on three main factors: the characteristics of the film, the intensity of the marketing strategy (mainly through the advertising budget and number of screens) and the reviews (from critics and moviegoers).

In this research context, a number of studies have analyzed sequels' performance (Table 1).

Broadly speaking, the term "sequel" is used to refer to the production of a film based on the success of a first, original movie [START_REF] Sood | Brand extensions of experiential goods: Movie sequel evaluations[END_REF]. These studies of sequels aimed to analyze their box office performance from two perspectives.

[insert Table 1 here] First, some studies compare sequels with non-sequel movies. Initial studies use the sequels as a control variable. Some conclude that this variable does not affect the existing models [START_REF] Basuroy | How critical are critical reviews? The box office effects of film critics, star power, and budgets[END_REF][START_REF] Liu | Word of mouth for movies: its dynamics and impact on box office revenue[END_REF], while others show that it has a significant impact [START_REF] Basuroy | An empirical investigation of signaling in the motion picture industry[END_REF][START_REF] Hennig-Thurau | Can good marketing carry a bad product? Evidence from the motion picture industry[END_REF][START_REF] Boatwright | Reviewing the reviewers: The impact of individual film critics on box office performance[END_REF][START_REF] Karniouchina | Impact of star and movie buzz on motion picture distribution and box office revenue[END_REF]. Other studies have evaluated the box office performance of sequels by comparing them to nonsequel movies released during the same period. [START_REF] Basuroy | Fast and frequent: investigating box office revenues of motion picture sequels[END_REF] show that sequels do better than contemporaneous non-sequels; [START_REF] Dhar | The long-term box office performance of sequel movies[END_REF] confirm this result. In both studies, the authors provide explanations based on brand extension theory [START_REF] Aaker | Consumer evaluations of brand extensions[END_REF]. They conceptualize sequels as brand extensions, as do several other studies [START_REF] Sood | Brand extensions of experiential goods: Movie sequel evaluations[END_REF][START_REF] Hennig-Thurau | Conceptualizing and measuring the monetary value of brand extensions: the case of motion pictures[END_REF]. In other words, the studios use existing brand names and look for ways to build on the similarity of characteristics between the original movie and the sequel (e.g., genre, stars, directors, storyline) in order to enhance brand awareness. The perceived similarity between the original movie (i.e., the brand-parent category) and the sequel (i.e., the extension category) leads to a process of assimilation [START_REF] Sood | Brand extensions of experiential goods: Movie sequel evaluations[END_REF], shapes quality perceptions [START_REF] Hennig-Thurau | Conceptualizing and measuring the monetary value of brand extensions: the case of motion pictures[END_REF] and positively influences the box office success of the extension [START_REF] Basuroy | Fast and frequent: investigating box office revenues of motion picture sequels[END_REF][START_REF] Dhar | The long-term box office performance of sequel movies[END_REF].

Second, some studies compare the sequel's performance with that of the original movie.

Using an economic approach [START_REF] Lazear | The Peter Principle: A theory of decline[END_REF], [START_REF] Basuroy | Fast and frequent: investigating box office revenues of motion picture sequels[END_REF] assume that the box office earnings of the original film will always be greater than those of the sequel due to the inevitable phenomenon of regression to the mean. They show this effect empirically on a sample of 11 sequels. Using a larger sample and a model based on brand extension value, [START_REF] Hennig-Thurau | Conceptualizing and measuring the monetary value of brand extensions: the case of motion pictures[END_REF] provide empirical evidence that sequels generate high average revenue and reduce the associated risk. Using an individual-level analysis, [START_REF] Moon | Dynamic effects among movie ratings, movie revenues, and viewer satisfaction[END_REF] emphasize that sequels have a better box office performance due to the original movie's brand power, the initial success of the original film and the established fan base of the original. They confirm this assumption during the release phase but find that this effect dissipates quickly after the first two weeks. [START_REF] Moon | Dynamic effects among movie ratings, movie revenues, and viewer satisfaction[END_REF] also observe that sequels receive lower ratings from moviegoers as a result of satiation (lack of novelty and surprise for an experiential product). [START_REF] Dhar | The long-term box office performance of sequel movies[END_REF] use a sample of movies spanning 26 years and demonstrate empirically that sequels attract more moviegoers than stand-alone movies released during the same period, but fewer than the original movies. However, they generate more profit than do the original movies. [START_REF] Filson | The performance of global film franchises: installment effects and extension decisions[END_REF] extend this to global film franchises and show that the performance of sequels tends to decline as extensions are introduced.

Several factors can explain the contradictory results obtained in these studies: the instability of the results given the small numbers of sequels in some of the samples, the different study periods in changing and complex environments and the adoption of different time horizons to determine a motion picture's box office performance. Although they arrive at different results and conclusions, these studies generally compare the sequel's box office results with those of its original movie or a contemporaneous non-sequel movie. They do not examine the specific mechanisms underlying a sequel's box office performance, in particular the role of preexisting signals from the original movie. These mechanisms deserve attention and should be considered in light of the initial release of the original movie on the market [START_REF] Chisholm | Economics of motion pictures: the state of the art[END_REF].

Specific mechanisms of sequels' box office performance

Based on previous research dedicated to box office performance, we assume that, like standalone movies, sequels' box office performance depends mainly on the characteristics of the movie (genre, director, actors, MPAA rating, country of origin, producer status), the intensity of the studios' actions (production budget and screens) and the reviews (from critics and moviegoers) of the sequel. We do not propose formal hypotheses about these effects as they are largely supported by previous empirical studies.

In addition to these expected effects, we assume that the original movie affects the sequel's box office performance through the persistence of its reviews. To identify these specific mechanisms, we use the accessibility-diagnosticity framework [START_REF] Feldman | Self-generated validity and other effects of measurement on belief, attitude, intention, and behavior[END_REF], which has been successfully applied in the context of motion picture box office performance [START_REF] Joshi | Adapting to succeed? Leveraging the brand equity of best sellers to succeed at the box office[END_REF][START_REF] Knapp | The importance of reciprocal spillover effects for the valuation of bestseller brands: introducing and testing a contingency model[END_REF][START_REF] Carrillat | Debates and assumptions about motion picture performance: A meta-analysis[END_REF]. According to this framework, consumers rely on the most diagnostic and accessible cues to make a judgment. More precisely, a piece of information is more likely to be used as a cue in a judgment if it is perceived as relevant to the judgment (diagnosticity), it is accessible for use in the judgment and other information is less accessible (accessibility). We use arguments based on this theoretical framework to explain the influence of the original movie's reviews on the sequel's box office performance.

First, consumers will use available signals to assess the quality of the sequel during the release phase [START_REF] Akdeniz | Cultural variations in the use of marketing signals: A multilevel analysis of the motion picture industry[END_REF]. In this context, moviegoers can draw on existing and credible signals based on their own consumption experience of the original movie and/or on information generated by other moviegoers who saw the original movie. Consumers will also associate the sequel with the original movie [START_REF] Basuroy | An empirical investigation of signaling in the motion picture industry[END_REF][START_REF] Hennig-Thurau | Conceptualizing and measuring the monetary value of brand extensions: the case of motion pictures[END_REF]. In other words, information generated about the original movie (through consumption and/or by third parties) contributes a priori to the reputation and image of the sequel. These cues are also more instructive than factual information (e.g., genre, MPAA ratings) as they are experiential information. Consequently, because of their accessibility and diagnosticity, the reviews associated with the original movies become an important information source for sequel judgments, especially during the release phase. Consequently, moviegoers can be motivated to choose to see the sequel early, without waiting for the emergence of sequelspecific reviews.

However, according to [START_REF] Joshi | Adapting to succeed? Leveraging the brand equity of best sellers to succeed at the box office[END_REF], in the first week after release, direct experiential cues about the sequel become more accessible. Consequently, the effect of the information used to evaluate the movie quality earlier on, including the reviews of the original movie, is likely to dissipate. It is thus possible to assume the reviews of the original movie influence the short-term box office performance of the sequel but not its long-term performance.

Previous studies suggest both a volume and a valence effect of reviews on box office performance (Table 1). However, for expert-based reviews, the volume effect is less persistent over time, in contrast to the volume effect of consumer reviews [START_REF] Larceneux | Buzz and recommendations on the Internet. What impacts on boxoffice success[END_REF].

The volume of critics' reviews also remains broadly constant, with each expert evaluating all the films that are launched. Finally, several studies highlight the prominence of a valence effect for critics' reviews [START_REF] Desai | Interactive influence of genre familiarity, star power, and critics' reviews in the cultural goods industry: The case of motion pictures[END_REF][START_REF] Basuroy | An empirical investigation of signaling in the motion picture industry[END_REF][START_REF] Dellarocas | Exploring the value of online product reviews in forecasting sales: The case of motion pictures[END_REF]. Therefore, we assume that the volume and valence of consumer reviews and the valence of critics' reviews of the original movie can directly impact the short-term box office performance of the sequel.

H1a. Consumer reviews (volume and valence) of the original movie have a positive impact on the sequel's short-term box office performance (first week) but do not affect the sequel's long-term performance (after the first week).

H1b. Critics' reviews (valence) of the original movie have a positive impact on the sequel's short-term box office performance (first week) but do not affect the sequel's long-term performance (after the first week).

Second, the effect of the original movie's reviews on the sequel's box office performance will probably be moderated by the time interval between the release of the two movies [START_REF] Basuroy | Fast and frequent: investigating box office revenues of motion picture sequels[END_REF][START_REF] Filson | The performance of global film franchises: installment effects and extension decisions[END_REF]. The persistence of reviews has already been documented in different studies [START_REF] Godes | Sequential and temporal dynamics of online opinion[END_REF][START_REF] King | What we know and don't know about online word-of-mouth: a review and synthesis of the literature[END_REF]. As noted by [START_REF] King | What we know and don't know about online word-of-mouth: a review and synthesis of the literature[END_REF], persistence of reviews means that existing reviews significantly influence future ones. According to the accessibility-diagnosticity framework, a short time period makes the reviews of the original movie more accessible to potential consumers of the sequel. In consequence, a short time period between the two movies should increase the influence of the original movie's reputation and image on the sequel's short-term box office performance. H2. The shorter the time interval between the release of the original movie and the sequel, the stronger is the impact of consumers' and critics' reviews on the sequel's short-term box office performance (first week).

Third, the reviews generated for the original movie can influence the box office performance of the sequel by affecting the reviews of the sequel. Like [START_REF] Duan | The dynamics of online word-of-mouth and product salesan empirical investigation of the movie industry[END_REF], we consider reviews to be an endogenous variable. In other words, consumers' and critics' reviews of a sequel depend on the reviews previously generated for the original movie. First, for a sequel, the evaluation can be general due to the emergence of brand equity [START_REF] Moon | Dynamic effects among movie ratings, movie revenues, and viewer satisfaction[END_REF]. The great similarity between the original movie and the sequel, which increases the perceived diagnosticity of cues associated with the original movie, will favorably impact the endogenous nature of the reviews [START_REF] Joshi | Adapting to succeed? Leveraging the brand equity of best sellers to succeed at the box office[END_REF]. Second, considering the consistency and perceived similarity between the sequel and the original movie [START_REF] Sood | Brand extensions of experiential goods: Movie sequel evaluations[END_REF], the assessment criteria will probably be the same and will be reactivated in a similar way [START_REF] Moon | Dynamic effects among movie ratings, movie revenues, and viewer satisfaction[END_REF]. Therefore, by distinguishing the consumers' and critics' reviews, we posit that the reviews associated with the original movie can influence the sequel's box office performance through their impact on the sequel's reviews. Formally: H3a. The consumer reviews (volume and valence) of the original movie have an indirect and positive impact on the sequel's long-term box office performance through the consumer reviews of the sequel.

H3b. The critics' reviews (valence) of the original movie have an indirect and positive impact on the sequel's long-term box office performance through the critics' reviews of the sequel.

Figure 1 summarizes the model of box office performance for a sequel. The model is based on standard effects identified for a movie (intra-movie effects). It also explicitly integrates the influence of the original movie and the associated signals that predated the release of the sequel (inter-movies effect).

[insert Figure 1 here]

Sequel box office prevision model

Data

Original data were collected on 232 movies (116 original movies and 116 first sequel movies) on the American market between 1999 and 2014 (Appendix 1). The data were collected from boxofficemojo.com, the-numbers.com, rottentomatoes.com and imdb.com (like [START_REF] Chakravarty | The differential effects of online word-ofmouth and critics' reviews on pre-release movie evaluation[END_REF]. As reviews on the IMDb platform began appearing in 1999, franchises that started before this date are excluded from the database. Indeed, certain factors are likely to change strongly over such long periods of time (e.g., economic conditions, critics' and audiences' tastes) and can therefore alter results [START_REF] Elberse | Demand and supply dynamics for sequentially released products in international markets: The case of motion pictures[END_REF].

Numerous studies assess box office performance dynamics by considering both the overall performance and that of the first week following a movie's release [START_REF] Basuroy | An empirical investigation of signaling in the motion picture industry[END_REF].

However, to test our hypotheses and avoid data nesting, we make a distinction between results in the first week (short-term performance) and after (long-term performance). To account for the temporal dimension, these data were adjusted for inflation over the period and for seasonal variations (annual and monthly trends). Seasonal correction coefficients were based on a broader film database (6,650 films shown over the same period).

We use three sets of variables to explain the commercial performance of a sequel: movie characteristics, studios' actions and reviews (Table 2).

[insert Table 2]

Like Hennig-Thurau et al. ( 2012), we choose several movie characteristics: country of origin (USA/outside the USA), status of the studio (major/independent), genre, MPAA classification, director and actors. For genre we use the four major categories on the IMDb website: action-adventure, animation, drama-thriller and comedy. Like [START_REF] Moon | Dynamic effects among movie ratings, movie revenues, and viewer satisfaction[END_REF], two categories are used for the MPAA classification: R and non-R (PG-13, PG and G). To analyze the role of the director and actors (the two main actors), the total box office performance of their previous movies is used as an indicator of attractiveness [START_REF] Hennig-Thurau | Can good marketing carry a bad product? Evidence from the motion picture industry[END_REF]. Using past success as a predictor of future success is the simplest indicator for measuring the effect of the director and/or "star" actors [START_REF] Rein | High visibility[END_REF][START_REF] Karniouchina | Impact of star and movie buzz on motion picture distribution and box office revenue[END_REF].

In addition, we include two main variables associated with studios' actions [START_REF] Hennig-Thurau | Can good marketing carry a bad product? Evidence from the motion picture industry[END_REF]: the production budget2 and the number of screens at the movie's release. These reflect the ambition of the producer and distributor, respectively.

Finally, for the reviews, the valence of the critics' reviews was captured by the Metascore index from the IMDb website, summarizing and standardizing some thirty professional sources, the scope of the critic being constant [START_REF] Hennig-Thurau | The relationship between reviewer judgments and motion picture success: re-analysis and extension[END_REF]. For consumers, the reviews variables were captured through the evaluations posted on the IMDb website (average score and number of ratings). For the temporal dynamic [START_REF] Liu | Word of mouth for movies: its dynamics and impact on box office revenue[END_REF], the sequel's reviews were recorded during the first week (intra-movie effect) and those of the original movie from its release period until the date of release of the sequel (inter-movie effect).

Model specification

Like [START_REF] Zufryden | Linking advertising to box office performance of new film releases-a marketing planning model[END_REF] and [START_REF] Elberse | Demand and supply dynamics for sequentially released products in international markets: The case of motion pictures[END_REF], we use log-log modeling. This makes it possible to take into account the multiplier effects of variables 3 and analyze the effects in the form of elasticities. The logarithmic transformation of continuous data also reduces the strong variance between films and limits heteroscedasticity. Moreover, the formulation of a multiplier model is consistent with the multi-level theoretical models used to estimate the commercial performance of a movie [START_REF] Duan | The dynamics of online word-of-mouth and product salesan empirical investigation of the movie industry[END_REF]. Finally, in order to compare results, we use the same choice process as in several other research studies looking at sequels [START_REF] Elberse | Demand and supply dynamics for sequentially released products in international markets: The case of motion pictures[END_REF][START_REF] Basuroy | An empirical investigation of signaling in the motion picture industry[END_REF][START_REF] Hennig-Thurau | Can good marketing carry a bad product? Evidence from the motion picture industry[END_REF].

The relationship between the endogenous variable and the exogenous variables is written as:

𝑅𝑒𝑣𝑒𝑛𝑢𝑒 𝑖 = 𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 . 𝑋 𝑖 𝑎 1 . 𝑒 𝑎 2 .𝑍 𝑖 . 𝑒 𝐸𝑟𝑟 𝑖
where X is the vector of continuous variables and Z the vector of dummy variables. 4 In order to evaluate the original movie's impact on the sequel, the analysis was carried out in two stages: first, the test of the intra-movie model (internal effects of the sequel's performance) and then the test of the inter-movie model (effect of the original movie on the sequel).

The intra-movie model of sequel performance

The first step is to estimate the sequel's performance through its internal dynamics: the movie's characteristics, the studios' actions and the reviews. As mentioned in the conceptual framework, we made no hypotheses on these effects given their validation in previous studies.

The production budget and the number of theaters can raise problems of endogeneity as they directly explain performance and are also determined by the expected performance of the first week and β = 0.254, p < 0.01 after the first week). The number of theaters also has a positive effect (β =1.695, p < 0.01 during the first week, β = 1.365, p < 0.01 after the first week). The effects of reviews also play a role in the commercial performance of the sequel.

The influence of professional reviews is strongest immediately after the film is released (β = 0.584, p < 0.01), before the influence of consumer reviews kicks in (both valence β = 0.441, p < 0.01, and volume β = 0.420, p < 0.05). On the other hand, the movie's characteristics do not affect the result. The "star" effect does not impact the sequel's commercial performance.

These initial results remain broadly consistent with those identified in the literature regarding the commercial performance of a movie, with a key role played by studios' actions and reviews. However, we note that the movie's own characteristics have almost no effect on commercial performance, which suggests the predominant influence of the sequel as a brand [START_REF] Sood | Brand extensions of experiential goods: Movie sequel evaluations[END_REF]).

[insert Table 3]

The inter-movies model of sequel performance

The second step is to analyze the box office release from an inter-movie perspective. This consists of assessing the extent to which a sequel's performance is affected by the original film. The analysis model is therefore based on explaining residuals of the first model. It reduces the number of parameters to be estimated and limits the endogeneity effects between the variables of the two movies (original movie and sequel).

We determine both the direct and the indirect effects of the original movie's reviews on the commercial performance of the sequel by using mediation tests on the hypotheses. Indirect effects are analyzed via the influence of variables related to the reviews of the sequel. This test follows the procedure described by [START_REF] Zhao | Reconsidering Baron and Kenny: Myths and truths about mediation analysis[END_REF] using the structural equation method. 5 The objective is to use the sequel's reviews to analyze the direct and indirect effects of the original movie's reviews on the sequel's performance.

The results first highlight the direct effects of the audience reviews associated with the original movie on the sequel's performance (Table 4). The audience reviews of the original movie (valence and volume) thus directly affect the performance of the sequel in the first week (β = 0.458, p < 0.01; β = 0.129, p < 0.01). However, after the first week, they no longer directly affect the performance of the sequel. Moreover, the professionals' reviews of the original movie do not directly affect the performance of the sequel in either the short (first week) or long term (after the first week). The results obtained therefore support H1a and reject H1b.

In the sequel box office model, the time interval between the original movie and the sequel can moderate the effect of the original movie's reviews on the sequel's box office performance (H2). Regressions were performed with an interaction effect (number of months between the two movies) explaining the sequel's performance through the reviews of the original movie (Table 5). The time interval between the original movie and the sequel has a weak and negative effect on the relationship between consumer reviews (volume) and the sequel's short-term box office performance (β = -0.005, p < 0.1). In other words, the shorter the time interval between original and sequel, the stronger is the effect of the consumer reviews (volume) on the sequel's performance. The effects of other signals associated with the original movie on the performance of the sequel are not moderated by the time interval;

these include the valence of consumer reviews (β = -0.009, n.s) and the valence of critics' reviews (β = 0.001, n.s). These results partially support H2. The nature of the reviews' characteristics can explain the results. The quantitative aspect (volume) of the reviews increases their accessibility, reactivates them easily and enhances consumer awareness of the sequel [START_REF] Liu | Word of mouth for movies: its dynamics and impact on box office revenue[END_REF], contrary to the qualitative nature of the cues (valence of reviews from consumers and critics), which can have inconsistent effects over time [START_REF] Godes | Sequential and temporal dynamics of online opinion[END_REF].

Secondly, the results show the indirect effects of audience reviews of the original movie (volume and valence) on the long-term performance of the sequel (Table 4). A good audience evaluation of the original film thus generates a favorable opinion of the sequel (β = 0.484, p < 0.01), which positively determines the sequel's box office results. Similarly, a large volume of reviews for the original movie positively affects the volume of reviews associated with the sequel (β = 0.837, p < 0.01), which then determines its commercial success. On the other hand, while the valence of critiques of the original movie affects the valence of the critiques of the sequel (β = 0.701, p < 0.01), there is no significant indirect effect on performance.

These results therefore support H3a and reject H3b.

[insert Table 4 here]

[insert Table 5 here] While these results only fully support two hypotheses (Table 6), they do confirm the unique situation of the sequel, which benefits from the previous existence of the original movie.

Unlike an original movie, where audience reviews only can play a role after the first week given the time it takes for them to emerge [START_REF] Liu | Word of mouth for movies: its dynamics and impact on box office revenue[END_REF], a sequel immediately benefits from the public reaction to the original movie, which will directly affect the short-term performance of the sequel. The results confirm the role played by some pre-existing experiential information both informative (volume) and persuasive (valence)associated with the original movie.

Because of their accessibility and diagnosticity, reviews of the original movies accelerate the viewers' decision-making about the sequel during the first week. Moreover, the influence of the reviews of the original movie on those of the sequel emphasizes the endogenous nature of the reviews [START_REF] Duan | The dynamics of online word-of-mouth and product salesan empirical investigation of the movie industry[END_REF]. Finally, consistent with the accessibility-diagnosticity framework [START_REF] Joshi | Adapting to succeed? Leveraging the brand equity of best sellers to succeed at the box office[END_REF], the direct impact of these quality signals becomes diluted as other quality signals directly associated with the sequel emerge.

[insert Table 6 here]

Conclusion

Contributions to the literature

In developing a model to forecast a sequel's box office performance, we make three main contributions to the literature. First, we identify the specific mechanisms underlying a sequel's box office performance and thus the need to develop dedicated performance models for sequels. Whereas the performance of a stand-alone movie is affected by cues related to a studio's prelaunch decisions (i.e., production budget, advertising budget, distribution intensity, star power, director) and cues related to third-party information (i.e., professional reviews from critics and consumer reviews) [START_REF] Bharadwaj | Predicting innovation success in the motion picture industry: The influence of multiple quality signals[END_REF], the performance of a sequel is also affected by the experiential information associated with the original movie. These peripheral signals impact the sequel's box office performance during the opening week. This result explains why sequels hold a unique position in the movie industry and can have a competitive advantage compared to their contemporaneous non-sequel movies [START_REF] Hadida | Motion picture performance: A review and research agenda[END_REF]. This strategy will specifically reduce the risk of failure, but does not necessarily ensure success (which is based more on the quality of the sequel).

Second, our paper adds to previous studies that have specifically analyzed sequels' performance. These studies have mainly compared the performance of the sequel with the performance of the original movie [START_REF] Basuroy | Fast and frequent: investigating box office revenues of motion picture sequels[END_REF][START_REF] Hennig-Thurau | Conceptualizing and measuring the monetary value of brand extensions: the case of motion pictures[END_REF][START_REF] Moon | Dynamic effects among movie ratings, movie revenues, and viewer satisfaction[END_REF][START_REF] Dhar | The long-term box office performance of sequel movies[END_REF][START_REF] Filson | The performance of global film franchises: installment effects and extension decisions[END_REF], using a brand extension effect to indirectly take into account the effect of the original movie on the sequel. Based on the accessibility-diagnosticity framework, the test in our model goes further by acknowledging the explicit impact of the original movie on the sequel's box office performance through the role of the reviews. The brand and product-related characteristics (genre, stars, director, storyline) are not the only signals affecting the performance of the sequel. The experiential information associated with the original movie and reactivated in this brand extension context will also directly impact the sequel's performance.

Third, our results demonstrate the persistence of reviews, whereas previous studies mainly emphasize the short-term effects of reviews in the context of a stand-alone movie's box office performance [START_REF] Liu | Word of mouth for movies: its dynamics and impact on box office revenue[END_REF]. Here, the accessibility-diagnosticity framework offers a convincing theoretical explanation for this persistence effect of reviews on sequels and confirms its relevance in assessing the effect of these signals [START_REF] Carrillat | Debates and assumptions about motion picture performance: A meta-analysis[END_REF]. Specifically, the volume and valence of consumer reviews affect the sequel's short-term performance given the availability and credibility of the signals that guide moviegoers in their decision-making process by minimizing uncertainty. The direct impact of these experiential signals then becomes diluted as other direct experiential cues about the sequel become more accessible.

Consequently, as expected, the original movie's reviews have no direct effect on the long-term performance of the sequel. Contrary to the idea that the influence of reviews diminishes quickly over time [START_REF] Duan | The dynamics of online word-of-mouth and product salesan empirical investigation of the movie industry[END_REF], this result suggests that reviews can be reactivated from an original movie to apply to a sequel and thus have an effect over time.

Managerial implications

From a managerial perspective, the results of this work can help studios during the development and launching of sequels, as the decision-making of the major studios regarding this type of movie remains a "complex equation" [START_REF] Eliashberg | The motion picture industry: Critical issues in practice, current research, and new research directions[END_REF].

At a strategic level, the existing reviews of the original movie are interesting signals available to the studios. First, analysis of these reviews can help studio executives select original movies for potential sequels that can be successfully launched onto the movie market.

Second, during the release phase, these signals can reassure risk-averse studio executives about a sequel's potential. While the existence of an original movie provides an overall revenue boost for the sequel [START_REF] Moon | Dynamic effects among movie ratings, movie revenues, and viewer satisfaction[END_REF], the reviews associated with the original movie will specifically facilitate the sequel's theatrical release. Third, the reviews of both critics and consumers will provide an indicator of the nature of the reviews that will be generated as part of a sequel.

At an operational level, our results encourage managers to call upon these quality signals during the release phase of the sequel. Currently, studios only have a short, one-off window to attract a potential audience: the average run for a movie is four weeks in a context where more films are launched each year (708 new movies were released throughout 2019, compared to 641 in 20186 ) and where development and launch costs are increasing, especially for sequels [START_REF] Bharadwaj | Predicting innovation success in the motion picture industry: The influence of multiple quality signals[END_REF]. Therefore, the main objective for cinema executives is to use as many quality signals as possible during the release phase in order to reduce information asymmetry and ensure rapid commercial success for the sequel. Our results provide an incentive to studios to integrate reviews into their operating strategy more effectively, especially in promotional operations. They can reactivate these quality signals in two ways.

First, studios can directly and explicitly refer to the reviews of the original film in the promotional campaigns at the launch of a sequel. They can be mentioned in trailers, teasers, posters or websites dedicated to the sequel by emphasizing the number of moviegoers who recommended the original movie (volume effect) or recalling good memories associated with the original movie (valence effect). Studios can also use internet ad campaigns targeting moviegoers who recommended the original film through display campaigns, for example. The importance of these reviews can also be mentioned in the press kits that the studios provide to movie critics. The use of reviews in terms of their experiential nature can lead to a positive attitude towards the sequel in the opening weekend and reassure moviegoers who want to avoid purchasing a "lemon" [START_REF] Akerlof | The market for 'lemons': quality uncertainty and the market mechanism[END_REF][START_REF] Carrillat | Debates and assumptions about motion picture performance: A meta-analysis[END_REF]. Secondly, studios can reactivate these signals indirectly by emphasizing the perceived similarity between the original film and the sequel. The aim here is to underline the existing proximity between the original film and the sequel, whether in the genre, the star cast, the director or the storyline.

Studios can also facilitate this reactivation of reviews by reducing the time interval between the release of the two movies.

Limits and perspectives

This research has some limitations. It may be interesting to analyze in more depth the time horizon associated with commercial performance. Indeed, the model developed in this research distinguishes between short-term (revenue during the first week of movie screening) and long-term performance (revenue after the first week of movie screening). However, given the current speed of the emergence of reviews associated with new products [START_REF] Hennig-Thurau | Does Twitter matter? The impact of microblogging word of mouth on consumers' adoption of new movies[END_REF], and using the accessibility-diagnosticity framework, analyzing the sequel's daily revenues would allow for a more detailed evaluation of how long the quality signals (access and relevance) associated with the original movie affect the sequel's success. It also seems relevant to adopt a differentiated time horizon with the reviews by distinguishing, like [START_REF] Berger | What drives immediate and ongoing word of mouth?[END_REF], the reviews generated in the launch phase (immediate word of mouth) from the ongoing reviews developed throughout the product's presence on the market (ongoing word of mouth). However, new products are likely to generate substantial reviews in the launch phase. Since sequels are by definition a derivative work, born out of a standardization rather than innovation approach, this distinction would make it possible to assess both the volume of reviews of a sequel throughout its presence in theatres, and the weight of the effect the reviews of the original movie have on those associated with the sequel. This perspective could also make it possible to examine the volume of reviews of critics whose weight is especially significant when starting a film [START_REF] Larceneux | Buzz and recommendations on the Internet. What impacts on boxoffice success[END_REF].

Beyond a better consideration of the temporal dimension, other variables characterizing sequels should also be integrated into the proposed model. From this point of view, this research simplified the format by reducing the analysis to the impact of the original movie on the first sequel. However, studios are tending to develop longer and longer formats [START_REF] Filson | The performance of global film franchises: installment effects and extension decisions[END_REF], prompting consideration of the number of sequels to assess the persistence of these signals according to the place of the sequel in the franchise [START_REF] Basuroy | Fast and frequent: investigating box office revenues of motion picture sequels[END_REF]. Similarly, as in [START_REF] Sood | Brand extensions of experiential goods: Movie sequel evaluations[END_REF], the homogeneous nature of movies could be integrated using indicators such as titles (descriptive or numbered, e.g., Terminator Genisys or Fast and Furious 8) or the continued participation of star actors from one movie to another.

The degree of similarity between the movies (i.e., diagnosticity of the franchise equity) is likely to increase the reactivation effects of the signals associated with the original movie [START_REF] Joshi | Adapting to succeed? Leveraging the brand equity of best sellers to succeed at the box office[END_REF]. It might also be interesting to distinguish the nature of sequels by incorporating an order perspective. Indeed, in this research, the term sequel generically covers all works derived from an original work with no distinction of the nature of the derivative works. However, studios deploy different script devices (i.e., prequel, sidequel, spin-off, reboot, remake, crossover). Integrating these script formats into box office forecasting models could also help refine the results.

Finally, the hypotheses proposed in this paper could be extended to other markets and product categories. First, this research drew from data from the U.S. market to test the box office forecasting model of a sequel. It might be interesting to assess the validity of the model in other markets, as the taste for this type of film product may vary depending on the cultural context [START_REF] Akdeniz | Cultural variations in the use of marketing signals: A multilevel analysis of the motion picture industry[END_REF]. Secondly, this research was limited to the analysis of the theatrical movie market. However, there are other experiential products where companies minimize the risks of a new launch by capitalizing on the success of an original product. From this point of view, strategies in the publishing, video game or music industries could be similar to those implemented in the movie industry. It would therefore be interesting to examine the role played by quality signals associated with products of the same brand in these sectors. Similarly, it might be interesting to assess the role of these signals in the creation of a product providing a similar experience (film, video game, comic book, book) on multiple media platforms.

  film. A three-equation model is therefore used: Performance = f (constant, budget, theaters, country, genre, MPAA, producer, director, actors, valence of critics' reviews, valence of consumer reviews, volume of consumer reviews) Budget = f (constant, country, genre, MPAA, producer, director, actors) Theaters = f(constant, budget, country, genre, MPAA, producer, director, actors) Parameters of the model were estimated using the structural equation modeling (partial least squares method). The classic model for forecasting a movie's box office performance is satisfactory in the sequel case (Table3). The performance of a sequel thus depends at first mainly on studios' actions (production budget and number of theaters) and professional reviews, and then, after the first week, on spectator's reviews. The production budget positively affects the commercial performance of the movie (β = 0.251, p < 0.01 during the 4 Continuous variables are transformed into logarithmic format. Some values can take a zero value; the applied transformation is: Y = ln (X+1). Dummy variables are introduced in exponential form to reflect the absence of the factor.

  significant at the 1% level, ** at the 5% level, * at the 10% level Table4-Direct and indirect effects of the original movie's reviews on the sequel's box office performance through the sequel's reviews 7 significant at the 1% level, ** at the 5% level, * at the 10% level7 The model is just-identified. Fit indices are not significant (RMSEA = 0; CFI = 1; TLI = 1).8 The total variance of Y explained by X is based on a direct effect c (X➔Y) and an indirect effect a x b (a X ➔ mediator and b mediator ➔ Y).

Table 3 -

 3 Model of the sequel's box office performance: intra-movie perspective

Table 5 -

 5 Moderating effect of the time interval on the relation between original movie's reviews and sequel's performance 9

	First week

Table 6 -

 6 Results summary

9

Only the interaction coefficient is reported.

Other characteristics were identified, including consistency(Karniouchina,

2011), dispersion[START_REF] Godes | Using online conversations to study word-of-mouth communication[END_REF], entropy[START_REF] Dellarocas | Exploring the value of online product reviews in forecasting sales: The case of motion pictures[END_REF] and observability[START_REF] Dellarocas | Are consumers more likely to contribute online reviews for hit or niche products[END_REF].

The production budget corresponds to what the North American film industry calls the "negative cost" or the expense of producing the film excluding distribution and promotional expenses. The amount is adjusted for inflation.

For example, there will be no income unless a copy is presented.

The analyses were performed by the Lavaan module of R software for analysis of covariance structures and the partial least squares method with Smartpls software for verification.

Motion Picture Association Industry Report (2019)

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Appendix -Movie sample