What makes a blockbuster? Economic analysis of film success in the United Kingdom

Copyright # 2002 John Wiley & Sons, Ltd.

MANAGERIAL AND DECISION ECONOMICS

Manage. Decis. Econ. 23: 343–354 (2002)

Published online in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/mde.1069

What Makes a Blockbuster?Economic Analysis of Film Success

in the United Kingdom

Alan Collins*, Chris Hand and Martin C. Snell

Department of Economics, University of Portsmouth, Milton, Southsea, Hants, UK

In this paper, we attempt to evaluate whether a film’s commercial performance can be

forecast. The statistical distribution of film revenues in the UK is examined and found to haveunbounded variance. This undermines much of the existing work relating a film’s performance

to its identifiable attributes within an OLS model. We adopt De Vany and Walls’ approachand transform the revenue data into a binary variable and estimate the probability that a film’s

revenue will exceed a given threshold value; in other words, the probability of a blockbuster.Furthermore, we provide a sensitivity analysis around these threshold values. Copyright #

2002 John Wiley & Sons, Ltd.

INTRODUCTION

Recent work (De Vany and Walls, 1999, 2001,2002; De Vany and Lee 2001) has suggested thatthe statistical distribution of revenues is markedlymore complex than the earlier empirical literaturehas assumed. Specifically, the data are betterdescribed by heavy-tailed distributions than bythe normal distribution. The distribution ofrevenues is highly skewed, with a few blockbusterfilms grabbing the lion’s share of the revenue,whilst other’s shares tail off. Film revenuedata appear to display a fractal-like distri-bution, with similar patterns emerging in weekly,monthly and annual data. The evidence suggeststhat the results would not be more robust if alarger sample was used (De Vany and Walls,1996).

This skewed distribution can be found in manynational markets. In North American data thereappear to be a durable relationship showingthe top 20% of films earning 80% of the revenue.

This has come to be known as ‘Murphy’s Law’after A.D. Murphy, a respected Variety jour-nalist (De Vany and Walls, 1996). This studyfinds that Murphy’s law also appears to holdin the UK, where the top 20% of films earned 85%of the revenue in 1997 and 83% of the revenuein 1998.

This paper first presents the results and outcomeof using orthodox econometric methods to analysefilm revenues. Like De Vany and Walls (1999), thestudy finds that no robust standard OLS modelscan be established. This is explained by filmrevenues following a heavy-tailed (Pareto) distri-bution (this could be seen as the blockbustereffect). The paper then reports on the applicationof alternative procedures that are more likely toproduce robust model estimates. This studyextends the literature by (i) providing a non-USA-based corroboration of the De Vany andWalls thesis regarding the validity of the use ofprobit and/or logit models to indicate film successand (ii) by additionally considering releases fromarchive.

The paper is organised in the following manner.The next section examines what has, until recently,been the dominant approach in the literature. The

*Correspondence to: Department of Economics, PortsmouthBusiness School, Locksway Road, Milton, Southsea, HantsPO4 8JF, UK.

following Section contains descriptive statisticsand background to the UK data used and thesection draws out the implications of the De Vanyand Walls critique. Results are then presented,with concluding remarks offered in the finalsection.

REVENUE AS A FUNCTION OF MOVIE

ATTRIBUTES

Most previous attempts to model film revenuehave drawn their samples from the USA.Smith and Smith (1986) present a ‘preliminaryanalysis’ of successful movies. From a dataset of‘rental champions’ (i.e. films that earned thehighest rental payments) they attempt to explainthe success of these films on the basis of AcademyAwards (Oscars) and year of release. Rentals arethe amount left after the cinema owners havetaken their share of the box office revenue. In theUK, box office revenue data are available, how-ever the distribution of this revenue is notreleased.1

Smith and Smith’s analysis makes a usefulstarting point for further investigation into thesuccess of films (success being measured in thisinstance by commercial success). They regressedfilm rentals on Academy award nominationsand awards. They found different results for thethree decades of their sample data. Thiswas interpreted as the effect of changingtastes. However, it can also be seen as evidenceof the instability of OLS estimates resulting fromthe nature of the distribution of film revenues.They conclude ‘. . .it may well be possible todevelop empirical models relating a film’s attri-butes to the likelihood of consumer demand.’ (p.506). Whilst Smith and Smith’s ‘preliminary’analysis was the first to appear in an economicsjournal, there are earlier studies in the commu-nications literature.

Simonet (1980) attempted to explain the perfor-mance of films in the US with reference to thecommercial performance of the director’s, produ-cer’s and stars’ previous films and the number ofawards they had won. The model was estimatedfrom a sample of rental champions and almostuniquely in the literature, Simonet tests the modelby generating forecasts on fresh data. Litman(1983) presents a more wide-ranging model of film

revenues including genre, Motion Picture Associa-tion of America (MPAA) rating, awards and stardummy variables as well as production cost databased on a sample of 125 films. There was no dataavailable on those films which grossed under $1million, so Litman allocated a value of $500 000 tothem. This undoubtedly has introduced a bias intohis results.

Wallace et al. (1993) focused on the impact ofstars on the box office revenue of films. In order tomeasure the impact of a star, other factors thatmay affect a film’s revenue should be controlledfor. The control variables they used were year ofrelease, quality rating, parental guide rating,country of origin, length in minutes, genre andcost.

Prag and Casavant (1994), extend Smith andSmith’s study both in terms of number ofobservations and explanatory variables employed.They argued that critical acclaim was an importantsignal of quality and should be included. The costof the production may also be a signal of quality,as studios would only be willing to spend largeamounts on a film that was more likely to be a boxoffice success. For estimation purposes, the finalcost of producing the negative was used, thisincludes production costs, payments to stars,editing costs, etc. They also included the MPAArating for each film and the genre. A constructedvariable for the impact of stars was also includedas were two dummies to represent first sequels andother sequels beyond the first separately. AnAcademy award variable is also included. Theirinitial model suggested that the negative cost,quality, star, sequel, award, and the MPAAcertificate variables all had a significant positiveimpact on film revenues. The only significant genredummy was that for drama which had a negativeimpact on revenue. The quality variable theyemploy is based on the rating in film guides asopposed to newspapers or film magazines. Thus, itis more a proxy for film quality rather than criticalacclaim as they refer to it in their article. However,it may not have been possible to collect filmreviews for all 652 films spanning a period of 77years.

Another recent contribution is from Sochay(1994) who introduced measures of competitionbetween films in their opening weekend to therevenue function model. Unlike Prag and Casa-vant, all the genre dummies were found to beinsignificant, but awards and nominations and

A. COLLINS ET AL.344

Copyright # 2002 John Wiley & Sons, Ltd. Manage. Decis. Econ. 23: 343–354 (2002)

time of release (Summer or Christmas release)were found to be significant.

The impact of reviews was investigated byHirschman and Pieros (1985). They make adistinction between reviews regarding films as anart form and the audience view of films asentertainment. They suggest that a film’s aestheticvalue and its entertainment value may be inverselyrelated. There is no clear, unambiguous relation-ship between critical and popular acclaim. There isa question mark over the role of critics asindicators of expected utility to the prospectiveconsumer (Cameron, 1995; Eliashberg and Shu-gan, 1997; Holbrook, 1999).

Thus in essence, the previous studies attemptedto explain the commercial performance of films interms of their identifiable attributes. Here, weattempt to do the same for the performance offilms in the UK cinema market in the light of thenature of the data.

THE DATA

The data were obtained from Empire film maga-zine in 1998–99. The data comprise the revenueearned by 216 films that opened and closedbetween January and November 1998. Filmswhich had not closed by November 1998 wereexcluded as the data presented would have givenmisleading results. A number of films were notsubmitted to the British Board of Film Classifica-tion and hence did not receive a rating certificate.These films were omitted from the sample as it islikely they were cleared by local authorities forlimited screenings. One might question the useful-ness of a model based on a relatively small samplesuch as this. Our objective is to illustrate theproblems that may beset OLS modelling of filmrevenues, rather than produce definitive results.The distribution of 1998 film revenues in the UK(Titanic excluded for scaling reasons) is presentedin Figure 1.

As is clear from Figure 1, the data show asmooth progression of diminishing film revenues.Only one outlier can be identified in the dataset}Titanic}whose success was unprecedented(the film stayed in the top 15 for 26 weeks wherewe calculate on average a film has a less 50%chance of staying for 4 weeks). Titanic took over£68 million at the box office, approximately 3.5times as much as the next highest earning film in

the sample. Subsequent econometric work fea-tured an inclusion and exclusion of this outlier. Inorder to estimate the models using OLS, thedependent variable (1998 total revenue) wastransformed using natural logarithms (LREV) to‘avoid’ the problem of non-normal errors. Whilstthis is a standard approach, we will show in a latersection that it is not always appropriate. Table 1presents a description of the variables used withbasic descriptive statistics.

A number of issues arise when coding ostensiblyqualitative data into quantitative measures. Prin-cipal amongst these is subjectivity fosteringunreliability in the coding. Where possible, wehave used objective measures drawn from pub-lished sources, but for some of the variables codinghas been undertaken independently by two of theauthors and where the sole discrepancy arose,relating to genre classification, a consensus wasarrived at. Looking at genre classification directly,coding was primarily guided by the dominantgenre suggested in Film Review 1998–99. Never-theless, we sought to establish independent agree-ment with this published source. Clearly, somefilms cross genres, but a dominant genre is stilltypically discernible. Following Wallace et al.(1993) and Prag and Casavant (1994), films havebeen allocated to a genre on the basis of theirdescriptions in reviews and film guides. The basecategory for the genre dummies is childrens’ films.The genre variables are included as controlvariables. We have no a priori expectation as tothe signs.

Turning to the certification variables, the BritishBoard of Film Classification classify films withreference to the level and amount of sexual and

0.0E+00

2.0E+06

4.0E+06

6.0E+06

8.0E+06

1.0E+07

1.2E+07

1.4E+07

1.6E+07

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2.0E+07

1 13 25 37 49 61 73 85 97 109

121

133

145

157

169

181

193

205

Film in rank order

Rev

enue

in£

Figure 1. UK film revenues (Titanic excluded) Source: Empire

January 1999.

FILM SUCCESS IN THE UK 345


violent acts. The certificates and the BBFC havelegal standing (unlike in the USA where ratings areissued by the Motion Picture Association, a tradebody). The BBFC certificates are a source ofinformation, a higher certificate (15 or 18) wouldindicate more adult themes would be explored inthe film. Austin (1980) has also suggested that amore restrictive certificate may increase interest inthe film, invoking Brehm’s (1966) theory ofreactance (i.e. generating appeal by a ‘forbiddenfruit’ effect). It may be reasonably contended thatthere could be some systematic joint effectsbetween the certification level and genre types.However, no evidence was found to support thiswhen product terms were considered in thesubsequent econometric phase. Again, certificatesare principally included as control variables,although an 18 rating clearly restricts the marketand we would expect then a negative sign, giventhe base category of U (universal).

Whilst producing a sequel may be a low-riskstrategy as the film has a clear and existing

audience, sequels do not normally outperformtheir predecessors at the box office. Hence, wemight expect a negative sign, although the effectsmay only be marginal, as there are only a fewsequels in our sample.

Defining star power is always problematic, aswitnessed by the fact that authors such asSedgwick (1998, 1999), De Vany and Walls(1999), and Prag and Casavant (1994) have alladopted different approaches. The definition of astar will vary from person to person. This studyemploys a name-recognition-driven definition ofstar power, based on the box office performanceof their last three films. This measure is in the spiritof Sedgwick’s POPSTAT approach in that pastperformance is used in the construction of a starpower measure. However, our definition is basedon a shorter time frame. As such we equate recentsuccess with name recognition and hence view thestar as a marketing device. The star power list,compiled by Screen International, is based on thecommercial performance of films in non-US

Table 1. Film Variable Names and Descriptive Statistics

Definition Mean SD Range Gini coefficient

Dependent variableLREV Logarithm of total revenue (1998£s) 12.097 2.046 4.890–18.049 0.114a

Explanatory variablesGenre NotesACTION Where 1=dominant genre is action movie Dummy variableADVENT. Where 1=dominant genre is adventure movie Dummy variableDRAMA Where 1=dominant genre is drama Dummy variableCOMEDY Where 1=dominant genre is comedy movie Dummy variableHORROR Where 1=dominant genre is horror movie Dummy variableRO/CO Where 1=dominant genre is romantic comedy Dummy variableSCI-FI Where 1=dominant genre is science fiction movie Dummy variableTHRILL. Where 1=dominant genre is thriller Dummy variableDOC. Where 1=dominant genre is documentary Dummy variable

BBFC certificateCERT PG Where 1=parental guidance advised Dummy variableCERT12 Where 1=viewing permitted by those aged 12+ Dummy variableCERT 15 Where 1=viewing permitted by those aged 15+ Dummy variableCERT 18 Where 1=viewing permitted by those aged 18+ Dummy variable

Film characteristicsSEQUEL Where 1=film is declared to be a continuation of

a previous storyDummy variable e.g Scream 2,

Lethal Weapon 4

STAR Number of cast members appearing on ScreenInternational star power list (Goodridge, 1997)

0–3 Star power definedby box office per-formance of lastthree movies innon-US markets

RE-RELEASE Where 1=film has been previously released Dummy variableEMPIRE Rating awarded by Empire magazine reviewers 1–5

aGini coefficient=0.83 before transformation.



markets, in contrast to other US-based lists ofstars (e.g. the Hollywood Reporter Power list). Thisdefinition of star power does not account for thepresence of up and coming stars, nor the transferof name recognition from other media (e.g.television or music). However, such stars maynot have established a sufficiently wide base ofname recognition, so that their use would be morelikely to entail a greater measure of risk by theproducers. That said, the risk may be offset tosome degree by the lower remuneration necessaryto secure their services. Generally speaking, onewould rationally expect a greater number of starsto contribute positively to revenue.

Regarding the RE-RELEASE variable, thearguments regarding sequels will broadly apply.The decision to re-release a film must rationallydenote acceptance of the view that in spite of ithaving already been seen by a large proportion ofthe prospective audience (on screen and video), itwill remain profitable to incur the prints, advertis-ing and distribution costs. Films which merit suchrepeat viewing will typically be critically andpopularly acclaimed classic films that may either(1) ride on the crest of a fashion wave of a bygoneera (e.g. Saturday Night Fever), (2) reclaim adominant position in a genre that is currently invogue (e.g. The Exorcist) or (3) serves as a focusfor cinema visits where parents act as indicators ofexpected utility for their children and re-experiencethe film with them (e.g. Star Wars or Grease).Hence, there is a type of quality filter that limitsthe extent of film re-releases from archives.

Opening weekend performance has been shownto be crucial to the long-term success of a film. Theinitial performance of a film is more an indicatorof awareness of a film. De Vany and Walls (1996)describe a wide opening as a double-edged sword,word of mouth comment, either good or bad willspread quickly. However, when a proxy foropening performance (a dummy variable indicat-ing whether the film opened in that week’s top 3films by revenue) was included, the logit resultsappeared to be unreliable.

THE IMPLICATIONS OF HEAVY-TAILED

DISTRIBUTIONS

Heavy-tailed distributions have been employed infinancial economics for some time, and are now

receiving more attention in other areas of econom-ics. The implications of these distributions areimportant for decision theory and practice as theyimply that standard statistical methods (such asOLS) are inappropriate. The mean and variance ofa normally distributed variable can be interpretedas the expectation of a future event and theassociated risk, respectively. However, the samplemean and variance of data described by a heavy-tailed tailed distribution will be specific to thesample from which they were derived; themean and variance of two different samplesdrawn from the same heavy-tailed distributionmay be very different. The variance (and poten-tially the mean) may not even be finite. The meanmay be dominated by extreme values in the tails,hence the mean may not represent the mostprobable outcome (indeed, the mean in our dataare clearly dominated by Titanic). Clearly then,any decision based on the assumption that thedata are normally distributed may be prone tolarge error. The instability of the mean andvariance may be better envisaged by plotting thecumulative sample mean and variance once thedata are arranged in release date order. The plotsof sample mean (Figure 2) and sample variance(Figure 3) have excluded Titanic to better allow thevolatility of both the mean and the variance to beseen (for comparison, cumulative mean andvariance plots including Titanic are included asan appendix).

A heavy-tailed distribution displays more massin the tail than is found in the normal distribution.The normal distribution and others are stabledistributions, that is they are invariant underaggregation. A heavy-tailed distribution can bedescribed by its four parameters: the tail index, a,05a52 for a stable distribution (=2 for thenormal distribution), which describes the thicknessof the tail; the skewness parameter, b, �15b51,the location parameter, which shifts the para-meter to the left or the right and the scaleparameter, s, s>1. Some authors, (e.g. Nolan,1999) use different notation to avoid confusing theshift and scale parameters with the mean andstandard error. Stable distributions are moreestablished in financial economics (see, for exam-ple, Mandelbrot, 1963a; Fama, 1963; Mueller et al.1998) but appear to be less well known in otherareas of economics.

It is known that where a52, the variance of thedistribution is unbounded, although the scale of



the distribution can still be defined (see, forexample, Mandelbrot, 1963b). If this is the casefor our data, OLS estimates would be considerablyweakened, the errors would follow the same stabledistribution and the t-statistics would be concen-trated between –1 and 1 (McCulloch, 1998). Afterexamining plots of log revenue (x) against logP (X>x) and of the mean excess function, weconcluded that our data approximates to thePareto distribution in the tail. Following Fama’s(1963) approach, we employed a number ofmethods of estimating a in an attempt to bracketthe true value for a: OLS regression of log(P (X>x)) on log (x), a generalised Pareto estima-tor known as the Hill estimator and quantileestimation of the parameters in Nolan’s (1999)program STABLE.

We conducted the regression on the top 21observations (the top 10% of the sample). Whilstthe value for a obtained will depend on the size ofthe tail selected, using 10% is an accepted rule ofthumb. The results of the regression appear inTable 2.

We obtain an estimate of a of 0.61, whichimplies our data have an unbounded variance.

We also employ the Hill, estimator (Hill, 1975),although again the estimates of a will depend onthe size of the tail selected (denoted as k). The Hillestimator also has limitations which should benoted: it is inaccurate for larger values of andwhere m is not equal to 0. We estimated a usingReiss and Thomas (1997) program XTREMES.This program allows automatic selection of the tailsize, although as Reiss and Thomas note, the

0

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10 30 50 70 90 110 130 150 170 190 210

Films over time

Mea

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Figure 2. Cumulative sample mean (Titanic excluded).

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Films over time

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ianc

e

Figure 3. Cumulative sample variance (Titanic excluded).



procedure is crude. Alternative methods of select-ing the tail size include plotting the values of a andselecting the tail size where the plot ceases tofluctuate. In addition to this, we estimate a wherethe tail size is assumed to be 10%. The results arepresented in Table 3, along with bootstrapped95% confidence intervals and the mean squareerror.

The estimates above differ quite dramaticallyfrom the OLS results reported earlier, which mightsuggest that the Hill estimator is not appropriatefor our data, given the limitations describedearlier.

Finally, we estimated the parameters of thedistribution using Nolan’s (1999) STABLE pro-gram (Table 4).2 This program offers the user theoption of using either maximum likelihood orquantile estimators. Only the quantile estimatorsare reported here because the maximum likelihoodmethod encounters problems where b ¼1.

The estimate of a is close to the OLS estimate.The results also suggest that the Hill estimator isnot appropriate for this data set as m is notequal to 0.

The estimates of a obtained from the OLSmodel and from STABLE are both 51, implyingthat not only the variance but also the mean isunbounded. This contrasts with the values ob-tained by De Vany and Walls (1999) of 1.72 forfilms with stars and 2.26 for films without starsand those obtained by Lee (1999) which rangedbetween 0.89 and 1.23 (depending on the estimatorused). This result is a little surprising, given thesimilarity in the distribution of weekly revenuebetween the US and UK markets (Hand, 2001).One explanation for this result is Titanic’sdomination at the UK box office and the relativelysmall sample size (n ¼216). However, differentsamples can be expected to yield different esti-mates of a, as is indicated by the different resultsobtained by De Vany and Walls (1999) and Lee(1999).

If one were to proceed with an OLS model onewould encounter the problem of non-normalerrors. The conventional approach in such situa-tions would be transform the dependent variable.However, in this case at least, one can raise twoobjections to this strategy. First, one might argueas Mandelbrot (1982) does that transforming thedependent variable is a fix just to fool the test: ‘Bydesign a fix can never be falsified, hence (rememberKarl Popper’s views) it cannot be a scientificmodel’ (p. 103). Rather than transform the data, itwould be more informative to investigate theactual (non-normal) distribution of the data. Thesecond objection is that transformation onlydelays the point when non-normal errors areencountered. Once a model has been estimated, itmay produce normal errors, but when the antilogis taken (say to produce forecasts) non-normalerror will be encountered again. As the error mayhave unbounded variance, one can have little ifany confidence in the forecasts generated.

EMPIRICAL FINDINGS

OLS Estimates of a Revenue Function

The OLS models were estimated using PcGiveversion 9.0 (Hendry and Doornik, 1996). Thepreferred model appears to pass all the standarddiagnostic tests except for one test for hetero-scedasticity. The results are presented in Table 5.

Reviews (EMPIRE) and the presence of a starname (STAR) are potential sources of information

Table 2. OLS Estimates of the Tail Index

Dependent variable: Log (P (X>x)

Variable Coefficient Standard error t-statistic

Constant 9.0680 0.64785 13.997Log (x) �0.61078 0.040299 15.156

R2 ¼0.9199, F (1, 19) =229.71, s ¼0.1074

Table 3. Hill Estimator Results

k ¼10% k selectedautomatically

Visualestimate

a 1.734 1.544 5195% CI 1.035–2.334 1.122–2.645 n/aMSE 0.115 0.1660 n/a

Confidence intervals based on 200 simulations.

Table 4. STABLE Estimates of Parameters

a b s m

0.773 1.000 125 820 �197 135



about a film and both of these variables aresignificant, although EMPIRE has the smallesteffect of any of the variables according the size ofthe coefficient. RE-RELEASE was significant, butnegative, perhaps more indicative of the fact thatthe potential audience for such films is likely to besmaller than the mainstream audience. Only fivegenres were found to be significant: comedy,drama, romance, thrillers and documentaries. Allhave negative signs suggesting they performed lesswell than the base category of children’s films.However, these results may be specific to thesample in that we would not expect children’s filmto always outperform comedies, dramas, ro-mances, thrillers and documentaries. If one couldeasily identify successful genres, and avoid un-successful ones, the variety of films on offer andthe risk borne by the producers would sharplydecline.

To investigate the stability of the parameters,we conducted Chow tests on the sample when

arranged in descending order of revenue and inrandom order. The Chow test suggests theparameters are unstable for the revenue orderdata (test statistic (F (19, 178)=18.63) but foundthe parameters to be stable in the randomisedorder sample (test statistic F (19, 178)=1.08).However, the re-scaling of the dependent variablemay weaken the Chow test. In a levels model, aChow test indicated the parameter values wereunstable when both data in revenue order and inrandomised order data were used to estimate themodels (the test statistics were F (19, 178)=2.54and F (19, 178)=3.35, respectively).

In essence, these OLS models tend to producehighly data specific parameter estimates which arenot robust and have potentially unboundedstandard errors. It is not surprising that a numberof economists have turned to more pragmaticmethods, which are not undermined by the heavy-tailed nature of the data. That said, such methodsnecessarily entail the definition of a threshold

Table 5. General and Preferred OLS Model Results

General model Preferred model

Coefficient t-value Coefficient t-value

Dependent variable: Lrev Constant 11.353 13.524 11.665 20.020AC �0.669 �0.612 }

ADV �1.048 �0.712 }CO �2.029 �2.111 �1.655 �3.372DR �2.670 �2.906 �2.273 �5.898HO 0.658 0.512 }RO �2.839 �2.453 �2.444 �3.101RO/CO �0.372 �0.336 }

SF �0.556 �0.408 }TH �2.157 �2.195 �1.810 �4.041DOC �4.760 �3.492 �4.390 �4.151PG 2.041 2.483 1.340 2.75412 2.296 2.730 1.553 3.41115 0.880 1.167 }

18 0.333 0.415 }SEQUEL 1.322 1.505 1.629 2.052EMPIRE 0.514 3.210 0.509 3.204STAR 1.5523 4.981 1.551 5.058RE-RELEASES �2.428 �2.906 �2.553 �3.274

DiagnosticsN 216 216R2 0.38 0.36F F(18, 197)=6.806 F(11, 204)=10.767s 1.978 1.969Normality w2(2)=1.4926 w2(2)=1.566Heteroscedastic errorsSquares F(20, 176)=0.862 F(13, 190)=1.218Squares and Cross-Products F(73, 123)=0.628 F(44, 159)=0.777Test of restrictions against general model F(7, 197)=0.0.736



value of success. Establishing the threshold valuesrequires informed judgements about the scale ofthe national market in which success is defined; DeVany and Walls used $50 million as the thresholdvalue of success in the US (the number of filmswhich exceeded this is not given), in our UK studyonly a single film}Titanic}exceeded $50 million.Necessarily therefore, the success threshold modelsreported below use more modest threshold values.In accepting such judgements as the appropriatethreshold values necessarily feature greater sub-jectivity, sensitivity analyses to the choice ofthreshold value were undertaken and are alsopresented below.

Success Threshold Model

One approach to heavy-tailed data has been totransform the data from continuous to binary datausing a threshold value. Extreme values willunduly influence the OLS estimates and trans-forming the dependent variable does not solve theproblem of unbounded variance. By discretisingthe data, the effect of the extreme values iseliminated. This has a natural interpretation inthis context: those films which exceed the thresholdcan be regarded as ‘hits’. Such a data series can

easily be modelled using logit or probit techni-ques. The logit approach to modelling filmsuccess is also intuitively appealing, as it empha-sises the probability of a particular characteristiccontributing to success, rather than the determi-nistic interpretation of linear equation models. DeVany and Walls (1999) use this technique tospecifically identify the impact of ‘stars’ that havea significant impact on film success. This studypresents a more generalised model in the sense thatthe impact of all of the film attributes identifiedabove on the probability of success are investi-gated, rather than serving purely as controlvariables.Thus, the model to be identified in logitformat is thus,

PrðRi > T Þ ¼eb

0xi

1þ eb0xi; ð1Þ

where Ri is the revenue of the ith film, T is thesuccess threshold revenue level and the xi terms arethe explanatory variables as defined in Table 1.The use of the logit is analogous to the testingprocedure given earlier, identifying a value wherethe tail begins (i.e. a threshold). The selection of athreshold value is necessarily subjective. De Vanyand Walls (1999) use a value of $50 million (in1982–84 dollars) which represents approximately

Table 6. Logit Model Results

Rev T=£1m Rev T=£2m Rev T=£3m Rev T=£4m

Constant �2.508** (1.057) �4.569** (1.359) �7.135** (1.883) �9.783** (2.384)AC 1.284 (1.115) 2.951** (1.302) 3.639** (1.469) 4.705** (1.637)ADV 0.693 (1.581) 2.498 (1.813) 3.393* (1.970) 5.189** (2.148)CO �0.07 (0.927) 0.460 (1.121) 1.189 (1.334) 0.392 (1.497)DR �0.470 (0.822) �0.315 (0.999) �0.172 (1.323) �0.390 (1.465)HO 3.666** (1.421) 3.640** (1.664) 3.801** (1.834) 3.809* (2.135)RO 0.724 (1.201) 0.930 (1.487) 1.568 (1.581) 1.997 (1.764)ROCO 3.216** (1.153) 3.768** (1.374) 4.102** (1.561) 5.557** (1.853)SF 0.879 (1.483) 2.599 (1.748) 1.807 (1.931) 3.591 (2.185)TH 1.179 (0.963) 2.223* (1.211) 1.669 (1.438) 1.976 (1.598)PG �0.416 (0.858) �0.453 (1.011) 1.301 (1.369) 1.908 (1.471)CERT12 0.033 (0.891) �0.277 (1.060) 0.923 (1.443) �0.713 (1.710)CERT15 �2.111** (0.821) �3.388** (1.067) �1.571 (1.409) �2.493 (1.571)CERT18 �2.396** (0.945) �2.773** (1.167) �0.277 (1.443) �0.837 (1.564)SEQUEL 1.576 (1.103) 1.909* (1.140) 1.126 (1.125) 0.723 (1.562)EMPIRE 0.695** (0.238) 1.050** (0.312) 1.196** (0.344) 1.900** (0.484)STAR 1.630** (0.425) 2.090** (0.506) 1.305** (0.479) 1.925** (0.583)RE-RELEASE �2.765** (1.209) �4.141** (1.617) �3.692** (1.767) �5.851** (2.364)

DiagnosticsN 60 40 32 27Log likelihood �89.82877 �61.91165 �55.07346 �41.95232w2 (17) 75.59 83.18 71.07 78.86

Standard errors in parentheses. **=significant at 5% level, *=significant at 10% level.



1.3% of 1983 gross box office revenue, corre-sponding to £4.9 million in our data set. However,they do not explain how this figure was obtained.Four values are used to investigate the sensitivityof the results to the level of the threshold. Theresults for the four T values selected are presentedin Table 6.

The models are similar with the exception of thehighest threshold value model where the highesttwo certification variables cease to be significant.In part this may be an artefact of the data, in thatthe most successful films in revenue terms in ourdataset, Titanic, Dr Dolittle and Armageddon,received 12, PG and 12 certificates, respectively.Turning to the significant variables commonacross all three models it may be observed thatthe RE-RELEASE variable remains significantlynegative at all selected values of T . Whilst such re-releases may be filtered by quality this resultsuggests that they are seemingly aimed at a moreniche market rather than a more mainstreamaudience.

The EMPIRE and STAR variables are signifi-cant and positive in all four models as expected.The STAR coefficients are higher than theEMPIRE coefficients, but also have higher stan-dard errors (although the gap between themnarrows as the threshold value is increased). Thus,our results imply that, although stars are positivelyassociated with box office success, their impact isless certain than a good review, following De Vanyand Walls’ interpretation of the standard error.

Turning attention to the genre dummies, onlyone genre, Romantic Comedy, is significant in allfour models, Horror is significant in the threelower threshold value models (and is significant inthe fourth at the 10% level). Surprisingly, Actionand Adventure become significant as the thresholdvalue rises. Whilst these genre dummies aresignificant, they exhibit standard errors far greaterthan those attached to the STAR or EMPIREcoefficients in any model. This suggests that eventhough some genres are significant, the effect is lesscertain. Finally, the genre results may be artefactsof the data and as such, the genre variables arebest regarded as control variables.

One potential objection to the logit modellingstrategy is that it wastes a lot of information.Accordingly, we experimented with an orderedprobit model, classifying the observations into 10groups initially. The results reflect those of thelogit models, with the same variables being

significant. Hence, the ordered probit resultscan be seen as a form of validation of the logitresults.

CONCLUDING REMARKS

The statistical distribution of film revenues in theUK appears to have unbounded variance, under-mining the assumptions of the classical linearregression model. An alternative modelling strat-egy, suggested by De Vany and Walls (1999)requires the data to be discretised, which whilstlosing information, overcomes the problem ofunbounded variance. This necessarily involvesthe selection of a threshold value which is largelysubjective. However, the actual value itself is lessimportant than may appear. Although it can easilybe interpreted as a definition of a ‘hit’, its primarypurpose is to provide a decision rule for designat-ing an individual observation to be 1 or 0. Theobjective is to transform the data so as to avoid theproblems of unbounded variance, which appearsto manifest itself in the non-normality of the data.The non-normality cannot be overcome by tradi-tional methods (such as dummy variables ortransforming the dependent variable) for reasonsoutlined above. The only solution appears to betransforming the continuous variable into adiscrete one. We have demonstrated the robustnessof the results by employing four threshold values.As expected, the presence of a star name andgaining positive reviews enhances the probabilityof success. Unlike a linear model, which suggests acausal link, the logit results emphasise thatalthough a star or good review may be associatedwith a ‘hit’, the impact is far from certain asrepresented by the standard error of the coeffi-cient.

Acknowledgements

The authors are grateful to two anonymous referees, the editorand to participants at the ESRC Study Group on theEconomics of Sports, Arts and Leisure meeting at UniversityCollege London, 8th May 2001 for their comments. The usualcaveat applies.

APPENDIX

A comparison of cumulative mean and varianceplots including Titanic is shown in Figures 4 and 5.



NOTES

1. Arguably, profit is less appropriate as a measure ofsuccess for films than it is for other areas as the costof the film (and hence profitability, given an expectedlevel of revenue) is determined by the type of film theproducer elects to make and who is cast in the leadingrole. In any case, the calculation of profit for a film isnot easy, given that a film will be released in anumber of different territories and on a number ofdifferent media. Such data is rarely available.

2. The parameterisation of stable distributions used bythe program are described in Nolan (1998).

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What makes a blockbuster? Economic analysis of film success in the United Kingdom

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