Measuring Word of Mouth's Impact on Theatrical Movie Admissions · 2014-08-06 · Measuring Word of Mouth’s Impact on Theatrical Movie Admissions CHARLES C. MOUL Washington University

Measuring Word of Mouth’s Impacton Theatrical Movie Admissions

CHARLES C. MOULWashington University Department of Economics

Campus Box 1208St. Louis, MO 63130-4899

[email protected]

Information transmission among consumers (i.e., word of mouth) has receivedlittle empirical examination. I offer a technique that can identify and measurethe impact of word of mouth, and apply it to data from U.S. theatrical movieadmissions. While variables and movie fixed effects comprise the bulk of observedvariation, the variance attributable to word of mouth is statistically significant.Results indicate approximately 10% of the variation in consumer expectationsof movies can be directly or indirectly attributed to information transmission.Information appears to affect consumer behavior quickly, with the length of amovie’s run mattering more than the number of prior admissions.

1. Introduction

Despite its widespread theoretical implications in environments ofincomplete information, information transmission among consumers(a.k.a. word of mouth) has received relatively little empirical support. Inthis paper, I show that an existing method of detecting word of mouth isoverly broad, in that its empirical prediction of autocorrelated growthcan also be generated by a simple model of saturation in demand. Iinstead offer a model of demand that can accommodate both saturationand word of mouth, and then consider its implications within an errorcomponents framework. Applying this technique to U.S. theatricaladmissions, my estimates suggest that word of mouth is statisticallyand economically significant and that information travels quickly to theaverage consumer in commonly observed situations. Simulations usingthese estimates confirm that word-of-mouth can have large impacts onhow movies play out in theaters.

I thank the editor and two anonymous referees for comments on an earlier draft thatgreatly improved the paper. Seminar participants at Washington University in St. Louisand the DeSantis Center’s Business and Economics Scholars Workshop also providedhelpful feedback. The usual caveat applies.

C© 2007, The Author(s)Journal Compilation C© 2007 Blackwell PublishingJournal of Economics & Management Strategy, Volume 16, Number 4, Winter 2007, 859–892

860 Journal of Economics & Management Strategy

In a world of incomplete information, consumers sharing informa-tion about experience goods can play a critical role in moving economicoutcomes closer to the full information ideal. This intuitive insight hasbeen formalized by Ellison and Fudenberg (1993, 1995) who presentmechanisms for and implications of what they refer to as social learning.Furthermore, either word of mouth or repeat purchases are essential inthe theoretical literature explaining how advertising can be used as asignal of quality in a separating equilibrium (Nelson, 1974; Milgromand Roberts, 1986). The speed and manner of information transmissionamong consumers, however, are inherently empirical questions, and it isthere that I will concentrate my efforts. Given the presumed importanceof word of mouth in the theatrical sector of the movie industry, theseresults also potentially have bearing on the best responses to informationtransmission among consumers.

I discern information transmission by interpreting my model’sresiduals, and thus, while I will refer throughout to this transmission as“word of mouth,” I am unable to distinguish between consumers shar-ing information among themselves and information that is exogenouslyrevealed after a movie’s release (e.g., late movie reviews, published boxoffice announcements, etc.). With that caveat in mind, the general ideaof my approach is that word of mouth will be revealed in a specificand well-defined manner. Products presumably have unique differencesbetween consumer expectations and realizations (the information thatis relayed by word of mouth). All products, however, will begin theircommercial lifespans in the absence of such information. If a productstays available for a long enough time and enough consumers purchaseit and share the product’s true quality, then the original consumerexpectations will be supplanted by the conveyed realized quality.1 Thissystematic spread of information has implications for serial correlationand heteroskedasticity, specifically that both will increase over a movie’stheatrical run. My use of movie fixed effects in estimation alters thisprediction, in that heteroskedasticity and serial correlation based uponthese residuals will be nonmonotonic (specifically U-shaped) over eachmovie’s run. The speed of information can then be inferred from thenature and importance of asymmetry in these U-shaped relationships.

1. Herding therefore does not arise in this context, as signals (in the form of word ofmouth) as well as actions are observable. See Bikhichandi et al. (1992). This frameworkalso implicitly assumes that consumers are aware of all products’ existence. Relaxing thisassumption and allowing word of mouth to affect the likelihood that a consumer knowsof a product’s existence is a potential extension, though a computationally burdensomeone. This burden arises as observed quantities are the weighted averages of all possiblecombinations of consumer awareness. At the 50 weekly movies observed in my sample,this would require the calculation of 250 − 1 probabilities of each potential combinationof movies and 50 ∗ 249 informationally conditional quantities.

Theatrical Movie Admissions 861

This proposed error components approach differs substantially from theprior literature which either exploits additional information regardingthe sign and extent of the information gap (e.g., Chevalier and Mayzlin,2006) or takes advantage of detailed microlevel data (e.g., Foster andRosenzweig, 1995).

This paper is not the first to use movie admissions in an attempt todocument word of mouth. De Vany and Walls (1996) show that informa-tion transmission among consumers will cause autocorrelated growthrates among movies. They then document rejections of a Pareto Lawrelationship in favor of positively autocorrelated growth, and interpretthis as evidence of word of mouth. This paper makes two improvementsupon that work. First, I show that positively autocorrelated growth canalso be generated by a simple model in which consumers typically buya product at most once (as seems likely in the theatrical movie industryand many others). Second, my approach can not only detect the presenceof word of mouth, but can also provide measures of the importance ofthat information transmission.

The movie industry has been the subject of several other studiesin recent years. Moul (2001) finds that, from the late 1920s to early1940s, studio revenues rose with experience using synchronous soundrecording technology and interprets this as evidence of qualitativelearning-by-doing. Einav (2007) decomposes the seasonal demand fortheatrical movies into an underlying component and the amplificationthat arises from endogenous industry practices. Corts (1998) looks atthe issue of theatrical release timing in finding that a studio’s divisionslargely behave as an integrated whole. On the exhibition side, Davis(2006) uses the location and prices of theaters to measure how cross-price elasticities change with distance, and, on the production side,Goettler and Leslie (2004) look at causes and consequences of twostudios cofinancing a movie. Finally, Ravid (1999) examines measuresof profitability over a movie’s entire commercial run rather than simplyrevenues in a particular sector.

This paper makes some contributions to this literature beyond itsconclusion regarding the importance of word of mouth in theatricaladmissions. My initial estimates of demand are generally plausible andconform well with implications of other studies. As expected, ignoringand imperfectly addressing saturation in demand substantially distortthe predicted impacts of Oscar nominations, awards, and abbreviatedweeks. Estimates of the full model suggest that Oscar nominations havea substantial impact on admissions in equilibrium, but indicate no suchcomparable bump from winning the award. Prior commercial perfor-mance of both starring cast and director have significant impacts onconsumer expectations in equilibrium. There is also strong evidence of


heterogeneity among consumers in how they substitute between moviesand other goods, as well as between family and nonfamily movies.

My error components approach reveals that information travelsquickly to the average consumer, though this is obviously dependentupon how many people have seen the movie. For example, a movie thathas been seen by 200,000 persons by its fourth week can expect thatconsumers behave as if they have incorporated 50% of the differencebetween the movie’s true and originally expected quality. This levelof incorporation exceeds 90% for movies of comparable age that havebeen seen by 1 million persons. Estimates of the importance of word ofmouth are also informative and robust. About 10% of the variance in themodel’s implied consumer expectations is attributable to informationtransmission. Of the unobserved disturbances, roughly 38% of thevariance can be attributed to word of mouth. Word of mouth is lesscritical in explaining serial correlation of unobserved demand shocks,explaining about 32% of that phenomenon. Simulations from theseestimates indicate that a movie of average expectations but with goodword of mouth will gross $30 M more than a movie with the sameexpectations and bad word of mouth. I conclude with a discussion ofimplications for research on movies and other similar industries.

2. Industry

While the length and importance of the theatrical window of a movie’scommercial run have recently diminished relative to the video market, itstill offers a unique advantage over other periods of a movie’s lifespan: atrelease, consumers have only their expectations upon which to base theirdecisions. These expectations will depend upon all information (e.g.,trailers, movie reviews, etc.) that is available prior to the movie’s release.As noted in De Vany and Walls (1996), the sector has institutionallyevolved to exploit favorable word of mouth. Moul and Shugan (2005)further argue that the current strategy of wide release that replaced themulti-run structure in the 1970s is at least in part an attempt to limit theadverse effects of negative word of mouth. In the original structure oftheaters sequentially showing older prints, only movies with favorableword of mouth could be expected to have long and lucrative runs.The new structure offers the chance for movies that generate negativeword of mouth to yield at least some returns in the initial wide release,even though the movie’s commercial run will be short as disappointedconsumers share their information.

Contractual details between movie distributors (usually studios)and exhibitors further suggest that information transmission and the


risks therein are paramount. Contracts during my sample centeredaround the rental rate, a percentage of exhibitor box office receipts thatis ceded to the distributor.2 This percentage typically declines with thelength of time since a movie’s release; a common nonblockbuster rentalschedule is 60% the opening week, followed by 50%, 40%, 35%, and30%. This declining rate attempts to compensate an exhibitor for notswitching to a newer movie.3 Other contractual details also suggest thepotential importance of information. Contracts during my data oftenspecified a 4-week timeline, but clauses required movies to be heldover if they did especially well. Conversely, exhibitors showing moviesthat performed especially poorly were often prematurely excused fromtheir contractual obligations or, in less extreme circumstances, givena split (allowed to show another of the distributor’s movies insteadof the underperforming title at some showtimes). One of the criticaldeterminants of demand, the number of exhibiting theaters, is thusable to adjust in response to information transmission. The distributorcan also unilaterally adjust a movie’s advertising to react to wordof mouth. Advertising and promotion is typically the largest cost ofdistribution, with printing the reels of film being the other primaryvariable cost. While general advertising budgets are often set duringa movie’s production, it is relatively common to see television andnewspaper ads that reference positive word of mouth.

3. Theory

3.1 Autocorrelated Growth and Its Causes

De Vany and Walls (1996) offer a detailed model of movie-goer behaviorand claim that word of mouth is the best explanation for the substantialautocorrelation of growth in demand that they document. Their primaryempirical tests reject the linear relation between log(Revenues) andlog(Rank) implied by Pareto’s Law in favor of positively autocorrelatedgrowth.4 The method by which word of mouth can generate autocorre-lated growth in demand is sufficiently intuitive that I will dispense witha formal model in the following explanation.

A subset of potential consumers sees a movie at its opening. Theseconsumers then share their opinions (i.e., how the movie compared totheir expectations) with their acquaintances, and these acquaintances

2. Filson et al. (2005) offer evidence that the best explanation of this contract is risk-sharing rather than a correction for a principal-agent problem.

3. Given the shortening theatrical window, an increasing number of movies arereplacing this traditional declining rate with a fixed rate (e.g., 50%) of cumulative revenues.

4. An application of Chesher’s (1979) more transparent approach yields the sameconclusion.


then make their decision the following period. When this secondgeneration of viewers share their information, the source of the au-tocorrelation in demand becomes apparent. Movies with realizationsthat far exceeded consumer expectations will benefit from positiveword of mouth in both weeks, while the converse occurs when amovie’s expectations exceed its realization. Consequently, growth ratesin demand will be positively correlated. While offering an explanationof this autocorrelation, the approach taken by De Vany and Walls cannotprovide any sense of the magnitude of word of mouth.

The presence of autocorrelated growth is a sufficient indicator ofword of mouth only if there are no other explanations. It is straightfor-ward, however, to show that products that consumers usually purchaseonly once will generally exhibit such autocorrelated growth. The modelof saturation that I consider can be characterized as

Qt, j = (Mj − PastAdmt, j )πt, j , (1)where Qt,j denotes weekly sales, Mj the potential consumer populationat the product’s launch, PastAdmt,j the cumulative admissions preced-ing that period, and πt,j the probability of purchase. A finite pool ofconsumers is gradually exhausted as people purchase the product. Forsimplicity, consider the case where purchase-probability is exogenouslydetermined.5 I specify the purchase-probability as depending upon aproduct-specific term and an idiosyncratic disturbance:

πt, j = θ j + εt, j , E(πt, j ) = θ j . (2)Growth (saturation) rates in sales then take the form

gt, j = πt, jπt−1, j

− πt, j − 1. (3)

Because the movie-specific component in the probability appears di-rectly in the “growth rate,” high saturation rates last week are likely to befollowed by high saturation rates this week, and positive autocorrelatedgrowth results.

An admittedly strong restriction on the above saturation modelhas an additional implication that I will exploit, namely that there isa direct transformation to relating log(Q) to a product’s age. Define amovie’s Age as the number of full weeks since its release and assume

5. It is straightforward to show that purchase-probabilities that include endogenousvariables such as screening intensity and advertising will amplify this autocorrelation.Allowing for such purchase-probabilities to decline over time exogenously, as wouldoccur if consumers with the highest expectations see the movie first, has the same impact.


that πt,j = π for all movies and weeks.6 A movie in its opening weektherefore has Age = 0. Quantities then take the formQt, j = Mj (1 − π )Aget, j π (4)and log-quantities

ln(Qt, j ) = ln(Mj ) + Aget, j ln(1 − π ) + ln(π ). (5)Given that the discrete-choice model which supports my later workeffectively uses a variation of log-quantities as the dependent variable,it is reassuring to know that there is some theoretical support for usingAge as a way to capture the saturation process.7

3.2 A Model of Demand

The model of demand that I consider here is very similar to that usedby Einav (2007), and one particular aspect of that application war-rants discussion before considering the formal model. Several factorswhich presumably affect consumer expectations are endogenously de-termined. The number of theaters exhibiting the movie and the amountof advertising for that movie are obvious examples. If word of mouth isimportant, these endogenously determined variables will presumablyreflect (and amplify) the underlying word of mouth. “Sleeper hits”(e.g., My Big Fat Greek Wedding) gradually expand their advertisingand number of showcases before eventually tapering off. Conversely,high expectation “bombs” (e.g., The Hulk) see especially fast decays inboth advertising and screening intensity. Because I want to consider theimpacts of word of mouth on screening and advertising, I consider areduced form expression of demand (like Einav) in which the numberof exhibiting theaters and the amount of advertising have been “solvedout.” While a structural approach in which exhibiting theaters andadvertising are explicitly included is possible, it would necessarily limitword of mouth to its direct (and presumably much smaller) effect. Forthis initial application, I improve my chances of discerning word ofmouth by using the reduced form, and thus the estimated impact ofvariables on demand in this paper should be interpreted as equilibriumeffects. For example, the estimated effect of an Oscar nomination isthe sum of both the immediate effect on consumer behavior and thefeedback effect of consumer responses to increased advertising and

6. This simplifying assumption of course removes the source of the autocorrelatedgrowth.

7. This specification has been the standard in the marketing literature using weeklydata. There it is interpreted to capture both saturation and consumer preferences for“fresh” products.


screening intensity. The same pertains to the estimated impact of wordof mouth.

Much of recent empirical industrial organization has made useof the discrete choice model of demand, and I follow in this literatureintroduced by Berry (1994). Let consumer i’s belief about the utility fromseeing movie j in week t take the form

Ui,t, j = δt, j + εi,t, j (6)so that δ is the mean value of consumer utility and ε is the individualdeviation from that average utility. A consumer’s choice set also includesthe outside option of seeing no movie, and the utility of that outsideoption is normalized to zero. Throughout, I will assume that meanconsumer utility takes the form

δt, j = Xt, jβ + � j + Wtγ + f (Aget, j , α) + ξt, j . (7)Variables that vary across both movies and weeks are included in X.The three variables that I consider here are an indicator for whether themovie’s week was abbreviated by a non-Friday release, and indicatorsfor whether the movie had been nominated or won a major AcademyAward prior to that week. Rather than estimate the impact of moviecharacteristics upon consumer expectations, I instead use movie-specificfixed effects � for movies observed for at least four weeks.8 Seasonalityvariables (e.g., month and holiday indicators) are included in W. Ithen consider the reduced form impact of a movie’s age on demand(both directly and through screening intensity and advertising) with thefunction f (•). I assume that all explanatory variables are uncorrelatedwith the disturbance ξ .

Consumers choose at most one movie from among their variousoptions to maximize utility. Under these conditions, Berry (1994) showsthat there exists a unique one-to-one mapping from observed quantitiesand market size to products’ mean utilities (δ). If ε is drawn from thelogit distribution (Type 1 extreme value), then a closed-form solution forthese predicted quantities exists and this mapping is especially tractable:

δt, j = ln(Qt, j ) − ln(

Mt −∑

k∈�(t)Qt,k

), (8)

where M denotes the market size (i.e., all potential consumers), �(t)denotes the set of movies available in week t, and Q again denotes

8. Movies that I observe 3 or fewer weeks have Xjβ + χj included in their mean utilityspecification. This matches the second-stage estimation where I use estimates of � asdependent variables.


weekly quantities.9 The demand for the entire set of products is thuscharacterized by the parametric specification of products’ mean utilities.

The logit assumption, however, comes with the well-known priceof unreasonable substitution patterns. In this context, it may be anonerous restriction to impose that all consumers are equally likelyto substitute to the option of seeing no movie should their favoritemovie become unavailable. I therefore separately use the nested logitframework to allow consumer heterogeneity along three dimensions:substitution between movies and nonmovies, between action and non-action movies, and between family and nonfamily movies.10 In eachcase the parameter µ equals zero if such heterogeneity is unimportantand is bounded above by one if there is total segmentation. Applyingthe assumptions appropriate for such a nesting, the transformation fromobserved quantities to mean consumer utilities is now

δt, j = ln(Qt, j ) − ln(

Mt −∑

k∈�(t)Qt,k

)− µ ln (s Nt, j), (9)

where s Nt, j = Qt, j∑N(k)=N( j) Qt,k and N(j) is the set of available movies that sharemovie j’s characteristic along dimension N. The general regression isthen

ln(Qt, j ) − ln(

Mt −∑

k∈�(t)Qt,k

)

= µ ln (s Nt, j) + Xt, jβ + � j + Wtγ + f (Aget, j , α) + ξt, j . (10)The disturbance ξ appears in contemporary quantities, and thus sNt,j,by construction. Least squares estimation will therefore bias each µupwards, overstating the impact of segmentation, and instrumentalvariable techniques are needed to consistently estimate µ.

As pointed out by Berry (1994), an advantage of the discretechoice framework beyond its parsimonious parameterization is theprovision of instruments based upon a product’s competitive envi-ronment. Intuitively, the characteristics of rival movies will affect amovie’s admissions, but those characteristics are themselves plausiblyuncorrelated with the disturbance ξ and excluded from the mean

9. For notational convenience, I have dropped the population size that often appearsin the denominators of both terms and thereby transforms quantities into unconditionalmarket shares.

10. Bresnahan et al. (1997) introduced the Principles of Differentiation GeneralizedExtreme Value to address multiple types of consumer heterogeneity simultaneously. Myattempts to apply it in this context were prevented by excessive collinearity.


utility specification.11 I discuss the specific movie characteristics andinstruments that I employ in the data section below.

3.3 Word of Mouth

After the above parameters are estimated, I can turn to the compositionof ξ . Fixed effects for most of the movies absorb what would presumablybe the biggest such component, namely the average effect on consumerexpectations of movie characteristics that I cannot observe or measure.Letting Dj be a binary variable indicating whether movie j has a fixedeffect (i.e., is observed at least four times) and PastAdmt,j be cumulativeadmissions for movie j in week t, four other components of ξ plausiblyremain:

ξt, j = υt + ωt, j + (1 − Dj )χ j + φ j P(PastAdmt, j , Aget, j , λ). (11)The first disturbance υt is the impact of week-specific variables that arenot captured by my variables in W. The second ωt,j is an idiosyncraticdisturbance that is specific to a particular movie in a particular week.The mean valuation of a movie j’s unobserved characteristics if it doesnot have a fixed effect is χj. Last is the word of mouth disturbance. Thegap between movie j’s true quality (�j) and its expected quality (�j)is represented by the parameter φj = �j − �j, so that φj > 0 indicatesthat movie j has good word of mouth. Consistent with the reducedform estimation of demand, I assume that consumers Bayesian updatetheir beliefs from the information provided by those who have seenthe movie. Given my lack of microlevel data, I assume that consumershave identical priors and receive identical information, which togetherimply that consumers have identical posteriors. That is, as informationabout the movie spreads, consumers smoothly revise their beliefs abouta movie. Pt,j(•) then denotes the share of movie j’s word of mouth gapthat is incorporated into consumer posteriors as of week t.12

The effective share of a movie’s word of mouth (henceforth WOMshare) will presumably depend upon both the length of a movie’stheatrical run and the number of people who have seen the movie inprior weeks. The relative importance of each of these variables willhinge upon how consumers share information. Consumers telling afixed number of friends about the movie’s true quality each week when amovie is in theatres will place special emphasis on the length of a movie’srun. The opposite story of consumers telling a fixed number of friends

11. As in Einav (2007), the identifying assumption within this reduced form context isthat the portions of equilibrium advertising and screening intensity that are uncapturedby the exogenous regressors are not affected by rival movie characteristics.

12. I am grateful to the referee who suggested this application of Bayesian updating.


regardless of a movie’s run length will instead focus more upon thenumber of past admissions. Estimates using a flexible functional formfor this share and its implied responsiveness to the two variables shouldbe able to distinguish which of these explanations better describe thedata. Along these lines, my empirics begin with a simple interactionof the two inputs (which imposes identical elasticities for age andpast admissions) and then examine a polynomial specification of theseinteractions that allows for these implied elasticities to differ.

Generally, P = 0 at a movie’s release, and λ are parameters thatcapture the speed with which information travels. As P → 1, consumerutilities are based upon a movie’s true quality �j rather than its expectedquality �j. Rational expectations among consumers ensure that the aver-age word of mouth gap across movies is zero, E(φj) = 0.13 For tractabilityI assume that each disturbance is uncorrelated with the other three.The variance of each component’s disturbance is assumed constant anddenoted by subscript: Var(υt) = σ 2υ , Var(ωt, j ) = σ 2ω, Var(χ j ) = σ 2χ , andVar(φj) = σ 2φ . The magnitude of σ 2φ and information’s speed captured byλ relative to the variance of consumer mean expectations will describethe importance of the word of mouth dynamic.

This structure for the aggregate disturbance means that moviefixed effects will not strictly capture a movie’s expectation � but willinstead reflect a weighted average of the expectation and the cumulativeeffect of word of mouth. Specifically, each movie’s fixed effect will be�̂ j = � j + φ j P• j , where P•j denotes the average WOM share over thatmovie’s observed lifetime. This mixed estimate then implies that theobserved residuals are actually characterized as

ξt, j = υt + ωt, j + (1 − Dj )χ j + φ j (Pt, j − Dj P• j ). (12)There are numerous ways that observed residuals could be inter-

acted to match correlations with these parameters. I specify first-orderautoregressive patterns for week-specific and movie-and-week-specificdisturbances and exploit both the heteroskedasticity and the first-orderserial correlation implied by the above formulation. Taking the squaredresiduals as the dependent variable generates the regression

ξ 2t, j = σ 2υ + σ 2ω + (1 − Dj )σ 2χ + σ 2φ (Pt, j − Dj P• j )2 + u1t, j . (13)Intuitively, if word of mouth is present, my results should reveal anonmonotonic relationship between a movie’s age and the extent of

13. Note that this restriction is over the set of movies, not all observations. It istherefore not inconsistent with the expectation that movies with good word of mouth willhave longer theatrical runs than movies with bad word of mouth, thereby comprising adisproportionately large share of observations.


its heteroskedasticity. The speed of information and the relevant shapeof the WOM share function are revealed by the extent of asymmetry in(Pt,j − DjP•j)2. If WOM shares rise evenly over a movie’s run, then therelationship is symmetric, but especially fast information diffusion early(late) in the run will generate steeper slopes on the left (right) side. Theseparate identification of σ 2φ and λ is provided by the quadratic formand the nonlinearity of P(•).

The basis of serial correlation can likewise be shown by interactinga movie’s residual from one week with its residual from the prior week.

ξt, jξt−1, j = ρυσ 2υ + ρωσ 2ω + (1 − Dj )σ 2χ+ σ 2φ (Pt, j − Dj P• j )(Pt−1, j − Dj P• j ) + u2t, j . (14)

The empirical task is then to disentangle the serial correlation thatcomes from the word of mouth process from the serial correlation thatstems from autocorrelation of weekly disturbances and idiosyncraticdisturbances. The same intuition regarding the identification of infor-mation speed applies. Common parameters across equations suggestjoint estimation, and results show that freely estimated parameters arequite similar to their restricted counterparts.

Estimates of σ 2φ and λ that are significantly greater than zerothen indicate the presence of word of mouth. The importance of wordof mouth in variance, however, is better captured by the ratio ofσ 2φ E((Pt,j(λ) − P•j(λ))2) to Var(δt,j). This measure captures the percentageof variation in consumer expectations that the model attributes to wordof mouth and its supply-side responses. Other instructive measures arethe percentages of the disturbance’s variance Var(ξt,j) or the extent ofserial correlation E(ξt,jξt−1, j) that can be traced back to word of mouth.

4. Data

I gather the data with which I will estimate the above equations fromVariety, the motion picture industry’s trade magazine. Variety publishesthe revenues (REVt,j) of the fifty highest grossing movies in the U.S. andCanada each week, where weeks run from Friday to Thursday. This Top50 listing is fairly exhaustive; the typical 50th ranked movie grossedonly $50,500. My data set begins in August 1990 and continues throughDecember 1996, spanning a total of 332 weeks. This sample then consistsof 16,600 observations of 1602 unique movies, 1252 of which I observefor at least 4 weeks.14 Because admissions prices rose by almost 20%over this time, analysis based upon revenues may be misleading. Using

14. The empirical measure of autocorrelation naturally has fewer observations (14494).


an annual average admissions price (Price),15 I linearly extrapolate andconstruct implied quantities (Qt,j = REVt,j/Pricet).16 Consumer popula-tion M is then the combined population of the U.S. and Canada.17 Thispopulation measure is almost assuredly an overstatement of the numberof consumers who might see a movie in a given week, and I will considera fraction of this population in robustness checks.

Even though I am exploiting movie fixed effects, movie-specificcharacteristics are useful to get a sense of what drives these fixed effectsand are essential to create sufficiently powerful instruments. The ap-pendix describes in detail my measures of cast and director appeal, butboth essentially make use of the box office history of movies within theprior five years (in billions of dollars). Demand estimation using thenested logit also requires some measure of a movie’s genre. I definethe action genre as any movie that is listed as Action or Adventure bythe Internet Movie Database. A movie falls within the family genre if itis rated either G or PG.

I also consider several variables that vary across both moviesand weeks. For both the demand and word-of-mouth regressions, Idefine a movie’s Age as the number of weeks that a movie has alreadyspent on Variety’s Top 50, so that a movie in its opening week facesAge = 0. This differs from the number of weeks since a movie’s releasebecause movies are sometimes removed from theatrical circulationand then reintroduced or alternatively fall from the Top 50 and thenreturn. PastAdm is defined as the cumulative admissions of a movieprior to a week (in millions), so that a movie has PastAdm = 0 at itsopening. The announcement of Academy Award nominations and theOscar awards themselves have received some attention in the movieeconomics literature (Nelson et al., 2001). Academy Award nominationsare traditionally announced on a Tuesday morning, and (during mydata’s time frame) the Oscar ceremony was held on a Monday night. Tothis end, I consider a OscNom?tj binary variable that equals one for allweeks following (but not including the week of) the announcement thatmovie j has received a nomination in any of the six major categories.18 Idefine OscWin?tj analogously, so that its estimated effect should indicatethe additional impact in equilibrium beyond the necessary nomination.

As mentioned in the discussion of the exogenous regressors,movies are sometimes released on days other than Friday, with

15. National Association of Theater Owners (2004).16. Admissions prices tend to be fixed over time and across movies at a given theater.

While the rigidity continues to trouble economists and lawyers (Orbach and Einav, 2007),this idiosyncrasy of the exhibition sector greatly facilitates modeling.

17. U.S. Census Bureau, Statistics Canada respectively.18. Best Picture, Best Director, Best Actor, Best Actress, Best Supporting Actor, and

Best Supporting Actress.


Wednesdays being the most common non-Friday release day. Thosemovies therefore have an abbreviated week over which to accumulatetheir admissions, a situation I denote by setting the binary variableAbbWk? equal to one, zero otherwise. For instance, the first week admis-sions for movies released on Wednesday are limited to sales on Wednes-day and Thursday. Institutional knowledge offers an opportunity tobound some of these parameter values in advance. Recent daily data(Davis, 2006; Switzer, 2004) indicate that weekends make up between66% and 72% of a nonholiday week’s admissions.19 Figures derived fromrevenues are comparable. Other days of the week are roughly similarand average between 7.2% and 8.4% of a week’s admissions.

Using these figures, the normal daily breakdown of admissionsover the week suggests that a movie with such a Wednesday release priorto an ordinary weekend would garner about 16% of the admissions thatit would have received with a counterfactual release on the prior Friday.Most of these non-Friday releases, however, precede holiday weeks,with Thanksgiving being a recurring example. In that case, the observedweek essentially replaces its Wednesday with a second Friday and itsThursday with a second Saturday. If the typical weekend days accuratelycapture the demand at these holiday weekdays, then a movie with aWednesday release prior to a holiday weekend would have 36%–39%of the admissions that it would have received with a release the Fridaybefore. Assuming that Thanksgiving (or any other weekday holiday) isno more convenient to see a movie than a normal Saturday then offers anupper bound on Q j (AbbWk?=1)Q j (AbbWk?=0) ≤ 0.4. Given that some Wednesday releasesoccur before ordinary weekends and Thanksgiving (in particular) isarguably less conducive to theatrical movies than an ordinary Saturday,the average of these predicted ratios being substantially less than 0.4 islikely.

Week-specific regressors include linear extrapolations of the an-nual average admissions price and the monthly U.S. unemployment ratein my week-specific variables. Given the important role of seasonalityin demand (Einav, 2007), I also include dummy variables for eachmonth (excluding January) and eleven major holidays.20 In the demandestimation, I estimate movie fixed effects only for those movies for whichI have at least four observations and include cast appeal, director appeal,

19. Davis (2006) exploits a national survey from a single week (June 21–27, 1996).Switzer (2004) considers a comprehensive data set from September 2001 to June 2002 inSt. Louis, MO.

20. In chronological order, these holidays are New Year’s Day, Martin Luther King,Jr. Day, Presidents’ Day, Easter, Memorial Day, Independence Day, Labor Day, ColumbusDay, Veteran’s Day, Thanksgiving, and Christmas.


Table I.

Variable Definitions

Rev Weekly revenuesPrice Average admissions priceQ Weekly admissions (Rev/Price)AbbWk? Indicator of non-Friday release (abbreviated week)OscNom? Indicator of Oscar nomination prior to given weekOscWin? Indicator of Oscar award prior to given weekAge Number of prior weeks spent in Variety Top 50PastAdm Cumulative admissions (in millions)CastApp Total prior 5-year revenue history of starring cast/# of opportunitiesDirApp Total prior 5-year revenue history of directorAC? Indicator of whether movie is action/adventureFA? Indicator of whether movie is family (G or PG rating)sMovie Conditional market share (Quantity/Total quantity sold that week)sAc Quantity/Total quantity of movies that share Action status that weeksFa Quantity/Total quantity of movies that share Family status that week

action and family dummies, and an intercept for movies with fewer thanfour observations.

Table I displays variable definitions and sources, and Table IIdisplays summary statistics. The use of movie fixed effects does notspare me from the necessity of finding some explanatory variables ofsufficient power in the case of the nested logit. As results from demandwill show, a movie’s cast appeal and director appeal (determined priorto release and defined in the Appendix) are both positively correlatedwith a movie’s fixed effect estimate. I therefore consider age-weightedmeasures of competing movies’ appeal as instruments. Specifically, Iutilize these variables for competing movies that have been releasedwithin the last 4 weeks (see Table III for instrument definitions). Thus,this measure of a movie’s competitive environment is higher whenhigh appeal rival movies are younger. The validity of these instrumentsobviously hinges upon the discrete choice model’s assumptions, buttheir power can be illustrated with the data. In first stage regressions(not reported) with ln (sN) as the dependent variable, all six proposedinstruments have t-statistics (in absolute value) that exceed six and thet-statistics of five instruments exceed eight. IV regressions thereforeshould not suffer from the weak instrument problem.

5. Evidence

5.1 Demand

Least squares estimates of the logit model of demand (µ imposed tobe zero) are shown in Table IV. Asymptotic standard errors make use


Table II.

Summary Statistics

Mean Median Min. Max. Std. Dev.

By observation (N = 16,600)Rev (in millions) 1.8781 0.3595 0.0025 79.2175 4.3208Q (in millions) 0.4419 0.0849 0.0006 19.1208 1.0135Q/M 0.0015 0.0003 2.13E-06 0.0668 0.0035δlogit = ln(Q) − ln(M − �Q) −7.8021 −8.0516 −12.9180 −2.5833 1.6553sMovie 0.0200 0.0042 1.60E-05 0.5903 0.0399ln(sMovie) −5.2640 −5.4774 −11.0441 −0.5271 1.6793sAc 0.0400 0.0084 2.56E-05 0.9154 0.0788ln(sAc) −4.6013 −4.7777 −10.5901 −0.0884 1.7182sFa 0.0400 0.0079 5.64E-05 0.9189 0.0823ln(sFa) −4.6688 −4.8354 −9.7838 −0.0846 1.7687Age 8.0008 6 0 70 7.8242PastAdm (in Ms) 6.8014 2.8936 0 83.9052 10.7196AbbWk? 0.0049 0 0 1 0.0697OscNom? 0.0502 0 0 1 0.2183OscWin? 0.0120 0 0 1 0.1088

By movie (n = 1602)AbbWk? 0.0506 0 0 1 0.2192CastApp 0.0161 0 0 0.1419 0.0223DirApp 0.0325 0 0 0.7175 0.0672Action? 0.2541 0 0 1 0.4355Family? 0.2010 0 0 1 0.4009

Table III.

Definitions of InstrumentsA(j, t) = {other movies available in week t that share Action or non-Action status

with movie j}F(j, t) = {other movies available in week t that share Family or non-Family status

with movie j}

MCastt, j =∑τ=t

k �= j,τ=t−3Cast Appτ,k

Ageτ,k+1 MDirt, j =∑τ=t

k �= j,τ=t−3Dir Appτ,kAgeτ,k+1

ACastt, j =∑τ=t

k=A( j,t),τ=t−3Cast Appτ,k

Ageτ,k+1 ADirt, j =∑τ=t

k=A( j,t),τ=t−3Dir Appτ,kAgeτ,k+1

F Castt, j =∑τ=t

k=F ( j,t),τ=t−3Cast Appτ,k

Ageτ,k+1 F Dirt, j =∑τ=t

k=F ( j,t),τ=t−3Dir Appτ,kAgeτ,k+1

of the Newey-West (1994) covariance matrix, allowing for arbitrary het-eroskedasticity and incorporating 3 weeks of lagged residuals to accountfor serial correlation. As the later residual analysis will make heavy useof the age regressor, it is important to ensure that the impact of age on theunderlying demand is sufficiently robust. Consequently, I estimate six


Tab

le

IV.

Least

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III

IVV

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ba.

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ba.

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ba.

s.e.

ba.

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ba.

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tage

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00,D

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Age

—−0

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0.01

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70.

01—

——

Age

2—

—0.

0037

0.00

02—

——

ln(A

ge+

1)—

——

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80.

02−0

.30

0.05

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(Age

+1)

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——

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.33

0.02

—α

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——

——

—0.

076

0.00

4ex

p(−α

Age

Age

)—

——

——

5.06

0.15

Abb

Wk?

0.50

0.14

0.57

0.12

−1.0

20.

12−1

.70

0.13

−1.2

00.

13−1

.24

0.12

Osc

Nom

?−1

.22

0.12

1.04

0.13

0.91

0.11

0.41

0.11

0.92

0.11

0.80

0.11

Osc

Win

?−0

.70

0.18

0.75

0.19

0.00

0.18

−0.2

20.

170.

180.

16−0

.08

0.16

R2

(ln(

s j/

s 0)a

sD

V)

0.42

0.67

0.73

0.71

0.73

0.74

R2

(Qj/

Mas

DV

)0.

070.

390.

580.

530.

580.

61

Ab%

1.65

0.57

0.36

0.19

0.30

0.29

Osc

Nom

%0.

302.

822.

481.

512.

502.

21O

scW

in%

0.50

2.11

1.00

0.80

1.20

0.92

2nd

stag

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=12

52,D

V=

�

Cas

tApp

eal

15.5

61.

4316

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1.58

17.6

21.

6417

.42

1.57

17.3

91.

6417

.67

1.65

Dir

ecto

rApp

eal

3.36

0.45

4.32

0.49

4.60

0.47

4.39

0.45

4.53

0.48

4.57

0.47

Act

ion?

0.33

0.07

0.40

0.07

0.41

0.07

0.40

0.07

0.41

0.07

0.41

0.07

Fam

ily?

0.21

0.08

0.50

0.08

0.55

0.09

0.51

0.08

0.55

0.09

0.55

0.09

Con

stan

t23

.54

0.05

−2.7

60.

05−8

.13

0.05

−3.6

80.

05−7

.65

0.05

−13.

230.

05

R2

(�j

asD

V)

0.20

0.25

0.26

0.26

0.26

0.26

R2

(Qj/

Mas

DV

)−0

.04

0.11

0.18

0.21

0.20

0.21

Not

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regressions reflecting different specifications of the function f (Aget,j, α).I then regress the estimated movie fixed effects on my cast and directorappeal variables, genre dummies, and a constant. Besides offering someempirical support for my instruments, these second-stage results canshed additional light in the movie economics literature on what pre-release variables have explanatory power. They also offer an opportu-nity to consider how much the industry’s variation in quantities can beexplained in the usual absence of such estimated movie fixed effects.

The differences between results that ignore even first-order im-pacts of age and those that include Age as a regressor are intuitive (TableIV (I and II). Excluding Age forces the model to inflate the estimated effectof an abbreviated week (because AbbWk? necessarily coincides with theyoungest movies), suggesting that abbreviated weeks actually increasedemand over the hypothetical full week. Likewise, ignoring saturationdramatically decreases the estimated impact of the Oscar variables(because both only occur late in a movie’s commercial run). Measuresof fit to the dependent variable δ and the more interesting purchase-probability (Qt,j/Mt) both rise appreciably when the Age regressor isincluded. The results of the second-stage regression do not differ muchacross the two specifications. While cast appeal has often been foundto affect demand, these results further confirm the less widely notedsignificant impact of a movie’s director on consumer expectations asfound by Chen, Mitra, and Shugan (2006).

The age quadratic (Table 4 (III)) extends this trend for the estimatedimpact of an abbreviated week. This specification yields an averageestimated ratio of actual revenues to hypothetical revenues of about 36%(shown below first stage measures of fit as Ab%), within the bounds indi-cated by both Davis and Switzer [0.15, 0.40]. The estimated impacts of theOscar variables, however, change markedly. While including Age aloneindicates that both nominations and awards have statistically significantimpacts on consumer expectation, the quadratic specification shows thatthe nomination result is somewhat inflated and that the award result isentirely spurious. At these point estimates, a few observations (184 of16,600) have such high ages that the quadratic specification suggeststhat mean utility is increasing in Age. I therefore also consider threespecifications where such nonmonotonicity is impossible or less likely.

Table IV (IV and V) display results when ln (Age + 1) is used aloneand when it is supplemented with ln (Age + 1)2. Using ln (Age + 1) aloneappears to overstate the initial impact of a movie’s age on its demand,but the quadratic specification generates results comparable to those ofTable 4(III) without the unappealing implication of mean utility increas-ing for especially long-lived movies. As a last functional form, Table IV(VI) shows NLLS estimates in which I use an exponential function as the


age specification: f (Aget,j, α) = α1exp(−α0Aget,j). The logit fit improvesonly marginally with the nonlinear specification, but there is a greaterimprovement in the fit to purchase-probabilities (Q/M). In other results,the impacts of an Oscar nomination and an abbreviated week are bothfurther diminished. Given these (slight) improvements, I will use thisexponential form for the remaining results. Going forward, it seemsthat one can conclude from the second-stage estimates that both actionand family movies gross more than their nonaction and non-familycounterparts and that this simple model can explain about 20% of theindustry’s variation in admissions.

While the logit results are useful for expressing correlations be-tween the regressors and quantities, the imposed restriction that con-sumers are homogeneous in their perceived substitutability betweenmovies of different genres or between movies and the nonmovie optionis likely untenable. I therefore reestimate the unrestricted demand usingthe Generalized Method of Moments (Hansen, 1982) and the afore-mentioned competitive environment instruments.21 Table V displaysresults, with the earlier logit results shown in Table V(I) for comparison.In all regressions, estimates indicate that segmentation is statisticallysignificant at conventional levels, and neither the movie or familysegmentation models are rejected by the implied J-statistic. Potentialsegmentation between action and nonaction movies is estimated to bethe weakest, and it could be argued that such segmentation is not eco-nomically important. Consumer heterogeneity regarding substitutionbetween movies and the nonmovie option and between family andnonfamily movies, however, are estimated to be quite important. Theconclusion regarding the latter (Table V(IV)) speaks to Ravid’s (1999)finding that G-rated movies are historically quite profitable. Whilethe average consumer preference may be a dislike for Family movies(evidenced by the negative coefficient in the second stage), there existsa population (e.g., parents with small children) that will only consider Gand PG rated movies. If competition for these consumers is light, such amovie could be lucrative, especially given the typically low productioncosts of such movies.

Implications of the demand estimates are stable across thesedifferent specifications. In all, receiving at least one Oscar nominationin a major category boosts demand about 120%, but winning a com-parable Oscar has no significant impact. Movies facing abbreviatedweeks receive about 30% of the demand from their counterfactualweek, again within the bounds suggested by other data. The variables

21. In each case, a Hausman statistic clearly rejects the hypothesis that least squaresestimation of the nested logit specification is consistent.

878 Journal of Economics & Management StrategyTab

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V.

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este

dL

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mate

s

III

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5.06

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and fixed effects can explain about 75% of the variation in mean utili-ties, and predicted purchase-probabilities using estimated fixed effectscapture between 60% and 70% of the variation in observed purchase-probabilities. Predicted purchase-probabilities using the second-stagecoefficients instead of the estimated fixed effects explain about 29% ofthe variation, as opposed to 21% for the straight logit. In all, the model(especially when making use of the fixed effects) appears to do a fair jobof matching the data.

As mentioned in Section 3, all these estimates are based uponthe pool of potential consumers being the combined population ofthe United States and Canada. Demand estimates using the discrete-choice model are typically robust to one’s choice of market size, but mymodel’s emphasis on the impact of word of mouth on mean consumerexpectation could generate difficulties when estimating the primaryparameters of interest. To see whether my information transmissionresults are robust to choice of market size, I therefore reestimate themore successful nested logit models (segmentation by movie and byfamily) using an assumed market size of 25% of the full population.Table V(V and VI) displays these results. The only differences by marketsize appear to be a lower estimation of the nested logit parameter µ(leading to an upward rescaling of all other multiplicative coefficients)and a higher probability of rejecting the validity of the exclusion restric-tions. Segmentation between inside and outside options is often used tominimize the importance of the choice of market size, so this is at somelevel unsurprising. The primary robustness concern, however, pertainsto the word of mouth parameters, and so I will return later to applythese quarter-population estimates.

5.2 Analysis of Error Components

This analysis hopes to exploit heteroskedasticity and serial correlationacross disturbances (all residuals are taken from the nested logit usingln (sMovie)). A logical first step is to document such features of the databefore applying additional structure. The evidence of serial correlation,albeit of undetermined source, is strong. Using residuals e = δ − Xβ̂from the 14,494 observations in which I see the same movie in consecu-tive weeks in a standard AR(1) regression yields

et, j = 0.662et−1, j + �t, j0.005. (15)

The standard error is beneath the point estimate, and the fit is reasonable(R2 = 0.55). The presence of heteroskedasticity is also clear (Var(e2tj) =0.05 vs. E(e2tj) = 0.11), but again the source is uncertain. Given that the


model’s predictions are regarding how these measures change over amovie’s run, these findings are necessary but far from sufficient foridentifying word of mouth.

It is straightforward to plot a time series of heteroskedasticity andserial correlation for any particular movie, but cross-movie comparisonis complicated by the varying length of movies’ theatrical runs. Thegeneral prediction, however, pertains to the location of observationsrelative to the total movie run. I therefore consider only movies thatI observe at least four times (the same criterion for the application ofmovie fixed effects) and for the entire theatrical run, focusing upon howthe residual relationships change over fractions of the movie’s run. Theserestrictions reduce my number of movies for the heteroskedasticitygraph to 1190. I then assign the opening and closing week’s values toendpoints and linearly extrapolate between intermediate points. Myapproach is essentially the same for the serial correlation graph, exceptthat I further restrict the movies so that only movies observed for 2consecutive weeks at least twice are included, reducing the sampleto 1186 movies. The following graphs are then simple averages acrossmovies at 101 points from 0 to 1 inclusive in 0.01 increments.

Figure 1 shows a graph of the average imputed e2 over the setof movies for different fractions of the total theatrical run. This het-eroskedasticity graph reaches its minimum at about 0.4, and aroundthis minimum there is a strongly asymmetric and nonmonotonic shape.Both the minimum being to the left of the midpoint and the steepdrop-off early in movie runs suggest that information is well dispersedquickly (i.e., increases in the WOM share are dramatic early in the runand modest later in the run). The same features are evident for serialcorrelation in Figure 2, which shows a graph of the average imputedetet−1 over the appropriate set of movies. Both figures then suggest thatthe residuals exhibit the underlying features for the following analysisto discern word of mouth and the speed of information.

I begin with a exponential functional form for the WOM share P:

Ptj = 1 − exp(−λAget, j Past Admt, j ). (16)Table VI(I) displays NLLS results of this joint estimation of equations(12) and (13) from Section 3:

e2t, j = σ 2υ + σ 2ω + (1 − Dj )σ 2χ + σ 2φ(Pt, j − Dj P• j

)2 + u1t, j (17)et, j et−1, j = ρυσ 2υ + ρωσ 2ω + (1 − Dj )σ 2χ

+ σ 2φ(Pt, j − Dj P• j

) (Pt−1, j − Dj P• j

) + u2t, j . (18)Identified parameters are λ, (σ 2υ + σ 2ω), σ 2χ , σ 2φ , and (ρυσ 2υ + ρωσ 2ω).


Average estimated heteroskedasticity (et,j2) over movie runs (1190 movies)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Fraction of total run length

Mea

n im

pute

d e

e*

Notes: Figure uses linear extrapolations from observed points to construct movie-specificheteroskedasticity graphs and then averages over movies. Included movies are observed frominitial release to final week of theatrical release.

FIGURE 1. HETEROSKEDASTICITY

All parameters are precisely estimated. Information is estimatedto travel quickly: these parameter estimates suggest that in a movie’sfourth week of theatrical release, the WOM share is 50% if 210,000persons have already seen the movie. Given the simple parameteriza-tion, any comparable combination of age and past admissions yieldsthe same share (e.g., 315,000 past admissions going into the thirdweek also generate a 50% WOM share). Information is almost fullyand immediately dispersed when 3 million people (i.e., about $15 Min box office) see a movie in its opening week. These estimates alsogive a sense of word of mouth’s importance in the industry. Interactingthe average WOM share terms with the estimate of σ 2φ indicates thatinformation transmission among consumers explains 9% of the variancein implied mean utilities. This same approach suggests that word ofmouth drives 35% of observed heteroskedasticity and 26% of observedserial correlation of the residuals.


Average estimated serial residuals (et,jet+1,j) over movie runs (1186 movies)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Fraction of total run length

Mea

n im

pute

de (

e te t

-1)

Notes: Figure uses linear extrapolations from observed points to construct movie-specific serialresidual graphs and then averages over movies. Included movies are observed from initial releaseto final week of theatrical release.They are further limited to those movies that are observed for two consecutive weeks at least twice.

FIGURE 2. SERIAL CORRELATION

Table VI(II and III) show that the simultaneous estimation of theheteroskedasticity and serial correlation equations are not driving theprimary results. While both obviously achieve higher measures of fit inthe absence of the cross-equation restrictions, neither is remarkably dif-ferent from the fits implied by joint estimation. The heteroskedasticity-alone equation accommodates word of mouth by allowing slightly fasterinformation transmission but reducing the variance in movies’ word-of-mouth gaps. The serial correlation-alone equation, however, puts moreemphasis on both parts of information transmission. This is confirmedby the fact that word of mouth is now estimated to explain almost40% of observed serial correlation. Despite this one curious result, theseparate estimations generally support the validity of the cross-equationrestrictions.

As mentioned above, the functional form for the WOM share isquite restrictive. For instance, it is straightforward to show that this


Tab

le

VI.

NL

LS

Esti

mati

on

of

Hete

ro

sked

asti

cit

yan

dS

er

ial

Co

rr

elati

on

Reg

ressio

ns

e2 t,j

=σ

2 ν+

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specification implies a movie’s elasticity of WOM share with respect toage will be the same as its elasticity of WOM share with respect to pastadmissions. Allowing the model more flexibility, however, may revealmore about how information moves among consumers. To this end,Table VI (IV) displays results in which I consider Age2 ∗ PastAdm andAge ∗ PastAdm2 as well as Age ∗ PastAdm as regressors in the WOM sharespecification. These estimates suggest that a movie’s length of theatricalrun dominates the number of past admissions in affecting the relevanceof word of mouth. While both implied effective share elasticities arepositive, the elasticity of WOM share with respect to age is everywherelarger than that with respect to past admissions. At the margin, word ofmouth is better spread by holding a movie an additional week than byhaving it seen by a comparable percentage increase of consumers. Thisexpanded specification does not otherwise substantively change any ofthe other parameters or implications.

The choice of the number of potential consumers has already beenexplored with respect to demand estimates, but it might be expected tohave a larger impact here on the speed with which information increasesthe WOM share. Specifically, if one reduces the relevant population from300 million to 75 million, this might suggest even faster informationdispersal. Table VI (V) displays results of joint estimation using theresiduals from the movie-nested logit with 25% of the population.Information speed increases slightly, but this increase is well withinthe margin of statistical error. Furthermore, the magnitudes of word ofmouth’s importance are virtually identical to those generated using fullpopulation. The differences in other parameters appear to be strictly amatter of scale. Much like the demand estimates themselves, these wordof mouth results appear to be robust to the choice of market size.

This measurement of word of mouth could also be driven by anoverly restrictive specification of the age decay in the demand estima-tion. For example, demand for horror movies is often thought to decayespecially quickly. My model could be misattributing this regularityto those horror movies all having bad word of mouth, and nonhorrormovies having favorable word of mouth. To this end, I considered richerspecifications in the original demand estimation (not reported). Thesespecifications include allowing movie decay to vary across genres andallowing movie decay to vary during the sample. While several of thesespecifications yielded significant results in the demand estimation, nonematerially affected the estimates of the speed of information or therelative magnitudes of the various σ 2 parameters.

My last robustness check pertains to the assumed functional formof the WOM share function. Prior estimation used an exponential form,but I also consider a fractional form:


Table VII.

Implied Word of Mouth Shares (Percentages ofWord of Mouth Gaps That Are Incorporated into

Consumer Posteriors)

PastAdm (in M)

Pr = 1 − exp(Zλ) 0.05 0.1 0.25 0.5 1 21 0.03 0.07 0.16 0.29 0.49 0.732 0.09 0.17 0.38 0.61 0.84 0.97

A 3 0.16 0.30 0.59 0.83 0.97 1.004 0.25 0.44 0.76 0.94 1.00 1.005 0.35 0.57 0.88 0.99 1.00 1.00

PastAdm (in M)

Pr = Zλ/(1 + Zλ) 0.05 0.1 0.25 0.5 1 21 0.04 0.08 0.18 0.31 0.47 0.632 0.12 0.21 0.40 0.57 0.72 0.84

A 3 0.21 0.35 0.57 0.73 0.84 0.914 0.31 0.47 0.69 0.81 0.90 0.945 0.40 0.57 0.77 0.87 0.93 0.96

Note: All probabilities use estimates from Table VI (IV and VI).

Ptj = λZt, j/(1 + λZt, j ). (19)

Results based upon this specification can be found in Table VI (VI). Thegeneral conclusions regarding information’s relative dependence uponage and past admissions remain. Other parameters are largely the same,as are measures of fit and the magnitudes of word of mouth’s variouscontributions. Table VII displays the implied WOM share under the twospecifications. While both are similar, the exponential form leads to vir-tually complete dispersal of information under weaker conditions thanthe fractional form. The underlying message of the results, however, isthat this functional form choice appears to be relatively unimportant.This is reinforced by results (not shown) that allowed for information tospread independently of the past admissions and length of movie run(i.e., a binary variable denoting nonopening weeks included in the WOMshare function). Such a variable being important would be consistentwith the story that information exogenously escapes after opening weekand unilaterally raises the effective WOM share. The coefficient on thisbinary variable, however, was always quite close to zero and neverattained any level of statistical significance, further confirming that theage and past admissions specification sufficiently captured the spreadof information.


5.3 Simulations

To explore the economic significance of word of mouth, I use the fullmodel’s estimates using the fractional probability specification (Table VI(VI)) to simulate market outcomes for single movies of varying expec-tation and word of mouth. I emphasize the impact of word of mouth byremoving a number of sources of additional noise. Specifically, I removeseasonality in demand, so that all weeks are assumed to have the sameintrinsic demand as a nonholiday week in January. The week-specificcomponent of the error (υt) is thus aggregated into the movie-and-week-specific component (ωt,j). There are no Oscars or abbreviated weeks.Finally, I assume that release dates are exogenous and that there arefive potential releases each week (note that a release will not necessarilybreak into the Top 50).

I use the sample of estimated movie fixed effects to guide mysimulated movies, assuming that their expectations are drawn froma normal distribution with mean of −7.56 and standard deviation of0.52.22 These estimates actually reflect a weighted average of openingexpectations and word of mouth adjustments, and so they are probablysomewhat higher than the underlying expectations. By construction,there are many more observations involving good word of mouththan poor. The following simulations, however, yielded similar resultswhen I attempted ad hoc corrections for this bias, and I continue withthe parameters suggested by the estimated fixed effects. Mean con-sumer utilities therefore take the form δt, j = � j + α1 exp(−α0 Aget, j ) +φ j (

λZt, j1+λZt, j ) + �t, j . Movie and week deviations � follow an AR-1 process

(�t,j = ρ�t−1, j + νt,j) where ρ =0.71 and the shocks ν are also drawnfrom a normal distribution. This value of ρ is derived from the ra-tio of (ρυσ 2υ + ρωσ 2ω) to (σ 2υ + σ 2ω). Assuming that V(�) equals the es-timated value of σ 2υ + σ 2ω = 0.062 and given this value of ρ , V(ν) =0.031, so that ν are drawn with mean zero and standard deviation of0.176.

I first create a population of Top 50 movies, none of which haveany word of mouth (φ = 0). That is, I take 50 draws from the movie fixedeffect � distribution, all of which represent newly released movies sothat Age = 0, and 50 draws from the disturbance ν distribution. Sharesare then constructed using the implied δs and the segmentation estimateµMovie = 0.62. To create a baseline with a plausible mix of old high-expectation movies and new movies of varying expectations, I allow thepopulation to evolve for 15 additional weeks with five potential newmovies released each week. For example, in the second week, I take

22. I cannot reject that the fixed effect sample is normally distributed with 99%confidence. The implied/t-statistics/ regarding skewness and kurtosis are 2.57 and 1.21.


five additional draws from the movie fixed effect distribution and 55additional draws from the disturbance distribution. Using these drawsand changing the original movies’ ages from 0 to 1, I create the newdisturbances �s and mean utilities δs. I then discard the five movieswith the lowest δs and construct shares for the remaining 50 movies.It is into this population of movies (the oldest of which is no morethan 16 weeks old) that I introduce each hypothetical movie (and fourother movies with no word of mouth as before). I then observe thishypothetical movie’s theatrical run as implied by the estimated model.Throughout I assume that the average admissions price is the samplemean (Price = 4.24) and that the combined U.S.-Canada population is300 million persons.

I begin with movies of average expectation (� = −7.56) and sep-arately consider three cases: good word of mouth (φ = +σ̂φ ), no wordof mouth (φ = 0), and poor word of mouth (φ = −σ̂φ). I then repeat theexercise for movies with low expectations (� = −7.56 − 0.52) and highexpectations (� = −7.56 + 0.52). Each simulation is repeated 100 times,and the following graphs report the average unconditional market share(Q/M) by the week of the movie’s release as well as cumulative revenuesand a crude estimate of theatrical rentals.

Figures 3–5 show the results of these simulations. Figure 3 displaysthe hypothetical runs of movies with average expectations. The moviewith favorable word of mouth has its admissions peak at 3–4 weeks(rather than at the opening) and exceeds its opening week’s receiptsthrough its eighth week. It plays in theaters for 20 weeks and grosses$33 M. This obviously contrasts with the movie with poor word of mouthwhich plays in theaters for only three weeks and grosses $3.2 M, but italso substantially differs from a movie with no word of mouth whichplays in theaters for seven or eight weeks and grosses about $7 M. If oneapplies the industry standard that half of box office receipts of returnedto the distributor in the form of rentals, the distributor collects $15 Mmore from the movie with good word of mouth than from the one withpoor word of mouth.

Contrasting these figures offers a way to visually compare theimpacts of age and past admissions in transmitting information amongconsumers. Figure 4 shows what happens with movies with low expec-tations. The movie with good word of mouth sees its admissions peak at4–5 weeks, a week later than in the case with average expectations. Thecomparable situation in the bottom panel’s movies with good expecta-tions reveals a more immediate peak at 3 weeks. The difference betweengood and bad word of mouth is most apparent when considering movieswith good expectations (shown in Figure 5). The movie with favorableword of mouth plays in theaters an average of 42 weeks, grossing $147 M


0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Week

mea

n(Q

/M)

Good WoM No WoM Bad WoM

Note: Good WOM Rev = 33.0M, No WOM Rev = 7.4M, Bad WOM Rev = 3.2M.

FIGURE 3. MOVIES WITH AVERAGE EXPECTATIONS (� = −7.56)

with likely rentals of $66 M.23 A movie with the same expectations butno word of mouth, however, is in theaters for 14 weeks and grosses only$29 M. Negative word of mouth substantially shortens both the run andtotal box office, to 6 weeks and $12 M.

6. Conclusions

This paper has provided a technique to measure the empirical impor-tance of word of mouth in a industry’s demand, and applied it to thedomestic theatrical movie sector. Unlike the approach advocated by DeVany and Walls (1996), this technique can identify word of mouth inthe presence of demand that saturates with prior purchases and offersinterpretations of magnitudes that suggest the economic importanceof information transmission. My results indicate that word of mouthexists, representing about 10% of the variation in implied consumerexpectations among theatrical movies. This information transmission isalso an important generator of autocorrelation and heteroskedasticity.Information appears to affect consumer behavior quickly, with ageplaying a larger role than past admissions. For those interested in more

23. Movies with such long runs tend to have lower average rental rates, and I thereforeassume an average rental rate of 45% for this case.


0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Week

mea

n(Q

/M)



FIGURE 4. MOVIES WITH LOW EXPECTATIONS (� = −8.08)

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Week

mea

n(Q

/M)



FIGURE 5. MOVIES WITH HIGH EXPECTATIONS (� = −7.04)

closely examining word of mouth, the industry may provide a goodstudy.

The fact that my model treats theatrical intensity and advertising asequilibrium values rather than explicitly modeling them limits policy


prescriptions, but one implication stands out. Exploiting good wordof mouth will be most difficult for those movies with relatively lowexpectations. The matter will largely resolve itself for such movieswith high expectations. As my results indicate that age plays a biggerrole than past admissions, these movies would seem to have a betterchance of receiving the necessary longer theatrical run if released attimes in which they do not face fierce competition for theatrical screens(e.g., January–April, September and October). The converse of high-expectation movies with bad word of mouth being released at high-demand periods also applies, of course, but that result has clearly beenemployed to great effect by the industry.

This paper has made a number of simplifying assumptions in anattempt to document the presence and magnitude of word of mouthin this context. Future work may relax these restrictions to address aricher set of hypotheses regarding the factors that influence informationtransmission among consumers. This particular sample ends at the timethat the Internet was beginning to have a real impact on consumerdecisions. A lengthened sample could consider how Internet accesschanged the speed with which age and prior purchases affected theeffective share of word of mouth. Likewise, the 1990s were an especiallydynamic decade with respect to theatrical exhibition, as evidenced bythe expansion boom and then bankruptcy of several of the largest theaterchains. How these supply-side changes and their consequent impacts onmovie decay rates affected the spread of information remains an openquestion.

Appendix

I define an actor or actress’s revenue history at the time of a specificmovie to be the sequence of final grosses of all recently released moviesin which he or she was a starring cast member. (Chen and Shugan,2004, use a similar measure.) In my data, this time frame ends with therelease of the specific movie and begins 5 years prior to that release.Various statistics can then be used to summarize this revenue history,and, in the case of multiple-star movies, other statistics aggregatethe several revenue histories and summarize the cast appeal of themovie as a whole. Examining directors is simpler, as movies usuallyhave a single director. There is correspondingly no issue regardingaggregation of multiple directors or regarding whether a director is a“star.” Directors of movies and their performance histories can be foundin The Annual Index to Motion Picture Credits and the Internet MovieDatabase.


Recognizing that distributors have an interest in informing thepublic about the presence of celebrities, I use movie advertising in theFriday New York Times as a guide to which cast members are the stars ofthe movie. Just as theaters of the past used their marquees to advertisestar presence, many Times ads early in a movie’s run include the namesof a few members of the cast. To maintain tractability, I limit this toprinted names and not pictures of cast members. The one exception isfor sequels, for which a picture of a recurring character is the equivalentof a printed name. I assume that these individuals are the starring cast ofthose movies (unless certain names are more prominent than others, inwhich case only the most prominent names are the movie’s stars). Whilea few movies listed many names, most ads that list any cast display onlytwo or three names.

I build my measure of cast appeal by summing up the revenuehistories of the marquee cast and dividing by the number of moviesreleased in the prior five years in which those cast had starred. Thismeasure is intuitive in that it tends to be lower when a movie’s stars arenumerous but not very successful at the box office (e.g., Robert Altmanfilms) and when a starring actor in a movie is prolific but not verylucrative (e.g., post-Ghostbusters Dan Aykroyd). I measure the appealof the director by simply summing that individual’s revenue history.Both these appeal variables are then scaled in billions of dollars. As anexample, 1993’s Jurassic Park’s director appeal is calculated as the totaldomestic box office of Steven Spielberg’s three movies in the 5 yearsprior (Hook, 1991; Always, 1989; and Indiana Jones and the Last Crusade,1989), or $0.36 B.

References

Berry, S., 1994, “Estimating Discrete Choice Models of Product Differentiation,” RANDJournal of Economics, 25, 242–262.

Bikhichandi, S., D. Hirshleiffer, and I. Welch, 1992, “A Theory of Fads, Fashion, Custom,and Cultural Change as Informational Cascades,” Journal of Political Economy, 100,992–1026.

Bresnahan, T., S. Stern, and M. Trajtenberg, 1997, “Market Segmentation and the Sourcesof Rents from Innovation: Personal Computers in the Late 1980s,” RAND Journal ofEconomics, S17–44.

Chen, Y., D. Mitra, and S. Shugan, 2006, “People Metrics for Preconcept Forecasting,”Working paper, University of Arizona Eller College of Management.

Chesher, A., 1979, “Testing the Law of Proportionate Effect,” Journal of Industrial Economics,27, 403–411.

Chevalier, J. and D. Mayzlin, 2006, “The Effect of Word-of-mouth on Sales: Online BookReviews,” Journal of Marketing Research, 43, 345–354.


Corts, K., 2001, “The Strategic Effects of Vertical Market Structure: Common Agencyand Divisionalization in the U.S. Motion Picture Industry,” Journal of Economics andManagement Strategy, 10, 509–528.

Davis, P., 2006, “Spatial Competition in Retail Markets: Movie Theaters,” RAND Journalof Economics, 37, 965–982.

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Measuring Word of Mouth's Impact on Theatrical Movie Admissions · 2014-08-06 · Measuring Word of Mouth’s Impact on Theatrical Movie Admissions CHARLES C. MOUL Washington University