Measuring Word of Mouth's Impact on Theatrical Movie Admissions
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Measuring Word of Mouth’s Impact
on Theatrical Movie Admissions
CHARLES C. MOUL
Washington University Department of Economics
Campus Box 1208
St. Louis, MO 63130-4899
moul@artsci.wustl.edu
Information transmission among consumers (i.e., word of mouth) has received
little empirical examination. I offer a technique that can identify and measure
the impact of word of mouth, and apply it to data from U.S. theatrical movie
admissions. While variables and movie fixed effects comprise the bulk of observed
variation, the variance attributable to word of mouth is statistically significant.
Results indicate approximately 10% of the variation in consumer expectations
of movies can be directly or indirectly attributed to information transmission.
Information appears to affect consumer behavior quickly, with the length of a
movie’s run mattering more than the number of prior admissions.
1. Introduction
Despite its widespread theoretical implications in environments of
incomplete information, information transmission among consumers
(a.k.a. word of mouth) has received relatively little empirical support. In
this paper, I show that an existing method of detecting word of mouth is
overly broad, in that its empirical prediction of autocorrelated growth
can also be generated by a simple model of saturation in demand. I
instead offer a model of demand that can accommodate both saturation
and word of mouth, and then consider its implications within an error
components framework. Applying this technique to U.S. theatrical
admissions, my estimates suggest that word of mouth is statistically
and economically significant and that information travels quickly to the
average consumer in commonly observed situations. Simulations using
these estimates confirm that word-of-mouth can have large impacts on
how movies play out in theaters.
I thank the editor and two anonymous referees for comments on an earlier draft that
greatly improved the paper. Seminar participants at Washington University in St. Louis
and the DeSantis Center’s Business and Economics Scholars Workshop also provided
helpful feedback. The usual caveat applies.
C 2007, The Author(s)
Journal Compilation C 2007 Blackwell Publishing
Journal of Economics & Management Strategy, Volume 16, Number 4, Winter 2007, 859–892860 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 economic
outcomes closer to the full information ideal. This intuitive insight has
been formalized by Ellison and Fudenberg (1993, 1995) who present
mechanisms for and implications of what they refer to as social learning.
Furthermore, either word of mouth or repeat purchases are essential in
the theoretical literature explaining how advertising can be used as a
signal of quality in a separating equilibrium (Nelson, 1974; Milgrom
and Roberts, 1986). The speed and manner of information transmission
among consumers, however, are inherently empirical questions, and it is
there that I will concentrate my efforts. Given the presumed importance
of word of mouth in the theatrical sector of the movie industry, these
results also potentially have bearing on the best responses to information
transmission among consumers.
I discern information transmission by interpreting my model’s
residuals, 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 exogenously
revealed after a movie’s release (e.g., late movie reviews, published box
office announcements, etc.). With that caveat in mind, the general idea
of my approach is that word of mouth will be revealed in a specific
and well-defined manner. Products presumably have unique differences
between consumer expectations and realizations (the information that
is relayed by word of mouth). All products, however, will begin their
commercial lifespans in the absence of such information. If a product
stays available for a long enough time and enough consumers purchase
it and share the product’s true quality, then the original consumer
expectations will be supplanted by the conveyed realized quality.1 This
systematic spread of information has implications for serial correlation
and heteroskedasticity, specifically that both will increase over a movie’s
theatrical run. My use of movie fixed effects in estimation alters this
prediction, in that heteroskedasticity and serial correlation based upon
these residuals will be nonmonotonic (specifically U-shaped) over each
movie’s run. The speed of information can then be inferred from the
nature 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 of
mouth) as well as actions are observable. See Bikhichandi et al. (1992). This framework
also implicitly assumes that consumers are aware of all products’ existence. Relaxing this
assumption and allowing word of mouth to affect the likelihood that a consumer knows
of a product’s existence is a potential extension, though a computationally burdensome
one. This burden arises as observed quantities are the weighted averages of all possible
combinations of consumer awareness. At the 50 weekly movies observed in my sample,
this would require the calculation of 250 − 1 probabilities of each potential combination
of movies and 50 ∗ 249 informationally conditional quantities.Theatrical Movie Admissions 861
This proposed error components approach differs substantially from the
prior literature which either exploits additional information regarding
the sign and extent of the information gap (e.g., Chevalier and Mayzlin,
2006) or takes advantage of detailed microlevel data (e.g., Foster and
Rosenzweig, 1995).
This paper is not the first to use movie admissions in an attempt to
document word of mouth. De Vany and Walls (1996) show that informa-
tion transmission among consumers will cause autocorrelated growth
rates among movies. They then document rejections of a Pareto Law
relationship in favor of positively autocorrelated growth, and interpret
this as evidence of word of mouth. This paper makes two improvements
upon that work. First, I show that positively autocorrelated growth can
also be generated by a simple model in which consumers typically buy
a product at most once (as seems likely in the theatrical movie industry
and many others). Second, my approach can not only detect the presence
of word of mouth, but can also provide measures of the importance of
that information transmission.
The movie industry has been the subject of several other studies
in recent years. Moul (2001) finds that, from the late 1920s to early
1940s, studio revenues rose with experience using synchronous sound
recording technology and interprets this as evidence of qualitative
learning-by-doing. Einav (2007) decomposes the seasonal demand for
theatrical movies into an underlying component and the amplification
that arises from endogenous industry practices. Corts (1998) looks at
the issue of theatrical release timing in finding that a studio’s divisions
largely 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 two
studios cofinancing a movie. Finally, Ravid (1999) examines measures
of profitability over a movie’s entire commercial run rather than simply
revenues in a particular sector.
This paper makes some contributions to this literature beyond its
conclusion regarding the importance of word of mouth in theatrical
admissions. My initial estimates of demand are generally plausible and
conform well with implications of other studies. As expected, ignoring
and imperfectly addressing saturation in demand substantially distort
the predicted impacts of Oscar nominations, awards, and abbreviated
weeks. Estimates of the full model suggest that Oscar nominations have
a substantial impact on admissions in equilibrium, but indicate no such
comparable bump from winning the award. Prior commercial perfor-
mance of both starring cast and director have significant impacts on
consumer expectations in equilibrium. There is also strong evidence of862 Journal of Economics & Management Strategy
heterogeneity among consumers in how they substitute between movies
and other goods, as well as between family and nonfamily movies.
My error components approach reveals that information travels
quickly to the average consumer, though this is obviously dependent
upon how many people have seen the movie. For example, a movie that
has been seen by 200,000 persons by its fourth week can expect that
consumers behave as if they have incorporated 50% of the difference
between the movie’s true and originally expected quality. This level
of incorporation exceeds 90% for movies of comparable age that have
been seen by 1 million persons. Estimates of the importance of word of
mouth are also informative and robust. About 10% of the variance in the
model’s implied consumer expectations is attributable to information
transmission. Of the unobserved disturbances, roughly 38% of the
variance can be attributed to word of mouth. Word of mouth is less
critical in explaining serial correlation of unobserved demand shocks,
explaining about 32% of that phenomenon. Simulations from these
estimates indicate that a movie of average expectations but with good
word of mouth will gross $30 M more than a movie with the same
expectations and bad word of mouth. I conclude with a discussion of
implications for research on movies and other similar industries.
2. Industry
While the length and importance of the theatrical window of a movie’s
commercial run have recently diminished relative to the video market, it
still offers a unique advantage over other periods of a movie’s lifespan: at
release, consumers have only their expectations upon which to base their
decisions. 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 institutionally
evolved to exploit favorable word of mouth. Moul and Shugan (2005)
further argue that the current strategy of wide release that replaced the
multi-run structure in the 1970s is at least in part an attempt to limit the
adverse effects of negative word of mouth. In the original structure of
theaters sequentially showing older prints, only movies with favorable
word of mouth could be expected to have long and lucrative runs.
The new structure offers the chance for movies that generate negative
word of mouth to yield at least some returns in the initial wide release,
even though the movie’s commercial run will be short as disappointed
consumers share their information.
Contractual details between movie distributors (usually studios)
and exhibitors further suggest that information transmission and theTheatrical Movie Admissions 863
risks therein are paramount. Contracts during my sample centered
around the rental rate, a percentage of exhibitor box office receipts that
is ceded to the distributor.2 This percentage typically declines with the
length of time since a movie’s release; a common nonblockbuster rental
schedule is 60% the opening week, followed by 50%, 40%, 35%, and
30%. This declining rate attempts to compensate an exhibitor for not
switching to a newer movie.3 Other contractual details also suggest the
potential importance of information. Contracts during my data often
specified a 4-week timeline, but clauses required movies to be held
over if they did especially well. Conversely, exhibitors showing movies
that performed especially poorly were often prematurely excused from
their contractual obligations or, in less extreme circumstances, given
a split (allowed to show another of the distributor’s movies instead
of the underperforming title at some showtimes). One of the critical
determinants of demand, the number of exhibiting theaters, is thus
able to adjust in response to information transmission. The distributor
can also unilaterally adjust a movie’s advertising to react to word
of mouth. Advertising and promotion is typically the largest cost of
distribution, with printing the reels of film being the other primary
variable cost. While general advertising budgets are often set during
a movie’s production, it is relatively common to see television and
newspaper 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 behavior
and claim that word of mouth is the best explanation for the substantial
autocorrelation of growth in demand that they document. Their primary
empirical tests reject the linear relation between log(Revenues) and
log(Rank) implied by Pareto’s Law in favor of positively autocorrelated
growth.4 The method by which word of mouth can generate autocorre-
lated growth in demand is sufficiently intuitive that I will dispense with
a formal model in the following explanation.
A subset of potential consumers sees a movie at its opening. These
consumers then share their opinions (i.e., how the movie compared to
their 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 are
replacing 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 same
conclusion.864 Journal of Economics & Management Strategy
then make their decision the following period. When this second
generation of viewers share their information, the source of the au-
tocorrelation in demand becomes apparent. Movies with realizations
that far exceeded consumer expectations will benefit from positive
word of mouth in both weeks, while the converse occurs when a
movie’s expectations exceed its realization. Consequently, growth rates
in demand will be positively correlated. While offering an explanation
of this autocorrelation, the approach taken by De Vany and Walls cannot
provide any sense of the magnitude of word of mouth.
The presence of autocorrelated growth is a sufficient indicator of
word of mouth only if there are no other explanations. It is straightfor-
ward, however, to show that products that consumers usually purchase
only once will generally exhibit such autocorrelated growth. The model
of 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 population
at the product’s launch, PastAdmt,j the cumulative admissions preced-
ing that period, and πt,j the probability of purchase. A finite pool of
consumers is gradually exhausted as people purchase the product. For
simplicity, consider the case where purchase-probability is exogenously
determined.5 I specify the purchase-probability as depending upon a
product-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
πt, j
gt, j = − πt, j − 1. (3)
πt−1, j
Because the movie-specific component in the probability appears di-
rectly in the “growth rate,” high saturation rates last week are likely to be
followed by high saturation rates this week, and positive autocorrelated
growth results.
An admittedly strong restriction on the above saturation model
has an additional implication that I will exploit, namely that there is
a direct transformation to relating log(Q) to a product’s age. Define a
movie’s Age as the number of full weeks since its release and assume
5. It is straightforward to show that purchase-probabilities that include endogenous
variables such as screening intensity and advertising will amplify this autocorrelation.
Allowing for such purchase-probabilities to decline over time exogenously, as would
occur if consumers with the highest expectations see the movie first, has the same impact.Theatrical Movie Admissions 865
that πt,j = π for all movies and weeks.6 A movie in its opening week
therefore has Age = 0. Quantities then take the form
Qt, 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 work
effectively uses a variation of log-quantities as the dependent variable,
it is reassuring to know that there is some theoretical support for using
Age 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 used
by Einav (2007), and one particular aspect of that application war-
rants discussion before considering the formal model. Several factors
which presumably affect consumer expectations are endogenously de-
termined. The number of theaters exhibiting the movie and the amount
of advertising for that movie are obvious examples. If word of mouth is
important, these endogenously determined variables will presumably
reflect (and amplify) the underlying word of mouth. “Sleeper hits”
(e.g., My Big Fat Greek Wedding) gradually expand their advertising
and number of showcases before eventually tapering off. Conversely,
high expectation “bombs” (e.g., The Hulk) see especially fast decays in
both advertising and screening intensity. Because I want to consider the
impacts of word of mouth on screening and advertising, I consider a
reduced form expression of demand (like Einav) in which the number
of exhibiting theaters and the amount of advertising have been “solved
out.” While a structural approach in which exhibiting theaters and
advertising are explicitly included is possible, it would necessarily limit
word of mouth to its direct (and presumably much smaller) effect. For
this initial application, I improve my chances of discerning word of
mouth by using the reduced form, and thus the estimated impact of
variables on demand in this paper should be interpreted as equilibrium
effects. For example, the estimated effect of an Oscar nomination is
the sum of both the immediate effect on consumer behavior and the
feedback effect of consumer responses to increased advertising and
6. This simplifying assumption of course removes the source of the autocorrelated
growth.
7. This specification has been the standard in the marketing literature using weekly
data. There it is interpreted to capture both saturation and consumer preferences for
“fresh” products.866 Journal of Economics & Management Strategy
screening intensity. The same pertains to the estimated impact of word
of mouth.
Much of recent empirical industrial organization has made use
of the discrete choice model of demand, and I follow in this literature
introduced by Berry (1994). Let consumer i’s belief about the utility from
seeing 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 individual
deviation from that average utility. A consumer’s choice set also includes
the outside option of seeing no movie, and the utility of that outside
option is normalized to zero. Throughout, I will assume that mean
consumer utility takes the form
δt, j = Xt, j β + j + Wt γ + 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 the
movie’s week was abbreviated by a non-Friday release, and indicators
for whether the movie had been nominated or won a major Academy
Award prior to that week. Rather than estimate the impact of movie
characteristics upon consumer expectations, I instead use movie-specific
fixed effects for movies observed for at least four weeks.8 Seasonality
variables (e.g., month and holiday indicators) are included in W. I
then consider the reduced form impact of a movie’s age on demand
(both directly and through screening intensity and advertising) with the
function f (•). I assume that all explanatory variables are uncorrelated
with the disturbance ξ .
Consumers choose at most one movie from among their various
options to maximize utility. Under these conditions, Berry (1994) shows
that there exists a unique one-to-one mapping from observed quantities
and market size to products’ mean utilities (δ). If ε is drawn from the
logit distribution (Type 1 extreme value), then a closed-form solution for
these predicted quantities exists and this mapping is especially tractable:
δt, j = ln(Qt, j ) − ln Mt − Qt,k , (8)
k∈(t)
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 Xj β + χj included in their mean utility
specification. This matches the second-stage estimation where I use estimates of as
dependent variables.Theatrical Movie Admissions 867
weekly quantities.9 The demand for the entire set of products is thus
characterized by the parametric specification of products’ mean utilities.
The logit assumption, however, comes with the well-known price
of unreasonable substitution patterns. In this context, it may be an
onerous restriction to impose that all consumers are equally likely
to substitute to the option of seeing no movie should their favorite
movie become unavailable. I therefore separately use the nested logit
framework 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 each
case the parameter µ equals zero if such heterogeneity is unimportant
and is bounded above by one if there is total segmentation. Applying
the assumptions appropriate for such a nesting, the transformation from
observed quantities to mean consumer utilities is now
δt, j = ln(Qt, j ) − ln Mt − Qt,k − µ ln st,Nj , (9)
k∈(t)
Q
where st,Nj = t, j
and N(j) is the set of available movies that share
N(k)=N( j) Qt,k
movie j’s characteristic along dimension N. The general regression is
then
ln(Qt, j ) − ln Mt − Qt,k
k∈(t)
= µ ln st,Nj + Xt, j β + j + Wt γ + f (Aget, j , α) + ξt, j . (10)
The disturbance ξ appears in contemporary quantities, and thus sN t,j ,
by construction. Least squares estimation will therefore bias each µ
upwards, overstating the impact of segmentation, and instrumental
variable techniques are needed to consistently estimate µ.
As pointed out by Berry (1994), an advantage of the discrete
choice framework beyond its parsimonious parameterization is the
provision of instruments based upon a product’s competitive envi-
ronment. Intuitively, the characteristics of rival movies will affect a
movie’s admissions, but those characteristics are themselves plausibly
uncorrelated with the disturbance ξ and excluded from the mean
9. For notational convenience, I have dropped the population size that often appears
in the denominators of both terms and thereby transforms quantities into unconditional
market shares.
10. Bresnahan et al. (1997) introduced the Principles of Differentiation Generalized
Extreme Value to address multiple types of consumer heterogeneity simultaneously. My
attempts to apply it in this context were prevented by excessive collinearity.868 Journal of Economics & Management Strategy
utility specification.11 I discuss the specific movie characteristics and
instruments that I employ in the data section below.
3.3 Word of Mouth
After the above parameters are estimated, I can turn to the composition
of ξ . Fixed effects for most of the movies absorb what would presumably
be the biggest such component, namely the average effect on consumer
expectations of movie characteristics that I cannot observe or measure.
Letting Dj be a binary variable indicating whether movie j has a fixed
effect (i.e., is observed at least four times) and PastAdmt,j be cumulative
admissions for movie j in week t, four other components of ξ plausibly
remain:
ξt, j = υt + ωt, j + (1 − D j )χ j + φ j P(PastAdmt, j , Aget, j , λ). (11)
The first disturbance υt is the impact of week-specific variables that are
not captured by my variables in W. The second ωt,j is an idiosyncratic
disturbance that is specific to a particular movie in a particular week.
The mean valuation of a movie j’s unobserved characteristics if it does
not have a fixed effect is χj . Last is the word of mouth disturbance. The
gap between movie j’s true quality (j ) and its expected quality (j )
is represented by the parameter φj = j − j , so that φj > 0 indicates
that movie j has good word of mouth. Consistent with the reduced
form estimation of demand, I assume that consumers Bayesian update
their beliefs from the information provided by those who have seen
the movie. Given my lack of microlevel data, I assume that consumers
have identical priors and receive identical information, which together
imply that consumers have identical posteriors. That is, as information
about the movie spreads, consumers smoothly revise their beliefs about
a movie. Pt,j (•) then denotes the share of movie j’s word of mouth gap
that is incorporated into consumer posteriors as of week t.12
The effective share of a movie’s word of mouth (henceforth WOM
share) will presumably depend upon both the length of a movie’s
theatrical run and the number of people who have seen the movie in
prior weeks. The relative importance of each of these variables will
hinge upon how consumers share information. Consumers telling a
fixed number of friends about the movie’s true quality each week when a
movie is in theatres will place special emphasis on the length of a movie’s
run. The opposite story of consumers telling a fixed number of friends
11. As in Einav (2007), the identifying assumption within this reduced form context is
that the portions of equilibrium advertising and screening intensity that are uncaptured
by the exogenous regressors are not affected by rival movie characteristics.
12. I am grateful to the referee who suggested this application of Bayesian updating.Theatrical Movie Admissions 869
regardless of a movie’s run length will instead focus more upon the
number of past admissions. Estimates using a flexible functional form
for this share and its implied responsiveness to the two variables should
be able to distinguish which of these explanations better describe the
data. Along these lines, my empirics begin with a simple interaction
of the two inputs (which imposes identical elasticities for age and
past admissions) and then examine a polynomial specification of these
interactions that allows for these implied elasticities to differ.
Generally, P = 0 at a movie’s release, and λ are parameters that
capture the speed with which information travels. As P → 1, consumer
utilities are based upon a movie’s true quality j rather than its expected
quality j . Rational expectations among consumers ensure that the aver-
age word of mouth gap across movies is zero, E(φj ) = 0.13 For tractability
I assume that each disturbance is uncorrelated with the other three.
The variance of each component’s disturbance is assumed constant and
denoted by subscript: Var(υt ) = συ2 , Var(ωt, j ) = σω2 , Var(χ j ) = σχ2 , and
Var(φj ) = σφ2 . The magnitude of σφ2 and information’s speed captured by
λ relative to the variance of consumer mean expectations will describe
the importance of the word of mouth dynamic.
This structure for the aggregate disturbance means that movie
fixed effects will not strictly capture a movie’s expectation but will
instead reflect a weighted average of the expectation and the cumulative
effect of word of mouth. Specifically, each movie’s fixed effect will be
ˆ j = j + φ j P• j , where P•j denotes the average WOM share over that
movie’s observed lifetime. This mixed estimate then implies that the
observed residuals are actually characterized as
ξt, j = υt + ωt, j + (1 − D j )χ j + φ j (Pt, j − D j P• j ). (12)
There are numerous ways that observed residuals could be inter-
acted to match correlations with these parameters. I specify first-order
autoregressive patterns for week-specific and movie-and-week-specific
disturbances and exploit both the heteroskedasticity and the first-order
serial correlation implied by the above formulation. Taking the squared
residuals as the dependent variable generates the regression
ξt,2 j = συ2 + σω2 + (1 − D j )σχ2 + σφ2 (Pt, j − D j P• j )2 + u1t, j . (13)
Intuitively, if word of mouth is present, my results should reveal a
nonmonotonic 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 is
therefore not inconsistent with the expectation that movies with good word of mouth will
have longer theatrical runs than movies with bad word of mouth, thereby comprising a
disproportionately large share of observations.870 Journal of Economics & Management Strategy
its heteroskedasticity. The speed of information and the relevant shape
of the WOM share function are revealed by the extent of asymmetry in
(Pt,j − Dj P•j )2 . If WOM shares rise evenly over a movie’s run, then the
relationship is symmetric, but especially fast information diffusion early
(late) in the run will generate steeper slopes on the left (right) side. The
separate identification of σφ2 and λ is provided by the quadratic form
and the nonlinearity of P(•).
The basis of serial correlation can likewise be shown by interacting
a movie’s residual from one week with its residual from the prior week.
ξt, j ξt−1, j = ρυ συ2 + ρω σω2 + (1 − D j )σχ2
+ σφ2 (Pt, j − D j P• j )(Pt−1, j − D j P• j ) + u2t, j . (14)
The empirical task is then to disentangle the serial correlation that
comes from the word of mouth process from the serial correlation that
stems from autocorrelation of weekly disturbances and idiosyncratic
disturbances. The same intuition regarding the identification of infor-
mation speed applies. Common parameters across equations suggest
joint estimation, and results show that freely estimated parameters are
quite similar to their restricted counterparts.
Estimates of σφ2 and λ that are significantly greater than zero
then indicate the presence of word of mouth. The importance of word
of mouth in variance, however, is better captured by the ratio of
σφ2 E((Pt,j (λ) − P•j (λ))2 ) to Var(δt,j ). This measure captures the percentage
of variation in consumer expectations that the model attributes to word
of mouth and its supply-side responses. Other instructive measures are
the percentages of the disturbance’s variance Var(ξt,j ) or the extent of
serial correlation E(ξt,j ξt−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 from
Variety, the motion picture industry’s trade magazine. Variety publishes
the revenues (REV t,j ) of the fifty highest grossing movies in the U.S. and
Canada each week, where weeks run from Friday to Thursday. This Top
50 listing is fairly exhaustive; the typical 50th ranked movie grossed
only $50,500. My data set begins in August 1990 and continues through
December 1996, spanning a total of 332 weeks. This sample then consists
of 16,600 observations of 1602 unique movies, 1252 of which I observe
for 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).Theatrical Movie Admissions 871
an annual average admissions price (Price),15 I linearly extrapolate and
construct implied quantities (Qt,j = REV t,j /Pricet ).16 Consumer popula-
tion M is then the combined population of the U.S. and Canada.17 This
population measure is almost assuredly an overstatement of the number
of consumers who might see a movie in a given week, and I will consider
a fraction of this population in robustness checks.
Even though I am exploiting movie fixed effects, movie-specific
characteristics are useful to get a sense of what drives these fixed effects
and are essential to create sufficiently powerful instruments. The ap-
pendix describes in detail my measures of cast and director appeal, but
both essentially make use of the box office history of movies within the
prior five years (in billions of dollars). Demand estimation using the
nested logit also requires some measure of a movie’s genre. I define
the action genre as any movie that is listed as Action or Adventure by
the Internet Movie Database. A movie falls within the family genre if it
is rated either G or PG.
I also consider several variables that vary across both movies
and weeks. For both the demand and word-of-mouth regressions, I
define a movie’s Age as the number of weeks that a movie has already
spent on Variety’s Top 50, so that a movie in its opening week faces
Age = 0. This differs from the number of weeks since a movie’s release
because movies are sometimes removed from theatrical circulation
and then reintroduced or alternatively fall from the Top 50 and then
return. PastAdm is defined as the cumulative admissions of a movie
prior to a week (in millions), so that a movie has PastAdm = 0 at its
opening. The announcement of Academy Award nominations and the
Oscar awards themselves have received some attention in the movie
economics literature (Nelson et al., 2001). Academy Award nominations
are traditionally announced on a Tuesday morning, and (during my
data’s time frame) the Oscar ceremony was held on a Monday night. To
this end, I consider a OscNom?tj binary variable that equals one for all
weeks following (but not including the week of) the announcement that
movie j has received a nomination in any of the six major categories.18 I
define OscWin?tj analogously, so that its estimated effect should indicate
the 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.872 Journal of Economics & Management Strategy
Wednesdays being the most common non-Friday release day. Those
movies therefore have an abbreviated week over which to accumulate
their admissions, a situation I denote by setting the binary variable
AbbWk? 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 to
bound some of these parameter values in advance. Recent daily data
(Davis, 2006; Switzer, 2004) indicate that weekends make up between
66% and 72% of a nonholiday week’s admissions.19 Figures derived from
revenues are comparable. Other days of the week are roughly similar
and average between 7.2% and 8.4% of a week’s admissions.
Using these figures, the normal daily breakdown of admissions
over the week suggests that a movie with such a Wednesday release prior
to an ordinary weekend would garner about 16% of the admissions that
it 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 observed
week essentially replaces its Wednesday with a second Friday and its
Thursday with a second Saturday. If the typical weekend days accurately
capture the demand at these holiday weekdays, then a movie with a
Wednesday release prior to a holiday weekend would have 36%–39%
of the admissions that it would have received with a release the Friday
before. Assuming that Thanksgiving (or any other weekday holiday) is
no more convenient to see a movie than a normal Saturday then offers an
Q (AbbWk?=1)
upper bound on Q jj (AbbWk?=0) ≤ 0.4. Given that some Wednesday releases
occur before ordinary weekends and Thanksgiving (in particular) is
arguably less conducive to theatrical movies than an ordinary Saturday,
the average of these predicted ratios being substantially less than 0.4 is
likely.
Week-specific regressors include linear extrapolations of the an-
nual average admissions price and the monthly U.S. unemployment rate
in my week-specific variables. Given the important role of seasonality
in demand (Einav, 2007), I also include dummy variables for each
month (excluding January) and eleven major holidays.20 In the demand
estimation, I estimate movie fixed effects only for those movies for which
I 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 in
St. 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, Columbus
Day, Veteran’s Day, Thanksgiving, and Christmas.Theatrical Movie Admissions 873
Table I.
Variable Definitions
Rev Weekly revenues
Price Average admissions price
Q Weekly admissions (Rev/Price)
AbbWk? Indicator of non-Friday release (abbreviated week)
OscNom? Indicator of Oscar nomination prior to given week
OscWin? Indicator of Oscar award prior to given week
Age Number of prior weeks spent in Variety Top 50
PastAdm Cumulative admissions (in millions)
CastApp Total prior 5-year revenue history of starring cast/# of opportunities
DirApp Total prior 5-year revenue history of director
AC? Indicator of whether movie is action/adventure
FA? 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 week
sFa Quantity/Total quantity of movies that share Family status that week
action and family dummies, and an intercept for movies with fewer than
four observations.
Table I displays variable definitions and sources, and Table II
displays summary statistics. The use of movie fixed effects does not
spare me from the necessity of finding some explanatory variables of
sufficient power in the case of the nested logit. As results from demand
will show, a movie’s cast appeal and director appeal (determined prior
to release and defined in the Appendix) are both positively correlated
with a movie’s fixed effect estimate. I therefore consider age-weighted
measures of competing movies’ appeal as instruments. Specifically, I
utilize these variables for competing movies that have been released
within the last 4 weeks (see Table III for instrument definitions). Thus,
this measure of a movie’s competitive environment is higher when
high appeal rival movies are younger. The validity of these instruments
obviously hinges upon the discrete choice model’s assumptions, but
their power can be illustrated with the data. In first stage regressions
(not reported) with ln (sN ) as the dependent variable, all six proposed
instruments have t-statistics (in absolute value) that exceed six and the
t-statistics of five instruments exceed eight. IV regressions therefore
should not suffer from the weak instrument problem.
5. Evidence
5.1 Demand
Least squares estimates of the logit model of demand (µ imposed to
be zero) are shown in Table IV. Asymptotic standard errors make use874 Journal of Economics & Management Strategy
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 4.3208
Q (in millions) 0.4419 0.0849 0.0006 19.1208 1.0135
Q/M 0.0015 0.0003 2.13E-06 0.0668 0.0035
δ logit = ln(Q) − ln(M − Q) −7.8021 −8.0516 −12.9180 −2.5833 1.6553
sMovie 0.0200 0.0042 1.60E-05 0.5903 0.0399
ln(sMovie ) −5.2640 −5.4774 −11.0441 −0.5271 1.6793
sAc 0.0400 0.0084 2.56E-05 0.9154 0.0788
ln(sAc ) −4.6013 −4.7777 −10.5901 −0.0884 1.7182
sFa 0.0400 0.0079 5.64E-05 0.9189 0.0823
ln(sFa ) −4.6688 −4.8354 −9.7838 −0.0846 1.7687
Age 8.0008 6 0 70 7.8242
PastAdm (in Ms) 6.8014 2.8936 0 83.9052 10.7196
AbbWk? 0.0049 0 0 1 0.0697
OscNom? 0.0502 0 0 1 0.2183
OscWin? 0.0120 0 0 1 0.1088
By movie (n = 1602)
AbbWk? 0.0506 0 0 1 0.2192
CastApp 0.0161 0 0 0.1419 0.0223
DirApp 0.0325 0 0 0.7175 0.0672
Action? 0.2541 0 0 1 0.4355
Family? 0.2010 0 0 1 0.4009
Table III.
Definitions of Instruments
A(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}
τ =t Ca st App τ,k τ =t Dir App τ,k
MCa st t, j = k = j,τ =t−3 Age τ,k +1 MDir t, j = k = j,τ =t−3 Age τ,k +1
τ =t Ca st App τ,k τ =t Dir App τ,k
ACa st t, j = k=A( j,t),τ =t−3 Age τ,k +1 ADir t, j = k=A( j,t),τ =t−3 Age τ,k +1
τ =t Ca st App τ,k τ =t Dir App τ,k
F Ca st t, j = k=F ( j,t),τ =t−3 Age τ,k +1 F Dir t, j = k=F ( j,t),τ =t−3 Age τ,k +1
of the Newey-West (1994) covariance matrix, allowing for arbitrary het-
eroskedasticity and incorporating 3 weeks of lagged residuals to account
for serial correlation. As the later residual analysis will make heavy use
of the age regressor, it is important to ensure that the impact of age on the
underlying demand is sufficiently robust. Consequently, I estimate sixTable IV.
Least Squares Logit Estimates of Demand
I II III IV V IV
b a.s.e. b a.s.e. b a.s.e. b a.s.e. b a.s.e. b a.s.e.
1st stage: n = 16,600, DV = ln(Qtj ) − ln(Mt − Qtk )
Age — −0.16 0.01 −0.27 0.01 — — —
Age2 — — 0.0037 0.0002 — — —
ln(Age + 1) — — — −1.28 0.02 −0.30 0.05 —
ln(Age + 1)2 — — — — −0.33 0.02 —
Theatrical Movie Admissions
α Age — — — — — 0.076 0.004
exp(−α Age Age) — — — — — 5.06 0.15
AbbWk? 0.50 0.14 0.57 0.12 −1.02 0.12 −1.70 0.13 −1.20 0.13 −1.24 0.12
OscNom? −1.22 0.12 1.04 0.13 0.91 0.11 0.41 0.11 0.92 0.11 0.80 0.11
OscWin? −0.70 0.18 0.75 0.19 0.00 0.18 −0.22 0.17 0.18 0.16 −0.08 0.16
R2 (ln(sj /s0 ) as DV) 0.42 0.67 0.73 0.71 0.73 0.74
R2 (Qj /M as DV) 0.07 0.39 0.58 0.53 0.58 0.61
Ab% 1.65 0.57 0.36 0.19 0.30 0.29
OscNom% 0.30 2.82 2.48 1.51 2.50 2.21
OscWin% 0.50 2.11 1.00 0.80 1.20 0.92
2nd stage: n = 1252, DV =
CastAppeal 15.56 1.43 16.45 1.58 17.62 1.64 17.42 1.57 17.39 1.64 17.67 1.65
DirectorAppeal 3.36 0.45 4.32 0.49 4.60 0.47 4.39 0.45 4.53 0.48 4.57 0.47
Action? 0.33 0.07 0.40 0.07 0.41 0.07 0.40 0.07 0.41 0.07 0.41 0.07
Family? 0.21 0.08 0.50 0.08 0.55 0.09 0.51 0.08 0.55 0.09 0.55 0.09
Constant 23.54 0.05 −2.76 0.05 −8.13 0.05 −3.68 0.05 −7.65 0.05 −13.23 0.05
R2 (j as DV) 0.20 0.25 0.26 0.26 0.26 0.26
R2 (Qj /M as DV) −0.04 0.11 0.18 0.21 0.20 0.21
875
Notes: All estimates use movie fixed effects for movies which are observed for at least 4 weeks. All first-stage a.s.e. are based upon Newey-West covariance structure with 3 week lag. Second stage
estimation uses OLS with White-corrected a.s.e. Estimated coefficients of weekly variables, movie characteristics for movies without fixed effects, and movie fixed effects not shown.876 Journal of Economics & Management Strategy
regressions reflecting different specifications of the function f (Aget,j , α).
I then regress the estimated movie fixed effects on my cast and director
appeal variables, genre dummies, and a constant. Besides offering some
empirical support for my instruments, these second-stage results can
shed 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 be
explained 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 (Table
IV (I and II). Excluding Age forces the model to inflate the estimated effect
of an abbreviated week (because AbbWk? necessarily coincides with the
youngest movies), suggesting that abbreviated weeks actually increase
demand over the hypothetical full week. Likewise, ignoring saturation
dramatically decreases the estimated impact of the Oscar variables
(because both only occur late in a movie’s commercial run). Measures
of fit to the dependent variable δ and the more interesting purchase-
probability (Qt,j /Mt ) both rise appreciably when the Age regressor is
included. The results of the second-stage regression do not differ much
across the two specifications. While cast appeal has often been found
to affect demand, these results further confirm the less widely noted
significant impact of a movie’s director on consumer expectations as
found by Chen, Mitra, and Shugan (2006).
The age quadratic (Table 4 (III)) extends this trend for the estimated
impact of an abbreviated week. This specification yields an average
estimated 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 the
Oscar variables, however, change markedly. While including Age alone
indicates that both nominations and awards have statistically significant
impacts on consumer expectation, the quadratic specification shows that
the nomination result is somewhat inflated and that the award result is
entirely spurious. At these point estimates, a few observations (184 of
16,600) have such high ages that the quadratic specification suggests
that mean utility is increasing in Age. I therefore also consider three
specifications where such nonmonotonicity is impossible or less likely.
Table IV (IV and V) display results when ln (Age + 1) is used alone
and when it is supplemented with ln (Age + 1)2 . Using ln (Age + 1) alone
appears to overstate the initial impact of a movie’s age on its demand,
but the quadratic specification generates results comparable to those of
Table 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 theTheatrical Movie Admissions 877
age specification: f (Aget,j , α) = α1 exp(−α0 Aget,j ). The logit fit improves
only marginally with the nonlinear specification, but there is a greater
improvement in the fit to purchase-probabilities (Q/M). In other results,
the impacts of an Oscar nomination and an abbreviated week are both
further diminished. Given these (slight) improvements, I will use this
exponential form for the remaining results. Going forward, it seems
that one can conclude from the second-stage estimates that both action
and family movies gross more than their nonaction and non-family
counterparts and that this simple model can explain about 20% of the
industry’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 between
movies of different genres or between movies and the nonmovie option
is likely untenable. I therefore reestimate the unrestricted demand using
the Generalized Method of Moments (Hansen, 1982) and the afore-
mentioned competitive environment instruments.21 Table V displays
results, with the earlier logit results shown in Table V(I) for comparison.
In all regressions, estimates indicate that segmentation is statistically
significant at conventional levels, and neither the movie or family
segmentation models are rejected by the implied J-statistic. Potential
segmentation between action and nonaction movies is estimated to be
the weakest, and it could be argued that such segmentation is not eco-
nomically important. Consumer heterogeneity regarding substitution
between movies and the nonmovie option and between family and
nonfamily movies, however, are estimated to be quite important. The
conclusion regarding the latter (Table V(IV)) speaks to Ravid’s (1999)
finding that G-rated movies are historically quite profitable. While
the average consumer preference may be a dislike for Family movies
(evidenced by the negative coefficient in the second stage), there exists
a population (e.g., parents with small children) that will only consider G
and PG rated movies. If competition for these consumers is light, such a
movie could be lucrative, especially given the typically low production
costs of such movies.
Implications of the demand estimates are stable across these
different specifications. In all, receiving at least one Oscar nomination
in a major category boosts demand about 120%, but winning a com-
parable Oscar has no significant impact. Movies facing abbreviated
weeks receive about 30% of the demand from their counterfactual
week, again within the bounds suggested by other data. The variables
21. In each case, a Hausman statistic clearly rejects the hypothesis that least squares
estimation of the nested logit specification is consistent.Table V.
878
Logit and Nested Logit Demand Estimates
I II III IV V VI
b a.s.e. b a.s.e. b a.s.e. b a.s.e. b a.s.e. b a.s.e.
1st stage: n = 16,600, DV = ln(Qtj ) − ln(Mt − Qtk ))
α0 0.076 0.004 0.076 0.004 0.076 0.004 0.076 0.004 0.076 0.004 0.076 0.004
exp(−α 0 Age) 5.06 0.15 1.92 0.18 4.40 0.26 2.76 0.17 2.49 0.24 3.01 0.19
ln(sMovie ) — 0.62 0.03 — — 0.51 0.04 —
ln(sAc ) — — 0.14 0.05 — — —
ln(sFa ) — — — 0.47 0.03 — 0.42 0.03
AbbWk? −1.24 0.12 −0.44 0.07 −1.06 0.12 −0.64 0.08 −0.56 0.09 −0.68 0.09
OscNom? 0.80 0.11 0.30 0.05 0.69 0.10 0.43 0.07 0.39 0.07 0.47 0.07
OscWin? −0.08 0.16 −0.04 0.06 −0.06 0.14 0.00 0.09 −0.04 0.08 −0.01 0.10
Mkt Size Pop Pop Pop Pop 0.25∗Pop 0.25∗Pop
method NLLS GMM GMM GMM GMM GMM
IVs None MCast, MDir ACast, ADir FCast, FDir MCast, MDir FCast, FDir
Ab% 0.29 0.32 0.29 0.31 0.33 0.30
OscNom% 2.21 2.21 2.22 2.21 2.21 2.12
Var(δ(µ)) 2.74 0.45 2.05 0.89 0.78 1.09
R2 (ln(sj /s0 ) as DV) 0.74 0.96 0.80 0.92 0.93 0.90
R2 (δ j (µ) as DV) 0.74 0.75 0.74 0.74 0.75 0.74
R2 (Qj /M as DV) 0.61 0.69 0.63 0.70 0.70 0.64
Pr(Don’t reject) — 0.24 0.05 0.17 0.11 0.05
2nd: n = 1252, DV =
CastAppeal 17.67 1.65 6.82 0.62 15.35 1.42 9.54 0.88 8.87 0.81 10.51 0.96
DirectorAppeal 4.57 0.47 1.75 0.18 3.94 0.41 2.47 0.26 2.27 0.23 2.71 0.28
Action? 0.41 0.07 0.16 0.03 0.29 0.06 0.22 0.04 0.20 0.04 0.24 0.04
Family? 0.55 0.09 0.22 0.03 0.48 0.07 −0.23 0.05 0.29 0.04 −0.14 0.05
Constant −13.23 0.05 −7.84 0.02 −11.69 0.05 −9.74 0.03 −7.88 0.03 −9.20 0.03
R2 (j as DV) 0.26 0.27 0.25 0.25 0.27 0.25
R2 (Qj /M as DV) 0.21 0.29 0.23 0.29 0.29 0.26
Notes: All estimates use movie fixed effects for movies observed for at least 4 weeks. GMM weights and all first-stage a.s.e. are based upon Newey-West covariance structure with 3 week lag.
Second stage estimation uses OLS with White-corrected a.s.e. Some coefficients not reported.
Journal of Economics & Management StrategyTheatrical Movie Admissions 879
and fixed effects can explain about 75% of the variation in mean utili-
ties, and predicted purchase-probabilities using estimated fixed effects
capture between 60% and 70% of the variation in observed purchase-
probabilities. Predicted purchase-probabilities using the second-stage
coefficients instead of the estimated fixed effects explain about 29% of
the 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 job
of matching the data.
As mentioned in Section 3, all these estimates are based upon
the pool of potential consumers being the combined population of
the United States and Canada. Demand estimates using the discrete-
choice model are typically robust to one’s choice of market size, but my
model’s emphasis on the impact of word of mouth on mean consumer
expectation could generate difficulties when estimating the primary
parameters of interest. To see whether my information transmission
results are robust to choice of market size, I therefore reestimate the
more successful nested logit models (segmentation by movie and by
family) using an assumed market size of 25% of the full population.
Table V(V and VI) displays these results. The only differences by market
size 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 to
minimize the importance of the choice of market size, so this is at some
level unsurprising. The primary robustness concern, however, pertains
to the word of mouth parameters, and so I will return later to apply
these quarter-population estimates.
5.2 Analysis of Error Components
This analysis hopes to exploit heteroskedasticity and serial correlation
across disturbances (all residuals are taken from the nested logit using
ln (sMovie )). A logical first step is to document such features of the data
before applying additional structure. The evidence of serial correlation,
albeit of undetermined source, is strong. Using residuals e = δ − Xβ̂
from the 14,494 observations in which I see the same movie in consecu-
tive weeks in a standard AR(1) regression yields
e t, j = 0.662e t−1, j + t, j
(15)
0.005.
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 the880 Journal of Economics & Management Strategy
model’s predictions are regarding how these measures change over a
movie’s run, these findings are necessary but far from sufficient for
identifying word of mouth.
It is straightforward to plot a time series of heteroskedasticity and
serial correlation for any particular movie, but cross-movie comparison
is complicated by the varying length of movies’ theatrical runs. The
general prediction, however, pertains to the location of observations
relative to the total movie run. I therefore consider only movies that
I observe at least four times (the same criterion for the application of
movie fixed effects) and for the entire theatrical run, focusing upon how
the residual relationships change over fractions of the movie’s run. These
restrictions reduce my number of movies for the heteroskedasticity
graph to 1190. I then assign the opening and closing week’s values to
endpoints and linearly extrapolate between intermediate points. My
approach is essentially the same for the serial correlation graph, except
that I further restrict the movies so that only movies observed for 2
consecutive weeks at least twice are included, reducing the sample
to 1186 movies. The following graphs are then simple averages across
movies at 101 points from 0 to 1 inclusive in 0.01 increments.
Figure 1 shows a graph of the average imputed e2 over the set
of movies for different fractions of the total theatrical run. This het-
eroskedasticity graph reaches its minimum at about 0.4, and around
this minimum there is a strongly asymmetric and nonmonotonic shape.
Both the minimum being to the left of the midpoint and the steep
drop-off early in movie runs suggest that information is well dispersed
quickly (i.e., increases in the WOM share are dramatic early in the run
and modest later in the run). The same features are evident for serial
correlation in Figure 2, which shows a graph of the average imputed
et et−1 over the appropriate set of movies. Both figures then suggest that
the residuals exhibit the underlying features for the following analysis
to discern word of mouth and the speed of information.
I begin with a exponential functional form for the WOM share P:
Ptj = 1 − exp(−λAge t, j Pa st Admt, j ). (16)
Table VI(I) displays NLLS results of this joint estimation of equations
(12) and (13) from Section 3:
2
e t,2 j = συ2 + σω2 + (1 − D j )σχ2 + σφ2 Pt, j − D j P• j + u1t, j (17)
e t, j e t−1, j = ρυ συ2 + ρω σω2 + (1 − D j )σχ2
+ σφ2 Pt, j − D j P• j Pt−1, j − D j P• j + u2t, j . (18)
Identified parameters are λ, (συ2 + σω2 ), σχ2 , σφ2 , and (ρυ συ2 + ρω σω2 ).You can also read
