Working Paper Series
Economics
No. 1704
http://shss.nu.edu.kz/shss/academics/departments/economics
June 2017
How Much Product Variety is Required? Evidence from
the Movie Theater Market
In Kyung Kim1
1
Department of Economics, Nazarbayev University, Astana, Kazakhstan
(c) copyright 2017, Kim. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit
permission provided that full credit, including © notice, is given to the source.
How Much Product Variety is Required? Evidence from the Movie
Theater Market
In Kyung Kim∗
June 2017
Abstract
This paper empirically investigates the effect of the entry of new theaters on the number
of movies playing in incumbent theaters and in the market as a whole, as well as its effect on
consumer welfare via the change in product variety and availability. Estimation results suggest
that whereas the entry of competitors to a market does not affect the number of movies playing
in a theater, the total number of movies playing in the market increases after the entry of new
theaters. These findings imply that a theater offers a movie lineup different from those of rivals
in order to ease competition, which leads to an increase in market-wide movie variety. We also
find robust evidence that the net effect of increased movie variety in the market after the entry of
new theaters on consumer welfare is non-monotonic; it is positive only for the first few entrants
to a monopoly market.
Keywords: product variety, consumer welfare, movie theater industry
JEL Classification Numbers: L13, L22, L82
∗
Department of Economics, Nazarbayev University, E-mail: [email protected].
1
1
Introduction
The range of product that a retailer offers to consumers is an important managerial decision. Wider
product variety may increase sales by attracting more consumers. However, the cost would also
rise due to the loss of economies of scale or increased inventory cost.1 Competition also affects
decisions on product variety. The entry of rival retailers into a market intensifies competition,
usually resulting in lower prices. At the same time, incumbents respond to the entry of new rivals
in many other ways, including changes to how much product variety they provide to consumers.
While decreases in sales would motivate retailers to reduce the number of products they offer
(business-stealing effect), retailers may also have an even stronger incentive to offer wider product
variety in order to attract more consumers (market-expansion effect).2 In addition, a retailer may
be willing to differentiate its product range from those of others to soften competition, which in
turn leads to a decrease in product overlap and an increase in market-wide product variety.
This paper empirically studies the effect of competitors’ entry on an incumbent retailer’s product
variety and differentiation, market-wide product variety, and consumer welfare via the change in
product variety and availability. Whereas previous empirical studies well document the impact
of competition on firm-level product range, little is known about its implication for market-wide
product variety, and, more importantly, how consumer welfare is affected. This paper attempts to
fill this gap in a particular context: the movie theater industry.
We use a novel panel data on the movie theater industry for the analysis. Using a web crawler,
we collect the daily screening schedules of theaters located in all 7 metropolitan cities in Korea
from 2005 to 2009. We merge it with theater information data and city-level weekly audience data,
and identify local movie theater markets within each city. Unlike previous works on this topic that
mostly use cross sectional data for the analysis, we exploit variations in the number of competitors
of a theater, the number of theaters in a market, and the number of movies playing in a theater and
in a market over time. In addition, a unique property of the data is that it separately reports the
weekday and weekend audience size of a movie, which enables us to simulate the weekend movie
demand and perform a welfare analysis.
We first explore how the entry of new theaters affects movie variety. We find no evidence that
entry of competitors affects the number of movies playing in an incumbent theater. In contrast, new
theaters’ entry increases market-wide movie variety. Specifically, the number of movies playing in a
market increases by 2.2 and 1.1 on average, after the second and third theater enters into the market,
respectively. The effect from later entrants is also positive and significant. These findings imply
that rather than increasing movie variety, a theater tries to ease competition by offering consumers
a movie lineup that is different from those of its rivals. This theater-level movie differentiation, in
turn, leads to an increase in market-wide movie variety.
Next, we investigate the welfare implication of increased movie variety in a market after the
1
See a survey by Lancaster (1990).
See Anderson and de Palma (1992), Anderson and de Palma (2006), and Cachon, Terwiesch, and Xu (2008) for
theoretical models of product variety competition among multi-product firms.
2
2
entry of new theaters. It may affect consumers in two opposing ways. On one hand, consumers
whose favorite movies were not playing before but are now available in the market would go to
the movie theater. On the other hand, as the number of both movies and theaters in the market
increases, the coordination among theaters to match the market-wide movie demand may become
more complicated and challenging. Consequently, the market-wide seat allocation would be distorted further than before, causing more consumers to be turned away from theaters. Whether or
not widened movie variety in the market resulting from the entry of new theaters is beneficial to
consumers depends on which effect dominates. This is an empirical question to be answered by the
data.
Facing the limit of data, we first simulate the market-level weekend movie demand from the
city-level weekday audience data. Then, by comparing the simulated movie demand and observed
number of seats allocated to movies on the weekend, we calculate the number of consumers that
are turned away from theaters in a market. Finally, we examine the extent to which the change
in movie variety and availability after the entry of new theaters affects the fraction of consumers
turned away in the market.
The counterfactual results suggest that the positive effect of increased movie variety dominates
its negative effect only for the first few entrants, whereas the two effects offset each other for
subsequent entrants. For instance, when the total weekend movie demand reaches 70 percent of
the seating capacity in a market, the first and second entrants to a monopoly market cause the
proportion of unserved consumers in the market to decrease respectively by 4.0 and 1.7 percentage
points through the change in movie variety and availability. Given that 25.5 percent of consumers
are turned away in a monopoly market on average, this is a strong decrease in the fraction of
unserved consumers, and hence, a strong improvement in market efficiency and consumer welfare.
In contrast, the entry of theaters thereafter has no impact on the proportion of unserved consumers.
These findings are robust across different assumptions and specifications.
While non-price implications of entry and competition have recently received growing attention
(e.g. Mazzeo (2003) and Orhun, Venkataraman, and Chintagunta (2015)), this paper is closely
related to the empirical literature on variety competition among multi-product retailers. Watson
(2009) finds a non-monotonic relationship between product range and competition in the retail
eyeglasses markets, and concludes that when a retailer faces only few rivals, the market-expansion
effect dominates the business-stealing effect and as a result, the retailer extends its product range
in response to the entry of a new rival. However, if an incumbent retailer already has enough
local competitors, then the business-stealing effect dampens the market-expansion effect, and the
incumbent reduces its product variety when facing more competition. Ren, Hu, Hu, and Hausman
(2011) show that while competition from distant rivals induces product variety in a consumer
electronics store to increase, collocated stores have fewer overlapped products than non-collocated
ones do in order to differentiate themselves and enjoy agglomeration gains.3
3
Other previous empirical research on product variety includes Bayus and Putsis (1999) and Hong and Lee (2015)
that examine whether firms deter the entry of rivals by increasing product variety. Also, Alexander (1997), Berry
and Waldfogel (2001), and George (2007) explore the impact of ownership concentration on product variety.
3
For retailers, product variety and availability are two sides of the same coin in that there
is a trade-off between depth (large inventory of each product) and breadth (product variety) of
inventory.4 Hence, our work is also related to the literature on product availability, inventory, and
competition in the retail industry. Olivares and Cachon (2009) find evidence that the entry of
rivals induces automobile dealers to improve their service level, measured by the amount of buffer
stock. Similarly, Matsa (2011) shows that competition reduces the likelihood of inventory shortfalls
(stockouts) in the supermarket industry.
Whereas previous studies mostly investigate firm-level implications of competition, we focus
more on examining its market-level implications, that is, how market-wide product range and
availability change, which in turn affect consumer welfare. By estimating this additional effect
of the entry of retailers on consumer welfare in a multi-product retailer market, this paper also
contributes to the literature on entry and efficiency (e.g. Spence (1976), Dixit and Stiglitz (1977),
Mankiw and Whinston (1986), Berry and Waldfogel (1999), Cohen and Mazzeo (2007), Dutta
(2011), and Berry, Eizenberg, and Waldfogel (2016)).
The movie theater industry possesses several advantages for our aim. First, several new movies
are released each week, incurring strategic movie choice and seat allocation decisions for theaters.
Second, breadth (the number of movies playing) and depth (the number of seats allocated to each
movie) of inventory is easily observable.5
The remainder of the paper proceeds as follows. The next section provides institutional details
about the movie theater industry, and explains how the data set is constructed. In Section 3, we
evaluate the effect of theater entry on the number of movies playing in an incumbent theater and
in a market. In Section 4, we describe how to measure the effect of the change in movie variety and
availability after the entry of theaters on consumer welfare, and report the estimation results. In
Section 5, we perform various robustness analyses of the main results. Lastly, Section 6 concludes.
2
Industry Background and Data
Movie theater industry
The movie theater industry in Korea drastically expanded during the late 1990s to mid 2000s.
According to the top left panel of Figure 1, the aggregate audience size was approximately 50
million in 1998. However, it tripled and reached 150 million by the mid 2000s. This rapid growth
of the audience size coincides with the replacement of old single screen theaters with new multiplex
ones. The top right panel and bottom left panel of Figure 1 show that between the late 1990s
and mid 2000s, the number of seats consistently increased, whereas the number of theaters sharply
declined. After the period of strong expansion, the industry stabilized in terms of the aggregate
4
Literature on a retailer’s optimal product assortment that incorporates both variety and inventory decisions
include Ryzin and Mahajan (1999), Smith and Agrawal (2000), Carlton and Dana (2008), and Honhon, Gaur, and
Seshadri (2010).
5
Previous empirical works that cover other aspects of the competition in the movie theater industry include Davis
(2006a), Davis (2006b), Gil (2007), Orhun, Venkataraman, and Chintagunta (2015), and Kim, Lee, and Yoon (2017).
4
Figure 1: Trends
Number of Theaters
400
300
1998 2000 2002 2004 2006 2008 2010
Year
Number of Seats (100)
Audiences per Seat (100)
4
5
1998 2000 2002 2004 2006 2008 2010
Year
2
2,000
3
3,000
4,000
5,000
10,000
500
15,000
Total Audience Size (10,000)
1998 2000 2002 2004 2006 2008 2010
Year
1998 2000 2002 2004 2006 2008 2010
Year
Note: The number of theaters and seats are as of the last day of each year. Source: Korean Film Council
(KOFIC) Annual Reports.
audience size and the number of seats and theaters. The bottom right panel of Figure 1 also
indicates that the audience per seat had kept increasing until the mid 2000s, but became stable
afterwards.
The Korean movie theater industry is also characterized with a high level of per capita attendance. Koreans went to the movies 4.22 times on average in 2015.6 Thanks to the rapid growth in
the past two decades and the high attendance rate, the Korean movie theater industry became one
of the largest in the world. In 2015, it had the 6th largest market in terms of box office revenue.
One important characteristic of the movie theater industry is that the ticket price is uniform
across movies and theaters in a city. For example, in 2009 it was mostly 7,000 Korean Won (or
approximately $5.5) on weekdays in Seoul.7 Davis (2005) finds no evidence that movie ticket prices
rise in response to an increase in geographic concentration in the U.S. movie theater industry.
Sorensen (2007) points out the rigidity of product price in the media industry, especially in the
movie theater industry. Orbach and Einav (2007) list perceived fairness, demand uncertainty, and
monitoring costs as possible explanations for this practice of uniform pricing. As a result, many
previous studies on the movie theater industry (e.g. Einav (2007), Sorensen (2007), and Gil (2009))
6
Source: MPAA Theatrical Market Statistics 2015, Korean Film Council Annual Report 2015.
The admission price can differ across times and days, however. It was 8,000 KRW ($6.3) on weekends and 4,000
KRW ($3.1) for early morning shows in Seoul in 2009.
7
5
assume price exogeneity in their analyses.
Whereas the revenue sharing between distribution and exhibition is negotiable in the middle
of a movie’s run, and also can differ from one movie to another in countries such as the US and
Spain, it is constant across movies and times in Korea; half of the after-tax box office revenue goes
to the theater, and the distributor, movie maker, and investors share the rest.8 Consequently, fixed
admission price and revenue sharing implies that the price-cost margin is constant across movies
and theaters in the Korean movie theater industry.
Data construction and market identification
In this paper, we analyze movie theaters located in the 7 largest metropolitan cities in Korea Seoul, Busan, Incheon, Daegu, Daejeon, Gwangju, and Ulsan - during the period from 2005 to
2009. Since art theaters are specialized in showing small art-house films that are not usually played
in commercial movie theaters, and hence are not competing with them, we exclude art theaters
and focus our analysis only on commercial movie theaters.
The Korean Film Council updates the list of existing theaters at the end of each year.9 This
yearly list also contains theater information such as location, number of screens and seats, and
opening and closing dates that are essential for the analysis. By combining these yearly lists, we
construct panel data of theaters in the 7 cities and keep track of the yearly changes in the number
of screens and seats in each theater.
For the empirical analysis, it is necessary to properly identify local movie theater markets. On
one hand, as we are analyzing theaters located in densely populated metropolitan cities, typical
approaches used in previous studies on retailer entry and local competition (e.g. Bresnahan and
Reiss (1991), Mazzeo (2002), Gowrisankaran and Krainer (2011), and Han and Hong (2011)) that
analyze small, isolated cities only are not applicable in our case. On the other hand, each city per
se is too big to be considered as a local movie theater market; the average size of the 7 cities is 769
km2 , while the average population is 3.3 million as of 2009. As Davis (2006b) shows, traveling cost
significantly affects a consumer’s movie theater choice, and therefore, it is unlikely that a consumer
who lives in one district of Seoul travels a long distance to a theater in another district.
We address this issue by adopting the procedure for identifying local retail markets proposed in
Kim, Lee, and Yoon (2015). Specifically, we treat a group of theaters as being located in the same
market, if for each of them there are one or more competitors within a one-mile (1.61 kilometer)
distance.10 For example, suppose that there are three theaters, x, y, and z, and the distance between
the first two theaters, x and y, and the distance between the last two theaters, y and z, are less
8
Unusually, theaters in Seoul take only 40 percent of the box office revenue from movies distributed by foreign
distributors after deducting taxes.
9
http://www.kofic.or.kr/
10
The one mile threshold value is based on the outcome of their analysis that the business-stealing effect (the
effect on revenue) of rival theaters located farther than one mile is not statistically significant in the Korean movie
theater industry. A one-mile distance is also used to separate collocated rivals from distant ones in previous works
(e.g. Watson (2009) and Ren, Hu, Hu, and Hausman (2011)). In Section 5, we conduct robustness checks by varying
the basis distance from 1.5 to 2.0 kilometers.
6
Figure 2: Local Movie Theater Markets Example
0
1
2
3 km
Note: This figure presents 4 local movie theater markets in the central region of Busan, the second largest
city in Korea.
than one mile. Then, we regard them as being in the same market, even if theaters x and z are
located farther than one mile from each other. Hence, our approach puts a theater, all of its nearby
rivals, and some of its distant rivals into the same market. In this way, we are able to identify 64
local movie theater markets from the sample data. All markets have 7 or fewer theaters during the
sample period except one market. As a matter of fact, it is the largest downtown area in Seoul
whose number of theaters varies from 8 to 12 over time. We drop this market from the analysis
since the market fixed effect can not be identified separately from the effect of the 8th entrant.
Figure 2 presents 4 local movie theater markets that are identified in the central region of Busan,
the second largest city in Korea. The market with 5 theaters is actually the largest downtown area
in Busan; the market with 3 theaters is also another main street. 2 monopoly markets are located
in less crowded residential districts. The figure suggests that our data fits in well with the market
identification procedure described above, in that clustered theaters are grouped into a market,
whereas there is a clear distinction among markets.11
Next, using a web crawler, we download the daily screening schedule of each theater from
the Korea Box Office Information System (KOBIS) maintained by the Korean Film Council.12
We merge this screening schedule data with the theater panel described above. This combined
11
12
The linear distance between two theaters located farthest away from each other in a market is 3.3 kilometers.
http://www.kobis.or.kr/
7
data is again merged with the data on the number of seats in each screen of a theater that is
also downloadable at KOBIS in order to calculate the daily number of seats allocated to each
movie in each theater. Then, we aggregate these daily observations into weekday (Monday through
Thursday) and weekend (Friday through Sunday) observations.
From this combined data set, for each theater and week we calculate the number of movies
playing and the number of competitors.13 Also, for each market and week we calculate the number
of theaters, the number of movies playing, and the number of seats allocated to each movie on
weekdays and weekends, separately.
Finally, the movie audience data that is available at KOBIS records the citywide audience size
for regular movies only. That is, the audience size of non-regular showings such as re-released
movies, previews, performances, and concerts is not reported. One unique and useful property
of this movie audience data compared to others used in previous works (e.g. Einav (2007), Moul
(2007), Moul (2008), and Gil (2009)) is that it provides weekday and weekend audience sizes,
separately. We exploit this property in our analysis of the effect of theater entry on consumer
welfare via the change in movie variety and availability. We combine the audience data with the
panel data constructed above, and further generate the following variables: the number of regular
showings in each theater and market in each week.
Table 1 provides summary information for the movies and theaters in the data. There are 147
theaters located in 63 markets in the sample data. Theaters show 11.2 movies in a week on average.
Among them, 8.7 are regular ones. The average theater is equipped with 7.9 screens and competes
with 1.8 rivals. Also, there are 1.8 theaters in a market on average, while 12.9 movies (9.9 regular
ones) are playing in the average market. On average, 2,572 seats are allocated to a movie in a
market on weekend, whereas a movie attracts 5,418 consumers in a city on weekdays.
3
Entry and Movie Variety
In this section, we investigate the impact of new theaters’ entry on the number of movies playing
in incumbent theaters and in the market as a whole.
Figure 3 plots the average number of movies across theaters and markets under different market
structures. Two things are noteworthy. First, movie variety in a market is wider than that in a
theater. For instance, theaters in a duopoly market play 10.9 movies on average, whereas the
average number of movies playing in a duopoly market is 13.9. Second, the more theaters are in
a market, the wider the movie variety in the market, whereas a theater’s movie variety remains
stable. According to the figure, the gap between the two averages increases from 2.9 to 9.2 as the
market number of theaters increases from 2 to 7.
In the following subsections, we formally examine how the entry of new theaters affects movie
variety in an incumbent theater and in the market.
13
New movies are usually released on Thursday or Friday, while theaters stop playing old movies on these days of
the week. Given this industry practice, a week starts on the weekend in our analysis.
8
20
Figure 3: Market Structure and Movie Variety
5
10
15
Avg. Market # Movies
Avg. Theater # Movies
1
2
3
4
5
6
7
Market Number of Theaters
Note: This figure plots the average number of movies across theaters and markets under different market
structures.
Econometric model
First, we estimate the effect of competitors’ entry on the number of movies playing in an incumbent
theater. We consider the following econometric specification that exploits variations in the number
of movies and competitors of each theater over time:
M oviesit = α +
J
X
βj 1[Competitorsit ≥ j] + xit λ + ψi + uit ,
(1)
j=1
where the dependent variable M oviesit is the number of movies playing in theater i at time t. The
indicator 1[Competitorsit ≥ j] is equal to one if there are j or more competitors for theater i at time
t in the market. Hence, the coefficient βj estimates the marginal effect of the j-th competitor’s entry
on the number of movies playing in an incumbent theater. As explained in the previous section,
we drop one market that has 8 or more theaters and set J equal to 6.14 The vector xit includes the
following control variables: the number of screens in theater i at time t, an opening week indicator
that is equal to 1 if theater i opened at time t and zero otherwise, a similarly defined closing week
indicator, time index, and week dummy variables.15 The theater fixed effect ψi controls for the
unobservable time-invariant theater and market specific characteristics, and solves the potential
endogeneity problem as long as regressors are correlated only with it.
Since we have a long panel data with relatively many time periods for few theaters, we allow
14
When there are 7 theaters in a market, each of them has 6 competitors.
Note that we only have yearly data on the number of screens. Hence, it is constant over time in a year. Also,
since there are 52 weeks in each of the 5 years in the sample period, 51 week dummy variables are added.
15
9
uit to be correlated over t:
uit = ρui,t−1 + εit ,
where |ρ| < 1 and εit is i.i.d with mean zero and variance σ 2 .
Second, we investigate how the entry of theaters affects market-wide movie variety by estimating
M oviesmt = α +
K
X
γk 1[T heatersmt ≥ k] + xmt λ + ψm + umt ,
(2)
k=2
where the dependent variable M oviesmt is the number of movies playing in market m at time t.
The indicator 1[T heatersmt ≥ k] is equal to one if there are k or more theaters in market m at
time t. Its coefficient γk estimates the marginal effect of the k-th theater’s entry on the number
of movies playing in the market. Since the largest market in the sample data has 7 theaters, K is
equal to 7. The vector xmt includes time index and 51 week dummy variables, while ψm controls
for the market fixed effect. Similar to (1), we allow umt to be correlated over t.
Estimation results
Estimation results of (1) are presented in Table 2. We estimate the model with or without week
dummies, using all movies or regular movies only. Across all specifications, there is no clear evidence
that movie variety in an incumbent theater is affected by the entry of competing theaters to the
market. For example, according to the results in the first column, the entry of the first competitor
induces the incumbent to increase its weekly number of movies by 0.14. However, this effect is not
statistically significant. Similarly, effects of subsequent theaters’ entry on movie variety are not
statistically significant in most cases. As for the effects of other controlling variables, an additional
screen enables a theater to play one more movie each week, while a theater plays fewer movies
during the first and last week of its business. Also, there is an increasing trend in the number of
movies playing in a theater over time.
Table 3 presents estimation results of (2). As before, we estimate the model with or without
week dummies, using all movies or regular movies only. As opposed to the previous findings, there is
strong evidence that the entry of new theaters widens movie variety in a market. For instance, the
results in the second column show that the total number of movies playing in a market increases by
approximately 2.2 and 1.1 when the second and third theaters enter into the market, respectively.
Effects of subsequent theaters’ entry on market-wide movie variety are also positive and statistically
significant. These findings are consistent across all 4 specifications considered in the analysis.
The results of the empirical analysis in this section reveal that the more theaters in a market,
the more movies playing in the market, whereas movie variety in each theater is not affected by
the entry of competitors. Combined together, the results suggest that a theater tries to soften
competition by offering a movie lineup different from those of rivals rather than providing wider
movie variety to consumers. This theater-level movie differentiation leads to an increase in the
number of movies playing in the market.
10
4
Entry, Efficiency in Seat Allocation, and Consumer Welfare
Increased market-wide movie variety resulting from the entry of new theaters may affect consumer
welfare in two ways that oppose each other. On one hand, it would attract those consumers who
did not go to the movie theater before because their favorite movies were not played in the market.
Consequently, there might be an increase in consumer welfare due to widened market-wide movie
variety after the entry of new theaters. On the other hand, as there are more movies and theaters
in the market, coordination among theaters would become more difficult, resulting in less efficient
market-wide seat allocation. Hence, wider movie variety in a market may exacerbate the mismatch
between supply and demand of movies in the market, which in turn negatively affects consumer
welfare. Which of these two effects dominates is an empirical question.
In this section, we examine the effect of theater entry on consumer welfare via increased movie
variety. Specifically, we investigate how the fraction of consumers turned away from theaters in a
market changes, as new theaters enter the market and more movies are playing.16 In any market,
the overall movie demand on weekdays would be low enough that any consumer can watch his
favorite movie once it is playing in the market, regardless of how seats are allocated across movies.
Therefore, we focus our attention only on the number of unserved consumers on weekends.
Counting unserved consumers
Ideally, we want to compare the number of consumers turned away from theaters in a market on
weekends after the entry of new theaters under the following two scenarios:
1. The same set of movies are played in the market with the same seat shares as before the entry
of new theaters.
2. Theaters adjust their seat allocations in response to the entry of rivals.
If the number of unserved consumers is larger (smaller) under the first case than the second case,
then it implies that the effect of theater entry via widened market-wide movie variety on consumer
welfare is positive (negative). However, this comparison is challenging. First of all, the outcome
under the first scenario is counterfactual. Second, the weekend movie demand is unobservable. On
weekends, the overall movie demand in a market is likely to be high enough that for several movies
demand exceeds supply of seats.17 As a result, the observed audience size might be endogenous to
the seat allocation of each theater, and hence is a biased estimate of the movie demand. Besides,
we observe not the market-level, but city-level audience size only. Facing these limits of the data,
we simulate the market-wide weekend movie demand from the citywide weekday audience size by
assuming that
16
Kim and Nora (2017) treat each theater as a local monopolist and compare the number of consumers turned
away from a vertically integrated theater to that from an independent theater. They show that facing uncertain
movie demand, a vertically integrated theater has a stronger incentive to better match up its seat allocation with the
movie demand than an independent theater does.
17
In our data, the average daily citywide audience size of a movie on weekend (4,834) is more than 2.3 times that
of weekdays (2,075).
11
Assumption 1 The market-level weekend (and weekday) demand share of each movie is the same
as its city-level weekday demand share.
Assumption 2 The ratio of the total weekend (and weekday) movie demand to the seating capacity
is the same across markets and over time.
Although Assumption 1 needs to be imposed due to the limit of the data, it may not lead to
biased estimates as long as consumer tastes in a market are not correlated with the number of
theaters in the market. The assumption also implies that consumer tastes in movies do not change
in a given week. Later in this section, we relax this assumption, and show that our empirical
findings are still valid.
Assumption 2 implies that the ratio of the total movie demand to the seating capacity in a
market does not change after the entry of new theaters in the market. This is reasonable because
given the exogeneity of the ticket price, there would be a linear relationship between the market
size and the number of theaters. Practically, according to the bottom right panel of Figure 1,
the audience per seat had been consistently increasing from the late 1990s to early 2000s, but has
stabilized since the mid 2000s, supporting our assumption of the constant ratio during the sample
period. We consider 0.7 as the ratio on weekends, κ, in the analysis, that is, on weekends the total
movie demand in a market reaches 70 percent of the seating capacity in the market. In the next
section, we perform a robustness check by considering a range of different values from 0.5 to 1 as
the ratio κ.
The following example describes how the market-level weekend movie demand is simulated.
Suppose that there are three movies and the observed city-level weekday audience size for each
movie is 30, 45, and 20 as shown in the second column. There are two markets - one monopoly and
one duopoly - in the city. We observe weekday and weekend seat allocations in each market; in the
monopoly market only the first two movies are showing, whereas all three movies are available in
the duopoly market. Note that the observed audience size for the third movie, 20, is recorded only
from the duopoly market, and hence is a biased estimate of the city-level demand for the movie.
The above assumptions imply that the weekday demand of the third movie in the monopoly market
is 10. Hence, the adjusted city-level weekday audience size for the third movie is 30.
Example: Adjusting City-level Weekday Audience
Movie
M1
M2
M3
Total
Citywide
Weekdays Audience
Observed Adjusted
30
30
45
45
20
30
95
105
Market-wide Supply
Monopoly
Duopoly
Weekday Weekend
Weekday Weekend
20
25
30
25
80
75
130
150
0
0
40
25
100
100
200
200
Next, the weekend movie demand in each market is simulated and presented in columns 4 and
6 of the next table; in both markets, the demand shares of the three movies are 28.5, 42.9, and 28.5
percent, respectively, while the total demand amounts to 70 percent of the seating capacity.
12
Example Continued: Simulating Market-wide Weekend Demand
Movie
M1
M2
M3
Total
Citywide
Weekdays Audience
Observed
Adjusted
30 30 (28.5%)
45 45 (42.9%)
20 30 (28.5%)
95 105 (100%)
Market-wide Weekend Demand & Supply
Monopoly
Duopoly
Demand Supply
Demand Supply
20
25
40
25
30
75
60
150
20
0
40
25
70
100
140
200
Based on Assumptions 1 and 2, we can identify the effect of theater entry on consumer welfare
through the change in movie variety and availability. In the above example, we can construct
a benchmark (duopoly) market from the monopoly market by proportionally increasing the seat
allocation of each movie until the seating capacity reaches 200, the seating capacity of the duopoly
market. Note that the number of served consumers increases from 50 to 100, as the monopoly
market is transformed to the benchmark market. This can be considered the mechanical result of
a new theater’s entry and market expansion. In addition, 10 more consumers watch movies in the
duopoly market than in the benchmark market. This is the net effect of increased movie variety
on consumer welfare; the positive effect of it (attracting consumers who could not watch the third
movie before the second theater’s entry) dominates its negative effect (less efficient market-wide
seat allocation), leading to a decrease in the number of unserved consumers, and therefore, an
increase in consumer welfare.
Example Continued: Benchmark Market vs. Duopoly Market
Demand
20
30
20
70
Monopoly
Supply Served
25
20
75
30
0
0
100
50
⇒
Benchmark
Demand Supply Served
40
50
40
60
150
60
40
0
0
140
200
100
vs.
Demand
40
60
40
140
Duopoly
Supply
25
150
25
200
Served
25
60
25
110
We measure this additional effect of theater entry on consumer welfare by tracking the change
in the number of unserved consumers in a market, as the number of theaters in the market varies.
The number of unserved consumers in market m at time t is counted as
U nservedmt =
X
max{Dlmt − Slmt , 0},
(3)
l∈Lct
where Lct is the set of all movies playing in city c where market m is located at time t. Dlmt and
Slmt are the weekend demand and supply of seats for movie l in market m at time t, respectively.
In the above example, 20 out of 70 consumers are turned away in the monopoly market, whereas
30 out of 140 consumers are turned away in the duopoly market.
13
10
Avg. % of Turned away Consumers
15
20
25
Figure 4: Market Structure and the Number of Unserved Consumers
1
2
3
4
5
6
7
Market Number of Theaters
Note: This figure plots the average percentage of turned away consumers across markets under different
market structures.
The percentage of consumers turned away from theaters in market m at time t is
U nservedmt
× 100
Dmt
P
max{κDSlmt − SSlmt , 0}
= l∈Lct
× 100,
κ
%U nservedmt =
(4)
where Dmt is the total weekend movie demand in market m at time t, and DSlmt and SSlmt are the
demand and seat shares of movie l in market m at time t, respectively. Note that DSlmt ≡ DSlm0 t
for markets m and m0 located in the same city. Continuing with the above example, 28.6 percent
of consumers are turned away in the monopoly market and hence in the benchmark market as
well, whereas only 21.4 percent of consumers are turned away in the duopoly market. Therefore,
the proportion of unserved consumers is approximately 7.2 percentage points lower in the duopoly
market compared to the benchmark market.
Figure 4 plots the average percentages of turned away consumers across markets under different
market structures. According to it, 25.5 percent of consumers are turned away in a single theater
market on average. However, the average percentage of unserved consumers across duopoly markets
declines to 20.1. Whereas there is a huge gap between monopoly and duopoly markets, the effect
of theater entry seems marginal for markets with 4 or more incumbents.
14
The effect of theater entry on the number of unserved consumers
For the formal analysis, we estimate
%U nservedmt = α +
K
X
ηk 1[T heatersmt ≥ k] + xmt λ + ψm + umt ,
(5)
k=2
which is the same as (2) except that now the dependent variable %U nservedmt is the percentage
of consumers turned away in market m at time t. We estimate the model with the percentage of
unserved consumers computed from the original city-level weekday audience size or the adjusted
one. As before, we set K = 7.
Estimation results of (5) presented in Table 4 show that the effect of increased movie variety
resulting from the entry of new theaters on the faction of consumers turned away in a market is
non-monotonic. For example, estimated coefficients in the last column suggest that the increase
in movie variety after the second theater’s entry induces the proportion of unserved consumers to
decrease by 4 percentage points. Given that 25.5 percent of consumers are turned away on average
in a monopoly market, this is quite a sharp decrease in the fraction of unserved consumers. The
effect of the third theater’s entry on consumer welfare via increased movie variety is also positive
and significant, reducing the proportion of consumers turned away in the market by 1.7 percentage
points. Interestingly, further change in movie variety and availability after the entry of subsequent
theaters has no statistically significant effect on the fraction of unserved consumers in the market.
As opposed to Assumption 1, in practice consumer tastes on movies may change from weekdays
to weekends. For instance, movies with universal ratings are more popular on weekends than on
weekdays, as parents usually go to the movies with children on weekends. Even in such a case,
however, consumer preference may remain stable for movies with the same rating. That is, if movies
A and B are both rated R and movie A is more popular than movie B on weekdays, then it would
also be more popular on weekends. Taking advantage of this point, we sort movies in the sample
data into 4 groups according to their ratings.18 In Korea, the film rating system classifies movies
into the following 4 ratings: ages of 12 or over, ages of 15 or over, ages of 18 or over, and universal.
Then, applying Assumptions 1 and 2 to each group of movies, we can calculate the (within group)
percentage of unserved consumers in market m at time t as
P
%U nservedrmt
=
l∈Lrct
r − SS r , 0}
max{κDSlmt
lmt
κ
× 100,
(6)
where Lrct is the set of all r-rated movies playing in city c where market m is located at time t.
r
r
DSlmt
and SSlmt
are the demand and supply shares of movie l among all r-rated movies in market
m at time t, respectively.
18
Movies can be also classified by genre. However, grouping movies by rating is more reliable for the following
reasons. First, a movie can be categorized into multiple genres. Second, it is clearer to understand why the relative
popularity of movies targeting consumers of a certain age band increases (or decreases) from weekdays to weekends
than why one genre is relatively more popular on weekdays than on weekends. Lastly, we do not have data on movie
genre.
15
For each movie rating, we estimate (5) using %U nservedrmt as the dependent variable. Estimation results reported in Table 5 are consistent with previous findings; the effect of the second
theater’s entry on consumer welfare through increased movie variety is positive and significant in
3 out of 4 movie ratings. However, the fraction of consumers turned away in the market tends to
be less affected by later entrants and, in the end, not affected.
The analysis in the previous section concludes that the more theaters in a market, the larger the
number of movies playing in the market. Our empirical findings in this section reveal that widened
movie variety in the market resulting from the entry of new theaters is not always beneficial to
consumers; its effect is positive only for the first and second entrants to a monopoly market. This
implies that the benefit of playing more movies (that is, attracting those consumers who could not
find a seat for their favorite movies before) outweighs its potential cost of reduced efficiency in the
market-wide seat allocation only for these theaters, whereas the two effects offset each other for
later entrants.
5
Robustness
In this section, we conduct various robustness analyses of the main results. First, we segment the
long panel data into short panels, and obtain the within estimators from each panel. Second, we
repeat the consumer welfare analysis in the previous section under different values of κ. Finally,
we examine how sensitive estimation results are to the change in the basis distance, that is, to the
change in the definition of the local movie theater market.
Short panel
Given that there are 52 weeks in each year during the sample period, we divide the long panel data
into 52 short panels on the basis of the observation week, and estimate the following three fixed
effect models using each of these 52 panels, separately.
First, we estimate the effect of competitors’ entry on movie variety in an incumbent theater
based on the specification:
M oviesiy = α +
J
X
βj 1[Competitorsiy ≥ j] + xiy λ + ψi + ψy + uiy ,
(7)
j=1
where M oviesiy and Competitorsiy are the number of movies playing in theater i and its rival
theaters at (the given week of) year y, respectively. The vector xiy contains binary variables for
opening and closing years as well as the number of theater screens. Also, theater and year fixed
effects, ψi and ψy , are included in the model.
Similarly, we estimate the effect of new theaters’ entry on market-wide movie variety using the
16
following model:
M oviesmy = α +
K
X
γk 1[T heatersmy ≥ k] + ψm + ψy + umy ,
(8)
k=2
where M oviesmy and T heatersmy are the number of movies and theaters in market m at (the given
week of) year y, respectively. Market and year fixed effects, ψm and ψy , are also considered in the
model.
We obtain the within estimators of (7) and (8) from each of the 52 short panels. Figures 5
and 6 present histograms of the estimated value of βj in (7) and its t-statistic for j = 1, · · · , 6,
and histograms of estimated value of γk in (8) and its t-statistic for k = 2, · · · , 7, respectively.
According to the first two panels in Figure 5, estimates of β1 range from -1 to 1, while their tstatistics are all less than 2 in absolute term, strongly suggesting that the number of movies playing
in an incumbent theater is not affected by the entry of its first competitor. Estimated effects of
subsequent theaters’ entry presented in the other panels are not statistically significant in most
cases. In contrast, Figure 6 shows that the entry of new theaters positively affects market-wide
movie variety. According to the first two panels, for instance, the average effect of the second
theater’s entry to a market on the number of movies playing in the market across 52 short panels
is 2.1, which is approximately the same as the estimated effect of 2.2 when the entire long panel is
used. Furthermore, in 47 out of 52 panels, the effect is estimated to be significant at the 5 percent
level. The distributions of the estimated coefficients and their t-statistics in other panels also
suggest that the entry of subsequent theaters positively affects market-wide movie variety. These
findings confirm our previous conclusion that a theater responds to the entry of competitors not
by increasing the number of movies, but by providing a differentiated movie lineup to consumers,
which leads to increased movie variety in the market as a whole.
Lastly, we consider the following model to estimate the effect of theater entry on the percentage
of unserved consumers through increased movie variety:
%U nservedmy = α +
K
X
ηk 1[T heatersmy ≥ k] + ψm + ψy + umy ,
(9)
k=2
where %U nservedmy is the percentage of consumers turned away in market m at (the given week
of) year y.
Figure 7 presents histograms of the estimated value of ηk in (9) and its t-statistic for k = 2, · · · , 7.
According to the first two panels, the average of the 52 estimates of η1 is -4.8, while out of these
52 estimates, 15 are significant at the 5 percent level. Estimation results presented in other panels
suggest that increased movie variety after the entry of theaters thereafter has weaker impact on
the percentage of unserved consumers.
17
Weekend market movie demand
In the previous analysis on the relationship between increased movie variety and the proportion of
unserved consumers, we assumed that the total weekend movie demand reaches 70 percent of the
seating capacity in each market. As a robustness check, we repeat the analysis with different values
of κ ranging from 50 to 100 percent.
Panels in Figure 8 plot the estimated marginal effects of theater entry on the percentage of
unserved consumers under different values of κ. Consistent with our main results, only the first
two entrants into a monopoly market reduces the proportion of consumers turned away in the
market; the estimated effect of the first entrant to a monopoly market on the percentage of unserved
consumers via increased movie variety ranges from -3.3 to -4, whereas it ranges from -1.6 to -1.8 for
the second entrant. However, the entry of theaters thereafter has no statistically significant effect
on the fraction of unserved consumers in the market.
Basis distance
So far, we have regarded one mile (1.61 kilometers) as the basis distance when identifying local
markets. Now, we apply different values from 1.5 to 2.0 kilometers as the basis distance, and
examine how sensitive empirical results are to the change in the local market definition.19
Panels in Figure 9 plot the estimated marginal effects of theater entry on movie variety and
their 95 percent confidence bands under different basis distances. Clearly, the entry of new theaters
tends to cause the total number of movies playing in the market to increase, whereas it has almost
no effect on movie variety in an incumbent theater. As for the effect of increased movie variety on
consumer welfare, panels in Figure 10 show that under any value of the basis distance, only the
first few entrants to a monopoly market induce the fraction of unserved consumers to decrease.
In sum, we check the robustness of our main results by analyzing short panels, varying the size
of the simulated total weekend movie demand in the market, and applying different values of the
basis distance in identifying local theater markets. Estimation results in this section confirm that
our main findings are robust to these changes in the assumptions and model specifications.
6
Conclusions
In this article we study the effect of the entry of new theaters on movie variety in incumbent
theaters and in the market. Further, we investigate how consumer welfare is affected by the change
in movie variety and availability that results from the entry of new theaters. Using a rich panel
data, we show that the more theaters in a market, the larger the number of movies playing in the
market, whereas movie variety in an incumbent theater is not affected. These findings imply that
theaters try to distinguish themselves from rivals by providing a differentiated movie lineup, which
leads to an increase in market-wide movie variety.
19
Using 2.0 kilometers as the basis distance, there are 2.2 theaters in a market on average.
18
Our main contribution consists of evaluating the impact of this increased product variety after
the entry of new theaters on consumer welfare. We find strong evidence that it is positive for the first
and second entrants into a monopoly market. However, the fraction of unserved consumers is not
affected by further increase in the number of movies, resulting from the entry of subsequent theaters.
We demonstrate that the positive effect of increased movie variety (allowing more consumers to
watch their favorite movies) dominates its negative effect (decreasing the efficiency in market-wide
seat allocation) only for the first few entrants to a monopoly market.
Our study can be extended in several ways. First, we assume that if a consumer can not find a
seat for his favorite movie, then he would not watch any other movie. Future research could take
the dynamic aspect of consumer’s movie choice decision into consideration. The empirical analysis
in this study is also based on assumptions that are imposed because of data limitations; consumer
tastes in movies are the same in all markets of a city, and the ratio of the total movie demand to
the seating capacity is constant across all markets. While they are reasonable, more detailed data
on market demand would let us relax these assumptions and conduct more precise analysis on the
relationship between product variety and consumer welfare.
19
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22
Table 1: Summary Statistics
Variables
Avg.
Std. Dev.
Min.
Max.
Panel A. Theater Level (147 theaters with 23,647 observations)
Number of Movies
All Movies
11.20
3.86
1
Regular Movies Only
8.67
2.95
0
Number of Competitors
1.80
1.88
0
Number of Screens
7.94
2.57
1
53
24
6
16
Panel B. Market Level (63 markets with 13,104 observations)
Number of Movies
All Movies
12.90
4.56
Regular Movies Only
9.91
3.49
Number of Theaters
1.80
1.34
Weekend Number of Seats per Movie 2,572
5,737
1
0
1
0
53
29
7
133,896
Panel C. City Level (7 cities with 27,263 observations)
Weekday Audience Size per Movie
5,418
16,469
0
545,033
23
Table 2: The Effect of Competition on a Theater’s Movie Variety
Variable
1[Competitors ≥ j]
j=1
j=2
j=3
j=4
j=5
j=6
Screens
Opening Week
Closing Week
Time
Constant
All Movies
(1)
(2)
0.141
(0.153)
-0.192
(0.133)
-0.004
(0.154)
0.250
(0.162)
0.012
(0.218)
-0.128
(0.141)
1.083
(0.175)***
-1.531
(0.240)***
-2.461
(0.353)***
0.008
(0.000)***
2.083
(1.409)
0.119
(0.131)
-0.227
(0.114)**
-0.105
(0.133)
0.170
(0.139)
0.151
(0.190)
-0.098
(0.121)
1.125
(0.149)***
-1.654
(0.217)***
-2.505
(0.319)***
0.009
(0.000)***
0.885
(1.200)
Regular Movies
(1)
(2)
0.171
(0.122)
-0.229
(0.106)**
0.131
(0.123)
0.103
(0.129)
0.115
(0.174)
0.001
(0.113)
1.021
(0.139)***
-2.720
(0.194)***
-1.508
(0.285)***
0.009
(0.000)***
-0.673
(1.119)
0.137
(0.100)
-0.237
(0.087)***
0.001
(0.102)
0.041
(0.105)
0.095
(0.147)
0.086
(0.092)
1.075
(0.112)***
-2.889
(0.175)***
-1.668
(0.258)***
0.009
(0.000)***
-1.063
(0.905)
Fixed Effects
Week
N
Y
N
Y
Theater
Y
Y
Y
Y
R squared
0.393
0.533
0.364
0.529
Theaters
147
147
147
147
Observations
23,647
23,647
23,647
23,647
Note: The table presents estimation results of (1) where M oviesit is the dependent variable. Standard errors
are in parentheses. The notation *** indicates significance at 1% level, ** at 5% level, * at 10% level.
24
Table 3: The Effect of Theater Entry on Market-wide Movie Variety
Variable
1[Theaters ≥ k]
k=2
k=3
k=4
k=5
k=6
k=7
Time
Constant
All Movies
(1)
(2)
2.275
(0.195)***
1.122
(0.228)***
1.529
(0.315)***
2.242
(0.406)***
0.893
(0.603)
1.068
(0.432)**
0.013
(0.001)***
8.695
(0.800)***
2.206
(0.159)***
1.114
(0.187)***
1.520
(0.260)***
2.170
(0.328)***
1.125
(0.510)**
1.049
(0.352)***
0.014
(0.001)***
7.127
(0.672)***
Regular Movies
(1)
(2)
1.709
(0.153)***
0.668
(0.179)***
1.255
(0.247)***
1.680
(0.317)***
0.962
(0.475)**
0.954
(0.338)***
0.012
(0.001)***
6.469
(0.626)***
1.653
(0.118)***
0.716
(0.140)***
1.236
(0.194)***
1.637
(0.243)***
0.941
(0.387)**
1.079
(0.262)***
0.013
(0.000)***
5.858
(0.503)***
Fixed Effects
Week
N
Y
N
Y
Market
Y
Y
Y
Y
R squared
0.336
0.511
0.320
0.522
Markets
63
63
63
63
Observations
13,104
13,104
13,104
13,104
Note: The table presents estimation results of (2) where M oviesmt is the dependent variable. Standard
errors are in parentheses. The notation *** indicates significance at 1% level, ** at 5% level, * at 10% level.
25
Table 4: The Effect of Theater Entry on the Percentage of Unserved Consumers
Variable
1[Theaters ≥ k]
k=2
k=3
k=4
k=5
k=6
k=7
Time
Constant
Original Demand
(1)
(2)
-4.118
(0.550)***
-1.991
(0.657)***
-0.113
(0.920)
0.931
(1.114)
0.170
(1.912)
0.709
(1.220)
0.011
(0.002)***
15.953
(2.312)***
-4.373
(0.494)***
-1.950
(0.591)***
-0.462
(0.828)
0.817
(1.000)
0.006
(1.724)
1.092
(1.096)
0.012
(0.002)***
18.450
(2.173)***
Adjusted Demand
(1)
(2)
-3.785
(0.607)***
-1.756
(0.724)**
-0.676
(1.012)
0.199
(1.231)
0.859
(2.091)
0.181
(1.345)
0.020
(0.002)***
24.430
(2.543)***
-4.048
(0.544)***
-1.738
(0.650)***
-1.184
(0.910)
0.075
(1.103)
0.612
(1.886)
0.674
(1.207)
0.022
(0.002)***
27.362
(2.380)***
Fixed Effects
Week
N
Y
N
Y
Market
Y
Y
Y
Y
R squared
0.312
0.424
0.338
0.442
Markets
63
63
63
63
Observations
13,081
13,081
13,081
13,081
Note: The table presents estimation results of (3) where %U nservedmt is the dependent variable. Standard
errors are in parentheses. The notation *** indicates significance at 1% level, ** at 5% level, * at 10% level.
26
Table 5: The Effect of Theater Entry on the Percentage of Unserved Consumers by Rating
Variable
1[Theaters ≥ k]
k=2
k=3
k=4
k=5
k=6
k=7
Time
Constant
12 or over
Movie Rating
15 or over 18 or over
Universal
-4.544
(1.048)***
-1.989
(1.240)
-0.238
(1.721)
1.656
(2.086)
0.028
(3.520)
0.328
(2.276)
0.013
(0.003)***
17.685
(4.477)***
-3.549
(0.888)***
-0.390
(1.058)
-2.692
(1.478)*
0.860
(1.788)
-2.462
(3.052)
0.688
(1.956)
0.007
(0.003)**
29.649
(3.865)***
-3.075
(1.719)*
1.522
(1.985)
0.999
(2.805)
-6.798
(3.423)**
6.127
(5.309)
1.526
(3.575)
0.073
(0.006)***
27.111
(7.001)***
-1.385
(1.079)
-3.737
(1.237)***
-3.911
(1.724)**
-1.307
(2.063)
4.430
(3.589)
-1.999
(2.254)
0.038
(0.004)***
24.497
(4.756)***
Fixed Effects
Week
Y
Y
Y
Y
Market
Y
Y
Y
Y
R squared
0.220
0.250
0.194
0.215
Markets
63
63
63
63
Observations
12,367
12,507
10,941
9,955
Note: The table presents estimation results of (3) where %U nservedrmt is the dependent variable. Standard
errors are in parentheses. The notation *** indicates significance at 1% level, ** at 5% level, * at 10% level.
27
Figure 5: Short Panel - Effects on a Theater’s Movie Variety
The Effect of the 1st Competitor
0
1
2
3
1.5
-1
1
2
1
2
1
2
-1
0
1
2
3
-3 -2 -1
0
1
2
3
2
3
The Effect of the 6th Competitor
Density
1
0
1
2
3
0
.5
Density
1.5
t-statistics
1.5
Estimated Effects
0
-3 -2 -1
2
0
-2
0 .2 .4 .6 .8 1
Density
Density
0
1
1.5
Density
1
3
t-statistics
0 .2 .4 .6 .8 1
-1
0
t-statistics
.5
Density
0
The Effect of the 5th Competitor
-2
-3 -2 -1
0
-3 -2 -1
Estimated Effects
2
1.5
1.5
1
Density
0
0
1
Estimated Effects
.5
1.5
1
Density
.5
-1
0
The Effect of the 4th Competitor
t-statistics
0
-2
1
Density
0
-2
The Effect of the 3rd Competitor
Estimated Effects
.5
1
Density
0
-3 -2 -1
1
2
.5
1
1
0
.5
-1
.5
1 1.5 2
0
0
-2
t-statistics
1.5
Estimated Effects
.5
Density
1 1.5 2
t-statistics
.5
Density
Estimated Effects
The Effect of the 2nd Competitor
-2
-1
0
1
2
-3 -2 -1
0
1
Note: This figure presents histograms of the estimated βj in (7) and its t-statistic from 52 short-panels for
j = 1, · · · , 6
28
Figure 6: Short Panel - Effects on Market-wide Movie Variety
The Effect of the 2nd Entrant
6
0
2
4
6
4
6
6
.8
4
6
4
6
Density
.2
2
4
6
-6 -4 -2
0
2
2
4
6
Density
Density
0
t-statistics
0 .2 .4 .6 .8 1
.4
Density
0
Estimated Effects
.3
-6 -4 -2
6
The Effect of the 7th Entrant
.1
6
4
0
-6 -4 -2
0
4
2
.8
.8
4
.2
.4
.3
.2
Density
.1
2
0
t-statistics
.6
Density
2
t-statistics
0
0
-6 -4 -2
.2
0
The Effect of the 6th Entrant
-6 -4 -2
6
0
-6 -4 -2
Estimated Effects
4
.4
.6
.4
Density
0
2
2
Estimated Effects
.2
.6
.4
Density
.2
0
0
The Effect of the 5th Entrant
t-statistics
0
-6 -4 -2
.6
Density
.2
0
-6 -4 -2
The Effect of the 4th Entrant
Estimated Effects
.4
.8
.6
.4
Density
.2
-6 -4 -2
.6
4
.4
2
-6 -4 -2
0
2
4
6
0 .2 .4 .6 .8 1
0
t-statistics
0
Density
-6 -4 -2
Estimated Effects
0 .2 .4 .6 .8 1
Density
t-statistics
0 .2 .4 .6 .8 1
Estimated Effects
The Effect of the 3rd Entrant
-6 -4 -2
0
2
Note: This figure presents histograms of the estimated γk in (8) and its t-statistic from 52 short-panels for
k = 2, · · · , 7
29
Figure 7: Short Panel - Effects on the Percentage of Unserved Consumers
The Effect of the 2nd Entrant
-8 -6 -4 -2 0 2 4 6 8
.6
.4
Density
0
.4
Density
.2
.4
Density
0
0
.2
.4
.3
.1
.6
t-statistics
.6
Estimated Effects
.2
Density
-8 -6 -4 -2 0 2 4 6 8
The Effect of the 7th Entrant
t-statistics
.4
.3
.2
Density
.1
0
.2
.6
.4
Density
.2
-8 -6 -4 -2 0 2 4 6 8
The Effect of the 6th Entrant
-8 -6 -4 -2 0 2 4 6 8
t-statistics
0
Density
0 .1 .2 .3 .4 .5
Density
0 .1 .2 .3 .4 .5
Estimated Effects
-8 -6 -4 -2 0 2 4 6 8
Estimated Effects
-8 -6 -4 -2 0 2 4 6 8
The Effect of the 5th Entrant
t-statistics
-8 -6 -4 -2 0 2 4 6 8
Density
-8 -6 -4 -2 0 2 4 6 8
The Effect of the 4th Entrant
Estimated Effects
0 .1 .2 .3 .4 .5
Density
-8 -6 -4 -2 0 2 4 6 8
t-statistics
0
-8 -6 -4 -2 0 2 4 6 8
0 .1 .2 .3 .4 .5
.6
0
.2
.4
Density
.6
.4
0
.2
Density
Estimated Effects
.8
t-statistics
.8
Estimated Effects
The Effect of the 3rd Entrant
-8 -6 -4 -2 0 2 4 6 8
-8 -6 -4 -2 0 2 4 6 8
Note: This figure presents histograms of the estimated ηk in (4) and its t-statistic from 52 short-panels for
k = 2, · · · , 7
30
Figure 8: Varying κ - Effects on the Percentage of Unserved Consumers
k: .6
-2
-6
-6
-4
-4
-2
0
0
2
2
4
4
k: .5
2
3
4
5
6
Market Number of Theaters
7
2
3
4
5
6
Market Number of Theaters
2
-2
-4
-6
-6
-4
-2
0
0
2
4
k: .8
4
k: .7
7
2
3
4
5
6
Market Number of Theaters
7
2
3
4
5
6
Market Number of Theaters
k: 1
2
0
-4
-6
-6
-4
-2
-2
0
2
4
4
k: .9
7
2
3
4
5
6
Market Number of Theaters
7
2
3
4
5
6
Market Number of Theaters
7
The Effect on the Percentage of Unserved Consumers
Note: Panels in this figure plot the estimated marginal effects of theaters’ entry on the percentage of unserved
consumers and their 95 percent confidence bands under different values of κ.
31
Figure 9: Varying Basis Distance - Effects on Movie Variety
Basis Distance: 1.61
-1
-1
0
0
1
1
2
2
3
3
Basis Distance: 1.5
2
3
4
5
6
Market Number of Theaters
7
2
7
Basis Distance: 1.8
1
0
-1
-1
0
1
2
2
3
3
Basis Distance: 1.7
3
4
5
6
Market Number of Theaters
2
3
4
5
6
Market Number of Theaters
7
2
7
2
1
-1
-1
0
0
1
2
3
Basis Distance: 2
3
Basis Distance: 1.9
3
4
5
6
Market Number of Theaters
2
3
4
5
6
Market Number of Theaters
7
2
3
4
5
6
Market Number of Theaters
7
The Effect on the Theater Number of Movies
The Effect on the Market Number of Movies
Note: Panels in this figure plot the estimated marginal effects of theaters’ entry on movie variety and their
95 percent confidence bands under different basis distances.
32
Figure 10: Varying Basis Distance - Effects on the Percentage of Unserved Consumers
Basis Distance: 1.61
-5
-10
-10
-5
0
0
5
5
Basis Distance: 1.5
2
3
4
5
6
Market Number of Theaters
7
2
7
Basis Distance: 1.8
0
-5
-10
-10
-5
0
5
5
Basis Distance: 1.7
3
4
5
6
Market Number of Theaters
2
3
4
5
6
Market Number of Theaters
7
2
7
-10
-10
-5
-5
0
0
5
Basis Distance: 2
5
Basis Distance: 1.9
3
4
5
6
Market Number of Theaters
2
3
4
5
6
Market Number of Theaters
7
2
3
4
5
6
Market Number of Theaters
7
The Effect on the Percentage of Unserved Consumers
Note: Panels in this figure plot the estimated marginal effects of theaters’ entry on the percentage of unserved
consumers and their 95 percent confidence bands under different basis distances.
33