## Abstract

Consumers can only choose to see a movie if it is available in theaters. Explicitly taking into account movie theater availability, we estimate a structural model of movie demand with the use of U.S. movie data from 1995 to 2017. Estimation results indicate that the impact of theater availability on movie demand is both statistically and economically significant. We also find that movie budget predictions based on the model that incorporates theater availability is more consistent with the data, while the model that ignores theater availability on average over-predict production budgets.

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## Notes

- 1.
*Everyone Says I Love You*has a rating of 6.8/10 on IMDb, compared to 6.3/10 for*My Best Friend’s Wedding*. - 2.
Theatrical box-office revenue is the largest income source for movie studio, see https://stephenfollows.com/how-movies-make-money-hollywood-blockbusters/.

- 3.
A related concept to theater availability is the concept of “stock-out”. For example, Mortimer (2008) finds that video rental stores often experience inventory problems, and some movie titles are unavailable to consumers because they are out of stock. An equivalent phenomenon in movie theaters would be sold-out performances of blockbuster movies. Under the assumption that every theater screen’s seating capacity is at least 100 people, and each screen has at least 3 showings a day, we find no movie in our data reaches more than 55% of the total aggregate seating capacity in any week. It is still possible that the sold-out performances happen in opening nights or are restricted to certain local theaters. However, because our movie data are weekly national level data, we do not have a reliable way to identify sold-out performances.

- 4.
In our data, about 13% of the movies were released on a day other than Fridays. For those movies, we used the eleventh week as the last full week.

- 5.
The sample covers only a fraction of weeks in the years 1994 and 2017; consequently they are excluded from the tables of summary statistics.

- 6.
The movie prices used are the national annual average prices. We follow Einav (2007) and use linear interpolation to obtain weekly average prices. The data do not have price variations by geographic areas or age groups. Therefore, in the calculation of weekly admissions per movie, we are implicitly assuming that all movies have the same proportional exposures to different geographic regions and age groups.

- 7.
Every year has 52 weeks with some filler weeks missing. For example, the year 2015 has only filler weeks 23, 33 and 53, while the year 2014 has only filler weeks 23, 43 and 55.

- 8.
Alternatively, we can use weekly revenues to calculate market shares. In this case, the potential market size is calculated by multiplying the total U.S. population and the average ticket price. This method of calculation would yield exactly the same market shares. In addition, the calculation of admissions does not depend on the method of inflation adjustment, because the numerator and denominator (weekly box-office revenues and average ticket prices) would both be adjusted by the same inflation measure.

- 9.
Implicitly, we are assuming that a potential audience goes to at most a movie per week. This assumption is reasonable because the annual admission per capita is only about 4, as shown in Table 1.

- 10.
The annual dummy variable (\(\psi _y\)) captures aggregate changes in the market, including changes in average ticket prices, national incomes, macroeconomic business cycles, etc. We do not use prices directly in the estimation, because only average national ticket prices are available in the data. This means that the aggregate price effect cannot be separately identified from the effect that is due to other possible aggregate factors. In addition, because individual movies in general do not compete on price margins: Conditional on everything else being the same, an audience pays the same price to see any available movies in the same theater. We do not expect unobserved idiosyncratic demand shocks would cause endogeneity bias on the estimation of the annual fixed effects.

- 11.
- 12.
The consumer choice probability in Eq. (4) has the theater availability directly entering consumers’ utility function. This is equivalent to defining separately a consideration probability \(\pi _{jt}=(m_{jt})^{\delta /(1-\sigma )}\), and a conditional choice probability \({\hat{s}}_{jt}=\frac{\exp \left( \frac{\theta _j-\lambda (t-r_j)+\tau _t+\xi _{jt}}{1-\sigma }\right) }{D_t^{\sigma }+D_t}\). Then \(s_{jt}=\pi _{jt}\cdot {\hat{s}}_{jt}\).

- 13.
The ratio \(R_j\) is at least 1. It equals 1 when a movie has no international sales.

- 14.
Removing this assumption would add more noise to the prediction of movie production budgets for individual movies. Because we only consider the average industry budget spending in the ensuing analysis, more noise at the individual level is less of a concern.

- 15.
For example, five major Hollywood studios formed a joint movies-on-demand venture, which allowed streaming via broadband Internet for the first time in 2002. In the same year, Netflix, reaching 1 million subscribers, made its initial public offering.

- 16.
Since the data do not report a movie’s weekly number of screens, we approximate it by using the product of its weekly number of theaters and the average number of screens per theater as reported in Table 3.

- 17.
The difference in parameter \(\lambda\) between the subsample after the year 2000 and the pooled sample is \(-\,0.005\,(0.174)\); the difference in \(\sigma\) is \(0.045\,(0.178)\); and the difference in \(\delta\) is \(-0.053\,(0.895)\). Using a Wald test, these differences are not significantly different from zero: \(P>\chi ^2 = 0.501\).

- 18.
The difference in \(\lambda\) between the subsample that contains only the Action/Adventure movies and the pooled sample is \(0.009\,(0.042)\); the difference in \(\sigma\) is \(0.008\,(0.045)\); and the difference in \(\delta\) is \(0.020\,(0.195)\). Using a Wald test, these differences are not significantly different from zero: \(P>\chi ^2 = 0.809\).

- 19.
Recently, multiple lawsuits have been filed against the large theater chains; the suits allege that these companies use their market power to coerce film distributors to grant them “clearances.” Clearance means that theaters can request that the film distributors decline to license their films to theaters that are located in zones that the large chains deem competitive, because of geographic proximity or shared audiences. See reports from the Washington Post.

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## Acknowledgements

We thank the editor and two anonymous referees for making our paper much better. We thank the participants for their useful comments in IIOC. The usual disclaimer applies.

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## Appendices

### Appendix 1

In this appendix, we provide the necessary steps in deriving Eqs. (4) and (5) in the main text. Let \(v_{jt}=\theta _j-\lambda (t-r_j)+\xi _{jt}+\delta \ln (m_{kt})\), where \(m_{jt}\) is the proxy for theater availability, and \(\theta _{j}\) is movie *j*’s perceived quality specified in Eq. (2) of the main text. Consumer *i*’s taste shock in week *t*, \(\varsigma _{it}+(1-\sigma )\varepsilon _{ijt}\), follows an extreme value distribution. In addition, the outside option is always considered by consumers, so \(v_{0t}=-\tau _t\). Using the standard nested logit specification (McFadden 1978), the probability of consumers choosing movie *j* in week *t* is:

In this specification, the outside option is in a different nest and can have a different substitutability from all the movies. The fraction of population that would go to theaters in given week is:

Correspondingly, the proportion of population choosing the outside option is:

where

The within-industry market share of movie *j* in week *t* is

Furthermore,

Taking a log-transformation, we have

Also from the derivation of \(s_{0t}\), we have \(1-s_{0t}=\frac{D_t}{D_t^{\sigma }+D_t}\). It follows that

### Appendix 2

In this appendix, we show the detailed derivation of Eq. (8) in the main text. Let \(\chi _{jt}=\exp \left( \frac{\theta _j-\lambda (t-r_j)+\tau _t+\delta \cdot \ln (m_{jt})+\xi _{jt}}{1-\sigma }\right)\), then from the “Appendix 1”, we know that \(s_{jt}=\chi _{jt} / (D_t^{\sigma }+D_t)\) and \(\frac{d \chi _{jt}}{d \theta _j}=\frac{\chi _{jt}}{1-\sigma }\). In addition, we know that \(D_t=\sum _k \chi _{kt}\), where \(\frac{\partial D_t}{\partial \chi _{jt}}=1\).

Therefore,

Notice that \(s_{0t}=\frac{D_t^{\sigma }}{D^{\sigma }_t+D_t}\), this means that \(D_t=\left( \frac{s_{0t}}{1-s_{0t}}\right) ^{\frac{1}{\sigma -1}}\), so the above becomes

From Eq. (2) of the main text, we also know that \(\frac{\partial \theta _{jt}}{\partial B_{j}}=\beta \frac{1}{B_{j}}\).

Assuming studio profit \((R(B_j)+q_j)\sum _t p_{jt} M_t W(t-r_j) s_{jt} -B_j\), where \(R(B_j)\) is the worldwide to domestic box-office ratio and \(q_j\) captures the additional revenue source outside of theaters. Then the first order condition is

We rearrange the above to get Eq. (8) in the manuscript.

### Appendix 3

The international box-office ratio is a function of production budget \(B_j\), a movie’s genre, and release year. We specify the regression model as the follows:

To control for the potential endogeneity, we use the total production budgets of the movie producer in the previous year as a instrument variable. The regression results are presented in the Table 7.

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Leung, T.C., Qi, S. & Yuan, J. Movie Industry Demand and Theater Availability.
*Rev Ind Organ* **56, **489–513 (2020). https://doi.org/10.1007/s11151-019-09706-5

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### Keywords

- Movie demand
- Theater availability
- Demand estimation