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1 This article was downloaded by: [University of Sydney] On: 30 March 2010 Access details: Access Details: [subscription number ] Publisher Routledge Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Applied Economics Letters Publication details, including instructions for authors and subscription information: Movie producers and the statistical distribution of achievement Jordi McKenzie a a Discipline of Economics, University of Sydney, Sydney, NSW, Australia First published on: 05 March 2010 To cite this Article McKenzie, Jordi(2010) 'Movie producers and the statistical distribution of achievement', Applied Economics Letters,, First published on: 05 March 2010 (ifirst) To link to this Article: DOI: / URL: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

2 Applied Economics Letters, 2010, 1 5, ifirst Movie producers and the statistical distribution of achievement Jordi McKenzie Discipline of Economics, University of Sydney, Sydney, NSW 2006, Australia j.mckenzie@econ.usyd.edu.au This article investigates De Vany s (2004) application of the Pareto distribution to the careers of actors and directors by considering a sample of movie producers. The results support the Pareto distribution for describing the number of films produced and the sum of box office revenue earned by a producer. The results suggest that a producer is more likely to produce another film as the number of films which they have already produced increases. Also, although an early career producer faces more chance of securing a further film by pure luck, an established producer greatly benefits from his/her previous success. I. Introduction In a collection of his own and various co-authors work on the film industry, De Vany (2004) provides compelling evidence that the stable Paretian class of distribution is appropriate for describing many aspects of the industry, including revenues, budgets, return ratios and profits (De Vany and Walls 1996, 1999, 2004). He also adds to this list the career expectations of artists specifically actors and directors. De Vany shows that the number of films directed and starred in by these artists similarly follows a rightskewed leptokurtic pattern, with evidence that success breeds success and that artists increase the probability of making more movies if greater is the number of films they have previously made. This article investigates such a potential relationship with respect to movie producers. The Pareto distribution has a long history in economics dating back to the work of Pareto (1897) on income distribution. Recently, the famous distribution has found application in areas of culture and entertainment. De Vany and Walls (1996), Walls (1997) and Hand (2001) apply the distribution to the motion picture industry in the USA, Hong Kong and the UK markets, respectively. Maddison (2004) and Giles (2007) use similar methodology to investigate Broadway theatre and the US popular music industry, respectively. The implication of the Pareto distribution in the context of these models is that past successes are leveraged into future successes through a dynamic mechanism, which was aptly termed increasing returns to information by De Vany and Walls (1996). These studies employ a general regression methodology of log (Size) on log (Rank) to show downward concavity in the distribution, which suggested autocorrelated growth as defined by Ijiri and Simon (1974). This methodology can also (theoretically) be used to determine the tail weight parameter by taking the inverse of the slope coefficient of log (Rank) although, for analytic purposes, estimation by maximum likelihood is preferable. II. Data The data were collected from the standard industry source Nielsen EDI. Using the 597 feature films of 2007 released in the North American market, films were randomly selected to provide a sample of 101 lead producers. 1 To avoid potential sample-selection bias issues the sample was constructed such that each decile of the ranked distribution provided 10 producers. From this list each producer s production credits 1 A full list of the films and producers used in this study is available from the author on request. Applied Economics Letters ISSN print/issn online Ó 2010 Taylor & Francis DOI: /

3 2 J. McKenzie Table 1. Top 20 grossing producers ranked by sum of box Producer Number of films produced Sum of box (US$m) Maximum box (US$m) Average box office revenue (US$m) 1 Frank Marshall Brian Grazer Ted Field Gary Barber Laura Ziskin Sydney Pollack Tim Bevan Ben Stiller Judd Apatow Michael Bay Ronald Bass Edward R. Pressman 13 Michael Tollin Peter Abrams Craig Zadan Steve Golin Paul Schiff Richard N. Gladstein 19 Mark Canton Richard B. Lewis were retrieved for films in which they were listed as a (co)producer or a (co)executive producer. This provided a sample of 839 titles spanning back to 1978 for the film Paradise Alley, produced by Edward Pressman. All film revenues were transformed to January 2007 prices. Table 1 provides evidence of the top 20 producers ranked by the sum of box office revenue takings and also reports maximum box and average box per film. Frank Marshall, producer of movie franchises such as Indiana Jones, Gremlins and Bourne, tops the list with over US$5 billion in box office takings (2007 prices) and a total of 47 films. Tim Bevan tops the list in terms of number of production credits with 65 titles, including Bridget Jones, Love Actually and the cult Cohen brothers films O Brother Where Art Thou and The Big Lebowski, and is ranked seventh in terms of summed box office takings. The correlations of Table 2 suggest that the number of films produced is positively correlated with all of the financial indicators of success and that the top-grossing producers generally produce films that achieve higher averages. Table 3 provides evidence that the number of movies produced by a producer is right skewed and kurtotic. Figure 1 shows that the majority of producers produce only one film, but those who go on to produce more, produce many. The summary statistics relating to sum of box over producer career suggest Table 2. Correlation matrix of key variables Number of films produced Sum of box Maximum box Average box Number of films 1.00 produced Sum of box Maximum box Average box

4 Movie producers 3 Table 3. Summary statistics: number of movies produced and sum of box Variable Observed Mean Median SD Min Max Skew Kurtosis Number of movies Sum of box office (US$m) III. Estimation Strategy and Results Fraction Fig. 1. Lorenz Number of movies produced Number of movies produced by producer s histogram Number of movies produced Sum of box Cumulative population proportion Fig. 2. Lorenz curves of number of films produced and sum of box even more skewness and kurtosis. To put these in the perspective of the famous Pareto principle, the top 20% of producers (in terms of number of films) produced 69% of all films in the sample and the top 20% of producers (in terms of sum of box ) earned 87% of the total revenues. These findings are also illustrated with conventional Lorenz curves as shown in Fig. 2. The respective Gini coefficients are estimated as 0.65 and 0.83 for number of films produced and sum of box. The well-known Pareto distribution can be written as PrðX>xjX x 0 Þ ¼ x ð1þ x 0 where represents the tail weight parameter and x 0. 0 is the minimum value of x. The density of Pareto distribution is obtained by differentiating the Cumulative Distribution Function (CDF) or the complement of Equation 1 fðx; ; x 0 Þ¼ x 0 x þ1 for x x 0 ð2þ The likelihood of the Pareto distribution is therefore given by Lð; x 0 Þ¼ Yn i¼1 x 0 x þ1 i Y n ¼ n x n 0 i¼1 1 x þ1 i ð3þ and taking the logarithmic transformation yields the log-likelihood lð; x 0 Þ¼n ln þ n ln x 0 ð þ 1Þ Xn i¼1 ln x i ð4þ The maximum-likelihood estimator of directly follows from differentiating Equation 4 n ^ ¼ P i ðln x i ln x 0 Þ ð5þ Following DuMouchel (1983), the estimate of is obtained by applying maximum-likelihood estimation to the top 10% of the right-hand tail of the ranked distribution. Table 4 reports the estimates of for both the number of films produced and the sum of box s. Not surprisingly the estimate of is found to be less for the sum of box and is consistent with the kurtosis observed between the two samples. More interesting is that each estimate is less than two and the 95% confidence interval supports this finding, suggesting that the distribution is characterized by an undefined second moment that is, infinite variance. This finding implies that the tail

5 4 J. McKenzie Table 4. Maximum-likelihood estimates of Pareto distribution Number of movies produced Sum of box office revenue SE Lower 95% Upper 95% Observations Log Likelihood probabilities do not converge in the conditioning event as would be the case, for example, under a Gaussian distribution. This finding is similar to those reported by De Vany (2004) for both directors and actors, for which he estimated at 1.5 and 1.8 for the number of films made, respectively. The finding of at 1.17 for the number of films produced suggests some interesting, if not peculiar, results. Given the density described in Equation 2, and assuming x 0 = 1, it is straightforward to calculate the various probabilities of producing n films. Table 5 details these various probabilities and also compares them to the random probability of chance given a simple coin toss with 50% probability. Under pure luck, a film producer faces the probability of producing n films by f(n) = 0.5 n. The probabilities subsequently suggest that luck provides more chance of securing a low number of films, but as n increases the Pareto probability rises above that of luck, which diminishes rapidly in the tail as shown in Fig. 3. Table 6 provides further evidence of the nature of the probability under the Pareto distribution by calculating the conditional probability of a producer producing more films conditional on having already made n films. Specifically, Equation 1 is estimated for increasing values of x 0. Table 5. Probability of making n movies n Pareto fit Coin flip E-05 Probability The probabilities suggest that a producer who has made just one film has a probability of 44% of making more films, whereas a producer who has made 15 films has a 93% probability of making more films. This is the exact mechanism that creates superstars (Rosen, 1981), wherein success breeds success. IV. Conclusion Pareto Coin flip Movies Fig. 3. Pareto fit of number of movies produced and random coin flip Table 6. Probability of making more movies conditional on having made n movies N P (movies. n n) This article has explored the suitability of the wellknown Pareto distribution for describing the career achievements of movie producers in terms of number of films produced and sum total of box dollars earned for these films. The results reveal that the distribution is highly appropriate with estimated tail parameters less than two suggesting theoretically

6 Movie producers 5 infinite variance. The implications are that a film producer has increasing probability of producing more films if greater is the number of films already produced and that the future expectation of number of films rises in the conditioning event. The Pareto distributions also suggest that although early career producers face more chance of securing another title through pure luck, an established producer increases the probability of further projects with the number they have already produced. Acknowledgements I am grateful to Arthur De Vany for guidance and the research assistance of Haishan Yuan. References De Vany, A. (2004) Hollywood Economics: How Extreme Uncertainty Shapes the Film Industry, Routledge, London. De Vany, A. and Walls, D. (1996) Bose Einstein dynamics and adaptive contracting in the motion picture industry, The Economic Journal, 106, De Vany, A. and Walls, D. (1999) Uncertainty in the movie industry: does star power reduce the terror of the box office?, Journal of Cultural Economics, 23, De Vany, A. and Walls, D. (2004) Motion picture profit, the stable Paretian hypothesis and the curse of the superstar, Journal of Economic Dynamics and Control, 28, DuMouchel, W. (1983) Estimating the stable index in order to measure tail thickness: a critique, The Annals of Statistics, 11, Giles, D. (2007) Increasing returns to information in the popular US music industry, Applied Economics Letters, 14, Hand, C. (2001) Increasing returns to information: further evidence from the UK film market, Applied Economics Letters, 8, Ijiri, Y. and Simon, H. (1974) Interpretations of departures from the Pareto curve firm-size distributions, Journal of Political Economy, 82, Maddison, D. (2004) Increasing returns to information and the survival of Broadway theatre productions, Applied Economic Letters, 11, Pareto, V. (1897) Cours d Economie Politique, Rouge, Paris. Rosen, S. (1981) The economics of superstars, American Economic Review, 71, Walls, D. (1997) Increasing returns to information: evidence from the Hong Kong movie market, Applied Economics Letters, 4,