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How do theatrical box office revenues affect DVD retail sales? Australian empirical evidence

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Abstract

This study considers the Australian DVD industry using a data set of retail sales for over 44,800 titles 1997–2007. A sub-sample of 760 titles which also received an initial theatrical release reveals that the DVD revenue distribution has thicker tails than the theatrical revenue distribution implying the top-ranked DVDs earning a greater share of revenues than their theatrical contemporaries. A comparison of revenues finds not only a high degree of correlation between the two markets, but a relationship that is nonlinear and increasing at higher theatrical revenue levels. This finding is consistent with a word-of-mouth momentum effect and more institutional flexibility in the DVD market. The high levels of correlation are present across all genres/ratings and are observed to be stronger for large release titles. Finally, a seemingly unrelated regression structure is proposed to jointly consider the two markets, which is shown to be empirically valid.

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Notes

  1. For example, the US Consumer Electronics Association estimate sales of digital direct-view TV receivers, HDTV, flat panel, projection TV and combination TVs increased sales from 5.5 million units in 2003 to 27.1 million units in 2007.

  2. Australian Film Commission (AFC) (2008).

  3. In Australia, companies such as HMV, JB Hi-Fi, Sanity, and Harvey Norman are examples.

  4. See Eliashberg et al. (2006) and Mckenzie (2010) for surveys of the literature. De Vany (2004) also provides a useful survey, in addition to his own (and various co-authors’) extensive and insightful research of the industry.

  5. Exceptions include Frank (1994), Ravid (1999), Carlton and Chevalier (2001), Dranove and Gandal (2003), Mortimer (2007), Nelson et al. (2008), Xing (2008), Elberse and Olberholzer-Gee (2008), Jozefowic et al. (2008), and Walls (2010).

  6. See De Vany and Walls (1996).

  7. This is done by employing a (log) size-rank regression with a quadratic term as initially considered by De Vany and Walls (1996) and subsequently Walls (1997) and Hand (2001).

  8. The 13-week data set means there is no bias from different survival times as all titles observed for the same length of time. Also, there is no truncation of revenues due to a ‘chart exit’ effect, meaning all revenues are observed for the full 13 weeks.

  9. Australian Visual Software Distributors Association (AVSDA) (2007).

  10. AFC 2008.

  11. GfK Marketing Services (2008).

  12. Motion Pictures Distributors Association of Australia (MPDAA) (2008).

  13. GfK, cited in AFC (2008).

  14. AFC (2008).

  15. Trade Services of Australia Video Source 2007, cited in AFC (2008).

  16. AFC (2008).

  17. Sales of DVDs in sell-through retail exceeded $1bn in 2004 (AVSDA 2008).

  18. The raw data also reports an 8 week sales figure. As an average, 8 week sales comprise 81% of the 13 week revenue figure.

  19. See Nelson et al. (2008) for an empirical analysis of the ‘out-of-market’ (release) gap for films released in the US market from 1998 to 2005.

  20. Placing several films in the population is the initialisation for the model, however, Ijiri and Simon (1964) show that after large t, the resulting distribution is insensitive to the number of firms (films) chosen.

  21. Ijiri and Simon (1964) show, by simulation, that the firm size distribution exhibits downward concavity if δ < 1, is a straight line if δ = 1, and has downward convexity if δ > 1. The curvature is greater as |δ − 1| is greater. The parameter δ has a simple economic interpretation and describes the relative significance of recent sales, as compared with earlier sales, in generating future sales. Both recent and prior sales contribute to future sales but the latter contributes less than the former if δ < 1 and vice versa. This is shown analytically in their (1974) paper for the case where 0 < δ < 1 (distribution concave downward).

  22. Ijiri and Simon (1964) show in their simulation that a slight deviation of δ = 0.95 was sufficient to create considerable curvature for the distribution.

  23. De Vany and Lee (2001) describe a simulation model in which agents relate quality information about films which they have seen. They show that the resulting statistical distribution is Pareto-Levy stable which is consistent with box office revenues observed empirically.

  24. Other closely related distributions include the Generalised Pareto, Generalised Extreme Value, Weibull, etc.

  25. Owing to the empirical density not exactly fitting the theoretical Pareto distribution in the upper tail, the estimate of α is necessarily sensitive to the size of the tail chosen. In saying this, however, regardless of the tail size chosen, estimated α is consistently less in the DVD sample consistent with the assertion that there is more probability mass in the distribution of DVD revenues than theatrical revenues.

  26. A simple regression of DVD sales on theatrical box office with a quadratic term yields \( {\text{DVD}}\,{\text{revenue}} = \begin{array}{*{20}c} { - 14785.12} & + & {0.1112\,{\text{theatrical}}\,{\text{revenue}}} & + & {3.49{\text{e}}-09\left( {{\text{theatrical}}\,{\text{revenue}}} \right)^{2} } \\ {\left( { - 0.45} \right)} & {} & {\left( {14.03} \right)} & {} & {\left( {15.18} \right)} \\ \end{array} \) where t-values are in parentheses. Note N = 760, R 2 = 0.8301.

  27. An alternative to this ‘approximation’ approach might be to transform the left hand side variable into a binary variable as done by De Vany and Walls (1999) and Collins et al. (2002), however, this approach necessarily entails loss of information in this transformation. Walls (2005a, b) has employed various remedial regression structures which explicitly account for skewness and heavy tails such as the skew-normal, skew-t and symmetric stable model, but often these remedial techniques come at high computational cost and would be econometrically intractable in a simultaneous regression structure.

  28. See, for example, Prag and Casavant (1994), De Vany and Walls (1999), Ravid (1999), Collins et al. (2002), Elberse and Eliashberg (2003), Jansen (2005), Walls (2005a), Ravid et al. (2006), Gemser et al. (2007), and Einav (2007).

  29. Formally, this statistic is given by \( \lambda = T\sum\nolimits_{s = 1}^{S} {\sum\nolimits_{r = 1}^{s - 1} {r_{sr}^{2} } } \), where r sr is the estimated correlation between the residuals of S equations, and T is the number of observations. Since S = 2 in this model, the statistic becomes λ = Tr 2 which is distributed χ 2 with 1 degree of freedom.

  30. Moul (2007) uses the serial-correlation in the error term as a measure of this word-of-mouth effect using a sample of weekly revenues in a nested logit model of demand.

  31. It is worth noting that the SUR structure doesn’t change the individual parameter estimates themselves but does change the standard errors associated with these estimates.

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Acknowledgments

I acknowledge the Motion Picture Distributor Association of Australia (MPDAA) and GfK Marketing Services for supplying data used in this study. I also acknowledge support of the Centre for Screen Business (CSB). I am grateful for the suggestions of two anonymous referees. All remaining errors are my own.

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  1. Discipline of Economics, University of Sydney, Sydney, NSW, 2006, Australia

    Jordi McKenzie

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McKenzie, J. How do theatrical box office revenues affect DVD retail sales? Australian empirical evidence. J Cult Econ 34, 159–179 (2010). https://doi.org/10.1007/s10824-010-9119-x

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