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Superstars and heavy tails in recorded entertainment: empirical analysis of the market for DVDs

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Abstract

This research presents a systematic empirical analysis of the market for digital versatile discs (DVDs). We examine a sample of 953 DVD titles that appeared on the weekly top-30 sales charts in North America over a 30-month interval. We find that the size distribution of weekly DVD sales revenue does not indicate the presence of increasing returns to information. The empirical results for DVD sales contrast starkly with previous results obtained for motion-picture box-office revenue, where a number of researchers have found evidence of positive feedback in demand. While the distribution of cumulative revenues across DVDs is highly unequal, the DVD market appears not to be characterized by the extreme heavy upper tail that so well describes the winner-take-all nature of the distribution of box-office success across motion pictures.

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Notes

  1. Of course there were interesting studies related to the movie business prior to the Smith and Smith (1986) paper—such as Cheung’s (1980) analysis of moral hazard and ticket pricing and Kenney and Klein’s (1983) analysis of exhibitor-distributor contracting practices—but the area has flourished only recently.

  2. A brief account of the analytics of movie demand dynamics—where filmgoers discover the films they like by consuming them and through the exchange of information—is provided in Walls (2008).

  3. The type of approach taken here is discussed at some length by Brock (1999), who argues that empirical regularities in the form of scaling laws, such as the Pareto law, may be useful in providing information on the process that is generating the data. Our use of the Pareto law here is similar to recent work in econophysics (Rosser 2008a, b).

  4. Vining (1976) provides further analysis and refinement of the Ijiri and Simon (1974) analytical framework. Vining’s (1976) insights will become useful in the interpretation of our empirical results, but to focus on the methodological issues raised in his research at this point in this paper would overly complicate the exposition of this section while not adding anything fundamental to the reader’s understanding.

  5. To simplify the prose, I will refer to the normal model where it will be implicit that I am referring to the logarithm of revenue as the random variable of interest.

  6. Because our data set contains only the top thirty DVDs—and not the entire population—we cannot provide an analysis of Anderson’s (2006) long tail hypothesis as is done by Elberse and Olberholzer-Gee (2008). However, our data do permit the estimation of the size–rank distribution as set out in the previous section; even the original De Vany and Walls (1996) analysis was based on the top fifty films as listed in Daily Variety. Estimation of the rank–revenue relationship is not affected by the top-earning products because it is a scale-invariant size distribution.

  7. DVDs may not appear on the chart continuously. That is a DVD on the chart may fall from the chart and re-enter the chart in subsequent weeks. The rank–revenue analysis of cumulative earnings across DVD titles will be unaffected by this. For the weekly analysis, our results are not substantively affected by this.

  8. Before estimating the Pareto law, we first plotted the size distribution of our data for each week of the top-30 sample, a plot of revenue against rank on logarithmic axes. The data appeared to follow the log-linearity implied by the strict Pareto law in Eq. 1 above. At the suggestion of a referee, this figure has been removed from the paper.

  9. The DVD market may have experienced large changes in demand over the span of data analyzed. The weekly dummy variables in the regression analysis control for this possibility; one can think of the weekly dummies as time-specific effects in the model.

  10. We estimated the stable model on log-Revenue using Nolan’s (2005) software, using both the McCulloch (1986) quantile estimator as well as the Nolan (2001) maximum likelihood estimator. The maximum likelihood results confirmed that the characteristic exponent is two.

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  1. Department of Economics, University of Calgary, Calgary, AB, T2N 1N4, Canada

    W. D. Walls

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Walls, W.D. Superstars and heavy tails in recorded entertainment: empirical analysis of the market for DVDs. J Cult Econ 34, 261–279 (2010). https://doi.org/10.1007/s10824-010-9125-z

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