Reviewing the reviewers: The impact of individual film critics on box office performance

Abstract

Critics and their opinions or critical reviews play a major role in many markets. Marketing research on how critics impact product performance has so far examined an aggregate critic effect. An obstacle in studies examining the relationship of aggregate critical opinion and product sales is the close association between the intrinsic quality of a product and the aggregate opinion regarding the product. Our analysis parses out these two effects, allowing us to distinguish individual critics who are simply good at identifying products with popular appeal from those who act as opinion leaders and engender early product sales. The role of critics is especially prominent in the film business, in which one finds multiple expert opinions about each movie and where critics’ endorsements are used in advertising. In the context of the motion picture industry, our research investigates the impact of individual film critics on the market performance of movies, where specific key critics and reviewers may serve as market gatekeepers, and where various critics may have different types of impacts on product performance.

Appendix

In this appendix we specify the prior distributions of the model parameters. Because we estimate model parameters with the Gibbs sampler, we also describe the conditional posterior distributions. Convergence of the MCMC chains was assessed with BOA version 1.0.1 (see Best et al. 1995).

For our prior on V _s , we use the covariance prior of Barnard et al. (2000), decomposing V _s into a vector of standard errors (ξ _s ) and a correlation matrix R _s . We use an independent inverse gamma prior on each element of the standard error vector, $\xi ^{2}_{{sl}} \sim IG{\left( {\nu _{{\xi s}} ,\kappa _{{\xi s}} } \right)},$ and we use a uniform prior over the space of positive definite correlation matrices for the prior on R _s . To complete the specification of our cluster-specific priors, we assume $\sigma ^{2} \sim IG{\left( {\nu _{\sigma } ,\kappa _{\sigma } } \right)}$ and $\psi _{\sigma } \sim N{\left( {\mu _{{\psi \sigma }} ,\omega _{{\psi \sigma }} } \right)}.$

We estimate model parameters using Gibbs sampling, drawing from the full set of conditional distributions. The conjugate priors on σ ², ψ _s , and β _s lead to well-known conditional distributions (inverse gamma and normal) for the following conditional posteriors:

$$ \begin{array}{*{20}l} {{{\left[ {\sigma ^{2}_{i} \left| {\phi _{i} ,\nu _{\sigma } ,\kappa _{\sigma } } \right.} \right]},} \hfill} \\ {{{\left[ {\psi _{s} \left| {{\left\{ {\phi _{i} } \right\}}_{s} ,s,\beta _{s} ,V_{s} ,\mu _{s} ,\omega _{s} ,\gamma _{s} } \right.} \right]},\,and} \hfill} \\ {{{\left[ {\beta _{s} \left| {{\left\{ {\phi _{i} } \right\}}_{s} ,s,\psi _{s} ,V_{s} ,c_{s} ,\tau _{s} ,\gamma _{s} } \right.} \right]}.} \hfill} \\ \end{array} $$

To simplify the structure of the algorithm while allowing the dimension of W _s to vary across clusters, we simply condition on certain elements of ψ _s and/or β _s as equal to zero; the conditional distributions of the remaining elements are still multivariate normal, and draws are easily obtained.

Our prior for γ _sj is

$$ f{\left( \gamma \right)} = {\prod {{\prod {\zeta ^{{\gamma _{{sj}} }}_{{sj}} } }{\left( {1 - \zeta _{{sj}} } \right)}^{{{\left( {1 - \gamma _{{sj}} } \right)}}} } } $$

Although this prior implies independence, this assumption has been found to work well in practice (George and McCulloch 1993). The discrete conditional posterior distribution ${\left[ {\gamma _{{sj}} \left| {\beta _{s} ,{\left\{ {\phi _{i} } \right\}}_{s} ,s,\psi _{s} ,V_{s} ,c_{s} ,\tau _{s} ,\zeta _{s} } \right.} \right]}$ is Bernoulli where

$$ p{\left( {\gamma _{{sj}} = 1} \right)} = \frac{{{\left[ {\beta _{s} \left| {{\left\{ {\phi _{i} } \right\}}_{s} ,s,\psi _{s} ,V_{s} ,c_{s} ,\tau _{s} \gamma _{{sj}} = 1} \right.} \right]}\zeta _{s} }} {{{\left[ {\beta _{s} \left| {{\left\{ {\phi _{i} } \right\}}_{s} ,s,\psi _{s} ,V_{s} ,c_{s} ,\tau _{s} \gamma _{{sj}} = 0} \right.} \right]}{\left( {1 - \zeta _{s} } \right)} + {\left[ {\beta _{s} \left| {{\left\{ {\phi _{i} } \right\}}_{s} ,s,\psi _{s} ,V_{s} ,c_{s} ,\tau _{s} \gamma _{{sj}} = 1} \right.} \right]}\zeta _{s} }} $$

The conditional distribution of the ϕ vector ${\left[ {\phi _{i} \left| {\sigma ^{2}_{i} ,\eta _{i} ,\theta _{s} ,V_{s} } \right.} \right]}$ is not conjugate, and we use a Metropolis Hastings algorithm to obtain draws of each ϕ _i . To make the draws, we transformed the third parameter from log(m _i ) to log${\left( {m_{i} - Y_{{iT_{i} }} - y_{{iT_{i} }} } \right)},$ because we know that sales potential must exceed observed sales. Not only did this transformation allow us to incorporate relevant information in the draws of m _i , but it also ensured that predicted sales from the Bass model would be non-negative. We used the multivariate t distribution as our proposal density, with a location set equal to the previous draw of ϕ _i and a covariance matrix equal to $a_{\phi } V_{s} ,$ where $a_{\phi }$ is a tuning constant.

Finally, we used the Griddy Gibbs algorithm (Ritter and Tanner 1992) to simulate from the conditional distribution of V ^s

$$ {\left[ {V_{s} \left| {\phi ,\eta ,\theta _{s} ,\nu _{{\xi s}} ,\kappa _{{\xi s}} ,s} \right.} \right]} $$

as was done by Barnard et al. (2000).