Theory Review

Abstract

In modeling data in the performing arts, the presence of highly paid ‘superstars’—earning the lion’s share of performance royalty for musical compositions or receipts from live concerts—causes the earnings distribution to be highly skewed. Incorrect probability judgments can be made in the analysis of economic data when normality is assumed, but asymmetry is present. The purpose of this chapter is to review the skew-normal and skew-t statistical distributions theory and present a model that can be used to estimate regression models when the distribution is highly skewed. To correct for asymmetrical forms in econometric data modeling, flexible forms of both the univariate and multivariate skew-normal and skew-t distributions have been developed. Walls (2005) suggests two reasons why the log-skew-t is appealing in economic modeling. First, it is easier—computationally—to implement the skew-t than some other distributions (like the stable Paretian model or the ’eevy stable regression model) using standard maximum likelihood statistical techniques that are within reach of applied researchers. Second, the skew-t extends the normal distribution by permitting tails that are heavy and asymmetric. The log-normal is just a special case of the log-skew-normal when α=0.