Last week, Eric Chemi and Ariana Giorgi published an interesting article on “The Pay-for-Performance Myth”

With all the public chatter about exorbitant executive compensation and income inequality, it’s useful to look at the relationship between chief executive officer pay and corporate performance. Typically, when the subject of their big pay packages arises, CEOs—usually through their spokespeople—say they are paid for performance. Does data back that up?

An analysis of compensation data publicly released by Equilar shows little correlation between CEO pay and company performance. Equilar ranked the salaries of 200 highly paid CEOs. When compared to metrics such as revenue, profitability, and stock return, the scattering of data looks pretty random, as though performance doesn’t matter. The comparison makes it look as if there is zero relationship between pay and performance.

In the article, they produce a copula-type plot (since ranks – only – are considered). Ariana kindly sent me the dataset (that was used in The Pay at the Top) to play with it

> base=read.table("ceo.csv",sep=";",header=TRUE)

Here I normalize (dividing by the size of the dataset) to have uniform distribution on the unit interval (instead of working with ranks, i.e. integers). If we remove that scaling factor, the scatterplot is that same as the one mentioned in the Pay-for-performance myth.

> n=nrow(base) > U=rank(base[,1])/(n+1) > V=rank(base[,2])/(n+1) > plot(U,V,xlab="Rank CEO Pay", + ylab="Rank Stock Return")

This is the copula type representation.

If we visualize the density of the copula (using the algorithm described in the joint paper with Gery and Davy), we get either

> library("copula") > library("ks") > library("MASS") > library("locfit") > n.res=32 > ctilde1=probtranscopkde(UVs,p=1, + u.out=seq(1/(2*n.res+1),1-1/(2*n.res+1), +length=n.res),plots=TRUE)