Posted by Jay Livingston
I’m not very good at looking at a scatterplot and estimating the correlation.
This morning’s Wall Street Journal had a front-page story about CEO pay. Here’s the lede:
Chief executives increasingly are being paid based on their companies' financial results and share prices, according to a Wall Street Journal analysis.The WSJ even had an outside source check their calculations and conclusions.
Pay was “highly correlated with performance,” says Steven Kaplan, a professor of finance at the University of Chicago's Booth School of Business who reviewed the Journal calculations.Here’s the scatterplot showing the 300 largest companies:
(Click on the chart for a larger view. Those wedge-shaped lines point to
very large photographs of individual CEOs, which I cropped out.)
very large photographs of individual CEOs, which I cropped out.)
I guess “highly correlated” is a term of art. Unfortunately, the WSJ does not provide a regression line or correlation coefficient, but apparently the slope is +0.6.
On average, for every additional 1% a company returned to shareholders between 2009 and 2011, the CEO was paid 0.6% more last year, the analysis found. For every 1% decline in shareholder return, the CEO was paid 0.6% less.I like that idea of considering the profitable CEOs separately from the CEOs whose firms lost money. Here is the same scatterplot split down the middle.
If you divide the Pay axis at $20 million, the relation becomes clear. For every $20M+ CEO in a losing company, there are three in profitable companies.
But here’s where my inability to look at the dots and estimate correlations messes me up. To me, it looks as though among the losing firms, there’s no relation between CEO pay and how well the company did (i.e., how small its losses). Same thing on the profit side, especially if you ignore the three $60M+ outliers. (Timothy Cook of Apple, at $378M, lies out so far he’s not even on the chart.)
I’m not sure to who to believe – the Wall Street Journal or my lyin’ eyes.
The WSJ site has a chart listing the compensation of all 300 – from Apple down to Whole Foods, whose CEO didn’t even snag $1 million.
The story also heralds 2011 as showing huge improvement over the previous year in rationality, or at least the proportionality of pay to profits,
In 2010, there was no correlation; for every 1% decrease in shareholder return, the average CEO was paid 0.02% more.Yes, you read that correctly. The correlation was negative – the smaller the profit (or larger the loss), the higher the CEO pay.
2 comments:
Lots of confounding factors here, a key one being reverse causation--are the CEOs being paid more because their companies are doing well, or do the companies do well because of the high pay?
Seems like they should be looking longitudinally.
If we knew that the pay packages were worked out after the P-L sheets were in, that would make this simpler. And maybe they are. But if not, then causal direction and simultaneity are a problem. You also have to control for size and sector and probably other variables.
My point was that “highly correlated” was difficult to see with the naked eye and that maybe the data didn’t merit a page one story.
The WSJ article attributes the small gain in the profits-pay correlation to increased “investor scrutiny” thanks to Dodd-Frank. That suggests that in the past, and to a great extent even with Dodd-Frank, the pay deal can be something worked out privately between the CEO and a friendly board without close attention to last year’s bottom line.
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