The 3/2 rule revisited

2006-10-19 12:16:00 Allan Engelhardt wrote in CYBAEA Journal:

We revisited the 3/2 rule of employee productivity using a larger data set and considering each sector independently.

For this second analysis we took the 4595 constituents of the Standard & Poor's Total Market Index (TMI) which offers broad market exposure to large-, mid-, small-, and micro-cap companies. After excluding companies where we could not get the data (and also companies with negative profits which are hard to show on the log-log plot), we were left with a broad selection of 4,099 listed US companies in nine sectors.

As before, we chose profits per employee as our metric for employee productivity and show it against the number of employees.

The resulting per-sector graphs are shown below (click through for a larger version). Broadly, all graphs are flat, i.e. there is little change in profits/employee with company size.

[Basic Materials] [Conglomerates] [Consumer Goods] [Financial] [Healthcare] [Industrial Goods] [Services] [Technology] [Utilities]

A couple of things are perhaps worth pointing out. The Healthcare sector has a large group of quoted companies that are clearly in the bottom left of the graph compared to the bulk of the distribution. I assume that many of these are R&D companies which are still in the process of trialling their new medicine. The Financial sector is large and has the opposite behavior: a number of small but very profitable companies, which are usually companies managing large funds.

In total, there is probably a downward trend with size but with a slope of perhaps -0.1 or thereabouts. That still means that when you add 10% employees you lose 1% productivity per employee, which is clearly problematic. It is a much smaller number than the one we found before, primarily because the previous data set (the S&P 500) is biased against small companies with low revenues per employee. In the current data set we still have a bias in that they are all quoted companies which implies a certain size or at least cash position, but much less biased than before.

These numbers are very useful for benchmarking, and they certainly debunk any myths that large companies are more efficient, an oft-quoted statement in merger situations. In HR there are no efficiencies of scale. If there are efficiencies of scale in the other areas combined, then HR must scale negatively with size to give the flat result.

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Weird Fit

2011-02-18 21:08:00 Elton Carvalho said:

There is something wrong with the fit for Conglomerates data, isn't there?

Data availability

2011-04-10 18:49:00 John Helm said:

Would it be possible to make the data set available as was done in the original post? Thanks in advance. /John Helm

This analysis is really really dubious

2011-06-07 18:22:00 aram said:

Your plots are interesting, but it is WAY over the line to call your theory a "rule."

Flaws include:

1. Selection bias (as previous a commenter mentioned): smaller companies are more likely to drop off the list, while big ones will stay on even if they have low profits.

2. Confounding factors: At least you broke it up by sector, but that's clearly not the only unobserved correlate.

3. Reverse causality: Maybe low-margin activities lead to more industry consolidation, or only work at larger scales. I'm not saying it's true, but your data are equally consistent with this hypothesis.

4. Fitting a log-log plot is tricky. You can't just take logs and do least squares. Google "0706.1062" to see what I mean.

5. No error bars.

It's good that you were honest enough to test your results for generalizability. But the fact that extrapolation fails doesn't mean you should just revise your estimate of the effect size: it should also cause you to rethink your methodology.