The Depth Spectrum

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The Depth Spectrum

Postby blairfix » Wed Feb 11, 2015 2:00 pm

The Distribution of Depth

In the capital as power framework, "depth" refers to the ratio of profit per employee, while "breadth" refers to the number of employees. Depth and breadth represent different methods for pursuing the accumulation of capital. Under a breadth regime, firms attempt to become more profitable by increasing their size (measured in employment), while under a depth regime, firms attempt to become more profitable by increasing profit per employee.

Rather than analyze changes in profitability per employee, in this post I look at the spectrum (or distribution) of depth. In order to make analysis easier, I have redefined depth as capitalization per employee (rather than profit). The reason for this change is that market cap, unlike profit, can never be negative. This makes analyzing the depth spectrum easier, because most skewed distribution functions (such as the lognormal distribution used here) can only take on positive values. Since market cap and profitability are closely related, this change shouldn't be too problematic.

To conduct this analysis, I used data from over 4000 firms in the Compustat USA database in the year 2012. I then constructed a histogram of this data using logarithmic bins, meaning bin size does not remain constant, but rather grows exponentially:

ie. bin 1 = market cap per employee of $1-$10
bin 2 = market cap per employee of $101-$1000
bin 3 = market cap per employee of $1001-$10,000

The result is the histogram below labeled "Empirical Data". The resulting distribution is plotted with the x-axis on a logarithmic scale, giving what appears to be a "normal" distribution. However, the spectrum of depth is not normally distributed at all ... it is lognormally distributed.

Depth Distribution.png
Depth Distribution.png (228.18 KiB) Viewed 1638 times

The lognormal distribution (
is heavily skewed rightward, and belongs to a class of "fat-tail" distributions. As the name implies, the lognormal distribution looks like a normal distribution when plotted on a log scale. Its skewness is easier to see without the log scale.

lognormal.png (224.71 KiB) Viewed 1638 times

Enough with mathematics ... what does this mean for political economy? Of particular interest is the right end of the depth spectrum. What kind of firm is capable of generating a market cap per employee of $1 billion? While I haven't conducted a thorough analysis, a quick look suggests that these firms are mostly trust funds and royalty funds.

Topping out the list is Western Asset Mortgage Capital Corporation, which manages residential mortgage-backed securities. Also on the list is Royal Gold, whose principal business activity is the acquisition and management of precious metal royalties. Also at the top is the North European Oil Royalty Trust, which manages oil royalties.

On the left hand of the spectrum, I expected to find mostly startup companies ... I was wrong. Bottoming out the list were large firms such as International Textile Group, Inc and Kelly Services, Inc (the largest temp agency in the US).
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Re: The Depth Spectrum

Postby blairfix » Sun Feb 22, 2015 4:20 pm

An Investigation into the Relation between Capital Intensity and Standard Industry Classification

In mainstream economics, capital exists as a physical and financial duality: it is both a physical stock of machines/infrastructure and a financial stock that supposedly quantifies this physical capital.

In order to avoid confusion, from now on, I refer to financial capital simply as "capital", and physical capital as "techno-mass".

According to neoclassical theory, capital intensity (market capitalization per employee) should be correlated with the amount of techno-mass used per worker. But how can we test this prediction? As the Cambridge capital controversy revealed, quantifying techno-mass is fraught with difficulties.

I propose here a methodology that avoids the pitfalls of directly measuring the techno-mass stock. I do this by using the standard industry classification system as a rough proxy for techno-mass intensity.

The standard industry classification (SIC) system gives a 4 digit number to each firm. SIC codes indicate the industry of the primary activity of a given firm. This system is convenient because lower SIC code industries are generally more techno-mass intensive than higher SIC code industries. For instance, lower numbers correspond to techno-mass intensive activities such as mining, construction, and manufacturing. Higher numbers correspond to activities such as trade and finance, which are much less techno-mass intensive. Therefore, we can think of techno-mass intensity as being inversely related to SIC code size.

SIC Code Range
Mining :1000 -1499
Construction/Manufacturing : 1500 - 3999
Transportation/Trade : 4000 - 5999
Finance/Services : 6000 - 8999

My methodology is to categorize capital intensity (market capitalization per employee) into logarithmic bins (see the previous post for a description of this process). For each such bin, I calculate the average capital intensity per firm.

For the same bin, I also calculate the average SIC code value. This SIC code average gives us an indication of the composition of the firms within each bin. For instance, if the average SIC is in the 1000s, we know that the bin consists mostly of mining firms. In the same manner, if the average SIC is above 6000, we know that the bin consists mostly of finance/service firms.

The SIC code average, I argue, gives us a rough indicator of the techno-mass intensity of the firms within each bin (with a lower SIC code average corresponding to higher techno-mass intensity, and vice versa).

If techno-mass intensity is correlated with capital intensity (as predicted by neoclassical theory), then we should see a linear downward trend between average SIC code and market capitalization per employee.

SIC.png (293.73 KiB) Viewed 1614 times

Looking first at the year 1960, we see that the resulting data is entirely consistent with neoclassical theory. Average SIC codes decline more or less linearly with capital intensity. However, the same cannot be said for the year 2013, which exhibits a startling nonlinearity. For firms with capital intensities less than $3 million per employee, the results are consistent with neoclassical theory: techno-mass intensity increases with capital intensity.

However, for firms with capital intensities above $3 million per employee, the reverse is true. SIC code averages increase with capital intensity. This means that techno-mass intensity becomes negatively correlated with capital intensity, directly contradicting the neoclassical prediction.

What does capital as power have to say about these results? For starters, we must recognize that, in the mind of the capitalist, techno-mass is mainly a tool for reducing costs, in order to increase profits. Given the strong connection between capitalization and profit, capital intensity is simply an indicator of the number of employees required to generate (or more appropriately "command") a given level of profit.

In 1960, more techno-mass intensive firms were generally able to generate more profit per employee than less techno-mass intensive firms. However, by 2013, it is clear that techno-mass is no longer a requirement for generating more profit per employee. Hedge funds are able to generate massive profits while employing only a small workforce and using very little techno-mass.
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Re: The Depth Spectrum

Postby Jonathan Nitzan » Mon Feb 23, 2015 4:03 am

Very interesting results, Blair, and fresh thinking.

Since 'techno mass', just like 'real capital', has no unique magnitude, it cannot be measured. And if it cannot be measured, its neoclassical association with the nominal quantity of capital (capitalization) cannot be demonstrated, let alone refuted.

One way to give the neoclassicists a run for their money is to use SIC numbers, assuming that these numbers are correlated with techno mass/real capital. Another way is to use the dollar value of plant and equipment, assuming that, at any point in time, this value is proportional the underlying techno mass/real capital.

We have done so in Ch. 10 of CasP, but mostly at the aggregate level and with only one disaggregate example comparing Microsoft and GM. It would be interesting to generalize this disaggregate analysis to the North American Compustat universe as a whole and compare it to your results here.
Jonathan Nitzan
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