Measuring Productivity

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Measuring Productivity

Postby blairfix » Sat Sep 03, 2016 8:26 pm

One of Nitzan and Bichler's central critiques of neoclassical theory is its immeasurability: its entire premise is based on non-existent units.

The neoclassical theory of marginal productivity is a prime example. The premise of the theory is simple: one's income is proportional to one's productivity. However, as soon as we try to test this theory, we run into a problem: how do we compare different types of output? How do we know if a farmer is more productive than a lawyer? The logical response is that an objective comparison cannot be made: the outputs of a farmer and a lawyer are incommensurable.

Of course, this has posed no problem for neoclassical theory. The time-honored solution is to compare different types of output in units of price. Low and behold, when we measure productivity in terms of the value that one “produces”, we find that individual income is indeed highly correlated with productivity.

It is remarkable that this slight of hand is standard practice. It works so well because it assumes what it aims to prove: it uses income to measure productivity, and then claims to prove that productivity predicts income.

But the theory does raise an interesting question: when is it possible to objectively compare the output of different workers? The requirements are stringent: the workers must be doing exactly the same task, using exactly the same technology, and the output must have physically countable units.

I was curious about this type of measurement, and it turns out that quite a few studies have compared the task-specific outputs of industrial workers. In particular, Hunter et al. (1990) document the task-specific productivity dispersion of over 50 different industrial tasks. For each task, Hunter reports the relative standard deviation of output (a measure of dispersion) among workers.

This leads to an important question: how large is this productivity dispersion in relation to the observed dispersion of incomes? The figure below makes the comparison by comparing the two in terms of the Gini index. The comparison requires transforming Hunter's relative standard deviation data into a Gini index of productivity. This calculation requires some parametric assumptions … I won't go into the details here … ask me if you are interested.

Productivity.png
Productivity.png (169.22 KiB) Viewed 907 times


The figure shows the distribution of inequality within all nations on Earth, over the entire time-period for which data is available. This is then compared to the distribution of productivity inequality between industrial workers. The result is telling – productivity dispersion is systematically too small (by a factor of 4, on average) to account for observed levels of inequality.

Of course, this result is not particularly surprising. It has long been known that human abilities are approximately normally distributed, but income distributions are highly skewed. The beauty of marginal productivity theory is that it is constructed so that it is immune to these uncomfortable facts.


References:

Hunter, J. E., Schmidt, F. L., & Judiesch, M. K. (1990). Individual differences in output variability as a function of job complexity. Journal of Applied Psychology, 75(1), 28.

National Gini indexes come from the World Bank, series SI.POV.GINI. The figure shows the distribution of all available data – all countries over all years.
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Re: Measuring Productivity

Postby DT Cochrane » Mon Sep 05, 2016 7:37 am

Politically powerful analysis, Blair.

Good work.
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Re: Measuring Productivity

Postby Jonathan Nitzan » Mon Sep 05, 2016 7:16 pm

A brilliant idea and exposition, Blair. It would be nice if you could articulate the method and perhaps even provide the data.

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Re: Measuring Productivity

Postby blairfix » Tue Sep 06, 2016 1:53 pm

Here is the method used for the calculation:
Method.pdf
(137.22 KiB) Downloaded 67 times


Here is a spreadsheet of the data used:
Hunter_Data.xls
(11 KiB) Downloaded 108 times


Here is the data source:
Hunter_1990.pdf
(1.25 MiB) Downloaded 96 times
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Re: Measuring Productivity

Postby DT Cochrane » Thu Sep 08, 2016 6:00 am

Is this analysis seriously hampered by its focus on industrial workers?

I'm imagining this argument: the distribution of income includes many people whose earnings are both above and below industrial workers. On the one hand, we have more poorly paid service industry workers, who one could assume are less productive (measurement issues notwithstanding). On the other hand, we have more handsomely paid white-collar workers, who one could assume are more productive (same caveat re. measurement).

I don't accept either claim, but such claims would seem to handily dismiss this analysis.

Thoughts?
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Re: Measuring Productivity

Postby blairfix » Thu Sep 08, 2016 9:08 am

Troy,

I think you've tapped into the magic of marginal productivity theory. As long as you put measurement issues aside, then the theory can always be justified.

Nonetheless, it would be interesting if we could extend the analysis to skilled workers such as engineers, lawyers, etc. But can we agree on an objective way of comparing output? That's the whole problem, in a nutshell. If we cannot agree on a measurement, then the comparison is moot.
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Re: Measuring Productivity

Postby DT Cochrane » Thu Sep 08, 2016 5:43 pm

blairfix wrote:Troy,

I think you've tapped into the magic of marginal productivity theory. As long as you put measurement issues aside, then the theory can always be justified.

Nonetheless, it would be interesting if we could extend the analysis to skilled workers such as engineers, lawyers, etc. But can we agree on an objective way of comparing output? That's the whole problem, in a nutshell. If we cannot agree on a measurement, then the comparison is moot.


Absolutely. The immeasurability should pull the rug out from under the N-C argument. Unfortunately, that hasn't mattered in the past.
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