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 (169.22 KiB) Viewed 5019 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.