Neo-classical factor shares

Note:   I want you all to be highly critical of my posts on factor shares – and where you can throw literature at me.  I wrote a bunch of posts in a single day based on one book (and some prior knowledge), I have no appeal to authority here and would love to have your ideas thrown in there 🙂

Just as a starting point here, if anyone comes on and goes “those neo-classical neo-liberals, like Friedman, this is all ideology – I’ve read Klein”, I am not likely to reply.  The key reason for this is because you’ve already shown a complete unwillingness to debate on reasonable terms, and are trying to base the discussion on prejudiced definitions that aren’t appropriate for this definition of neo-classical economics.

In this context, neo-classical is a description of economists who applied a certain set of methods at a  point in time – economics is a discipline with “many models”, and the development of these tools is of huge value.  The start of this method came with the “marginalist revolution”.

The Marginalists in this case were Jevons, Walras, and Menger.  Those who work in certain areas will recognise some of the names (eg Walras law, Menger as a founder of the Austrian school of Economics).  Fundamentally, the purposefully use of the concept of “marginal” gains and losses (rather than average) allowed us to consider individual choice more directly.  More than that, value switched from having “objective” value in its labour time/cost of production to having “subjective” value (potentially on the basis of “satisfaction” or “utility”).  Note:  This is not to say classical economists didn’t think in this way as well, John S Mill was a student of Bentham and wrote a book called utilitarianism!  But the change in focus did help to “solve” many of the perceived paradox of classical economics (eg Giffen goods).

It is no coincidence that at this time sociology and psychology were ramping up as disciplines.  With the growing acceptance of the idea of a “science of society” a number of ways of discussing social facts were being described.  Within economics, the recognition that it may be useful to think about action stemming from individual choice had found its time, and the mechanistic tools of calculus had a place to help us consider certain assumptions about this choice (methodological individualism) – this compares to the classical use of factor shares, and some prices (wages) being set by social convention.

You will find me say critical things in here, and talk about this literature as a “starting point” to real analysis.  So let us consider it in this way.

Note:  Unlike the previous essays, this one is relatively full of comments from me – rather than just the essay.  That would likely be because this and GE (which gets a post later on) are closest to the form of analysis I would use for these types of questions (aggregate production function as shorthand, GE as a more disciplined form of analysis).  Sorry if it makes this long 🙁

Still, enough history.  I was going to talk about the essay 😛

The change in focus regarding factor shares in neo-classical economics is nicely described at the start of the essay:

Surplus to landowner or to capitalist was to the classicist, the result of privilege, ownership, and exploitation.  The neo-classicist shifted the main concern from distributive shares to the allocation of scarce resources, and to the linking of input rewards to productive contributions.

However, my view is that this can exaggerate what is going on by mixing normative views of authors with the descriptive form of the analysis – essentially, both classicists and neo-classicists are defining “types”, endowing them with a choice rule, and deducing outcomes.  They are then asking how these idealised types relate to reality, to ask if we can inductively infer anything for the analysis of these “types”.

So having recently discussed the classical types in recent posts, what is neo-classical?

Neo-classical models started with the idea of marginalism (marginal utility, marginal product) and went about discussing outcomes as the result of the simultaneous solution of a system where individuals follow a “no-arbitrage” condition – thereby choosing to equate relative marginal utilities/marginal products to relative prices.  Previous models of factor shares had “kept things fixed” to discuss what is going on (eg capital-output ratios or real wages) – however, with a marginalist model this wasn’t the case.  Relatedly, there was no need for anything to be a “residual”, as factors of production within this framework were fundamentally substitutable!

Neo-classicals as dismissive to distributional issues?

There is a common complaint that some neo-classical economists were themselves dismissive of distributional issues.  As Schumpeter is quoted as saying:

And it means on the other hand, that, in as much as costs to firms are income to householdss, the same marginal principle, with the same proviso, automatically covers the phenomena of income formation or of “distribution”, which really ceases to be a distinct topic.

However, these types of quotes are not saying distributional matters aren’t important – just that they should be thought of within the same framework as other economic issues.  The importance of endowment in the allocation of resources was often mentioned (Edgeworth boxes, the second fundamental welfare theorem).

But we also need to remember the neo-classical economists were coming up with a new type of “idealised world” to discuss issues of social allocation.  In that environment there were conclusions that sound dismissive of distributional issues, but that is due to the type of counterfactual world they were discussing – and the assumptions that embodied.

However, it is this process of simultaneity that is focused on.  As Wicksell says:

workers and the means of production are separate factors but all on the same footing, without regard to the differences in their social relationships.

Sidenote:  Simultaneity illustrates the “cooperative” nature of production, as opposed to the conflict based focus of class analysis.  This also illustrates one of the key shortcomings when it comes to political economy and this type of analysis – the lack of description about the development of endowment and opportunity which was presumed in class based analysis.

Aggregate production functions

It is at this point we start moving towards a more modern view of considering factor shares, and the long-term aggregate economy – aggregate production functions.  This direct framework started with J. B. Clark (1899) we have a perfectly competitive world with a single wage rate, single interest rate, a linear homogenous production function, homogenous capital, and fixed supplies of productive services.

Yes these assumptions are strong, and many of them will drive the resulting analysis he has of factor shares – but I think we sometimes forget just how strong the classical assumptions were (as many of these are equivalent).  Furthermore, this is a great example of a situation where assumptions have been continuously loosened over a long period of time.  In the end the framework helped to show that given assumptions about perfect competition and set endowments, factor shares were simply the result of individuals earning their “share” of production.

Another neat quote in this chapter:

The Ricardian concept of unearned surplus, which derives from ownership of superior land or from the Marxian rate of surplus value or exploitation in the capitalist mode of production, is associated in neo-classical writing with imperfect markets or competitive markets in disequilibrium

As a result, discussions around factor shares in (macro) neo-classical work will tend to be focused on estimating the production function and the elasticity of substitution (between factors).  This is incredibly fraught, and arguably different parts of the discipline have handled this shortcoming in three ways:

  1. Admitting that the issues of aggregating capital are too large and focusing on smaller, conditional, questions we can answer (mainstream economics)
  2. Staying within this level of aggregation and testing out different forms of meso and macro assumptions to generate results (Post-Keynesian economics)
  3. Reverting to class based analysis.

However, as I noted at the start the use of an aggregate production function can be a useful starting point for analysis.  In this context, the Cobb-Douglas production function was king – both because it matched data at the time, and provided an elasticity of substitution of 1 (which implies that labour and capital income shares are constant as production expands).  Furthermore, the income share to each factor (price times the factor to output ratio) appeared to be close to the estimate one would get from the Cobb-Douglas production function, as a result this was seen as a good stylized fact of the macroeconomy. [Note:  I believe it was Hicks who gave us the most complete and compelling first treatment of this in Theory of Wages, but I haven’t read it so am relying on what I’ve heard 🙂 ]

For the starting point of much analysis this is used as a stylised fact (especially as it appeared to fit a lot of developed economies for some time), however in more recent times it has been more heavily questioned.  The key point is that this was a “stylized fact” that was observed, a single fact such as this could be the result of a myriad of “microrelationships” and potential “secular changes” – implying that the relevance for policy is unclear even if this holds.  We are still in the world of aggregation.

Here the author mentions Kuznets observation (among a large series of observations) that there are two stages of growth, one where a developing nation builds up capital pushing down the labour share, then a following stage where the economy is developed and labour’s share rises over time.  At this point he was explaining a “stylized fact” – one that has received a bunch of mixed evidence (here and here) and may not be appropriate to assume going forward (although what that means is also debatable).  This illustrates one of the issues with the production function approach, allow it allows us to think about specific shifts we don’t necessarily have sufficient data to mediate between competing arguments – we can build contradictory arguments, which provide different forecasts, from the same dataset.

For dealing with this, and trying to make a larger role for technical change, constant elasticity of substitution (CES) production functions become more popular.  Technical change can then be viewed as “capital saving”, “neutral”, or “labour savings”.  In this way the change in factor shares depends on the nature of the technical change as well as the elasticity of substitution.  Our prices of interest are the real wage rate and the interest rate (noting that we have issues measuring the stock of capital unless the interest rate is given – one of the key reasons why the interest rate is treated as exogenous and given often.  Note more so that Sraffa and more recently Mas Colell have pointed out that this makes the idea of a downward sloping factor demand curve for capital more difficult to justify), while our quantities are labour and capital inputs.

In this way, considering the factor shares in an economy is akin to asking about the “cost minimisation” problem for the economy as a whole.  However, this indicates one of the problems – we have increasing population, and often assume constant returns to scale in order to discuss our results.  In fact, part of the result may be due to the existence of increasing returns to scale.


Overall this has been a relatively quick tour of the idea of a “neo-classical” model of factor shares – namely thinking about factor shares through the lens of an aggregate production function.  It is a useful way to get some key concepts – but it both ignores the normative content of previous theories (both a blessing and a curse), and is vulnerable to the complexities that exist over an entire economy (specifically in terms of heterogeneous capital goods, factor demand, and the general difficulty of aggregation and valuation).  An interesting point raised in the essay was:

The critical problems of political economy relate more to the older classification of distributive shares than to the analytical income categories [ed that we now measure].

Modern GDP and GDP related statistics are based on this production function view of the economy, and as a result our ability to apply “value” regarding distributive shares based on older arguments is weaker than we may think at first glance.

While the author believes that we should then try to have that expresses the old categories, I would instead say that we need to think about data and measurement that represent the trade-offs we are interested in for current social arrangements.  Household microdata that combines groups based on characteristics, and then describes that, is the modern way of doing this – and in my opinion a useful and fruitful direction.

Neo-classical tools, especially given the additional 80 years of development from what we’ve discussed here, are useful for a wide variety of things.  Furthermore, the raw idea of a production function is a good “first start” when I’m sitting down with issues.  If we want to go further in “answering a given question” economists know it is important to loosen more assumptions – which captures part of the reason why my own lack of focus on factor shares as a means to interpret distributional data 😉