Against marginal product

David Moyes says Jordan Pickford has been a better player than Dele Alli this season. This set me wondering about marginal productivity theory.

To see my point, think about how we’d test Moyes’ claim. We could look at what the two teams did in games which Alli and Pickford missed. But there are too few of these to draw robust inferences, and doing so would be impossible for a player who hadn’t missed any games*. Instead, we could compare how Sunderland would have done if Pickford were replaced with a next-best alternative to how S***s would have done with a next-best replacement for Alli. In effect, we’re asking: what are their marginal products?

I suspect that Pickford’s marginal product consists in converting heavy defeats into narrower ones: this still leaves Sunderland relegated, only with a lesser goal difference. Alli, by contrast, has converted draws or losses into wins. That’s a bigger difference.

This, I think, highlights three problems with marginal productivity analysis.

The first is that marginal product is the result of a hypothetical question. For example, in considering my own marginal product, I ask: how would the IC do without me? That’s a hypothetical to which we cannot give a precise answer. This is true of much of neoclassical economics. As Noah says:

Demand curves aren't actually directly observable. They're hypotheticals - "If the price were X, how much would you buy?"

In this, he’s echoing Sraffa:

The marginal approach requires attention to be focused on change, for without change either in the scale of an industry or in the ‘proportions of the factors of production’ there can be neither marginal product nor marginal cost. In a system in which, day after day, production continued unchanged in those respects, the marginal product of a factor (or alternatively the marginal cost of a product) would not merely be hard to find - it just would not be there to be found. (Production of Commodities by Means of Commodities, pv)

Secondly, in football there’s a high ratio of noise to signal: performances are due in part to luck. This is true not just in football. Consider two men of equal ability who become CFOs of start-ups. One start-up becomes massive, the other struggles. The man who joined the former will be many times richer than the latter. But that’s more to do with fortune than with human capital or marginal product: firms don’t usually grow big because they've got a slightly better CFO than the firm down the road. Anyone who’s mind isn’t befuddled by Randian nonsense will know that our lives and incomes are the product of luck. But we know that people are terrible at distinguishing luck from skill – in part because they suffer from the outcome bias.

Thirdly, imagine a top goalkeeper were playing for a better side than Sunderland. His performances would then make a difference to his team’s points: a couple of great saves per game would convert losses to draws or wins, rather than 4-0 defeats into 2-0 ones. His marginal product would be higher.

This tells us that, in teams, an individual’s marginal product is beyond his control: if Pickford had better colleagues, his marginal product would be higher. A similar problem arises in many large firms. As the late Herbert Scarf wrote:

If economists are to study economies of scale, and the division of labor in the large firm, the first step is to take our trusty derivatives, pack them up carefully in mothballs and put them away respectfully; they have served us well for many a year. But derivatives are prices, and in the presence of indivisibilities in production, prices simply don't do the jobs that they were meant to do. They do not detect optimality; they aren't useful in comparative statics; and they tell us very little about the organized complexity of the large firm.

For me, flaws such as these mean that marginal product theory doesn’t make much sense as an explanation of wage levels. We should abandon it as a mental model in favour of bargaining (pdf) models. In these, matches between workers and jobs lead to surpluses, and the surplus is divided according to the balance of power.

In such models, human capital raises wages insofar as it generates surplus and gives its holders outside options which enhance their bargaining power.  But human capital and “marginal product” aren’t the whole story. All the things that affect bargaining power, such as technology and unions, also matter. Such models are consistent with the theory that inequality is due to the rise of superstar firms (pdf). They’re also consistent with the fact that minimum wages don’t destroy many jobs. And they help explain rising CEO pay better than marginal product theory.

What I’m appealing for here is for economists to abandon unscientific just-so stories and to think instead about the real world. In this world, wages are determined not by unobservable entities such as marginal product but by – among other things – power (pdf).

* S***s did well during Harry Kane’s injury. Few would say this is evidence that Kane is a poor player, and not should they.

Comments

[Luis Enrique]

Marginal products are usually beyond the individual's control. Production functions usually have other inputs than labour, which affect the MPL and aren't controlled by the worker.

IMO you just have to see marginal product theory for what it is: a convenient simplification. It should not be 'abandoned' but used when appropriate.

The question "how much 'output' - whatever that may be - will be added by the addition of this worker, is always a sensible place to start, even if one needs to introduce things like indivisibilities or O-rings or whatever to do full justice to certain cases.

Seeing things in terms of bargaining over a surplus doesn't do away with that question, it has merely been recast as: " how much surplus does this match create?" - which really is not so very different to asking about the marginal product.

Of course I agree that the best idea of bargaining over a surplus is much more useful when it comes to thinking about CEO pay, for example. But it too is a simplification you could find 'flaws' in.

[Jonathon Hazell]

Chris,

I think you'll enjoy this paper, which formalises and expands on your insights.

http://www.aalto-econ.fi/tervio/DifferenceThatCEOsMake2007.pdf

[Kevin Carson]

The real problem with marginal product is that it's circular, and always secondary to power and institutional considerations. If marginal productity is what your "services" add to the price of the final product, then by definition anything anyone can charge a price for has "marginal productivity" -- including hiring out the services of one's slaves, allowing use of one's "intellectual property," or simply charging a toll for not obstructing production. Marginalism takes all "property rights" in the power to impede production, whether artificial or not, at face value.

[Blissex]

«Marginalism takes all "property rights" in the power to impede production, whether artificial or not, at face value.»

Indeed, and I shall expand this statement:

* The central truthiness of Economics is that absent government intervention the distribution of income is optimally unequal and perfectly fair; only theories that are validated by that truthiness are acceptable in Economics.

* Therefore JB Clark expunged "land" as a "factor of production" from marginalist theories because the existence of "rent" is not very compatible with the central truthiness of Economics.

M Gaffney, a georgist marginalist, has extensively documented and argued against that clever elimination of "land" from marginalist theories:

http://www.masongaffney.org/publications/K1Neo-classical_Stratagem.CV.pdf
https://www.researchgate.net/profile/Mason_Gaffney/publication/229809320_Keeping_Land_in_Capital_Theory_Ricardo_Faustmann_Wicksell_and_George/links/55818ea008ae12bde6e4a74b.pdf
http://www.cooperative-individualism.org/gaffney-mason_donald-stabile-on-henry-george-and-john-bates-clark-1995.htm
http://www.wealthandwant.com/docs/Gaffney_Intro_TCOE.html
http://www.eurotrib.com/story/2009/3/9/14049/58398
https://www.amazon.co.uk/Corruption-Economics-Georgist-Paradigm/dp/0856832448
http://www.emeraldinsight.com/doi/abs/10.1108/03068290910947949

[aragon]

Via CapX.co

Prioritizing Economics is Crippling the U.S. Economy

https://medium.com/@jamesallworth/the-slow-decay-of-americas-entrepreneurial-society-f9aeb6145891

"It seems counter-intuitive that the best way to keep an economy healthy is to deprioritize the economy. But that’s exactly what needs to happen. So much of what is going wrong right now in America’s economy can be traced to the priorities being all wrong."

Unlearning Economics is right it is the social consequences that matter in politics.

Automation will exasperate the balance in favour of capital and resources (rents) to an intolerable degree.

[nicholas]

I have to side with Luis on this one; on reflection I think Chris is in danger of generalising from 'the special case'.
CEO's and Premier League Footballers are a very small minority of 'workers'. In particular, CEO's pay may not reflect their marginal product because of market failure: remuneration committees may not actually strive to minimise CEO's pay because they are packed with insiders. The majority of workers probably do earn much close to their marginal product.
Instead of CEO's and Harry Kane, consider instead Harry the Window Cleaner. He is self employed, and charges as much as he can to clean people's windows. Clearly, Harry the WC earns exactly his marginal product. Now consider the workers for a competing window cleaning company. They cannot earn much different from Harry WC. Similarly Harry the Self Employed Motor Mechanic and so on. There are millions of these self employed and competing with other self employed Harrys.
Chris's analysis only applies when markets are not competitive, and Harry has some sort of advantage due to restrictive practices: eg Harry the CEO, Harry the Lawyer, Harry the hospital consultant, Harry the Investment Banker etc.

[aragon]

All cases are special cases at least when it come to monopolies and competition (except at Harry the window cleaner).

Microsoft, Google, Amazon, Wallmart (ASDA) all markets are dominated bay a small group of companies from Banks (Barcleys, Lloyds etc) to Cars (VW Group), to Supermarkets (Tesco etc), to Power companies, to Railways etc.

Via exponent.fm

https://www.theatlantic.com/politics/archive/2016/10/how-democrats-killed-their-populist-soul/504710/

"By 2008, the ideas that took hold in the 1970s had been Democratic orthodoxy for two generations. "Left-wing" meant opposing war, supporting social tolerance, advocating environmentalism, and accepting corporatism and big finance while also seeking redistribution via taxes."

[...]

"Financial crises are a regular feature of the U.S. banking system, and prices for essential goods and services reflect monopoly power rather than free citizens buying and selling to each other. Americans, sullen and unmoored from community structures, are turning to rage, apathy, protest, and tribalism, like white supremacy."

Anti-monopoly seems to be the issue of the day...

[Blissex]

«consider instead Harry the Window Cleaner. He is self employed, and charges as much as he can to clean people's windows. Clearly, Harry the WC earns exactly his marginal product. Now consider the workers for a competing window cleaning company. They cannot earn much different from Harry WC.»

Someone fairly recently wrote a thesis and a per on this, taking advantage of a "natural experiment, and this was discussed a year ago in this same blog:

http://stumblingandmumbling.typepad.com/stumbling_and_mumbling/2016/04/limits-of-marginal-productivity-theory-.html

The problem with that paper and the "Harry the Window Cleaner" argument is that the claim of income and marginal productivity is about the marginal contribution *to the utility of the whole economy*, not to the employer money revenue, which is a rather different concept.

Clearly few employers are going to pay someone more money than they money revenue that they expect to gain by hiring them, but that is quite unrelated as to whether the new hire's contribution to total utility corresponds to the utility of the wage they earn, it takes pretty extreme assumptions to bridge that gap. Even in small businesses where the owner can more easily determine the money revenue that the new hire can generate.

The general difficulty is that the utility of a worker's activity depends critically on that of complementary capital, and to investigate that requires a theory of capital and profit, while marginalists in general and especially JB Clark with his elimination of "land" have only handwaving instead of a theory.