Hollis Robbins on Average vs. Marginal
her gloss on Tyler Cowen's book
here’s the short version of Tyler’s argument. Two things happened as statistics developed in the nineteenth century: first, the rise of marginalism, the idea that economic value comes from the effect of one additional unit under fixed conditions (one more loaf of bread, one more hour of labor). Second was the rise of averageism, the idea that aggregates are best described through averages
She then applies this theme to teaching literature.
Tyler might recharacterize the “average Victorian novel” as an averageist object: a construct built from many novels. The “average novel” is only a concept in relation to the corpus (let’s say the average novel was a certain number of pages or has a certain plot structure or cost a certain amount) not at the level of the individual classroom text.
A novel on a syllabus becomes “marginal” when you move from “what is typical of the whole corpus?” to “what does one more novel add?” This second question can even be “what does one more novel bring to the reader who has read all the others?” Tyler’s marginalism is about the effect of an additional unit under fixed conditions, and he keeps insisting that what we observe are average magnitudes while the real analytic task is to infer the marginal effect from them.
She reminds us that theory tells us to pay attention to the marginal unit, while statistical observation typically gives us the average unit.
For me, this brings to mind Solow’s empirical work on productivity. Within the analytical construct of the production function, what matters is the marginal product of labor. But Solow used the factor shares of labor and capital, which measure average returns. To get from average to marginal, you wave your hands and say “assume constant returns to scale and equilibrium under perfect competition.”
Tyler argues that economists are losing interest in the underlying marginalist theory. In the Solow context, this might mean that we do the empirical work without caring whether we are recovering the marginal product of labor as a parameter in the production function. We just want to do our best to get good data and make valid causal inferences.
I posed the argument in the preceding paragraph to the AI in Tyler's book, and it responded,
Yes, that’s exactly the kind of inference Tyler’s argument supports, even if he doesn’t make the Solow connection explicitly.
The empirical turn Tyler describes is precisely about researchers caring more about clean causal identification than about whether the quantity being estimated maps neatly onto a theoretical concept like marginal product of labor. A Card and Krueger-style minimum wage study, for instance, is laser-focused on whether the wage increase caused employment changes—using a natural experiment and difference-in-differences. The question “but is this measuring the marginal product of labor?” is just not on the agenda. [See text: Ch.4 · Explicit ties between empirical work and margin...] The theoretical scaffolding that used to connect empirical estimates back to marginal concepts gets quietly dropped.
Machine learning pushes this even further, and Tyler is explicit about it: you let the algorithm build the “theory” from tens of millions of variables, and the result isn’t interpretable as a theory in any human-digestible sense—let alone one organized around marginal products. So the Solow move—using average factor shares as proxies for marginal products under competitive assumptions—looks like a transitional methodology: more theoretically disciplined than modern ML, but already loosening the tight connection between measurement and marginalist concepts.
Tyler’s punchline would probably be: the field stopped asking “am I measuring the right marginal quantity?” and started asking “is my identification strategy credible?” Those are very different questions, and the second one doesn’t need marginalism at all.
substacks referenced above: @
I fear that statistical analysis and/or marginal analysis of novels will miss a crucial issue: Is X a great novel? By "great," I mean "has exceptional, durable, cognitive-and-aesthetic value".
The cognitive value lies in its contribution to our understanding of human nature (psychology) and society.
Examples are _The Betrothed_ (Manzoni), _War and Peace_ (Tolstoy), and _An Artist of the Floating World_ (Ishiguru).
But I must be missing something!
Her mention of China - and we all know they have oversized busts of people like Burke littering the landscape, itself a weird cultural translation of the “tasteful” library bust - reminded me of something I’d forgotten.
My dear evangelical friends ran a church that happened to be situated in the vicinity of a large university and the transient population that attended it.
Thus among the usual attendees would be scattered a few university-associated people.
Once it was a couple from China, both academics, both I believe in the philosophy department, a temporary assignment. The guy’s scholarly focus was the Greeks.
I remember being curious how it was they happened into that church. Well, they lived in an apartment down the street.
My friend, who of course had no sense of the possibly comic nature of the juxtaposition, suggested that they simply viewed it as a chance to explore a different value system, from the buffet that included, you know, Plato. And I think they were curious.
Like, here is another Western or American thing!
Of course my friends would’ve been delighted if they had dropped philosophy for Jesus. And Jesus was the sum of their teaching, there is nothing of the intellectual or the historical (intellectually conceived, as against magical objects, etc.) in evangelical Christianity obviously.
I didn’t say so, but I did think this was kind of funny. But it didn’t surprise me that this couple became committed attendees of the church though sadly, to my friends, not Christians - because my friends were literally the kindest best people in the city.
And then tragedy struck, which I won’t go into, and suddenly that couple really needed help. And they really got it, from my friends, who as they did with so many hapless people, generously got tangled up in their lives in the time they had remaining in the US.
You can completely tease out who my friends are, genetically, constitutionally - from their religion. It’s an open question for me.
But let’s simplify as economists do and assume that these were the goods on offer: a university philosophy department, and a non-mainstream-denominational, fairly liberal if not in terms of church leadership (male), more Godspell-inflected church.
I was prompted to recall this ridiculous example by a commenter on her blog arguing, in another context, that we are not dealing with “standard” marginal units, nor identical effects.