Friday, December 9, 2016

Economy And History Livin' In Perfect Harmony

"The paths up and down are the same."
- Heraclitus

I actually have quite a few blog posts percolating right now, but this is the one being written instead. It's about history, economics and accounting a little bit. You'll see where Heraclitus comes in later.

Economic history blogger Pseudoerasmus recently wrote a brief tweetstorm about the excellent Eric Foner's boneheaded comment on methodology. Foner seems to have implied that counterfactuals have no place in history at all, which is shocking to the point of incomprehensibility. Even a simple statement of fact like "Cotton was core to the southern economy." can hide a counterfactual (perhaps "If cotton didn't exist, nothing would take it's place."?). An absolutely core question to the analysis of the Civil War is certainly whether southern cotton plantations were seeing output growth in the way that northern factories were. In order to talk about this, we simply must talk about the "growth" paths cut off by the Civil War.

David Hume

To see why, let's have a cartoon sketch of the use of  "causality" in historical argument. I, a Humean, think most causality talk is confused. Causality is only a way of talking about underlying functional relationships. If the path of history is A B C, we might not want to say C is just the damn stupid thing after B.

Alexander Hamilton

When Alexander Hamilton left the British West Indies for America, he was leaving a place where whites were not just relatively but absolutely rich to a place where they were poor - relative to whites in the British West Indies. But it is the USA that became rich and not the British West Indies. These are historical facts of no interest. What is of interest is why this outcome occurred and not vice versa. What might be interesting is the claim that the reason is that the British West Indies made slavery too central to their institutions, making them "extractive" (i.e. they want to get rich by chiseling) rather than "progressive" (i.e. they want to get rich by raising productivity). Someone, maybe John Stuart Mill, can draw some deep political conclusions from that.

Robert Fogel

We can talk about politics and metaphysics now because there's causality, slavery -> low productivity -> bad institutions (even long after slavery is abolished). A is slavery and C is poverty. But here comes our friend Robert Fogel. He tells us that slavery in the Old South didn't necessarily reduce productivity (recall that productivity is just a relationship between inputs and outputs), that large slave plantations might have had even higher productivity (more output per unit input) than free farms. The simple Millian story of progressive institutions is not simple.

But what does buddy Bobby's story have to do with the British West Indies? What we are really saying is that if British West Indies could adapt high productivity technologies of the Old South, then the slavery -> low productivity link would break down. Historians and economists evaluate counterfactuals by looking at close analogies. Now we can bring this up to date - if Baptist was right and productivity change was all about whipping machines, those technologies could have been (those magic words!) adapted by British West Indies slave drivers. Counterfactuals within counterfactuals!

(Aside: you know, some economic historians have taken Baptist to task for exaggerating the iniquities of slave masters by tending to take the darkest testimonials. But constructing a representative slave by taking the \( \min_i(U_i)\) over all slaves \( i\ ) is not an obviously methodologically unsound procedure. The representative firm, consumer, slave, etc. is not the average!)

Robinson Crusoe

Now that we know what we mean, I will play good cop to Pseudoerasmus's bad cop (this implies we are both after the same thing and I think we are). A warning: there's gonna be an equation coming up. It is necessary to use an equation as a metaphor for the difference between how economic historians and narrative historians. I won't be doing any real economics or history because that will just cloud up the methodological point.

I will start with the narrative history. Once upon a time, there was an island inhabited by people. Later settlers will call it "Crusonia", but the natives called it "Atlantis". By far the dominate food of the Atlantians was rose hips. Sometimes they'd catch a rabbit, sometimes they'd eat worms. But it was almost all rose hips. The Atlantians died 800 years before settlers came to Crusonia, after a blight killed off all Atlantian Roses.

How would an idealized economist approach this story? The big variable is the number of rose hips \( Y \). Obviously, the count of rose hips on the island at any particular time is exactly the number of rose hips per rose \( g \) times the number of roses \( K \). This is just counting ... but hey, there's another way of counting. We can count the rose hips not just by number born but by number used. Each rose hip is either eaten or used to grow another rose. Let \( r \) be the number of rose hips per rose that grow into new roses and \( C \) be the number of rose hips eaten.

The number of rose hips doesn't care about how we count them. By metaphysical necessity,  "The paths up and down are the same.". This gives us the governing equation

$$ K = \frac{C}{g-r} $$

I've written this to be as simple as possible, but I do have a point. The above equation is just accounting, it is automatically true. It's a thin description, even thinner than any real cliometric analysis. But now we can talk about causality (functional relationships). If \( g \) and \( r \) were constants, then increasing consumption should increase the number of roses. Well, why do you think roses grow rose hips in the first place? Or maybe the causal arrow moves in the opposite direction - it makes perfect sense to think higher consumption is associated with more roses. But why should \( g \) and \( r \) be constants? Doesn't it make sense that the number of rose hips per rose that grow into roses should vary inversely with the number eaten? Then you have \( r(C) \). Or perhaps if there are too many roses, then they start competing with each other for land - then you'd get \(g(K)\).

We can now approach the narrative above. During the end times of the rose blight, \( K \) tended towards 0. This will force C to be zero (which kills everyone), but its impact on \(g\) and \(r) is ambiguous. Did the Atlantians foolishly continue eating at the same rates? Did they desperately change their habits but were doomed by the rose blight? These questions are statements about functional relationships - a thick historical description will answer them (at least qualitatively).

If we want to go on to do real economics, we have to start worrying about equilbria - the points at which the annual stock of roses balances the flow of rose hips (into bellies and the ground). This is also useful, but takes us far afield.

Le Penseur

So this is my good cop routine in a nutshell: A thick historical narrative description is very, very important - it should give us good qualitative reasons to believe in casual relationships. A thin cliometric numerical description is equally important - not only can it clarify those descriptions but it can also serve as a sanity check on thicker descriptions.

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