Friday, December 23, 2016

Why Was Keynes Different?

John Maynard Keynes

This is a post for all and none. Initiates to economics will see the fast one I'm trying to pull a mile a way, novices will have no idea what I'm blathering about. It's my attempt at writing a Nick Rowe post. I want to apologize in advance if I get the numbers wrong. The medium I'm using to write this is not conducive to editing and I am a poor enough craftsman to blame my tools. What I want to do is to make Keynes and monetarism strange to you again. Strange in the way it felt to Lionel Robbins and Jacob Viner in the 40's, when they were new. It won't be easy, since their language has pervaded thought so perfectly that it is hard to even talk without it...

Jacob Viner

A warning: Keynes was not different because he advocated spending out of depressions and saving out of inflations. Every sober person recommended this. Jacob Viner & Keynes on policy were indistinguishable - but there is no Vinerian economics. It is not because Keynes invented some black magic called "aggregation" - Giffen (yes, that Giffen) and his student Flux (who was the first to recognize Euler as the author of his famous theorem on homogeneous functions) had a spat on measuring national income a decade before the General Theory. Keynes was not different because he was a "statist" or because he was secretly had a labor theory of value or etc, etc, etc. The world was full of those types, but they didn't become Keynes. So what was it? Where to start...

Adam Smith

Adam Smith was a wise man as well as a great economist, a man who knew where to start things. Smith gave us the following "State Of Nature" argument, or just-so story:

"If among a nation of hunters, for example, it usually costs twice the labour to kill an eager which it does to kill a deer, one beaver should naturally exchange for or be worth two deer."

Isn't that lovely?

David Hume

The state of nature argument was well established in 18th century thought, not least by Smith's mentor Hume. The point of a state of nature argument is not historical account (it his said that in the throes of the unguarded ecstasy of madness Rousseau actually believed in the historicity of such thoughts - I doubt this is so), but rather to show, in Voltaire's famous phrase, if something did not exist it would be necessary to invent it. Hume's famous rowers showed that social equilibrium would be invented even without language, demonstrating that conventions come first (logically speaking) and linguistic agreement after. Smith's hunters show that a market and a (relative) price system "come first" and formal markets after. It also demonstrates why ratios of prices are fundamental, rather than differences (try the argument with differences and see what happens). When labor is the only input the hunter can use (which is, for the economist, "production"), one has an easy and agreeable labour theory of value - though, of course, once there are multiple inputs this story loses its agreeability. But this is unnecessary, Keynes is a marginalist like any other. Subjective value is part of his analysis, just like it was your high school Econ teacher.

Keynes - who was also a great and wise man whatever anyone tells you - did not start with a just-so story about the existence of trade and the balance of demands, though he probably should have. Unlike the other world changing theses of its era (such as Frank Knight's Risk, Uncertainty And Profit), his General Theory assumes that you walk in capable of doing marginal economics on the level of a Pigou off the bat rather than spending a chapter on his personal conception of the supply and demand lines. As a matter of historical fact, Keynes never wrote a introductory book on basic conceptions (he and Pigou would just say "It's all in Marshall."!). Most of his serious writing is on money on the international stage, but the General Theory is about an "Isolated State", as it were. This might explain why students and the unserious had such difficulty but it wasn't just them...

Irving Fisher 

We have to keep going past Adam Smith now. Here comes Irving Fisher, perhaps the greatest economist of all time ... though not gifted with deep personal wisdom. His American accent will be more familiar than Smith's 18th century Scottish brogue. He asks us to consider not hunting today, but hunting tomorrow as well. Let's say that a deer in the hand is worth two in the bush. How many deer today is a beaver tomorrow worth? The answer must be four - a beaver is worth two deer and a tomorrow is worth half a today.

But what if the difficulty of hunting changes with the seasons? Let's say that hunting is easier next season, so that the same amount of labor that gets one beaver today will also get two deer tomorow, three beaver tomorrow or four deer tomorrow. Then a promise of a deer tomorrow is worth half a deer today, the promise of a beaver tomorrow is worth a third of a deer today and the promise of a beaver tomorrow is worth 3/2 of a deer today. In terms of marginal analysis, this is the product rule for derivatives applied to a simple spot & future market. If the market left this so-called "intertemporal equilibrium", then anyone could gain just by cyclically trading beaver & deer.  This arbitrage argument is in Keynes's General Theory (Chapter 17, part II).

Frederich Hayek

So far, so good. Right now we're telling the story that Brad DeLong calls The Story Of The 20th Century - that of production increases & galloping scientific innovation. Economics is a serious subject about the things of our lives - the clean water, the iPhones and the clothes all together. Knight, Hayek and Schumpeter see that the entrepreneur is the central actor, able to take on uninsurable risks because they have local knowledge that others can't get - and the romantic temperament that drives the will to power. And this is - as far as it goes - undeniably true.

But it doesn't go all the way. The ancients called wise he who can control his enemies - and Keynes was a wise guy as well as a great man. The name The General Theory Of Employment, Interest And Money was a trick but not an underhanded one. It is that, but this isn't mainly that. The book is really an exposition of a Money Theory Of Production. Keynes announced such a book before writing it and admits it in the aforementioned Chapter 17.

Knight and Viner - the Old Men of Chicago - obsessed over the poorly named concept of the "long run". What this really means is that the path of production is picked out more or less like the beavers and the deer above, except lucky years are replaced by lucky (or, rarely, talented) entrepreneurs. In modern terms, this is called "golden path growth" and the obsession is justified by "turnpike theorems".  But Keynes, the greatest of the international monetary theorists and practitioners, saw that in many countries unbalanced flow & pricing of gold destroyed industries even though they were stocked to the gills with gutsy entrepreneurs and genius scientists.



Why, back with our hunters, do you think that just because they can get the deer and beaver at the rates quoted they necessarily will? Must every hunter go out for the hunt? This is a very crude way of thinking about "output in general". Surely a hunter could become irrationally exuberant (filled with romance, let's say) about his ability to kill beaver and hunt it in defiance of logic - and surely this would alter the price ratio whether he gets lucky or not. Surely each level of output, in terms of labor spent, is associated with a particular price system - in economic terms, each quantity of labour to spend gives a different production possibility frontier which, as it's dragged out doesn't necessarily touch the indifference curve at a locus of points drawing a straight line.

That's 2deep4me. Let's hear one last folk tale instead. Next year doesn't make it easier to hunt in general. Instead, next year the amount of labor to catch a beaver will be four times what it takes to hunt a deer tomorrow - and that amount will stay static. Now nobody would buy a promise for a deer tomorrow at a market clearing price. The asset whose rate of production has climbed most rapidly with output in general has knocked out the other assets - exactly as Keynes taught in Chapter 17!

You might be thinking "Where's the unemployment, the interest rates & the money?". They're all there.  The fast one I pulled is to talk about the path of production instead of the "interest rate". Interest rates are an abstraction, what exists are things and prices. Only after acclimatization in the polite fiction of interest rates does the intertemporal & Keynesian world make obvious sense. If I had said "The money-rate of interest rules the roost." one would be off talking about unrelated things. But when I say the identical, but differently worded "The production path of money knocks out less profitable production paths." it suddenly feels alien, requiring proof and argument. Which is what Keynes did.

Joseph Schumpeter 

Keynes ruined economists lives in order to save civilians. Before Keynes, all economists agreed that just because the story of the 20th century was about innovation and not money it should be the story that economists tell. Schumpeter the romantic was so furious that he said that if Keynes would not tell this story he wasn't an economist at all! It seemed so obvious that economists must focus on The Story, right? Keynes made economists not the epic poets of innovation but mere dentists checking Ulysses teeth before he goes to war.

Monday, December 19, 2016

What Do Their Deaths Mean?

Thomas Schelling

The late Thomas Schelling is often described as a "game theorist", but what that means is rarely clearly discussed. Game Theory is usually conceived as a branch of mathematics, an abstruse brand of pseudo-psychology inspired contests between hyper-rational contestants. And it is true, game theory is an abstruse brand of mathematics. It can and has been used by philosophers such as Jaako Hinitikka to ground our idea of quantifiers. It can and has been used by mathematicians such as Abraham Wald to ground our idea of statistics.

I don't think Thomas Schelling ever used mathematics beyond a high school level. In that sense, he was not a game theorist in the sense of Von Neumann and Bob Aumann. Schelling's contributions were not mathematical, they were philosophical. Thomas Schelling is one of the most consequential social philosophers of the 20th century. What was important to Schelling was not Game Theory's difficult technical content, but rather the important constraint that everyone's decision depends on everyone else - at least on that. This concept of equilibrium - the balance of the personal actions of each actor - lead Schelling to the concept of commitment. Equilibria allowed Schelling to escape escalation.

"As little as possible..."
- Chinatown

War, and especially nuclear war, was Schelling's great fear. Why did the great powers go to war in World War 1? There are many, many historical roots, but certainly the basic answer is for various reasons the high command of each European country badly missestimated the willingness of every other European country to go to war. Norman Angell was wrong - France & Germany would go to war over Alasce-Lorraine even if it meant breaking linkages and reducing output. Why couldn't the Great Powers after a year of war (which certainly revealed the true willingness to fight) get together to multi-laterally deescalate? The War cut off their ability to communicate, there was no focal point at which they could come together. Even though everyone knew that their opponent was more ferocious than they had allowed, they couldn't act on it.

Or take the famous Camp David Accords. Israel and Egypt both wanted to avoid further war. But Egypt didn't know for sure that Israel wouldn't become belligerent. And so Israel couldn't know if Egypt knew that Israel didn't want further war. And so on and so on. If you're Jimmy Carter, how do you make the true intentions of Egypt & Israel "common knowledge" (an expression coined by Schelling - who also coined "focal point", "collateral damage", ...).

The concept of international politics that is developed by Schelling in his book Arms And Influence is that of a broken, abusive family. Schelling's goal was to stop them from murdering each other, despite the gaslighting, the stealing and the drunken brawls. Who can forget his infamous analysis of rational irrationality? If you can convince them you're crazy enough to burn the whole thing down, they have to give into your demands. So when North Korea acts up again, the last thing you want to do is over commit and escalate...

Thomas Schelling's work went beyond war, of course. There are two pieces I'd like to pick out as particularly interesting.

The first is the famous Schelling Discrimination model. This model is exposited in his book Micromotives And Macrobehavior. One sunny day, Schelling was listening to an interview of Fidel Castro. Castro called America a "racist nation". Schelling, of course, didn't think the descriptor fair but then how can you explain all the obvious discrimination? Schelling decided to define down discrimination and examine the consequences when everyone had weak preferences but they all had to be satisfied together. Using pennies & nickels on a chessboard, he found that he could construct scenarios where initially mixed neighborhoods spontaneously segregated even though nobody particularly wanted to be in the majority (as long as they had a couple friends).

Now, as a model of racial discrimination in neighborhoods this model is a nullity. Racial discrimination in neighborhoods was not spontaneous. As to spatial economics it isn't up to snuff, since there aren't any prices. One can't do comparative statics of an anti-discrimination law with a Schelling model. As a mathematical model it already existed under the name "Ising model" and had been solved in the 40's. The contribution of the model was philosophical. The contribution of the model was to introduce complex system behavior. These complex systems can't necessarily be captured by aggregate models. In the Schelling model there lurks a representative agent. The agent isn't "racist" - he doesn't necessarily dislike being in the minority. But he lives in a segregated society and does nothing about it.

The second contribution of Schelling's I want to pick out is his discussion of addiction. His thoughts on addiction are developed in his book Choice And Consequence. The first economist to seriously discuss addiction was Gary Becker, who posited that addiction was a "rational" behavior - that is, increases in the price of cigarettes (and reduction of prices of cigarette substitutes, etc. etc.) will tend to reduce the use of cigarette demand. Schelling offered a much more radical interpretation that addiction is the result of internal bargaining. In order to become an ex-addict, the addict must engage in the kind of commitment strategies analyzed by Schelling in the field of international relations. Anyone who has known addicts has even seen them act out Schelling's famous rational irrationality in order to convince themselves and others that they will remain addicts.

This is also a philosophical contribution. Students will recall from their micro classes that a group may be licitly aggregated in a supply & demand model if the aggregate obeys "WARP", otherwise they must be distinguished. Schelling recognized that there was no secret sauce on a man's skin that made this axiom true within him.

One could go on and describe Schelling's influence - such as inspiring the David Lewis/Brian Skyrms approach to reviving the Humean project of reducing meaning to preference theory or inspiring a million internet types to call every possible behavior as "signaling". But that would be an injustice to his own creativity. Instead, the best thing to do is to remind ourselves of the moral weight. In Schelling's analysis, when other channels breakdown governments murder in order to communicate. Even if we are saddened, we must go on. What does all that death mean?

Saturday, December 10, 2016

All My Possessions For A Moment Of Time

Another commentary on a Twitter spat, you say? Well, my throat glands are returning to normal, so I can go back to normal soon. Until then...

Clio, Muse Of History

The brilliant blogger & economist Brad DeLong opens his economics class by giving a defense of economics as history, perhaps the unique history of the 20th century. The history of the 20th century in this viewing is a Whig's history, perhaps an authentic one.

DeLong's world is one of amazing, galloping productivity increase - a world were man's ability to create and control comes to dominate all things, where even the will of heaven is a plaything of this global engine. A world of "growth", economically defined.

The great economist of inequality Branko Milanović politely fired back with a defense of Eric Hobshawm's "short twentieth century". Neville Morely, another economic historian, also came to Hobshawm's aid.

Uh, great photo of Hobshawm, Wikipedia

I'm not much of a Hobshawm scholar, in the sense that I've never read his books. In the same way, I'm the third best French speaker among my siblings. But it seems a reasonable gloss that in essence, Hobshawm saw the 19th century as the rise of Capitalism (as Marx saw it) and the 20th century as the rise of Communism (as actually existed in Russia and elsewhere). When you write this story, the 19th century is very long. Surely it was already starting in 1776, as Adam Smith's analysis of Capitalism needed a Capitalism to analyze. Also, there was some kind of political revolution in that year of slight importance. Surely this phase of history was still present in the actual Leopoldville of the 1950's. Not only was the 19th century very long - it was unevenly distributed.

The distribution of actually existing Communism in that "short 20th century" was also mercifully uneven.

General Mobutu

The facts are not open to doubt. The 20th century opened with a demon haunted world embroiled in imperial depredations and closed with ... if not "freedom" per se, at least significant bourgeois freedom ("Freedom's just another word for 'Nothin' Left To Lose' ... and nothin' ain't worth nothin', but it's free..."). When a Belgian hit squad (with US money) killed Lumbumba and burned away his bones with acid, they still could not install a Belgian government. Instead, the Congo got the fearsome General Mobutu. Mobutu was many things: a violent hypocrite who took Western money and condemned foreigners with equal ease, an embezzler and inflationist - but one thing he was not was Belgian. No amount of cruelty would return the old empires. There was no want of trying. De Gaulle can cry out for "Algerian France" all he wants, it made no difference. Times were somehow ... somehow different. This is a story worth telling, an understanding worth coming to.

Engles, Marx and three of the Jenny Marxes

A specter floats behind this debate. The specter of Karl Marx. Not communism, Communism, Actually Existing Communism, c0mnU1sm or anything like that. But Karl Marx, the German born philosopher, socialist, economist, journalist, etc. with his carbuncles and his Party and his beloved wife and daughters. How does Hobshawm's view fit with Marx's exactly? It seems that there is an underlying idea in Hobshawm that Stalin or Mao or ... was the realization (or a direct precursor to the realization) of Marx's epic tale of historical progress from primitive communism to ... well, Communism. But Russia, China, the Congo, Vietnam, North Korea, etc. etc. etc. were not late capitalist societies that underwent a fall in the rate of profit making collapse of the Capitalist systems and the rise of Communist ones inevitable. They were agrarian empires. Frankly, they were all sorely lacking in capital. The organic composition of capital in those countries was ... to be honest, still pretty damn organic. The outlines of Hobshawm's story as I understand them are not compatible with the outlines of the Marxist story as I understand them.

The Marxist story as I understand it is a (precursor to? perhaps a bitter uncle ...) DeLong's story! DeLong's is a story of changes in the organic composition of capital - no, we can be more clear. In the language of this post, DeLong's is a story of the distribution matrix changing through time in ways that cause \( \lambda \) to fall to near 0, which is just a way of saying that the maximum rate of profit is rising by leaps and bounds.

John Maynard Keynes

It's interesting, since I feel that if DeLong were to nominate a man for economist of the 20th Century, he would nominate John Maynard Keynes, the great slayer of Say's Law. The 20th Century is surely the century of the Great Depression and WWII. Were these times of galloping productivity? Everyone believes in Say's Law when the discussion is not about Say's Law - even you and me (and, yes, even Keynes made mistakes like this). DeLong implies but does not state that the long run history is a full employment history. He implicitly assumes that a balanced growth path is an acceptable behind the scenes driver of history.

I'm not so sure the 20th century will be remembered in this way.

E P Thompson

But let's go back to Hobshawm. I can't make sense of what I've read of him in terms of what I've read of Marx. What I've read of Hobshawm reminds me much, much more of E.P. Thompson. Thompson wrote of artisans and William Blake resisting capital deepening through moral action. Thompson had a beautiful, Blakean vision of a socialist state: "I am going to create a world of beauty. My eyes will see as through a new mind."*

Okay, Thompson's vision was incredibly vague and its relationship with Marx more elective affinity than anything comprehensible. Leszek Kołakowski rightly ridiculed Thompson on these grounds. It's difficult for me to understand these Thompson and Hobshawm characters, being a vastly different age and temperament. But I think that I can.

Let me tell you a story. It's a story about a pencil. I am holding it in my hand right now. To make this pencil, trees had to be cut down, pulped and reglued to be soft enough to easily sharpen. Somebody when cutting down these trees cut themselves and bled on the wood. Their blood is in my hands. Aluminum ore had to be dug out of the ground, processed at great difficulty, pressed and painted. These miners are worked to the bone in non-union mines. Their sweat is in my hands. Paint had to be synthesized. Precursors to the chemicals making this unnaturally red paint had to be synthesized. Everything that happens in every one of those chemical factories is part of this pencil. Open pit graphite mines are giving miners lung cancer. Those deaths are on my hands, are they not? Forget the labor theory of value, it's a will-o'-the-wisp. Isn't the fact that those deaths and all that pain happened because I wanted a damn pencil just the plain meaning of imputation?

Economists have a word for the fact that everything in this world is connected - well, actually they have dozens of words for hundreds of the closely related concepts that capture this idea with precision. Their special word is "equilibrium". Equilibrium means me, you, Sumatran loggers and Chinese graphite miners are all trapped in a single point in price space (which may be infinitely dimensional, or even have continuously many dimensions!) trapped unable to move. The tar that sticks us to this point has many names, the names of the great theorists: Nash, Pareto, Walras, Bayes ...

I don't fault Hobshawm or Thompson for cowering before this beautiful and horrifying vision.. It is a terrifying vision - whether set out by Marx or Walras. It is the real world in which we live, with all that implies. It is important to understand that. But I can and will fault them for not seeing that other visions can be equally or more terrifying. That they could let themselves only see the good of Stalin, Mao and Ho Chi Minh while fearing and hating bank managers and their ilk is something I can and will fault them for.

Hobshawm had to admit that Stalin did not create a world of beauty. Communist Poland was not a world of beauty. The idea of a short 20th century is a tacit, backhanded way of making this admission.

I prefer to be more direct.

The Long 20th Century?

So, the question becomes: Is the 20th Century the century of Marx's ideas (as DeLong thinks - after a fashion) or of Marxist parties (as Hobshawm seems to think)? Or perhaps it was the story of John Maynard Keynes and Milton Friedman, a story of uneven progress with the promise of balance. Perhaps it is the story of Lumumba & Mobutu, or the Park family versus the Korean people or Nixon or... Maybe it is billions of stories babbling from their intertemporal equilibrium trap.

In the end, I am on the side of Hume, such metaphysical talk should be burned for warmth...

*I cheated here. This is actually a quote from the 2002 cartoon Ghost In The Shell: Stand Alone Complex. It just captures beautifully what they wanted to say.

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.