I Am The Very Model Of A Modern Macro Textbook

Alexander Douglas, a professor of philosophy at the University of St. Andrews, recently posed a group of interesting questions on Medium. The first question is the more interesting one. Douglas tortures a pair of equations from a fairly modern macro textbook, but finds they will not confess. That equation pair is

\[ b_t =  \frac{b_{t+N}}{(1+r)^N}+ \sum_{i=1}^{N} \frac{s_{t+i}}{(1+r)^i}\]
\[ b_t =  \sum_{i=1}^{\infty} \frac{s_{t+i}}{(1+r)^i}\]

where \( b_t \) is the value of outlaying government bonds, \( r \) is the real interest rate (assumed given & constant) and \( s_t \) is the primary surplus. These equations say*, respectively:

The current value of outlaying government bonds (of a finitely lived government) is exactly the present value of the lump of remaining government bonds at the end of its life plus the present value of government surplus over that time.

The current value of outlaying government bonds is exactly the present value of its surplus over time.

The book treats these as more or less accounting terms, though since they involve value they aren't really accounting. Douglas asks how the second equation relates to the first. I give my answer in the paragraph with the underlined sentence. What seems to have given Douglas fits is the following sentence:

"The governments solvency ... condition can therefore be seen to be ... that ... debt must be backed at all times be backed by primary surpluses with a present value equal to the debt's face value."


This sentence in it's full version refers to a "transversality condition", a name that comes from optimization models but is a meaningless meme in the textbook's approach.

Economist Nick Rowe gave a very nice response - his point of view was that too answer Douglas's question the best thing to do is to throw out the book situation and give an example tailored to Douglas's question. Brian Romanchuck have another nice response, it seems to be his idea also to throw out the book's description but with more force.

My own initial response was displeasure that Douglas (and Romanchuck) seem to criticize the very idea of infinite mathematical objects. In these modern days of lazy evaluation, even constructive finitists shouldn't do that! But Douglas and Romanchuck have had time to lay out their objections in more detail and I don't think pure math is the relevant issue.

I think the relevant issue is economics.

There is an implicit causality to the story in the textbook that doesn't come through in the equations. The causality - in both equations - is from left to right. The sequence \( s_t \) is the cause and the sequence \( b_t \) is the effect. The desired story is "Governments can only increase debt by promising surplus in the future.". The story of how \( s_t \) evolves is the model, if it fits the equations then we accept it - otherwise reject it.

There's an implicit institutional structure there, that \( r \) is determined by an independent and fierce central bank. In the US and Europe, of course, \( r_t \)  is actually determined by cybernetic feedback process by a politically constrained central bank (the constraints seem weaker in Europe for some reason).

On the bottom of page 185, the story suddenly stops being about \( r \), \( s_t \) and \( b_t \) and suddenly starts being about \( r - g \). Implicitly \( g \) is an independent variable set by technological process, as in the Solow models**. This is a strong, but common assumption. In reality, even "just" technological growth is a complex process that involves discovery, distributional concerns, government backing of science and lots and lots of complex non-linear feedback.

The textbook implicitly assumes we're looking at a 'long run' in which both these feedback processes have settled down.

In the finite story, \( N \) is outside the model - the government implodes on a predetermined date. The implicit institutional structure sets \( r > g \) so that \( b_{t+N} \)  will have a positive value - but its present value is proportional to \( r - g \). The implicit Central Bank chooses that variable. If \(N = \infty \), the implicit Central Bank is constrained to choose \( r \) such that the second equation comes out of the first. This is the answer to Douglas's question.

Romanchuck has a further objection - there's no optimization in this model (it's not just macro, it's very macro). That doesn't matter to this textbook - it doesn't care because \( s_t \) and \( b_t \) are assumed to be measurable. If you have a microfounded theory that gives the wrong values (such as infinity), who cares, that just means that either the theory is wrong - or that the implicit theories of the equations are wrong. Both are valid answers.

Is this good economics? Well, it's definitely standard economics. The ideas were invented by Irving Fisher and reinvented many times after him. This model isn't perfectly general. There's an implicit institutional structure patterned on the US and Europe. Maybe in the previous six chapters, the textbook went over all these implicit assumptions. In the immortal words of Dom Mazzetti "Doubt it".

One helpful question is "What would it mean for it to be wrong?". Well, for one, bonds can be worth more than the present value of government surplus. This is probably true but due to risk and uncertainty, which are left out of this model.

This is all that I can get out of these poor equations. But I'll end on one slightly more "philosophical" (maybe I should be careful with that word around a philosophy professor!) observation:

In macroeconomics, there is no data, only models.

*There's no uncertainty or randomness in these equations, so I'm not gonna keep saying "under rational expectations", "assuming expected value exists", "certainty equivalent", "common knowledge", blah blah blah. That's all under the rug.

** Fish don't see the water they swim in. To many economists, Solow is just accounting. C'est la vie.

Accounting For Cultural Appropriation

In today's web-media-nerd environment, a lot of people complain about "cultural appropriation" without explaining what it is or why it's bad. If you know, good job! You don't have to read this!

But, still, even if you know what "cultural appropriation" means, the concept can be hard to explain. I know what "Lebesgue measure of a set of real numbers" means, but that doesn't mean I can explain it quickly. Some people don't think "cultural appropriation" exists at all! I think they're wrong. I think there is a useful concept around this phrase.

Gilbert Ryle

What is so complicated about explaining "cultural appropriation"? It just means taking from another culture, right? No, I don't think that's right. You might say that you can define anything you want how you want it - if you say "cultural appropriation" means "sausage" then it does. I disagree, at least in this context. The smarter thing in this case to do is to see how people actually use, get offended etc, not self-importantly prescribe some arbitrary definition and chase its implications. Ryle-Wittgenstein-Anscombe ordinary language is more useful than Hilbert-Frege arbitrariness of sign.

Counterexamples to the "taking [anything?] from another culture" definition about in ordinary usage. Samurai Jack is an American cartoon about a Japanese man, is it culturally appropriative? I don't see people complaining! Wikipedia says that K-Pop incorporates "Western pop music, rock, jazz, hip-hop, R&B, reggae, electronica, techno, rave, nu metal, folk, country and classical on top of its traditional Korean music roots.". Is that culturally appropriative? Again, I don't see people complaining...

 Ernest Gellner

The simplistic, but wrong definition makes it sound like we have to define "culture" first, then "appropriation". Both of these are hard to do (if possible at all), boring and have nothing to do with the task at hand!

This definition seems to assume that a "culture" is a well-defined and monolithic object, which is just untrue. Cultures are created by politically motivated elites suffering from false consciousness (which doesn't make them bad! All of the greatest works of art of all time were made within cultures!). Gellner, to take one arbitrary name out of an entire discipline, extensively documented this process in Nations And Nationalism.

This is true even for supposedly "insular" cultures. "Bushido" - a supposed traditional warrior ethic - was created by Japanese Confucian scholars in peace time. Jamaicans have been toasting over drum heavy tracks since the 50's - but New Yorkers duel over who "created" hip hop.

Well, I think of New York as an insular culture anyway. They sure talk about themselves a lot!

Similarly "appropriation" must be well-defined and monolithic for the simplistic definition to work, which is - again - just untrue. Appropriation, in this sense, means stealing (basically). Stealing what? Ideas? This is impossible to define clearly. Fela Kuti & Toots Hibbert were inspired by soul music. Did they "steal" from American culture? Of course not, that's stupid. But then what does theft even mean in this context?

 Daniel Dennett

The name "cultural appropriation" is an uninformative meme. We don't get the best names every time. Do you know what Von Neumann-Bernays-Godel Set Theory is? "Set Theory With Large Classes" would be a better name. We don't get that name.

Cultures don't have to be monolithic for "cultural appropriation" to exist. Cultures don't have to exist for "cultural appropriation" to exist. Justice doesn't have to be monolithic for "cultural appropriation" to exist. Justice doesn't have to exist for "cultural appropriation" to exist.

Herbert Simon, apparently???

Cultural appropriation is about ... *extremely economist voice* incentives. Please, stop booing and throwing Molotov Cocktails, I'm going somewhere with this!
 

"Little" Richard Penniman

After that lengthy kung fu battle, let's go back to the original example of cultural appropriation - the bedrock case upon which all others are conceived. The complex career of the above pictured Richard Penniman was fraught with bad incentives which lead to an enormous undervaluing of his considerable musical genius. He started out in the gospel scene, where it was impossible to make money. He moved on to the gay nightclub scene (!!!) which was both dangerous and impossible to make money. Finally he moved on to the R&B scene, where it was conceivable that he could make some scratch, at least in the abstract.

These may have been "bad incentives", but they weren't "cultural appropriation". That didn't start until the center of the 50's.



In 1955, Penniman's composition "Tutti Frutti" went to number 17 on the charts - a top 20 hit! The record company pressured Pat Boone to record a cover, which he eventually did. Boone hated the song and made no effort to hide it. This version went to number 12, despite being just the worst.

There's no reason that Boone and the record company should have gotten so rich off this performance. Not only Boone's singing generally awful, he's not even pretending to try. The arrangement is bland. Boone didn't get what the song was about but wouldn't have even sung it if he did.

This is a misaligned incentive. Boone is being rewarded for his astonishing ability to not be Little Richard. To not be black, gay or flamboyant. That he sucked on ice was not a detriment, maybe even helpful.

This is what "cultural appropriation" is - making it hard for innovators to capitalize on their innovations because of, essentially, politics. Like all discrimination, cultural appropriation is a form of so-called "market failure" (because such markets fail certain models, not because people fail on those markets! It's a weird name). It presumes that certain actors have a form of power - which may not be "market power" strictly but is strategically related.

Wocka Wocka Wocka

If we pretend justice exists for a bit, cultural appropriation is unjust - it robs innovators of their due. If we pretend morals exist for a bit, cultural appropriation is bad - it reduces the incentive to innovate (which is very important). If we pretend that airplanes in the sky are like shooting stars then they'll burn up in our minds or something.

Fela Kuti

This explains why Fela Kuti isn't cultural appropriation - his sales don't detract from Motown's sales. He took ideas, but didn't realign incentives. If he had somehow realigned incentives, it might have been unfair and unjust cultural appropriation. There's nothing logically impossible about this, even though it didn't occur and there are reasons it didn't.

Thinking about Fela Kuti further shows why the simplistic definition isn't just incoherent and contrary to use, it's actively pernicious. Not only does it create an outrage culture where using innovative ideas is bad, but also completely fails to point toward the underlying economic and political problems. Anger and impotence are unwelcome bedfellows.

Rupert Sanders

Here's a 10 cent question - is the new Ghost In The Shell cultural appropriation (by this definition)? I don't think so. Something tells me that the innovators - Shirow Masamune, Oshii, etc - are gonna be just fine. This movie is not gonna reduce their sales etc. Oshii in particular is an innovative filmmaker and I hope he is able continue without incident. The new Ghost In The Shell did get caught up in Hollywood's representation problems, which is a seperate issue.

Also, the new Ghost In The Shell is really bad.