A New Pareto Liberal Paradox (reposted from 2004)

One of the core principles of Liberalism is that there must be equality before the law. The law must not discriminate. In practice, this principle is often restricted to citizens and people are citizens only if they are born in the liberal polity or have the right ancestors. I personally consider this restriction absolutely inconsistent with my core beliefs.

In any case, equality before the law is a core principle. Liberals might consider equality of income very important or not at all important, but we must defend legal equality or else we are not liberals.

I naively imagine that I am pretty utilitarian. Consequentialist enough to accept Pareto improvements anyway. I reconcile my absolute respect for legal equality with my absolute respect for utils ideologically, that is by convincing myself that reality is such that I can hold both moral beliefs. In plain English, I am deeply convinced that legal equality is not just good in itself but also is the most efficient legal rule. I think that hereditary priviledge is not only wrong but also leads to incompetence in key positions.

However, I can imagine an alternative world in which a law which discriminates can cause a Pareto improvement. I am absolutely unwilling to name such a law clearly, because I consider it obscene. I will discuss the issue only in complete abstraction. The reader will have guessed that I am more liberal than utilitarian and would reject the Pareto improvement in the unhappy alternative universe.

The model is a case of the Matsuyama model (QJE 1991 vol 104 pp 617-650) built on the Murphy Shleifer and Vishny big push model and analysed by Herrendorf Valentinyi and Waldmann (ReStud 2000 Vol. 67 no. 2 pp. 295-307). This is a model in which different people leave villages where they farmed and move to cities where they work in industry. It is assumed that different people either face a different moving cost or have different productivity in manufacturing. This means that for intermediate values of the present value of wages in the city, some people move to the city and some stay on the farm.

The interesting dynamic arises because there are Marshallian spillovers or something (in MSV imperfectly competative firms with increasing returns to scale). Thus it is not wise to move to the city if no one else does. In an early draft of HVR 2000 Akos suggested considering congestion as well. In an unpublished draf, for very high urban populations, wages in the city decline as more and more people move to the city creating congestion. The math doesn’t change if this is a non pecuniary disutility of living in a crowded city. In the model all aspects of living in the city today are summarised by the “wage” which is the income which would give the same utility if earned in the villages minus the income which would be earned in the village. Clearly the "wage" is not just a wage. It is, at least, a wage differential.

will further assume that the income of villagers goes up as more people move to the city. This makes sense as simply supply and demand. The key variable which depends on urbanisation (n) is the difference between the income in the city and the income on the farm which first increases in urbanisation then decreases in urbanisation (n). This should be called a wage differential, but I will call it the “wage” to create confusion.

Given the risk of congestion, it might be Pareto improving to restrict migration to the City. The model becomes evil, because it is also assumed that the state is inept and can only do this by choosing an arbitrary inate characteristic of people and restricting migration based on that characteristic. That is, the State can’t say you are allowed in the city if you moved here already because it can’t keep track of it citizens. Also it can’t tax and transfer because its employees are crooks or something.

People die at a constant rate and new people are born in villages so the population is constant. Babies are all somehow born in the countryside, because … well I forget why but it is a model meant to clarify thought.

It changes in a very simple way. For any n, there is a present value of “wages” such that n remains constant. The graph of this is called the ndot =0 curve where ndot is the derivative of n with respect to time. For higher V (above the ndot =0 curve) n increases and for lower V n decreases. At n = 1, the ndot =0 curve goes to infinity. In the example in figure 1 it is horizontal for n close to 1 then becomes vertical.

Recall that the wage is really a differential between the value of income plus non pecuniary amenities in the city minus that in the countryside (randomly called “villages” farm and all sorts of things because this is a blog and I am the editor).

Another key variable is the present value of “wages” V. V changes according to Bellman’s equation, because it is a present value. This means that for any n there is a V such that V does not change which defines the Vdot=0 curve. Such a V is the “wage” dividied by the sum of the real interest rate and the death rate. Importantly present value has the property that if V is above the Vdot = 0 curve V is increasing. That is present values tend to be unstable. This makes perfect sense when you realise that in the present value equation with perfect foresite the future causes the present. (that was a joke).

It is possible for the model to have a steady state which is a “saddle” that is such that n near steady state n can, in perfect foresight equilibrium converge to steady state n (I have corrected figure 1 so that it shows a saddle steady state). This requires exactly the right initial V on the saddle path. Let’s make everything linear near such an equilibrium. Then the saddle path is a line as shown on figure 1. There is also an explosive path which leads away from the steady state. The saddle path is also called the stable manifold and the explosive path is also called the unstable manifold.

Assume that initial n is very slightly above the steady state n of the saddle steady state. A question of interest (to ecotheroy geeks) is whether n must decline to the saddle steady state n or whether it can increase and get to some other steady state. This would be another perfect foresight equilibrium. In the example this second equilibrium would definitely be Pareto better than moving down the saddle path to the saddle steady state.

ne possibility is to move out the unstable line and see what happens. Given initial n near the saddle steady state, this is pretty much the only alternative. Initial n and V minus saddle steady state n and V must be a linear combination of (delta n, delta V) on the saddle path and (delta n, deltaV) on the explosive path (because all vectors are). The equations are all linear for a large region around the saddle steady state in the example so you can think of these to vectors seperately. The one on the saddle path gets smaller and smaller and (n,V) gets closer and closer to the explosive path. Figure 1 illustrates this among other things.

update: In fact it is possible to characterise the lowest explosive path with increasing V in (n,V), that is, the one with lowest V for given n. This lowest path is the one followed if the economy starts on the n dot = 0 line and hence above the Vdot = 0 line. If one starts with higher V, then V is higher for any n, since perfect foresight paths can't cross. If one starts with lower V but still above the saddle path, (n,V) moves up and to the left till it touches the n dot=0 line then up and to the right and passes over n_o above the n dot = 0 line, above the lowest explosive path with increasing V and stays above it. If V is below the saddle path , n goes to 0 and V violates the transversality condition. Figure 2 to illustrate this.

Figure 2 is a closeup of figure 1 near the saddle steady state. The red curve is the explosive path with increasing V which has the lowest V for any n. I have added another path, drawn in purple to show why this is the lowest such path.

Possible paths leading to steady state with higher n must be very close the explosive path. Weird assumptions about the “wage" can be made so that these paths cross the V dot = 0 curve but stay above the ndot=0 curve and are not on the Vdot = 0 curve at n = 1 (see figure 1). If n is not changing because everyone is in the city, V must be on the Vdot = 0 curve. Otherwise the transversality condition is violated.

No equilibrium with high n is possible because people don’t stop going to the city when the possible equilibrium path hits the V dot = 0 curve. Let’s say this happens at n =0.9. This good steady state can be reached, at the end of a perfect foresight equilibrium path, if one tenth of people chosen at random are forced to stay in the country side. The equilibrium is better than the saddle steady state for them too, because the relative price of food is high. The unspeakable policy causes a Pareto improvement.

OK all this depends on the figure which I will feebly try to explain. The red curve is the lowest curve whith increasing V for initial n n_0. The very key Vdot = 0 curve is hard to see. It slopes up from 0 to s as more people in the city help each produce (s for Solow or standard or something because after that, for a while nothing weird happens). At g the “wage” jumps up. This is like the late 90s in the US somehow with a growth spurt. G is for Greenspan or Glassman or Gilder or anyway someone who thought the tech bubble would last. At meverything begins to go wrong and society starts to collapse in the city. This is named Mathus or Marx or anyway someone gloomy. So the Vdot =0 curve slopes up, goes flat, slopes up steeply then slopes down very steeply. If congestion problem went critical very suddently, the V dot curve could jump down and wouldn’t be continuous. In this case the saddle path to the saddle steady state (low n steady state) could be the only equilibrium.

The blue curve is the n dot = 0 curve with the discriminatory policy. The policy is descigned so that it stops urbanisation just before (or just after) congestion kicks in. It makes the red curve an equilibrium path. The new blue ndod=0 curve and the old black ndot = 0 curve should be superimposed when they are horizontal. The policy shifts the ndot =0 curve n/10 to the left because 10% of migration is banned.

Thoughts on Capehart on Kagan

I ì'm reading the Washington Post and note one very outstanding op-ed by Catharine Rampell which you should just read. She links to excellent summaries of social science research and notes that Republicans don't listen to experts and aren't reality based.

But I want to write about a dumb op-ed by Jonathan Capehart. I'm picking on him partly to explain what is so extraordinary about Rampell. The op-ed is a summary and review of a speech by noted neoconserviative Robert Kagan. Writing it did not involve googling. Capehart is, more or less, reporting a speech. He didn't check claims of fact with various competing published sources. Now I don't work enough to complain about his work effort. I really just want to stress that it is amazing how much Rampell taught me.

I also want to discuss Kagan. Kagan notes that the post WWII liberal world order is an aberration. Such a period of near peace with so many once rival countries working together is extraordinary. His valid and important point is that we should not assume it is the natural order of things and assume it will last. He argues that US engagement is necessary to preserve the (relatively) peaceful order and that America first isolationism is unacceptable.

Oddly, the op-ed doesn't identify him as a neoconservative. This is, I think, highly relevant context. As briefly summarised Kagan doesn't explain how he thinks the US should engage. In practice he has advocated invading countries. Does his respect for the world order require the USA to submit to the rules imposed on other countries ? What does he think of foreign aid ? How about global warming ?

I think Capehart is trying to unite anti-ùTrumpers, bury hachets and refrain from grinding old axes. He presents Kagan as an idealistic internationalist and doesn't get around to discussing whether he is a hawk or a dove. On reflection, I think this is good strategy and will post this post only because almost no one will read it.

Kagan's version of recent history and the rise of neo-isolationism includes

But after the end of the Cold War, Kagan says, “A lot of Americans increasingly [began] asking, ‘Why are we doing this?’” The question got louder as the United States began ongoing wars in Iraq and Afghanistan in the early part of the last decade and as the economy collapsed in 2008.

I object to lumping together Iraq and Afghanistan. I think that, while the longest US war in Afghanistan with no hint of victory in sight is very frustrating, that it would not have caused a neo-isolationaist public reaction. The decision to invade is as close to unanimous as is possible with 340 million people. It is still rarely questioned. In contrast, at least with the benefit of hindsight, invading Iraq seems insane.

Furthermore, the invasion of Iraq was a break with the previous 58 years of US foreign policy, and was presented as such by advocates. Advocates of invasion treated stability as a dirty word. I think that 2003 was the breaking point, and neoconservatives did every thing they could to break the old order. It would be uncharitable to suggest that Kagan bears as much of the blame for the current situation as his limited power allows and to suggest that he might consider shutting up forever. I am feeling uncharitable.

But what is even odder is that he basically leaves two rather important countries out of his discussion of the late lammented liberal world order -- the USSR and the People's Republic of China. He decides that japan and Germany finally became peaceful because of the extraordinary virtue of the USA. The possibility that the peaceful coexistence and then close alliance of ancient adversaries had more to do with a common enemy than a common ally is barely mentioned. The cited phrase "cold war" is literally the only hint.

I too am a nationalist, but the excessive credit Kagan gives the USA is absurd. This is actually relevant. He must argue that the USA played an essential role *and* that we can do so again even though Putin and Xi are only moderately terrifying. If the relative near peace since 1945 was based on a balance of power between super-powers, deterrence and mutual assured destruction, it will be harder to recreate it with good intentions.

Anyway I just wanted to get that off my chest here where almost no one will read it.

Matt Bruenig Tries to Figure out Harry Potter from op-eds

So it turns out that Noted commentator Matt Bruenig has an almost unique perspective because he can read but hasn't read any Harry Potter books. So Elisabeth Bruenig interviewed him trying to find out what he could figure out about Harry Potter based on Harry Potter references in political commentary.

It is actually very interesting. https://soundcloud.com/ebruenig/matt-tries-to-understand-harry-potter

Matt Bruenig is a total hero, because he is willing to display total ignorance on a topic where many (most) people are well informed. He is especially a hero, because the actual content of the interview will not be helpful to his causes.

Bruenig is notably a leftist (no he's not old, his twitter avatar is a photo of John Rawls). His view of Harry Potter is largely based on a Ross Douthat collumn and he, oddly, assumes that Douthat is more or less fair to JK Rowling (who is also a leftist even if Bruenig seems unconvinced).

There are two interesting misconceptions. Bruenig guesses that Voldemort is the dean of Hogwarts & can't figure out what Dumbledore is doing in the book. And Bruenig assumes that wizards don't just segregate themselves from muggles but also act as a ruling class (not just death eaters and in book 7 but all of them starting in book 1).

I think it is mildly interesting that Bruenig assumes the bad guy is in power at the beginning of the series. Listening to the podcast, I am struck by the importance of the very first chapters of the first book in which the Dursley's abuse Harry Potter. After that, it is not easy to think of muggles as an oppressed under-class.

Bruenig denounces the good guy wizards and Rowling for segregating. He sure doesn't believe in separate but equal. But the point is that no one (successfully) communicated to him that the Harry Potter books are set in the contemporary UK with parliament and prime ministers and such. He doesn't consider the possibility of separate but equal as fantasy. It might be that Douthat was being mischievous and trying to portray the leftist Rowling as an elitist & Bruenig just assumed that things were as insinuated by Douthat. It is certainly true that the premise of the books is not plausible (for example, magic would be even more widely abused -- oh and magic doesn't really exist -- that's implausible too).

I am now reading the Douthat column. I must admit that "For the six readers who have never read the Potter books but who have stuck with the column thus far nonetheless:" is a good line. By that point, however, Douthat had left no doubt that he considers Rowling a political enemy -- she will not be forgiven by a never Trump Republican for unfavorably comparing Trump to Voldemort. Rowling is quite left wing, but it would be nice if one conservative left politics out of it once, just to see what it's like. Oh and it would also be nice if one ever accepted that non-conservatives don't reject all thoughts of conservatives out of tribal hostility (and projection ?).

Douthat honorably notes that he got his idea from someone who uses the pseudonym Spotted Toad. Mr Toad doesn't make much sense. He says the appeal of Rowland is to people who are loyal to a school like Hogwarts. Uh Spotted (can I call you spotted) if Rowland appealed only to people loyal to elite educational institutions, she wouldn't be so rich. There aren't enough such people to buy a book onto the best sellers list (notably there are lots of people, including Douthat, who are ostentatiously disloyal to the elite educational institution without which they would not be prominent). On the other hand, Bruenig's belief that muggles are an underclass is based on ignoring Douthat's clear explanation "Muggles are non-magical folks, the billions of regular everyday human beings who live and work in blissful ignorance that the wizarding world exists. " which is actually also a good line -- a very brief very clear summary of a point that Bruenig missed. Douthat does insist that, in real life, Hogwarts graduates rule the world & that this is a problem. This is forcing the discussion to the home territory of an pseudo anti-elitist member of the elite of the elite. This may have confused Bruenig, but it wasn't a trick. In contrast, Douthat did assert that Hogwarts is coterminous with the wizarding world & the challenges to Hogwarts come from inside the school which explains why Bruenig thought Voldemort was at Hogwarts and had no idea that there is a Ministry of Magic in the books.

I think we do actually learn something about Bruenig from the fact that he seems to assume that power will be abused, so even the nicer wizards rule over muggles. It is certainly true that the Rowling idea of wizards hiding, even though they have the power is not plausible.

But the very alarming thing is that Bruenig proposes violent overthrow of wizards followed by something along the line of genocide -- he conceeds that Harry Potter seems to be a nice guy so it would be OK to just sterilize him. But he has the idea that there can't be peace and equality with some people so much more capable than the rest of us.

I have to admit that he might be right -- disbelief in the possibility that wizards generally hide their skills can be suspended, but disbelief sure makes a good bit of sense. But the idea that rough equality of ability must be achieved by sterilization and a sort of egalitarian eugenics does sound a good bit like a right wing parody of the left.

I suppose, the open mindedness based on not reading the books and suspending disbelief has its advantages. I do wonder what humanicy could do with the extreme inequality of ability of wizards and muggles (this is also a big theme in the generally underappreciated Marion Zimmer Bradley Darkover novels).