Saturday, December 25, 2004
I did not use pairs of countries but rather OLS on a cross section. Also I do not work at Columbia University. Still I am very flattered to be criticized in "The Public Interest."
Universita' di Roma "Tor Vergata" Facolta' di Economia Via Columbia 2 00177 RM Italy.
Wednesday, December 22, 2004
I didn't know whether to laugh or cry when I read " We wanted to release a Windows version as part of Windows 98, but sadly, Microsoft has effective building security." The guy wouldn't use a mild word like "sadly" if he had to use a Windows machine.
A New Pareto Liberal Paradox
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.
Update: Figure corrected.
Sunday, December 19, 2004
Sen’s Paradox replicated
Recall Sen’s èaradox. There are two agents Lewd and prude. Lewd likes to read pornography, Prude does not, but what really disturbs Prude is the thought that Prude is reading pornography and enjoying it. Similarly, while Lewd enjoys porn what would really get him off is the thought of Prude reading porn and being shocked. A liberal would consider each to have the right to do what he wishes so Lewd would read porn and Prude would not. Pareto would say this is an unacceptable outcome and propose a Pareto improvement in which Lewd is not allowed to read porn and Prude is forced to read porn. Both Lewd and Prude are happier so this is a Pareto improvement. Thus one can not be a Paretian liberal.
The point is that liberals like to think that they can be consequentialists too. That is that liberal rules lead to desirable outcomes and certainly, at least, to Pareto efficient outcomes (in which to make an agent happier some other agent must be made less happy so no Pareto improvement is possible). Now even if one agrees that liberal policies lead to good outcomes in the real world, Sen showed that the philosophical problem remains. Considering his hypothetical world, we see that we might have to decide if we consider liberty good as a means to the end of making people happy or good in itself.
Brad Delong (I think I can’t find it on his blog so no link) finds it hard to accept Sen’s world in which the only possibilities are compulsion or each acting alone without interacting with the other. He asked why don’t Lewd and Prude sign a contract in which Lewd promises not to read porn and Prude promises to read porn. Then the Optimal outcome is achieved via the liberal principal that the state should enforce contracts.
Personally, I am willing to accept the assumption that they can’t contract as much as I am willing to accept the assumption that they have weird preferences. However there is also a standard way to make private contracting ineffective – replicate the model.
Imagine a million prudes and a million lewd people. The prudes don’t want lewd people to read porn. The lewd people really really want prudes to read porn. A proper moral tone in which no one is reading porn and enjoying it is a public good for prudes. A hilarious world in which all prudes are being shocked by porn is a public good for lewd people. A Pareto efficient outcome would be for all prudes and no lewd people to read porn. This can not be achieved without compulsion because there is a collective action problem. Consider one of the many identical prudes P. P does not care if other prudes read porn. To read porn causes P 100 units of pain. For a lewd person to read porn causes P 1 of pain. Now consider lewd L. To read porn gives L 100 units of pleasure. For a prude to read porn causes L one unit of pleasure. The best contract for L and P is to leave each other free to choose. There is no set of prudes which can gain from contracting with L. There is no set of lewd people who can gain from contracting with P. There is a free rider problem. The immoral prude who shirks his or her duty to read porn leaving the whole burden of keeping lewd people from reading porn to the public spirited prudes who, sad to say, given the assumptions above don’t exist.
Now this example is very unrealistic, because people are totally selfish and incapable of shared sacrifice. However that is an assumption about preferences not about what contracts are allowed. Two agents can write a contract to achieve Pareto efficiency. 200,000,000 can’t or rather the contract is called the social contract and it’s particular clauses are called laws.
Prudes seem to positively enjoy collective action. In fact, as far a as I can tell that is the main fun of being a prude. Consider kiddie porn. I hate it. I think I would enjoy fighting the good fight against kiddie porn in community of anti kiddie porn activists (so long as we could keep the prudes out of our campaign). I am almost ready to claim that the problem is not that I am lazy and selfish but one of coordination. I am willing to note that even in the hypothetical case that I were not lazy and selfish there would still be a coordination problem.
My conclusion is that Sen’s claim does not require the extraordinary assumption that people can not contract. It holds if contracts are arrived provided the original model is replication a few million times.
Historical digression. Why have I been talking about “reading” porn on a web page even. If it’s like a book which you read, it can’t be porn right ? This is roughly the state of current jurisprudence (which is I admit more grammatical). Sen was writing just after an English court decided that “Lady Chatterley’s Lover” was not porn. In a name dropping digression from the digression, I heard Sen present Sen’s paradox to graduate students and he apologised profusely for his benighted generation born early enough to see judges who thought that “Lady Chatterley’s Lover” might be porn. I mean a bit preachy yes but porn ??? Why it is a classic. Clearly part of the Canon as defined by Microsoft Word which just corrected my spelling of
Saturday, December 18, 2004
Learning by example, I denounce the Fijian nuclear weapons program. I hope to be wrong enough to claim an increased role in intelligence gathering. And a posting to the Fijian provisional authority wouldn't be bad at all.
Tuesday, December 14, 2004
Some time ago, my link to the internet was threatened when a car hit a telephone pole (I wasn't there at the time but I think there were no injuries). The broken pole was held up with twine for a while (see the white twine in the photo) and I was planning to photograph it for a funny post post on the variety of the internet. As ususal I left things till the last possible moment.
These two nice guys from telecom Italia are making sure that I will be able to continue bloggin (I forgot to get their names).
Saturday, December 11, 2004
In the New York Times Ian Fisher has a very good story on this event A key point of the verdict and the article is "One crucial charge of paying off a judge was dropped essentially on procedural grounds, because the statute of limitations had run out." This is an improvement over the already good instant story whose timing was noted with awed admiration at La Repubblica. In the instant story Fisher rushed past the statute of limitations a bit quickly. I put it in the headline. If Berlusconi had been judged innocent on the merits on all charges, he would be assolto.
The case was complex. On one charge the verdict refers to the statute of limitations. On one to the absence of proof of guilt. On one the 3 judge panel appears to have concluded that the cash handed by the deputy the honorable Cesare Previtti (already convicted in two earlier trials) to the judge his honor Renato Squillante (already convicted in the same two trials) was on behalf of other clients (presumably the very rich Rovelli's who don't have fancy titles but have a ton of money due to being relatives of an extraordinarily incompetent and corrupt businessman).
One charge was dropped because of the statute of limitations. It was transferring money to the judge Renato Squillante via his lawyer the deputy and former defence minister Cesare Previtti via the Swiss Bank account "polifemo" Polyphemus the ironically named.
English speaking people might imagine that the statute of limitations is simple enough that prosecutors and judges would not disagree about the application of the statute of limitations. How naive, the Italian "prescrizione" is very complicated and often binding. Crucially any factor which can affect the sentence can affect the statue of limitations. For the second time, the concession of the "attenuanti generici"(non discript attenuating factors) implies that Berlusconi can not be punished. The announcement by the 3 judge panel begins
"Visto l'articolo 531 CPP dichiara non doversi procedere nei confronti di Berlusconi Silvio in ordine al reato di corruzione ascrittogli al capo A) limitatamente al bonifico in data 06-07 marzo 1991 perché, qualificato il fatto per l'imputato come violazione degli articoli 319 e 321 C.P. e riconosciute le circostanze attenuanti generiche, lo stesso è estinto per intervenuta prescrizione; visto l'articolo 530 CO.2 C.P.P."
"Based on article 531 of the Penal procedures Code [statue of limitations] the court declares that is must not act on the accusation of bribery made in Part A of the accusation with regard only to the bank to bank transfer on the 6th and 7th of March 1991 one because it describes the act [for] the accused as a violation of articles 319 and 321 of the criminal code [corruption of a public official not corruption of a judicial action which is a more serious crime] and recogniseing the non descript attenating factors, the accusation has expired. "
Notice it is quite explicit that other charges are not "prescritto" because it was not proven that Berlusconi did the dead. This makes it very clear that the judges concluded that Berlusconi gave money to Squillante and that this was an act of corruption. Less clear to me is the translation of
" il fatto per l'imputato" il= the, Fatto = act or deed, l'imputato = Silvio Berlusconi. "per" would generally be translated "for". This is important because if the judges had declared "the deed of the defendent" they would have said he done it. As it is, the preposition "per" means we will have to wait 90 days for the explanation of the verdict to be absolutely sure.
The claim that the transfer of money to Squillante was criminal was already made in an earlier trial when Squillante and Previtti were convicted. The claim that Berlusconi must have known about it is based, in part, on the fact that his lawyers have explicitely claimed that the money in "polifemo" belonged to him and not to his firm (Fininvest). This is a subtle distinction in Italy expecially in the case of paragons of disinterested devotion to the shareholders' interests such as Berlusconi, but it was key at the time it was made because the account (also used to send a huge sum to Bettino Craxi) was not on the Fininvest books and the statute of limitations for false accounting ran longer than that for illegal contributions to a politician (Berlusconi was convicted then appealed and was prosciolto when the statue of limitatiosn ran out). Thus Berlusconi's problem is that at the Swiss money laundry he was using something was singular when it should have been double, just like the single eye of Polyphemus. This should be the basis of a joke, but after a week of trying, I hereby give up.
By the way, I learned this the from La Repubblica and the other such case was bribing judges in an attempt to gain control of La Repubblica and the presumably fire its then current staff. Previtti and Squillante were convicted in that case too, while Berlusconi was not even tried, because the court, which indicted other defendents, declared that he was covered by the statute of limitations. So La Repubblica is biased. That's life. In Italy journalists either work for Berlusconi or hate him because he tried to get them fired.
The key issue therefore is the concession of the attenuante generici. I am proud to note that I knew the was the key issue before the verdict. As the name suggests, judges have more or less complete discretion in granting attenuanti generici. In the case of trying to take over the firm that owned La Repubblica, the court explicitely said they were conceded because Berlusconi has a prominent public role. It is worse stressing that "attenuating circumstances" is not a correct translation, since the concession may depend entirely on events separate from the illegal act.
Previous verdicts based on the statue of limitations (1 conviction 1 indictment) amnesties (2) or recent changes in the law by his parliamentary majority (2) are sufficient to conclude that Berlusconi is not an ex con.
The presiding judge Francesco Castellano has publically declared that he thinks prosecuters are persecuting Berlusconi's firm and that there should be a moratorium on trials of Berlusconi. The prosecuters obviously asked him to recuse himself, the asked the President of the tribunal of Milan to recuse him. Both refused demonstrated a depraved determination to betray their office and their hostility to law and truth. As much as Renato Squillante, these vile beings illustrate what a judge should not be. While blatently partisan, they used the public trust which they betrayed, to impose their wishes. The panel includes two other judges. The depraved presiding judge clearly agreed to declare, along with his colleagues, that it has been proven yet again that Berlusconi committed a crime. However, in addition to declaring that Berlusconi should not be subject to crime, he used his office, and the inevitable discretion which must not be combined with blatant partisanship, to declare him unpunishable in this case.
I note that I am writing this in Italy where slander is a crime colunnia and there is no special standard for slander of a public figure.
Saturday, December 04, 2004
Thursday, December 02, 2004
There seems to have been a serious error at the NYT op ed page today. An article clearly written by Paul Krugman has Tom Friedman's byline and photograph. Seriously folks I think that Friedman has earned an honorary stay in the ancient and hermetic order of the shrill
""provided it is not very long.""
Update: Checking the Shrillblog URL I find that Friedman is already a member and, indeed, falsely described as the founder. That order is more hermetic than I thought.