Nochmal zur Wiederholung: Das Rätsel ist, warum trotz einer Senkung der Körperschaftssteuer von 34 auf 25% des Unternehmensgewinns die Einnahmen aus dieser Steuer konstant geblieben bzw. sogar leicht gestiegen sind.

Rudis Theorie lautet, dass der Effekt durch Umgründungen von Personengesellschaften in Kapitalgesellschaften entstanden ist. Die Steuerreform bietet einen Anreiz dafür. Um das zu verstehen betrachten wir eine Unternehmerin mit 100.000 Euro Jahresgewinn. Sie hat vereinfacht gesagt zwei Möglichkeiten diesen zu versteuern. Entweder sie versteuert ihn als Einzelunternehmerin gemäß ihrem persönlichen Einkommenssteuertarif. Damit zahlt sie ca. 45.000 Euro***** an Einkommenssteuern (der genaue Betrag hängt von vielen Details ab), also 45% von ihrem Bruttoeinkommen. Die andere Möglichkeit wäre eine Kapitalgesellschaft zu gründen. Dann würde sie 100.000 Euro als Unternehmensgewinn deklarieren, davon zunächst die Körperschaftssteuer und dann bei Auszahlung des Nettogewinns nochmal Kapitalertragssteuer abführen. Nachstehende Tabelle zeigt wie viel sie vor und nach der Steuerreform von 2005 zahlen müsste:

Bei einer Umgründung hätte unsere Unternehmerin vor der Reform etwa 5,500 Euro jährlich mehr an Steuern gezahlt. Nach der Reform erspart sie sich durch Umgründung ca. 1,250 Euro pro Jahr.

Tatsächlich kam es nach 2005 zu einer solchen Umgründungswelle. Laut diesem Artikel in der „Presse” (ich danke Timon für den Link!) stieg die Zahl der GmbHs im relevanten Zeitraum um 5,2% während die Zahl der Personengesellschaften nur um 1,4% gestiegen ist. Im Zuge dieser Umgründungswelle stiegen die Einnahmen aus der Körperschaftssteuer, aber gleichzeitig sanken die Einnahmen aus der veranlagen Einkommenssteuer.

Also ist das Rätsel damit gelöst? Ich glaube nicht. Hier ist mein empirischer Einwand gegen Rudis Theorie.

Wenn der Umgründungseffekt der einzige Effekt der Steuerreform gewesen wäre, hätten die Gesamteinnahmen aus Körperschafts-, Kapitalertrags- und Einkommenssteuer sinken müssen. Jede Umgründung bewirkt ja, dass in Summe weniger Steuern gezahlt werden, andernfalls würde sich eine Umgründung nicht auszahlen. Außerdem sinken die Einnahmen aus der KöSt der schon bestehenden Kapitalgesellschaften.

Die nachfolgende Grafik kann diese Hypothese nicht wirklich bestätigen. Sie zeigt die inflationsbereinigten Einnahmen aus den drei relevanten Steuerarten vor und nach der Reform. (Datenquellen: Steuerstatistik der “Statistik Austria” und Konsumentenpreisindex von Eurostat.)

Man sieht: die grünen Balken (Einkommenssteuer) werden nach 2005 etwas kürzer, die roten (Körperschaftssteuer) und blauen (Kapitalertragssteuer) etwas länger, aber die Gesamtlänge der Balken verändert sich kaum. Vergleicht man den Durchschnitt der Einnahmen aus den drei Jahren vor der Reform (2002-2004) mit dem Durchschnitt der drei Jahre nach der Reform (2005-2007) ergibt sich folgendes Bild: Zwar sanken die realen Einnahmen aus der ESt um 443 Mio., jedoch wurde diese Abnahme mehr als kompensiert durch den Anstieg der Einnahmen aus KöSt (+585 Mio.) und KESt (+483 Mio.). In Summe stiegen die Gesamteinnahmen real um 625 Mio. also um ca. 6%.

Natürlich gab es im betrachteten Zeitraum jede Menge anderer Ereignisse, die die Steuereinnahmen beeinflusst haben könnten. Unter anderem gab es einen allgemeinen Konjunkturaufschwung, der besonders in den Jahren 2007 und 2008 die Unternehmensgewinne sprudeln ließ. Aber auch wenn man die Zeitreihe weiterzieht, sieht man keinen langfristigen Abwärtstrend in den Unternehmenssteuern.

Ich schließe daraus, dass die Senkung der KöSt sehr wohl einen positiven Effekt über die Umgründungen hinaus gehabt haben muss. Wie genau dieser Effekt ausgesehen haben könnte, würde eine genauere Untersuchung verlangen. Vielleicht möchte ja eine oder einer unserer emsigen VWL-Studierenden eine Bachelor-Arbeit dazu schreiben.

Bis dahin sage ich mal ein vorsichtiges Hurra für die Laffer-Kurve!

***) Berichtigung**: Der sachkundige Martin Kremsner schreibt, dass meine Berechnung der Einkommenssteuerlast fehlerhaft ist. Bei einem Einkommen von 100,000 Euro wäre die Steuerlast laut damaligem ESt-Tarif ca. 40,000 Euro. D.h. der steuerliche Anreiz zur Umgründung würde hier nicht bestehen. Ich habe das Zahlenbeispiel so gelassen um das zugrundeliegende Prinzip von Rudis Theorie zu erläutern. Ein besser gewähltes Beispiel wäre ein Unternehmen mit 200,000 Euro Gewinn, deren ESt-Last ca. 90,000 Euro betragen würde. Für so ein Unternehmen betrug die Steuerlast aus KöSt und KESt vor der Reform 101.000 Euro und danach 87.500 Euro. https://www.bruttonettorechner.at/einkommensteuer

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Let us first approach this problem from the viewpoint of the resort. How did they decide how many lounge chairs they would provide? Probably there is a bit of a space problem. Or let’s say it differently, there is probably a temptation for the resort management to divide the space between hotel rooms and lounge chair space in such a way that there are more rooms so that they can have more paying guests. It probably makes little sense to have more lounge chairs than beds (unless the resort was open to day visitors as well – which we shall not assume here). But should one have fewer lounge chairs than beds? I can imagine the conversation in management about this issue. Somebody will have pointed out that it’s probably ok to have more beds than lounge chairs because not all people who sleep in the resort will also need a lounge chair. Some guests may make day trips to other places. Also even if all guests will want a lounge chair, they probably do not all need one at the same time. The average guest might spend, let’s say four hours every day in a lounge chair (seems a long time to me). And not all guests will want to spend the same four hours in lounge chairs. There may be morning people and afternoon people, before lunch people and after lunch people, early lunch and late lunch people, et cetera.

In fact they are probably right (these are after all just the managers I imagine in my head). It is probably true for many resorts that at any given moment during the day the actual number of lounge chairs needed is smaller than the total number of lounge chairs in the resort. After all we often observe many lounge chairs with only a towel on it. So there is actually no real scarcity and yet we find that there are some people who cannot find a lounge chair when they want one. The problem is that this “game” between the resort guests can have two equilibria and it is easy to get stuck in the “bad” equilibrium.

To see this consider this. What do you do the next day do when you observe that all lounge chairs are reserved through the early placing of towels? Well, you have two options. Either you give up your hope of getting a lounge chair or you get up early and place a towel on a chair yourself.

What do you do if you find that there are always lounge chairs available (in nice locations around the pool)? You don’t even think about getting up early just to place a towel on a chair.

This means that both situations are self-enforcing. If no one places towels in the morning (and there is no real scarcity at any given moment in time) then no one will even consider reserving lounge chairs with towels in the morning. If however people do place towels in the morning and, if you do not you do not find a lounge chair when you need one, you will quite possibly get up early in the morning to do the same. In fact, there may be a race such that you have to get up earlier and earlier to find an empty lounge chair for your towel. An equilibrium is then found in such a way that exactly (in pure theory only) so many people get up early enough to place a towel on a lounge chair as there are lounge chairs. These people are those that care relatively less about sleeping in the morning. This, by the way, is called Harsanyi purification (of mixed Nash equilibria).

So how can you slip from the “good” equilibrium to the “bad” one and what could the resort do to prevent the “bad” equilibrium? I guess that most resorts have a variety of more or less attractive lounge chair locations. So I guess it is possible that some people start putting towels on the most attractive locations, which then starts a gradual chain reaction that eventually all lounge chairs get “toweled” if I am allowed to invent this word (it is not underlined in my editor, so I guess this word exists already). Another possibility is that some large enough group of tourists, perhaps with experience from other resorts and not knowing that in their current resort there is no real need for this, do get up and place towels and cover so many chairs that for the remaining chairs there now is a real scarcity at some point in time.

If the true reason for the lounge chair is that we are indeed simply in a bad equilibrium then the resort can introduce some simple and effective policy measures to restore the good equilibrium. They could, for instance, simply not allow the “toweling” of lounge chairs. They could remove towels after some time. A bit costly, this one, as someone has to monitor the pool area and enforce this rule. But they may not need to do it for too long as, once the good equilibrium has reestablished itself, they can stop enforcing the rule (as it is self-enforcing).

So what about the parking spots and job protection, the other two topics I mentioned in the title? Well, you can figure out for yourself how one could use the towels as an analogy for these two problems.

]]>Die folgende Grafik zeigt drei breite Steueraggregate im Verhältnis zum Bruttoinlandsprodukt: Einkommenssteuern (inkludiert Lohn- und Einkommenssteuer von Haushalten sowie Steuern auf das Einkommen von Kapitalgesellschaften), Gütersteuern (inkl. Mehrwertsteuern, Mineralölsteuer, Tabaksteuer, u. dgl.) und die Gesamtsumme aus Steuern und Sozialabgaben.

Was ich so erstaunlich daran finde? Wie flach alle diese Linien sind!

Das Gesamtsteueraufkommen bewegt sich immer um die 43% des BIP. Je 12% davon kommen von Einkommenssteuern und Gütersteuern, weiter 15% kommen aus Sozialbeiträgen und der Rest auf vermögensbezogene Steuern.

Und an dieser Struktur hat sich in den letzten zwei Jahrzehnten nichts verändert. Gar nichts. Weder die schwarz-blaue „Wende-Regierung“ zwischen 2000 und 2006, noch die „Große Koalition“ zwischen 2007 und 2016 lässt sich an dieser Grafik wirklich erkennen. In jeder Nationalratswahl wurde mindestens eine „Große Steuerreform“ angekündigt. Es gab drei Konjunkturzyklen und eine schwere Rezession. Nichts ist davon zu sehen.

Noch erstaunlicher: Wenn wir uns unsere europäischen Nachbarn anschauen, stellen wir fest, dass die fast genau dieselbe Steuerstruktur haben. Deutschland, Italien, Frankreich besteuern ihre Bürger auf ziemlich genau dieselbe Art und Weise – trotz erheblicher Unterschiede in der politischen Verfassung und der Struktur der Volkswirtschaft. (Die Schweiz stellt insofern eine Ausnahme dar, als sie wesentlich geringere Sozialabgaben haben, aber die Aufteilung von Einkommens- und Gütersteuern ist fast ident zu Österreich.)

Eine weitere erstaunliche Geschichte erzählen die Daten der Körperschaftssteuern:

Sehen Sie was 2005 passiert ist? Nein? Keine Sorge, ich auch nicht. Und das, obwohl in diesem Jahr der Körperschaftssteuersatz von 34% auf 25% gesenkt wurde! Der Steuersatz wurde um 9%-Punkte gesenkt, aber das Steueraufkommen blieb danach wie davor bei 2,3% des BIP. Die Laffer-Kurve lässt grüßen!

Der österreichische Lohn- und Einkommenssteuertarif wurde mehrmals verändert. Die Progressionsstufen wurden angepasst, die Grenzsteuersätze neu bestimmt… und am Ende kamen immer 10% vom BIP raus.

Die Sozialversicherungssyteme in Italien, Spanien und Griechenland sind in ihren Details sicher sehr unterschiedlich. Im Aggregat nehmen sie alle genau dieselben 13% vom BIP in Anspruch – nur 2%-Punkte weniger als Deutschland und Österreich.

Ich habe keine Ahnung was das alles bedeutet. Aber ich finde es faszinierend.

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I am continuing with my game theory inspired by Goffman’s work. This is an excerpt of what Goffman says about this on page 95, Part Three “Focused Interaction”, Chapter 6 “Face Engagements” in his “Behavior in Public places”:

“As these various examples suggest, mutual glances ordinarily must be withheld if an encounter is to be avoided, for eye contact opens one up for face engagement. I would like to add, finally, that there is a relationship between the use of eye-to-eye glances as a means of communicating a request for initiation of an encounter, and other communication practices. The more clearly individuals are obliged to refrain from staring directly at others, the more effectively will they be able to attach special significance to a stare, in this case, a request for an encounter. The rule of civil inattention thus makes possible, and “fits” with, the clearance function given to looks into others’ eyes. The rule similarly makes possible the giving of a special function to “prolonged” holding of a stranger’s glance, as when unacquainted persons who had arranged to meet each other manage to discover one another in this way.”

This is wonderful stuff. I am here just going to explain in game theoretic terms what is going on in the background of the last sentence of the quote. So we have two people who would like to meet. But there are many other people there as well, who we cannot ex-ante distinguish from the person we would like to meet. So how should we model this? I would like to model this as a one-at-a-time two person game of two people potentially trying to engage with each other. I would say that there are two types of individuals, type A who would like to meet another type A and type B who would like to be left in peace. This is private information. Only I know whether I am type A (trying to find another type A) or type B (hoping to be left in peace). This means we have a game of incomplete information. So there are two players and each one could be of type A or type B. To close the model informationally, so that we can work with it, it makes sense here to assume that both players of all types have common knowledge of the likelihood of anyone being of type A, let’s say of , and type B, then obviously . This is, of course, an empirically completely implausible assumption, but you will see that it actually does not play a huge role. In fact we will find an equilibrium of this game that will be an equilibrium for any positive (and relatively small) . The game has a first stage, which I will describe in a bit. Let me first describe the second (and last) stage. Eventually both players can unilaterally choose to verbally engage with the other player. So let us give both players two strategies each: engage (E) and not engage (N). So we have players (each of possibly different types) and we have strategies for each player. All that is left is to specify their payoffs. Well, what do we want? We want that B types do not want to engage. So let’s give B types a zero payoff whenever they choose E and let’s give B types a payoff of one if they choose N. Note that this gives B types a (strictly) dominant action of choosing N (not to engage).

What about A types? They want to engage with other A types but do not want to engage with B types (consider the embarrassment and need for a lengthy further explanation when you inadvertently try to engage with the wrong person). So they should get a payoff of zero if they engage with a B type and a one if they do not engage with a B type. They should get a zero if they fail to engage with an A type and get a one if they do engage with a B type. All that matters, of course, is that one is larger than zero. We could have chosen 100 and 6 and it would all be the same.

So let us summarize this in matrix form. There are four possible encounters, I am an A type and meet another A type, I am an A type and meet a B type, I am a B type and meet an A type, and I am an A type and meet a B type. Here are the payoffs we just chose for me in these for encounters (I choose row, my opponent chooses column):

If this is the game and there is nothing else, and if , then there is a unique equilibrium in this game in which both A and B types choose not to engage. B types do this because they find not to engage a dominant strategy (maybe they don’t even think about the possibility of engaging anyone) and the (in equilibrium sad) A types do this because it is (sufficiently) more likely that their opponent is a B type so that they are too worried about being embarrassed if they try to engage them.

So this is all very sad. But luckily the game people actually play is not fully described yet. We have not taken into account Goffman’s statement about the “special function to “prolonged” holding of a stranger’s glance”. Before the two players decide whether or not to engage verbally, they can first both send a (not very costly) “message” to their opponent by holding a prolonged stare. Now Goffman in his book in the pages leading up to the quote I provided above discusses at length why prolonged stares are typically not used by people as these are considered rude. You can read this for yourself. Whatever the reason, it seems a fact that people do not ordinarily treat other people to a prolonged stare. This means, that we can choose to deliberately employ this otherwise almost never used “message” in special encounters. This “message” can then act as a secret handshake. By the way I first encountered this secret handshake in a just slightly different context in a 1990 paper by Arthur Robson (Journal of Theoretical Biology 144, 379-396). It supposedly is very similar (but I again think the context is slightly different – actually quite different – one has to be careful to distinguish between cooperation and coordination I think) to the so-called green beard effect allegedly proposed by William Hamilton in 1964 and Richard Dawkins in his popular 1976 “selfish gene” book.

So how does this secret handshake work here and how do we model it? Before the two players play this game as described so far, they can first choose whether or not to send this message of the prolonged stare. So how can this generate new outcomes? Well, the two players can condition their engagement level on whether or not their opponent (and they themselves) employed this prolonged stare. In fact the following behavior is an equilibrium of this game. Every A type first uses a prolonged stare, B types do not. Then an A type decides to engage if and only if their opponent gave them a prolonged stare as well. In this equilibrium everyone is now as happy as they can be. B types get briefly stared at by some A types, but are then not engaged and they of course never engage their opponent themselves, while A types by means of the prolonged stare are able to identify other A types and engage exactly those. This is I think a fair description of how and why indeed two strangers can thus meet in a busy hotel lobby in such a way that disinterested others would not even notice that the two did not know each other before.

One of my PhD students at CICS (Research Center for Social Complexity at the Universidad del Desarrollo in Santiago, Chile) told me the following story. There used to be a bar in Santiago called the Club Amsterdam. You could order a beer, get a beer and then pay. You could also, allegedly, order a beer and at the same time put down a 5000 pesos note on the table and you would get a beer and a small portion of cocaine. No more communication was needed. I am not sure whether this situation should be modelled by the game I provided above – maybe one should have to think about the police here – but the problem seems quite similar and its solution employs a secret handshake as well.

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I found this in Chapter 2 “Territories of the self” part I “Preserves” in Goffman’s Relations in Public (recall my objectives):

“All of this may be seen in miniature in elevator behavior. Passengers have two problems: to allocate the space equably, and to maintain a defensible position, which in this context means orientation to the door and center with the back up against the wall if possible. The first few individuals can enter without anyone present having to rearrange himself, but very shortly each new entrant – up to a certain number – causes all those present to shift position and reorient themselves in sequence. Leave-taking introduces a tendency to reverse the cycle, but this is tempered by the countervailing resistance to appearing uncomfortable in an established distance from another. Thus, as the car empties, passengers acquire a measure of uneasiness, caught between two opposing inclinations – to obtain maximum distance from others and to inhibit avoidance behavior that might give offense.”

I have decided to write this blog post partly (especially when it comes to writing down the model) in the grand style of state of the art theory research papers. You will see what this means.

While I do not know of any specific game theory model that addresses this particular problem I am pretty confident that there is such a model out there in the literature. Please let me know if you know of one and I am happy to refer to it. If there is such a model out there I am pretty confident that it will be very similar to the one I am going to put forward here.

My first imitation of grand theory papers is to narrow down my vocabulary. While I would like the reader to think of any room in which people wait, such as lifts, busses, doctor’s waiting rooms, etc., I will refer to all of these as lifts.

Goffman then talks about three concerns individuals may have while on a lift. First, individuals care about the physical distance from other lift passengers; second, they care about “maintain[ing] a defensible position”; and third they do not want to offend others (unduly). I have decided to focus my blog post on one of these motivations, the first (and main one I think). Future blog posts (I am not planning any though) could tackle the other additional motivations. So the people in my lift will care only about the distance between them and their fellow lift passengers.

So what would a grand theory paper on this topic look like? Recall that a game has to have players, strategies, and outcomes (in terms of payoffs or “utils”). I don’t think we need incomplete information (information that is not shared by everyone in the game) here, so the game is one of complete information. While, of course, in any real-life lift individual passengers will have private information about many things, all this does not seem germane to the issue of where to place yourself. I am also ignoring that different people may have different desires about how close they would like to stand or sit to specific other fellow passengers. Again, an interested reader can modify the basic model to include a stalker or whatever other motive they would like to address for whatever situation they have in mind.

So we have reduced the problem to lifts and the single motivation of keeping one’s distance from other lift passengers. For a formal model we still have to make this even more concrete. Do we care about the average distance from all other fellow passengers or some other function of all these distances? My feeling here is that most likely we all care about the minimal distance from all other passengers. Suppose that all but one of the other passengers are bunched together in the far end of the lift, but the one remaining passenger has his or her nose almost touching yours (recall that this person is an uninteresting stranger to you). Contrast this with a situation in which all of your fellow passengers are evenly distributed in the lift with nobody standing super-close to you. You would probably prefer the second situation over the first. If you do, modelling your preference as caring about the minimal distance to your fellow passengers is probably not such a bad approximation to your real preferences.

Now let me finally express all this in the grand style of grand theory papers.

A lift, denoted by , is a closed and bounded subset of two-dimensional Euclidean space, i.e., . There are players. Each player’s strategy space is . Let denote player i’s choice of spot in the lift. [Note that we are assuming here that people have zero width, another assumption we could modify if we felt this would change things in an interesting way – which I doubt. We are also assuming that people can stand right on the boundary of the lift. This is for technical reasons that M. G. can explain to you if you insist.] For any pair of points let be the Euclidian distance between these two points. Let denote the vector of player placement in the lift. Each player i’s utility function is then given by .

It feels good to write this sort of thing.

So we have a model – a fictitious world with hypothesized people. What do we now expect to happen in this fictitious world we just created? As I argued before the most reasonable expectation in my view in situations like this (which we face over and over with always different opponents) is that we will get an evolutionary stable equilibrium of this game.

Now let’s play with our model and let’s find (evolutionary stable) equilibria of this game. Let’s do this by going through some real-life lift inspired examples. Suppose our lift is a square of some arbitrary size. Suppose first we have only two people. Where will they stand in our fictitious world? As far as I can see all equilibria are permutations of the two people standing in opposite corners of the lift. Why? Let me first suppose that one player places herself somewhere that is not on the boundary of the lift. But then she can always increase the distance from her fellow passengers by moving away from her fellow passenger. As she is not on the boundary she is able to do this. So both players (in equilibrium) must be on the boundary. Suppose at least one of them is not in a corner of the lift. Call her person one. But then no matter where person two is located person one can again increase her distance from the other person by moving along the boundary one way or the other (or both if person two is standing on a perpendicular to the boundary side of the lift that person one is standing on). Finally, suppose the two people are placed in adjacent corners. Then one of them could increase the distance by moving towards the next corner away from the other person. This proves what I claimed. In this case the any equilibrium has the two people standing in opposite corners (as at the beginning of a boxing match).

Let’s stay with the square lift, but let us now consider three and then four players. These cases are already much more complicated. Take three players. Let us first see what constellations are not equilibria. Even before that let me say that I think one can prove that all three people need to be on the boundary in any equilibrium. Suppose two individuals are in adjacent corners. Then the optimal placement of the third person is exactly in the middle of the lift side that is opposite to the two other passengers. But then the other two passengers finding this third person further away than the one standing in the adjacent corner next to them, can increase the minimal distance by moving along the boundary of the lift closer towards the third person. So this is not an equilibrium. If both corner people were to move in such a fashion we will not reach an equilibrium either, I think, as then at some point each of them will find it better to move away to their original corner again.

Now suppose all three people place themselves in distinct corners of the lift. Then one corner is unfilled. Then the two people in corners adjacent to the empty corner could each unilaterally increase the minimal distance to their fellow lift passengers by moving a little bit towards the empty corner. If they keep doing this at the same speed then they would at some point each hit a place where each finds that they are no equidistant from both of their fellow passengers. The third passenger can also not reduce the distance to the other two. We have reached an equilibrium. In fact one, with a non-trivial and empirically testable implication of placement in the largest equilateral that could fit in a square.

It is possible that the game with three people has multiple equilibria. I have not explored this further. The game with four people, however, definitely has multiple equilibria. In fact it has infinitely many equilibria (all with different equilibrium happiness – I mean payoff). I am not sure whether one can generally prove that in the four player case in equilibrium all people must be on the boundary of the lift. For five players this is definitely not true. But let me give you an infinity of equilibria in which all four players are placed in symmetric positions on the boundary of the lift. Take any side of the lift and place one player on any point on this side. Then put the other three players on the same position on the other three boundary sides in such a way that the four players form a square. Note that, no matter what initial point you chose for the first player, if any player now moves in any feasible direction she will only reduce the distance to one of her closest neighbors. This means that any such constellation is a Nash equilibrium. I do not know whether they are all evolutionary stable. I would certainly only expect the equilibrium in which all four people stand, respectively, in the four corners of the lift. If it is true that this is what happens empirically in real square lifts, then we would need to think about why it is that the people do not put themselves in one of the infinitely other equilibrium positions. I guess these may not be evolutionary stable, but maybe the reason lies somewhere else.

The more I think about it, the more I realize that my blog post has only scratched the surface of already undertaken or yet to be done lift placement research.

]]>I then looked at the expected return to a one Euro bet on the various countries winning the world cup under the assumption that gracenote’s estimates are completely correct. So if you believe in gracenote’s estimates as the abolute truth, what should you bet on?

Well, Brazil is the favorite according to gracenote but also in the betting odds. Gracenote gives them a 21% chance of winning the world cup, and at current best odds of 9:2 you would win 4,50 Euros if you put 1 Euro on Brazil. This means you would expect to get 4,5 * 0,21 = 0,945 Euros back. So if you are risk averse or risk neutral you should not bet on Brazil at these odds, but if you had to you could put a Euro on Brazil. Germany has similar best odds of 5:1, but gracenote does not rate them so highly, giving Germany only an 8% chance of winning. So you would only expect to win back 5*0,08=0,40 Euros for every Euro you place on Germany. This means that, if you could, you should “short sell” Germany to make money in expectation. This is not so easy to do in sports betting markets so let’s not pursue this here. It turns out that most of the better teams are not rated as highly by gracenote as they are in the betting odds.

So, again, what should you bet on if you believe in gracenote’s estimates? According to gracenote Peru has a 5% chance of winning the world cup. At current odds of 325:1 you would get an expected payout of 325*0,05=16,25 Euros for every Euro you put on them. This is an expected return better than anything you can get on the stock market I would guess. Mexico, Switzerland, Colombia (with expected payout of 3,75, 3,50, and 2,60 Euros for every Euro you put on them) are also high return bets.

I am afraid, though, that I believe in the efficiency of sport betting markets much more than in one sports data company’s estimates, so I will not follow these suggestions myself. If you want to know more about the efficiency or inefficiency of betting markets a good starting point would be a 1988 survey by Thaler and Ziemba.

One day later, on the 8th of June, I noticed that Peru’s odds have gone down to 200:1. Perhaps this was a reaction to the new information provided by gracenote (although I am not quite sure when their estimates were posted). You would, however, still make an expected winning of 200*0,05 = 10 Euros for every Euro you put on Peru if you believe gracenote’s estimates.

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Is it because the Italian government was fiscally irresponsible, spending too much and taxing too litte? Or is it because investors demand such high interest rates on Italian government bonds? Or is it a consequence of Italy’s dismal economic performance in recent years?

To answer this question, we can take a simple decomposition of the debt-to-GDP ratio. First, remember the government budget constraint:

where B is public debt, G is spending, T is revenue and r is the interest rate. Second, take the time derivative of the debt-to-GDP ratio

Combine the two equations and denote the GDP growth rate dY/Y by g:

This equation allows us to decompose the total change in the debt-to-GDP ratio into a primary deficit component, an interest component and a growth component. The graph below shows this composition for Italy during the pre-crisis period (2000-2008) and the post-crisis period (2009-now).

In the years between the introduction of the euro and the financial crisis, Italy’s debt ratio decreased slightly by about 2 percent of GDP. During the years after the crisis, it increased by almost 30 percent of GDP.

What changed? As you can see by looking at the yellow and blue areas in the graph, it wasn’t interest payments or the primary surplus. Interest payments were around 5 percent of GDP both before and after the crisis and the Italian actually ran a primary surplus in both periods. What changed was the green area: the recent rise in the debt ratio is almost entirely due to Italy’s shrinking economy.

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David Hume, the great skeptical philosopher, answered: practically never. His argument ran as follows: Miracles are extremely rare events and thus have a very low prior probability. On the other hand, people can be misled rather easily either by their own senses or by other people. Therefore, the rational reaction to hearing a miracle story is to reject it, except the evidence supporting it is overwhelming. “Extraordinary events require extraordinary evidence” became a popular summary of Hume’s point of view.

Here is a famous passage from Hume’s “Of Miracles” explaining the point:

When anyone tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened. I weigh the one miracle against the other; and according to the superiority, which I discover, I pronounce my decision, and always reject the greater miracle.

This argument sounds intuitively plausible and compelling, but it is mistaken. In fact Hume is committing an elementary error in probability theory, which shouldn’t be held against him since “Of Miracles” predates the writings of Bayes and Laplace.

In the language of modern probability theory, Hume asks us as to compare the *prior probability* that miracle X occurred, , to the probability of seeing the evidence Y supporting miracle X even though X did not in fact occur, i.e. the conditional probability of Y given the negation of X, Econometricians would call the latter the *likelihood* of Y under the hypothesis not-X. If Hume says we should reject X in favor of not-X.

But this inference is unwarranted. What a rational observer ought to ask is: Given the evidence Y, is it more likely that X occurred or that it didn’t occur? We are looking for the *posterior odds* of X conditional on Y:

Bayes’ theorem immediately gives us what we are looking for:

This equation makes it clear that even if Hume’s inequality holds, it is possible that the posterior odds of X are greater than 1. All we need for such as result is that the likelihood of having evidence Y under the hypothesis that X occurred is sufficiently higher than the likelihood of Y under the alternative hypothesis that X did not occur. In econometric terms, the likelihood ratio must exceed a critical value which depends on the prior odds against the miracle:

To conclude: A rational observer is justified in believing a miracle if the evidence for it is sufficiently more likely under the hypothesis that the miracle really did occur than under the hypothesis that it didn’t so as to offset the low prior odds for the miracle. Just comparing the low prior probability of a miracle to the probability of receiving false evidence in favor of it is not enough and can be misleading.

]]>But in this post I want to take up Goffman’s brief mention (on pages 14-15) of special circumstances that seem to necessarily lead to what he calls “gallantry”. This is when a path that pedestrians take in both directions at some point becomes too narrow for two people to pass simultaneously. Then one has to wait to let the other person pass. But who should wait and who should be first to pass?

There are indeed often “norms” in place that dictate a form of “gallantry”. For instance, men should give way to women, younger people should give way to older people, or people going down should give way to people coming up (if the path has a non-negligible slope).

Before I go deeper into this subject, let me quickly state that there are other forms of gallantry which I (and Goffman) do not talk about here (there). One could, for instance, go out of one’s way to open a door for someone else, perhaps even a door that one is not going through oneself, such as a car door. This is interesting also, but not the subject of this post. Here I only look at cases in which some form of “gallantry” is really almost required for these two people to (eventually) go on with their lives: in the end one person has to let the other person pass first. There is no other way.

A nice illustration of the potential problem in such cases is described by Lady Mary Montagu (thanks to my father for pointing this out to me!) in her letter XI to Mrs. J. 26 September 1716 of her collected correspondence (http://ota.ox.ac.uk/id/N31507), when she was travelling through Europe and writing about it. This is something she wrote about Vienna. See also footnote 20, page 15 in Goffman’s book for a similar story.

“It is not from Austria that one can write with vivacity, and I am already infected with the phlegm of the country. Even their amours and their quarrels are carried on with a surprising temper, and they are never lively, but upon points of ceremony. There, I own, they shew all their passions, and ’tis not long since two coaches meeting in a narrow street at night, the ladies in them not being able to adjust the ceremonial of which should go back, sat there with equal gallantry till two in the morning, and were both so fully determined to die upon the spot rather than yield, in a point of that importance, that the street would never have been cleared till their deaths, if the Emperor had not sent his guards to part them, and even then they refused to stir, till the expedient could be found out, of taking them both our in chairs, exactly in the same moment. After the ladies were agreed, it was with some difficulty, that the pass was decided between the two coachmen, no less tenacious of their rank than the ladies.”

There are many ways one could model this situation as a game. One could emphasize the time dimension of the problem, which would lead us to call this a game of attrition, as perhaps the quote from Lady Mary Montagu suggests we should. I think, however, that this is typically not the most important issue in this situation. I want to model a situation where the two people would in principle not mind terribly if they are the one to wait, but in which they still, at least slightly, prefer to pass first if possible.

While in reality this game often has incomplete information as well – see for instance my blog post on this very problem that drivers face when navigating the narrow lanes in Cornwall – I will here model this as a game with complete information. This will suffice for my purposes here as you will see.

So the idea is this. Each person can decide between “Go” and “Wait”. If both Go or both Wait they have not yet solved the problem and I normalize these cases (equally) as giving them both zero payoffs. We could give them different payoffs in the two cases, but this does not affect the analysis as long as these payoffs are less than one. You can see that each person would prefer to be the one to Go while the other Waits.

The important thing for my discussion of this problem is that the game is symmetric. This means that, without any other information, the two players are in exactly the same position and will find it impossible to coordinate on an asymmetric outcome unless by luck.

In fact the theory suggests that play in such cases (that can be emulated in the artificial environment of a lab – see more about this below) eventually will converge to the unique symmetric evolutionary stable strategy. Here this would be that 2/3 of all people play Go and 1/3 play Wait.

Note that this is not a great outcome as in most cases (in 5 out of 9 cases) the two individuals will do the same thing (to which as you remember we attached payoffs of zero). In reality this means that the two individuals will now engage in some form of communication and additional maneuvering necessitating some delay with some loss of payoff (in the form of time) to both.

When, however, the two individuals have commonly understandable observable differences, such as one being a man and one a woman, or one being old and the other young, or one coming from a low place and the other a high one (this could also be in terms of status), norms can develop that take this possible information into account. In fact the theory suggests that this would be the case. The theory I am here referring to is developed by Selten (1980, “A Note on Evolutionary Stable Strategies in Asymmetric Animal Conflicts,” Journal of theoretical Biology, 84, 93-101) building on the ground-breaking work by Maynard-Smith and Price (who have invented the concept of evolutionary stability in a symmetric game very much like this one). There is a lovely lab experiment about this, very much confirming the theoretical findings in both cases (symmetric outcome without information and asymmetric outcomes with information about the characteristics of the opponents) by Oprea, Henwood, and Friedman (2011) “Separating the Hawks from the Doves: Evidence from continuous time laboratory games”, Journal of Economic Theory, 146 (6), 2206—2225).

Note that sometime these norms turn into laws, such as the car driving down has to give way to a car driving up when the street is too narrow for both cars at the same time. I believe this to be a law in Austria, for instance. It does not seem to be enforced much, perhaps exactly for the very reason that it is a norm, an evolutionary stable equilibrium. In some cases such norms have made it into books of etiquette. In these cases a violation of the norm is not only against your immediate interest but may also be severely frowned upon by others with possible social sanctions being imposed afterwards. Although this seems unnecessary, again, for the very reason that it is already in everyone’s best interest to adhere to this norm (if all others do).

What I would find interesting would be a study of which characteristics are more likely to be used in such a norm. It seems to me that a person’s height, for instance, would not be such a great choice, as there would be many cases where it would be unclear who of the two is actually the taller. I suppose age suffers from the same problem, though. A binary and very obvious characteristic, such as man and woman, seems a very natural first thing to condition on. But of course it also does not solve the problem fully. What if two women meet at this narrow path? Then they have to use a more refined subnorm.

I guess it would also be bad to use a characteristic that one could influence. Imagine that we use hair color as a characteristic and suppose we have a norm that dark hair goes first and light hair has to wait. Then there would be an incentive (albeit I admit a very small one – possibly overridden by other more important incentives about hair color) to die your hair dark so as to always have the right to go first. In any case, in principle one could condition on all sorts of characteristics such as eye color or size of ears or who approached the narrow bit of the path first (actually probably a norm that is often in place) or who saw the other first. No matter what the norm is, I guess it will never be so perfect as to allow individuals to solve the problem perfectly in all cases. For any norm there is probably still a positive likelihood of the two individuals being the same as far as the norm is concerned (such as both being women of roughly the same age who have arrived at this narrow bit of the path more or less at the same time) and if this does not happen too often, evolutionary pressure to put a subnorm in place in such cases is pretty small.

]]>An obvious caveat: My observations are biased due to the fact that I’ve only seen parts of America (California, part of the Northwest, part of the Midwest, and New England), and only parts of Europe (Central Europe, part of Scandinavia, part of France and England). One should realize that large cultural, political and economic differences exist both within the US and Europe, so all the statements below refer to averages with wide confidence bands around them.

Economic life:

- Prices are normally stated net of sales taxes. (high confidence, uncontroversial)
- Tips are higher and more common. (high confidence, uncontroversial)
- Tap water is much more heavily chlorinated. (high confidence, uncontroversial)
- Air-conditioning is vastly more common both in private homes and offices. (high confidence, uncontroversial)
- The average quality of houses is much lower. (high confidence, somewhat controversial)
- The proportion of people living in single-family houses as opposed to apartment buildings is much higher. (medium confidence, uncontroversial)
- The price of gasoline is about 50% lower. (high confidence, uncontroversial)
- There are both more cars per person and cars are much bigger on average. (medium confidence, uncontroversial)
- Automatic cars are vastly more common. (high confidence, uncontroversial)
- The price of necessities (food, clothing, personal hygiene) is lower, but not much, and the quality is generally lower. (low confidence, highly controversial)
- Food is bought and sold in much larger quantities. For instance, the smallest available bottle size for milk is usually half a gallon (about 1.9 liters). (high confidence, uncontroversial)
- Extreme obesity is vastly more common. (high confidence, uncontroversial)
- The quality of infrastructure (roads, railways, electricity grid) is lower. (medium confidence, somewhat controversial)
- Roads are more often built in strictly rectangular patterns, both in cities and on the countryside. (high confidence, uncontroversial)

Social life:

- Racial diversity is immensely higher, especially in urban areas, but also in rural areas. (high confidence, uncontroversial)
- So is religious diversity. (high confidence, uncontroversial)
- Religion plays a more central part of public life, including in politics (high confidence, uncontroversial)
- Interest in family history and genealogy is much higher. (high confidence, uncontroversial)
- Bodily contact between people in everyday interactions is much less frequent and more often regarded as inappropriate. (medium confidence, somewhat controversial)
- Conversations are much less formal both in professional and private contexts. (medium confidence, uncontroversial)
- Small talk is a much more important part of everyday life both in professional and private contexts. (high confidence, uncontroversial)
- Adolescents and young adults seem to be more mature both in terms of physical appearance and character development. (low confidence, highly controversial)
- Elderly people seem to be more familiar with, and more adept at, using new technology as well as social media. (high confidence, somewhat controversial)
- Knowledge about foreign countries (geography, history, politics) is generally much poorer. (high confidence, highly controversial)
- Patriotism is more wide-spread, more frequently expressed and more strongly felt. (high confidence, somewhat controversial)

Political life:

- There are more elected (as opposed to appointed) public officials and elections occur at higher frequencies. (high confidence, uncontroversial)
- Personal political opinions are more frequently expressed in public. For instance, pumper stickers with political messages are a much more common sight. (medium confidence, somewhat controversial)
- Political polarization is more profound. (medium confidence, somewhat controversial)
- There are more prohibition and warning signs on the streets as well as in public and private buildings and facilities. (low confidence, highly controversial)
- There are more local political initiatives such as petitions, awareness campaigns, fund raising events etc. (medium confidence, somewhat controversial)