About a year ago, I chanced to remark upon the state of Intermediate Micro within the hearing of my colleagues. It was remarkable, I said, that the nature of the course had not changed in half a century. What is more, the order in which topics were presented was mistaken and the exercises on a par with Vogon poetry, which I reproduce below for comparison:

“Oh freddled gruntbuggly,
Thy micturations are to me
As plurdled gabbleblotchits on a lurgid bee.
Groop, I implore thee, my foonting turlingdromes,
And hooptiously drangle me with crinkly bindlewurdles,
Or I will rend thee in the gobberwarts
With my blurglecruncheon, see if I don’t!”

The mistake was not to think these things, or even say them. It was to utter them within earshot of one’s colleagues. For this carelessness, my chair very kindly gave me the chance to put the world to rights. Thus trapped, I obliged. I begin next week. By the way, according to Alvin Roth, when an ancient like myself chooses to teach intermediate micro-economics it is a sure sign of senility.

What do I intend to do differently? First, re order the sequence of topics. Begin with monopoly, followed by imperfect competition, consumer theory, perfect competition, externalities and close with Coase.

Why monopoly first? Two reasons. First it involves single variable calculus rather than multivariable calculus and the lagrangean. Second, student enter the class thinking that firms `do things’ like set prices. The traditional sequence begins with a world where no one does anything. Undergraduates are not yet like the white queen, willing to believe 6 impossible things before breakfast.

But doesn’t one need preferences to do monopoly? Yes, but quasi-linear will suffice. Easy to communicate and easy to accept, upto a point. Someone will ask about budget constraints and one may remark that this is an excellent question whose answer will be discussed later in the course when we come to consumer theory. In this way consumer theory is set up to be an answer to a challenge that the students have identified.

What about producer theory? Covered under monopoly, avoiding needless duplication.

Orwell’s review of Penguin books is in the news today courtesy of Amazon vs Hachette. You can read here about that here. I wish, however, to draw your attention to an example that Orwell makes in his review:

It is, of course, a great mistake to imagine that cheap books are good for the book trade. Actually it is just the other way around. If you have, for instance, five shillings to spend and the normal price of a book is half-a-crown, you are quite likely to spend your whole five shillings on two books. But if books are sixpence each you are not going to buy ten of them, because you don’t want as many as ten; your saturation-point will have been reached long before that. Probably you will buy three sixpenny books and spend the rest of your five shillings on seats at the ‘movies’. Hence the cheaper the books become, the less money is spent on books.

Milton Friedman in his textbook Price Theory, as an exercise, asks readers to analyze the passage. He does not explicitly say what he is looking for, but I would guess this: what can you say about the preferences for such a statement to be true. Its a delightful question. A budget line is given and a point that maximizes utility on the budget lie is identified. Now the price of one of the goods falls, and another utility maximizing point is identified. What kind of utility function would exhibit such behavior?
By the way, there are 60 pence to a shilling and a half a crown is six pennies.

The news of Stanley Reiter’s passing arrived over the weekend. Born in a turbulent age long since passed, he lived a life few of us could replicate. He saw service in WW2 (having lied about his age), and survived the Battle of the Bulge. On the wings of the GI bill he went through City College, which  in those days, was the gate through which many outsiders passed on their way to the intellectual aristocracy.

But in the importance and noise of to-morrow
When the brokers are roaring like beasts on the floor of the Bourse

Perhaps  a minute to recall to what Stan left behind.

Stan, is well known of his important contributions to mechanism design in collaboration with Hurwicz and Mount. The most well known example of this is the notion of the size of the message space of a mechanism. Nisan and Segal pointed out the connection between this and the notion of communication complexity. Stan would have been delighted to learn about the connection between this and extension complexity.

Stan was in fact half a century ahead of the curve in his interest in the intersection of algorithms and economics. He was one of the first scholars to tackle the job shop problem. He proposed a simple index policy that was subsequently implemented and reported on in Business Week: “Computer Planning Unsnarls the Job Shop,” April 2, 1966, pp. 60-61.

In 1965, with G. Sherman, he proposed a local-search algorithm for the TSP (“Discrete optimizing”, SIAM Journal on Applied Mathematics 13, 864-889, 1965). Their algorithm was able to produce a tour at least as good as the tours that were reported in earlier papers. The ideas were extended with Don Rice  to a local search heuristic for  non-concave mixed integer programs along with a computation study of performance.

Stan was also remarkable as a builder. At Purdue, he developed a lively school of economic theory attracting the likes of Afriat, Kamien, Sonnenschein, Ledyard and Vernon Smith. He convinced them all to come telling them Purdue was just like New York! Then, to Northwestern to build two groups one in the Economics department and another (in collaboration with Mort Kamien) in the business school.

The Fields medals will be awarded this week in Seoul. What does the future hold for the winners? According to Borjas and Doran, declining productivity caused by a surfeit of dilettantism. The data point to a decline in productivity. By itself this is uninteresting. Perhaps all those on the cusp of 40, see a decline in productivity. What Borjas and Doran rely on is a degree of randomness in who gets a medal. First, there is the variation in tastes of the selection committee (Harish Chandra, for example, was eliminated on the grounds that one Bourbaki camp follower sufficed). Second, the arbitrary age cutoff (the case of the late Oded Schramm is an example of this). Finally, what is the underlying population? Borjas and Doran argue that by using a collection of lesser prizes and honors one can accurately identify the subset of mathematicians who can be considered potential medalists. These are the many who are called, of which only a few will be chosen. The winners are compared to the remaining members of this group. Here is the conclusion (from the abstract):

We compare the productivity of Fields medalists (winners of the top mathematics prize) to that of similarly brilliant contenders. The two groups have similar publication rates until the award year, after which the winners’ productivity declines. The medalists begin to `play the field,’ studying unfamiliar topics at the expense of writing papers.

The prize, Borjas and Doran suggest, like added wealth, allows the winners to consumer more leisure in the sense of riskier projects. However, the behavior of the near winners is a puzzle. After 40, the greatest prize is beyond their grasp. One’s reputation has already been established. Why don’t they `play the field’ as well?

A Bayesian agent is observing a sequence of outcomes in {\{S,F\}}. The agent does not know the outcomes in advance, so he forms some belief {\mu} over sequences of outcomes. Suppose that the agent believes that the number {d} of successes in {k} consecutive outcomes is distributed uniformly in {\{0,1,\dots k\}} and that all configuration with {d} successes are equally likely:

\displaystyle \mu\left(a_0,a_1,\dots,a_{k-1} \right)=\frac{1}{(k+1)\cdot {\binom{k}{d}}}

for every {a_0,a_1,\dots,a_{k-1}\in \{S,F\}} where {d=\#\{0\le i<k|a_i=S\}}.

You have seen this belief {\mu} already though maybe not in this form. It is a belief of an agent who tosses an i.i.d. coin and has some uncertainty over the parameter of the coin, given by a uniform distribution over {[0,1]}.

In this post I am gonna make a fuss about the fact that as time goes by the agent learns the parameter of the coin. The word `learning’ has several legitimate formalizations and today I am talking about the oldest and probably the most important one — consistency of posterior beliefs. My focus is somewhat different from that of textbooks because 1) As in the first paragraph, my starting point is the belief {\mu} about outcome sequences, before there are any parameters and 2) I emphasize some aspects of consistency which are unsatisfactory in the sense that they don’t really capture our intuition about learning. Of course this is all part of the grand marketing campaign for my paper with Nabil, which uses a different notion of learning, so this discussion of consistency is a bit of a sidetrack. But I have already came across some VIP who i suspect was unaware of the distinction between different formulations of learning, and it wasn’t easy to treat his cocky blabbering in a respectful way. So it’s better to start with the basics.

 

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The August 3rd NY Times has an article about the advertising of Fishoil and Facebook. As sometimes happens with a NYT article, the interesting issues are buried beneath moderately interesting anecdotes that may be traded with others at the dinner table in what passes for serious discussion.

The story is about a company called MegaRed, that peddles fish oil. It wants to target consumers who are receptive to the idea of fish oil because they believe that it confers health benefits. The goal is to get them to try out and perhaps switch to MegaRed.

Facebook proposes a campaign which raises the eyebrows of the marketing director, J. Rodrigo:

“I can go to television at a quarter the price.”

Brett Prescott of Facebook agrees, that yes, Facebook is more expensive than TV. But offers an analogy between advertising on Facebook and firing a shotgun.

“And you are firing that buckshot knowing where every splinter of that bullet is landing.”

If biology is the study of bios, life, and geology is the study of goes, the earth, what does that make analogy?

Some arithmetic to clarify matters. Suppose 1 in 100 of all people would be receptive to the idea of MegaRed’s message. Suppose each of these people is worth $1 on average to MegaRed. If you could reach all 100 of these people via TV, then MegaRed should pay no more than 10 cents per person and so $1 in total.

Enter, stage left, Facebook. It claims that it can target its ads so that they go just to the right person. How much is that worth? $1. In this example, Facebook is no better or worse than TV.

If Facebook has any added value compared to TV it does not come from better targeting because one can always compensate for that by paying TV less and reaching more eyeballs. It must come from access to eyeballs unreachable via TV, or, identifying eyeballs that MegaRed would not initially have identified as receptive to their message, or that the medium itself is more persuasive than TV. Is this true for Facebook? If not, MegaRed is better off with TV.

Over a lunch of burgers and envy, Mallesh Pai and discussed an odd feature of medical reidencies. This post is a summary of that discussion. It began with this question: Who should pay for the apprenticeship portion of a Doctor’s training? In the US, the apprenticeship, residency, is covered by Medicare. This was `enshrined’ in the 1965 act that established Medicare:

Educational activities enhance the quality of care in an institution, and it is intended, until the community undertakes to bear such education costs in some other way, that a part of the net cost of such activities (including stipends of trainees, as well as compensation of teachers and other costs) should be borne to an appropriate extent by the hospital insurance program .

House Report, Number 213, 89th Congress, 1st session 32 (1965) and Senate Report, Number 404 Pt. 1 89th Congress 1 Session 36 (1965)).

Each year about $9.5 billion in medicare funds and another $2 billion in medicaid dollars go towards residency programs. There is also state government support (multiplied by Federal matching funds). At 100K residents a year, this translates into about about $100 K per resident. The actual amounts each program receives per resident can vary (we’ve seen figures in the range of $50K to $150K) because of the formula used to compute the subsidy. In 1997, Congress capped the amount that Medicare would provide, which results in about 30K medical school graduates competing for about 22.5K slots.

Why should the costs of apprenticeship be borne by the government? Lawyers, also undertake 7 years of studies before they apprentice. The cost of their apprenticeship is borne by the organization that hires them out of law school. What makes Physicians different?

Two arguments we are aware of. First, were one to rely on the market to supply physicians, it is possible that we might get to few (think of booms and busts) in some periods. Assuming sufficient risk aversion on the part of society, there will be an interest in ensuring a sufficient supply of physicians. Note similar arguments are also used to justify farm subsidies. In other words, insurance against shortfalls. Interestingly, we know of no Lawyer with the `dershowitz’ to make such a claim. Perhaps, Dick the butcher (Henry VI, Part 2 Act 4) has cowed them.

The second is summarized in the following from Gbadebo and Reinhardt:

“Thus, it might be argued … that the complete self-financing of medical education with interest-bearing debt … would so commercialize the medical profession as to rob it of its traditional ethos to always put the interest of patients above its own. Indeed, it can be argued that even the current extent of partial financing of their education by medical students has so indebted them as to place the profession’s traditional ethos in peril.”

Note, the Scottish master said as much:

“We trust our health to the physician: our fortune and sometimes our life and reputation to the lawyer and attorney. Such confidence could not safely be reposed in people of a very mean or low condition. Their reward must be such, therefore, as may give them that rank in the society which so important a trust requires. The long time and the great expense which must be laid out in their education, when combined with this circumstance, necessarily enhance still further the price of their labour.”

Interestingly, he includes Lawyers.

If we turn the clock back to before WWII, Hospitals paid for trainees (since internships were based in hospitals, not medical schools) and recovered the costs from patient charges. Interns were inexpensive and provided cheap labor. After WWII, the GI Bill provides subsidies for graduate medical education, residency slots increased and institutions were able to pass along the costs to insurers. Medicare opened up the spigot and residencies become firmly ensconced in the system. Not only do they provide training but they allow hospitals to perform a variety of other functions such as care for the indigent at lower cost than otherwise.

Ignoring the complications associated with the complementary activities that surround residency programs, who should pay for the residency? Three obvious candidates: insurers, hospitals and the doctors themselves. From Coase we know that in a world without frictions, it does not matter. With frictions, who knows?

Having medicare pay makes residency slots an endowment to the institution. The slots assign to a hospital will not reflect what’s best for the intern or the healthcare system. Indeed a recent report by from the Institute of Medicine summarizes some of these distortions.  However, their response to is urge for better rules governing the distribution of monies.

If hospitals themselves pay, its unclear what the effect might be. For example, as residents costs less than doctors, large hospitals my bulk up of residents and reduce their reliance of doctors. However, assuming no increases in the supply of residents, wages for residents will rise etc etc. If insurers pay there might be overprovision of residents.

What about doctors? To practice, a doctor must have a license. The renewal fee on a medical license is, at the top end (California), around $450 a year. In Florida it is about half that amount. There are currently about 800K active physicians in the US. To recover $10 billion (current cost of residency programs) one would have to raise the fee by a $1000 a year at least. The average annual salary for the least remunerative specialties is around $150K. At the high end about $400K. From these summary statistics, it does not appear that an extra $1K a year will break the bank, or corrupt physicians, particularly if it is pegged as a percentage rather than flat amount. The monies collected can be funneled to the program in which the physician completed his or her residency.

Four agents are observing infinite streams of outcomes in {\{S,F\}}. None of them knows the future outcomes and as good Bayesianists they represent their beliefs about unknowns as probability distributions:

  • Agent 1 believes that outcomes are i.i.d. with probability {1/2} of success.
  • Agent 2 believes that outcomes are i.i.d. with probability {\theta} of success. She does not know {\theta}; She believes that {\theta} is either {2/3} or {1/3}, and attaches probability {1/2} to each possibility.
  • Agent 3 believes that outcomes follow a markov process: every day’s outcome equals yesterday’s outcome with probability {3/4}.
  • Agent 4 believes that outcomes follow a markov process: every day’s outcome equals yesterday’s outcome with probability {\theta}. She does not know {\theta}; Her belief about {\theta} is the uniform distribution over {[0,1]}.

I denote by {\mu_1,\dots,\mu_4\in\Delta\left(\{S,F\}^\mathbb{N}\right)} the agents’ beliefs about future outcomes.

We have an intuition that Agents 2 and 4 are in a different situations from Agents 1 and 3, in the sense that are uncertain about some fundamental properties of the stochastic process they are facing. I will say that they have `structural uncertainty’. The purpose of this post is to formalize this intuition. More explicitly, I am looking for a property of a belief {\mu} over {\Omega} that will distinguish between beliefs that reflect some structural uncertainty and beliefs that don’t. This property is ergodicity.

 

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Abraham Neyman and Sergiu Hart are two of the prominent mathematical game theorists to date. Neyman contributed immensely to the study of the Shapley value, stochastic games, and repeated games and complexity. Hart contributed significantly to the study of correlated equilibrium and adaptive processes leading to it, value theory, and formation of coalitions.
Both Abraham and Sergiu will be 66 next year. To celebrate this rare occasion, the Center for the Study of Rationality at the Hebrew University of Jerusalem organizes two conferences, one in honor of each of them. The conference in honor of Abraham will be held on June 16–19, 2015, and the conference in honor of Sergiu will follow on June 21–24, 2015.
Mark the dates and reserve tickets.

You may have heard about ResearchGate, the so called facebook of scientists. Yes, another social network. Its structure is actually more similar to twitter: each user is a node and you can create directed edges from yourself to other users. Since I finally got rid of my facebook account (I am a Bellwether. In five years all the cool guys will not be on facebook), I decided to try ResearchGate. I wanted a stable platform to upload my preferable versions of my papers so that they will be the first to pop up on google. Also, I figured if I am returning to blogging then I need stuff to bitch about. ResearchGate only partially fulfill the first goal, but it does pretty well with the second.

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