One of the last remaining links to this period who straddled, like a Colossus, both Economic Theory and Operations Research, Herbert Eli Scarf, passed away on November 15th, 2015.

Scarf came to Economics and Operations Research by way of Princeton’s mathematics department. Among his classmates was Gomory of the cutting plane method Milnor of topology fame and Shapley. Subsequently, he went on to Rand ( Dantzig, Bellman, Ford & Fulkerson). While there he met Samuel Karlin and Kenneth Arrow who introduced him to inventory theory. It was in this subject that Scarf made the first of many important contributions: the optimality of (S, s) polices. He would go on to establish equivalence of the core and competitive equilibrium (jointly with Debreu), identify a sufficient condition for non-emptiness of the core of a NTU game (now known as Scarf’s Lemma), anticipated the application of Groebner basis in integer programming (neighborhood systems) and of course his magnificent `Computation of Economic Equilibria’.

Exegi monumentum aere perennnius regalique situ pyramidum altius, quod non imber edax, non Aquilo impotens possit diruere aut innumerabilis annorum series et fuga temporum. Non omnis moriar…….

I have finished a monument more lasting than bronze and higher than the royal structure of the pyramids, which neither the destructive rain, nor wild North wind is able to destroy, nor the countless series of years and flight of ages. I will not wholly die………….

]]>The process starts at the initial state s(0). At every stage n, the current state s(n) is known, the decision maker chooses an action a(n) in A(s(n)), receives the stage payoff r(s(n),a(n)), and a new state s(n+1) is chosen according to q(. | s(n),a(n)) and is told to the decision maker. The decision maker’s goal is to maximize the discounted sum of his stage payoffs:

sum-over-n-from-0-to-infty of λ-to-the-power-n times r(s(n),a(n)).

The value of the MDP, that is, the maximum that the decision maker can obtain, depends on the discount factor λ. Denote by v(λ) the value function of the MDP. Which functions can be obtained as the value function of some MDP with finite sets of states and actions?

From now on I restrict the discussion to MDP’s with finite sets of states and actions. Blackwell (1965) proved that for every discount factor λ the decision maker has a pure stationary optimal strategy. It is easy to see that the payoff that corresponds to a pure stationary optimal strategy is the solution of a set of equations, which are linear in λ, and whose coefficients are determined by the payoff function r and the transition function q. It follows that for every pure stationary strategy σ, the corresponding payoff function g(λ ; σ,s) is a rational function of λ. Since there are finitely many pure stationary strategies, we deduce that the value function is the maximum of finitely many rational functions.

Can we obtain any maximum of rational functions as the value function of some MDP? The answer is negative. For example, since the set of states and actions are finite, the payoff function r is bounded, say, by M. In particular, the payoff function of any strategy is bounded by M/(1-λ). In particular, any rational function whose denominator has a root inside the unit ball of the complex plane, or that has a root on the unit ball of the complex plane that has multiplicity larger than 1, cannot be the value function of an MDP.

Is that the only restriction that we have? The answer is still negative. It is not difficult to see that the roots of the denominator of the payoff function of a pure stationary strategy are the inverse of the eigenvalues of the transition matrix, which by a known result in matrix theory must be unit roots, that is, for any root ω of the denominator (which is a complex number) there is an integer k such that ω-to-the-power-k is equal to 1. Thus, a rational function whose denominator has a root that lies on the unit ball of the complex plane and is not a unit root cannot be the value function of an MDP.

Is that all? Yes. Let F be the set of all rational functions f : [0,1) → **R **that satisfy the following property: any root of the denominator either (a) lies outside the unit ball of the complex plane, or (b) lies on the unit ball of the complex plane, has multiplicity 1, and is a unit root. Let V be the set of all functions that are the maximum of finitely many functions in F. A function v is the value function of some MDP if and only if it is in V.

In this post I outlined one direction of the proof. Anyone who is interested in reading the construction that proves the other direction is referred to this paper.

]]>“…...modern microeconomists are more likely to spend their days knee-deep in large-scale data sets describing the real-world decisions made by millions of people, and less likely to be mired in Greek-letter abstractions.”

Knee-deep usually goes with shit, while mired with bog. I’ll pick bog over shit, but suspect that that was not Wolfers’ intent.

The recent paper by Chang and Li about the difficulty of replicating empirical papers does rather take the wind out of the empirical sails. One cannot help but wonder about the replicability of replicability studies. No doubt, a paper on the subject will be forthcoming.

Noah Smith on his blog wrote:

So the supply of both good and mediocre empirics has increased, but only the supply of mediocre theory has increased. And demand for good papers – in the form of top-journal publications – is basically constant. The natural result is that empirical papers are crowding out theory papers.

Even if one accepts the last sentence, the first can only be conjecture. One might very well think that the supply of mediocre empirical papers is caused entirely by an increase in the supply of mediocre theory papers whose deficiencies are glossed over with a patina of empirics. Interestingly, when reviewers could find nothing nice to say about Piketty’s theories they praised his data instead. Its like praising the author of a false theorem by saying while the proof is wrong, it is long.

The whole business has the feel of tulip mania. Empirical papers as abundant as weeds. Analytics startups as plentiful as hedge funds. Analytics degree programs spreading like herpes. Positively Gradgrindian.

“THOMAS GRADGRIND, sir. A man of realities. A man of facts and calculations. A man who proceeds upon the principle that two and two are four, and nothing over, and who is not to be talked into allowing for anything over.”

In empirical econ classes around the world I imagine (because I’ve never been in one) Gradgrindian figures laying down the law:

“Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of any service to them.”

I have nothing against facts. I am quite partial to some. But, they do not speak for themselves without an underlying theory.

]]>The results are similar to findings in other disciplines (the report refers to some of these). The top 10 departments place 5 times as many students in the top 20 departments as do those ranked 11 through 20. If you score a top 10 placement as +1, any other academic placement as a 0 and a non-academic placement as a -1, and then compute an average score per school, only one school gets a positive average score: MIT.

Chan also compares ranking of departments by placement with a ranking based on a measure of scholarly impact proposed by Glen Ellison. What is interesting is that departments that are very close to each other in the scholarly impact rating can differ quite a lot in terms of placement outcomes.

Read in tandem with the Card & Della Vigna study on falling acceptance rates in top journals and the recent Baghestanian & Popov piece on alma mater effects makes me glad not to be young again!

]]>According to Ms. Levy Tyller, the issue that bothers her most is coordination among the bidders. In a small country like Israel, in which everybody knows everybody else and have friends who know the rest, participants do their best to talk, exchange information, and dissuade others from increasing their bid. When the bidders are all present at the same hall, the auction turns into an oriental bazaar with a lot of psychological pressure on participants.

To overcome this difficulty, Ms. Levy Tyller assigns each participant to a different room and asks the participants to arrive to their designated rooms at different times. During the auction she moves with her team from one room to the next, informing each participant of the current highest bid and asking them whether they increase their bid. This is a slow process that requires the participants’ trust in the auctioneer, a trust that she gained with the dozens of auctions she had already organized.

What are the issues that affect the participants’ behavior? According to Ms. Levy Tyller, the expectation to win the auction and the tension that builds along the process causes the bidders to increase their bids. Pressure from other participants, on the other hand, hinders price increase.

Most winners are the calculated and level-headed participants. Anxious bidders who make plenty of noise usually quit before the end. Moreover, those who come prepared and know well the status of the auctioned item, tend to win more often.

At the end of our conversation Ms. Levy Tyller admitted that I was the first game theory consultant she ever met. I take it as a good sign: the utility function of game theorists puts higher weight to research and teaching than to consulting jobs. I am glad to be part of this group.]]>

Bush II:

I looked the man in the eye. I found him to be very straight forward and trustworthy and we had a very good dialogue.

Mike Rogers, GOP chairman of the House Intelligence Committee:

Putin is playing chess while Obama is playing marbles.

Sarah Palin:

Look it, people are looking at Putin as one who wrestles bears and drills for oil. They look at our president as one who wears mom jeans and equivocates and bloviates.

Rudolph Giuliani:

But he makes a decision and he executes it, quickly. Then everybody reacts. That’s what you call a leader.

If you think the comparison to Putin far fetched, here is Putin:

For the first time in the past 200–300 years, it (Russia) is facing the real threat of slipping down to the second, and possibly even third, rank of world states.

Now, compare with Trump’s slogan to make America great again.

]]>Using surge pricing to allocate transportation services — such as Uber does with its cars — raises consumer welfare through various potential channels, such as increasing the supply of those services, allocating them to people who desire them the most, and reducing search and queuing costs.

The correct answer to this question is: it depends. See below for the explanation. Back to the IMG panel. What is its purpose? According to the web site:

This panel explores the extent to which economists agree or disagree on major public policy issues. To assess such beliefs we assembled this panel of expert economists. Statistics teaches that a sample of (say) 40 opinions will be adequate to reflect a broader population if the sample is representative of that population.

Yes, but what is the underlying population? The IMG site does not say, instead it summarizes the cv’s of the sample:

The panel members are all senior faculty at the most elite research universities in the United States. The panel includes Nobel Laureates, John Bates Clark Medalists, fellows of the Econometric society, past Presidents of both the American Economics Association and American Finance Association, past Democratic and Republican members of the President’s Council of Economics, and past and current editors of the leading journals in the profession. This selection process has the advantage of not only providing a set of panelists whose names will be familiar to other economists and the media, but also delivers a group with impeccable qualifications to speak on public policy matters.

This is the high table of Economists, a group so select that the sample probably is the population. Why bother with the remarks about sampling?

How did the panelists respond to the surge pricing question? One strongly agreed with the statement but with a level of confidence of 1 (which I think is the lowest). This panelist also provided an explanation that makes clear that the reported confidence level was incorrect. Another, offers an `Agree’ with level of confidence of 3. Why not declare `uncertainty’? Or is the panelists trying to say: generally true but with some exceptions. The other responses suggest busy people trying to be helpful (recall Truman) on a task that is low priority for them.

Only one panelist provides an answer that can be interpreted as `it depends’. That panelist reports being uncertain with a level of confidence of 10. This panelist also provides an explanation:

`Consumer plus producer surplus should rise but in the absence of competition consumer surplus may not. With competition consumers will gain.’

Two make things concrete, consider a monopolist who faces two states of the world characterized by two demand curves: peak and off-peak, with off-peak state occurring most of the time. Now compare consumer surplus in two scenarios: same price in both states of the world, different price in each state. In which scenario will consumer surplus be higher? Which is a lovely intermediate micro question! In addition, if buyers are liquidity constrained, a price mechanism will not efficiently match rides to riders who value them the most.

I think the answer to the question posed reveals less about agreement on policy than the default assumption of the responder about the nature of the underlying market (passenger transportation).

]]>Returning to topic, the Economist piece I linked to above, gets it about right. With a fall in certain transaction costs, trades that were otherwise infeasible, are realized. At a high level there is nothing more to be said beyond what we know already about exchange economies.

A closer looks suggests something of interest in the role of the mediator (eBay, Uber) responsible for the reduction in transaction costs. They are not indifferent Walrasian auctioneers but self interested ones. eBay and Uber provide an interesting contrast in `intrusiveness’. The first reduces the costs with respect to search, alleviates the lemons problem and moral hazard by providing information and managing payments. It does not, however, set prices. These are left to participants to decide. In sum, eBay it appears, tries to eliminate the textbook obstacles to a perfectly competitive market. Uber, also does these things but more. It chooses prices and the supplier who will meet the reported demand. One might think eBay does not because of the multitude of products it would have to track. The same is true for Uber. A product on Uber is a triple of origin, destination and time of day. The rider and driver may not be thinking about things in this way, but Uber certainly must in deciding prices and which supplier will be chosen to meet the demand. Why doesn’t Uber allow riders to post bids and drivers to post asks?

]]>We must set funding priorities that ensure America remains first in the global marketplace of basic research and technological innovation, while preventing misuse of Americans’ hard-earned tax dollars. Unfortunately, in the past NSF has funded too many questionable research grants – money that should have gone to projects in the national interest. For example, how does the federal government justify spending $220,000 to study animal photos in National Geographic? Or $50,000 to study lawsuits in Peru from 1600 – 1700? Federal research agencies have an obligation to explain to American taxpayers why their money is being used on such research instead of on more worthy projects.

To ensure that the NSF is not profligate, the bill requires that each grant award

“be accompanied by a non-technical explanation of the project’s scientific merits and how it serves the national interest.”

Why stop with the NSF? Public education consumes an even larger share of my tax dollars. Why must I support the good for nothing offspring of my neighbors who grow up to be actors, musicians and worse, number theorists? If they want their children to be artsy-fartsy pseudo intellectuals they should do it on their own dime. Would be parents should be required to submit, a grant proposal justifying their desire for children. Each successful award should be accompanied by an explanation of how their child will serve the national interest.

]]>According the simulations in the New York Times, Kasich, Jindal, Fiorina, Graham and Pataki will most likely not make the cut. One of Perry, Christie and Santorum will by chance make the cut. Importantly, the alternative debate would not contain Trump. Or Cruz, who by some accounts has not left any part of Trump’s posterior unmoistened. Spun right, MSNBC could market their alternative debate as the one for grown ups while the official one would be for the children.

To make all this work, they should invite Kasich, Jindal, Florin, Graham, Pataki, Perry, Christie and Santroum now and ask for commitments before Fox announces it selections. For the three on the bubble, it gives them the chance to say no to Fox before being barred. This may be attractive to each of them. It might cause an unraveling of the Fox debate. Which debate would Bush, for example, prefer to be a part of?

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