Samurai in Brazil

Another cool TV commercial was made by CUPNOODLE. The Samurai in the movie is Kotaro TOKUDA, the world champion of the freestyle football!

Special CM featuring #10

A special TV commercial made by KIRIN BEER was broadcasted only on May 31, the last day of National Stadium (国立競技場). This CM features a Japanese football player Shinji Kagawa, the number 10 of our national team, whom I believe makes a big surprise in the FIFA world cup :) Go Shinji! Go Japan!!

Athey et al. (2005)

Original article (link) posted: 07/11/2005

Athey, Atkeson and Kehoe (2005) "The Optimal Degree of Discretion in Monetary Policy" Econometrica

The paper examines a monetary policy game in which the monetary authority has private information about the state of the economy. In the literature, two seminal papers, Taylor (1983) and Canzoneri (1985), established no discretion should be left to the monetary authority if there is no such private information; the best outcomes can be achieved by rules that specify the action of the monetary authority as a function of observables. The introduction of private information creates a tension between discretion and time inconsistency. Tight constraints on discretion mitigate the time inconsistency problem in which the monetary authority is tempted to claim repeatedly that the current state of the economy justifies a monetary stimulus to output. However, tight constraints leave little room for the monetary authority to time-tune its policy to its private information. In short, loose constraints allow the monetary authority to do that fine tuning, but they also allow more room for the monetary authority to stimulate the economy with surprise inflation.

Making use of dynamic mechanism design techniques, they find that the optimal mechanism is quite simple; for a broad class of economics, the optimal mechanism is static (policies depend only on the current report by the monetary authority) and can be implemented by setting an inflation cap, an upper limit on the permitted inflation rate. It is also shown that the optimal degree of monetary policy discretion turns out to shrink as the severity of the time inconsistency problem increases relative to the importance of private information.


Comment
The results they derive seem to be very interesting. In particular, the “inflation cap” result is directly related to the optimal inflation targets and has strong importance with actual monetary policies. As they mention, their work provides one theoretical rationale for the type of constrained discretion advocated by Bernanke and Mishkin (1997). This paper might become a must-read paper for those who work in monetary policies.


References
Bernanke and Mishkin (1997) "Inflation Targeting: A New Framework for Monetary Policy?" J. of Econ, Perspectives, 11
Canzoneri (1985) "Monetary Policy Games and the Role of Private Information" AER, 75
Taylor (1983) "Rules, Discretion, and Reputation in a Model of Monetary Policy: Comments" JME, 12

Echenique (2003)

Echenique, F. (2003), The Equilibrium Set of a Two Player Game with Complementarities is a Sublattice, Economic Theory, 22: 903-905.  Link 

Summary  I prove that the equilibrium set in a two-player game with complementarities, and totally ordered strategy spaces, is a sublattice of the joint strategy space.

It is widely known that in games with strategic complementarities (GSC), i.e., best reply correspondings are monotone increasing for all players, the set of pure-strategy Nash equilibria forms a non-empty complete lattice. This result implies the existence of smallest and largest Nash equilibria.

The current paper looks further into the structure of the equilibrium set of GSC, and shows that under certain restrictions the equilibrium set becomes not just a complete lattice but also a sublattice, as is written down in the Summary above.

The practical importance of this result, according to the author, is:

If the equilibrium set of a game is a sublattice, then we can find new equilibria from knowing that two profiles are equilibria, and by taking the componentwise join and meet of players’ strategies.

Note that we cannot obtain such strong property by a complete lattice structure alone. In this sense, a sublattice is indeed critical. The proof is extremely simple, which makes use of the observation that (a) when there are only 2 players and (b) their strategy spaces are completely ordered, (c) the other player's strategy must be completely ordered. The property (c) does not hold either (a) or (b) is not satisfied. Once (c) is verified, the rest of the proof is just to follow the definition of GSC.

My random thought: A sublattice property also arises in one-to-one two-sided matching markets (but neither in one-to-many nor many-to-many markets). I'm wondering if the idea of this paper can be somehow connected to the sublattice property of the set of stable matchings.

A final remark: A nicely written but a bit uninformative note.

Sotomayor (1996)

Sotomayor, M. (1996), A non constructive elementary proof of the existence of stable marriages, Games and Economic Behavior, 13: 135–7.  Link 

Abstract  Gale and Shapley showed in their well known paper of 1962 (Amer. Math. Monthly 69, 9–14) that stable matchings always exist for the marriage market. Their proof was constructed by means of an algorithm. Except for the existence of stable matchings, all the results for the marriage market which were proved by making use of the Gale and Shapley algorithm could also be proved without the algorithm. The purpose of this note is to fill out this case. We present here a nonconstructive proof of the existence of a stable matching for the marriage market, which is quite short and simple and applies directly to both cases of preferences: strict and nonstrict. 

In this short note, the author establishes the existence of stable matchings for the marriage market, i.e., one-to-one matching market, without employing any algorithms. Her key idea is a new concept that she calls a simple matching, which is defined as follows:

A matching is simple if, in the case a blocking pair (m, w) exists, w is single.

Since the set of simple matchings is nonempty and finite, there must exist a specific matching that I call here (for notational convenience) an M-simple matching:

A simple matching is M-simple if it cannot be (weakly) Pareto dominated for men by any other simple matching.

Then, she shows that such M-simple matching is stable. The basic logic is that the existence of blocking pair necessarily induces Pareto improvement for men (since w is single), which contradicts to the Pareto efficiency of M-simple matching for men.

As the author claims, the proof is very shout and simple, yet quite novel I think. To explain her proof strategy in a different way, she

1. focuses on the subset of stable matchings, 
2. characterize it by "M-simple matching," and
3. shows that the set is non-empty. 

It is immediate that M-simple matching is unique and coincides with M-optimal stable matching when all the preferences are strict. In this way, we can see that her idea is somewhat related to the existence of one-sided optimal stable matchings, a widely known result in the literature.

A minor remark: The definition of matching in the paper incorporates individual rationality, and consequently that of of stable matchings pays attention only on blocking pairs. This looks a bit non-standard while nothing is lost in her analysis.

A final remark: I like this paper very much :)

How did GS algorithm come out?

Roth, A. (2008), Deferred acceptance algorithms: history, theory, practice, and open questions, International Journal of Game Theory, 36: 537-569.

In this survey article on the Gale-Shapley's deferred acceptance algorithm, Al Roth mentions (in footnote 3) an amazing story about how GS discovered the algorithm (which of course established the theory of two-sided matchings):

At his birthday celebration in Stony Brook on 12 July 2007, David Gale related the story of his collaboration with Shapley to produce GS by saying that he (Gale) had proposed the model and definition of stability, and had sent to a number of colleagues the conjecture that a stable matching always existed. By return mail, Shapley proposed the deferred acceptance algorithm and the corresponding proof. 

IO Seminar (Rysman)

Original article (link) posted: 04/11/2005

Gowrisankaran and Rysman "Dynamics of Consumer Demand for New Durable Consumer Goods"

The paper proposes a dynamic model of consumer preferences for new consumer durable goods and estimates it. Consumers in their model are heterogeneous. They are assumed to choose between purchasing a current product and waiting for future products, making rational forecasts about the future distribution of prices and qualities. Two actual industries, DVD players and digital cameras are estimated.

Comment
The model seems to be attractive because it examines dynamic aspects and heterogeneity of consumers that have not been done successfully in the literature, although everyone agrees the importance. I am bit wondering if incorporating the uncertain of the future markets has serious effects to the estimated results or not. In their model, consumers fully know when and what kind of products will appear. However, if the future market is uncertain in the sense that consumers only know the probability distribution of future products, there might be an additional waiting value. That is, consumers may be better off by postponing their purchase to resolve uncertainty. This option value of waiting is known as "Real Option" in finance. In real world, the arrival of new products typically depends on the result of R&D investments which is presumably stochastic. So, even firms cannot exactly know the schedule of future products in many cases. Therefore, to incorporate future uncertainty is an important extension I think.

Review on "The New Geography of Jobs" (by Enrico Moretti)

I found a nice review on the following book written by Aaron M. Renn in his blog:

The New Geography of Jobs by Enrico Moretti

Aaron spells out quite a few suggestions and cautions on the materials, yet his last paragraph below clearly indicates appreciation of what this new book achieved:

Despite a few things I thought could have been more developed or stronger, I think that, as a book making the case for the innovation economy and what it means, The New Geography of Jobs is a strong one, and I again would suggest it to people in cities that have not yet fully found their place in the new century.

In Memory of Prof. Hayami

I found an interesting article (through this tweet by Prof. Sawada) about Prof. Yujiro HAYAMI, a leading agricultural/development economist who passed away last December:
"Death of a layman's economist" (by Prof. Abdul Bayes at Financial Express)

The article says:

Leaving aside for a moment his hundreds of technical articles published in reputed international journals, I shall take the privilege of citing from his famous book on development economics that I have mentioned before. Using the concept of Prisoner's Dilemma - when two persons convicted of a murder are kept in separate cells without one knowing what the other person is saying to the investigating officer - he illustrates how much loss the inability among people to establish cooperative relationship due to lack of communication and trust could generate for the society. This loss can happen in all economic transactions. "For example, in the transaction of a commodity, a buyer may try to reduce payment to a seller on the false charge of quality deficiency in delivered commodities. Then, the seller will deliver low-quality commodities thereafter. As their mutual distrust is heightened, they will stop transactions and thereby close off a mutually profitable business opportunity".

Prof. Hayami's famous book mentioned above is the following.

It is very interesting to know that Hayami has applied game theoretical ideas to his work on developmental studies. I should have tried to talk with him (Actually, Prof. Hayami was my colleague in GRIPS...)

Hayami cites another example regarding the costs of non-cooperation: "If employment is so insecure that employees may be discharged any moment, they would make little effort to acquire specific knowledge and skill for efficient work in his organisation. Their employer would then be inclined to discharge these employees for their lack of effort. In this way, cooperative relationship will not be established with the little accumulation of skill and knowledge needed for efficient functioning of this organisation". 

According to Hayami hypothesis, if mutual trust between particular individuals is thus elevated to a moral code in the society, huge savings would be made in transaction costs. If such cooperative negotiations could be guaranteed, business plans could be promoted ex-post much more flexibly and efficiently than by rigid ex-ante specification of contingencies, especially in long-term transactions subject to high risk and uncertainty. By and large, trust is a social capital that needs to be nurtured, if necessary, by structuring the cooperative relations into a hierarchical organisation. If mutual trust between workers and management ceases to work, the cost of monitoring and enforcing the contract would be large.

(made bold by yyasuda)

Uzawa-Equivalence Theorem

I found an interesting section in a nice intermediate textbook on General Equilibrium Theory by Ross M. Starr:




In Section 18.4 titled "Uzawa-Equivalence Theorem" shows the equivalence of two existence theorems:

1. The existence of equilibrium in an economy characterized by a continuous excess demand function fulfilling Walras' Law 
2. The Brouwer Fixed-Point Theorem

Interestingly, the two apparently distinct results are mathematically equivalent, which is originally shown by Hirofumi Uzawa (1962) in his short note: "Walras' Existence Theorem and Brouwer's Fixed Point Theorem." Economic Studies Quarterly, 8: 59-62.

The importance of the theorem is stressed by Prof. Starr as follows:

What are we to make of the Uzawa Equivalence Theorem? It says that use of the Brouwer Fixed-Point Theorem is not merely one way to prove the existence of equilibrium.  In a fundamental sense, it is the only way. Any alternative proof of existence will include, inter alia, an implicit proof of the Brouwer Theorem. Hence, this mathematical method is essential; one cannot pursue this branch of economics without the Brouwer Theorem. If Walras (1874) provided an incomplete proof of existence of equilibrium, it was in part because the necessary mathematics was not yet available.

The paper is included in this volume of Uzawa's collected papers. (I thank Prof. Kawamura for the information.)