Reports

Advisory Editor:

I apologize for the delay in responding to this submission but I had great trouble finding suitable referees who would agree to write a report.

I have now received two reports from published experts on coordination problems involving monetary exchange systems. The two reports are found below.

As you will see, goth reviewers expressed difficulties with the model, which involves a finite horizon without discounting. They both suggest that this version of the model, while simple, is less realistic with regard to understanding the collapse of the baby-sitting co-operative and related implications for monetary policy. Both reviewers also had difficulty understanding the contributions of sections 6-8 (there are two sections 6).

Unfortunately, both reviewers recommend against publication. I think the objections of the referees are substantial as they go to the heart of the matter -the model- and so I think that even a major revision is unlikely to be successful. For this reason I must recommend rejection of the paper as well, but hope the author finds some benefit from the reviewers' comments.

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Reviewer #1:

The author discusses a new "model" for the baby sitting coop in which the time horizon is finite and no discounting occurs. Based on these assumptions the author derives different predictions than other authors studying the baby sitting coop. According to the authors, the benefit of the model—compared to previous work—is that it does not need sophisticated mathematics. Hence, by formulating simple equations, it makes predictions capturing the core of the baby sitting coop.

Major Issues

* Page 3, first paragraph: Conventionally, I would expect the first paragraph of a paper to briefly introduce into the paper and motivate the research question. The first paragraph of this paper, however, does not do this. In contrast, the first paragraph tries to do this and, thereby, gives a review of the related work in the field. Unfortunately, the paragraph fails to meet high standard. The citations are to general/slack (e.g. "... have provided a rigorous model which supports intuitive and anecdotal claim about the existence of an optimal..."). what is special about the modelling? What are the anecdotal claims confirmed? Thus, the paragraph failed to lead the reader in any direction.

* Page 3 and 4, introduction: The whole introduction misses structure. I would typically expect (after the first paragraph), a thorough motivation of the research question based on existing literature. Then a paragraph should follow which describes the results and contributions of the recent paper (probably extended by a paragraph telling the reader why reading the paper is worthwhile). The current manuscript mixes these components (motivation, contribution, related work, etc.) and often is too unspecific/imprecise to be comprehensive (some examples: "Since this is exactly the forte of behavioral economics, the problem has been studied in different contexts in many experimental studies. Duffy (2008) has provided an extensive survey of this literature." Why are these experiments relevant for this paper? What do the experiments show? "In this paper, we create a natural model of the BSC economy which has multiplesunspot equilibria" What is different in your model compared to

the existing ones? Why is your model better?). I would suggest to completely rewrite the introduction.

* Page 4, paragraph 3: You suggest a model with finite horizon and zero discount rate. I can see, that these assumptions simplify the analysis. But I do not see, how this makes the model more realistic or improves existing modelling in any way. Washington's Baby Sitting Coop (the baby sitting coop building the foundation of your related work) exists since 1950. Given that children need to be babysit for a maximum of 15 years, up to now 5 generations of parents used the service. From their perspective, it has an infinite horizon (It existed when they joined and left the cooperative). In my opinion, the same holds for every other bartering economy that I am able to think of.

* Page 4, paragraph 4: Why do you model the states of need "Z" and action "I" and then specify the utility of it (no matter in what combination) with 0. You should probably consider removing "Z" and "I" from your model in order to keep it simple and more comprehensible.

* Page 4, paragraph 4: What is "S" in "U(S|H) < U(S|L) < 0=U(S|Z)"? You never introduced it.

* Page 6, technical note: The last sentence of this paragraph captures the main issue of the paper (until this point): "Our treatment provides conceptual clarity with a minimum of mathematics". After reading the first two results I do not see the need of any mathematics to proof the tautology that excess supply exists, if more sell than buy (Identical criticism holds for section 4).

* Section 5: I do not get the benefit of this section. If it tries to relate your work to related literature, I would suggest to discuss the benefits of your (different) modeling first before discussing its consequences. As written above, I do not believe in your assumptions. More precisely, I assume that they make the models more unrealistic than those used in previous work. In addition, most results are not surprising (e.g., Subsection 5.1: Here you discuss recession in related work and make conclusions to your work. As your work does not allow for discounting, where should recession come from?).

* Section 6.1: I would love to have a discussion here, why Markov chains are adequate for the current model. As the game is finite, each new state (in each new period) differs from any previous state as the new period brings the decision maker closer to termination.

* Second Section 6: I do not get the benefit of this section. Please motivate what you do, why you do it and why I should read it.

* Sections 7 and 8: You intensively discuss the consequences of your model. However, I would have expected any form of mathematical reasoning. From my perspective, simplifying existing models and making obvious conclusions is not sufficient.

* Page 17, 18, references: The references of this paper are problematic. Of the 14 references, 7 are books or contributions to books, 1 a computer science conference and only 6 economic publications. The most recent reference is from 2008. I would suggest to do a thorough literature review. At the current state this is not the case.

Minor Issues

* Please add page numbers.

* Please check the paper for consistency (e.g. "co-ordination" and "coordination", ...)

* Check for typing errors. There are just too many errors to mention (E.g. p.3, "sunspotequilibra Our model", point missing; "cannot be solve" should read "cannot be solved"; ...).

* Two sections 6 exist. Please renumber them. All sections after Section 6 are numbered incorrectly (either inconsistent with the subsections or wrong).

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Reviewer #2:

This paper provides a new, more "natural" model of the Capitol Hill babysitting co-op (BSC) illustration of faulty monetary policy as first identified by Sweeny and Sweeny (1971) and later popularized by Krugman (2012). The author argues that many inferences made about monetary policy and behavior in this model are sensitive to assumptions and the equilibriumchosen. The author goes on to argue that different money supplies are akin to differentsunspot equilibria and serve only as coordination devices, and that flexible prices will not matter for whether the co-operative scheme succeeds or fails.

I found this paper challenging to read as it was never clear to me what the aim was aside from arguing that others are wrong about the fragility of monetary policy using the baby sitting co-op analogy. The lack of formalism of the ideas presented in this paper is a major limitation and not an advantage as the author seems to suggest.

As far as I can determine, the more "natural" model proposed by the author has fixed prices, a known finite horizon, no discounting and requires budget balance, so that each household has to produce babysitting services as many times at it consumes them.

This budget balance requirement, however, amounts to an exogenous enforcement mechanism that is both unnatural and completely counter to the decentralized nature of the babysitting exchange process. If we had such a centralized matching authority, there would be no role for money at all, so the author's changes, to my mind, assume away the problem of the optimal money supply.

Even more problematic is the issue of who enforces the budget balance requirement. Without enforcement, the whole notion that exchange will take place falls apart. For instance, in the known last period of the model, if I owe babysitting services, why should I provide them? Who can demand that I do so? By backward induction, services will never be provided. By contrast, with an infinite horizon, the shadow of the future can play a role that provides some discipline against such strategic behavior. But that type of mechanism is absent here. I contend that the budget balance enforcement requirement is more stringent, less natural and, contrary to the author's belief, it is unenforceable.

The implicit demographic structure underlying the author's version of the model is that all households have children at the same time and can thus all can cease with such services at the same time. However, this is not a natural either. A more realistic setting is an infinite horizon with overlapping generations of participants having children of different ages.

Given the limitations of the model, I do not find the observations made about behavior in the BSC relative to the existing literature to be very informative. In thinking about how the varioussunspot equilibria could be implemented, the paper reads more like a survey of related behavioral research than a paper making a sharp contribution.

Overall, I did not learn anything from this analysis. The paper is clearly below the bar for publication in GEB or any other mainline economics journal. I am sorry to say that I have little constructive to say due to my strong objection to the modeling approach.

Marginal decision making can help explain some otherwise puzzling eco-nomic phenomena. Here is a classic question: Why is water so cheap, while

diamonds are so expensive? Humans need water to survive, while diamonds

are unnecessary; but for some reason, people are willing to pay much more for

a diamond than for a cup of water. The reason is that a person’s willingness to

pay for a good is based on the marginal benefit that an extra unit of the good

would yield. The marginal benefit, in turn, depends on how many units a person

already has. Water is essential, but the marginal benefit of an extra cup is small

because water is plentiful. By contrast, no one needs diamonds to survive, but

because diamonds are so rare, people consider the marginal benefit of an extra

diamond to be large.

Diamonds and Water -- may relate to Kiyotaki Wright model