Reading Journal
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to learn how to avoid being deceived by the economists
Two‑Sided Matching with Indifferences: Using Heuristics to Improve Properties of Stable Matchings 2022.10.20
This paper considers improvement on traditional Deferred Acceptance (DA) Algorithm with respect to wider set of potential allocation, and purposes the use of heuristic algorithms for calculating solutions to the general Two-Sided Matching problem. Based on the allocation provided by DA, AMRO or FE, Genetic Algorithm (GA) and a Threshold Accepting (TA) algorithm are applied to generate a consequent allocation. The paper evaluates characteristics of the latter allocation based on number of matched pairs (NUM), average matched rank (AMR), and fairness. As for the indifferences, the paper applied the tie-breaking rule for indifferences and used the Worker-Optimal-Stable-Matching (WOSMA) which considers Pareto-improvements for one side (in their case called workers) for incomplete preferences to develop further discussion of the number of matched pairs.
Overall, for both complete and incomplete preferences with indifferences, matchings found by the studied heuristics have improved properties for the respective goal in most of the studied cases. For complete preferences with indifferences, GA improved AMR. For incomplete preferences, GA improved NUM. In both case, fairness is improved.
This paper applied WOSMA to focus on matched pairs, but it may be possible to apply Efficient-Stable-Matching-Algorithm (ESMA) which considers Pareto-improvements of both sides for improving average matching ranks for either or both sides.
(My presentation of this paper can be found here.)
PROMISES AND PARTNERSHIP 2021.11.18
Charness, G., & Dufwenberg, M. (2006). Promises and Partnership. Econometrica, 74(6), 1579–1601.
This paper aims at researching the impact of communication on motivation and behavior. The researchers designed a one-shot principal–agent trust game with hidden action, in which the agent is free to exert less effort due to unobservable effort to the principal. Then, the concept of guilt aversion is introduced, a guilt-averse player suffers from guilt to the extent he believes he hurts others relative to what they believe they will get, and the sensitivity of guilt are measured by asking players to guess the payoff of the counterpart. The main guilt-aversion hypothesis of the paper is that, exert effort is more common in message treatment and coinside with higher “guesses”.
Results show a strong correlation between B’s second-order beliefs and behavior, the likelihood of both parties to exert effort, which is in accordance with guilt aversion hypothesis and contrary to the null hypothesis of no relationship between B’s beliefs and behavior, as supposed by the cheap talk theory. Besides the success in predicting the outcome in this game, guilt aversion is also more generally adaptable than fixed cost of lying in explaining selfless choice in scenarios that lying do not occur, or decision makers do not suffer if they lie.
The conclusion, promises (or statements of intent) sent from agents to principals enhance trust, cooperation, and efficiency, seems common. However, the paper did not clearly distinguish between guilt aversion and moral expectation. That is, to avoid harming others, and to do what is expected to do. There may exist some causal relationship or interconnection between the two. Also, manipulating guilt aversion for certain purposes is possible in this game and worth researching.
(My presentation of this paper can be found here.)
The Impact of Divorce Laws on Marriage-Specific Capital 2022.12.11
The paper examines investment decisions of couples in their first 2 years of marriage using 1970 and 1980 censuses of the US, takes states that change their divorce laws as treatment group with those in states that do not as control group, and compares changes in the behavior (female labor force participation, full-time labor market work by both spouses, supporting a spouse’s investment in education, children, and home ownership) of newlyweds.
Based on the trend of adopting unilateral divorce, this paper argues that influences of decreased divorce cost on decreasing incentive to invest in marriage-specific capital is fourfold. Firstly, with higher divorce rate, spouses benefit less from marriage-specific capital, reducing the incentive to invest jointly. Secondly, changes in divorce laws are followed by changes in bargaining power and likely by changes in marital investment decision. Thirdly, divorce laws can shape the ability to commit to the distribution of future investment payoff. Fourthly, to strategically go against divorce law changes, it is possible to overinvest today to constrain future selves to prefer to remain married than to divorce. On the other hand, unilateral divorce laws may increase the incentive to invest as a precommit to not divorcing, which should lead to increasing symmetric investment that increases the value of marriage in future, with little effet on asymmetric, intertemporal investments.
Results show that comparing to the treatment group, the control group is 10% less likely to be supporting a spouse through school, 8% more likely to have both spouses employed in the labor force full time and are 5% more likely to have a wife in the labor force. Finally, they are about 6% less likely to have a child. The exception is home ownership, where the removal of fault in property settlements appears to encourage home ownership in the early years of a marriage.
A Treatise on the Family 2022.12.10
- chapter 2
This chapter discusses the fundamental reason of marriage and the benefits, as well as the limitation on the size of the family.
Firstly, the purpose of the family is to ensure comparative advantage is made to its fullest, which is “determined partly by biological differences and partly by different experiences and different investments in human capital [Becker, 1991, p. 30].” Even when there is no obvious comparative advantage, if there is differnt initial endowment, and “if commodity production functions have constant or increasing returns to scale, all members of efficient households would specialize completely in the market or household sectors and would invest only in market or household capital [Becker, 1991, p. 35]”. Terefore, Labor division will lead to two n-person household form a single 2n-person union for the benefits from labor division and specialization in the allocation of time and in the accumulation of human capital.
However, the merging is not endless, because people still value privacy and fairness of labor division. Therefore, the upper bond is created by dishonesty and shrinking or cheating of duties, which increases with the specialization and division of labor within families. Here, privacy is regarded as a goods whose marginal utility is positive, then its price is the marginal benefit of expansion. It constraints the unlimited expansion of family to the equilibrium, with the optimal degree of specialization and privacy determined. This restricts the size of family and not all the n’s will combine to be 2n’s. (privacy as agood is discussed in Posner, 1979)
Finally, this chapter defines marriage as a a long-term commitment between a man and a woman: “Since married women have been specialized to childbearing and other domestic activities, they have demanded long-term “contracts” from their husbands to protect them against abandonment and other adversities ([Becker, 1991, p. 50].”
Marriage: Past, Present, Future? 2022.12.16
This article talks about the meaning and benefits of marriage from a biological, or reproduction, perspective. As marriage guarantees the husband sexual access to his wife, and given people’s preference for children with kinship (proven by Becker in A treatise of the Family, Cpt. 5), marriage is used as a legal method for the husband to ensure the production of children and paternity presumption. Consequently, as marriage constrains the freedom of the female and provides fatherhood for the male, males can be regarded as buyers while females are sellers, which provides a theoretical basis for bride-price. It also explains the female marry-up (hypergamy): females give up cuatodial rights against a compensation, resulting in a female-marrying-up equilibrium.
Although it is mentioned that “bride-price has been absent from individual consent regimes (Edlund, 2006, p. 10)”, what happens in China is that males have to pay about 10,000 yuan (USD 1,600) to 135,000 yuan (USD 21,170).
Also, the quote of Trivers[1972] for Bateman principle – male reproductive success is limited by partner access, while female reproductive success is limited by resource availability – may be reversed in the reality. With the improving environment for female lablor participation and the elimination of gender income gap, female have been competing among themselves for members of the opposite sex as well as food, whereas males compete for resources as food and social status. In this scenario, we would expect women to be buyers and men to be sellers on the sex market. That is, female (on average) gradually become better at providing food and thus the choosier ones. This may explain increasing position of the women’s in the modern days.
School Choice: A Mechanism Design Approach 2022.12.17
The paper first analyzed the differences between one-sided school choice and two-sided college admission and then introduced two completing mechanisms, the Gale-Shapley student optimal mechanism and the top trading cycles mechanism. Finally, the paper raised optimal applications for each: the former for complete elimination of justified envy before full efficiency, and the latter for stability, ensuring students who have high priorities for their local schools are all guaranteed seats that are at least as good, provided that they truthfully report their preference. The method of separating the ethical quotas to different schools with unacceptable students of each is especially inspiring.
There are several possible extensions of the paper. Firstly, in the reality, there exist students who become unsatisfied after enrollment and wish to transfer. Concerning meeting children’s “individualized needs”, schools should leave some quota unfilled for the possibilities. Then, how should we allocate the students who wish to transfer? To solve it on a case-by-case basis, is it optimal to repeat the current algorithms, or even some new algorithm is needed? How will the welfare in the secondary rematching market be? Secondly, is there any possibility of an optimal mix strategy under the Columbus student assignment mechanism? Can they maximize their payoff, or expected payoff, by strategically manipulating their preferences? It may also be possible to derive a model that measures the welfare for the families side, the school side, and the market as a whole.
A Design for College and Graduate School Admission 2022.12.17
The paper designs a mechanism for graduate school admission, which is fair (if for any student A and B, A prefers school S which admits B but not A, then S must rank A higher than B), non-wasteful (if for any student A who prefer school S that does not admit A, then S must have met its quota), individually rational (for any student A, being match is better than not going to school), strategy-proof (for any student A, the outcome of reporting real preference is better than reporting strategy preference) and Pareto efficient (for any student A, there does not exist another matching that is Pareto improvement).
The paper also criticized the parallel application for students being placed in worse-off colleges and consequent efficiency loss and concluded that a single-time, ununiform admission mechanism would always result in utility loss for the school and the student unless every student is admitted by most preferred schools. In the reality, according to the paper, strong institutions start admission exams in March while weak ones start in April. Furthermore, the earlier weak institutions send acceptance to students, the more utility loss it suffers. Therefore, acknowledging that institutions are unable to set a uniform time for sending admissions, the author suggests that the strongest school can declare the time of admission, and the second strongest, after observing the decision of the first, declares consequently.
However, in Japan, the timeline of institutions sending admission acceptance is Waseda the first, Keio the second, and Tokyo University the third. Moreover, every acceptance requires a commitment fee before true enrollment is kept valid. As a result, some students would pay three times, with their utility loss of the additional expenditure (keeping the acceptance, or withdrawing it and waiting for later schools). Whether the contradiction is due to cultural differences or historical reasons is worth thinking about.
Endogenous insurance and informal relationships 2022.12.17
The article proves that heterogeneously risk-averse individuals who fact exogenous risk can match with each other against risk and benefit risk-averseness: a less risk-averse individual provides more value by informally ensuring a more risk-averse individual. This is following the Coase Theorem where the party whose cost to reduce loss is lower should take responsibility and the modal hazard problem where the risk is shifted from the risk-averse party to the risk-neutral counterpart. This paper also raises the opinion that a risk-reduction policy is not a Pareto improvement but the more risk-averse agents are worse off after the implementation.
However, the work still can be enriched as follows. Firstly, in the reality, types of agents are not distinguishable at the first glance. Furthermore, as the development is a long-term process, the game is likely to be played over again. Therefore, misunderstanding may take place at the first step, and as the writer has suggested, dynamic rematching may be possible after the first mismatch. Whether the potential loss would encourage more risk-averse agents’ selection is worth discussing.
Moreover, one benefit of an informal relationship is that it does not evolve the cost of decommitment. That is, people may lack incentive in terms of long-term investment because it is easy to break the commitment and re-match with another agent. In the article, the payoff is determined instantly. Therefore, expanding the short-term to long-term may drive another equilibrium, and provide more applicable policy implications: to what extent should public institutions provide formal risk protection, and if the currently developed countries should also leave more space for informal, endogenous commitment to take place.
Relational contracts for household formation, fertility choice and separation 2022.12.19
The paper built a model about relational contract concentrating on the fertility decision, which is captured as the decision to have children. The core assumption in this model is that, children is raised as public goods, but the second earner has to bear the cost of raising, while the first earner enjoys the utility from children and transfer some income as a compensation to maintain the sufficient condition for remaining a marriage. The efficient outcome is reached household’s marginal benefit of the public good equals to its marginal costs, which consist of child care costs plus loss of human capital to the second earner.