Fertility and self-control

The Beckerian theory of fertility decisions in the family is based on the rationality and self-control of the involved parties, which is in stark contrast of the Malthusian theory of population growth, which relies on people breeding without control. As so often, the truth lies somewhere in between, as it is clear people guide their fertility outcomes but their is a substantial stochastic element to it.

Bertrand Wigniolle reinterprets Becker's theory by adding lack of self-control in the for of hyperbolic discounting, that is, discounted values fall rapidly in the near future and more slowly for the distant future. Wigniolle uses a three period model with parents valuing number and quality of children. In period 1, they choose the number of children and pay time costs for rearing them. In period 2, they choose their education, and support the associated costs. In period 3, they only enjoy their children. Hyperbolic discounting implies that every period they regret some of their past choices. The model yields very different results depending on parameter values. If parents have grounds to invest in the education of their children, then fertility is lower due to the lack of self-control. Call this a developed economy. If parents have no reason to invest in education (say because its return is low), then fertility gets higher with hyperbolic discounting. Call this a developing economy. And this is very sensitive to parameter values. A further reason to push for more schools and opportunities to use human capital in developing economies.

Rent seeking in divorce

Divorce is breaking a marriage, and courts rule on the compensation of the involved parties. In countries where no-fault divorce is allowed, how compensation is allocated is very much dependent on the outside option of each party, particularly when negotiations happen without the involvement of a judge, who is then just a threat point. For example, when there is only consensual divorce allowed, the partner not seeking divorce has all the bargaining power. But when no-fault unilateral divorce is allowed, the roles are completely reversed.

Sietse Bracke, Koen Schoors and Gerd Verschelden study how the introduction of unilateral divorce changes outcomes in Belgium, where consensual divorce was already permitted. In particular they look at self-sacrifice, for example how some household member may specialize in home production and thus jeopardize her labor market potential and bargaining position in case of divorce, especially when there is no-fault unilateral divorce. Indeed, one can view this specialization as an investment in future rents from marriage, and divorce annihilates those.

To analyze this, the authors collected survey data from divorces in four cities for a year. Using alimony as a signal of bargaining power, they find that alimonies are higher or more likely for long marriages, for no-fault divorces, and when there is significant self-sacrifice. That would all be consistent by theory, but unfortunately these results are somewhat tainted by the fact that the law gives judges very similar directives for handling divorces outcomes.

Properly weighting social welfare functions

When it comes to evaluating optimal policies, one has to define a social welfare criterion. That is problematic as soon as there is heterogeneity. A popular criterion is Pareto Optimality, but this is a weak criterion in the sense that it is not very restricting. Or one can look at a political equilibrium, but this ignores how much people care about various policy outcomes. Another way that makes microeconomic theoreticians cringe is to add up the utility of everyone. They cringe because utility functions are only defined up to a Paretian transformation, and thus not comparable across individuals. But sometimes you have to find a way, and it is commonly assumed that all individuals have the same utility function, but potentially different utilities. Yet, adding utilities up has the drawback to the optimal policy will always be about equalizing income and consumption across individuals, because poorer ones have a higher marginal utility of consumption. But not all policies should be primarily about redistribution. The typical solution to this problem is to apply so-called Negishi weights, which essentially freezes the initial distribution of income, and thus allows to concentrate on the purpose on the policy.

Alexis Anagnostopoulos, Eva Carceles-Poveda and Yair Tauman offer a different solution to this problem. While Negishi amounts to weigh each individual by the inverse of her marginal utility at the maximal outcome, this results relies on the existence of complete markets. Under incomplete markets, the set of weights may be different. To give credit to the precise formulation of the problem, I quote the authors here:

We first define for every set of individual weights and for every social welfare function the contribution of every individual to the total welfare through the individual’s initial endowments. We then provide an axiomatic approach to the notion of the per unit contribution of every good and every individual, where the contribution of an individual to the total welfare is the total contribution of his initial endowments. We then define a set of individual weights to be proper iff the weighted utilities of every individual from this allocation are proportional to the contribution of the individual to the total welfare as defined by this set of weights.

The axiomatic approach consists of four axioms that characterize an elegant family of contribution mechanisms. The first axiom asserts that the per unit contribution should be independent of the units of measurement of the goods. The second asserts that if two (or more) goods play the same role in the welfare function, they should have the same per unit contribution. The third axiom asserts that if the welfare function can be broken into different components, then the per unit contribution of a given good is the sum of the per unit contributions arising from the different components. The last axiom guarantees that the per unit contribution is a continuous mapping with respect to an appropriate norm.

It is shown that every contribution mechanism that satisfies these four axioms is uniquely determined by a non negative measure on the unit interval. The selection of a specific contribution mechanism (or equivalently the selection of a specific nonnegative measure on the unit interval) determines for a given economy and a given set of weights a proper constrained efficient allocation and a proper set of weights.

This is a very exciting paper that should lay the foundation for a better assessment of policies than the silly adding up of utilities that is typically done.

Health cults in ancient Greece

Ancient Greece is a fascinating period as this is the start of the rational and scientific study of the world and many scientific principles were laid down. The Greek philosophers where in particular the first to think seriously about the role of institutions, markets and the functioning of government. In terms of health and medicine, we have all learned about the first attempts to explore and rationalize the human body, using a secular and scientific approach that was unparalleled until much later in history.

Carl Hampus Lyttkens points out that there was also a counter-movement where health care was leaning much more on religion. He also remarks that this is not unlike what we experience now with alternative medicine that has many followers and is even part of state sponsored health care in some countries. Calling these health cults, Hampus Lyttkens claims they arise because people are afraid of the uncertainties of life and cling to anything to reassure themselves. Just think about how many people believe in life after death while there is no scientific evidence for it. And healing cults are often, now and then, the realm of those who cannot afford the services of the scientific healers.

Peer effects in education

The reason parents try get their children in good schools is not because of the better teachers, it is because of the better class mates. If they are among stable, studious and ambitious students, they are expected to perform better in expected terms. (Of course there is also the tactic to send your kid to an inner-city school, where she outperforms the others and lands easy acceptances in colleges, with scholarships, if all goes right). But how much do these peer effects matter?

Eleonora Patacchini, Edoardo Rainone and Yves Zenou study the social networks of children in the AddHealth longitudinal survey and find that it is the very last years of high school that matter, but those years matter a lot as their impact is very persistent. Specifically, they observe that if a child's friends have the equivalent of two more completed high school educations, that child will get 3.5 months more education. But it would be good to know whether this dominates any effect from neighborhoods, which is taken into account but not reported.

On the decline of the US manufacturing wage

It is always interesting to see how real wages evolve, as they allow to understand how much a worker can buy from his income. Usually, this is done by dividing the nominal wage by a price index, usually the commodities said worker would typically buy. The results may vary considerably, as a different price index is needed for different workers, and the basket of goods may also vary over time. The latter is particularly important when the sample period is long. It also depends whether you look a hourly, weekly or annual income, and how benefits are included.

John Pencavel reviews a centuries old literature on the topic that came to the conclusion that except for some periods on stagnation, real wages generally were upward bound. He then comes up with his own indexing procedure, and finds that real wages in the US manufacturing sector have declined by 40% since 1960. Wow, this seems to be a real big result, and this requires understanding how this was computed. Indeed, Pencavel does not measure the real wage in the conventional way, but rather the ratio of what workers get to what they could get if the firm made no profit. This does not necessarily mean that the buying power of the worker has decreased by 40%. but rather that a smaller share of firm income goes to labor. With the increased mechanization of manufacturing, this evolution should not surprise many people. But this is not necessarily a 40% fall in real wages as advertised in the paper's abstract.

Using the WTO to overcome a prisoner's dilemma

It looks like the threat of competitive increases in trade tariffs has vanished, at least for the moment, as economies are getting back in shape. This episode highlighted how tariffs are part of a prisoner's dilemma: increasing tariffs is good for you, at least in the short term, as it gives more market share to local firms and/or more revenue to the state. But it hurts the foreign country, and if everybody does it, joint welfare is reduced because of the lower gains from exchange, the misallocation of productive resources and the loss of competitiveness of protected industries. It is precisely because of this prisoner's dilemma that the GATT (General Agreement on Tariffs and Trade) and then the WTO (World Trade Organization) were put in place.

Renee Bowen takes this reasoning further by looking a at a multilateral prisoner's dilemma, and interestingly the optimal institution that emerges looks very much like WTO's dispute settlement mechanism, in that countries cannot retaliate while a dispute is being settled. The key is that once a large enough number of countries participate in the WTO, the threat of sanctions is sufficient to obtain settlement and nobody is compelled to jump the gun with retaliations.