Essays on Mechanism Design and Family Economics

Abstract

The first chapter, Criteria to compare mechanisms that partially satisfy a property: an axiomatic study introduces and axiomatize three criteria to be used as tools for making informed choices between mechanisms. In the illustrative example,we shift to the comparison of two matching mechanisms for school seat allocation: DA² and BOS², constrained versions of the Deferred Acceptance (DA) and Boston (BOS) mechanisms. These mechanisms are compared based on their stability with respect to the "stable" social choice correspondence. The comparison highlights the challenges of our first criterion, the Proportion criterion, in assessing stability. Even in this simplified setting, determining the proportion of stable equilibria for each mechanism involves complex clculations. The study then introduces the PHO and the PHO* criteria ($PHO for Profiles of Homogeneous Outcomes), which overcome the limitations of the Proportion criterion. The increased discriminatory power of $PHO$ allows for a clearer comparison of stability between DA² and $BOS^2$. The example is used to show that DA² performs better than BOS² in terms of stability according to the PHO criterion. The paper also establishes relationships between PHO and PHO*, enabling deductions about the relative performance of mechanisms based on these criteria. \\

The second chapter, Sex-Selective Abortions and Instrumental Births as the two faces of the Stopping Rule. New measures and world evidence, highlights the prevalence of the stopping rule in a large set of countries. This includes countries widely known for their strong preference for sons such as India, Bangladesh and Nepal, but also countries which are much less often mentioned in the literature like Armenia, Albania, Azerbaijan or Ukraine. These countries exhibit a wide range of gender preference biases, with desired sex ratios varying between 109 and 232, always significantly surpassing 'natural' sex ratios. We also show that instrumental births overwhelmingly contribute to the prevalence of the stopping rule, accounting for more than two-thirds of its impact. In stark contrast to previous studies that predominantly focus on sex-selective abortion, our comprehensive approach unveils a far more extensive influence of instrumental births. As expected, girls are consistently more likely to be instrumental. For instance, in Armenia, 64.5% of girls are considered instrumental compared to 25.3% of boys, and in India, the corresponding figures are 53.4% and 34.2%. Finally, a more detailed analysis within India reveals distinct patterns across states and social groups. Gender-biased preferences follow well-established caste hierarchies, with higher castes exhibiting stronger biases. For instance, among high castes, the desired sex ratio reaches an average of 246%, while among Muslims, it falls to 140%. \\

The third chapter, titled Stopping Rule and Girls Mortality: Insights from South Asian Nations, delves into the implications of the fertility consequences associated with the stopping rule, as explored in the preceding chapter, on the under-five mortality rate. Within this context, we define the mechanism involving the indirect impacts of the gender-biased stopping rule on health outcomes as 'passive discrimination'. The investigation reveals compelling evidence of substantial gender-specific differentials in the levels of intra-household competition experienced by boys and girls. Moreover, these disparities in competition intensity exhibit variations upon household characteristics, notably wealth. Concurrently, the study establishes a statistically significant influence of sibling competition on mortality rates. For instance, the findings show that in India, the presence of an additional sibling during the initial five years of a child’s life increase the likelihood of her death before the age of five by an average of approximately 12.61 percentage points. This effect is particularly pronounced within the poorest strata of the population. From these two estimations, we quantify the association between passive discrimination and female mortality. Over the period spanning from 1980 to 2015, the analysis attributes over 2,500,000 girl deaths in India directly to the passive discrimination mechanism. Analogously, the estimated figures for Bangladesh, Pakistan, and Nepal amount to 120,000, 90,000, and 25,000 respectively. These represent a substantial proportion of girls' deaths, with India facing an impact that accounts for up to 20% of under-five female mortality. As expected, most of these cases occur within the poorest segments of the population.

Date of Award	13 Sept 2023
Original language	English
Awarding Institution	University of Namur
Sponsors	University of Namur
Supervisor	Jean-Marie Baland (Supervisor), Guilhem Cassan (Co-Supervisor), Lorenzo Trimarchi (President), Siwan Anderson (Jury), Pauline Rossi (Jury) & Paula Gobbi (Jury)