The impact of student loans on educational attainment: the case of a program at the pontifical catholic university of Peru

During the past decades, the Pontifical Catholic University of Peru (known as PUCP) has been giving student loans to some of its students with satisfactory academic performance but who face certain economic problems which might interrupt their studies. Although this program was created more than forty years ago, its results have not been rigorously evaluated. This document attempts to assess to what extent the program has benefited students. Because the collected data come from academic and social records, the completion of this task requires using modern techniques specifically designed to work with non experimental data. After estimating by propensity score matching with multiple treatments, I find a statistically significant impact of this program on the time a student employs to complete the course of study at PUCP (measured in semesters) only when a student was awarded with a loan for 6 semesters or more. That effect is not significantly different from zero when the loan lasts less than 6 semesters. Similar results were found when I analyzed the impact on the probability of degree completion of student loans, where students with loan were more likely to meet all graduation requirements by 6 years and a half after they start studying at PUCP. Again this effect was significant only when the student participates in the program for six semesters or more. However, the impact on that probability was small.Student Loans, Matching, Treatment Effect

Generalized Lyubeznik numbers

Given a local ring containing a field, we define and investigate a family of invariants that includes the Lyubeznik numbers, but that captures finer information. These "generalized Lyubeznik numbers" are defined as lengths of certain iterated local cohomology modules in a category of D-modules, and in order to define them, we develop the theory of a functor Lyubeznik utilized in proving that his original invariants are well defined. In particular, this functor gives an equivalence of categories with a category of D-modules. These new invariants are indicators of F-regularity and F-rationality in characteristic p>0, and have close connections with characteristic cycle multiplicities in characteristic zero. We compute the generalized Lyubeznik numbers associated to monomial ideals using interpretations as lengths in a category of straight modules, as well as provide examples of these invariants associated to certain determinantal ideals.Comment: 25 pages; comments welcom

A sufficient condition for strong FF-regularity

Let $(R,\mathfrak{m},K)$ be an $F$-finite Noetherian local ring which has a canonical ideal $I \subsetneq R$. We prove that if $R$ is $S_2$ and $H^{d-1}_{\mathfrak{m}}(R/I)$ is a simple $R\{F\}$-module, then $R$ is a strongly $F$-regular ring. In particular, under these assumptions, $R$ is a Cohen-Macaulay normal domain.Comment: 9 pages, to appear in Proceedings of the American Mathematical Societ