Parental Illness and the Labour Supply of Adult Children

An important demographic trend is the aging of the population. As a result, demand for health care services for the sick and elderly is likely to increase. Since care for the sick and elderly is often provided informally by family members, parental illness may have important implications for the labour supply of adult children. Although previous studies show a negative relationship between hours worked and caregiving, they do not account for the potential endogeneity of the parental living arrangement to the child's labour supply. Using panel data and controlling for such endogeneity, I find that caregiving and cohabiting with a sick, elderly parent appear to have smaller effects on labour supply than the past literature suggests. Nonetheless, since cohabiting with a sick elderly parent does have negative effects on the labour supply of women and given that this form of living arrangement is relatively common, the aggregate costs associated with informal caregiving in an intergenerational living arrangement are considerable.aging; labour supply

Directed polymer near a hard wall and KPZ equation in the half-space

We study the directed polymer with fixed endpoints near an absorbing wall, in the continuum and in presence of disorder, equivalent to the KPZ equation on the half space with droplet initial conditions. From a Bethe Ansatz solution of the equivalent attractive boson model we obtain the exact expression for the free energy distribution at all times. It converges at large time to the Tracy Widom distribution $F_4$ of the Gaussian Symplectic Ensemble (GSE). We compare our results with numerical simulations of the lattice directed polymer, both at zero and high temperature.Comment: 7 pages 4 figures one paragraph and one reference adde

Commensurable continued fractions

We compare two families of continued fractions algorithms, the symmetrized Rosen algorithm and the Veech algorithm. Each of these algorithms expands real numbers in terms of certain algebraic integers. We give explicit models of the natural extension of the maps associated with these algorithms; prove that these natural extensions are in fact conjugate to the first return map of the geodesic flow on a related surface; and, deduce that, up to a conjugacy, almost every real number has an infinite number of common approximants for both algorithms.Comment: 41 pages, 10 figure