Macroeconomic Consequences of Alternative Reforms to the Health Insurance System in the U.S.

This paper examines the macroeconomic and welfare implications of alternative re- forms to the U.S. health insurance system. In particular, I study the effect of the expansion of Medicare to the entire population, the expansion of Medicaid, an individ- ual mandate, the removal of the tax break to purchase group insurance and providing a refundable tax credit for insurance purchases. To do so, I develop a stochastic OLG model with heterogenous agents facing uncertain health shocks. In this model individ- uals make optimal labor supply, health insurance, and medical usage decisions. Since buying insurance is endogenous, my model captures how the reforms may affect the characteristics of the insured as well as health insurance premiums. I use the Medi- cal Expenditure Panel Survey to calibrate the model and succeed in closely matching the current pattern of health expenditure and insurance demand as observed in the data. Numerical simulations indicate that reforming the health insurance system has a quantitatively relevant impact on the number of uninsured, hours worked, and welfare.Health insurance reform, Heterogeneous agent model, Welfare analysis

Principal Boundary on Riemannian Manifolds

We consider the classification problem and focus on nonlinear methods for classification on manifolds. For multivariate datasets lying on an embedded nonlinear Riemannian manifold within the higher-dimensional ambient space, we aim to acquire a classification boundary for the classes with labels, using the intrinsic metric on the manifolds. Motivated by finding an optimal boundary between the two classes, we invent a novel approach -- the principal boundary. From the perspective of classification, the principal boundary is defined as an optimal curve that moves in between the principal flows traced out from two classes of data, and at any point on the boundary, it maximizes the margin between the two classes. We estimate the boundary in quality with its direction, supervised by the two principal flows. We show that the principal boundary yields the usual decision boundary found by the support vector machine in the sense that locally, the two boundaries coincide. Some optimality and convergence properties of the random principal boundary and its population counterpart are also shown. We illustrate how to find, use and interpret the principal boundary with an application in real data.Comment: 31 pages,10 figure

A Faster Algorithm to Build New Users Similarity List in Neighbourhood-based Collaborative Filtering

Neighbourhood-based Collaborative Filtering (CF) has been applied in the industry for several decades, because of the easy implementation and high recommendation accuracy. As the core of neighbourhood-based CF, the task of dynamically maintaining users' similarity list is challenged by cold-start problem and scalability problem. Recently, several methods are presented on solving the two problems. However, these methods applied an $O(n^2)$ algorithm to compute the similarity list in a special case, where the new users, with enough recommendation data, have the same rating list. To address the problem of large computational cost caused by the special case, we design a faster ($O(\frac{1}{125}n^2)$) algorithm, TwinSearch Algorithm, to avoid computing and sorting the similarity list for the new users repeatedly to save the computational resources. Both theoretical and experimental results show that the TwinSearch Algorithm achieves better running time than the traditional method