Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument

Pension Policy: The Search for Better Solutions

Turner identifies the current problems facing pension policy for U.S. employer-provided pension plans and recommends solutions to those problems based on his examination of pension systems in other industrialized nations.https://research.upjohn.org/up_press/1027/thumbnail.jp

Longevity Policy: Facing Up to Longevity Issues Affecting Social Security, Pensions, and Older Workers

Turner argues that public policy should recognize longevity policy as a distinct policy area. Rather than separately treating issues raised by life expectancy (e.g., Social Security, pensions, older workers), a unified approach should be developed that recognizes their interrelationship.https://research.upjohn.org/up_press/1226/thumbnail.jp

Sustaining Social Security in an Era of Population Aging

John A. Turner offers a set of reforms for restoring solvency to Social Security that are deemed to have merit in the current political climate. These reforms relate to several vexing issues including increased life expectancy, the growing relationship between income and life expectancy, the declines in the physical demands of jobs, growing income inequality, and the pattern of poverty increasing at older ages.https://research.upjohn.org/up_press/1257/thumbnail.jp