The senescence of generations across time and space

At adult ages x, the force of mortality increases more or less exponentially with age, and the parameter associated with age, Beta, can be used to gauge the rate of senescence (ageing) of a generation. The hypothesis has recently been advanced that, with rare exceptions, the rate of senescence at the individual level is constant through space and time, and not far from 0.1.
We contribute to this discussion in two ways: first, we propose a new and simpler method to estimate the rate of senescence Beta when frailty and period effects operate, and, secondly, we offer a few empirical estimates for Beta, for various cohorts, in different countries (all data taken from the Human Mortality Database). The transformation that we suggest leads to a linear estimation, which is considerably simpler than all the others we are aware of, characterized by non-linear equations, numerical recursive likelihood maximization, etc.
Our estimates of the rate of senescence Beta are all very close to 0.1, but most of the differences that we detect (e.g. by country) are statistically significant, and there appears to be a decreasing trend of Beta over time.