At adult ages x, the force of mortality increases more or less exponentially with age, and the parameter associated with age, ?, can be used to gauge the rate of senescence (ageing) of a generation. The hypothesis has recently been advanced that the rate of senescence at the individual level may be a biological constant, not far from 0.1. This article contributes to this discussion in two ways: first, it proposes a simple method based on standard longitudinal panel data analysis to compare the rate of senescence ? between different cohorts and groups when frailty and period effects operate, and, secondly, it offers a few empirical estimates of ?, by gender, for various cohorts, in different countries. The proposed methodology is applied to data taken from the Human Mortality Database for selected birth cohorts (Denmark, Finland, Norway, Sweden, and Switzerland), born between 1878 and 1912, observed at ages 65 to 98, in the calendar years 1943 to 2010. The rate of senescence ? appears indeed to be close to 0.1: most of the differences that emerge from the analysis (by country, gender, birth cohort or age), although statistically significant, are very small in absolute terms, especially for women.