Ulpian's life table is an ancient Roman annuities table. It is known through a passage, originating from the jurist Aemilius Macer, preserved in edited form in Justinian's Digest. The table appears to provide a rough outline of life expectancy in the early third century CE, but it is not clear what population the life table refers to, or how its data was gathered.
Aemilius Macer probably lived in the 230s CE. His recording of the table came from Macer's systematic commentary on the lex Julia de vicesima hereditatium, an Augustan law of 6 CE that put a 5 percent tax on inheritances. Despite its many numbers, the fragment does not appear to be afflicted by any serious textual corruption.
Table
Macer's text provides two figures: a forma, or schedule, presented by Ulpian (d. 223), and a customary (solitum est) schedule that antedates Ulpian's. The forma is described as a means of calculating tax for alimenta and usufructs. The age of the legatee is checked against the table; the figure recorded on the table is multiplied by annuity's annual value. Five percent of this last figure is what is owed in tax. Ulpian's life table gives figures broadly consistent with the Model West: female life expectancy at birth is 22.5 years, male life expectancy is 20.4. Its mortality figures are thus higher than those of most models, though the statistical flaws in the evidence itself has encouraged interpretative caution.
Although, among moderns, "life expectancy" tends to mean "the average number of years lived after age x", the table figures probably represent median life expectancy: the number of years elapsed before half the selected population is dead. After childhood, the two figures are quite close, but childhood mortality causes the figures for the first years of life to diverge. The figures given are too high to represent the predicted market valueB of the annuity at a conservative rate of return on capital (on the calculation in the table, a person with a lifespan of sixty years would only have twenty-three years worth of annuity at death). The table therefore most likely represents the rate at which the annual tax payment on the annuity was staggered: a 5% tax was paid on each annual payment received by the legatee until the tax office had received the figure produced by the table. If the legatee died before the median age, leaving part of the tax unpaid, the tax would either be forgiven (out of sympathy for the family so bereaved) or added on to the tax fees of the legatee's heir.
The table does not plausibly represent life expectancy either in early childhood, between forty and fifty, or after sixty. This may be because these ages were difficult for the creators of the table to handle, or because they may have been easily ignored; children do not often receive annuities, for example. But, in spite of these errors, and although Keith Hopkins called the table not "demographically possible", the table corresponds well to other observed populations with abnormally high mortality rates (such as postwar Mauritius), and to a priori constructions of plausible Roman age structures. In any case, the picture they present is appalling: a society with one of the highest mortality rates on record, with a predicted life expectancy at birth of between 19 and 23.