Ulpian's life 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.[5] 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.[6] Ulpian's life table gives figures broadly consistent with the Coale–Demeny Model West life table: 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.[7]

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 (i.e., the number of years elapsed before half the selected population is dead).[8] After childhood, the two figures are quite close, but childhood mortality causes the figures for the first years of life to diverge.[9] The figures given are too high to represent the predicted market value of the annuity at a conservative rate of return on capital (assuming the annual rate of 4%, the present value of an annuity for a person with a lifespan of sixty years would be approximately twenty-three times the annual value of the annuity, compared to 30 given in the table for the first group). 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.[10] 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.[11]

Frier states that 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.[12] Despite these errors, 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.[13] The picture the table presents 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.[14]

Keith Hopkins called the table not "demographically possible".[15] Richard P. Saller concluded that the table "includes too many schematic and unrealistic elements" to persuade him that it was "based on good data using appropriate demographic techniques".[16] Richard Duncan-Jones observes that the corresponding figure for Mauritius – a male life expectancy at birth of 32.25 – far exceeded the table figure of 21.11, as did all the corresponding readings from the Princeton South model life table. The implied reproduction rate under the table is accordingly very high, and perhaps higher than any rate observed in modern history.[17]

Duncan-Jones suggests that the subjects of Ulpian's table were largely slaves or ex-slaves. Ulpian's life table was produced to assess the value of bequests of maintenance annuities in money or in kind, and specifically for maintenance grants, which ceased on the death of the recipient. The beneficiaries of life annuities were typically members of the decedent's household, which meant slaves or ex-slaves.[18] Pliny the Younger's will, for example, supported 100 of his freedmen.[19] If Ulpian's table is empirical, it would reflect life expectancy of this population, to which it would have been applied. As such, its figures may be relatively plausible, if very crude.[20]

Digest 35.2.68, tr. S. P. Scott[21]

• Life annuity