Correcting missing-data bias in historical demography

Abstract

Studies on population history are often based on incomplete records of life histories. For instance, in studies using data obtained from family reconstitution, the date of death is right censored (by migration) and the censoring time is never observed. Several methods for the correction of mortality estimates are proposed in the literature, most of which first estimate the number of individuals at risk and then use standard techniques to estimate mortality. Other methods are based on statistical models. In this paper all methods are reviewed, and their merits are compared by applying them to simulated and to seventeenth-century data from the English parish of Reigate. An ad hoc method proposed by Ruggles performs reasonably well. Methods based on statistical models, provided they are sufficiently realistic, give comparable accuracy and allow the estimation of several other quantities of interest, such as the distribution of migration times.

Keywords:

• parish registers
• lifespan
• missing data
• estimation
• bias correction
• imputation methods
• maximum likelihood method
• right censoring
• unobserved censoring time
• simulation study

Notes

1. M. A. Jonker and A. W. van der Vaart are at the Department of Mathematics, Faculty of Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, the Netherlands. E-mail: [email protected] and [email protected]

2. The authors were introduced to family reconstitution data by Richard Gill, who himself was drawn into the problem by Jim Oeppen from the Cambridge Group for the History of Population and Social Structure. The authors are statisticians, not demographers, and learned much about family reconstitution data in conversations with Jim Oeppen, who also kindly provided the data we used in Section 6. We also wish to thank Steven Ruggles for sending us parameter values for our simulation study in Section 5.