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The author describes a model for estimating and projecting the populations of communities living in small areas within cities. The model provides a means of updating the demographic inputs needed for projection between censuses and means of developing scenarios of demographic change and housing development. The method for estimating small-area populations between censuses is evaluated with recently published 1991 Census data. Single-year age-group detail is provided and the associated databases are embedded in a flexible user interface. Illustrative projections are discussed and interpreted for the northern English city of Bradford.

The form in which migration information is likely to be provided from the 1991 Census is reviewed, and suggestions are made about how this provision can be improved for the academic research community, building on the experience of the 1981 Census. The recommendations add considerable value to the information at relatively low cost.

People live in many regions and move between those regions over time. These facts have been incorporated into demographic analysis via the subfield of multiregional mathematical demography. In this paper the author reviews themes in that subfield over the past two decades and discusses current issues that have yet to be resolved.

Accounting frameworks developed in the field of economics are applied to the problem of measuring changes-in-state of populations. Examples of accounts in the educational sector, in the job market, and in a regional system are described. Proper estimation of multistate demographic accounts involves attention to data sources, much initial estimation of variables, construction of a model to estimate missing items, and use of the possible constraints on the accounts matrix. These steps in accounts estimation are illustrated for a set of accounts for British regions for 1970–1976. Data are assembled for a base period, 1970–1971. Alternative methods of constructing accounts are tested by running the estimation model in projective mode for 1971–1976. One method is selected and used to complete the set of accounts.

The paper examines the problem of the estimation of the correct probabilities needed as input to a multiregional life table. A variety of alternative methods are examined by use of an expanded notation and a hypothetical test case. This theoretical investigation suggests that methods proposed by previous researchers are in error and an alternative method is proposed. However, this error is likely to be small in cases where the probabilities of transition from one region to another are small.

In the first part of the paper a general classification of migration measures is introduced. The rates corresponding to these measures are defined together with the associated populations at risk. A particular problem in migration analysis is then tackled. The questions asked in the British censuses of 1966 and 1971 about migration generate tabulations of migrants over the one year, and over the five years, preceding the census date. It is often observed that the numbers of migrants in the two periods are not linearly related; that is, the number of migrants over five years is less than five times the number over one year. A simple stochastic model embodying population-accounting principles is developed to show why this is the case, and that the relationship between one-year and five-year figures is a complex one involving some multiple migrations, some return migrations, and some deaths.

A revised notation is developed in which the accounting and model relationships that characterize multiregional population systems can be expressed. The variable K represents population as a stock, as a flow, and as an event count. People move from one state and location to another state and location over time. A special set of location—state labels for variable K describe the transitions possible. The hope is expressed that the notation will contribute to fruitful synthesis in the field of spatial demography.