Part ii

a measurement error model for Estimating the Population Sizes of Preindustrial Cities

Institute for Research on World-Systems

University of California, Riverside


Daniel Pasciuti


To create a Measurement Error Model for estimating the population of cities requires multiple indicators to compute available estimates that are common to all urban areas. Using these various factors will allow us to create a working model that includes variable estimates that are unique for each city and specific standard estimates that remain constant in the model.


The variable indicators include:

Ø      Area of the City within the Wall

Ø      Built-up Urban Area of the Whole City

Ø      Total Residential Area

Ø      Total Number of Residential Hearths in the Urban Area

Ø      Total Number of Houses in the Urban Area

Ø      Total Non-Residential Area

Ø      Total Number of Families


Area of the City within the Wall:

                This is one of the most common estimates to be found on cities throughout history. Cities throughout the Afroeurasian Region have commonly used walls to surround and protect the city and its inhabitants from invasions and environmental disasters with many cities having concentric rings of walls built over time. It is also one of the easiest and most distinctive remnants of a city that can be identified by archaeologists.


The Built-up Urban Area of the Whole City:

This is a much harder estimate to account for since this includes the urban area outside the walls of the city. This area is usually a poorer or industrial section of the city where the inhabitants of the city either cannot afford to live within the current city walls or are not wanted within the walls due to pollution or noise.


Total Residential Area

            This includes only the residential buildings in the urban area and the total space they take up. This does not include the roads or other un-utilized living space around the residential housing such as open squares or water wells.


Total Number of Residential Hearths in the Urban Area

            This is another common estimate that can be found in archaeological work done on cities based on the distinctive residue a domestic hearth leaves behind in soil. This can also be sometimes found in historical records taken for census or tax purposes as in the case of the 1691 Hearth Tax in Edinburgh.

Total Number of Houses in the Urban Area

            The number of houses in the urban area makes up the total residential area and is usually found as estimates in historical documents or is calculated by archaeologists and demographers from the number of domestic hearths in the city.


Total Non-Residential Area

            The Non-Residential Area includes all religious and military buildings that make up the city as well as the total area that is taken up by roads, sewers, baths, and other space not specifically used for residential space including vacant spaces.


Total Number of Families

            The number of families in a city provides a counter estimate to the total number of homes in an urban area and was commonly used in early censuses done in cities.


The specific indicators are calculated to be the averages within an urban area and include:

Ø      Average Number of People per Dwelling

Ø      Average Number of Families per Dwelling

Ø      Average Number of People per Family

Ø      Average Size of Dwellings

Ø      Percentage of Residential Area to Total Area

Ø      Average Population Density of the Whole City

Ø      Average Population Density of the Residential Area



Average Number of People per Dwelling

             This number is an estimated standard from Alston (2002) who calculated an average of 5.40 – 5.52 people per house. Others, like Dingwall (1994) and Adamson (1981), use an average of 4.5 per house while Galley uses an average of 6.1.


Average Number of Families per Dwelling

This average is estimated to be 1.4 families per house in urban areas from Alston (2002).[1]  This is supported by the 1.5 families per house when averaging the 1.96 families per dwelling from the 1801 census of London and the 1.07 families per dwelling for 1638 by Finlay (1981).


Average Number of People per Family

            The number is represented in a range from 3.9 to 4.1 people per family. An average of 4.1 people per family was reached from the 4.09 per family found in North London from the 1801 census. When multiplied by the 1.4 families per dwelling this reaches 5.74 people per house. The other end of the range is estimated by dividing the 5.5 people per house estimate by the 1.4 families per house to achieve an average of 3.9 people per family. While the range of variation appears very small, any change in the estimate affects the overall population estimate. In a comparison of the model of London for 1800, the estimate of 3.9 per family became an average total population estimate in the model while using the 4.1 became the high total population estimate. See Table 1. Using the 3.9 per family constant creates only a four-percent variance in population estimates while using 4.1 for the constant creates a seven-percent variance in population estimates for the model.


London 1800

Total Population Estimate

Range of Total Population Estimate (all variables)

3.9 per family


948,150 – 974,732

4.1 per family


948,150 – 1,017,267

Table 1: Number of People per Family (London 1800 comparison)


Average Size of Dwellings

The Average Size of Dwellings is computed by two measures. First the average total floor area of the dwelling and then divided by the average number of stories per dwelling.

The average total floor area was estimated using the standard dwelling sizes of several cities, calculated by Alston in Table 2[2], to compute an average dwelling size for all cities of 214 meters squared per house. The average number of stories per house is estimated at two from Alston (2002) [3] and Hobson (1985)[4].

This then creates an average of 107 meters squared, 214 meters squared of total floor area divided by an average of two stories, when calculating the total residential area in an urban area from the number of houses in the urban area.


City Name

Avg. Floor Area

City Name

Avg. Floor Area







Dur Eruopos










Table 2: House Sizes by Alston (2002)


Percentage of Residential Area to Total Area

This estimate has been derived using the estimates generated from London in 1650, 1681, and 1700 where the total residential area consistently accounted for 49 percent of the total urban area[5]. This matches estimates by others including Bagnall (1993) who used an estimate of 50 percent residential when looking at Hermopolis[6].


Average Population Density of the Whole City

This is one of the most common estimates used to estimate city sizes and has varied greatly depending on who is doing the research. The estimate reached for the model was computed by taking the average density from several population estimates to the total urban area of London in Table 2 to reach an average of 214 per hectare and rounded up to 250 for the model.[7]


London Area**

Chandler Est.*

Bairoch Est.*

Brett-James Est.*

Galley Est.*

Avg. per Hectare






















* Population estimates in thousands

** London area in hectares

Table 3: Average Density per London Hectare 


Average Population Density of the Residential Area

An average of 500 persons per hectare for the residential area is estimated. This was calculated from the results of the 1801 census and the 1639 census of London, which found an average of 490.41[8] and 498.46[9] people per hectare within the walled area respectively. This also matches the total of doubling the average per hectare for the total area (Since the total residential area accounts for 49 percent of the total area).


This then creates a total of 14 individual factors for our measurement error model to use when estimating the population of a city. Seven of the factors are fixed estimates that remain constant in the model and are used in conjunction with the other seven variable estimates that are unique for the specific city being used in the model. The model then is divided into four groups while allowing variables to cross between the groups to fill in for any missing information. The use of four groups of variables allows for a range of four estimates to be calculated and therefore not rely on a set estimate for the population.
By combing all of the factors into one we create a measurement error model of the following:





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[1] Alston (2002) p70

[2] Alston (2002) p53 on House Sizes.

[3] Alston (2002) p59. According to Alston the number of stories varies between 1 and 4 in an urban area with some exceptional cases as high as 7 stories for one house in Alexandria. He considers about 40% of urban housing being two stories with the average house to be two stories.

[4] Hobson (1985) p217 Hobson is looking at houses in Karanis where she found three one-story houses, six two-story houses, and three three-story houses in a represenative sample to reach an average of two stories per house.

[5] While this estimate appears to hold for English cities it did not hold for Hermopolis in 275CE. However the estimate of 120 hectares for the area reached by Delia may either be short of the total area or may represent only the area contained by the wall and not the total urban area. (Requires further research into Hermopolis)

[6] Bagnall (1992) p53. While Bagnall uses an estimate of 50 percent for Hermopolis he uses this to determine an estimate of 115 houses per hectare and 87 meters squared. The 87 meters squared per house does not match the average household reached here using Alston (2002).

[7] Hermopolis does not support the use of 250 per hectare but this may be due to the questionable total area computed by Delia.

[8] This estimate came from the 1801 census and the total area within the walls form Finlay (1981) p168-171.

[9] This estimate came from totaling Appendix 3 for the total area within the walls and from the total population in 1631 in Appendix 4. Finlay (1981) p168-173.