Part
ii
a
measurement
error
model
for Estimating the Population Sizes of Preindustrial Cities
Institute for
Research on WorldSystems
University of
California, Riverside
112502
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
Builtup 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 NonResidential Area
Ø
Total Number of Families
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 Builtup 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.
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 unutilized 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usually found as estimates in historical documents or is calculated by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.
The
NonResidential 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.
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
London 1800 
Total Population Estimate 
Range of Total Population Estimate (all variables) 
3.9 per family 
967,645 
948,150 – 974,732 
4.1 per family 
1,017,267 
948,150 – 1,017,267 
Table 1: Number of People per Family (London 1800
comparison)
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 
Priene 
207m2 
Abdera 
161m2 
Kassope 
210m2 
Dur Eruopos 
256m2 
Karanis 
75.2m2 
Olynthus 
289m2 
Pompeii 
271m2 
Herculaneum 
241m2 
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]
Decade 
London Area** 
Chandler Est.* 
Bairoch Est.* 
BrettJames Est.* 
Galley Est.* 
Avg. per Hectare 
1600 
1166 
187 
200 
250 
200 
214.41 
1650 
1713 
410 

350 

204.32 
1700 
2333 
550 
575 
527 
575 
225.89 
* Population
estimates in thousands
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 onestory houses, six twostory houses, and three threestory 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) p168171.
[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) p168173.