SNZ Summary Profile for Information about the Life Tables

Life table definitions
Life tables are one of the basic demographic tools for analysing mortality. They are a tabular numerical representation of mortality and survivorship of a cohort at each age of life.

Period (or current) life tables relate to the mortality experience of a population over a short period of time (eg 1995–97). These life tables commence with a hypothetical cohort of newborn babies and assume that they experience the observed age-specific mortality rates of a given period. Complete life tables are constructed from single year of age data, while abridged life tables are constructed from grouped age data.

Cohort (or generation) life tables relate to the mortality experience of a designated group (eg persons born in a given year) over their lifetime. Cohort life tables are rarely constructed because of the difficulties in obtaining appropriate historical data over many years. However, New Zealand is one of few countries with relatively complete and detailed demographic data sources back to the late 1800s. This has enabled the painstaking compilation of detailed historical birth, death and migration data to produce life tables for each birth cohort (people born in each year) from 1876.
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New Zealand cohort life tables
Complete cohort life tables at the national level have been constructed which track the mortality experience of the New Zealand population born in each year from 1876. More information, including a detailed technical report and tables, are freely available from the Statistics NZ website: Cohort life tables.

New Zealand period life tables
Complete period life tables at the national level are constructed every five years. These tables, which are based on data for a three-year period centred around each census year, are produced separately for the Mäori, non-Mäori and total New Zealand male and female populations. The latest tables are for the period 2005–07 and were released via a Hot Off The Press (Cat 31.913) on 10 November 2008.

Complete period life tables for the Mäori and total New Zealand male and female populations are available from 1950–52. Complete period life tables for the non-Mäori male and female populations are available for various periods from 1880–92. Life tables from 1934–38 are available from the Statistics NZ website: Period life tables.

Abridged period life tables, based on data for the most recent three-year period centred around a non-census year, are constructed for the total population only. They provide an indication of the trends in life expectancy in the years between the construction of complete period life tables. Abridged period life tables are available in February (provisional) and May (final) after the reference period, via the Statistics NZ website: Abridged period life tables.
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Subnational period life tables
Abridged period life tables are constructed for subnational areas every five years. These tables, which are based on data for a three-year period centred around each census year, are produced separately for the male and female population of each area. The latest subnational period life tables are for the period 2005–07 and are available for all 16 regional council areas and 40 of the 73 territorial authority areas of New Zealand (boundaries at 30 June 2006). These territorial authority areas have death and population numbers sufficient to produce abridged life tables. Note, however, that standardised death rates are available for all regional council and territorial authority areas. Nevertheless, because of fluctuations in death and population numbers, and the migration of people between geographic areas, all subnational mortality measures should be interpreted with caution.

Period	Deaths measure	Population measure⁽¹⁾
2005–07	Deaths registered in New Zealand of people resident in each area.	Estimated resident population of each area at 30 June 2006 (based on census usually resident population count of each area at 7 March 2006).
2000–02	Deaths registered in New Zealand of people resident in each area.	Estimated resident population of each area at 30 June 2001 (based on census usually resident population count of each area at 6 March 2001).
1995–97 revised	Deaths registered in New Zealand of people resident in each area.	Estimated resident population of each area at 30 June 1996 revised (based on census usually resident population count of each area at 5 March 1996).
1995–97	Deaths registered in New Zealand of people resident in each area.	Estimated resident population of each area at 30 June 1996 (based on census usually resident population count of each area at 5 March 1996).
1990–92	Deaths registered in New Zealand of people resident in each area.	Census usually resident population count of each area at 5 March 1991.

(1) For more information on different population concepts and measures refer to:

Population Counts and Estimates Overview

Population Counts and Estimates Fact Sheet

Population Terms Standard

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Mäori and non-Mäori period life tables
From 1995–97, Mäori and non-Mäori period life tables were constructed using data from the new birth and death registration forms introduced in September 1995. The ethnic concept used in the 1995–97, 2000–02, and 2005–07 period life tables is the ethnic group or groups that people identify with or feel they belong to. Ethnicity is self-perceived and people can belong to more than one ethnic group. For example, people may identify with the Mäori ethnicity even though they may not be descended from a Mäori ancestor. Conversely, people may choose to not identify with the Mäori ethnicity even though they are descended from a Mäori ancestor. Ethnicity does not equate to a birthplace description.

Mäori and non-Mäori period life tables from 1995–97 are not directly comparable with earlier life tables because of conceptual differences between data from the old and new death registration forms. Users should also be aware of numerator-denominator differences in period life tables before 1995–97.

Period	Ethnic concept	Deaths measure	Population measure⁽¹⁾
2005–07	Mäori period life tables based on deaths of people with Mäori ethnicity and the population of Mäori ethnicity. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables. Both the Mäori and non-Mäori period life tables make an allowance for deaths and population with no ethnic response.	Deaths registered in New Zealand of people resident in New Zealand.	Estimated resident population at 30 June 2006 (based on census usually resident population count at 7 March 2006).
2000–02	Mäori period life tables based on deaths of people with Mäori ethnicity and the population of Mäori ethnicity. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables. Both the Mäori and non-Mäori period life tables make an allowance for deaths and population with no ethnic response.	Deaths registered in New Zealand of people resident in New Zealand.	Estimated resident population at 30 June 2001 (based on census usually resident population count at 6 March 2001).
1995–97 revised	Mäori period life tables based on deaths of people with Mäori ethnicity and the population of Mäori ethnicity. Non-Mäori period life tables based on deaths and population not included in the Mäori life tables. Both the Mäori and non-Mäori period life tables make an allowance for deaths and population with no ethnic response. An adjustment made to Mäori/non-Mäori deaths for undercount of Mäori deaths using the adjustment ratios presented in Ajwani (2003).	Deaths registered in New Zealand of people resident in New Zealand.	Estimated resident population at 30 June 1996 revised (based on census usually resident population count at 5 March 1996).
1995–97	Mäori period life tables based on deaths of people with Mäori ethnicity and the population of Mäori ethnicity. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables, including deaths and population with no ethnic response.	Deaths registered in New Zealand of people resident in New Zealand.	Estimated resident population at 30 June 1996 (based on census usually resident population count at 5 March 1996).
1990–92	Mäori period life tables based on deaths of people with any degree of Mäori blood and the population of Mäori ethnicity. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables, including deaths with no indication of the degree of Mäori blood and population with no ethnic response.	Deaths registered in New Zealand of people resident in New Zealand and people visiting from overseas.	Census usually resident population count at 5 March 1991.
1985–87	Mäori period life tables based on deaths of people with 'half or more Mäori blood' and the population of 'single ethnic response' Mäori. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables, including deaths with no indication of the degree of Mäori blood and including population with no ethnic response.	Deaths registered in New Zealand of people resident in New Zealand and people visiting from overseas.	Estimated de facto population mean year ended 31 December 1985–87 (based on census night population count at 4 March 1986).
1980–82 revised	Mäori period life tables based on deaths of people with 'half or more Mäori blood' and the population of 'half or more Mäori blood'. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables, including deaths and population with no indication of the degree of Mäori blood. No adjustment made to Mäori/non-Mäori deaths for undercount of Mäori deaths.	Deaths registered in New Zealand of people resident in New Zealand and people visiting from overseas.	Estimated de facto population mean year ended 31 December 1980–82 (based on census night population count at 24 March 1981).
1980–82	Mäori period life tables based on deaths of people with any degree of Mäori blood and the population of 'half or more Mäori blood'. Deaths with any degree of Maori blood were used as a proxy adjustment for the undercount of Mäori 'half or more' deaths. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables, including deaths and population with no indication of the degree of Mäori blood.	Deaths registered in New Zealand of people resident in New Zealand and people visiting from overseas.	Estimated de facto population mean year ended 31 December 1980–82 (based on census night population count at 24 March 1981).
1975–77	Mäori period life tables based on deaths of people with 'half or more Mäori blood' and the population of 'half or more Mäori blood'. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables, including deaths and population with no indication of the degree of Mäori blood.	Deaths registered in New Zealand of people resident in New Zealand and people visiting from overseas.	Estimated de facto population mean year ended 31 December 1975–77 (based on census night population count at 23 March 1976).
1970–72	Mäori period life tables based on deaths of people with 'half or more Mäori blood' and the population of 'half or more Mäori blood'. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables, including deaths and population with no indication of the degree of Mäori blood.	Deaths registered in New Zealand of people resident in New Zealand and people visiting from overseas.	Estimated de facto population mean year ended 31 December 1970–72 (based on census night population count at 23 March 1971).
1965–67	Mäori period life tables based on deaths of people with 'half or more Mäori blood' and the population of 'half or more Mäori blood'. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables, including deaths and population with no indication of the degree of Mäori blood.	Deaths registered in New Zealand of people resident in New Zealand and people visiting from overseas.	Estimated de facto population mean year ended 31 December 1965–67 (based on census night population count at 22 March 1966).
1960–62	Mäori period life tables based on deaths of people with 'half or more Mäori blood provided that the remaining blood is European or Polynesian' and the population of 'half or more Mäori blood provided that the remaining blood is European or Polynesian'. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables, including deaths and population with no indication of the degree of Mäori blood.	Deaths registered in New Zealand of people resident in New Zealand and people visiting from overseas.	Estimated de facto population mean year ended 31 December 1960–62 (based on census night population count at 18 April 1961).
1955–57	Mäori period life tables based on deaths of people with 'half or more Mäori blood provided that the remaining blood is European or Polynesian' and the population of 'half or more Mäori blood provided that the remaining blood is European or Polynesian'. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables, including deaths and population with no indication of the degree of Mäori blood.	Deaths registered in New Zealand of people resident in New Zealand and people visiting from overseas.	Estimated de facto population at 30 June 1956 (based on census night population count at 17 April 1956).
1950–52	Mäori period life tables based on deaths of people with 'half or more Mäori blood provided that the remaining blood is European or Polynesian' and the population of 'half or more Mäori blood provided that the remaining blood is European or Polynesian'. Non-Mäori period life tables based on deaths and population not included in the Mäori period life tables, including deaths and population with no indication of the degree of Mäori blood.	Deaths registered in New Zealand of people resident in New Zealand and people visiting from overseas.	Estimated de facto population at 30 June 1951 (based on census night population count at 17 April 1951).

(1) For more information on different population concepts and measures refer to:

Population counts and estimates overview

Population counts and estimates fact sheet

Statistical standard for population terms

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Changes to birth and death registration forms
In September 1995, new birth and death registration forms were introduced carrying a revised question on ethnicity. Previously the ethnic question on the death registration form asked for the degree of Mäori or "Pacific Island" blood, if any, of the deceased person's parents. The new ethnic question is the same, in principle, as the questions used in the 1996 Census, instructs the respondent to "tick as many circles as needed to show which ethnic group(s) deceased belonged to". This has resulted in a number of changes:

the ethnic concept is now self-identified ethnicity (previously Mäori and Pacific respondents were classified by their 'degree of blood')
ethnic vital statistics are now available for a wider range of ethnic groups (previously information was sought only for Mäori and Pacific groups)
ethnic data is now directly available for newborn babies and the deceased (in both cases this was previously derived from ethnicity of one or both parents)
multiple response to the ethnicity question is now possible (previously the degree of Mäori or Pacific blood, but not both, could be identified)
non-response to the ethnicity question can now be quantified.

In the case of births and deaths, ethnicity is identified by the person completing the registration form. For births this is usually the parent(s), while for deaths this is most likely to be the funeral director (on the advice of a family member).
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Availability and comparability of ethnic period life tables
Statistics NZ has produced period life tables for the Māori and non-Māori populations in addition to period life tables for the total New Zealand population. Following the introduction of new birth and death registration forms in September 1995, Statistics NZ has also evaluated the production of life tables for other ethnic groups such as Asian and Pacific. However, official life tables for other ethnic groups have not been produced because of the relatively small size of these ethnic populations, relatively few death registrations, and uncertainty associated with ethnic identification and measurement. For example, a person's ethnic identity can change over time and between different data collections, depending on the respondent and the context of collection. Hence, Statistics NZ is not yet confident that life tables provide a statistically robust measure of the mortality and survival experience of these ethnic populations for a given period (eg 2005–07) or over time (eg between 2000–02 and 2005–07), other than for Māori and non-Māori. All ethnic mortality measures, including those for Māori and non-Māori, should be interpreted with due caution.

Customised and non-official life tables for the Pacific and 'European or Other (including New Zealander)' ethnic groups are available on request from Statistics NZ. For more information and quotes email demography@stats.govt.nz.

There is evidence that Māori deaths were significantly under-reported, and hence non-Māori deaths were over-reported, before the new vitals registration forms were introduced in 1995. Following the redesign of the forms, death registrations and population data are broadly comparable for ethnic groups. The 1995–97 Māori and non-Māori life tables published in July 1998 were the first to be constructed using data derived from the new registration forms. However, because numerator-denominator ethnic differences are significant before 1995–97, ethnic mortality measures from 1995–97 are not comparable with those from earlier years. For alternative estimates of life expectancy of different ethnic populations before 1995–97, see Ajwani (2003). Note, however, that these estimates may not be directly comparable to mortality measures produced by Statistics NZ because of differences in both the deaths numerator and population denominator.
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Information on period life tables before 1995–97

Publication title	Publication date	Catalogue number
Life Tables 1990-92	April 1994	03.301
Life Tables 1985-87	June 1991	03.301
New Zealand Life Tables 1980-82	April 1986	02.301
New Zealand Life Tables 1975-77	November 1979	02.301
New Zealand Life Tables 1970-72	June 1975
New Zealand Life Tables and Life Annuity Tables 1965-67	December 1969
Population Census, 1961, New Zealand Life Tables 1960-62	October 1965
Population Census, 1956, New Zealand Life Tables 1955-57	1960
Population Census, 1951, New Zealand Life Tables, 1950-52 and Values of Annuities	1953
Population Census, 1936, Life Tables	1944

x	Exact age (eg exact age 5 corresponds to 5 years and 0 days).
l_x	Number of people alive at exact age x from the original group of 100,000 (l₀).
L_x	Average number of persons alive in the age interval x to x+ 1.
d_x	Number of deaths in the age interval x to x+ 1.
q_x	Probability that a person at exact age x dies within a year.
₅q_x	Probability that a person at exact age x dies within 5 years.
p_x	Probability that a person at exact age x lives another year.
₅p_x	Probability that a person at exact age x lives another 5 years.
₅m_x	Central death rate for population in the age group x to x+ 5.
₅s_x	Proportion of population in the age group x to x+ 5 surviving another 5 years.
e_x	Expected number of years of life remaining at exact age x.

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Methodology of New Zealand complete period life tables, 1995–97 to 2005–07
The data used to construct the 1995–97 (revised), 2000–02 and 2005–07 period life tables comprised:

deaths registered in New Zealand of people resident in New Zealand in the December years 1995–97, 2000–02, and 2005–07, respectively, by single-year of age, sex and ethnicity.
live births registered in New Zealand to mothers resident in New Zealand in the December years 1994–97, 1999–2002 and 2004–07, respectively, by sex and ethnicity.
the estimated resident population of New Zealand at 30 June 1996, 30 June 2001 and 30 June 2006, respectively, by single-year of age, sex and ethnicity.

Deaths numerator
The period life tables are compiled from deaths registered, rather than deaths occurring, in each respective three-year period. Most death statistics refer to registrations rather than occurrences for a given time period, because of the time lag between when the death occurred and when it is registered. Hence, the number of death registrations can be confirmed before the number of death occurrences for a given time period. For periods of a year or more, the difference between registrations and occurrences is generally small, so death statistics referring to registrations are suitable for most purposes.

Ethnic birth and death data from the new registration forms were not available for the entire three-year period 1995–97. To ensure consistency of data over the 1995–97 period, ethnic vital statistics for 1995 were estimated using the age-sex-ethnic distribution of vitals data for 1996 and 1997. An allowance for ethnic non-response among deaths was also made. There was no response to the ethnicity question for about 2.4 percent of deaths in 1996–97, 3.5 percent of deaths in 2000–02, and 4.9 percent of deaths in 2005–07.

Because deaths in the first year of life are skewed towards the early part of this age, infant death rates were calculated from more detailed data. This involved the division of the first year of life into more detailed ages.
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Population denominator (exposed-to-risk population)
Usually the mean population of each period is used as the denominator to calculate death rates. However, mean population estimates are not available for all ethnic populations. To ensure consistency of method among all population subgroups, the estimated resident population at 30 June (the midpoint) of each period was used. The impact of using 'midpoint' rather than 'mean' population estimates is generally insignificant.

The estimated resident populations at 30 June 1996, 30 June 2001 and 30 June 2006 were based on the census usually resident population counts at 5 March 1996, 6 March 2001 and 7 March 2006, respectively, and adjusted for:

non-response to the census ethnicity question
net census undercount
residents temporarily overseas on census night
births, deaths and net migration between census night and 30 June of the census year
reconciliation with demographic estimates at ages 0–9 years for 1996 and 2001, and 0–4 years for 2006.

The 1996 Census asked people to "Tick as many circles as you need to show which ethnic group(s) you belong to". The census usually resident population count of 3,618,303 included 523,371 who identified with the Mäori ethnicity and 151,713 who gave no specific ethnic response. The 1995–97 life tables use as a population denominator the estimated resident population of each ethnicity of New Zealand at 30 June 1996. New Zealand's estimated resident population of 3,732,000 included 573,000 who identified with the Mäori ethnicity.

The 2001 Census asked people "Which ethnic group do you belong to? Mark the space or spaces which apply to you". The census usually resident population count of 3,737,277 included 526,281 who identified with the Mäori ethnicity and 150,546 who gave no specific ethnic response. The 2000–02 life tables use as a population denominator the estimated resident population of each ethnicity of New Zealand at 30 June 2001. New Zealand's estimated resident population of 3,880,000 included 586,000 who identified with the Mäori ethnicity.

The 2006 Census asked people "Which ethnic group do you belong to? Mark the space or spaces which apply to you". The census usually resident population count of 4,027,947 included 565,329 who identified with the Māori ethnicity and 167,784 who gave no specific ethnic response. The 2005–07 life tables use as a population denominator the estimated resident population of each ethnicity of New Zealand at 30 June 2006. New Zealand's estimated resident population of 4,185,000 included 624,000 who identified with the Mäori ethnicity.

Because of changes to the census ethnicity question between 1996 and 2001, the 1996, 2001 and 2006 population estimates for ethnic groups are not necessarily comparable. Nevertheless, the derived mortality measures presented here are considered to give a statistically satisfactory description of Mäori and non-Mäori mortality experience during the 1995–97, 2000–02, and 2005–07 periods. Note that all population estimates used in the 1995–97, 2000–02, and 2005–07 life tables have been derived using the same methodology. In addition, the ethnicity question used in the 1996 Census is the same as that used in birth and death registration forms from September 1995. The use of population estimates based on the 1996 Census also allows the adjustment ratios presented in Ajwani (2003) to be incorporated.

For more information about the estimated resident population, refer to "Information about the population estimates".
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Derived rates
The period life tables were based on deaths averaged over three years. This is designed to reduce the impact of year-to-year statistical variations, particularly at younger ages where there is a small number of deaths and at very old ages where the population at risk is small. In some cases the New Zealand data does not enable death rates to be reliably estimated at all ages. For most ages above 90 years, death rates of the total New Zealand population have been modelled on the mortality trends of other countries such as Australia, Canada, Japan, United Kingdom and United States. At the older ages it is assumed that the rate of change in q_x(probability of dying within a year) decreases linearly with increasing age. For the Mäori and non-Mäori populations, death rates have also been modelled at some younger ages.

There are some small observed numerator-denominator ethnic differences since 1995 in comparison with 1996, 2001 and 2006 census data. For the 2000–02 and 2005–07 life tables, these estimated differences are not significant enough to reliably adjust death numbers by age, sex and ethnicity. For the 1995–97 life tables, the smooth adjustment factors presented in Ajwani (2003) have been applied to Mäori deaths by age to allow for under-reporting of Mäori deaths (relative to the Mäori population). The adjustment factors range from 0.94 (ie a deflation in deaths) at age 0 years to 1.14 at ages 20–24 years. For the non-Mäori period life tables, corresponding adjustments have been applied to non-Mäori deaths by age. These adjustment factors affect Mäori life expectancy at birth by about 0.7 years and non-Mäori life expectancy at birth by about 0.1 years. The 1995–97 period life tables for the total New Zealand, Mäori and non-Mäori populations published in July 1998 have therefore been revised. For all populations the revision also incorporates updated population estimates (at 30 June 1996) and a revised method of estimating death rates at the oldest ages.

The construction of each complete period life table involved two stages. First, the central death rates (m_x) were calculated for each age (x), except the first year of life, and were then smoothed to eliminate any apparent irregularities. Second, the smoothed rates were used to calculate a set of age-specific probabilities of death (q_x), which were then used to derive other life table functions. The derivation of the mortality rate in the first year of life differed from all other ages and required special formulae as detailed below in Age 0 years.
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Age 0 years
The probability of dying in the first year of life (q₀) required special treatment because infant deaths are skewed towards the early part of this age. The first year of life was divided into eight minor age intervals (n):

less than 1 day
from 1 day to less than 2 days
from 2 days to less than 7 days
from 1 week to less than 4 weeks
from 4 weeks to less than 3 months
from 3 months to less than 6 months
from 6 months to less than 9 months
from 9 months to less than 12 months.

For each of these age intervals the values of q₀(n), l₀(n) and d₀(n) were calculated. The following examples show the formula for calculating q₀(n) for two of these age intervals for 2005–07 where the denominator reflects the exposed-to-risk population:

For n = 3
For n = 5

where, for example:

		probability of dying between 4 weeks and 3 months of life
		live births in 2007
		live births in the fourth (December) quarter of 2007
	k	is an adjustment for deaths and migration made to the denominator to exclude those persons in the original birth cohort who died in an earlier age interval, and to allow for the effect of net migration, in order to give the correct 'exposed-to-risk' population

The values of q₀(n) were then used to calculate l₀(n) and d₀(n):

Given		the radix of a life table
then		for = 2, 3,..., 8

		for = 2, 3,..., 8

and

The value of L₀ was calculated as follows:

		for = 1, 2,..., 7
		where

where w(n) is the weight given by the fraction of the year covered by the age interval (n). For example, for n = 6:

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Age 1 year and over
The central death rates (m_x) were first calculated for each single year of age by dividing the average annual deaths of New Zealand residents for the period by the estimated resident population at the midpoint of the period. For 2005–07:

Some minor refinement of data was made in the very old ages, above 90 years, to offset the effects of age misreporting and small death numbers. The central death rates derived from actual data also showed minor fluctuations across other ages. To minimise these fluctuations the rates were smoothed using a cubic spline method. The smoothed central death rates were then used to calculate the corresponding values of q_xfor each age using the equation:

Each series of q_x was tested to ensure that the deviations between the actual and expected deaths were minimal. The values of q_x were then used to derive the remaining life table functions:

		the radix of a life table




		where h is the highest age of a given population group

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Supplementary functions for five-year age groups
In addition to the main life table functions, the following supplementary functions for five-year age groups have been calculated for 2005–07:

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Methodology of subnational abridged period life tables, 1995–97 to 2005–07
The data used to construct the 1995–97 (revised), 2000–02 and 2005-07 subnational abridged period life tables and standardised death rates comprised:

deaths registered in New Zealand of people resident in each area in the December years 1995–97, 2000–02, and 2005–07, respectively, by age groups (0, 1–4, 5–9, 10–15, ... , 80–84, 85 and over) and sex
live births registered in New Zealand to mothers resident in each area in the December years 1995–97, 2000–02, and 2005–07, respectively, by sex
the estimated resident population of each area at 30 June 1996, 30 June 2001, and 30 June 2006, respectively, by age groups (1–4, 5–9, 10–15, ... , 80–84, 85 and over) and sex.

Deaths numerator
The period life tables were compiled from deaths registered, rather than deaths occurring, in each respective three-year period. Most death statistics refer to registrations rather than occurrences for a given time period, because of the time lag between when the death occurred and when it is registered. Hence, the number of death registrations can be confirmed before the number of death occurrences for a given time period. For periods of a year or more, the difference between registrations and occurrences is generally small, so death statistics referring to registrations are suitable for most purposes.

An adjustment for address non-response among deaths was made. There was no response to the address question for 0.0 percent of deaths in 1995–97, 0.2 percent of deaths in 2000–02, and 0.5 percent of deaths in 2005–07.
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Population denominator (exposed-to-risk population)
The estimated resident population of each area at 30 June (the midpoint) for each period was used as the denominator to calculate death rates. The estimated resident populations at 30 June 1996, 30 June 2001, and 30 June 2006 were based on the census usually resident population counts at 5 March 1996, 6 March 2001, and 7 March 2006 respectively, and adjusted for:

net census undercount
residents temporarily overseas on census night
births, deaths and net migration between census night and 30 June of the census year
reconciliation with demographic estimates at ages 0–9 years.

For more information about the estimated resident population, refer to "Information about the population estimates".
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Derived rates
The period life tables were based on deaths averaged over three years. This is designed to reduce the impact of year-to-year statistical variations, particularly at younger ages where there may be a small number of deaths and at very old ages where the population at risk may be small. In some cases the subnational data does not enable death rates to be reliably estimated at all ages.

The construction of each abridged period life table involved three stages. First, central death rates (m_x)were calculated for each age interval, except the first year of life. Second, the Brass logit system was used to smooth age-specific death rates for all areas. Third, the smoothed rates were used to calculate a set of age-specific probabilities of death (q_x), which were then used to derive other life table functions. The derivation of the mortality rate in the first year of life differed from all other ages and required special formulae as detailed below in Age 0 years.
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Age 0 years
The probability of dying in the first year of life (q₀) required special treatment because infant deaths are skewed towards the early part of this age. The following example shows the formula for calculating q₀ for 2005–07, where the denominator approximates the exposed-to-risk population:

The value for q₀ is then used to derive the following life table functions:

		the radix of a life table

		where 0.85 and 0.15 approximate the proportion of infant deaths occurring in the first 6 months of life and second 6 months of life, respectively

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Age 1–4 years
The central death rate (m_x) for this age group was calculated by dividing the average annual deaths of residents of each area by the estimated resident population of each area at the midpoint of the period. For 2005–07:

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Age 5–84 years
The central death rates (m_x) were calculated for each five-year age group by dividing the average annual deaths of residents of each area by the estimated resident population at the midpoint of the period. For 2005–07:

		for x =5, 10, 15,..., 80
		for x= 5, 10, 15,..., 80
		for x= 5, 10, 15,..., 80
		for x= 5, 10, 15,..., 80
		for x= 5, 10, 15,..., 80
		for x= 5, 10, 15,..., 80
		for x= 5, 10, 15,..., 80

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Age 85 years and over
Data for those aged 85 years and over were combined into one age group. Because it is an open-ended interval, some unique formulae were required:

For all ages:

for x= 0, 1, 5, 10, 15,..., 85
where x + h= 85.

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Brass logit system
The Brass logit technique enables the calculation of smooth abridged period life tables for areas that have unreliable and/or zero age-specific death rates, by adjusting the observed rates with reference to a standard life table. The technique does not alter the overall level of mortality, but the age-specific functions of the life table are smoothed. Essentially, the technique compares mortality between the area and a standard life table across ages, then a line of best fit is calculated to describe that relationship by age. The line of best fit is then used in conjunction with the standard life table to determine death rates for the small area life table.

The subnational abridged period life tables for 1995–97 to 2005–07 use the Brass logit system and the complete period life tables for New Zealand for 1995–97 to 2005–07, respectively, as the standard.
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A note on the matching of infant death to birth records
Electronic infant death matching
The electronic capture and transfer of birth and death registration records from 1 July 1998 means infant death matching is now a viable option. The Demography Division of Statistics New Zealand undertook a trial electronic matching exercise involving infant deaths (under one year of age) registered between 1 July 1998 and 30 September 1999. The purpose of this exercise was to establish that matches could be done electronically, and whether matching would reveal marked inconsistencies between ethnic reporting on the birth and death registration forms.

Electronic matching involved a series of SAS programs, which attempted to match an infant's death record against its birth record. The variables considered included name, date of birth, sex and meshblock of residence. Matches were achieved by searching for possible matching birth records. Subsequently, visually checking the printed files of all the birth and death records was carried out to ensure the match was genuine. Inconsistencies in variables and minor variations in the spelling of names meant that this visual check was very important. To ensure the highest possible match rate, searches were carried out independently using date of birth, meshblock (home address) and name (character strings down to 3 characters were searched for). Other variables such as the child's sex were also used to speed up the matching exercise.

The following observations follow from the trial:

There was a 81 percent match for those infant death records which were captured electronically (ie the death was registered after 1 July 1998).
Matching infant deaths to births which were registered before 1 July 1998 is more difficult because the birth record file did not carry the name of the child before July 1998.
Despite extensive searching, 72 infant deaths were unable to be matched, or 19 percent of the total occurring between 1 July 1998 and 30 September 1999. In some cases the birth may not yet have been registered.

Forty percent of infant deaths occur in the first 7 days of life. Without prompting, however, parents often do not realise that they are required to register the birth even after the child's death. The process of contacting parents often takes time, thus the birth may be registered several months after the death. It is also possible that because of hospital transfers and other complications at birth, the hospital birth notification form may not have been sent to Internal Affairs. Without a notification form, Internal Affairs would not know to prompt the parents to register the birth.

There are a number of other factors that may contribute to the 19 percent non-match rate. For example, information critical to matching may be wrong (we may be trying to match an overseas born child, or names may have been changed, or date of birth may be incorrectly recorded, etc.). Alternatively, insufficient details may have been recorded on the birth registration form and Internal Affairs may have delayed birth registration to seek more information.

Summary of Results

302 infant deaths were matched, or 81 percent of the total infant deaths which were registered between 1 July 1998 and 30 September 1999. Of those matches, the following table gives the ethnicities recorded on the birth certificate and the death certificate.

Infant Deaths Matched to Births

Ethnicity	Number belonging to each ethnicity		Ratio of Deaths to Births
Ethnicity	Birth registration form	Death registration form	Ratio of Deaths to Births
Single ethnic response Mäori	67	90	1.34
Mäori ethnic group	129	125	0.97
Non-Mäori ethnic group	173	177	1.02

Total matched infant deaths	302	302

(1) Includes single ethnic response Mäori.

The ethnicity of the 72 unmatched infant deaths was as follows: 20 single ethnic response Mäori, 28 Mäori ethnic group (includes single ethnic response Mäori), and 44 non-Mäori ethnic group. This is virtually the same ethnic distribution as that recorded on the death certificates for the 302 matched infant deaths. Thus, if successful matches had been found for the remaining 72 infant deaths, it is probable that the pattern of response shift would be similar to that already identified.

Conclusion
Infant death matching for the period 1 July 1998 to 30 September 1999, suggests that the number of Mäori ethnic group infant deaths are understated in death registrations by 3 percent. However, infant deaths for the single ethnic response Mäori population appear to be overstated in death registrations by 34 percent. These conclusions are based on the assumption that ethnic data is recorded more correctly on the birth registration form (completed by the parents) than on the death registration form (completed by the funeral director).

Although an electronic match was not achieved for 19 percent of the infant deaths in the study, the ethnic distribution of these unmatched deaths suggests that the above conclusion would be unlikely to be significantly affected if they had been matched.
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Output Variables

Output variables are pieces of individual information that can be extracted from the survey/output data. Often output variables can be cross tabulated with other output variables, for example sales by industry classification. The list below contains all current and past output variables which have been released for this survey/output.

Variable Name Description

Exact age (eg exact age 5 corresponds to 5 years and 0 days).

Number of persons alive at exact age x from the original cohort of 100,000 (l₀).

Average number of persons alive in the age interval x to x+1.

Number of deaths in the age interval x to x+1.

Number of deaths in the age interval x to x+5.

Probability that a person at exact age x dies within a year.

Probability that a person at exact age x dies within 5 years.

Probability that a person at exact age x lives another year.

Probability that a person at exact age x lives another 5 years.

Central death rate for population in the age group x to x+1.

Central death rate for population in the age group x to x+5.

Proportion of the population in the age group x to x+1 surviving another year.

Proportion of the population in the age group x to x+5 surviving another 5 years.

Expected number of years of life remaining at exact age x.

Changes in Output Variables over time

Guide to Interpreting Data

Summary of Changes to Survey/Output ..

1895 First non-Mäori life tables published. These were for the period 1880–92.

1953 First Mäori life tables published, where a Mäori is defined as a person of half or more Mäori blood. These were for the period 1950–52. (A non-Mäori is defined as any person who is not a Mäori.)

1954 First total New Zealand population life tables published. These were for the period 1950–52.

1990 Last ethnic life tables published for Mäori and non-Mäori populations based on the "half or more Mäori blood" concept. These were for the period 1985–87. (Non-Mäori is defined here as any person who is not Mäori).

1991 The ethnicity question on the 1991 Census personal form asked, "which ethnic group do you belong to?" and allowed people to tick a box or boxes which applied to them.

1993 First Mäori and non-Mäori ethnic group life tables published. These were for the period 1990–92. This is a broader concept and is based on self-identification of ethnicity irrespective of a persons degree of Mäori blood.

1994 First regional life tables published. These were for the period 1990–92.

1995 Change in birth and death registration forms from September 1995 means that the ethnic classification on these forms is no longer according to 'degree of blood' but according to ethnic affiliation and consistent with the 1996 Census question on ethnicity. Also a greater range of ethnic groups can be identified and multi-ethnic responses can be generated. This has resulted in a greater number of Mäori and Pacific deaths being recorded compared with the old registration forms. For more information on the change in forms, refer to "Information about the births" and "Information about the deaths".

1996 Population concept used in the calculation of mortality rates changed from 'de facto' to 'resident'.

The ethnicity question used in the 1996 Census of Population and Dwellings differed from that used in the 1991 Census and resulted in a larger than expected Mäori ethnic group population in 1996. On the 1996 Census form the ethnicity question was changed to an instruction: "tick as many circles as you need to show which ethnic group(s) you belong to". It encouraged people to identify multiple ethnicities. Also, the scope of the responses was broadened by including sub-categories under the 'other European' category (eg Irish, English, Australian). These changes contributed to more people identifying with more than one ethnic group at the 1996 Census. For example, the Mäori ethnic group population (ie people who identified with Mäori either as their single ethnic response or as one of several ethnic groups) jumped by 89,000 or 20 percent between 1991 and 1996, compared with previous five-yearly increases of between 5 and 8 percent. The 'mixed Mäori' population (ie Mäori with other ethnic groups) more than doubled between 1991 and 1996, from 111,000 to 250,000. By contrast, there was a 15 percent drop in the number of 'single ethnic response Mäori' (ie Mäori without other ethnic groups), from 323,000 in 1991 to 273,000 in 1996.

1998 Mäori and non-Mäori complete life tables for 1995–97 constructed with birth and death data from the new registration forms. Because of the change in registration forms the 1995–97 Mäori and non-Mäori life tables are not directly comparable with Mäori and non-Mäori life tables from earlier periods.

2004 Complete life tables for 2000–02 for the Mäori, non-Mäori and total populations released. Revised complete life tables for 1995–97 released. Abridged life tables for 16 regional council areas for 1995–97 (revised) and 2000–02 released. Abridged life tables for 35 selected territorial authority areas for 1995–97 and 2000–02 released.

2008

2009 Complete life tables for 2005–07 for the Mäori, non-Mäori and total populations released.

Abridged life tables for 16 regional council areas for 1995–97 to 2005–07 released. Abridged life tables for 40 selected territorial authority areas for 2000–02 and 2005–07, and 39 territorial authority areas for 1995–97 released.

Usage and Limitations of the Data ..Most life tables are period life tables which commence with a hypothetical group of newborn babies, and assume that they experience the observed mortality rates of a given period throughout their life. The derived life expectancies give an indication of the average longevity of the population but do not necessarily reflect the longevity of an individual.

The consistency of the deaths numerator with the population denominator is an issue for ethnic life tables. There is evidence that Mäori deaths were under-reported, and hence non-Mäori deaths were over-reported, before new deaths (and births) registration forms were introduced in September 1995. The 1995–97 Mäori and non-Mäori life tables were the first to be constructed using data derived from the new registration forms. Mäori and non-Mäori life tables from 1995–97 are not directly comparable with earlier life tables because of conceptual differences between data from the old and new death registration forms. Users should also be aware of numerator-denominator differences in life tables before 1995–97.

Related Data Sources ..Deaths

Sampling Errors ..

Non-sampling errors

Caveats on Release ..Most life tables are period life tables which commence with a hypothetical group of newborn babies, and assume that they experience the observed mortality rates of a given period throughout their life. The derived life expectancies give an indication of the average longevity of the population but do not necessarily reflect the longevity of an individual.

The consistency of the deaths numerator with the population denominator is an issue for ethnic life tables. There is evidence that Mäori deaths were under-reported, and hence non-Mäori deaths were over-reported, before new deaths (and births) registration forms were introduced in September 1995. The 1995–97 Mäori and non-Mäori life tables were the first to be constructed using data derived from the new registration forms. Mäori and non-Mäori life tables from 1995–97 are not directly comparable with earlier life tables because of conceptual differences between data from the old and new death registration forms. Users should also be aware of numerator-denominator differences in life tables before 1995–97.

Customised Output

Complete Life Tables

Abridged Life Tables

Catalogue & Reference Numbers

INFOS:
Regional Life Expectancy, DRLC.

Other Comments

Classification(s) used

Classifications	Classification Versions	Classification Type
ETHNIC05 - Ethnicity New Zealand Standard Classification 2005	V1.0	Standard
SEX - Sex - New Zealand Standard Classification	V1.0	NZ Standard
TA06 - Territorial Authority 2006	V2.0	NZ Standard
REGC06 - Regional Council 2006	V1.0	NZ Standard

Glossary of Terms

Term Description

Death

The permanent disappearance of all evidence of life at any time after live birth has taken place (post-natal cessation of vital functions without capability of resuscitation). This definition therefore excludes foetal deaths.

Estimated de facto population An estimate of all people present in a given area at a given date.

The estimated de facto population of New Zealand includes all people present in New Zealand and counted by the census (census night population count). This estimate includes visitors from overseas who are counted on census night, but excludes New Zealand residents who are temporarily overseas.

Estimated resident population An estimate of all people who usually live in a given area at a given date.

The estimated resident population of New Zealand includes all residents present in New Zealand and counted by the census (census usually resident population count), residents who are temporarily overseas (who are not included in the census), and an adjustment for residents missed or counted more than once by the census (net census undercount). Visitors from overseas are excluded.

Life expectancy (expectation of life) The average length of life remaining at a given age.

In a period life table, it is the average length of life from a given age, assuming people experience the age-specific mortality rates of a given period from the given age onwards.

In a cohort life table, it is the average length of life from a given age, of people born in a given period, based on the mortality rates actually experienced by them from that given age onwards.

Live birth The birth of a child, who breathes or shows any other evidence of life, such as beating of the heart, pulsation of the umbilical cord, or definite movement of voluntary muscles, whether or not the umbilical cord has been cut or the placenta is attached. Each product of such a birth is considered liveborn. All liveborn infants should be registered and counted as such, irrespective of gestation or whether alive or dead at the time of registration. If they die at any time following birth they should also be registered and counted as deaths.

Mäori population People who identify with the Mäori ethnicity with or without other ethnicities.

Because ethnicity is self-perceived, people can identify with Mäori ethnicity even though they may not be descended from Mäori ancestors. Conversely, people may choose to not identify with Mäori ethnicity even though they are descended from Mäori ancestors.

Non-Mäori population People identifying with an ethnicity excluding those who identified with Mäori ethnicity.

Contact Details

Customer Service E-mail Contact:	info@stats.govt.nz

Survey Enquiries E-mail Contact:	demography@stats.govt.nz

Liability

Statistics New Zealand gives no warranty that the information or data supplied contains no errors. However, all care and diligence has been used in processing, analysing and extracting the information. Statistics New Zealand shall not be liable for any loss or damage suffered by the customer consequent upon the use directly, or indirectly, of the information supplied in this product.