Cohort analyses

Cohort analyses are a powerful tool for examining population changes because it allows us to obtain a more detailed picture of the growth dynamics happening at a sub-group level. In this case, the population patterns of age and birth cohorts are examined. A cohort is defined as: “a group of people who experience the same demographic event during a particular period” (Siegel & Swanson, 2004). This thesis uses two types of analyses: cohort component method and birth cohort

analysis.

Cohort component method

The cohort component method has a longstanding tradition in demography (Smith, Tayman, & Swanson, 2001). The method is essentially a population projection tool that calculates the expected population at a future time based on a

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number of demographic assumptions. A key strength of this method is that it offers a very flexible approach to understanding population change. Although it is a tool primarily designed to compute future population numbers, the expected population numbers for past periods can be computed. Thus, this method is used to compare the observed (actual) iwi population data against the expected iwi population data for the purpose of presenting and identifying the key variances, and to contemplate the underlying reasons for those variances.

In this thesis, observed and expected population numbers of five-year age cohorts (0-4, 5-9, 10-14 etc.) are compared, using a spread sheet tool that has been

formulated to calculate the expected population for various periods20. There are two components in using the cohort component method for analysing iwi population dynamics. The first is to calculate the expected population and the second is to compare the observed population. Four steps are involved in calculating the expected population.

First, the expected population of the age cohorts at each census period are

calculated using a baseline population. The baseline population is the population at the beginning of the projection period. Our only available baseline is the iwi population numbers of each age cohort by sex in 1991, thus, we can only compute the expected population numbers for 1996, 2001 and 2006.

The second step is to survive this 1991 population by applying survival rates21, meaning that the number of persons expected to survive at the end of the period is computed. In other words, the mortality effects of a population are considered. To do this, age-sex specific survival rates are applied to each age-sex cohort.

20 _{The statistical model was prepared by Professor Natalie Jackson, Director of the National} Institute of Demographic and Economic Analysis (NIDEA), Waikato University, Hamilton, New Zealand.

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Survival rate is a rate that expresses “the probability f survival of a population group, usually an age group, from one date to another and from one age to another. A survival rate can be based on life tables or two censuses. When based on two censuses, the rate includes not only the effects of mortality, but also the effects of net migration and relative census enumeration error” (Siegel & Swanson, 2004, p. 776). For this thesis, I use life table data obtained from Statistics New Zealand.

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Third, the expected migration is calculated during the period using age-sex net migration data22. The net migration data is then added (or subtracted) to the survival population numbers. For this thesis, however, I make the assumption that the Māori population (and therefore iwi) is a closed population. A closed

population is one in which inward migration and outward migration is very minimal, if at all. This is discussed further in chapter five. Furthermore, no net- migration data is available or collected for the Māori or iwi populations. Because I have made this assumption and due to the lack of migration data, I have not applied this step in the process.

The fourth and final step in the process is to project the number of births in the interval between the baseline and end period. This is accomplished by applying age-specific birth rates23 to the corresponding at-risk population. The at-risk population are those whom an event (i.e. births) can potentially occur. In this regard, I apply age-specific birth rates to females aged 15 to 49 to cover the child- bearing years. Once the age-specific birth rates are applied, these births are then added to the survived and migration-adjusted population numbers of the age cohort 0-4, and distinguished between males and females. On this note, the statistical tool that is in this thesis distinguishes between males and females based on gender probabilities. For example, if there were 1000 births in a particular interval and the probability of males is 0.52 then the birth numbers would be distributed as 520 males and 480 females.

By the end of the process, the expected population by age cohort (and/or sex) at the end of the period (i.e. 1996) has been calculated. This population now serves as the base population to calculate the expected population of the following period (i.e. 2001) and so forth (Smith et al., 2001). A comparison can now be made between the expected population and the actual population for the same census period.

22 _{Net migration is the difference between the number of inward migrants and outward migrants} for a particular area over a period of time (Siegel & Swanson, 2004). Migration data is obtained from Statistics New Zealand.

23 _{Age-specific birth rate is the rate of births for a specific age or age group of the corresponding} at-risk group (i.e. females aged 15-49) (Siegel & Swanson, 2004; Smith et al., 2001). For this thesis, I use age-specific fertility data obtained from Statistics New Zealand.

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The cohort component method is a very useful for this thesis analysis. It allows one to calculate the expected population for past periods so comparisons can be made between what was anticipated with what actually happened. Because the method computes the expected population by applying mortality, migration and birth effects, to a certain extent one can confidently assume that differences between the expected population and actual population are due to non-

demographic factors, that is, ethnic mobility. In saying this, however, one cannot overlook that the cohort component method and the statistical tools used in this thesis is constructed on a set of assumptions, rates and probabilities about a population. These assumptions can be overestimated or underestimated, and therefore, undermine data analyses. To overcome this issue, the data is analysed and interpreted in the context of a variety of statistical models and theoretical framework.

Birth cohort analysis

The birth cohort method monitors the intercensal population patterns of birth cohorts. A birth cohort is defined as members of a population born in a given period (Siegel & Swanson, 2004). In this thesis, we track five-year birth cohorts (e.g. 1992-1996, 1997-2001, 2002-2006 etc.) for the purpose of identifying mainly any intercensal increases in the size of the cohort. For this analysis, we use the same statistical models for analysing intercensal population changes (i.e. absolute and percentage change formulas).

Theoretically, we know that as a birth cohort ages through time, their population numbers are suppose to decrease because of mortality effects. The size of a birth cohort can only increase through migration. However, in this analysis, we have assumed that Māori and iwi are a closed population. Based on historical trends however, we know that the Māori population has experienced greater out-

migration than in-migration, and therefore, anticipate decreases in the cohort size of the at-risk population. In light of this, we theorise that any increases in the size of the population, is likely to be the effect of ethnic mobility.

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