18 Population projection

Shalini Singh and Gautam Kshatriya

Contents:

1) Introduction

2) History : Population Projection

3) Strategies for projecting population

3.1) Total method

3.2) Cohort component method

4) Model for Total Methods for population projection

4.1) Zero population growth

4.2) Arithmetic growth

4.3) Exponential growth

4.4) Logistic growth

5) Cohort component method

5.1) Steps of population projection

5.2) Applying the Method

5.3) Key points to Remember

Learning Objectives:

To understand the key concepts and history of population projection.
To demonstrate knowledge and understanding of the key concepts used in population projections and forecasting
To discuss the main methods demographers use to project, or forecast future demographic developments.

1) INTRODUCTION

Human beings evolved under conditions of high mortality due to famines, accidents, illnesses, infections and war and therefore the relatively high fertility rates were essential for species survival. In spite of the relatively high fertility rates it took all the time from evolution of mankind to the middle of the 19th century for the global population to reach one billion. The twentieth century witnessed an unprecedented rapid improvement in health care technologies and access to health care all over the world; as a result there was a steep fall in the mortality and steep increase in longevity. The population realized these changes and took steps to reduce their fertility but the decline in fertility was not so steep. As a result the global population has undergone a fourfold increase in a hundred years and has reached 6 billion. Population refers to human aggregates within a defined space. The single outstanding fact about the population is the rapidity of its growth in the past two hundred years. A rapid accelerated expansion in the population can be seen since 1750, According to the world health organisation, 4 human beings are born every second: the net increment works out at 250 per minute, 15,000 per hour, 360,000 per day, or nearly 2.25 million per week. At current rate of growth (1.9 per cent annually) the world population estimated to , if the current trend continues, and there is little to suggest that it will be interpted or changed by 2000 AD.

The human population have two fundamental characteristics that reduce uncertainity about how they will develop in the future.

A substantial overlap exists between the current population and the future population.
One fundamental aspect of the human condition is that we grow older by one year until we eventually die.

These two facts constrain possible future developments in a population equivalent in other fields. Methods involved in population projevction take advantage of both the points.

A population projection can be defined as “a computional procedure to calculate population size and structure at one time from population size and structure at another, together with a specification of how changes takes place during the interim period”. It can be distinguished from a forecast as it can be defined as a projecton based on assumption that are preductive and considered to yield the most probable estimes of the development in the future. An important [point can be noted that all the forecasts of the population are projections while not all projections are forecast.

It deals with computations of future projection size and characteristitcs attempt to peep into the future population scenario, by using the assumptions and probability of adhering in future. Projections are merely an intelligent exercise for predicting the fate of current population under specifid assumptions of fertility, mortality and migration. Since it is not possible to predict the future trends in fertility, mortality and migration with cent percent certainty, it is also not possible to predict the future size and characteristics of a population accurately. The data used for predicting the various fertility rates were related to the past available at that point of time. Assumptions used and their probability of adhering in future, forms a critical input in this mathematical effort. Predicting the future course of human fertility and mortality is not easy, especially when looking beyond much further in time. Medical and health intervention strategies, food production and its equitable availability, climatic variability, socio-cultural setting, politicoeconomic conditions and a host of other factors influence population dynamics, making it a somewhat unpredictable exercise. Therefore, much caution must be exercised when either making or using the population projections and the context of various conditions imposed, should not be lost sight of on the basis of past behaviour and the likely future scenario assumed.

At the country level, different population projections are made by the Government, National and International agencies from time to time adding to it individual demographers make projections for the country as a whole and sometimes at the sub-national level also. World Bank, United Nations Population Divisions, the United nations Population Fund are among the international agencies who make projections for the world as a whole and also for individual countries.

2) HISTORY: POPULATION PROJECTION

The need for population projection in India at various levels and by different components like age, sex, rural-urban etc., for the use by the official agencies uniformly, both at the center and the states was keenly felt in 1958 on the eve of the formulation of the third five year plan. Beginning in 1958, it has been customary for the Office of the Registrar General and Census Commissioner, India to undertake the exercise of population projection on behalf of the Planning Commission of India. The first Expert Committee on Population Projections was set up by the Planning Commission in 1958 under the chairmanship of the Registrar General, India to provide a set of population projections for India and states. The projections upto 1971 were then made available to the Planning Commission pending the release of 1961 Census data. Subsequently, with the release of the final population totals of the 1961 Census as well as taking into account the life table values of 1951-60, the Expert Committee was reactivated in 1963 for effecting a further revision of the projections and extending them up to 1981.The Committee gave its report in 1964. Out of the three sets of projections namely high, medium and low, the second one, that is, the medium one was recommended for official use. Following the release of the 1971 Census provisional population totals, the Expert Committee was once again reconstituted to revise the existing official series of population projections of 1964. The Planning Commission again felt the need for another series of projections based on more recent data and subsequently constituted another Expert Committee in 1974, which submitted its report in 1978. After the release of the five per cent sample data of the 1981 Census, Planning Commission reconstituted the Expert Committee on Population Projections in 1984. Population Projections for the period 1981-2001 were prepared under three assumptions on the basis of trends in fertility. This report was published in 1988 and the medium projections were recommended for official use. In the light of the trends observed during 1980’s in major demographic parameters, as revealed by the Sample Registration System (SRS), the Planning Commission apprehended that the future size 3 of India’s population might be higher than that projected by the Expert Committee. In order to have a fresh look at the projections, the Planning Commission set up a Standing Committee of Experts on Population Projections towards the end of October, 1988. This Committee reviewed the medium projections made by the Expert Committee of 1984, in light of the further data available on fertility, mortality and contraceptive prevalence (family planning) and submitted its report in 1989. With the availability of age-sex distribution of population from the 1991 Census, the latest data relating to family planning performances and recent levels and trends in fertility and mortality as emerging from the SRS, a fresh need was felt by the Planning Commission for a new set of population projections. As such, the Planning Commission constituted a Technical Group on Population Projections in 1996 under the chairmanship of the Registrar General, India with the following objectives

To review the methodology of Population Projections adopted in the past
To prepare fresh projections of mortality status and parameters of fertility conditions based on changed pattern of contraceptive use and proportion of married females (1991 Census) and other characteristics
To make population projections afresh up to 2016
To prepare projections of the possible period when NRR = 1 will be achieved by the States / UTs and the country as a whole.

The assumptions made to project the population of India up to 2016 are discussed below:- The Technical Group considered the Total Fertility Rate (TFR) as the overall indicator of fertility. The earlier approach of taking NRR=1 as the replacement level of fertility was changed to TFR =2.1. The TFR estimates based on the SRS data for India and major states were adopted. The lowest threshold of TFR was assumed to be 1.6. Two sets of TFR values from the SRS for India and major states for two time periods 1981-93 and 1985-93 were considered by the Group. On careful examination, the Group recommended the use of projected values of TFRs based on the period 1985-93 except for the states of Madhya Pradesh, Punjab, Rajasthan and Uttar Pradesh. For these four states, the projected levels of TFR based on the period 1981-93 were adopted. The projected levels of TFRs assumed for India for the initial period 1996-2001 and terminal period 2011-2016 were 3.13 and 2.52 respectively. ¨ Although the SRS based sex ratio at birth of 110 for the period 1981-90, was found to be much higher than the internationally accepted conventional sex ratio at birth of 105-106, yet the Technical Group recommended the use of sex ratio at birth as obtained from the SRS in view of the overall broad consistency and reliability of the SRS data. ¨ For projecting the mortality levels, initially the Group considered two sets of mortality projections.

The first one was based on five-yearly abridged life tables constructed from SRS Age Specific Death Rates (ASDR) for the periods 1981-85 to 1989-93. The second set of mortality projections were considered by utilizing the projected survival ratios based on the observed ASDR value from the SRS. After examining the merits of the two sets of mortality projections, the later one, that is, the survivorship ratio method was recommended for undertaking the population projections. An upper limit of 70 years for the expectation of life for males and females was recommended for all India and major states except for Kerala and Tamil Nadu. The projected levels of expectation of life at birth for males were 62.30 years for the period 1996-2001 and 67.04 years for the duration 2011- 2016. Similarly, for females, these figures were 65.27 years and 69.18 years respectively. 4 ¨ In addition to considering the increase in the expectation of life at birth, the Group also considered the likely impact of AIDS on death rate. After considering the effect of likely deaths due to AIDS, it was found that future levels of the expectation of life at birth would have no significant impact of AIDS in the next 25 years. In Statement 11 are given the mortality and fertility assumptions used for projecting India’s

3) STRATEGIES FOR PROJECTING POPULATION

Two different and contrasting approaches are carried out to calculate population projections.

Total methods- It calculates the trends in the size of the population as a whole by using the mathematical model of population growth. It may further distribute into sub groups in ratio to the current structure of the population.
Cohort component methods- It projects each age group, sex and other category of interest separately. Aggregated results are used to obtain the total population. The term cohort indicates to the age group of people born at the same time who go through life together. The size of a cohort at one age is strongly predictive of its size at other ages.

Many population projections are combined through approaches, although projections are largely dominated by the cohort component approach. Cohort component methods further require many more input data and assumptions than total methods

Total methods of projections

Total methods of projection involves fitting a mathematical model to data based on past trends in the size of the population.

The main steps involved in the procedure are

Selecting an appropriate model of the growth process

Estimating the parameters of the model of the growth process

Extrapolating the fitted curves and read off the projected population.

The four mathematical functions used to model population growth are

1. Zero population growth

2. Arithmetic growth

3. Exponential growth

4. Logistic growth

3.1) Zero Population Growth

Zero population growth model is the simplest model of population growth where there is a zero population growth. It also assumes that the size of the population is unchanging. This assumption is implied even if one only has a single existing estimate of the size of the population which can project its size at other dates.

3.2) Arithmetic growth

The next simplest population projection model is that of arithmetic or linear growth. The model assumes that a constant numeric change occurs in the size of the population in every period of the same length. A minimum of two estimates of the population for different dates were required to estimate the annual increment in the population and to also project the size. The model can be fitted to a longer series of population estimates by means of simple linear regression of population size on time. Thus, if P(t) refers to the population at time t and P(t+n) refers to the population n years later:

P(t+n)= P(t)+a×n

where a is the constant annual increase in the population a= (P(t+n)-P(t)/n

3.3) Exponential growth

Instead of assuming that the population by a constant amount, the exponential model assumes that the population is growing at a constant rate. The growth rate tends to be negative if the population is shrinking over time, can also fit to this model. A constant negative growth is described as exponential decay. For the purpose of projecting population forward or backward, one requires to estimate its growth rate. A minimum of two estimates of the population by means of a linear regression of the log of population size on time.

In this model

P(t+n)= P(t) × ern

Where r is the constant growth rate:

r= loge(P(t+n)/P(t))/n

The exponential model can be further be used to estimate the doubling time of a population with a constant growth rate, the time when the population takes to double its initial size. The general exponential model equation goes

P(t+n)= P(t) × ern

When the population is doubling every n years,

n= loge(2)/r= 0.693/r

4.1) Logistic Growth

The logistic growth model of the population growth is applicable when the growth rate slows over time, eventually when it drops to zero, a point where the population stabilizes. The equation for logistic model goes-

P(t)= P(∞)/(1+e-s(t-h))

Where P(∞) represents the final size of the population growth and time is measured relative to point h,

date at which the population reaches half of its final size, s determines the growth rate, r, at each time it

reaches its final size.

r=s(1-P(t)/P(∞))

thus the growth rate declines over time to zero, equalling s/2 at time when the population reaches half its final size.

5) Cohort component method population projections:

It models the age sex structure of Population and components of their Demographic change- fertility, mortality and migration.

Whelpton in the 1930s developed the procedures for making cohort component population projections. It can be considered as an elaboration of the ideas encapsulated in the demographic balancing equation

P(t+n)= P(t)+B(t)-D(t)+I(t)-E(t)

Where,

P(t) is the population at time t

B(t) and D(t) are number of births and deaths occurring between t and t+n.

I(t) and E(t) are the number of immigrants and of emigrants from the country during the period t to t+n. There are two possible ways of joining a population: one can be by taking birth into it and the other can be by migrating into it. Similarly, the only ways to leave a population are to emigrate or to die.

Cohort component projections extend this concept to individual age cohorts. They make use of the fact that every year of time that pasees, every member ofa population becomes a year older. Thus, after 5 years the survivors of the cohort aged 0-4 years at some baseline date will be aged 5-9years and after 5 years they will be aged 10-14 years and so on.

Figure- 1 Steps of a Cohort Component Projection

Before moving on to repeat the procedure to project the population to the end of the next interval one uses dta on n year age groups. Thus, populations are usually projected either one year at a time, using data on single year age groups, or by five years age groups.

Men and women have a varying age specific mortality rates, the population is usually segmented into two sexes and separate projections are made for male and female populations. One can also segment the population into further sub groups with different mortality, migration and fertility rates.

In order to carry a cohort component projection, detailed assumptions of size and structure of the baseline population has to be made, each of the component for population growth is to be covered by the projection.

1) Base line population has to be subdivided by age and sex

2) Sex specific life tables for each projection interval in the projection

3) Age specific fertility rates for each projection interval in the projection period.

4) Age and sex specific net migration for each interval in the projection period.

5.1) Steps for Population Projection

Steps required to project a population

Calculate members of each living age cohort surviving the current projection interval.
The immigrants to each cohort are added and the emigrants are subtracted.
Number of births are calculated during current projection interval and are further divided into boys and girls.
Further calculate these births of each sex at the end of the projection interval and adjust for net migration into the youngest age group.
The next projection interval is calculated.

The method does not require an assumption of constant vital rates and different assumptions are made about fertility, mortality and migration.

5.2) Application of Method

Applying the method : Table for projecting the population of females for Year 2005

The first row in Column 1 shows the births that take place from years 2000–2005. The age groups have been aligned so that women ages 20–24 in year 2000 will be 25–29 in year 2005, as presented in column 2. This first step is important. It helps determine where to put the census data that is required for the projection. The census data for year 2000 is entered in the column 3. The census information should be provided for the age groups in column 1. Notice that the first cell is empty in column 3. This is where births will be added that take place throughout the projection period. Next, add 5-year survival rates to the table, as shown in column 4. By multipling Column 3 by Column 4 we find out the number of females alive in 2005.
Finding the Number of Females Alive in 2005

Once the table has been created and census information and survival rates have been added, it is possible to find out the number of women that survive the next 5 years. Multiply Column 3 by Column 4 to find out the number of females that will be alive in 2005. The results are in Column 5. Notice some of the females in each age group died.

Adding the Number of Births

Estimating the number of births taking place during the projection period is a two-stage process. First, calculate age-specific fertility rates. To do this, obtain information on the number of births by age of mother for a three year period around the date of the last census taking. If the number of births by age of mother is not available, use regional or national age-specific fertility rates. Demographic and Health Surveys (DHS) are available for most developing countries and provide age-specific fertility rates.

Total Annual Births = 1522.8599

Births during the projection period= annual births * projection period

= (1522.86) (5)

= 7614

Female births= expected births * 0.49

(7614) (0.49) = 3731

Number of projected births = 3731*survival rate

3731* 0.9809= 3659.7379

Column 1 indicates the ages of women in their reproductive years. Columns 2-4 present the number of births for the 3 years surrounding the last census period. An average was taken of the births prior to calculating the age-specific fertility rate (Column 2 + Column 3 + Column 4)/3)).

Once the average of births is obtained, the Year 2000 census data is used for women in their reproductive years to calculate age-specific fertility rates. To do this, the number of births is divided by the number of women in a given age group. Once the age-specific fertility rates are calculated, they are multiplied by the number of survived women in each age group. The sum of Column 9 provides the number of expected annual births.

To find the number of expected births for the projection period, the number of annual births were multiplied by the projection interval of 5 years. It was also necessary to find the number of female births. To do this, the number of expected births was multiplied by .49 (.49 is based on the use of Equations 8-2 and 8-3).

The final step is to multiply the expected births by a survival rate, which is provided in Table 8-2 (3,731 x .9809 = 3,659.7 projected female births).

Estimating Net Migration

The last part of the projection involves accounting for population movements in and out of the projection area. Two methods of estimating the number of net migrants will be introduced in this section. Both methods rely on survival rates and census information. First, it is important to be familiar with the definitions for migration and net migration.

Net Migration Rate

Net migration rate= Immigrants- out migrants *k

Population

K is a constant,usually 100.

Obtaining Migration Information

Populationt+n = populationt-1 + births- deaths+ net migrants

Net migrants= (population – population)- (births- deaths)

Populationt+n = current population

Populationt-1 = the last census

5.3) Key Points

Key points to remember about cohort- component projections

The model requires and makes full use of information on the population change component.

It provides estimates of the future population by age and sex.

The calculations involved are more mathematical explotation of the total population and can be easily done in a spreadsheet.

Summary

A population projection calculates the population size and structure at one time from population size at another based on assumed population change over time. A population forecast is a kind of population projection that aims to predict the future population size and component of the population.

Extrapolated trends in the growth of the total population or age and sex wise cohort projection is used to project population separately by using assumptions about age specific rates of fertility, mortality and migration.

The Total method of projection involves straightforward calculations and minimal data, it also fits a mathematical model to data on past trends in the size of the population and extrapolating the fitted curve to project population at other dates.

The cohort component method of population projection involves age and sex specific input data and it also projects the age and sex structure of the population. It carries out one step at a time for one year or five year projection intervals.

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References & Suggested Readings

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Hinde A (1998). Demographic Methods. London: Arnold Publishers.
Kleinman, D. S. (1980). Human adaptation and population growth: a non-Malthusian perspective. Rowman & Littlefield.
National Academy of Sciences (US). Office of the Foreign Secretary. (1971). Rapid population growth: consequences and policy implications (Vol. 1). National Academy of Sciences.
Nisbet, R. M., & Gurney, W. (2003). Modelling fluctuating populations: reprint of first Edition (1982). Blackburn Press.
Preston SH, Heuveline P and Guillot M (2001). Demography. Measuring and Modelling Population Processes. Oxford: Blakwell.
Renshaw, E. (1993). Modelling biological populations in space and time (Vol. 11). Cambridge University Press.
Rogers, A., & Todaro, M. V. (1985). Regional population projection models.
Mehta, B. C. (1978). Regional population growth: a case study of Rajasthan.