DEMOGRAPHY : Vital Statistics, Mortality (Death) Rates ; CDR,SDR, ASDR, STDR; Fertility (Birth) Rates and Groth Rates (GRR & NRR).

 

Elements of demography ©

Life is a three pages book, two are already written by God.

The first is birth, last is death, the middle page is empty.

Fill it with smile, love, faith and honey.

introduction:

 Demography means population studies. In demography, we study the events related to human life. Events related to human life such as birth, death, sickness, marriage, divorce, migration etc. are called vital events. Vital statistics is a study of vital events. Vital statistics give numerical summary regarding vital events. It is necessary to study the methods of population projection to estimate average life expectancy, sex ratio, dependency ratio, population density, infant mortality rate and percentage of literacy etc.

In this chapter, we study statistical methods of measuring birth rates, death rates, population growth rates.

3.1 Methods of Obtaining Vital Statistics

The raw data of the vital statistics are generally obtained from the following sources.

1) Census Method:

Population censuses are undertaken in almost all countries, generally at 10 years of interval. A Census may be defined as an enumeration at a specified area during which particulars are collected regarding age, sex and some social and economic characteristics (vital events) of the individuals.

2) Vital Statistics Registers

In many countries, there is a system of registering the occurrence of every important vital event, under legal requirement. For instance, while a child is born, the matter has to be reported to the proper authorities, together with such information as the sex of child, age of mother, religion of parents etc.

      Similarly every death occurring in the community gets automatically recorded, because disposal of the body requires a death certificate from the authorities.

3) Data of vital events may also be obtained from hospital records.

4) Sample Surveys:

Sometimes special sample surveys are conducted to get the information which is not available in census or by registration of the vital events.

Remarks:

       The vital statistics collected by using above method is not enough. For example, population for intercensal year is not available. Statistical methods are used to estimate these figures.

Population Measurement:

In order to determine population foe at time say t, we may use number of procedures. A very common method is to make use of birth & death statistics as well as migration statistics.

The population P_t ,at time t is given by,

                                                              P_t = P₀ + (B – D) + (I – E)

Where,    P₀: Total population at last census.

 B: Total births during last census to period time ‘t’.

 D: Total deaths during last census to period time ‘t’.

I: Total immigrants during last census to period time ‘t’.

E: Total emigrants during last census to period time ‘t’.

3.2 Rates of Vital Events:

The raw data of vital statistics are given in the form of frequencies of vital events. For example,

n₁ babies are born, n₂  persons are died,  n₃ couples get married during a period ‘t’ in any community or region. To study vital events, mainly the rates of vital events are used.

 The general definition of rate is,  

Where, k is constant. The ratio in the above relation is usually very smaller in magnitude, hence for convenience it is multiplied by, K=1000.

Note: The number of persons exposed to the risk of a vital event is usually the population of given area, during the given period. This population P_t  is does not remains same throughout. So one may use the population in the middle of the periods ‘t₁’ and ‘t₂’,  which is mean population and denoted by P.

                                   Thus, mean population = ( Pt_{1 +}  Pt₂) / 2  

 

3. 3 Mortality Rates  or Death rates:

We discuss below different mortality rates or death rates.

1.   Crude Death Rate (CDR)

         This is the simplest death rate used to measure mortality, which is defined as, the number of deaths (from all causes) per K persons in the population of any given region or community during a given period. Thus,

                                                  m = C.D.R. = (D/P) *  K                Where, K =1000

D = no. of deaths in the population of any given region during a given period.

P = total population of any given region during the same period.

If period is of one year, then C.D.R. is called as ‘annual C.D.R.’

Also, we may define C.D.R. for males,

C.D.R. for males = m_m  = (m_D/m_P)*    K  

m_D = no. of male deaths in a given population during a given period.

m_P = total male  population during a given period.

Similarly C.D.R. for females,

C.D.R. for females = f_m  =   (f_D/f_P)*    K        

f_D = no. of female deaths in a given population during a given period.

f_P = total female  population during a given period.

Merits and Demerits:

Merits: CDR is easy to understand and easy to compute. It is perhaps the most widely used vital   statistical rate. As an index of mortality it is used in public health problems.

Demerits: It’s serious drawback is that, it completely ignores the age & sex distribution of the population. These are the important factors which influence the mortality of the population. So CDR cannot be used for comparison of mortality of two populations which widely differs in  age or sex distribution.

Note:

 i. CDR usually lies between 3 and 23 per thousand.

ii. Since population varies over time, denominator in C.D.R. considered as mid-year population.

2.   Specific Death Rate (S.D.R.)

         

    The death rate computed for a specific segment of a population is called specific death rate. Various segments may be Age, Sex and Occupation etc. Thus specific death rate is given by;

Usually, S.D.R. are made specific with respect to age & sex.

3.   Age Specific Death Rate (A.S.D.R.)

                        The death rate computed for a specific age group of the population is called age specific death rate. The age specific death rate for the i^th age group is denoted by M_i & is defined as:    

                                       

where        D_i = No. of deaths in i^th age group,

                 P_i = Total population of i^th age group.

 

Note:  We may define S.D.R. for age and sex also. Thus, age S.D.R. for male:

                                               

. where , 

                           

          

Merits and Demerits:

SDR is the best measure of mortality. It is very much useful in the construction of life tables, fixing LIC premium etc. But they cannot be used for comparison of mortality of two populations directly.

The nature of Age SDR is as shown below,

 

Infant Mortality Rate (IMR):

Generally IMR is high. It varies from country to country. It is small in developed countries. It shows the social and economic development of the country.

Note: Age S.D.R. of babies before completing their first year.

 3. Adjusted or Standardized Death Rate ( STDR )

 Age-SDR is useful for the age group wise comparison of mortality of two populations or years. However, population contains several age groups. It is likely to happen that for one population SDR is higher in some age groups than that of other but it is smaller for some other age groups. In this situation to overcome this difficulty for comparison purposes, we need a unique representative value of all SDR^s. This can be done very well by taking weighted average of SDR^s. For comparison of death rates of two populations we consider the same set of weights to compute average SDR. A third population is taken as a standard population and age-group wise population is taken as weights to find average of SDR. Therefore, the average obtained by this manner is called as a Standardized Death Rate (STDR). There are two methods of obtaining STDR which we discuss below;

a) Direct Method of Standardization:

If P_i^S is a standard population of i^th age group then under this method STDR for population A and B are given as fallows;

For simplicity we denote age specific death rates of i^th age group of population A by A_i and that of population B by B_i therefore;

Note: i. STDR for standard population is CDR.

Proof :

Thus, CDR can be computed from Age SDR and age wise population

ii. Sometimes one of the two populations A or B is taken as standard population.

iii. Choice of standard population is a difficult task.

For computation of STDR of state, we can take population of country to be standard population. Similarly population of the same state in earlier census may be taken as standard population.

 Drawback of Direct Method: If age SDR A_i’s are unknown then we cannot compute STDR by direct method. In this situation indirect method can be used.

b) Indirect Method of Standardization:

Suppose, A_i: age SDR of i^th age group of population A.

S_i: age SDR of i^th age group of standard population.

P_i^S: Standard population of i^th age group.

P_i^A: Population of i^th age group of locality A.

Clearly, P^A = Σ P_i^A and P^S = Σ P_i^S.

We choose standard population for which S_i is known (or can be computed) i.e.  number of deaths in each age group is available. In direct method of finding STDR we consider C, such that,   

        STDR = C × CDR. The factor ‘C’ is called as adjustment factor. It comes out to be,

Our main difficulty is that A_i’s are unknown. Therefore, we replace A_i by S_i and estimate the value      of C.   

       It is given by the following formula, 

3.4 Fertility Rates:

1. Crude Birth Rate (CBR): 

It is the simplest measure of fertility rate or birth rate. It is defined as similar to CDR. It is given by,

Merits: It is easy to understand and easy to compute.

Demerits:

 i. CBR provides very approximate fertility rate.

ii. It ignores age and sex distribution.

iii. In this case entire population is considered and only a part of it (women in the child bearing age group) is exposed to the chance of reproduction. It is a serious drawback of the method. 

     Hence, CBR underestimates fertility rate.

Note: CBR generally lies between 10 to 55 per 1000 persons. In order to overcome the drawback in             CBR, general fertility rate and age specific fertility rates are used.

2. General Fertility Rate (GRR): 

In this rate live births to the females in the reproductive age group are considered. It is defined as ,

In general, reproductive age group is considered to be 15 to 49 years. It is called as child bearing period. GFR for India is 95.3 and for 2011 the CDR is 7.2 and CBR is 20.6.                                                  GFR is superior to CBR, but it does not take into account the fact that the fertility differs from age group to age group. Therefore, Age-Specific Fertility Rate (ASFR) is necessary.

3. Age-Specific Fertility Rate (ASFR): 

      Age-Specific Fertility Rate is given by,

Where, B_i = Number of births to the females in the i^th age group.

P_i^f = Female population in the i^th age group.

Note: i. If we take age group as a single year then it is called annual ASFR.

        ii. Age-SFR removes the drawback present in GFR but for comparison purpose we require a                      single   value. 

            A more suitable and useful method to combine the age-SFR to a single value, is a  total fertility rate is discussed below.

4. Total Fertility Rate (TFR):

        Age SFR is not useful for comparison, since for comparison we require a single value. A more suitable and useful method to combine the age-SFR to a single value is a total fertility rate.  In order to find the total fertility rate we need to add up ASFR. It gives the average number of children born to 1000 women in the entire reproductive age period.

        If C is the width of an age group, then ASFR is the average fertility rate for the corresponding c years. 

 Thus the total fertility for the corresponding group is C × ASFR.

 Hence, TFR for all reproductive age groups taken together is given by the formula; 

                                  TFR = Σ C × ASFR = C Σ ASFR.

Note: i. C is taken to be constant.

ii. If annual ASFR are available (i.e. C = 1) then TFR = Σ ASFR.

Interpretation: 

TFR gives the total number of children born to per 1000 women in the entire reproductive age period. Thus, T.F.R. = 2200 means, on an average 1000 females give 2200  births over their entire reproductive age period i.e. every women gives birth to 2.2 children in her entire reproductive age period. 

Limitations of TFR:

i. In computing TFR we assume that all the women will survive up to the end of the reproductive age period, which is not true  in general.

ii. We consider entire female population in the reproductive age period. Actually in computing GFR, as well as ASFR we have to consider only the married female population.

iii. TFR (GFR,ASFR) does not consider effect of infertility.

Uses of Vital Statistics:

 i. The documents and records regarding birth, death, marriage etc. have legal importance. Individual requires concerned certificates from time to time during his life.

ii. They are very useful for government agencies to forecast population, make provision for future, to control the death rates, to reduce infant mortality rates, to control infectious diseases, to conduct family planning and welfare activities, to prepare program for public health etc. Vital statistics also helps to verify effectiveness of efforts. Population trends, Population composition according to sex, education, religion, marital states etc. can also be studied. It can be used to compare general health conditions of two countries with the help of death rates, average longevity, infant mortality rates.

iii. It is used in research activities to establish relation between different vital events. Analytical study is also possible with help of vital statistics.

iv. It helps in social and economic programs.

v. Actuarial sciences use vital statistics every now and then. Mortality rates are very much useful for LIC.

3.5 Population Growth Rates:

After studying mortality and fertility rates, we are interesting in measures of population growth. These  are two basic factors in the net change in the population. In general, we see that fertility rate is larger than the  mortality rate. Average life of an individual, average age at marriage, female population in a child bearing period are some more factors which directly influence the population growth. In general, the following methods are used to measure the population growth.

I. Crude Rate of Natural Increase:

It is the simplest and easiest way of measuring population growth. It is defined as,

Crude rate of natural increase = CBR – CDR.

 If it is positive population is increasing and If it is negative, population is decreasing..

II. Pearls Vital Index:

It is defined as,

If the index is greater than unity, population is increasing. On the other hand if it is less than unity, population is decreasing.

 Both these measures are considered unsuitable, since they carry all the drawbacks of CBR and CDR. More sophisticated measures are the Gross Reproduction Rate (GRR) and the Net Reproduction Rate (GRR). 

1. Gross reproduction Rate (GRR):

To get a proper measure of population growth, it is necessary to take account the age sex composition of the population. To measure  population growth, we consider only female births because the female children will be the future mothers. (Since population mainly increases through females). Thus, to get appropriate measure of growth, we need to know the number of female births in the every age group of woman population.

Thus, if  B_i^f is number of female births and  P_i^f is female population of i^th age group then female age specific fertility rate is given by,   

Summing these rates of all ages in  reproductive period a measure of population growth called (Gross Reproduction Rate -GRR) is obtained  as fallows;

If 'W' is the width of age group,  then

However, many times female births are not separately recorded for each age group. Only total births and total female births are given i.e. female birth ratio is given which is assumed to be constant , over all the age groups.   Sex ratio can be used to get proportion of female births. It is defined as follows;

Thus, sex ratio is a number of females per 1000 males. We assume that the sex ratio at the birth is constant.

If B^f is total female births and B is the total number of births then GRR can be modified as fallows;

Note:

i.  

ii. Generally, GRR per women lies between o and 5 and GRR < TFR.

iii. GRR per women is interpreted as the average number of daughters to a woman in a child bearing period.

Limitations of GRR:

           In computations of GRR we have assumed that every female child born at present will grow and survive up to the child bearing age period. Hence, GRR overestimates the growth rate.

2. Net Reproduction Rate (NRR):

In order to remove the drawback (i) of GRR, we consider probable population in every age group. This can be done by using survival factor, which is the proportion of women who will survive for the corresponding age group. If π_i (0≤ π_i ≤1) is the survival factor of females in the i^th age group then we define NRR, the improved measure of population growth as follows;

Note:

i. Here we assume that all age groups are of uniform width.

ii. Among B_i^f female babies born at present, only B_i^f × π_i will survive up to end of i^th age group in reproductive age period.

iii. Since, π_i ≤1, NRR ≤ GRR.

iv. NRR per women (i.e. without multiplier 1000) is a average number of daughter born per women. Thus NRR gives future mothers replaced by present women in the reproduction age group in the population.

Interpretation: on the basis of NRR per women;

i. Suppose NRR = 1, this clearly means that number of women in the reproductive age period at present will be same in future also. Hence, in the population number of potential mothers will remain same. Therefore, the total population will remain same.

ii. If NRR > 1, then number of potential mothers in future will be larger than that of at present. This will clearly result into increase in population.

iii. If NRR < 1, then number of potential mothers in future will be smaller than that of at present. Therefore, eventually the total population will be decreasing.

Limitations of NRR:

i. In the computation of NRR we do not take into account infertility factor, Widows, unmarried female population etc. hence it cannot be directly used for population projection. Therefore, altogether different methods are used for population projection.

ii. We assume same fertility conditions in the next generations, which may not be the reality.©

 

                                                                Multiple Choice Questions

Q:1 Choose the correct alternative.                                                                                           

1. S.T.D.R. of standard population is ………

a)   C.B.R.        b) I.M.R.     c)   C.D.R.  d) none of these 

2. If N.R.R. < 1, then population is ………

a)  increases        b)  remains as  it  is     c)  doubles   d)  decreases 

3. The collection of information (data) about each & every individual of a country is known as  -----

a) sample survey    b) demography    c) census   d) population studies

4. Specific death rate may be calculated according to  ....…

a) age         b) sex     c) region or locality   d) none of these

5. Population for intercensal year (t) is calculated as  ………

a) P_t  = P₀ + (B-D)+ (I-E)  b) P_t  = (B-D)+ (I-E)  c) P_t  = P₀ + (B-D)* (I-E)  d) P_t  = P₀ + (B-D)- (I-E) 

6. If N.R.R. > 1, then population is ………

a)  increases        b)  remains as  it  is     c)  doubles   d)  decreases 

Q:2 Attempt any two.

                                                                                                                

1. What is demography?  State the uses of vital statistics.  

2. Define vital statistics? What are the methods of obtaining vital statistics.

3. Explain G.F.R. & T.F.R.

4. Define age S.F.R. and infant mortality rate.

Q:3 Attempt any one.

                                                                                                                

1. Explain STDR by direct and indirect method of standardization.

2. Define a) C.D.R.  b) S.D.R.  c)  G.R.R.  d)  N.R.R.

©  ****