19 and none of the ratios exceeded unity for the other age groups of

women. This might also be due to misplacement of births in time in addition

to the under-reporting of births. Thus, according to Brass and Rashad (1980 : 16),

if fertility in Bangladesh remained constant, the rates for the period 1971-75

were under-stated and the rates for the period 1966-70 were over-stated.

"Under the assumption of declining fertility over the last five years, the P/F ratios for 1966-70 and 1961-65 suggest that the fall was preceeded by a substantial increase in period fertility at ages above twenty-five years"

(Brass and Rashad, 1980 : 16).

This situation is unlikely because of the high fertility rates implied for the

period 1966-70. It was argued that even if some decline in fertility occurred,

misplacement of events in time was the dominating factor (Brass and Rashad,

1980 : 16).

The P/F ratio method was also applied for first births and 4+ order births

for the most recent period (0-5 years preceding the survey). The results are

reproduced in Appendix Table C 2. In case of a real decline in fertility it is

expected that the 4+ order births would be more affected than the first births

But quite the opposite situation was revealed by the P/F ratios which strongly suggests that the data were affected by errors. It was argued that with some increase in age at marriage the P/F ratios for first births show that "....the mean age of women at first birth would have to be increasing by more than one year in five calendar years steadily over some twenty years to account for the P/F ratios" (Brass and Rashad, 1980 : 16). Using P /Fn as the correction factor, the adjusted total fertility rates for the years 1971-75 and 1975 were found to be 7.50 and 7.36 respectively under the assumption of constant fertility. It is to be noted that Brass and Rashad (1980 : 15) found the unadjusted

total fertility rates to be 6.34 and 5.37 for the years 1971-75 and 1975 respectively.

Brass and Rashad (1980 : 18) by applying the P/F ratio method concluded that the low levels of fertility for Bangladesh in the years 1971-75 and 1975 were mainly due to event misplacement errors in the location of births. Although it was argued that fertility in the period 5-10 years before the survey was

overstated and that in the period 0-5 years before the survey was under-stated (as discussed earlier),Brass and Rashad (1980 : 18) were of the opinion that there was no significant fertility decline in the period 1971-75. This is contradictory to what has been observed in the present study. As pointed out earlier, evidence of a significant decline in fertility was found from the reasonably complete vital registration data in Matlab Thana during the same period. Amin and Faruqee (1980 : 6) using the data from the Bangladesh

Fertility Survey, 1975-76 also found a sharp decline in marital fertility for currently married women in the period 1974-75. The adjusted total fertility for the period 1971-75 by P/F ratio method is also found to be much higher than the corresponding observed total fertility estimated in the present study.

3.8.3 Gompertz Relational Mode1

The P/F ratio method, though simple, has some limitations. It can provide effective estimation of the total fertility only for a relatively short period before the survey under unchanging or moderately changing fertility and when the data are mainly affected by reference scale error in the location of births.

It is also not quite satisfactory for detecting fertility trends when

complicated response errors influence the data. Moreover, the method is

incapable of displaying the patterns of age-specific fertility rates. Attempts

were made by Brass (1979 : 40-53) and Brass and Rashad (1980 : 18-28) to over­

come those shortcomings by imposing an underlying pattern of fertility by age

and time.

The variation of fertility with age of women can be represented by the (x-x )

B o

Gompertz curve as F (x)/f = A where F(x) is the cumulative fertility to

age x, F is the total fertility, A and B are positive constants less than

unity and x^ is a convenient origin for age. Taking natural logarithm

twice and simplifying, the above equation becomes Y(x) = a + ßx where Y(x) =

-£n [-&n (F(x)/F)j. According to Brass and Rashad (1980 : 19), this model

does not represent the pattern of fertility adequately at the tails of the

distribution. Here Y(x) is related linearly to x. It was suggested that

the model would be improved if Y(x) was related to a standard set of

fertility pattern Y s (x) where Y s (x) = -&n [-£n (Fs (x)/Fs) ]• Heather Booth

(Cited in Brass 1979 : 47, and Brass and Rashad, 1980 : 12) derived a

standard set of Y s (x) from an extensive study of observed fertility patterns

and the Coale-Trussell(1974) fertility model. The relational Gompertz model

Y(x) = a + B Y (x) with parameters a, B and F is found to be more accurate

than the original Gompertz.

The parameters

ct

B

women are known. In this case, F(x)/F and taking the negative of the double

natural logarithm Y(x) can be calculated for a given x. A comparison of

Y(x) and Y s (x) graphically gives the characteristics of the observed

fertility rates. It is then possible to estimate a and

B

1980 : 20) employs the distribution of mean parity of a cohort up to the time of survey for estimating a , 3 and F. This method involves the ratios of cumulative fertility measures (mean parity) in two successive 5-year age groups within a cohort of women. Let P , P ^ , ... be the mean parity of women aged 15-19, 20-24, 25-29 .... years respectively for a cohort over time.

Fh is defined as Pi-p/P-^ (R^ = PQ/Pp where P^ is the mean parity of women

aged 10-14, R = P-./P , R = P./P etc.). It has been shown approximately by

2 ± 2 3 z 3

Zaba that G(i) = - £ (-£ R.) = e. + a + 3 <}>(i) where e. and (f)(i) are the

n n l l l

*

values calculated by using the Booth relational standard and ot is approximated 2

by a + 0.48 (3-1) . To apply the procedure, the values of [G (i ) - e j are obtained and compared with the cj)(i) values graphically or by some other means.

*

3 and a can be estimated by fitting a straight line. It has been noted that *

a is very close to a in most cases. After estimating a and

3

reported fertility measures, Py/F can be estimated by Z (i) = - £ (Pp/F)] = a +

3

z

standard. Equating Pp/F with the reported cumulative fertility measures provides a series of estimates of F. These F values are averaged in a

suitable way. These are denoted by F where c refers to age cohorts of women c

at the time of survey.

The next step is the estimation of a and 3 for each cohort of women.

c c

Attempts were made to estimate these by varying them linearly over time, that is, by fitting models ac =a+ca and 3c = 3 + cb. However, by applying these procedures to a number of sets of pregnancy history data, it was noted that

".... the two trend measures a and b left too much freedom so that the fitting was distorted by the effects of particular reference scale errors" (Brass and Rashad, 1980 : 21). It was suggested that the a could be fixed as a and

3

c c

could be varied linearly with c. The argument for this is that the spread of fertility (as estimated by inverse of 3) reduces with level due to greater influence of family planning at later ages in the childbearing period while

the behaviour of a cannot be well predicted because of its dependence on

both family planning and changes in age at marriage. Thus the model becomes

a relational Gompertz over age with parameters F ^ a and 3 + cb. The fitting

procedure is illustrated in Brass and Rashad (1980) for Bangladesh and for

more educated women in Sri Lanka. Important findings derived by the

application of the model in the context of Bangladesh are presented below.

Observed fertility rates for birth cohorts aged 25-29, 30-34, 35-39 and

40-44 years at the time of survey were compared with those obtained by fitting

the model. It was noted that the reported births per woman for the period