Estimates of birth intervals in Pakistan, with and without the WFS restrictions.

Khan, Zubeda ; Soomro, Ghulam Y.

Almost all the World Fertility Surveys (WFS), and those repeating a similar pattern of pregnancy history data collection, like the Population, Labour Force, and Migration Survey (PLM) carried out in Pakistan in 1979-80, covered information on proximate determinants for the last closed and open birth intervals. This paper, based on the PLM data, discusses the methodological issue of data collection. The types of restriction used have often been doubted as they have produced biased estimates of contraceptive use and duration of breast-feeding, which are important in the estimation of birth interval and in the ultimate estimation of the structures of the relationship predicting fertility. The representativeness of the last closed and open birth intervals is limited if these are probed deeper in the time before survey, as the proportion of births gets quite small. It is inappropriate to estimate proximate determinants on fertility data that do not provide information on all the births. Therefore, an attempt has been made to estimate contraceptive use and breast-feeding with and without the WFS restrictions. The logit model has been used with a dichotomous variable, 'whether the next live birth occurs or not', on proximate determinants and other socio-economic variables to estimate the amount of biasedness. The results reveal that there appears to be a higher proportion of unbiased estimates if they are derived through the unrestricted sample; and these results are in conformity with the results found elsewhere. The biasedness of the restricted samples also affects the studies aimed at observing the relationship between the predictor and the dependent variables.

INTRODUCTION

In 1975 a large number of countries participated in the World Fertility Survey (WFS) programme, in which a detailed information on maternity history was collected with a view to assessing the fertility and family planning-related behaviour of women. In a majority of the cases, the information on breastfeeding and contraception was obtained for only the last closed and open intervals] Such a restriction on fertility histories has raised many doubts about the possibility of the sample selection bias in the results. A number of researchers have used the WFS data for examining the effect of breastfeeding and use of contraception on the length of birth intervals [Jain and Bongaarts (1981); Smith (1985)]. They have acknowledged that due to the restriction of the sample to the last closed and open intervals, there is a potential bias in the results. This requires measures to minimise such biases in fertility estimates. It is, therefore, of significance to examine the magnitude of such biases in the case of Pakistan-to see what impact it has on the estimates of birth intervals and fertility.

This leads us to the two main questions of this study: The first is: To what extent does the selection of the last closed and open intervals affect the estimates of the levels of contraceptive use and breastfeeding duration? The second is: Does the selectivity bias in data collection on the last closed and open intervals affect the pattern of relationships between these intermediate variables of fertility and other crucial socio-economic variables?

THE DATA

The data for this paper have been obtained from the Fertility Module of the Population, Labour Force, and Migration Survey (PLM) conducted in Pakistan in 1979-80. In this survey, the Pakistan Fertility Survey (PFS) questionnaire was repeated and information was collected on maternity history, fertility, and family planning. An important difference between the two surveys was that the number of observations in the PLM was twice the size of that of the PFS, and contained detailed information on reproductive histories of 9416 currently married women selected from about 11,000 households. Information was gathered in the survey for each child (a total of 38,746 in the survey) that the respondent had borne, including their sex, date of birth, and age of death. In case the exact dates of birth or death of any child were not given, they were taken as inferred by taking into account all the other information probed and provided by the mother, such as her age at marriage and the ages of all other children. The survey also collected information on duration of breastfeeding for every child, use of contraception for each birth interval, and any other occurrence such as miscarriage or abortion.

METHODOLOGICAL ISSUES AND PROCEDURES

The use of the last closed and open birth intervals in a selective fashion can best be examined by taking cohorts of birth intervals begun in various years preceding the survey year. All birth intervals originated in the 12 month-period before the survey date would be represented since such recent ones would have started by the last or next to the last birth. However, these intervals do not provide any information pertaining to birth spacing practices because a large number of them would not be closed so soon by another birth. The representativeness of the last or next to the last births is affected as one moves back in time, because many of those women would have started their fertility earlier; this is particularly true in high fertility situations like that of Pakistan.

To examine the representativeness of the last closed and open intervals in various time-periods preceding the survey, Figure 1 shows the percentage of births in each year that began in the last closed or open birth interval. As we can see, the proportion of births is quite small, the longer is the period before the survey. However, the proportion of births becomes quite substantial five years prior to the date of the survey, because all those women who began their birth intervals during the past five years are also included. It is evident from Figure 1 that the last closed or open birth intervals reach far back in time. As the figure shows, about 14 percent of these intervals were initiated 10 years before the survey year, whereas 9 percent of women had their last closed and open birth intervals about 19 years before the survey year. Therefore, it would not be appropriate to base estimates of current breastfeeding or contraception on data for all births with restrictions of the last closed and open birth intervals. This has also been proved in some earlier studies [Akin et al. (1981); Palloni (1984) and Pebley et al. (1986)].

[FIGURE 1 OMITTED]

After examining the sources of bias in the number of births due to birth interval restrictions, we shall proceed to examine the variations in fertility by selected background variables-to see the extent to which such restrictions bias the results regarding the structure of the relationship between the predictor variables and fertility. These variables include contraception, abortion, breastfeeding, and infant mortality as intermediate variables and age, education, residence, and the number of sons as socio-economic variables. Son-preference variable is of particular interest because some studies suggest that women who do not have at least one son may intentionally curtail breastfeeding in order to hasten the birth of the next child [Bumpass et al. (1982); Rindfuss et al. (1982)].

Our dependent variable, "whether the next live birth occurs or not", is a dichotomous one and takes discrete values 1 if a live birth occurs and 0 otherwise. The use of the ordinary least square (OLS) method in such circumstances is inappropriate not only because of the problems associated with heteroscedasticity but also because there is nothing to constrain the dependent variable to the unit interval. The most commonly used methods to examine the behaviour of binary dependent variables by regression analysis are: (i) the Linear Probability (LP) Model, (ii) the Probit (P) Model, and (iii) the Logit (L) Model. These models differ from each other in terms of the different cumulative distribution function assumed in the regression relationship. (2) As the conditional probability interpretation of the L-model is not always fully satisfied, the non-linear functional form--e.g., the probit and the logit models-is preferred. In the case of binary variable, however, because the normal and logistic distribution are very close to each other except at the tails, the estimates obtained using the probit and the logit forms are likely to be close. The methodology adopted in this study was developed by Rindfuss, Bumpass and Palmore (1987) to estimate the biases in birth intervals. They chose the logit model to measure the amount of biases arising from the introduction of the restrictions in the WFS methodology of data collection on the contraceptive use and breastfeeding practices almost in all the 42 participating countries. In this paper also, the logit model has been applied to estimate our model. [Rindfuss, Bumpass and Palmore (1987)]. A brief description of the logistic regression is followed by the discussion of results. If y is the binary dependent variable and Xs are explanatory variables, then the logistic model, for instance [x.sub.1] and [x.sub.2] implies that the probability of success (y-hat), which, in our case, is the probability of having a live birth, can be written as,

[??] = 1/[1 + [exp.sup.-]([alpha] + [[beta].sub.1][x.sub.1] + [[beta].sub.2][x.sub.2])] ... ... ... (1)

and with no live birth,

1 - [??] = 1 1/[1 + [exp.sup.-] ([alpha] + [[beta].sub.1][x.sub.1] + [[beta].sub.2][x.sub.2])] ... ... ... (2)

The odds of an event to occur in the logistic function will be,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Therefore, the odds of an event ([x.sub.1] = 1) for having a live birth with the odds of having no birth ([x.sub.1] = 0) will be,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

To linearise the odds of an event, we take natural logarithm,

In odds = ln ([??]/1-[??]) = [alpha] + [[beta].sub.1][x.sub.1] + [[beta].sub.2][x.sub.2] ... ... ... (5)

The 95 percent confidence limits of the estimated odds ratio (OR).

ln O[??] [+ or -] 1.96 SE (In O[??]) ... ... ... (6)

The estimation of [y.sub.i] values obtained through the logistic function provide the required properties of the estimation of the probabilities because this function is the one that increases with the increasing values of,

[alpha] + [summation] [[beta].sub.i][x.sub.i] ... ... ... ... ... (7)

and the estimated probabilities are within the range of zero and unity. If we substitute the range of plus and minus infinity for Equation 7 in Equation 1, we get,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

This shows that if the exponent of e is positive and very large, the probability is close to the unity; and if it is negative and small, then it is close to zero.

The analytical procedure uses the birth interval covering the period from 2 to 12 years before the survey. In order to further see whether there was any systematic variation associated with the decreasing selectivity, we used three different durations of birth intervals that began 2-6 years, 2-5 years, and 2-4 years preceding the survey) These sets of intervals, while providing a large enough sample, not only permit stable estimates of the coefficients but are also expected to minimise the selection biases associated with the fertility histories of currently married women. The intervals that began 2 years before the interview are not included in the analysis because women failing within these intervals would not have had sufficient time to have these intervals closed. The procedure adopted divides the birth interval into four segments, and within each segment a logistic regression is used, in which the dependent variable is, "whether the next live birth occurs or not". In order to capture a stable pattern of birth intervals, we have examined the 2, 3, and 4-8 birth orders separately.

As a first step, the estimates were obtained based on the intervals that began 2-12 years before the survey and without WFS restrictions; and estimates were obtained for this interval again after imposing the WFS restrictions. Further, we also estimated the birth intervals that began 2-6 years, 2-5 years, and 2-4 years preceding the survey with and without the WFS restrictions. These results were then compared with the estimates of our model. For this approach, we generate a large number of logistic regression estimates such as:

3 sets of birth order intervals (2, 3, and 4-8);

4 sets of segments (months 17-22, 23-28, 29-34, 35-40);

4 sets of time periods (2-12, 2-6, 2-5, 2-4 years preceding the interview); and

2 sets of restrictions (imposing or not imposing the WFS restrictions). This yields 96 logistic regression runs. (4)

Using the original results as the basis for comparison, that is, the estimates based on the intervals begun at 2-12 years before the interview and without the WFS restriction, we establish a confidence interval around the betas from this unrestricted model. We then examine the corresponding betas from the other models to see whether they fall within this interval or not. If they do, we accept the hypothesis that the results from the two sets of universes are identical. If they do not, we reject the null hypothesis and conclude that the results are different. For the interpretation of the results, the signs of the coefficients and the direction of the change are also examined.

RESULTS AND DISCUSSION

The results of the basic analysis are summarised in Tables 1 and 2 in the text, while the estimates for each explanatory variable are presented in Appendix Tables A-1 - A-3.

Since the duration of breastfeeding and contraceptive use are considered to be important determinants of birth intervals, it is of interest to examine the biases they produce in fertility estimates. Table 1 provides the percentage of betas falling within the confidence intervals for these two variables.

In Table 1, for the no-restriction model in the period 2-4 years before the survey, 75 percent of the betas fell within the confidence interval with breastfeeding as explanatory variable, and 92 percent for contraceptive use. When we restrict the fertility history to the last closed and open birth intervals, only 25 percent and 50 percent of the betas fall within the confidence interval for the two variables separately.

However, when the period preceding the survey is 2-6 years, 58 percent estimates are biased for breastfeeding as compared to 100 percent with no restriction, and 67 percent for contraception as against 92 percent with restriction.

This confirms the earlier findings that the longer the duration of the period before the survey, the higher is the proportion of the unbiased estimates falling within the confidence intervals; and that the magnitude of biased results in higher in the restricted than in the unrestricted sample. We may then say that from a biased restricted sample of births, we get biased results, and the relationship between the predictor and the dependent variables would not depict the true picture. It would not be meaningful, therefore, to make the estimates of breastfeeding duration and contraceptive use for all births under the WFS restriction.

Table 2 summarises the results obtained from the betas falling within the confidence limits for betas in the 2-12 years of the unrestricted model, by type of restriction and different background variables. Taking the socio-economic and intermediate variables separately as well as combined in the four time-periods under study, we can see from Table 2 that the longer the period preceding the interview with unrestricted sample, the higher is the proportion of unbiased results. In this table, for all variables in the unrestricted sample, 95 percent of the betas fall within the confidence interval for the period preceding the survey of 2-6 years, as compared to 87 percent for 2-5 years, and 80 percent for the 2-4 years period preceding the survey. But when we restrict the fertility history to the last closed and open birth intervals, only 26 to 52 percent of the betas fall within the confidence intervals under different time-periods before the survey. When we look at the results separately for socio-economic and intermediate variables, we find that the proportion of unbiased estimates is higher for proximate variables. For example, for the period preceding the survey of 2-6 years, 57 percent of the betas fall within the confidence intervals for proximate variables as compared to 48 percent for socioeconomic variables. This may mean that the socio-economic variables have a higher potential for biased estimates than the intermediate variables. This may be so because the intermediate variables are strongly related with the fertility outcome. We may then infer that the coefficients for the restricted sample are substantially different from those of the unrestricted (complete) samples. This difference is larger when the longer time-periods preceding the survey are observed.

CONCLUSIONS

Collection of fertility data in the surveys with the restrictions discussed severely limits the number of birth intervals available for analysis and, thus, incorporate a selection bias which is reflected in the results. It is not appropriate to base estimates of proportions of women who practice contraception, or those who breastfeed, on data for births restricted to the last closed and open intervals because the number of births in the later periods preceding the survey is quite small.

These restrictions do bias estimates of the structure of relationships predicting fertility because our procedure only looks at the first 40 months of experience in the birth intervals. A procedure that incorporates the long tails of the birth interval distribution may obtain different results.

Estimates based on socio-economic variables have a higher potential for biased estimates than those based on intermediate variables, perhaps because the latter are more directly related with the fertility outcome.

Appendix

Table A-1

Results ([B.sub.s]) from Logistic Regression Analysis
of the Determinants of Child Spacing in Pakistan
(PLM Survey), by Type of Restriction: Second Birth
Interval

 Number of Years Preceding the Survey
 and Restriction Status

Birth 2-12 Years
Interval
Segment No Restriction
and
Variable Beta Confidence Interval

Second Birth Interval, Segment 17-22

EDUL -.03687 -.24383 Thru
EDUH .04998 -.13918 Thru
RES .03707 -.06951 Thru
SON .11903 .02171 Thru
AGE -.00064 -.01398 Thru
CONT .04524 -.19056 Thru
ABOR -.11191 -.28243 Thru
BREF -.01766 -.21086 Thru
INF .05866 -.12682 Thru

Second Birth Interval, Segment 23-28

EDUL .12254 -.06268 Thru
EDUH -.03800 -.22608 Thru
RES .03698 -.06394 Thru
SON -.00284 -.09446 Thru
AGE .00031 -.01231 Thru
CON -.12051 -.36301 Thru
ABOR -.02222 -.17830 Thru
BREF .45960 .29026 Thru

Second Birth Interval, Segment 29-34

EDUL -.08475 -.34319 Thru
EDUH -.03332 -.27382 Thru
RES -.11554 -.24726 Thru
SON -.11198 -.22750 Thru
AGE -.00253 -.01845 Thru
CON .25726 -.00792 Thru
ABOR -.05620 -.25886 Thru
BREF .08952 -.09270 Thru

Second Birth Interval, Segment 35-40

EDUL -.05095 -.36633 Thru
EDUH -.07193 -.38929 Thru
RES -.17575 -.33581 Thru
SON -.08025 -.21767 Thru
AGE .00965 -.00869 Thru
CON -.30750 -.78296 Thru
ABOR -.04902 -.29490 Thru
BREF .26486 .01680 Thru

 Number of Years Preceding
 the Survey
 and Restriction Status

 2-12 Years

 No Res-
 triction

Birth
Interval
Segment Beta
and Confidence WFS Res-
Variable Interval triction

Second Birth Interval, Segment 17-22

EDUL .17009 -.23361
EDUH .23914 -.30129
RES .14365 .11514
SON .21635 .11762
AGE .01270 -.01476
CONT .28104 .08809
ABOR .05861 -.13282
BREF .17554 .04943
INF .24414 .12351

Second Birth Interval, Segment 23-28

EDUL .30776 .20310
EDUH .15008 -.01326
RES .13790 -.14453
SON .08878 -.10220
AGE .01293 -.00626
CON .12199 .15913
ABOR .13386 .-37895
BREF .62894 .34607

Second Birth Interval, Segment 29-34

EDUL .17369 .04405
EDUH .20718 -.47383
RES .01618 .14782
SON .00354 -.02897
AGE .01339 .00042
CON .52244 .40696
ABOR .14646 -.22727
BREF .27174 .23764

Second Birth Interval, Segment 35-40

EDUL .26443 .42393
EDUH .24543 .22635
RES -.01569 -.27357
SON .05717 -.18987
AGE .02799 .04330
CON .16796 -.39747
ABOR .19686 .39866
BREF .51292 .35721

 Number of Years Preceding
 the Survey
 and Restriction Status

Birth 2-6 Years
Interval
Segment
and No Res- WFS Res-
Variable triction triction

Second Birth Interval, Segment 17-22

EDUL .04185 .08881
EDUH .03197 .06581
RES .12848 .07695
SON .16975 -.02587
AGE .01057 .00418
CONT .01437 .19768
ABOR -.14027 .01059
BREF -.09642 .33760
INF .06042 .04810

Second Birth Interval, Segment 23-28

EDUL .21940 .73259
EDUH -.01143 -.16497
RES -.03030 -.35606
SON .02254 -.03140
AGE -.00152 .01641
CON -.21546 .05684
ABOR -.03917 -.27125
BREF .47366 .27275

Second Birth Interval, Segment 29-34

EDUL -.34579 -.21372
EDUH .00809 -.43640
RES -.24060 .11793
SON -.25342 -.36138
AGE -.01144 .04581
CON .30230 .45799
ABOR .04839 -.66436
BREF -.06310 .12904

Second Birth Interval, Segment 35-40

EDUL -.09795 -3.50878
EDUH -.07284 -.08870
RES -.22150 -.46657
SON -.08695 -.35682
AGE .02073 .03420
CON -.36493 .21981
ABOR .05634 .43237
BREF .33735 3.66345

 Number of Years Preceding
 the Survey
 and Restriction Status

Birth 2-5 Years
Interval
Segment
and No Res- WFS Res-
Variable triction triction

Second Birth Interval, Segment 17-22

EDUL .19625 -.18148
EDUH .00439 -.24705
RES .08540 .17228
SON .25932 .07733
AGE .00386 -.01915
CONT -.02104 .15319
ABOR -.04832 .30661
BREF .06812 .07571
INF .12954 .14515

Second Birth Interval, Segment 23-28

EDUL .24951 .70111
EDUH .00575 -.09582
RES .01170 -.12354
SON -.02196 -.02027
AGE .00093 .02218
CON -.27278 .01060
ABOR .05022 -.22212
BREF .48353 .75066

Second Birth Interval, Segment 29-34

EDUL -.48698 .01838
EDUH -.12329 -.51609
RES -.25579 .16226
SON -.32499 -.27021
AGE -.01348 .05207
CON .48711 .64638
ABOR .08788 -.20020
BREF -.05375 .35146

Second Birth Interval, Segment 35-40

EDUL -.06645 -3.13128
EDUH .14913 .90281
RES -.34917 -1.56729
SON -.04201 -1.27055
AGE .02343 .02848
CON -.42629 .40631
ABOR .24027 .49833
BREF .24160 2.94542

 Number of Years Preceding
 the Survey
 and Restriction Status

Birth 2-4 Years
Interval
Segment
and No Res- WFS Res-
Variable triction triction

Second Birth Interval, Segment 17-22

EDUL .20058 .05720
EDUH .16371 .80463
RES .07047 .09451
SON .20710 -.07292
AGE .00282 .03480
CONT -.04391 -.64479
ABOR .01477 .74007
BREF .12907 .28754
INF .14532 .30733

Second Birth Interval, Segment 23-28

EDUL .30466 .63882
EDUH .00225 .42254
RES -.00981 -.19032
SON -.04274 .00912
AGE .00090 .02806
CON -.20304 -.02244
ABOR .03288 -.51375
BREF .35569 .29970

Second Birth Interval, Segment 29-34

EDUL -.62131 -1.95668
EDUH -.55116 -10.96304
RES -.29631 .37155
SON -.24870 .08181
AGE -.03232 .05100
CON .45497 8.35344
ABOR .18623 -2.43412
BREF .05708 3.21524

Second Birth Interval, Segment 35-40

EDUL -.09761 -7.01349
EDUH .03629 -1.22388
RES -.55684 -2.92038
SON -.19241 -1.15721
AGE .02861 -1.03175
CON .06950 4.15063
ABOR .23263 .84011
BREF .59792 2.53239

Table A-2

Results ([B.sub.s]) from Logistic Regression Analysis
of the Determinants of Child Spacing in Pakistan (PLM
Survey), by Type of Restriction: Third Birth Interval

 Number of Years Preceding
 the Survey
 and Restriction Status

Birth 2-12 Years
Interval
Segment No Restriction
and
Variable Beta Confidence Interval

Third Birth Interval, Segment 17-22

EDUL -.03236 -.25928 Thru
EDUH -.12268 -.34150 Thru
RES .04896 -.06210 Thru
SON -.03301 -.13555 Thru
AGE .00561 -.00829 Thru
CON .09161 -.13667 Thru
ABOR -.10597 -.27559 Thru
BREF .15126 -.08978 Thru
INF .20586 -.00402 Thru

Third Birth Interval, Segment 23-28

EDUL .12230 -.07598 Thru
EDUH .19136 .00822 Thru
RES -.00657 -.10901 Thru
SON .02796 -.06582 Thnr
AGE -.00087 -.01371 Thru
CON -.08940 -.30542 Thru
ABOR .03960 -.10612 Thru
BREF -.06988 -.09576 Thru

Third Birth Interval, Segment 29-34

EDUL .03134 -.23000 Thru
EDUH -.03911 -.29559 Thru
RES -.03587 -.16893 Thru
SON -.00971 -.12973 Thru
AGE .01123 -.00477 Thru
CON .10385 -.16021 Thru
ABOR -.02262 -.21638 Thru
BREF .18956 -.04482 Thru

Third Birth Interval, Segment 35-40

EDUL -.52617 -.99173 Thru
EDUH -.18539 -.51229 Thru
RES -.00684 -.15984 Thru
SON -.07611 -.21761 Thru
AGE -.01533 -.03535 Thru
CON -.09788 -.46414 Thru
ABOR .06430 -.28298 Thru
BREF .23128 -.05590 Thru

 Number of Years Preceding
 the Survey
 and Restriction Status

 2-12 Years

 No Res-
Birth triction
Interval
Segment Beta
and Confidence WFS Res-
Variable Interval triction

Third Birth Interval, Segment 17-22

EDUL .19456 .23004
EDUH .09614 .07192
RES .16002 -.16467
SON .06953 -.20036
AGE .01951 .00166
CON .31989 .24777
ABOR .06365 -.23455
BREF .39230 .27080
INF .41574 .58767

Third Birth Interval, Segment 23-28

EDUL .32058 -.19725
EDUH .37450 -.06664
RES .09587 .07831
SON .12174 .26079
AGE .01197 .00348
CON .12662 -.16016
ABOR .18532 .07191
BREF .23552 -.09270

Third Birth Interval, Segment 29-34

EDUL .29270 .02699
EDUH .21737 .10656
RES .09719 .02694
SON .11031 .08628
AGE .02730 .02632
CON .36791 .06753
ABOR .17114 -.04436
BREF .42394 -.00051

Third Birth Interval, Segment 35-40

EDUL -.06061 -.28888
EDUH .14151 -.20378
RES .14616 .25243
SON .06539 -.28674
AGE .00469 -.01650
CON .26838 -.50360
ABOR .15438 .02623
BREF .51846 .43469

 Number of Years Preceding
 the Survey
 and Restriction Status
Birth
Interval 2-6 Years
Segment
and No Res- WFS Res-
Variable triction triction

Third Birth Interval, Segment 17-22

EDUL -.11250 .45324
EDUH -.23953 .33626
RES .03533 -.20527
SON -.05042 -.31374
AGE .01515 -.01301
CON .28678 .22971
ABOR -.06951 -.36878
BREF .18049 .09485
INF .23164 .54265

Third Birth Interval, Segment 23-28

EDUL .18957 -.40086
EDUH .28940 -.00061
RES -.06045 -.06710
SON .06099 .25809
AGE -.01428 -.00591
CON -.19168 .02226
ABOR .05125 .05532
BREF .06399 -.13447

Third Birth Interval, Segment 29-34

EDUL .12167 .12368
EDUH .01408 -.28167
RES -.12505 .22194
SON .03932 .20597
AGE .00971 .00425
CON .00354 .21559
ABOR -.07186 -.13761
BREF .25214 -.04047

Third Birth Interval, Segment 35-40

EDUL -.46682 -.15112
EDUH -.17488 .15349
RES .06878 .37400
SON -.01167 -.08675
AGE -.00430 .04931
CON -.46416 -3.90963
ABOR .27889 .30090
BREF .38462 3.85588

 Number of Years Preceding
 the Survey
 and Restriction Status
Birth
Interval 2-5 Years
Segment
and No Res- WFS Res-
Variable triction triction

Third Birth Interval, Segment 17-22

EDUL -.05705 1.26582
EDUH -.18694 .59357
RES .02427 .07632
SON -.05801 -.11920
AGE .01197 .01000
CON .24372 .02053
ABOR -.18989 -.59862
BREF .18226 .18190
INF .22633 .78696

Third Birth Interval, Segment 23-28

EDUL .14777 -.74531
EDUH .27694 -.11453
RES -.01662 -.07866
SON .09995 .29964
AGE -.01476 -.01542
CON -.10554 .20395
ABOR .03397 .14612
BREF .10121 -.10115

Third Birth Interval, Segment 29-34

EDUL .13809 .25918
EDUH .08715 -.12933
RES -.17227 .03018
SON -.04272 -.08007
AGE .00685 .00512
CON .04616 .21878
ABOR .01504 -.39108
BREF .22590 .00316

Third Birth Interval, Segment 35-40

EDUL -.90493 -2.75577
EDUH -.28279 -.04718
RES .11564 .67976
SON -.00399 .25716
AGE -.00864 .06054
CON -.27097 -3.56311
ABOR .23860 .18407
BREF .48385 3.66226

 Number of Years Preceding
 the Survey
 and Restriction Status
Birth
Interval 2-4 Years
Segment
and No Res- WFS Res-
Variable triction triction

Third Birth Interval, Segment 17-22

EDUL -.06904 2.70623
EDUH -.20287 1.24085
RES -.03460 .70933
SON -.12597 -.45674
AGE -.00772 -.01959
CON .30447 -.82374
ABOR -.28797 -.65059
BREF .51665 1.68516
INF .32498 2.15395

Third Birth Interval, Segment 23-28

EDUL .20088 -.72719
EDUH .40878 -.60298
RES -.21434 -.41529
SON .22177 .53369
AGE -.01438 -.01500
CON -.44551 .44167
ABOR .13982 -.16707
BREF .03940 -.07659

Third Birth Interval, Segment 29-34

EDUL -.09960 3.48253
EDUH .07966 -.52914
RES -.11456 -.10405
SON -.06314 -.00416
AGE .01415 .01144
CON .05644 .41706
ABOR .18612 -3.64784
BREF .50414 .10571

Third Birth Interval, Segment 35-40

EDUL -.59889 -2.00684
EDUH -.24020 .40737
RES .04963 .17079
SON -.01647 .16263
AGE -.00559 .04510
CON -.29730 -3.17319
ABOR .14297 -3.04474
BREF .34656 3.34312

Table A-3

Results ([B.sub.s]) from Logistic Regression Analysis of the
Determinants of Child Spacing in Pakistan (PLM Survey), by Type
of Restriction: Fourth Through Eight Birth Interval

 Number of Years Preceding
 the Survey
 and Restriction Status

Birth 2-12 Years
Interval
Segment No Restriction
and
Variable Beta Confidence Interval

Fourth through Eight Birth Interval, Segment 17-22

EDUL -.08984 -.25228 Thru
EDUH -.17538 -.33926 Thru
RES .07820 .00622 Thru
SON .05741 -.17697 T1nr
AGE .00021 -.00947 Thru
CON .05020 -.08706 Thnr
ABOR -.01431 -.11601 Thnr
BREF -.05002 -.29476 Thnr
INF .18662 -.11352 Thru

Fourth through Eight Birth Interval, Segment 23-28

EDUL -.13571 -.29735 Thru
EDUH -.21757 -.38013 Thru
RES .11018 .03792 Thnr
SON .40394 .15908 Thru
AGE -.00418 -.01388 Thru
CON .08458 -.05392 Thru
ABOR -.03374 -.13502 Thru
BREF .08503 -.15887 Thru

Fourth through Eight Birth Interval, Segment 29-34

EDUL .08945 -.07301 Thru
EDUH -.10655 -.27535 Thru
RES .02324 -.04978 Thru
SON -.05820 -.29364 Thru
AGE -.00991 -.01983 Thru
CON .02621 -.11307 11ru
ABOR -.07265 -.17687 Thru
BREF .14134 -.11698 Thru

Fourth through Eight Birth Interval, Segment 35-40

EDUL .00383 -.17439 Thru
EDUH -.09826 -.28652 Thru
RES -.02845 -.10757 Thru
SON .05458 -.20938 Thru
AGE -.01968 -.03060 Thru
CON .00843 -.14205 Thru
ABOR .00859 -.10281 Thru
BREF .26659 -.04453 Thru

 Number of Years Preceding
 the Survey
 and Restriction Status

 2-12 Years

 No Res-
Birth triction
Interval
Segment Beta
and Confidence WFS Res-
Variable Interval triction

Fourth through Eight Birth Interval, Segment 17-22

EDUL .07260 -.06626
EDUH -.01150 -.26668
RES .15018 .07995
SON .29179 .10567
AGE .00989 -.00598
CON .18746 .04126
ABOR .08739 -.14617
BREF .19472 .03396
INF .25972 .22236

Fourth through Eight Birth Interval, Segment 23-28

EDUL .02593 -.19652
EDUH -.05501 -.16445
RES .18244 .10308
SON .64880 .30471
AGE .00552 -.00277
CON .22308 .03162
ABOR .06754 -.13330
BREF .32893 .19631

Fourth through Eight Birth Interval, Segment 29-34

EDUL .25191 .04451
EDUH .06225 .12077
RES .09626 .00118
SON .17724 -.29276
AGE .00001 -.00854
CON .16549 .03196
ABOR .03157 -.04113
BREF .39966 .04265

Fourth through Eight Birth Interval, Segment 35-40

EDUL .18205 .00849
EDUH .09000 -.26574
RES .05067 -.02162
SON .31854 1.32479
AGE .00876 -.02108
CON .16091 .01657
ABOR .11999 .09078
BREF .57771 .67863

 Number of Years Preceding
 the Survey
 and Restriction Status

Birth
Interval 2-6 Years
Segment
and No Res- WFS Res-
Variable triction triction

Fourth through Eight Birth Interval, Segment 17-22

EDUL -.08794 -.10255
EDUH -.18405 -.20296
RES .08278 .08331
SON .05028 .11328
AGE .00153 .00394
CON .04853 .08932
ABOR .01458 -.16289
BREF -.03003 .03351
INF .19661 .11384

Fourth through Eight Birth Interval, Segment 23-28

EDUL -.08945 -.00499
EDUH -.23072 .00965
RES .09180 -.01142
SON .38645 .37594
AGE -.00367 -.00312
CON .08067 -.13328
ABOR -.01626 -.14841
BREF .08439 .14602

Fourth through Eight Birth Interval, Segment 29-34

EDUL .07152 .03118
EDUH -.14919 .14539
RES .03979 -.05579
SON -.10091 -.15213
AGE -.00651 -.00478
CON .04177 .19251
ABOR -.08189 -.00746
BREF .21304 .04019

Fourth through Eight Birth Interval, Segment 35-40

EDUL .03540 .05417
EDUH -.13434 -.61876
RES -.04789 -.02226
SON .03283 4.68733
AGE -.01509 -.01011
CON .00815 .04821
ABOR -.03771 -.02919
BREF .20158 .87155

 Number of Years Preceding
 the Survey
 and Restriction Status

Birth
Interval 2-5 Years
Segment
and No Res- WFS Res-
Variable triction triction

Fourth through Eight Birth Interval, Segment 17-22

EDUL -.10952 -.01067
EDUH -.16404 -.12514
RES .09733 .17117
SON .04728 .10797
AGE .00224 -.00512
CON .04707 .13372
ABOR .01180 -.18733
BREF -.03489 .17540
INF .18436 .18081

Fourth through Eight Birth Interval, Segment 23-28


EDUL -.09527 -.02844
EDUH -.25018 -.00758
RES .10535 -.00412
SON .43113 .54526
AGE -.00375 -.00663
CON .06166 -.13786
ABOR .00063 -.12869
BREF .03868 .13346

Fourth through Eight Birth Interval, Segment 29-34

EDUL .07757 -.02197
EDUH -.12256 .18734
RES .06004 -.12519
SON -.07701 .05840
AGE -.00612 -.01418
CON .01727 .13437
ABOR -.08357 .11252
BREF .21162 .20345

Fourth through Eight Birth Interval, Segment 35-40

EDUL -.01452 -.12924
EDUH -.15675 -.45551
RES -.05464 -.01168
SON .00489 4.70869
AGE -.01517 .00627
CON -.00480 -.08146
ABOR -.07554 -.12491
BREF .23770 4.56014

 Number of Years Preceding
 the Survey
 and Restriction Status

Birth
Interval 2-4 Years
Segment
and No Res- WFS Res-
Variable triction triction

Fourth through Eight Birth Interval, Segment 17-22

EDUL -.08241 .16237
EDUH -.15662 -.20695
RES .10155 .18440
SON .02521 .11398
AGE .00070 -.01227
CON .04351 .11171
ABOR -.00770 -.12239
BREF -.04076 .03691
INF .18074 .10319

Fourth through Eight Birth Interval, Segment 23-28

EDUL -.10139 .11054
EDUH -.22640 .16849
RES .11287 -.02082
SON .41750 .37214
AGE -.00513 -.00507
CON .03253 -.21101
ABOR .00700 -.16339
BREF .00115 .20771

Fourth through Eight Birth Interval, Segment 29-34

EDUL .05467 .07236
EDUH -.16732 .25647
RES .04464 -.11598
SON -.06696 .00219
AGE -.00613 .00110
CON .02043 -.17110
ABOR -.06546 -.06911
BREF .19480 .06765

Fourth through Eight Birth Interval, Segment 35-40

EDUL .02515 -.15590
EDUH -.18864 -.25587
RES -.06057 -.15226
SON -.02365 4.64846
AGE -.01335 -.01726
CON .03336 -.07104
ABOR -.06021 -.18220
BREF .24652 4.43643

REFERENCES

Akin, J., R. Bilsborrow, D. Guilkey, D. Benoit, P. Cantrell M. Garenne and P. Levi (1981) The Determinants of Breast Feeding in Sri Lanka. Demography 18: 287-307.

Bumpass, L. L., R. R. Rindfuss, A. Palmore, M. Conception and B. M. Choe (1982) Intermediate Variables and Educational Differentials in Fertility in Korea and the Philippines. Demography 19: 241-260.

Goldfeld, S. M., and R. E. Quandt (1972) Non-linear Methods in Econometrics. Amsterdam: North-Holland Publishing Company.

Jain, A. K., and J. Bongaarts (1981) Breastfeeding: Patterns, Correlates, and Fertility Effects. Studies in Family Planning 12:3 79-99.

Kmenta, J. (1986) Elements of Econometrics. New York: Manillan.

Maddala, G. S. (1983) Limited Dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press.

Palloni, A. (1984) Assessing the Effects of Intermediate Variables on Birth Interval Specific Measures of Fertility. Population Index 50: 623-627.

Pebley, A. R., N. Goldman and M. K. Choe (1986) Evaluation of Contraceptive History Data in the Republic of Korea. Studies in Family Planning 17:1 22-35.

Rindfuss, R. R., L. L. Bumpass, J. A. Palmore and D. W. Han (1982) The Transformation of Korean Child Spacing Practices. Population Studies 36: 84-104.

Rindfuss, R. R., L. L. Bumpass and J. A. Palmore (1987) Analyzing Fertility Histories: Do Restrictions Bias Results? Demography 24:113-122.

Smith, D. P. (1985) Breastfeeding, Contraception and Birth Intervals in Developing Countries. Studies in Family Planning 16:3 154-163.

(1) The "open birth interval" is the birth interval begun at the birth of the last (i.e., the youngest) child and terminated by the interview. Another birth may occur after the interview and hence the term "the last closed birth interval" is the interval terminated by the last child.

(2) For detailed discussion on each of these models, see Kmenta (1986, Ch. 11), Goldfeld and Quandt (1972, Ch. 4), and Maddala (1983, Ch. 2).

(3) A smaller number of cases may affect the results obtained because of the well-known relationship between the sample size and the sampling variability associated with estimated coefficients.

(4) Detailed results from these runs are presented in the Appendix Tables A-l, A-2, and A-3.

Zubeda Khan and Ghulam Y. Soomro are Senior Research Demographer and Research Demographer, respectively, at the Pakistan Institute of Development Economics, Islamabad.

Table 1

Percentage of [beta]s Falling within the Confidence Limits
for [beta]s in the 2-12-Year Unrestricted Model, by Type
of Restriction, Type of Variable, and Number of Years
Preceding the PLM Survey 1979

 Number of Years
 Preceding Survey
Type of Variable
and Restriction 2-12 2-6 2-5 2-4

Contraceptive Use

WFS Restriction 83 67 58 25
No Restriction 100 92 100 92

Breastfeeding

WFS Restriction 92 58 50 50
No Restriction 100 100 100 75

Table 2

Percentage of [beta]s Falling within the Confidence
Limits for [beta]s in the 2-12-Year Unrestricted Model,
by Type of Restriction, Type of Variable, and Number of
Years Preceding the PLM Survey 1979

 Number of Years
 Preceding the Survey
 Type of Variable
 and Restriction 2-12 2-6 2-5 2-4

Intermediate Variables

WFS Restriction 82 57 46 28
No Restriction 100 95 95 80

Socio-economic Variables

WFS Restriction 70 48 47 25
No Restriction 100 95 87 80

All Variables

WFS Restriction 75 52 47 26
No Restriction 100 95 90 80