(World Population Prospects: The 1994 Revision, United Nations, New York, 1995, pages 674-675. The medium variant projected total population for India is 1.6 billion in 2050. The low and high variants are 1.3 and 2.0 billion, respectively. The same source gives total fertility rates for 1950-1990 noted in the following paragraph.)
The level of fertility in India has declined in recent decades, with the total fertility rate (TFR) falling from about six children per woman in the 1950s to 3.4 children per woman in the early 1990s. The rate of decline was about one child per woman per decade, not slow in historical perspective, nor by comparison with other South Asian countries, but far slower than declines in East Asia. In China, for example, a somewhat larger decline occurred in the first seven years of the 1970s.
(India National Family Health Survey 1992-93, International Institute for Population Sciences, Bombay, 1995. The figuress noted in the preceding paragraph are from Table 6.4, pages 133-34. Subsequent references to published NFHS data are to this report unless otherwise indicated. References to question numbers are to the woman's questionnaire that appears in Appendix F of this report.)
The NFHS showed a substantial unmet need for contraception for spacing. Table 7.5 of the NFHS National Report shows 11 percent of currently married women having unmet need for contraception for spacing. This unmet need represents one quarter of current contraceptive use. Meeting this need would increase current use from 40 to 51 percent. The international relationship between contraceptive prevalence and total fertility (The Reproductive Revolution: New Survey Findings, Tables 1 and 2 and Figure 2) indicates that each 10 percent point increase in contraceptive prevalence reduces the TFR by about 0.6 children per woman.
These figures suggest that the national family planning program in India should consider expanding access to modern temporary methods of family planning, but the gross national level relation between contraceptive use and fertility levels can give only a rough indication of the impact of relatively small changes in use over time within a population. A more detailed and specific investigation is needed to determine the fertility impact of meeting the unmet need for spacing methods.
Some women who say they want an additional child after an interval of two or more years will act accordingly, if the means are available, first adopting and then discontinuing use of a temporary method in an attempt to realize another child after the desired interval. Other women in this group will change their minds about having another child before conceiving one, transforming themselves from spacers to stoppers.
The behavior of the first group will push fertility down because various contingencies, such as onset of natural sterility or widowhood, will reduce the likelihood that deferred birth will ever occur. It will also reduce fertility by stretching out the period over which births occur.
The behavior of the second group will push fertility down as well. Some of these women will merely be uncertain about their desire for another birth, an uncertainty that may in part reflect the survival chances of their living children, and therefore be reluctant to undergo sterilization. Some of these uncertain women will end up deciding against additional children. The importance of this second group of women is underscored by the concentration of unmet need for spacing among young women with small numbers of children (NFHS National Report, Table 7.5).
The Dictionary of Demography (Roland Pressat/Christopher Wilson, Blackwell Reference, Oxford, 1985) defines open birth intervals as those between a woman's most recent birth and the time of a census or survey. We would remove the necessary connection to data collection and define open intervals to include as well the interval between a woman's last birth and her death or arrival at the end of reproductive age, whichever comes sooner. A woman's reproductive history then resolves into three components, the interval before first birth, the interbirth (closed) intervals, and the open interval following her last birth.
There are various ways of selecting sets of closed birth intervals for analysis. Forward selection, in which intervals initiated during a particular time period are selected, is conceptually preferable but raises the problem of right truncation by interview date. Backward selection, in which intervals terminating during a particular time period are selected, introduces errors in the case of non-stationary populations but has the advantage of avoiding truncation where complete birth histories are available.
Forward selection defines, by analogy to the role of birth cohorts in the study of mortality (forward selection of life times), the standard by which other selections are judged. The rationale for this is that the only way to insure against selection bias is to rule out the use of information that becomes available only after the intervals in question have begun, since such information assures that there will be some discrimination between intervals on the basis of their length. It is of course permissible to select intervals on the basis of characteristics of intervals defined at the time of initiation, such as, for birth intervals, sex, birth order, weight, multiple birth status, age or education of mother, and so on.
Backward selection of closed birth intervals is analogous to selection of data on length of life by death cohort, an approach sometimes used in historical demography, where lifetimes recorded on tombstones are more likely to be concentrated by period of death than by period of birth. In a growing population, the excess of births in recent periods will result in larger numbers of deaths at younger ages and consequently in mean lifetimes that are biased low. Only in a stationary population may the distribution of deaths in the population be identified with the distribution of deaths in the life table.
Right truncation bias may be ameliorated in either of two ways. One is to select distributions initiated during a period that ended five, ten or more years prior to the the survey and consider only intervals less than the implied limit. Truncation bias goes to zero as the selection period becomes more remote in time, but at the cost of securing information only on birth intervals initiated long before the survey.
Life table methods provide another solution, and one that allows utilization of the most recent data available by producing synthetic closed birth interval distributions based on parity and duration-specific birth rates. Rather complex calculations are required, however, and the computation of the synthetic closed birth interval distribution requires estimating the parity progression ratio. Calculating the parity progression ratio for truncation intervals greater than five years requires large numbers of cases because of the low incidence of longer intervals.
The DHS survey reports since about 1990 include data on last closed birth intervals terminated by births ending within a given number of years prior to the survey, suggesting a decision in favor of the simplicity of backward selection over the complications of forward selection. All things considered, we are inclined to agree with this decision, though we would like to have an indication of the magnitude of the bias resulting from backward selection given typical departures from stationarity, which include both seasonal variations and secular trends in births.
Our interest in this general issue is very specific. We want to know what would happen if the unmet need for contraception for spacing in India were met. What proportion of the resulting use segments would fall in closed birth intervals (women fulfilling their intention to have another child), and what proportion would fall in open intervals (women stopping childbearing despite the declared intention to space)? Establishing some empirical patterns for how contraceptive use at different levels is distributed between spacing and stopping may enable us to make indirect inferences about the effect of meeting the unmet need for contraceptive spacing.
It should perhaps be noted that classification of contraceptive use segments according to where they fall in a woman's reproductive history will not in general agree precisely with women's intentions with respect to contraceptive use. A woman may experience contraceptive failure, turning what would have been a terminal open interval into a closed interval; and a woman who uses contraception to delay a desired additional birth may prove unable to conceive, turning what she intended to be a closed interval into a terminal open interval.
*|888999 NEBraz Paragu Philip DomRep Madaga Pakist 3|000000111 Bolivi Egypt Niger Nigeri Camero Haiti Peru Moroc Zambia t|23333 Rwanda Malawi Colomb ICoast Tanzan f|455 Namibi BurkFa Bangla s|67 Ghana Zimbab .| 4| t|2 Indonesia(The stem value 3 is for values 30-31, the following t for values 32-33, the following f for values 34-35, the following s for values 36-37, the following . for values 38-39; thus the values represented here are, in increasing order, 28 (3), 29 (3), 30 (6), 31 (3), 32 (1), 33 (4), and so on.)
The median interval is 31 months and the interquartile range is 30-33 months. Indonesia is an extreme outlier with a median interval of 42 months, 5 months longer than the next longest value (Zimbabwe, 37 months).
There is unfortunately no strictly comparable data for developed countries, or at any rate none that we have been able to locate (time does not permit special tabulations from the original survey data), but we have assembled roughly comparable median closed birth intervals for 12 European countries and for the USA. These medians are derived from synthetic cumulative distribution functions for interbirth intervals derived by life table methods. Since the distributions end at 84 months duration, the medians are necessarily conditional on this interval, making them slightly lower than they would be if the truncation point were higher. The magnitude of the bias may be assessed by assuming that three percent of all intervals are longer than 84 months, a conservatively high figure, and recomputing the medians on this basis. This calculation shows biases varying from country to country, but in no case exceeding one month.
As no overall figures for all birth intervals are available, intervals for first to second birth and for second to third birth are shown separately.
1ST TO 2ND 2ND TO 3RD
s|7 Belgium s|
.|999 GrtBrit Spain Yugo .|89 Belgium GrtBrit
3|0 Nether 3|01 Yugo Spain
t|223 USA Poland France t|2233 Nether Poland USA France
f|444 Norway Finland Italy f|555 Italy Hungary Norway
s|67 Hungary Czech s|6 Finland
.| .|8 Czech
The median intervals are 32 and 33 months for 1st to 2nd and 2nd to
3rd intervals, respectively, and the corresponding interquartile
ranges are 29-34 and 30h-35 months (h denoting half).(Kathleen Ford, Timing and Spacing of Births, WFS Comparative Studies, ECE Analyses of WFS Surveys in Europe and USA, International Statistical Institute, December 1984, Table 2.)
This evidence indicates rather clearly that birth intervals in developed countries are not very much different than birth intervals in developing countries. Intervals in developed countries appear on this evidence to be slightly longer, but the difference is modest indeed in relation to the vast differences in level of contraceptive use.
This evidence alone would suggest that most contraceptive use functions as stopping, with little or no use serving to lengthen closed intervals. Other things being equal, however, breastfeeding practices would make intervals in developing countries substantially longer than intervals in developed countries, so the correct conclusion is that there is significant contraceptive spacing in developed countries. In view of the very different combination of influences operating on birth intervals it is remarkable that the distributions are as similar as they are.
Figure 1 plots median last closed
birth interval against the percentage of currently married women using
modern temporary methods of contraception for the 25 states included in
the NFHS. The plot shows no tendency of higher levels of use to be
associated with longer intervals. Since 23 of the 25 states
represented have use levels under or barely above 10 percent, however,
the evidence has limited scope. It may be that contraceptive spacing
becomes substantial only at higher use levels.
In view of this, it makes sense to look for other evidence involving higher levels of use. The DHS surveys reports published since about 1990 include data on last closed birth intervals.
Figure 2 shows the same
relationship shown in Figure 1, but for 26 countries for which we
have been able to locate the necessary data. Initial scrutiny
suggests a very slight positive relationship, but closer inspection
indicates that this first impression is due largely to a single
point, Indonesia (which we saw above is an extreme outlier). An
ordinary least squares (OLS) regression line with this point excluded
shows a slope very close to zero, and excluding the marginally
outlying point for Zimbabwe as well gives a slightly negative slope.
Overall, no relationship is indicated.
We have a further source of aggregate evidence, however, because several of the DHS survey reports provide these statistics not just for the country as a whole, but for subnational units. We have found six such countries, Bangladesh, Colombia, Indonesia, Morocco, Peru, and Tanzania. Rather surprisingly, in view of the evidence just presented, four of these cases indicate a rather strong positive relationship between use of a modern temporary method and median last closed birth interval.
There are only five points for
Bangladesh, but they fall sufficiently close to the fitted line to
indicate a relationship, with an increase of 10 percent in use
resulting in a 2 month increase in median interval.
The points for Colombia suggest a
stronger positive relationship, with a 10 percent increase in use
yielding a 5 month increase in median interval, though the spread of
the points about the fitted line is considerable and discounts the
magnitude of the effect.
The ranges of both median interval and of use of modern temporary
methods are so much larger for Indonesia that for the other countries
considered that very different plotting scales must be used (scales in
the preceding and following plots are identical for visual
comparability), but the aspect ratio in 
There are only seven points for
Morocco , but the fit is comparable to that for Bangladesh, though
with a slightly weaker relationship, a 10 percent increase in use
giving just over a 1.5 month increase in median last closed
interval.
At first glance, the data for Peru
suggest a strong positive relationship, but on closer inspection this
is seen to be due entirely to two outlying points. Ordinary least
squares (OLS) regression gives a strong positive relationship, but
least trimmed squares (LTS) regression, a robust technique, gives a
negative relationship. There is no relationship for the 11 regions
with use levels between 10 and 30 percent, but a clear relationship
when these regions are contrasted with the two regions with use levels
approaching 40 percent.
shows evidence for the final
country, Tanzania. The ordinary least squares line indicates a mildly
positive relationship, but does not appear to be a particularly good
fit. This is evidently due to the cluster of points at lower left,
which the eye tends to perceive as single point, and which are
therefore visually deemphasized, but which pull the OLS line down on
the left. Least trimmed squares regression discards the upper and
lower clusters of points and fits the middle group, which show a mildly
negative relation. Overall, no relationship is indicated.
The data for the 25 states of India and for the 26 countries indicate no tendency for higher levels of contraceptive use (modern, temporary methods) to be associated with longer closed birth intervals. The subnational data for four of the six countries considered indicate a strong relationship. How are these results to be reconciled?
The absence of a relationship in India is evidently due to the overall low levels of use. Tanzania has similarly low levels of use and a similar absence of relationship. The disparity between the 26 country data set and the four national data sets is probably explained by the confounding effect of influences on birth interval length other than contraceptive use. It is plausible that these other influences will in general be more similar between subgroups within a country than they are between countries. Thus the relationship that is obscured by the international comparison is revealed by the subnational comparisons.
The subnational comparisons for four of the six countries considered indicates that birth intervals do tend to increase as the use of temporary contraceptive methods increases. Tanzania, in which overall use is very low, does not constitute a significant exception to this pattern, for the India and Tanzania data taken together suggest that increases in the length of closed birth intervals due to increased contraceptive use will be detected only when overall use rises well over 10 percent.
The overall use level for Peru is well over 10 percent, however, without any clear relation ship between use level and length of birth intervals. Close scrutiny of all the intra-country plots shows, however, that no relation between use and birth interval is indicated when use lies below about 30 percent, suggesting that contraceptive spacing comes into play only when overall use of temporary methods rises above this level.
Despite the contrary to the impression given by the 26 country data, the data for the 25 Indian states, and the relatively small difference between median birth intervals between developed and developing countries, closed birth intervals do indeed appear to get longer as contraceptive use increases, indicating that a non-negligible fraction of use is being allocated to spacing.
The magnitude of the effect is more difficult to assess. The data for Bangladesh, Colombia, Indonesia and Morocco indicate increases of 2 months, 5 months, 4 months, and 2 months increase, respectively, in median birth interval for a ten percent increase in use of temporary contraceptive methods. The median of these four figures is 3 months. Against a median birth interval of slightly over 30 months this represents a relative increase of slightly under 10 percent, neither a negligible effect nor a very large one.
Applied over a wide range of observed use levels, from 20 to 70 percent, say, this effect would lengthen birth intervals by as much as two years. The very modest differences in median intervals between developing and developed countries suggest that such large effects are unlikely, however. Large shifts in levels of use are evidently accompanied by other changes (declines in breastfeeding being perhaps the most obvious candidate) that reduce the lengthening effect of higher use levels.
Meeting the unmet need for spacing methods of contraception in India would increase use of temporary methods by about 10 percent, and on the preceding analysis this could lengthen closed birth intervals by about 3 months. This is a rather large effect in relation to the variation in interval lengths both among Indian states and the 26 countries considered above, so it is reasonable to expect that the effect would not be much larger than this.
Accumulated over three closed intervals, corresponding to four live births, this would increase age at last birth by only 9 months. Since the 1992-93 TFR for India is 3.4 children per woman (National Report, Table 5.2, page 96), this is evidently a conservative reckoning of the effect. Based on Henry's estimated figures for the increase of natural sterility with age (John Bongaarts and Robert G. Potter, Fertility, Biology, and Behavior: An Analysis of the Proximate Determinants, Academic Press, New York, 1983, page 156), an increase of one year of age during a woman's early 30s would reduce fertility by 1-2 percent. This suggests that the fertility reducing effect of longer birth intervals is likely to be very small indeed.
If there is a substantial fertility effect of meeting the unmet need for temporary methods of contraception, then, it must result from the conversion of women from spacers to stoppers and not from the lengthening of birth intervals. Is it possible to estimate the magnitude of this effect from the preceding analysis?
Over the long term, assuming equilibrium conditions, an increase of 10 percent in contraceptive use among currently married women of reproductive age corresponds to women using contraception for an additional 10 percent of the portion of their reproductive life spans they spend in the currently married state. This average period may be approximated by summing proportions currently married in five year age groups (NFHS National Report, Table 4.2, page 76) over the reproductive life span and multiplying by 5, giving a period of 27 years.
This suggests that increasing use of contraception by 10 percent implies increasing the average number of years women use contraception by 2.7 years. If only 0.75 years of this use falls in closed birth intervals, as suggested by the above analysis, nearly 2 years of this 2.7 year increase would have to fall either prior to the first birth or in the open interval following the last birth.
This suggests, albeit more tenuously than we would like, than a substantial portion of increased use of contraception would, even though satisfying a stated need for spacing rather than stopping, translate into use for stopping. The impact on fertility may be gauged roughly by considering a few examples. A woman with two children who stops at two children, rather than going on to a third, as a result of using contraception with the initial intention of spacing, has reduced her fertility by one third. A women with three children who stops at three rather than four children under similar circumstances has reduced her fertility by 25 percent. These figures suggest that the impact may be substantial.
We are therefore obliged to proceed indirectly, using the use information that is available as a proxy for use in closed intervals. Since women who have never used contraception obviously did not do so in any closed birth interval, knowing that a woman has ever used or is currently using increases the likelihood that she used in the last closed interval. Relationships between use indicators and birth interval lengths will be muted, but will reveal themselves if sufficiently strong.
It is possible that survey respondents who are currently or have ever used contraception will have shorter last closed intervals than never users. Since it is impossible for contraceptive use in a closed interval to shorten the interval this would indicate causality in the reverse direction. We would conclude that women with characteristics pointing to shorter intervals use contraception more than other women.
Should this turn out to be the case (and it does) it will be possible to estimate the effect of contraceptive use on birth spacing only if the characteristics on the basis of which women have self-selected themselves can be introduced as control variables. The indicated approach would thus be to identify variables available in the survey that might serve this purpose and study the relation between contraceptive use and birth spacing controlling for these variables.
If introducing these controls yields a positive relationship between use and spacing, we will have an estimate, presumably conservative, of the relationship. If we cannot obtain a positive relationship, the conclusion must be that the survey does not contain (or perhaps that we have failed in finding) sufficient information to control for self-selection and cannot provide an estimate of the influence of contraceptive use on birth spacing.
It may be noted that the problem of self-selection could arise even if we had direct information on contraceptive use within closed birth intervals.
To select a self-weighting subsample we need to select observations without replacement and with probability proportional to the all India sample weights. Summing these weights over all women and dividing each weight by this sum gives a probability for each woman in the original sample. Passing through the survey records and selecting each woman with this probability would yield a subsample with an expected size of one. We want a larger subsample than this, indeed, we want the largest possible subsample, so we multiply these initial probabilities by the largest possible factor, the constraint being that no probability can exceed one. To insure that the sequence in which the records appear in the data file does not influence the outcome we randomly permute the order of the records before selecting the subsample.
Figure 9 shows the normal Q-Q plot
(Visualizing Data, William S. Cleveland, Hobart Press, 1993,
books@hobart.com, pages 28-33) of all last closed intervals. The
longest intervals are nearly 300 months (25 years); there is a
smattering of negative intervals, indicating data problems; that
there are a considerable number of intervals of length zero,
corresponding to twins; and that the main portion of the plot curves
sharply upward, indicating substantial departure from normality. The
departure from normality reflects the substantial skewness of the
distribution toward longer intervals.
The total number of points plotted here is the number of observations for which century month of most recent birth and century month of next most recent birth are both available, a total of 23,883 observations. The frequency of the values shows 9 negative intervals, 222 zero intervals, 3 intervals between 2 and 8 months long, 74 9 month intervals, and progressively larger numbers of larger intervals.
For the subsequent analysis we consider only intervals 9 months or longer. The rationale for setting this lower limit is that the data show a clear discontinuity between intervals less than 9 months and greater than or equal to 9 months, but no discontinuity for intervals greater than or equal to 9 months. We do not thereby express a belief that these exceptionally short intervals are valid, merely that the data gives no basis for excluding them. It should not be assumed too readily that a birth interval of 9 months is impossibly short, however, for the incidence of these intervals is only 0.31 percent, too low for any but a very large survey to estimate. The total number of last closed intervals greater than or equal to 9 months is 23,649.
Figure 10 shows the normal Q-Q
plot for the log of these last closed intervals. The plateau effect
at lower right reflects the relatively discrete values of the logs of
the short intervals (ln(9) = 2.20, ln(10) = 2.30, ln(11) = 2.40).
This is the main departure from a straight line, at least in this
full range perspective, and indicates that the distribution of last
closed intervals is very nearly log linear.
Summary statistics of the last closed intervals are as follows.
Min Q1 Median Mean Q3 Max
9 23 32 36.66 44 282
The integral value of the median requires special comment. No sample
sample weights are involved, all observations are integral numbers of
months, and there are large numbers of observations assuming every
value in the vicinity of the median (there are, for example, more than
500 observations for every birth interval length between 21 and 37
months inclusive). The median must therefore be either integral or an
integer plus 0.5, and in view of the density of observations in the
vicinity of the median it is virtually certain that the median will be
integral. The same remarks apply to the other medians presented
below. The fractional values for median intervals given in the
published report are an artifact of the sample weights.The median last closed interval of 32 months agrees with the value published in the NFHS National Report (31.6 months, Table 5.14, Page 111) despite the difference in the group of intervals represented, all intervals in the SWS here and intervals terminating in the five years preceding the survey for the complete sample in the published report.
Min Q1 Median Mean Q3 Max Cases
0-59 9 24 33 37.43 45 282 11,473
60-119 9 23 30 36.25 42 269 5,785
120-179 9 23 31 37.11 44 239 3,573
180-239 9 23 29 34.58 41 169 2,011
240-299 9 21 28 31.61 38 119 686
300+ 9 22 29 32.62 41 108 121
This shows a clear tendency for median closed birth interval to
increase with time over the 25 years prior to the survey, with the
median rising from 29 to 33 months over the two decades prior to the
survey. It is unclear how much, if any significance should be
attached to the dip 60-119 months (5-9 years) prior to the survey.
The rise in maximum values presumably represents the larger numbers of
cases during more recent periods rather than a time trend.The occurrence of 9 month intervals in ever category, even the last one, containing only 121 cases total, is curious. One supposes that this is telling us something about these unreasonably short intervals, but we have yet to divine what this something might be.
The long tails of these distributions suggests that medians will in general be preferable to means as measures of central tendency.
The analysis of length of last closed birth interval in relation to contraceptive use should be restricted insofar as possible to intervals spanning the period to which the available contraceptive use information refers. As already noted, the NFHS (and DHS surveys generally) contain very little information on contraceptive use in calendar time. In the following paragraphs we assess what little information is available.
Question 341 asks how long the appropriate group of women (currently married, not pregnant or not sure, currently using some method of contraception, neither the woman nor her husband sterilized) have been continuously using the current method of contraception. Responses are available for only 902 women and the responses are very heavily heaped on 0 months (266 cases) and multiples of 12 months. The median duration of use is 12 months, the mean duration 32 months, the maximum duration 99 months. Limited as this indication is, it clearly suggests that most current use segments represent use in the five years preceding the survey.
The overall level of use cannot as a matter of pure logic tell us anything about use in the past, for it is a logical possibility that all this use was initiated immediately prior to the survey. If we work from empirical plausibility, however, some inference should be possible. On the equilibrium assumption analysis noted above, the current use of 40 percent indicates that women spend an average of 40 percent of 27 years, or nearly 11 years, using contraception. Since survey respondents are on the average something less than half way through their reproductive years, this indication suggests that most contraceptive use by survey women occurred within the five years prior to the survey, in broad agreement with the result of the preceding paragraph.
The absence of information on use during the last closed interval forces the use of current and/or ever use as a proxy. As current use constitutes the great majority of ever use, results are not likely to be very different for these two choices. We have chosen current use on the grounds that the use information is both more time-specific and more recent.
Because current use is surely a better proxy of use in the recent than in the more distant past, last closed intervals ending long before the survey should be excluded. Based on the analysis of the preceding section, and following the precedent of the NFHS National Report, the analysis that follows is based on last closed intervals ending within five years of month of interview. There are 11,473 such intervals in the self-weighting sample.
The median length of last closed intervals for all these women is 33 months (mean 37.4 months). For women currently using no method, any modern temporary method, male or female sterilization, and any traditional method, the corresponding numbers are 34 (37.85), 31 (34.97), 32 (36.27), and 36 (41.09). Note that although a closed birth interval cannot by definition involve use of a permanent contraceptive method, current sterilization is as plausible a proxy for past use of a temporary method as current use of temporary methods.
Since contraceptive use cannot shorten birth intervals, this definitively demonstrates the presence of selection effects for use of modern contraceptive methods. (A logically conceivable but thoroughly implausible alternative interpretation would be that current use of these methods is a proxy for non-use in the last closed interval.)
Birth intervals for women currently using traditional methods are longer than for women using no methods by 3 months on the median, but it would be unwise to accept this as an indication of the birth interval lengthening effect of contraceptive use. Since self-selection is operating to increase the proportion of high risk women among those using modern methods of contraception, it is probably operating as well to decrease the proportion of these women among those using traditional methods.
Regressing the log of last closed interval on dichotomous variables representing use of any modern method, sterilization of wife or husband, and any traditional method gives the following results.
Value Std Err t value Pr(>|t|)
(Intercept) 3.5129 0.0056 632.8865 0.0000
Mod Temp -0.0837 0.0186 -4.5046 0.0000
Ster -0.0441 0.0111 -3.9677 0.0001
Trad 0.0594 0.0238 2.4971 0.0125
The use of log last closed interval rather than last closed interval
creates a minor nuisance in interpretation, but is indicated by the
extreme skewness of the birth interval distribution and the success of
the log in normalizing it. Exponentiating a coefficient gives
the factor by which the average birth interval length will be increased
or decreased, other things being equal, by use of a given class of
methods. Thus current use of a modern temporary method decreases the
average length of the last close birth interval by exp(-0.0837) =
0.920, i.e., by 8 percent.The use variables explain almost none of the variation in birth interval lengths (the interquartile range of the residuals is slightly larger than the interquartile range of the observations), but there is a clearly discernible negative impact of use of modern methods as well as a positive impact of use of traditional methods.
The regression sharpens the picture given by simple comparison of medians for the various groups without changing the interpretation. No conclusion about the birth interval lengthening effect of contraceptive use can be drawn from these statistics because self-selection effects are overwhelming whatever lengthing effects are present.
Women self-select for contraception on the basis of information about themselves that enables them to assess their risk of conception. If the NFHS data provides variables that capture this information, introducing them into the analysis should control out the selection effects and permit estimation of the positive effect of contraceptive use on birth interval length.
On the basis of various exploratory analyses we have concluded that it is unlikely that the information collected in the survey will allow this sort of control. Certain of the information collected, such as age and birth history, is clearly relevant to assessing risk of conception, but it seems likely that women use more fine grained and particularistic information that surveys of this (and quite possibly any) type can collect.
The attempt to utilize the NFHS data to estimate how much birth intervals are lengthed by contraceptive use thus turns into a dead end. The absence of direct information on use in last closed intervals and the overall low level of use (which our aggregate analysis suggests may mean that there are no lengthening effects to speak of) are problematic, but the more important difficulty is self-selection, which would probably defeat effects at estimation of this sort even in the absence of the other problems.
Aggregation to the level of states in India shows no relation between use of temporary methods and length of birth intervals, but the analysis of international data suggests that this is because the range of variation in use between states is too low. Choosing smaller aggregate units in a suitable way is likely to yield a wider range of variation despite the low overall use levels and may allow us to estimate the desired effect.
The individual level data permit aggregation in any manner that seems appropriate. One might choose administrative units smaller than states, sampling units, or any other aggregates. Suppose for example that we draw n samples of m individuals from the survey records, without replacement, compute median last closed birth intervals, levels of contraceptive use, and other relevant variables for each of these n samples, and analyze the resulting n data points as we did the national and subnational aggregates at the beginning of the paper.
The rationale for this proceeding is as follows. Suppose that women self-select themselves for contraceptive use on the basis of a single variable, 'risk of conception,' and that we have identified, for some group of women, those who are high risk and those who are low risk as well as other relevant information. It is axiomatic that a woman's use of contraception in a closed birth interval cannot decrease the length of that interval: either their will be no effect on the length, or the length will increase.
Low risk women who use contraception in a closed interval will thus have longer intervals, on the average, than women who do not, and similarly for high risk women. High risk women who do not use contraception will have shorter intervals than low risk women who do not use contraception. The comparative length of intervals for high and low risk women who use contraception will depend on the lengthening effect for the two groups.
Figure XX presents a plausible schematic picture of this situation. The horizontal axis represents contraceptive use in the closed interval, with nonusers at far left and users at far right. The vertical axis represents length of closed interval. The two upper points represent birth intervals of low risk women using and not using contraception. The dotted line connecting them serves both to identify them as referring to low risk women and to emphasize an illustrative lengthening effect of contraception in the closed interval. The two lower points represent the same thing for high risk women.
The four points as plotted represent length of birth intervals and use or non-use of contraception, but they also correspond to the cells of the contingency table classifying women by use or non-use of contraception and risk category, high or low. If contraceptive use is independent of risk in this table, contracepting women will be equally represented among low and high risk women and collapsing over the two risk groups will show contracepting women having longer intervals than non-contracepting women.
If high risk women are more likely to adopt contraception than low risk women, however, high risk women will be over represented among contraceptive users. In the extreme case in which all contraceptive use is concentrated among high risk women, the comparison of birth interval lengths between contracepting and non-contracepting women is a comparison between high risk and low risk women. If the lengthing effect of contraception is small relative to the difference in birth interval lengths between high and low risk women, high risk users of contraception have shorter intervals than low risk non-users. This is the situation illustrated in the diagram and, to the extent that this simple model is applicable, the situation that obtains in the NFHS data on use of modern contraceptive methods.
The diagram as thus far discussed refers to the classification of individual women. Suppose however that instead of considering individual women we consider randomly chosen pairs of women. Pairs of high risk women and pairs of low risk women will behave in the same way as individual women having these risk values, but mixed pairs, consisting of one low risk and one high risk woman and indicated by circles in the diagram, will show intervals intermediate between high and low risk women. Since we may assume without loss of generality that there are equal numbers of low and high risk women, a sufficiently large number of pairs of women will show close to one quarter high risk, one quarter low risk, and one half mixed.
Given the magnitudes indicated in the diagram, it would appear that the impact of self-selection will be mitigated, for half of the women have effectively been removed from the high and low risk categories, which are responsible for the effect, and placed into the mixed category in which use by either or both women will increase the expected average length of interval for the pair.
There is no assurance that this mitigating effect will be sufficient to indicate a positive effect of contraceptive use on length of closed birth interval, and any positive effect that does emerge will clearly be biased low, but it does appear hat working with micro-aggregates of two women will give better results than working with individual women.
Larger aggregates will give a lower range of variation in the resulting birth interval length measures, though this may not be an important advantage if the distribution is well-behaved. Larger aggregates place more women in mixed groups and fewer women in groups consisting exclusively of high and low risk women. This would appear on the evidence of the diagram to reduce the effect of self-selection, which would of course be advantageous. Larger aggregates would also mean more mixing with respect to contraceptive use, however, and this would reduce the variance of use rates for the microaggregates. This is disadvantageous in that it tends to higher standard errors in regression results.
Larger aggregates will of course give smaller numbers of points, and this will tend to reduce the statistical significance of any results. This effect must be controlled for by weighting aggregates in proportion to their size. The simplest way to accomplish this is to create data sets that contain n copies of every point derived from an n-person aggregate.
We have conducted a series of experiments, drawing samples of 2, 3, 5, 10 and 50 persons, without replacement, that exhaust the self-weighting sample. The expectation, based on the argument detailed at the beginning of this section, is that analyzing data sets comprised of these microaggregates instead of individual respondents will attenuate self-selection effects, resulting in regression coefficients for use of all classes of methods that are either insignificant or significantly positive.
Insignificant results would be positive results in this context, for it is possible (and indeed suggested by the aggregate data considered at the beginning of the paper) that birth interval lengthening effects of contraception in India are negligible.
As it has turned out thus far, the experiments do not bear out the expectation. The negative impact of use of modern temporary methods and sterilization on birth interval lengths stubbornly persists through nearly all the results. The experiments show some anomalies that may indicate errors in implementing the microaggregation scheme, and it is possible that further work will yield positive results.
On balance at this point, however, this appears unlikely, which raises two questions. Is there a flaw in the argument given at the beginning of this section indicating that microaggregation should attenuate the impact of self-selection effects? Are self-selection effects so strong that they overwhelm the approach (making birth intervals for high and low risk intervals sufficiently far apart in Figure XX suggests that this might happen)? Is there another sampling scheme for microaggregates that can be made to yield positive results? If microaggregation along these lines can be shown not to accomplish the desired effect, how is it that the non-random aggregations of national and subnational results do?
Because the declared need is for spacing, rather than for stopping, the naive expectation would be that meeting this need would have no effect on the level of fertility, that the women declaring this need would realize longer intervals between births if this need were met, but would have the same total number of births as before.
This argument overlooks various formal and empirical demographic complexities, but one of the conclusions of our analysis is that it is, in its own terms, essentially correct. If women who say they would like to delay having another child do so, the resulting tendency to increased age at childbearing is unlikely to depress fertility significantly. This conclusion is based on our estimate that contraception occuring in closed birth intervals is unlikely to lengthen them by more than about 3 months.
If fertility declines significantly, it must result from women converting from spacers into stoppers. Women who say they want another child later and adopt a temporary method to delay conception must decide, in time, that they are content with the number of children they have already. The availability of temporary methods of contraception gives women time to come to this conclusion before another birth arrives.
We have presented some statistical evidence that this transformation, which might at first appear implausible, is indeed likely to occur. The main technique has been to attempt to estimate what proportion of overall contraceptive use occurs in closed birth intervals and what proportion occurs in terminal open intervals, that is, in the interval following the last birth a woman has (in her reproductive lifetime, not by the time of a particular survey). This estimation is problematic in the extreme, but the lengthening of birth intervals resulting from contraception turns out to be so small that even large errors are unlikely to affect the conclusion.
The conclusion is that most contraception ends up being for stopping rather than for spacing. This is not implausible, once it is recognized that typical birth intervals in low fertility countries are not much longer than intervals in high fertility countries, for as fertility declines, the share of closed birth intervals in a woman's reproductive life span declines and the share of the terminal open interval increases.