Analyzing fertility histories: do restrictions bias results?

The straightforward tests we have conducted lead to two major conclusions. First, parameter estimates, such as the proportions that practice contraception or that breastfeed, can be biased in data restricted to the last closed and open interval. This is particularly true the further back in time one goes. However, the second conclusion is that these restrictions do not bias estimates of the structure of the relationships predicting fertility. This may seem surprising, and perhaps even magical. The reason is that multivariate life table techniques allow one to reach the same conclusion even if the proportions in various categories are altered by a criterion such as limiting the analysis to intervals begun by the last and next-to-last live births. Limiting the analysis in this way means that there are fewer short intervals and thus fewer cases of intervals with characteristics associated with short intervals (e.g., no contraceptive use, no breastfeeding, or infant mortality). As long as the model specified in the multivariate life table is an appropriate one, that is, it is not misspecified, and as long as the skew produced by the WFS restriction is not too extreme, then the multivariate life table procedures can produce unbiased estimates of the structure of the relationships predicting birth interval dynamics. Thus even though the WFS data are in fact inappropriate for some simple parameter estimation procedures, they appear to be adequate for the more complex multivariate procedures of the sort used here. Several caveats must be added to the foregoing results. First, we have performed this test in only one country, Korea; it is possible that the same results might not be obtained in other countries. We expect, however, that they would. Second, our procedure only looks at the first 40 months of experience in the birth interval. A procedure that incorporates the long tails of the birth interval distribution may obtain different results. In fact, we caution against analyzing the tail of the distributions using data from the normal WFS sample, since these would be most affected by the restriction to last closed and open intervals. Third, the extent to which these results are generalizable to other types of substantive problems is unknown at present. We suspect, however, that examining the determinants of lengths of breastfeeding will produce similar results. Finally, even with multivariate procedures, it would be highly misleading to impose the WFS restrictions and then examine trends in the length of birth intervals.(ABSTRACT TRUNCATED AT 400 WORDS)