The way I’ve approached this problem is to classify as first-time mothers all those respondents who gave birth in the last year (fertyr == TRUE), have one child (nchild == 1), and the eldest child’s age is less than or equal to one (eldch <= 1).
My problem is that when I do a sanity check and compare the number of mothers using the method above with a method of classification where I count all mothers who gave birth in the last year and have one child, I get different numbers. Shouldn’t these different classifications yield the same answer? That is, if I know you gave birth in the last year and have one child, isn’t it the case that by definition that child has to be no older than 1?
YNGCH reflects the reported age of the youngest own child in the household, regardless of FERTYR. The variable FERTYR is directly adopted from the Census Bureau’s PUMS files, meaning that IPUMS-USA does not manipulate these values in any way. Based on further investigation of the data, it appears that FERTYR is incorrect for many cases. The discrepancy you are seeing may be due to a combination of respondent error and infant mortality, but it is not possible to verify either.
While your method of identifying first-time mothers makes sense, I recommend that you proceed with caution when using the FERTYR variable, as it seems to be less accurate than the IPUMS-constructed YNGCH and NCHILD variables.