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The Total Marital Fertility Rate and Its Extensions

Le taux de fécondité totale dans le mariage et ses extensions

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Abstract

What we will call the age-based TMFR is computed conventionally by adding up age-specific marital fertility rates in the hope of estimating the number of children ever born to a woman who is married throughout her childbearing years. Demographers have long been strongly skeptical about this quantity because it normally indicates implausibly many children. Our analysis of data from the Romanian GGS confirms this finding, and we propose an alternative duration-based TMFR computed in the spirit of parity-progression ratios. At the same time, we extend the method to cover any type of living arrangement (cohabitation, marriage, non-partnered arrangement, and so on). Because each resulting total union-type fertility rate (TUFR) explicitly accounts for the living arrangement, it improves on the conventional total fertility rate (TFR), which does not. We embed the investigation in an event-history analysis with fixed and time-varying control covariates and find patterns of relative risks for such variables that reveal interesting features of childbearing behavior in the Romanian data, which we use to illustrate the method. In most cases, these patterns are quite robust against model re-specification, including the shift from the age-based to the duration-based approach. Since, the number of female respondents is “only” about 6,000 (minus records that cannot be used for the current purpose) in a normal single-round GGS, there is considerable inherent random variation in the data set, but we show that simple few-term moving average graduation suffices to overcome this problem.

Résumé

Le taux de fécondité totale en mariage (TFTM) selon l’âge est calculé par convention en sommant les taux de fécondité par âge dans le mariage en vue d’obtenir une estimation du nombre total d’enfants nés d’une femme qui aurait été mariée tout au long de sa vie reproductive. Depuis longtemps les démographes considèrent cette mesure avec scepticisme car elle aboutit souvent à un nombre total d’enfants beaucoup trop élevé. Notre analyse des données du EGG roumain confirme cette constatation et nous proposons dès lors, comme alternative, un TFTM selon la durée, dans l’esprit des probabilités d’agrandissement des familles. Par ailleurs, nous étendons la méthode à tous types de situation de couple (cohabitation, mariage, sans partenaire, etc.). Comme le taux de fécondité totale selon le type d’union (TFTU) tient compte explicitement de la situation de couple, il doit être préféré au TFTM qui ne tient pas compte de ce critère. Notre étude est conduite dans le cadre d’une analyse biographique tenant compte de covariables fixes ou dépendantes du temps. Les résultats de l’analyse nous permettent de découvrir des caractéristiques intéressantes de la fécondité roumaine, que nous utilisons pour illustrer la méthode. Dans la plupart des cas, ces caractéristiques sont robustes face à une re-spécification du modèle, notamment le passage de l’approche basée sur l’âge à l’approche tenant compte de la durée. Comme le nombre de répondants à l’enquête EGG à un passage n’est ‘que’ de l’ordre de 6000 (moins les cas qui n’ont pas pu être utilisés pour le présent travail), il existe une fluctuation aléatoire importante dans les données. Nous montrons toutefois qu’un lissage par moyenne mobile à quelques termes seulement nous permet de surmonter cette difficulté.

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Notes

  1. Though the concept of the TMFR has been around for a long time, the literature on its interpretation and properties seems to be very sparse. The most insightful contributions known to us are by Rodriguez and Cleland (1988) and particularly by Hinde (1998, Sect. 10.3).

  2. This observation is in fact the basis for the study of parity-progression ratios, in a tradition that goes back to Henry (1951, 1952) and Ryder (1951). An overview has been given by Ni Bhrolchain (1987); for some later contributions see Feeney (1991) and Hosseini-Chavoshi et al. (2006).

  3. For a recent contribution concerning stepchildren, see Holland and Thomson (2011). Thomson and Li (forthcoming) give an interesting overview of the empirical literature.

  4. The TUFR tu is interpreted in analogy with the usual understanding of the common TFR. We pay some further attention to its interpretation in Sect. 3.

  5. This means that a smoothed curve value for any year is computed as the straightforward mean of seven annual values, centered on the year in question. The first and last smoothed values are means of five annual values. Two smoothed annual values are then lost in each tail of the curve, and in the diagrams we have used unsmoothed values in those positions. To avoid smoothing away interesting irregularities caused by the strong variations in Romanian public policies over previous years (Mureşan and Hoem 2010) rather than by random variation, we have only included the years between 1985 and 2005 here.

  6. In the mean, it varies between a low of 2.93 for cohabiting women and a high of 3.17 for women who have married without earlier cohabitation.

  7. See Mureşan and Hoem (2010), for more exact definitions.

  8. Mureşan (2007, 2009) has shown that this gradient actually appeared only after the fall of state socialism for the first birth, and only 5 years before the fall for the second birth (i.e., after 1985, which is also the starting year of the current investigation).

  9. We doubt that the negative educational gradient really is specific to Romania. It may extend to all countries where highly educated women find it difficult to establish themselves in the labor market. For the Czech Republic, see Kantorova (2004b).

  10. For a nice counterexample and some theoretical argumentation see Kantorova (2004b).

  11. For a particularly sharp-worded expression of this position, see Pressat (1972, p. 190).

  12. As one among many examples, we mention that the age-based TMFR for Norway was about 7 in 1959–1962 and that from there to 1969–1970, 1971–1975, and 1976–1980 it dropped by about 0.8 from one period to the next, to reach 4.6 by 1980. (Computed by the present authors from Table 3.6 in Statistisk Sentralbyrå 1984.) Very few marriages had such high numbers of offspring at the time. (The TFR for Norway was 1.7 in 1980.)

  13. This means (i) that any children born before marriage are not included in the count of children in the marriage, and (ii) that the duration in Fig. 3 is counted from marriage formation and not from union formation. Alternatively, we could have used the formation of the consensual union as a starting time, but we wanted to avoid some minor corresponding complications at the present stage. Our simplification is unlikely to be important in a population, where a consensual union is quickly converted to a marriage when a pregnancy occurs.

  14. The increase from the first to the second year of union for ages below 30 most likely reflects the arrival of children conceived shortly after union formation. We speculate that women who start their union/marriage at ages 30–34 are less fecund or less in a hurry to start a pregnancy since their curve does not have a similar peak.

  15. The pattern of these types of diagrams has been quite stable over the sub-periods 1985–1989, 1990–1999, and 2000–2005 (documentation not shown here).

  16. This conceptual construct may look strange at first sight (how many women who enter a cohabitational union stay in the union without marrying for the 15 years during which the group remains under observation as a collective?), but it ought to be no stranger than many other thought constructs used by demographers. Just think of cause-deleted mortality concepts, and of the gross reproduction rate, which is simply a mortality-deleted net reproduction rate. Our purpose in suggesting the TUFR is to provide an interpretable statistical parameter that can serve as a measure of the fertility level for women in a given type of marriage/union, while not suggesting that surviving for all those years in a union of the given type is a common or even frequent behavior.

  17. In most of our diagrams, we have used a five-term moving average to filter away random variation and better bring out the patterns in the curves. In Figs. 1 and 5, we have used seven-term smoothing to get sufficiently smooth curves. We have also started the smoothing at the point for the fourth year of union duration to avoid smoothing away the pattern at brief durations.

  18. Some of the women in post-cohabitational marriages may have had children in the consensual union before marriage, i.e., not in the marriage itself. Such children are not counted in their TUFR for the marriage, and this might reduce the child count in the marriage. However, we believe this to be a minor element in the difference observed. If a cohabitational union is transformed into a marriage, this is most likely to happen before the first birth in the union, while women who have a birth during cohabitation are less likely to convert their union into a marriage later.

  19. The estimated mean levels are 1.57 for direct marriages, 1.44 for consensual unions, and 1.39 for post-consensual marriages.

  20. See Hinde (1998, p. 124) for a particularly clear discussion of issues concerning the conventional TMFR. Like several others he suggests that it may make sense to aggregate age-specific marital fertility rates from age 20 only (or from a later age) in order to reduce the over-estimation inherent in the age-based TMFR.

  21. The patterns of relative risks are also very robust against changes in the selection of covariates with respect to which we choose to standardize (not documented here).

  22. See also the reflections by Rotariu (2009). Note that the age-based and the duration-based approaches coincide for never-partnered women.

  23. For an overview, see Thomson and Li (forthcoming).

  24. We could also include time since completion of current educational level, as has been done by Kantorova (2004a, b), Skirbekk et al. (2004), and possibly others, but we will leave this possibility aside in the current context.

  25. As in the rest of this study, we have computed these estimates from the data of the Romanian GGS of 2005. More details and the rest of our empirical results are available from the authors on request.

  26. A period “in between unions” starts at the end of the last previous union and ends at the formation of a new union or at censoring. (To call it “in between unions” may actually be a misnomer since the period need not end by the formation of a new union.) There are so few births “in between unions” that we have not estimated a childbearing risk that may change over time but have assumed that it is constant until the start of any new union.

  27. Note that (as we have discussed above) this particular rate is computed (and plotted) by the duration of the marriage, not including the duration of the pre-marital consensual union. The same comment pertains to Figs. 7 and 8.

  28. We have actually made use of the first of these definitions in part of our work for the present paper, viz., in the computation of the TUFR values for those never in a union, given as the lowermost curve in Fig. 1. We have then operated with much longer durations for women in this group (in order to cover all fertile ages) than the duration span for partnered women (as in Figs. 3, 4). For the never-partnered women, there is no difference between proper age-based and the duration-based computations.

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Acknowledgments

We are grateful to Gerda Neyer for many helpful comments and to Tomas Sobotka for reminding us about the connection of our duration-based features to parity-progression ratios and for providing useful references. The comments by the journal’s editor and referees have been very useful.

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Authors and Affiliations

  1. Max Planck Institute for Demographic Research, Konrad-Zuse-Strasse 1, 18057, Rostock, Germany

    Jan M. Hoem

  2. Faculty of Sociology and Social Work, Centre for Population Studies, Babes-Bolyai University, Bd. 21 Decembrie 1989, No. 128, 400604, Cluj-Napoca, Romania

    Cornelia Mureşan

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Correspondence to Jan M. Hoem.

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Hoem, J.M., Mureşan, C. The Total Marital Fertility Rate and Its Extensions. Eur J Population 27, 295–312 (2011). https://doi.org/10.1007/s10680-011-9237-y

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