Following on from previous studies of the marriage market process, this article aims to define a better indicator of partner availability, with the incorporation of partner age preferences as a key innovation. Máire Ní Bhrolcháin and WendySigle-Rushton replace the weights generally based on sex ratios or estimated from observation of respective male and female ages at marriage with the age preferences expressed by the clients of a dating agency. This innovation reveals that though older men are advantaged by the marriage market structure, young women are advantaged by age preferences.

Ideally, a partner supply measure should be embedded in a well grounded behavioural model of the marriage market that gives clarity to the availability concept and specifies its empirical form. In addition, the indicator would need to be well validated. Since such a model is not yet available, a definitive measure cannot yet be specified. One empirical difficulty is the fact that partner supply is, ultimately, an individual-level concept and can strictly be measured only via individual-level data. Not only is such information not available, it is not at all clear how the number of potential partners available to individuals would be defined and measured.

We define as in the marriage market those who are legally unmarried (single, divorced and widowed) and are therefore in a legal position to marry. However, not all those who are unmarried are candidates either for marriage or for heterosexual relationships. The following groups are problematic:

Many recent marriage market studies incorporate characteristics other than age as constraints on matching, notably education and economic status, particularly of men (Goldman et al. 1984; Lichter et al. 1992; South and Lloyd 1992; Qian and Preston 1993; Wood 1995; Raley 1996; Lewis and Oppenheimer 2000; Blau et al. 2000). However, we choose not to include additional matching factors (apart from race, as we confine our US estimates to the white population) for two reasons. First, our objective is to estimate relative numbers in pure demographic terms. Evidence of long standing that marriage rates are positively associated with economic conditions (Yule 1906; Glass 1938; Galbraith and Thomas 1941; Oppenheimer 1994, 2000; Oppenheimer et al. 1997) means that the marriageability of available potential partners in economic terms is a function of economic rather than of demographic conditions, our primary concern here. Potential marriage opportunities, and any constraints on these, resulting purely from numbers by age — demographic structure — can and should be distinguished from those grounded either in the economy or in social practices such as endogamy within social class, educational, ethnic, racial or religious groups. Second, information is lacking both on the nature of preferences for personal attributes such as education or employment status and on how rigid or flexible these are. The explicitly stated age preference data we use here reveal that age preferences are more flexible than is often assumed and also that sex differentials in age preferences are in some respects at variance with common supposition (Ní Bhrolcháin 2001). The same may be true of preferences for social characteristics. Finally, Goldman et al (1984) show that estimates of partner availability are highly sensitive to assumptions regarding educational assortative mating and hence satisfactory estimates incorporating educational and other social attributes cannot be made without a firm basis for the preferences assumed.

Summary information on the age preferences is given in Figure 1 which shows the mean preferred age difference by age and sex in the UK Dateline data, together with mean observed age differences at marriage in the US 1990 and in England and Wales 1991. Clearly, the profile by age and sex of the mean preferences corresponds well with observed age differences in England and Wales 1991. Furthermore, since the US 1990 averages are very close to those for England and Wales 1991, the mean preferences correspond well with the US 1990 age differences also. While the British preference data are seen in Figure 1 to apply equally well in the two countries in 1990-91, a further advantage of using the same weights for comparative purposes is that they can be seen as having a standardizing role, thus allowing the relevant aspects of population structure to be compared fairly. Note that the discrepancies between preferred and actual age differences for each sex are consistent with the idea that each sex’s preferences constrain the actual age difference of the other sex. At younger ages, women would prefer a larger age gap than they achieve and men would prefer a smaller one than actually occurs; at older ages the opposite holds, in both countries.

The England and Wales data used are mid-year population estimates by sex, marital status and single year of age, 17-70, for 1991. These are rolled forward from the 1991 Census, the final figures for which were based on a combination of demographic analysis and the age-sex distribution of the enumerated population; they therefore incorporate adjustments for selective underenumeration by age and sex (Heady et al. 1994). For comparative purposes, we use US 1990 census data, drawn from the Integrated Public Use Microdata Series (Ruggles and Sobek 1997). We confine the sample to the white population because marriage patterns and marriage markets in the black population differ from the white [2]. Sample numbers by age, sex and marital status are adjusted for undercount by the factors given in Robinson et al. (1993: Table 3). These factors are for 5-year age groups and are not specific by marital status and so we apply them to each single year age within 5-year age groups without reference to marital status. We have also made estimates of partner availability for all 20th century census years for which data were available in England and Wales and the US, the results of which are reported elsewhere. We refer occasionally in this paper to selected findings from the historical series.

The levels of partner supply by age and sex as assessed by the iterated availability ratio are given in Figure 2 for the US, 1990 and England and Wales, 1991. Partner availability peaks for women at very young ages and declines thereafter. The opposite is true of men: the youngest men have the fewest potential partners available, but partner supply increases with rising male age. Availability for women at age 18 reaches an average in 1990-91 of 1.8-1.9 potential partners, remains above 1.0 until the early to mid 30s and by age 60 has declined to 0.45 (US) and 0.59 (E & W), though, as noted above, estimates of partner supply for women in their 50s depend heavily on the validity of our age preference assumptions beyond age 59. Among men, average partner supply is 0.4 at age 17, reaches and goes above 1.0 at around 30 in the US and at 45 in England and Wales (though also, briefly, at age 30) and then rises to 2.0 (US) and 1.6 (E&W) by age 60. On these estimates, a 50-year-old American man had around the same number of potential partners as an American woman of 20 in 1990, and, in Britain, a man of this age was in the same position as a 26-year-old woman, in 1991. Partner supply for a white woman of 50 in the US in 1990 was, at 0.6 per woman, about on a par with the situation of a 20-year-old man, while in Britain in 1991 a woman of this age was, at 0.9 potential partners, on a level pegging with a 25-year-old man. Partner availability is, thus, highly differentiated by age and sex, with a range by age of 1.3-1.4 potential partners per woman, and ranges of 1.2 and 1.6 partners per man in England and Wales and the US, respectively. The decline in partner supply with rising age for women and the increase in supply with age for men is common to other twentieth century census dates in both countries, though there is considerable variation through time in the precise ages at which partner supply for each sex reaches parity. Although not true of earlier periods, absolute levels of partner supply in the two countries are virtually identical in 1990-91 for both sexes up to the mid-30s, but diverge at older ages. British women of 40+ had around 14-23 more potential partners per 100 available than their American counterparts in 1990-91. The comparative position of older men is the reverse, with average partner supply for men of 40+ between 21-41 per 100 higher in the US than in England and Wales.

In pure demographic terms, then, and taking these figures at face value, men and women of the same age encounter quite dissimilar levels of partner supply at most ages. In 1990-91, average availability for women far exceeds that for men at younger ages and the reverse is true at older ages. In both countries in 1990-91, unmarried women aged 20-24 had between 34% and 163% more potential partners on average than did men, and those aged 25-29 between 8% and 28% more. Among those in their 30s, partner supply for the two sexes was not greatly out of balance in England and Wales in 1991, with a female advantage of between 4% and 8%, but in 1990 in the US average partner availability for women in their mid-30s and above was well below that of men. From age 36 onwards in the US, and from 46 on in England and Wales, men had at least 15% more potential partners on average than did women, a male advantage that increased with age. Much the same is true throughout the twentieth century. Adopting as a criterion of gender balance a ratio of female to male partner supply in the range 0.95 to 1.05, partner supply has been in balance at relatively few single year ages over the course of the twentieth century in the two countries. Of the 17 censuses from 1900-91 in the US and England and Wales for which we have estimated IARs (Table 1), the female/male ratio was in the range 0.95-1.05 at 3 or fewer single years of age in 14, this was true of 4 single years of age at two dates and in one case partner supply was in balance at 7 single year ages. Not only has gender balance in marriage market position usually been confined to a restricted age range, it occurs largely at ages when the majority of women and men are already married. In 11 of the 17 census years examined, the male availability ratio does not reach within 5% of the female value before age 29, and in 7 census years, gender balance, on the present definition, does not occur before age 35. In all, women have a decided advantage over men in relation to partner supply at the prime ages of both male and female marriage, even in some cases of poor female marriage markets. We return to this issue in a later section, having first examined the factors influencing the IAR.

What accounts for age and sex differentials in partner supply? Decomposition can answer this question in relation to demographic determinants. There are two inputs to the iterated availability ratio: the age preference weights and the age-sex distribution of unmarrieds. The age-sex distribution of the unmarried population can, in turn, be expressed as the product of overall age-sex structure and the proportions unmarried by age and sex. Of these factors, the preference weights are a major influence on the profile of partner availability by age and sex at ages under about 35. This is shown in Figure 3 which plots IARs obtained for a population with a rectangular age distribution, thus removing the effect of population structure. The weights being the sole influence on the pattern of availability in Figure 3, age preferences clearly account for the basic age pattern of decline from abundant supply at young ages for women, and for the increase from shortages at young male ages. Between the mid 30s and the late 40s, preferences for both men and women remain fairly level at around parity, but with a slight female advantage. By the late 50s, age preferences create a small female disadvantage and a corresponding male advantage — but the pattern at these later ages is, of course, heavily influenced by the extrapolated preferences beyond age 60. Young women benefit from the structure of preferences both because their joint preferences remain high over a wide range of male ages and because they have little competition from older women for the young men of their own age, or a little older, who interest them. The opposite is true of young men, who are doubly disadvantaged by the more restricted range of female ages over which joint preferences are high, and by competition from older men for the young women who both interest them and would accept somewhat older men [3]. With rising age, men progressively favour larger age differences, but this appears to produce little pure preference-based advantage in their 50s because of competition for women in their 50s from older men — assuming, of course, accuracy in the assigned preferences. The difference between the actual availability ratios for the unmarried and those obtained in a rectangular age structure measures the effect on availability ratios of the overall age-sex distribution and of structure by marital status and is plotted in Figure 4A; the overall structural effect is further decomposed into effects due to age-sex structure and to marital status composition, shown for women and men in Figures 4B and 4C respectively [4] These two factors combined give a boost to younger women’s partner supply (responsible for an additional 15 potential partners for 100 women aged 18 in the USA and an additional 21 in England and Wales), but have little or no impact on availability for younger men, in both countries in 1990-91. The structural advantage to young women is about evenly divided between age-sex and marital status components. At older ages, age-sex structure and marital status have a much larger effect, especially for men. For example, by age 55, the overall structural effect is responsible for an additional 50 potential partners per 100 men in the US and 21 per 100 in England and Wales; the corresponding reductions for women of this age are 46 per 100 and 28 per 100, respectively. Structure by marital status rather than by age is the larger of the two components in absolute terms at older ages in both sexes. Both structural effects are more pronounced in the United States than in England and Wales, in 1990-91.

A curious feature of gender differences in the demography of marriage came to light earlier — an apparently substantial gender asymmetry in partner availability around the peak ages of marriage. Partner supply is most abundant for women before and at the prime ages of female marriage, but male marriage markets are at their worst, in relative terms, at the ages at which most men marry. Most women, it appears, marry when the supply of partners is to their advantage and the majority of men at ages when their marriage market situation is unfavourable. In both the US and England and Wales in 1990-91 the earliest age at which the male IAR reached or exceeded 1.0 was 30; 71.6% of American and 61.2% of British men of this age were ever married [5]. The corresponding figures for American women are 86.9% ever married by age 33, and 88% of British women ever married by age 36, when the female IARs in each case reached or fell below 1.0. This gender disparity is true of all census dates examined in the present study with the exception of the early decades of the twentieth century in England and Wales. In all US censuses 1900-90 (no data are available for 1930), at least 77% of women were ever married and from 1951 onwards in England and Wales at least 79% were so by the age at which female availability ratios dropped below 1. This is true even in the very unfavourable US female marriage market of 1970: although the female availability ratio was below 1.0 by age 23 in that year, 77% of 23 year-old women had already been married. At least 67% of white American men in all years except 1980 (when the figure is 59%) and at least 78% in Britain from 1950 onwards (but 61% in 1991) were ever married by the age at which with average partner supply reached parity [6]. Even if we relax the definition of parity in partner supply to the range 0.95 to 1.05, the finding remains broadly true: 69%+ of British and American women from 1950 onwards, 59%+ of American men and at least 70% of British men in 1951-81, but 50% in 1991, were already married by the age at which the availability ratios reach the range 0.95-1.05. An exception occurs in England and Wales in 1911-31 when only a minority of both sexes (about 20-33%) had married by the ages at which the marriage market favoured men, reflecting both the low marriage rates and relatively low sex ratios in Britain during that period.

Do these findings reveal a neglected feature of male marriage? Are the majority of men at a disadvantage in the marriage market around the time of marriage and if so, what are the implications? That most men in developed societies should marry when partner supply is relatively poor for them is not empirically impossible. Marriage rates at each single year of age are well below the maximum possible [7], and so there is no numerical paradox here. The possibility of such an effect at the aggregate level has also been noted in the literature, though not in relation to the life course (Martin 1963; Muhsam 1974; Guttentag and Secord 1983) [8]. But the finding requires further scrutiny. In pursuing it, we encounter several issues relating to the nature of marriage markets that need conceptual and empirical clarification. The validity of the observation that most men marry in poor marriage markets and most women in good markets depends on two main elements: (A) the validity of our measure of partner supply; and (B) whether a given level of availability has the same significance for men and women. We consider each of these in turn, together with some ancillary factors.

The availability ratios calculated here are for aggregate groups — i.e. groups of men and women at single years of age. Partner supply is, strictly, an individual level concept. How valid is the IAR as a summary of the marriage market position of individuals of each age? As noted earlier, there appear as yet to be no studies that attempt to validate availability ratios or any of the wide range of partner supply indicators used in the marriage market literature against individual level data. Since an independent criterion of supply is not available, we proceed indirectly, examining first evidence of the validity of the Dateline dating agency preference data. We then look at the correspondence between the IAR and sex ratios, consider an indirect indicator of imbalance in the marriage market, and finally examine the relationship between availability ratios and marriage rates.

As the age preferences used here appear to be the only detailed, large scale explicit preference data available currently, validation is, of necessity, indirect [9]. Several features of the Dateline preferences are consistent with external sources. First, the preference data suggest that at ages under 30 women are strongly biased against younger men, but men are quite accepting of a slightly older woman. For example, while just 16% of women aged 24 would accept a man of 22, a full 91% of 22-year-old men would accept a woman of 24; the corresponding figures for 28-year-old women and 26-year-old men are 33% and 75%. This asymmetry in preferences between the sexes corresponds with the findings of a 1984 survey of French couples, based on a sample of the general population (Bozon 1991: 123). Second, variation by age and sex in both the mean and the distribution of age difference preferences in the dating agency sample corresponds broadly to differentials by age and sex in actual age differences at marriage (cf. Figure 1). Finally, expected age differences based on the dating agency preferences provide, in most comparisons at census dates from 1921-91 for England and Wales and 1950-90 for the US, a closer fit to observed age differences, evaluated by the root mean square error, than either a fixed preference of 2 or 3 years across the age range or inferring preferences from observed age differences using Goldman et al’s (1984) empirical method [10]. In other words, these weights outperform conventional weighting schemes currently available in the literature (see Ní Bhrolcháin (2004b) for this and further validation evidence).

Comparison of the availability ratios with straightforward sex ratios is a weak form of validation, since there are good reasons to doubt that sex ratios are a valid measure of partner supply. Nevertheless, they are familiar and widely used and so the comparison is informative. Availability ratios differ substantially from sex ratios at young ages with sex ratios having a much flatter age profile than do availability ratios. Sex ratios with a 3-year gap between men and women show either no disadvantage for young men, or a much lesser one, and either disadvantage or a much reduced advantage to young women compared with availability ratios, in 1990-91 [11]. At ages 30 and above, IARs and sex ratios with a 3-year gap are at similar levels; at ages 40-60, the two measures are very close in both countries, with unweighted averages of the ratio of the IAR to the sex ratio across these ages for the US and England and Wales, respectively, being 0.99 and 0.94 (female), and 0.94 and 0.99 (male). Judging by sex ratios, then, there would be nothing odd in male marriage patterns in Britain and the US in recent decades since, unlike the IARs, sex ratios at younger ages show little or no disadvantage for men and little or no advantage for women. However, while useful in practice, sex ratios are conceptually unsatisfactory. They imply rigidity in age preferences — an assumption clearly at variance with actual age difference distributions (Levy and Sardon 1982; Goldman et al. 1984; Lampard 1993) —, they make only elementary provision for competition, assume that the preferred age gap is independent of age and that male and female preferences are complementary. For these reasons, the weighted IAR, based on actual preferences, is a better measure of partner availability than the sex ratio.

If men experience partner shortages at the prime ages of male marriage, we would expect to find young men over-represented in the dating agency client population. This is indeed the case. Between ages 21 and 40 the age-specific sex ratio among Dateline clients is between 1.4 and 2.6, compared with sex ratios of between 1.1 and 1.3 among the unmarried in England and Wales in 1996. A difficulty with this argument, however, is that sex ratios well below 1 would be expected at older ages, reflecting the disadvantaged position of older women. In the 1996 sample of clients sex ratios do not drop below 1 until age 54, though in a further sample of 36,443 clients in 2001, the sex ratio at ages 51-60 is 0.8 and at ages 61+ it is 0.7 (single years of age not available). The data thus lend some support to the age-sex differentials in marriage market position suggested by the IARs, though must obviously be treated with caution because the reasons why people decide to make use of dating agencies are unknown — cultural factors may well influence perceptions of how appropriate it is for men and women of varying ages to find a partner by this means.

Marriage rates might be thought of as an indirect source of validation since it is often supposed that measures of partner availability are accurate to the extent that they are associated with marriage propensities. However, this is not necessarily so. It is entirely conceivable that, except when extreme imbalances occur, marriage rates could be independent of, or only very weakly related to, the volume of potential partners, so an association with marriage rates is not integral to the concept of partner availability. The expectation that the two are so related is a hypothesis, the evidence for which is decidedly weak [12].

The picture of low male availability ratios at the prime ages of male marriage might, however, be modified if the absolute level of partner supply has a different meaning for each sex. This could be so if one sex is more demanding than the other in relation to partner characteristics. Women are likely candidates as the choosier sex, by analogy with the animal world. Some information is to hand that backs up the hypothesis of greater female choosiness. A first source is the age preference data. Women specify a narrower range of acceptable partner ages than do men, the mean ranges being 7.8 and 10.3 years, respectively. In addition, up to the mid 30s, at each age the acceptability of the most popular single-year partner ages and those adjacent to them is lower among women than men (though the reverse is true at older ages) [13]. That women are more discriminating is also evident in an additional set of preference data, from a further sample of 36,443 Dateline clients in 2001. In relation to each partner attribute, clients have three options: they may state a positive preference for a partner with that attribute, or reject such a partner, or they may choose neither of these, implying that they “do not mind”. More women than men state a definite preference — positive or negative — with just two exceptions (among a total of 11 characteristics). Averaging over all characteristics, 8% more women than men state a definite preference in relation to partner attributes. Disparities in relation to some traits are quite substantial — for example, 49% of women in contrast to 24% of men would reject a partner with no educational qualifications.

The picture presented of sizeable disparities between the sexes in partner availability at the prime ages of marriage might be modified if several further factors could be allowed for, notably possible sex differentials by age in demand for marriage. Measures of availability generally ignore differentials in demand by age and sex, and this is no surprise since data on the subject are rare. Several American studies suggest both that the ideal age at marriage is younger among women, and that women expect to marry at younger ages than men (Thornton and Freedman 1982; Thornton and Young-DeMarco 2001). However, even if young men want to marry later on average than young women, it seems likely that demand on the part of young people for at least a dating relationship has been fairly high in recent decades, and comparable between the sexes. Hence, sex differentials in availability ratios would probably be modified little if demand for at least a dating relationship were taken into account.

Partner supply by means of a weighted version of the Iterated Availability Ratio (Lampard 1993) suggests that women have an abundant supply of potential mates at young ages and that this declines steadily with age. Men, by contrast, experience a decided shortage of prospective partners at young ages, but a progressive increase in supply with age. In 1990-91, age preferences are the primary determinant of partner supply among the young, with population structure playing a minor role. At older ages, preferences, as attributed, have little effect on gender differentials but the contribution of structural factors increases with age. Although it is often assumed that the marriage market advantage of older men compared with older women results from higher male mortality, our findings suggest that population structure by marital status has a larger effect than mortality differentials (on this point, see also Goldman et al. (1984) and Davis and van den Oever (1982)) [15].