would equal the sex ratio at birth, adjusted for mortality by sex and age. The downside to choosing a narrower gap would be the increasing possibility that the model is too restrictive, while a wider age gap may risk becoming divorced from reality. While the age gap serves to reduce the share failing to marry, the reason share of males in a particular age group such as 3039 can be higher than the SRB due to the fact that females’ preference for educated spouses means that younger men (males enter the marriage market at age 25) can take brides first. In an education-naive model, the share never-married should never exceed the SRB (in fact it should be predictably below the SRB due to the age gap between spouses).

The marriage model is female dominant: in order to maximize the matches generated, males are not attributed any preference function for females.<sup>18</sup> We assume that females prefer the most educated males, and prefer older males to younger males. Since sex ratios at birth rose only after the 1980s, older men faced little bride shortage. Therefore, we report projections for men aged 30-39 in order to reflect more closely the never-married rates experienced by male cohorts entering the marriage market today and in coming years. Where shares never married cannot be calculated for closed age groups, we report statistics for share unmarried limiting the population to men above 30, by which age the rate of first marriage historically observed in the Census drops to minimal levels. Here a distinction should be made – although marriage for males in China is rare above age 30, we continue to hold males on the marriage market until age 40 (although it is unlikely for women to remain single through age 32, the minimum age for marriage to a male age 40).

Our simulation makes the assumption that ethnicity does not affect likelihood of marriage. In the model, a man of the Han majority ethnicity has no preference between a Han woman and one of a minority ethnicity. Similarly, women’s preferences are based solely on economic and social status. A woman will prefer an educated man of a different ethnicity to an uneducated man of her own ethnicity. Outcomes from the marriage simulation are very similar when the sample is restricted to Han men and women. A Han man in a poor minority area like Xinjiang, Ningxia, and Tibet will still do poorly in the marriage market due to his educational background, since Han men living in minority provinces tend to be of similar educational levels as non-Han in the same place.<sup>19</sup> We believe that this is a tenable assumption, because sociological research indicates that a potential mate’s ethnicity is not a first-order consideration in mate selection in China today, including in rural areas (Wei 2007). In addition, many who identify as minorities are actually of mixed ethnicity and may have more cultural affinity with the Han majority (Wei & Cao 2007). The marriage market for minority populations in China is a

> 18 We use the calculated national-level education-specific marriage failure rates for men, and apply it to the current age and education distribution observed in 2000. This highlights areas where a large percentage of the males have education below junior-middle school ( _xiao zhong_ ) level. The results are illustrated in the map. Higher educated men have lower rates of overall marriage failure for males, but the problem of unmarried males is widespread and located in peripheries, especially in Xinjiang, Xizang (Tibet), Qinghai, Sichuan, Yunnan provinces and nearby areas. Our projections assume no ethnic preferences of Han males for or against minority females (and vice versa). However, the results are robust to limiting to the Han population only.

> 19 Historical precedent exists for high rates of non-marriage in Tibet due to the customary practice of fraternal polyandry. As recently as the 1990 and 2000 Census, non-marriage in Tibet, which is more prevalent for males than for females, exceeds the national average (suggesting that polyandry is insufficient to explain high rates of nonmarriage in Tibet, and that educational, economic, and other population characteristics may also play a role).

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