Demography(2012)49:77-100 D0I10.1007/s13524-011-0083-7 Skewed Sex Ratios at Birth and Future Marriage Squeeze in China and India,2005-2100 Christophe Z.Guilmoto Published online:17 December 2011 C Population Association of America 2011 Abstract I examine the potential impact of the anticipated future marriage squeeze on nuptiality patterns in China and India during the twenty-first century.I use population projections from 2005 to 2100 based on three different scenarios for the sex ratio at birth (SRB).To counteract the limitations of cross-sectional methods commonly used to assess the severity of marriage squeezes,I use a two-sex cohort-based procedure to simulate marriage pattems over the twenty-first century based on the female dominance model.I also examine two more-flexible marriage functions to illustrate the potential impact of changes in marriage schedules as a response to the marriage squeeze. Longitudinal indicators of marriage squeeze indicate that the number of prospective grooms in both countries will exceed that of prospective brides by more 50%for three decades in the most favorable scenario.Rates of male bachelorhood will not peak before 2050,and the squeeze conditions will be felt several decades thereafter,even among cohorts unaffected by adverse SRB.Ifthe SRB is allowed to return to normalcy by 2020, the proportion of men unmarried at age 50 is expected to rise to 15%in China by 2055 and to 10%in India by 2065.India suffers from the additional impact of a delayed fertility transition on its age structures. Keywords China.India.Sex ratio at birth.Marriage simulation.Marriage squeeze Introduction The proportion of male birth cohorts has reached unusually high levels over the last 20 years in several Asian countries.'In many countries,the sex ratio at birth The literature on the sex ratio issues in Asia is now abundant and describes in particular determinants of gender discrimination.On the diversity of situations across Asia,see Croll(2000),Miller(2001),Attane and Guilmoto (2007),and UNFPA-sponsored case studies (UNFPA 2007). C.Z.Guilmoto(☒ Institut de recherche pour le developpement/CEPED,19 rue Jacob,75006 Paris,France e-mail:christophe.guilmoto @ird.fr ②Springer
Skewed Sex Ratios at Birth and Future Marriage Squeeze in China and India, 2005–2100 Christophe Z. Guilmoto Published online: 17 December 2011 # Population Association of America 2011 Abstract I examine the potential impact of the anticipated future marriage squeeze on nuptiality patterns in China and India during the twenty-first century. I use population projections from 2005 to 2100 based on three different scenarios for the sex ratio at birth (SRB). To counteract the limitations of cross-sectional methods commonly used to assess the severity of marriage squeezes, I use a two-sex cohort-based procedure to simulate marriage patterns over the twenty-first century based on the female dominance model. I also examine two more-flexible marriage functions to illustrate the potential impact of changes in marriage schedules as a response to the marriage squeeze. Longitudinal indicators of marriage squeeze indicate that the number of prospective grooms in both countries will exceed that of prospective brides by more 50% for three decades in the most favorable scenario. Rates of male bachelorhood will not peak before 2050, and the squeeze conditions will be felt several decades thereafter, even among cohorts unaffected by adverse SRB. If the SRB is allowed to return to normalcy by 2020, the proportion of men unmarried at age 50 is expected to rise to 15% in China by 2055 and to 10% in India by 2065. India suffers from the additional impact of a delayed fertility transition on its age structures. Keywords China . India . Sex ratio at birth . Marriage simulation . Marriage squeeze Introduction The proportion of male birth cohorts has reached unusually high levels over the last 20 years in several Asian countries.1 In many countries, the sex ratio at birth Demography (2012) 49:77–100 DOI 10.1007/s13524-011-0083-7 1 The literature on the sex ratio issues in Asia is now abundant and describes in particular determinants of gender discrimination. On the diversity of situations across Asia, see Croll (2000), Miller (2001), Attané and Guilmoto (2007), and UNFPA-sponsored case studies (UNFPA 2007). C. Z. Guilmoto (*) Institut de recherche pour le développement/CEPED, 19 rue Jacob, 75006 Paris, France e-mail: christophe.guilmoto@ird.fr
78 C.Z.Guilmoto (hereafter SRB)has increased above the standard range of 104-106 male births per 100 female births,reaching values above 110 or even 120.This process of demographic masculinization stems mostly from the increasing frequency of sex- selective abortions across Asia,from the Caucasus to South and East Asia.While discrimination against unborn girls today is a dismal reflection of the status of women,sex imbalances may also lead tomorrow to the potential disruption of marriage systems set off by the unavoidable shortage in prospective brides. In this article,I aim to evaluate the potential severity of the marriage crisis and to explore the potential responses of nuptiality systems to future changes in China and India.I selected these two countries because of their demographic weight in the world and their early rise in SRB over the last two decades.For this article, compared with previous studies,demographic parameters have been updated and the study period extended from the conventional year 2050 to 2100 in view of the especially long-term impact of SRB imbalances on marriage patterns.But the most important difference from previous research is the use of a longitudinal simulation procedure to simulate future male and female marriages rather than relying on cross- sectional indicators of sex ratio imbalances. The article starts with a presentation of the data and models used to simulate future marriage patterns.Taking 2005 as baseline year,my simulations rely on various population projections based on three scenarios of change in SRB over the coming decades.I also describe the different marriage models used in the simulations.Next,I present results from the simulations,starting with new estimates of the extent of the marriage squeeze and the analysis of the respective contribution to it of changes in age structures and in birth masculinity.Two additional simulations illustrate the extent to which mere changes in marriage timing could reduce the intensity of the marriage squeeze.The article concludes with a synthesis of the results and a review of some of the implications of my findings. Data and Models for Marriage Simulations The simulation of marriage pattems in China and India requires first a set of population projections based on different SRB scenarios for the future.Since other long-term trends in age structures may also affect the marriage-sex ratio,I also develop a set of projections without rise in SRB levels.I examine two dimensions of population change in the first sections and describe the parameters used in the population projections.I then discuss the limitations of the cross-sectional sex ratio indicators of marriage squeeze and present a more realistic indicator of marriage squeeze based on longitudinal marriage simulations.These simulations are based on specific parameters for projecting female marriage patterns in the future.At the end of this section,I also explore what other responses of male nuptiality to the increasing marriage squeeze conditions could be by presenting two alternative marriage functions. Impact of Population Structures on Sex Imbalances Since men usually marry younger women,the birth cohorts of future husbands tend to be older (Esteve and Cabre 2005;McDonald 1995).But the size of these birth ②Springer
(hereafter SRB) has increased above the standard range of 104–106 male births per 100 female births, reaching values above 110 or even 120. This process of demographic masculinization stems mostly from the increasing frequency of sexselective abortions across Asia, from the Caucasus to South and East Asia. While discrimination against unborn girls today is a dismal reflection of the status of women, sex imbalances may also lead tomorrow to the potential disruption of marriage systems set off by the unavoidable shortage in prospective brides. In this article, I aim to evaluate the potential severity of the marriage crisis and to explore the potential responses of nuptiality systems to future changes in China and India. I selected these two countries because of their demographic weight in the world and their early rise in SRB over the last two decades. For this article, compared with previous studies, demographic parameters have been updated and the study period extended from the conventional year 2050 to 2100 in view of the especially long-term impact of SRB imbalances on marriage patterns. But the most important difference from previous research is the use of a longitudinal simulation procedure to simulate future male and female marriages rather than relying on crosssectional indicators of sex ratio imbalances. The article starts with a presentation of the data and models used to simulate future marriage patterns. Taking 2005 as baseline year, my simulations rely on various population projections based on three scenarios of change in SRB over the coming decades. I also describe the different marriage models used in the simulations. Next, I present results from the simulations, starting with new estimates of the extent of the marriage squeeze and the analysis of the respective contribution to it of changes in age structures and in birth masculinity. Two additional simulations illustrate the extent to which mere changes in marriage timing could reduce the intensity of the marriage squeeze. The article concludes with a synthesis of the results and a review of some of the implications of my findings. Data and Models for Marriage Simulations The simulation of marriage patterns in China and India requires first a set of population projections based on different SRB scenarios for the future. Since other long-term trends in age structures may also affect the marriage-sex ratio, I also develop a set of projections without rise in SRB levels. I examine two dimensions of population change in the first sections and describe the parameters used in the population projections. I then discuss the limitations of the cross-sectional sex ratio indicators of marriage squeeze and present a more realistic indicator of marriage squeeze based on longitudinal marriage simulations. These simulations are based on specific parameters for projecting female marriage patterns in the future. At the end of this section, I also explore what other responses of male nuptiality to the increasing marriage squeeze conditions could be by presenting two alternative marriage functions. Impact of Population Structures on Sex Imbalances Since men usually marry younger women, the birth cohorts of future husbands tend to be older (Esteve and Cabré 2005; McDonald 1995). But the size of these birth 78 C.Z. Guilmoto
Skewed Sex Ratios at Birth and Future Marriage Squeeze 79 cohorts stems also from long-term trends:the number of annual births tends to increase during the first phase of the demographic transition but decreases later after prolonged fertility decline.India's case is probably emblematic of this situation because the number of births recorded a regular increment until 1990.For instance, the annual increase in the birth cohort size reached 1.5%during the 1970s.This means that there were,on average,7.7%more prospective wives born during this decade than husbands born five years earlier (five years being the current age difference at marriage),and this imbalance affected the marriage market 20 years later.Incidentally,this disequilibrium in the past is often associated with the concomitant rise in dowry observed in India after independence (Mari Bhat and Halli 1999).But with decreases in fertility and further changes in age structures,the number of births started declining in the 1990s,and,according to my population projections,this reduction in the size of birth cohorts is expected to accelerate in the future.For instance,by 2025,an average birth cohort in a given year would be 7% larger than the cohort born five years later.Without any rise in the SRB,male adults would therefore become more numerous than their prospective brides. China presents an undoubtedly more complicated picture because of the irregular size of its birth cohorts since the 1950s.While the number of births has,on the whole,decreased since the 1980s,this decline is less rapid than in India and also is disturbed by the regular ups and downs that are a legacy of China's volatile demographic past.Short-term fluctuations therefore have a marked effect on age and sex distributions in China and will directly influence the sex ratio of adults-a point highlighted by Goodkind(2006)and Rallu(2006).But the decline in the number of births will also be pronounced in China,especially during 2020-2035.3 As a result, the impact of skewed SRBs in China and India on adult sex ratios is likely to be compounded by future age-structural transformations.I therefore insert a separate projection set designed to assess the potential influences of changes in age structures on marriage imbalances. Birth Imbalances in the Future My demographic projections for China and India will start from 2005 and extend to 2100.They are based on the most recent demographic estimates as well as on assumptions that are different from previous attempts.Parameters for these projections have mostly been borrowed from the 2006 prospects by the United Nations Population Division,but several adjustments and corrections have been made (see Appendix A). SRB levels for the future decades are also essential to my projections.SRB started to increase above normal values 20 years ago in China and India (for China, Data used in this section are based on United Nations estimates for 1950-2005 complemented by projection results for the period beyond 2005. According to my projections,the overall yearly decline in birth cohort size during the 2005-2100 period is 0.25%in China and 0.4%in India (rapid transition scenario). No projection exists for India.Forecasts of China's future sex imbalances (Attane 2006;Tuljapurkar et al.1995)are based on 1990 or 2000 census data and on fixed fertility and mortality assumptions. Estimates provided by Jiang et al.(2007)follow a more realistic demographic scenario.An alternative method based on nuptiality tables has also been proposed by Jiang (2011). ②Springer
cohorts stems also from long-term trends: the number of annual births tends to increase during the first phase of the demographic transition but decreases later after prolonged fertility decline. India’s case is probably emblematic of this situation because the number of births recorded a regular increment until 1990. For instance, the annual increase in the birth cohort size reached 1.5% during the 1970s. This means that there were, on average, 7.7% more prospective wives born during this decade than husbands born five years earlier (five years being the current age difference at marriage), and this imbalance affected the marriage market 20 years later.2 Incidentally, this disequilibrium in the past is often associated with the concomitant rise in dowry observed in India after independence (Mari Bhat and Halli 1999). But with decreases in fertility and further changes in age structures, the number of births started declining in the 1990s, and, according to my population projections, this reduction in the size of birth cohorts is expected to accelerate in the future. For instance, by 2025, an average birth cohort in a given year would be 7% larger than the cohort born five years later. Without any rise in the SRB, male adults would therefore become more numerous than their prospective brides. China presents an undoubtedly more complicated picture because of the irregular size of its birth cohorts since the 1950s. While the number of births has, on the whole, decreased since the 1980s, this decline is less rapid than in India and also is disturbed by the regular ups and downs that are a legacy of China’s volatile demographic past. Short-term fluctuations therefore have a marked effect on age and sex distributions in China and will directly influence the sex ratio of adults—a point highlighted by Goodkind (2006) and Rallu (2006). But the decline in the number of births will also be pronounced in China, especially during 2020–2035.3 As a result, the impact of skewed SRBs in China and India on adult sex ratios is likely to be compounded by future age-structural transformations. I therefore insert a separate projection set designed to assess the potential influences of changes in age structures on marriage imbalances. Birth Imbalances in the Future My demographic projections for China and India will start from 2005 and extend to 2100. They are based on the most recent demographic estimates as well as on assumptions that are different from previous attempts.4 Parameters for these projections have mostly been borrowed from the 2006 prospects by the United Nations Population Division, but several adjustments and corrections have been made (see Appendix A). SRB levels for the future decades are also essential to my projections. SRB started to increase above normal values 20 years ago in China and India (for China, 2 Data used in this section are based on United Nations estimates for 1950–2005 complemented by projection results for the period beyond 2005. 3 According to my projections, the overall yearly decline in birth cohort size during the 2005–2100 period is 0.25% in China and 0.4% in India (rapid transition scenario). 4 No projection exists for India. Forecasts of China’s future sex imbalances (Attané 2006; Tuljapurkar et al. 1995) are based on 1990 or 2000 census data and on fixed fertility and mortality assumptions. Estimates provided by Jiang et al. (2007) follow a more realistic demographic scenario. An alternative method based on nuptiality tables has also been proposed by Jiang (2011). Skewed Sex Ratios at Birth and Future Marriage Squeeze 79
80 C.Z.Guilmoto see,e.g.,Banister(2004),Li et al.(2007),and Zeng et al.(1993);for India,see Mari Bhat (2002a,b)and Patel (2006)).As available data indicate,SRB has risen to a level of above 115 in many Asian countries,from Armenia to China,and seems to have leveled off since 2000.There are,in fact,reasons to believe that SRB levels will not increase indefinitely and may ultimately decline.Both China and India during the last decade have introduced or strengthened comprehensive programmes to tackle sex-selective abortions (Joseph and Center for Youth Development and Activities(CYDA)2007;Li et al.2007).Moreover,recent trends indicate that in several areas,the SRB may be about to level off or to decline.For instance,data for China based on the 2000 census (long form)and on the 2005 1%sample survey reflects a near stagnation of the national average,from 119.9 in 2000 to 120.5 in 2005,which has already been interpreted as the beginning of a turnaround,with a significant decline in birth masculinity being observed in southeastem provinces such as Guangdong or Guangxi.There has also been a perceptible shift in SRB since 2002 in several states of northwest India,such as Haryana,Delhi,and Punjab.In addition to these concordant traces of moderate decrease,the remarkable experience of South Korea-where SRB first rose to 116 in 1990 and then gradually declined to 106 in 2008-suggests that SRB may follow typical transitional patterns,with an initial rise followed by a later decline (Guilmoto 2009). In order to explore the possible consequences of future gender imbalances,it seems crucial to consider several different SRB scenarios.First,according to a no- transition scenario,SRB will remain at its current level until 2100;the SRB would therefore stay at 120 in China and at 113 in India during the entire twenty-first century.Second,according to a rapid-transition scenario,the SRB starts decreasing immediately after 2005 and declines to a normal 105 level in 15 years-at a pace slightly faster than that observed in South Korea after 1990.This is admittedly a rather optimistic transitional scenario in which birth imbalances would have vanished by 2020.Both scenarios are deliberately extreme.The first,"business-as- usual"scenario implies,for instance,that a high SRB would remain sustainable,in demographic and social terms,during the entire century,a proposition that seems rather implausible in view of the implications of abnormal sex ratios in the long run. In contrast,the second,transitional scenario would require a complete change in gender attitudes in 15 years,something that government interventions or spontaneous social change may not be able to achieve.But taken together,these first two scenarios may reasonably be seen as the upper and lower limits for simulating sex-transitional change in China and India. I have also included an entirely different scenario based on the hypothesis of the absence of any sex ratio imbalance since 1980.This third baseline scenario of normal SRB posits a constant SRB of 105 and will serve to highlight the specific impact on marriage imbalances of age-structural changes caused in particular by the process of fertility decline in China and India (see Appendix A for details). 5 Kulkarni(2010)analyzed the recent SRB downturn in India;see also Sharma and Haub(2008).Chinese trends are described in Das Gupta et al.(2009)and Guilmoto and Ren(2011).Preliminary data from the Chinese 2010 census put the sex ratio at birth at 118,confirming the slight downturn.Original data are found in the reports of the 2000 census and of the 2005 1%sample survey for China,while Indian data are from the annual reports of the Sample Registration System. ②Springer
see, e.g., Banister (2004), Li et al. (2007), and Zeng et al. (1993); for India, see Mari Bhat (2002a, b) and Patel (2006)). As available data indicate, SRB has risen to a level of above 115 in many Asian countries, from Armenia to China, and seems to have leveled off since 2000. There are, in fact, reasons to believe that SRB levels will not increase indefinitely and may ultimately decline. Both China and India during the last decade have introduced or strengthened comprehensive programmes to tackle sex-selective abortions (Joseph and Center for Youth Development and Activities (CYDA) 2007; Li et al. 2007). Moreover, recent trends indicate that in several areas, the SRB may be about to level off or to decline. For instance, data for China based on the 2000 census (long form) and on the 2005 1% sample survey reflects a near stagnation of the national average, from 119.9 in 2000 to 120.5 in 2005, which has already been interpreted as the beginning of a turnaround, with a significant decline in birth masculinity being observed in southeastern provinces such as Guangdong or Guangxi. There has also been a perceptible shift in SRB since 2002 in several states of northwest India, such as Haryana, Delhi, and Punjab.5 In addition to these concordant traces of moderate decrease, the remarkable experience of South Korea—where SRB first rose to 116 in 1990 and then gradually declined to 106 in 2008—suggests that SRB may follow typical transitional patterns, with an initial rise followed by a later decline (Guilmoto 2009). In order to explore the possible consequences of future gender imbalances, it seems crucial to consider several different SRB scenarios. First, according to a notransition scenario, SRB will remain at its current level until 2100; the SRB would therefore stay at 120 in China and at 113 in India during the entire twenty-first century. Second, according to a rapid-transition scenario, the SRB starts decreasing immediately after 2005 and declines to a normal 105 level in 15 years—at a pace slightly faster than that observed in South Korea after 1990. This is admittedly a rather optimistic transitional scenario in which birth imbalances would have vanished by 2020. Both scenarios are deliberately extreme. The first, “business-asusual” scenario implies, for instance, that a high SRB would remain sustainable, in demographic and social terms, during the entire century, a proposition that seems rather implausible in view of the implications of abnormal sex ratios in the long run. In contrast, the second, transitional scenario would require a complete change in gender attitudes in 15 years, something that government interventions or spontaneous social change may not be able to achieve. But taken together, these first two scenarios may reasonably be seen as the upper and lower limits for simulating sex-transitional change in China and India. I have also included an entirely different scenario based on the hypothesis of the absence of any sex ratio imbalance since 1980. This third baseline scenario of normal SRB posits a constant SRB of 105 and will serve to highlight the specific impact on marriage imbalances of age-structural changes caused in particular by the process of fertility decline in China and India (see Appendix A for details). 5 Kulkarni (2010) analyzed the recent SRB downturn in India; see also Sharma and Haub (2008). Chinese trends are described in Das Gupta et al. (2009) and Guilmoto and Ren (2011). Preliminary data from the Chinese 2010 census put the sex ratio at birth at 118, confirming the slight downturn. Original data are found in the reports of the 2000 census and of the 2005 1% sample survey for China, while Indian data are from the annual reports of the Sample Registration System. 80 C.Z. Guilmoto
Skewed Sex Ratios at Birth and Future Marriage Squeeze 81 Measuring Marriage Squeeze Adult sex ratios weighted by marriage rates provide the usual index to assess the intensity of demographic disequilibria in the marriage market.This indicator allows the incorporation ofboth the size of specific cohorts and the effects ofage-specific nuptiality rates in my computations.However,it presents serious limitations for the appraisal ofthe actual impact of sustained sex imbalances.The major issue related to strictly synchronic indicators,such as weighted sex ratios,is that they do not take the potential effects ofthe past nuptiality experience of each cohort into consideration.When surplus male bachelors fail to marry in a given year,they will unavoidably inflate the pool of potential grooms in the following year,and if the sex disequilibrium does not reduce rapidly, unmarried bachelors will accumulate in the marriage market and further aggravate the squeeze conditions.This is a direct application of a basic law in queuing theory according to which the number of people in a system (here the marriage market)is a function not only of arrival rates(cohort size)but also of the queuing time(number of years unmarried).But usual cross-sectional sex ratio indicators fail to reflect the cumulative impact of the marriage squeeze in the previous periods. A more appropriate solution to this conundrum is the two-sex cohort-based simulation of marriages.In this approach,I compute the number of first unions by using the estimated number of single men and women during each five-year period starting from 2005.In so doing,I deduce the size of the unmarried population at the end of each period and use it to simulate marriages taking place during the next period.This approach is longitudinal as we follow individual cohorts and their nuptiality over the years.It also makes it possible to estimate the mean age at marriage and the proportion of people unmarried at age 50.To assess the intensity of the future marriage squeeze,I use a cohort-based ratio of expected first male marriages to expected first female marriages,which I refer to here as the marriage squeeze indicator (MSD).In addition to the specific effect of cohort sizes (also captured by the weighted sex ratio),the MSI is influenced by the population who did not marry during the previous periods.This simulation technique is based on first- marriage tables by age,sex,and period.But while weighted sex ratios are computed from first-marriage rates applied to the projected population,the cohort-based method uses marriage probabilities(ratio of marriages to single population by age and sex)and is therefore affected by any backlog of unmarried men or women. A key component in the simulations is the adjustment function used to quantify the number of marriages occurring in case of marriage squeeze,when the expected numbers of male and female marriages differ.The main marriage function used in the simulations is a modified female dominance (FD)model,which is applicable when there is a deficit of women.In the original FD model,the number of marriages is determined only by female marriage rates.'Since not all men are able to marry, their nuptiality rates must be adjusted downward.The FD model presupposes that female marriage rates will follow a fixed trajectory and that they will not be affected by variations in the number of unmarried men as long as there is a male surplus.I Little's law states that the average number in a given stable system is equal to the rate of new arrivals in the system multiplied by their average time in the system(Tijms 2003:50-52). 7 See Keyfitz and Caswell (2005)and Iannelli et al.(2005)for a broader discussion of marriage models. ②Springer
Measuring Marriage Squeeze Adult sex ratios weighted by marriage rates provide the usual index to assess the intensity of demographic disequilibria in the marriage market. This indicator allows the incorporation of both the size of specific cohorts and the effects of age-specific nuptiality rates in my computations. However, it presents serious limitations for the appraisal of the actual impact of sustained sex imbalances. The major issue related to strictly synchronic indicators, such as weighted sex ratios, is that they do not take the potential effects of the past nuptiality experience of each cohort into consideration. When surplus male bachelors fail to marry in a given year, they will unavoidably inflate the pool of potential grooms in the following year, and if the sex disequilibrium does not reduce rapidly, unmarried bachelors will accumulate in the marriage market and further aggravate the squeeze conditions. This is a direct application of a basic law in queuing theory according to which the number of people in a system (here the marriage market) is a function not only of arrival rates (cohort size) but also of the queuing time (number of years unmarried).6 But usual cross-sectional sex ratio indicators fail to reflect the cumulative impact of the marriage squeeze in the previous periods. A more appropriate solution to this conundrum is the two-sex cohort-based simulation of marriages. In this approach, I compute the number of first unions by using the estimated number of single men and women during each five-year period starting from 2005. In so doing, I deduce the size of the unmarried population at the end of each period and use it to simulate marriages taking place during the next period. This approach is longitudinal as we follow individual cohorts and their nuptiality over the years. It also makes it possible to estimate the mean age at marriage and the proportion of people unmarried at age 50. To assess the intensity of the future marriage squeeze, I use a cohort-based ratio of expected first male marriages to expected first female marriages, which I refer to here as the marriage squeeze indicator (MSI). In addition to the specific effect of cohort sizes (also captured by the weighted sex ratio), the MSI is influenced by the population who did not marry during the previous periods. This simulation technique is based on firstmarriage tables by age, sex, and period. But while weighted sex ratios are computed from first-marriage rates applied to the projected population, the cohort-based method uses marriage probabilities (ratio of marriages to single population by age and sex) and is therefore affected by any backlog of unmarried men or women. A key component in the simulations is the adjustment function used to quantify the number of marriages occurring in case of marriage squeeze, when the expected numbers of male and female marriages differ. The main marriage function used in the simulations is a modified female dominance (FD) model, which is applicable when there is a deficit of women. In the original FD model, the number of marriages is determined only by female marriage rates.7 Since not all men are able to marry, their nuptiality rates must be adjusted downward. The FD model presupposes that female marriage rates will follow a fixed trajectory and that they will not be affected by variations in the number of unmarried men as long as there is a male surplus. I 6 Little’s law states that the average number in a given stable system is equal to the rate of new arrivals in the system multiplied by their average time in the system (Tijms 2003:50–52). 7 See Keyfitz and Caswell (2005) and Iannelli et al. (2005) for a broader discussion of marriage models. Skewed Sex Ratios at Birth and Future Marriage Squeeze 81