A lot of criticism is leveled at Singapore for privileging married mothers with more benefits than single mothers (as a side note, mothers get more benefits than fathers - but that's another question).
Yet, people respond to incentives - even for such major life decisions such as marriage or the decision to have a child.
Since there is a ton of evidence that children of single parents do worse on a variety of measures than children with two, it is a reasonable (even prudent) public policy objective to promote the bearing of children in a two-parent family.
There isn't a lot of research on the topic, but here is what I've found:
The Impact of Welfare Benefits on the Conjugal Status of Single Mothers in Canada: Estimates from a Hazard Model
"This paper focuses on the determinants of the likelihood of a remarriage (marriage) for female heads with children... The empirical analysis is carried out using a pro- portional hazards model which permits the estimation of the effects of various covariates on the hazard of exiting single parenthood. The most striking result is the strong effect of provincial welfare benefits on conjugal union formation"
Marriage and Economic Incentives: Evidence from a Welfare Experiment
"Can economic incentives be used to affect marriage behavior and slow the growth of single-parent families? This paper provides new evidence on the effects of welfare benefit levels on the marital decisions of poor women. Exogenous variation in welfare benefit incentives arises from a randomized experiment carried out in California that allows me to measure responses beyond simple year-to-year changes in benefit levels. I find that a regime of lower benefits and stronger work incentives encourages married aid recipients to stay married, but has little effect on the probability that single-parent aid recipients marry. The effects on married recipients become larger over time, suggesting that long-run effects may exist."
Welfare and the Family: The Canadian Experience
"This article exploits the variation in payments and uses microdata to estimate the effect of changes in welfare benefits on welfare participation, single parenthood, births out of wedlock, divorce, and labor force participation among low—income women. In Canada, it would appear that welfare benefits influence these decisions"
The effect of economic stability on family stability among welfare recipients
"This paper explores the hypothesis that husband’s unemployment increases union dissolution among welfare recipients. The analysis uses data from California’s Link-Up demonstration project. A discrete-time event-history methodology was employed to examine family instability. The findings show that husband’s unemployment and the family’s long-term welfare dependency lead to breakup, net of race, age, and number of children"
The Effect of Welfare on Marriage and Fertility: What Do We Know and What Do We Need to Know?
"The recent literature on the effects of welfare on marriage and fertility includes studies employing a wide variety of methodologies and data sets and covering different time periods. A majority of the studies show that welfare has a significantly negative effect on marriage or positive effect on fertility rather than none at all, and thus the current consensus is that the welfare system probably has some effect on these demographic outcomes"
Addendum:
The Effects of In-Work Benefit Reform in Britain on Couples: Theory and Evidence
"This paper examines the effects of theWorking Families’ Tax Credit (WFTC) on couples in Britain. We develop a simple model of household decisions which explicitly accounts for the role played by the tax and benefit system. Its main implications are then tested using panel data from the British Household Panel Survey collected between 1991 and 2002. Overall, the financial incentives of the reform had negligible effects on a wide range of married mothers’ decisions, such as eligible (working at least 16 hours per week) and full-time employment (working at least 30 hours per week), employment transitions, childcare use, and divorce rates. Women’s responses, however, were highly heterogeneous, depending on their partners’ labour supply and earnings. Mothers married to low- income men showed larger responses in employment, especially if they had younger children. They were more likely to remain in the labour force and had higher rates at which they entered it. While more likely to receive the tax credit, they also experienced a greater risk of divorce. We find virtually no effect for women with higher-income husbands. Likewise, there are no statistically significant responses among married men."
Summarised by Alasdair Palmer:
"the introduction of the Working Families Tax Credit has increased the divorce or separation rate by a staggering 160 per cent among women married to or living with a partner who either does not work, or who earns very little because he works part-time"