In Chapter 4 of Good Intentions, we discuss various social welfare programs, including Temporary Aid to Needy Families, or TANF. This program is the one that most people think of under the term "welfare" - direct cash payments to poor women with children. The study suggests that TANF benefits tend to go down when the mother gets married, and that this leads to a strong disincentive to marry. An extended quote from the paper's executive summary provides more detail: 

Our surveys show that the incentives of TANF-eligible women with children to cohabit or marry are affected by TANF program rules. The way in which incentives are affected depends on the financial resources of the male with whom the woman might cohabit or marry and on the male’s relationship to the children.. The relevant TANF rules that affect these incentives are those governing eligibility, how the basic grant is structured, how blended families are treated, how unrelated cohabitors are treated, and work rules.

Concerning eligibility, our main finding is that if a male has financial resources, TANF provides the greatest disincentive to form and/or maintain a biological family, and the least disincentive, if not an incentive, to form an unrelated cohabitor family. In a biological family, where the male is the father of all the children, he must be included in the unit and his resources counted. In an unrelated cohabitor family, where he is father of none of the children, he is not included and his resources are not counted. In addition, most states disregard unrelated cohabitor vendor and cash payments to the TANF recipient and her children.

Step-parent and blended families fall somewhere in between these two cases, with rules varying from state to state. For stepparent families, where the male is unrelated to any of the children and is married to the mother, a little less than half the states require that the stepfather be included in the unit and about an equal number require his exclusion. If included, his resources are fully counted and, if excluded, only a portion of his resources are counted. For blended families, where the male is the father of some of the children but not all, the majority of states treat such families as biological and require the male to be included in the unit and his resources are counted. In most of the remaining states, marital status does matter, and blended families are treated more favorably if they are unmarried than if they are married.

These findings point strongly toward disincentives to marry in general and specific disincentives to marry a male who is father of some or all of the children. Reinforcing these incentives are work rules, which are imposed on the male if he is the father of all of the children regardless of whether he and the mother marry or cohabit, for example.

Working against these disincentives to marry, however, is the structure of the basic grant in those states which do not have a flat-grant structure. In variable grant states, inclusion of the male in the unit will raise the basic grant, and this could fully or partially offset the disincentives arising from increases in countable resources and the work rules. All of these incentives arise if the male in question has financial resources. If he does not, the marriage-disincentive effects from increased countable resources no longer arise. Also mitigating these disincentives are policies adopted in certain states that ignore a new spouse’s income, although such disregards are only for a short period so the strength of the mitigation is unclear.

In sum, despite some states adopting express policies to encourage and favor marriage, the TANF eligibility and work-rule structures in these states appear to work against such policies. Further, those structures may discourage marriage the most in the situations where the state would most want to encourage marriage, namely, where the male has financial resources. In addition, the most favored living arrangement is not to remain single but to cohabit with a male who is not the father of any of the children.

 The bottom line is that TANF eligibility rules still provide disincentives to the formation of intact families, and thus they continue to provide a barrier to exiting poverty at the same time that they try to alleviate it.