Simple Descriptive Analyses
Table
1 shows descriptive statistics for the base sample (6,032 mothers) as well as results by subsamples of mothers who experienced the three possible events in the base sample (considered in the MNL competing-risks models). Results are weighted to account for the sampling of mothers (for details, see Appendix
1). Almost one-half of the mothers (48 %) had a second pregnancy within the 62 months after their first birth; 15 % of mothers had a second pregnancy with the same father; and 33 % of mothers had a second pregnancy with a new partner. Twelve percent of sample mothers experienced the imprisonment of their first child’s father between the time they became pregnant with their first child and either the time they became pregnant again (exit) or 62 months following the first child’s birth (censoring). That about one-eighth of the children of these mothers experienced their father being imprisoned confirms the high levels of incarceration and the importance of this research topic.
Table 1
Descriptive statistics for demographics, as well as economic variables at exit or censoring
Whether Mother Experienced Focal Father Imprisonment Before Second Birth (exit) or Censoring | 12.0 | 7.7 | 14.4 | 11.6 |
Mean Log Mother’s Earnings at Exit or Censoring | 4.1 | 4.0 | 3.5 | 4.5 |
Whether Mother Received Any Food Benefits at Exit or Censoring | 41.6 | 58.9 | 53.2 | 29.4 |
Whether Mother Received Any TANF Cash Benefits at Exit or Censoring | 5.3 | 5.6 | 10.7 | 1.9 |
Age of Mother at the Focal Child’s Birth |
Under 18 | 21.5 | 22.9 | 28.5 | 16.8 |
18–20 | 44.8 | 45.6 | 50.0 | 41.4 |
21–23 | 20.7 | 19.9 | 15.6 | 24.1 |
24–27 | 7.2 | 7.7 | 4.1 | 9.0 |
28+ | 5.8 | 4.0 | 1.8 | 8.8 |
Race of Mother and the Focal Father |
Both black | 21.4 | 30.5 | 26.7 | 15.6 |
Both white | 43.0 | 28.5 | 42.0 | 47.7 |
Both Hispanic | 2.5 | 5.8 | 2.4 | 1.7 |
Mother white/Father black | 7.3 | 7.7 | 6.9 | 7.5 |
Mother white/Father Hispanic | 3.7 | 4.3 | 3.5 | 3.7 |
All other combinations | 6.7 | 7.5 | 7.0 | 6.3 |
Either unknown | 15.4 | 15.8 | 11.5 | 17.6 |
Year of the Focal Child’s Birth |
1998 | 16.6 | 6.2 | 6.1 | 6.2 |
1999 | 17.1 | 25.9 | 24.2 | 25.8 |
2000 | 17.2 | 26.9 | 26.6 | 24.0 |
2001 | 17.3 | 25.0 | 25.8 | 25.7 |
2002 | 14.9 | 16.1 | 17.3 | 18.4 |
County of the Focal Child’s Residence |
Milwaukee | 29.9 | 36.3 | 32.8 | 26.2 |
Urban counties | 45.7 | 43.6 | 41.5 | 49.0 |
Rural counties | 24.4 | 20.1 | 25.7 | 24.8 |
At the descriptive level, MPF is related to partner imprisonment. Among mothers who experienced MPF, 14.4 % experienced the imprisonment of the focal father before the occurrence of MPF, while among mothers who had a second birth with the same father, 7.7 % experienced the imprisonment of the focal father before the second birth. Of the mothers who did not have additional children during the time observed, 11.6 % experienced the imprisonment of the focal father by the end of the observation period.
9
Most mothers had formal earnings at the time of exit or censoring; in fact, the rate of the mother’s employment remained high throughout the time considered in the analysis. The mothers were generally very young: more than 65 % were younger than age 20 when their first child was born. Both parents were white in about one-half of the couples of known race, and both parents were black in about one-quarter of the couples. Considering differences across fertility outcomes, MPF was more common for mothers who were younger at first birth (p < .01), and Hispanic and black couples were more likely than white couples to have had a second child together (p < .01).
Multivariate Analyses: Multinomial Logistic (MNL) Competing-Risks Models
Table
2 shows the results of three MNL competing-risks analyses, distinguishing between a pregnancy with the same father and a pregnancy with a new father. The models also consider both the cumulative and point-in-time measures of fathers’ imprisonment. Both the coefficients and their odds ratios (relative risk ratios, or RRR) are shown. Dummy variables for each month are included in all models but are not shown.
Table 2
Estimates of multinomial competing-risks models: Effects of fathers’ imprisonment on second birth to same father or to a different father
Imprisonment by t – 1 (cumulative) | –0.044 | 0.957 | 0.438** | 1.550** | 0.747** | 2.111** | 0.284** | 1.328** | 0.526** | 1.692** | 0.100 | 1.105 |
(0.095) | (0.091) | (0.053) | (0.082) | (0.110) | (0.233) | (0.0682) | (0.0906) | (0.114) | (0.192) | (0.070) | (0.077) |
Imprisonment at t
|
(point-in-time) | | | | | –1.992** | 0.136** | 0.269** | 1.309** | –2.031** | 0.131** | 0.206** | 1.229** |
| | | | (0.193) | (0.026) | (0.072) | (0.094) | (0.193) | (0.025) | (0.071) | (0.087) |
Whether Mother Was Employed at t – 2 | | | | | | | | | 1.625** | 5.077** | 1.023** | 2.781** |
| | | | | | | | (0.587) | (2.979) | (0.338) | (0.941) |
Log Mother’s Formal Earningsa at t – 2 | | | | | | | | | –0.161** | 0.851** | –0.099** | 0.906** |
| | | | | | | | (0.053) | (0.045) | (0.031) | (0.028) |
Any Food Stamp Receipt | | | | | | | | | 0.078 | 1.081 | 0.262** | 1.300** |
| | | | | | | | (0.127) | (0.138) | (0.069) | (0.090) |
Any TANF Cash Benefit Receipt | | | | | | | | | 0.110 | 1.116 | 0.032 | 1.032 |
| | | | | | | | (0.183) | (0.204) | (0.111) | (0.115) |
Age of Mother at Focal Child’s Birth (ref. = 21–23) |
Under 18 | | | | | | | | | –0.030 | 0.971 | 0.610** | 1.840** |
| | | | | | | | (0.170) | (0.165) | (0.105) | (0.192) |
18–20 | | | | | | | | | 0.113 | 1.120 | 0.489** | 1.631** |
| | | | | | | | (0.145) | (0.163) | (0.095) | (0.155) |
24–27 | | | | | | | | | 0.067 | 1.070 | –0.267 | 0.765 |
| | | | | | | | (0.235) | (0.251) | (0.181) | (0.138) |
28+ | | | | | | | | | –0.324 | 0.724 | –0.940** | 0.391** |
| | | | | | | | (0.336) | (0.243) | (0.299) | (0.117) |
Parents’ Race, Combined (ref. = both white) |
Both black | | | | | | | | | 1.029** | 2.799** | 0.333** | 1.395** |
| | | | | | | | (0.166) | (0.465) | (0.104) | (0.145) |
Both Hispanic | | | | | | | | | 1.552** | 4.722** | 0.156 | 1.169 |
| | | | | | | | (0.267) | (1.259) | (0.219) | (0.256) |
Mother white/Father black | | | | | | | | | 0.540* | 1.716* | 0.067 | 1.070 |
| | | | | | | | (0.216) | (0.370) | (0.127) | (0.136) |
Mother white/Father Hispanic | | | | | | | | | 0.656* | 1.927* | 0.065 | 1.067 |
| | | | | | | | (0.274) | (0.529) | (0.175) | (0.187) |
All other combinations | | | | | | | | | 0.619** | 1.857** | 0.103 | 1.109 |
| | | | | | | | (0.219) | (0.406) | (0.133) | (0.147) |
Either unknown | | | | | | | | | 0.508** | 1.662** | –0.184 | 0.832 |
| | | | | | | | (0.175) | (0.291) | (0.113) | (0.094) |
Year of Focal Child’s Birth (ref. = 1998) |
1999 | | | | | | | | | 0.009 | 1.009 | –0.127 | 0.881 |
| | | | | | | | (0.231) | (0.233) | (0.129) | (0.114) |
2000 | | | | | | | | | –0.002 | 0.998 | –0.024 | 0.976 |
| | | | | | | | (0.234) | (0.233) | (0.130) | (0.127) |
2001 | | | | | | | | | –0.065 | 0.937 | –0.063 | 0.939 |
| | | | | | | | (0.234) | (0.220) | (0.132) | (0.124) |
2002 | | | | | | | | | –0.159 | 0.853 | –0.110 | 0.896 |
| | | | | | | | (0.249) | (0.212) | (0.138) | (0.124) |
County of Residence (ref. = rural) |
Milwaukee | | | | | | | | | –0.184 | 0.832 | –0.225* | 0.799* |
| | | | | | | | (0.176) | (0.147) | (0.110) | (0.088) |
Urban counties | | | | | | | | | 0.044 | 1.045 | –0.213* | 0.809* |
| | | | | | | | (0.154) | (0.161) | (0.085) | (0.068) |
Constant | –8.365** | 0.000** | –6.281** | 0.002** | –8.37** | 0.000** | 0.000** | 0.002** | –9.565** | 0.000** | –6.926** | 0.001** |
(0.379) | (0.000) | (0.322) | (0.001) | (0.379) | (0.000) | (0.000) | (0.001) | (0.525) | (0.000) | (0.392) | (0.000) |
R
2
| .34161 | .34239 | .40735 |
Model 1 includes a cumulative measure of imprisonment only, without adjusting for controls that might affect both the father’s imprisonment and mother’s MPF. In this model, fathers’ imprisonment is associated with a 55 % greater relative risk of MPF compared with no additional birth, and the association is statistically significant. The association between fathers’ imprisonment and having a second child with the same father is not statistically significant. When controls are added to Model 1, the results (not shown in the table) suggest that fathers’ imprisonment (the cumulative measure) is associated positively and statistically significantly with mothers’ MPF (an increase of 23 % in relative risk) and is associated negatively and statistically significantly with having a second child with the same father (a decrease of 24 %).
Because a father’s imprisonment may result in irreversible consequences for families once it occurs, the results of a model that includes only the cumulative imprisonment measure (Model 1) may be useful, especially if detailed data on timing of imprisonment and MPF are not available (e.g., Carlson and Furstenberg
2006). However, we can distinguish between the influence of current imprisonment and a history of imprisonment.
Model 2 in Table
2 includes both measures (but no controls). Both imprisonment measures show statistically significant and positive associations with MPF among mothers (a 33 % increase in relative risk for prior imprisonment and a 31 % increase in relative risk for current imprisonment). In other words, if the father was incarcerated at some point after the first pregnancy of the mother but not at the time of her second pregnancy, the risk of the mother’s MPF increased by 33 %. If the father was incarcerated after the first pregnancy of the mother and remained incarcerated at the time of the second pregnancy of the mother, the risk increased by an estimated 74 % (from
e
.284 + .269). In comparison, the association of current imprisonment with the risk of having a second child with the same father is negative (and statistically significant). This result is to be expected given the limited opportunities to conceive a second child while the father is incarcerated.
In contrast, prior imprisonment, alone, is positively (and statistically significantly) associated with the risk of having a second child with the same father in the results shown for Model 2. This result is less expected and persists in Model 3 (with additional controls). It may be that mothers who have a first birth with someone who becomes imprisoned are more likely to have a second birth; if the imprisonment is fairly short,
10 the mother’s second birth could be with either the same father or a different father. If the mother waits for the father to be released, the second birth is more likely to be with the focal father than another partner (ratios of 2.111 and 1.328, respectively, as shown in Model 2).
11 Alternatively, the unexpected positive association between father’s prior imprisonment and mother’s fertility with the same father also suggests the possibility of an unmeasured difference in commitment to the existing relationship between mothers who experienced partner imprisonment but remained without an additional pregnancy until partner release and those who did not experience partner imprisonment and remained without an additional pregnancy. For example, mothers who experienced a focal father’s imprisonment but did not engage in MPF until the focal father’s release may have a strong commitment to the relationship. In this case, mothers with a previously imprisoned partner (and without an additional birth until release) may be more likely to have a second child with the same father compared with their counterparts who do not experience partner imprisonment and remain without an additional birth. If so, we may observe a positive correlation between prior imprisonment and having a second child with the same father, even when a father’s prior imprisonment does not cause increased risk of having an additional child(ren) with the same father. Consistent with this, the positive correlation is reduced when observed characteristics are controlled, as shown in Model 3; the associated RRR presented in Table
2 changed from 2.11 in Model 2 to 1.69 in Model 3.
Model 3 (our primary MNL model specification) adds controls to Model 2. The relative risk of MPF was 23 % higher if a father was currently imprisoned, but a history of imprisonment did not have statistically discernible relationships. Because of the role of control variables that are potentially associated with partner imprisonment and mothers’ fertility decisions, including controls in the model reduces the magnitudes of the associations between measures of partner imprisonment and mothers’ MPF, although it does not change the direction of the coefficients. Because the coefficient for current imprisonment is statistically significant (but the cumulative measure is not), the results confirm the incapacitation effect (i.e., mothers have children with other fathers because the fathers of their first children are not physically accessible) and suggest that physical incapacitation is an important mechanism underlying the association between father’s imprisonment and mother’s MPF. This finding is consistent with prior research on marital dissolution and prior and current imprisonment (Lopoo and Western
2005; Massoglia et al.
2011). In contrast, the cumulative measure of imprisonment does not have a discernable relationship with MPF. Additional research is needed to better understand the timeframe for the relationship between incarceration and MPF, the potential effect of sentence lengths per se, as well as the unobserved heterogeneity of imprisonment (e.g., crime types).
12
Results from Model 3 suggest that whereas fathers’ current imprisonment reduced the likelihood of having a second child with the same father by 87 %, prior partner imprisonment (after release) was associated with a 69 % increase in having a second child with the same father. Compared with Model 2, the absolute magnitudes of the associations between imprisonment (either current imprisonment or prior imprisonment) and the risk of having a second child in Model 3 generally decreased with the inclusion of controls.
The results for other variables in Model 3 also deserve mention. Consistent with previous studies, receipt of food stamp benefits was positively associated with MPF (Cancian et al.
2011; Meyer et al.
2005), which may reflect a range of disadvantages associated with both family instability and public assistance participation. Couples in which both parents are black had a higher risk of mother’s MPF (Cancian et al.
2011; Carlson and Furstenberg
2006; Guzzo and Furstenberg
2007; Kim et al.
2015; Manlove et al.
2008). On the other hand, although previous studies have found a negative relationship between employment and earnings in the previous year and the risk of the mother having a child with another partner (e.g., Cancian et al.
2011), our multivariate analyses suggest that mothers who recently worked and those who had lower earnings measured at the time of two preceding months were more likely to have MPF compared with mothers who did not work or who had higher earnings, respectively. Finally, we note no detectable time trend: the mothers of children born in 1998 were no more or less likely to have MPF than mothers of children born in 2002.
Additional analyses with alternative model specifications and alternative samples (not shown in Table
2) confirmed our main findings of imprisonment being associated with an increased risk of MPF. An analysis that includes only a point-in-time measure of partner imprisonment (without the cumulative measure) and has control variables produced evidence consistent with statistically significant positive effects of imprisonment on MPF and statistically negative effects of imprisonment on having a second child with the same father.
Key results were also robust to alternative specifications of time-varying covariates. For example, in additional analysis, pregnancy was estimated to occur at 8 or 10 full months prior to the birth of the child, instead of 9 full months. Time-varying covariates—such as mother’s earnings and public program participation—were measured at t – 4 or t – 3, instead of t – 2, to reflect the mother’s previous economic circumstances prior to a conception when t is the calendar month in which conception is measured. In addition, to examine the robustness of the key results to the restriction of the sample to cases in which the focal father was not incarcerated at the time the mother became pregnant with her first child, an additional analysis was conducted using a sample that also includes those excluded cases. The results from these analyses (not shown) were substantially similar to the base results discussed earlier.
Included in all three models but not shown in Table
2 were time controls that included dummy variables for each month. Alternatively, additional analyses estimated the models with time and time squared as an alternative specification. The magnitudes and direction of the key coefficients were largely consistent with the base results, but model fit was generally lower in the alternative models than in the base results.
Overall, our models suggest that father’s imprisonment is associated with a higher risk of mother’s MPF. However, if unobserved characteristics of mothers affect both their partnering decision and their later fertility decisions, such unobserved heterogeneity may bias the estimates and undercut a causal interpretation.
Multivariate Analyses: Case-Time-Control Analyses
To control for unobserved individual differences, we used a fixed-effects method: case-time-control analysis, as described earlier. Also as noted earlier, the case-time-control models use smaller samples. In our main models, we use only mothers who experienced partner imprisonment and MPF (
n = 723); an alternative also includes mothers who experienced partner imprisonment but who did not have MPF during the observation period (total
n = 1,998). As shown in Appendix
1 the mothers in these analyses are more likely to be black and tend to be younger and more disadvantaged in terms of employment, earnings, and public welfare use than the base sample of 6,032.
Table
3 reports the coefficients and relative risk ratios for the effects of imprisonment. As indicated, the models differ in terms of inclusion of controls in the model, time-dependence specifications, and sample selection decisions (whether to include right-censored cases). Model 5 is our primary case-time-control analysis. The results suggest that fathers’ imprisonment increases the relative risk of MPF among mothers—compared with remaining without an additional birth or having a second birth with the same father—by 39 %. Depending on model specifications and inclusion of censored cases, the relative risk of MPF was between 39 % and 74 % higher if the focal father was imprisoned.
Table 3
Estimates of case-time-control models: Effects of fathers’ imprisonment on mothers’ MPF
Imprisonment (point-in-time) | 0.327** | 1.387** | 0.328** | 1.388** | 0.384** | 1.468** | 0.553** | 1.739** |
(0.112) | (0.156) | (0.112) | (0.156) | (0.111) | (0.162) | (0.105) | (0.182) |
Inclusion of Time-Varying Control Variablea
| No | Yes | Yes | Yes |
Specification of Time Dependence | Time (61-month) dummy variables | Time (61-month) dummy variables | Month and month squared | Time (61-month) dummy variables |
Whether Right-Censored Cases (those who did not experience MPF) Were Included | No | No | No | Yes |
Number of Observations (mother-months) | 23,022 | 23,022 | 23,022 | 90,802 |
Number of Observations (mothers) | 723 | 723 | 723 | 1,998 |
R
2
| .19217 | .19256 | .17662 | .11141 |
Table 4
Samples used in the multivariate analyses
Sample Selection | Base sample | Those in the base sample who experienced partner imprisonment | Those in the base sample who experienced partner imprisonment and MPF |
Variables (%) |
Whether mother experienced focal father imprisonment before second birth (exit) or censoring | 12.0 | 100.0 | 100.0 |
Whether mother’s MPF occurred | 33.0 | 38.1 | 100.0 |
Mother’s earnings one year prior to the focal child's birth |
No report | 16.2 | 20.6 | 25.6 |
$1–$5,000 | 33.9 | 40.6 | 41.9 |
$5,001–$10,000 | 19.7 | 18.1 | 19.2 |
$10,001–$20,000 | 19.7 | 14.8 | 11.1 |
$20,000+ | 10.6 | 5.9 | 2.2 |
Whether mother received any TANF cash benefits at one year after focal child’s birth | 25.7 | 37.2 | 39.1 |
Whether mother received any food stamps benefits at one year prior to until one year after focal child’s birth | 47.7 | 64.9 | 69.2 |
Age of mother at the focal child’s birth |
Under 18 | 21.5 | 30.6 | 37.5 |
18–20 | 44.8 | 46.6 | 49.7 |
21–23 | 20.7 | 15.1 | 10.7 |
24–27 | 7.2 | 4.5 | 1.5 |
28+ | 5.8 | 3.3 | 0.7 |
Race of mother and the focal father |
Both black | 21.4 | 39.7 | 43.0 |
Both white | 43.0 | 28.8 | 27.0 |
Both Hispanic | 2.5 | 2.2 | 2.8 |
Mother white/Father black | 7.3 | 10.0 | 10.8 |
Mother white/Father Hispanic | 3.7 | 3.9 | 3.0 |
All other combinations | 6.7 | 7.2 | 7.3 |
Either unknown | 15.4 | 8.3 | 6.1 |
Year of the focal child’s birth |
1998 | 6.2 | 6.3 | 6.8 |
1999 | 25.3 | 24.2 | 22.5 |
2000 | 25.3 | 24.3 | 24.2 |
2001 | 25.6 | 25.5 | 24.2 |
2002 | 17.7 | 19.7 | 22.3 |
County of the focal child’s residence |
Milwaukee | 29.9 | 43.5 | 46.1 |
Urban counties | 45.7 | 42.2 | 41.1 |
Rural counties | 24.4 | 14.3 | 12.9 |
Consistent with the results of the MNL competing-risks analyses, the results of the case-time-control analyses across models with different specifications and alternative samples suggest that father’s imprisonment is associated with increased MPF among mothers. The results from the fixed-effects method support a causal interpretation of the relationship between father’s imprisonment and mother’s MPF. However, because the sample is restricted to those with an experience of partner imprisonment, the generalizability of the analyses that support a causal relationship are limited. If patterns of incarceration changed and more advantaged individuals experienced incarceration, implications for rates of MPF might be expected to differ.