Gender Wage Gap and Male Perpetrated Child Sexual Abuse

Given the fact that child abuse and intimate partner violence often co-occur, intra-household bargaining models provide a useful framework to investigate the relationship between macro-economic factors and child sexual abuse (CSA). Non-cooperative bargaining models predict that labor market opportunities that benefit women improve their bargaining power and lead to lower levels of intimate partner violence against them. We posit that this protective effect extends to children as well, and exploit exogenous variation in macro-economic factors to examine the impact of gender specific wages and employment on police reported CSA in South Carolina, Tennessee, and Virginia from 2006 to 2019. The empirical analysis provides evidence that narrowing the gender wage gap leads to a decline in police reported CSA incidents perpetrated by mothers’ intimate partners, whereas improvements in relative employment opportunities do not yield any such effects. Consistent with previous literature, our results show that wages, not employment, determine bargaining power. The findings also underscore important spillover benefits of policy solutions directed towards narrowing the gender wage gap.


Introduction
. While all forms of maltreatment can lead to adverse outcomes, abuse speci cally has signi cant repercussions for young victims (Nemeroff, 2016, Fry et al. 2018). Among children who experience it, 58% are subjected to physical abuse and 24% are subjected to sexual abuse (Finkelhor et al., 2015). A recent meta-analysis showed that prominent risk factors for child sexual abuse (CSA) include intimate partner violence (IPV), exposure to physical child abuse, and presence of a non-biological parental gure (Assink et al., 2019). Violence in the home ( Slack et al., 2004) also put children at risk for physical abuse. Previous investigations into the relationship between child welfare and economic conditions show that indicators of nancial stress experienced by parents such as mortgage foreclosure, delinquency rates (Wood et al., 2012), and residential insecurity (Bullinger & Fong, 2021) are associated with child maltreatment. An inverse relationship between child abuse and parental employment (Frioux et  This body of literature highlights several mechanisms through which macro-economic factors can affect children's welfare. Higher wages and stable employment can lower child abuse by relieving nancial burden on families, and attenuating stress related triggers that can prompt violence. While the stress relieving mechanism of improved labor market opportunities provide an explanation for reduction in physical child abuse, it is an unlikely explanation for CSA that occurs within households. Sexual victimization of children is predatory and coercive (Craven et al., 2006;Katz & Barnetz, 2016), and its pathways differ from that of physical violence (Winters & Jeglic, 2017). Therefore, the link between larger economic macro-economic factors and CSA remains unclear.
Fortunately, there has been a noted decline in CSA since the 1990s (Finkelhor, 2020;Finkelhor et al., 2018). This is often attributed to prevention efforts that have centered around initiatives focused on raising awareness, encouraging disclosure, and offender management. However, a dearth of empirical evidence makes it di cult to ascertain the effectiveness of these interventions in reducing CSA (Finkelhor, 2009). Given that IPV and child abuse frequently co-occur (Adhia et al., 2019;Bidarra et al. 2016;Fry & Elliott, 2017), we employ an intra-household bargaining framework to show that improvements in women's economic prospects are protective against CSA perpetrated by mothers' male partners. While previous studies have extended the intra-household bargaining framework and provided theoretical justi cations for a negative relationship between child victimization and mothers' bargaining power (Berger, 2005), causal inferences have been hampered by data constraints. Our study lls this gap by presenting the rst empirical evidence of a causal relationship between macro-economic factors and police reported CSA. We construct a longitudinal panel of CSA perpetrated by biological fathers and mothers' male intimate partners using data from the National Incident Based Reporting System (NIBRS). Employing a wellestablished strategy to exploit exogenous variation in gender speci c labor market opportunities, we demonstrate a causal relationship between mothers' bargaining power and male perpetrated CSA reported to law enforcement.
Since literature on intra-household bargaining highlights that wages, not employment, determine bargaining power at threat point (Pollak, 2005), we consider both in our analysis. The results show that narrowing of the gender wage gap leads to a reduction in police reported CSA but improvements in relative employment opportunities yield no such effects. Our study makes several unique and valuable contributions to the existing literature. First, it shows that improvements in women's bargaining power have a protective effect on children and as such identi es a powerful primary prevention tool for policy makers. Second, it highlights that in studying macro-economic factors associated with child abuse it is important to consider the mechanisms through which these factors impact family interactions within households. While wages and employment may appear analogous as measures of women's economic empowerment, their effects are not equivalent, and these differences should inform policy decisions.

Intra-household Bargaining and Child Wellbeing
Existing evidence indicates that child outcomes improve when mothers have greater bargaining power (Ahmed, 2006;Echeverría et al., 2019). Greater control over household nances by women is related to lower levels of mortality and morbidity in children (Thomas, 1990), as well as increased in expenditures on necessities such as clothing (Lundberg et al., 1997). Female autonomy and empowerment are also linked to improvements in children's anthropometric status (Heckert et al., 2019;Malapit et al., 2015). These ndings suggest that mothers are more invested in children's health and wellbeing and leverage their bargaining power to facilitate better outcomes for their offspring.
There is also compelling evidence to show that IPV decreases in response to improvements in women's economic status (Aizer, 2010;Anderberg et al., 2016;Bhattacharyya et al., 2011), indicating that women can use the increased bargaining power to negotiate lower levels of violence against themselves. A natural extension of these models, where a woman's utility function incorporates her child's wellbeing, implies that the protective effect will extend to the child as well. There are two plausible channels through which this protection may be operationalized. Economic empowerment can equip mothers with resources necessary to leave abusive relationships which can reduce children's exposure to abusive adults. Favorable economic prospects can also endow mothers with greater bargaining power which can be leveraged to ensure children's safety.

Measures of Child Sexual Abuse
Measures of CSA used in this study are constructed using the National Incident Based Reporting System (NIBRS) data from 2006 to 2019. NIBRS extracts data from police incident reports and contain rich demographic information on victims and offenders, as well as information on the relationship between the two. Law enforcement agencies (LEAs) voluntarily opt into the NIBRS system. Consequently, data is not available for all jurisdictions. There is also temporal variation in NIBRS adoption across agencies, therefore, to create a stable panel of police reports, three states, South Carolina; Tennessee; and Virginia, are included in the analysis.
Comparing child abuse cases from NIBRS to those reported by the child welfare system in South Carolina, Finkelhor, and Ormrod found that the number of CSA cases reported by both systems were the same (Finkelhor & Ormrod, 2001). Tennessee law requires immediate noti cation of sexual abuse cases to the district attorney and the judge. Virginia has similarly enacted statutes that require law enforcement to be noti ed of all incidents of actual and suspected CSA reported to child protective services (Virginia Department of Health and Human Services). As such, NIBRS data likely captures a vast majority, if not all, of CSA reported to authorities in these states... Utilizing information on the victim's age and relationship to the perpetrator, county-year measures of CSA perpetrated by biological fathers, stepfathers, and mothers' intimate partners were created by aggregating the following offenses: forcible rape; forcible sodomy; sexual assault with an object; and forcible fondling for victims under 18. To avoid differential reporting across time and space, we include agencies that reported 12 months of data for each year in our study but include agencies that submitted their data to NIBRS through another agency but later became direct contributors. Relationship information was missing in about 15% of all CSA incidents reported by NIBRS. This was imputed using information on victim and incident characteristics. Of the total CSA incidents perpetrated by biological fathers and mother's intimate partners, 3.2% were reported by state police and other federal agencies over the analysis period. These were excluded since the origination county of these reports cannot be determined.
Since there may be important limitations inherent in the bargaining process as biological fathers' parental rights do not terminate upon the dissolution of relationship with the mother, it is important to distinguish between relationship categories to avoid obscuring important differences. We estimate the models for each category separately. For ease, we group stepfathers and mothers' dating partners together into a single category. Additional measures of sexual assault perpetrated by family members (such as siblings, grandparents, other related individuals) and strangers are employed for comparison. While as a rule NIBRS does not contain unfounded cases, sexual assault is an exception and a small percentage of cases may be determined to be unfounded (Kaplan, 2021). However previous studies examining reported cases of child abuse show that risk to children is similar in both instances (Kohl et al., 2009) and that a large proportion of subsequent reports are substantiated after an initial denial (Jedwab et al., 2017).

Control Variables
The choice of control variables is informed by literature. Previous research shows that factors like prosecution and probability of conviction can deter perpetration (Loughran et al., 2016). However publicly provided services, like the prosecutor's o ce, suffer from greater ine ciencies that are associated with the economic status of the county within which they operate (Gorman & Ruggiero, 2009). If improvements in economic conditions lead to greater resources and thereby higher conviction rates which discourages perpetration, than omitting controls to capture this effect can bias the estimated effect of our variable of interest on child abuse. We include the Yost Index to control for socio-economic differences between counties. Yost index is a composite measure of median household income; median rent; median home value; percentage of population living below 150% of the poverty line; percentage of population that is unemployed; percentage of population employed in blue collar jobs; and an education index (Yost et al., 2001). Disadvantaged communities and communities with high crime rates often receive more scrutiny by law enforcement and are policed aggressively (Edwards, 2019). Families engaged in the welfare system are also more likely to be involved with child protective services (Berger et al., 2009). It is important to account for disproportionate exposure and scrutiny that may arise because of involvement in the welfare system. We include a log of total households receiving Supplemental Nutrition Assistance Program (SNAP) in each county to control for such exposure. If reporting and/or perpetration is affected by the size of the police force, then one also needs to control for it (Anderberg et al., 2016;Lindo et al., 2018). We include the log of total number of police o cers in each county using FBI's Law Enforcement O cers Killed and Assaulted (LEOKA) data.
High rates of violent crime can also trigger stress in the residents of a community which can contribute to intrahousehold violence (Beyer et al., 2015;Wallace et al., 2021). This environmental effect is approximated by including a variable that captures the occurrence of violent crimes (aggravated assault, rape, robbery, and murder) in each county. Since IPV and child abuse tends to co-occur, we also include the log of county-year aggregates of IPV assaults calculated from NIBRS data.
Given the signi cant variation in county sizes and their respective populations, we use county level population data, for children under 18, from the National Cancer Institute's Surveillance, Epidemiology, and End Results (SEER) program to include proportion of children in each county that is white, black, or other minority race as controls and use the total child population as an offset. Finally, we use county to county migration data from the internal revenue services (IRS) to proxy the in-migration of individuals to each county to control for the possibility of counties with better economic conditions attracting individuals who have lower propensity to commit CSA (e.g. better educated Individuals). Descriptive statistics are provided in Table 1.  Where p gnc is the base period proportion of each gender employed in industry n in county c, and i ncy is the industry wage for each county c in year y. The base period shares of employment by each gender are held constant over the length of the analysis period to ensure that changes in wages are driven by the demand side. Therefore, gender speci c wages vary depending on the relative concentration of industries within each county and whether these industries employ a larger proportion of male or female workers (Aizer, 2010).
Since time allocation to labor market can change at threat point if non-working individuals choose to obtain employment or employed individuals increase the number of hours worked, employment should not have a determinate impact on bargaining power (Pollak, 2005). We use predicted employment rates to con rm that changes in sexual victimization of children arise from changes in bargaining power. We construct gender speci c employment rates following the same approach used in creating wages. The base period shares of statewide NAICS industry employment for each gender in each county are multiplied by total statewide industry employment and aggregated across all industries for each year. Our empirical strategy was motivated by the nature and features of the data. Our dependent variable is overdispersed with a non-trivial number of zeros even after aggregation and exclusion of counties with very small populations from the analysis to increase statistical power. Additionally, dependencies can arise due to temporal hierarchies as well as larger legal and socio-economic constructs (Johnson, 2006). These methodological and theoretical concerns necessitate the use of a multilevel model to properly accommodate the hierarchical nature of the data. We employ a negative binomial model with a group mean centering approach to capture both the within- where x jct is an explanatory variable belonging to county c, nested in state j measured at time t; x ̅ jc is the vector of subject-speci c means of the explanatory variables, x jct -x ̅ jc is the deviation from the mean, and µ jc and e jct are the error terms associated with subjects and time periods respectively. This allows us to model the average between and within effects distinctly in one coherent framework while controlling for unobserved time-invariant characteristics for each county and ensuring that there is no correlation between x ̅ jc and x jct by apportioning out µ jc . p ct is the offset that accounts for the variation in child population across the different counties; τ jt is the vector of state-year xed effects, is the linear time trend. Table 2 presents the coe cients from models estimating the impact of wage ratio on CSA by different relationship categories. Column 1 shows the results of sexual abuse perpetrated by biological fathers and column 2 shows sexual abuse perpetrated by mother's intimate partners while columns 3 and 4 show abuse by other family members and by strangers respectively. Since the predominant household structure in the US comprises of a nuclear family and intra-household bargaining does not extend to strangers, models 3 and 4 serve as falsi cation checks for the primary models in column 1 and 2. Our main objective is to establish a causal relationship and obtain unbiased estimates of the effects of wage gap over time, therefore we primarily focus on the within wage ratio and restrict the interpretation of as differences between counties.

Biological Fathers Mothers' Partner Family Members Strangers
Standard errors in parentheses *** p < 0.001, ** p < 0.01, * p < 0.05 Notes: Estimates are based on a random effect multi-level negative binomial model where outcome variable is aggregated county-year measure of sexual assaults perpetrated against children under 18 by fathers, mothers' romantic partners, family members and strangers. Sexual assault includes forcible rape, forcible sodomy, sexual assault with an object, forcible fondling. The main variable of interest is the ratio of female and male wages. County speci c means of independent variables are included to control for xed effects. Within effects represent the change in demeaned independent variables over time.
Looking at the within effects, wage ratio is negative and signi cant at the one percent level for mother's partner, showing that as gender wage gap closes there is a statistically signi cant decline in police reports of CSA. The within effect of wage ratio is insigni cant in columns 3 and 4, indicating that the protective effect of female wages is restricted to abuse that occurs within a household instead of some general mechanism that provides broader immunity to children and insulates them from sexual violence regardless of the source of perpetration. Wage ratio also does not have a signi cant effect on CSA by biological fathers. Exponentiating the coe cients in column 2 and interpreting them as incidence rate ratios show that a one unit increase in the wage ratio reduces police reports of child sexual abuse by a factor of 0.11 (IRR 0.11, 95% C.I. 0.027-0.456). Admittedly a one unit increase in wage ratio is not intuitive. Estimating the effect of one standard deviation in wage ratio yields 0.64 (or 23%) fewer incidents of CSA when the wage ratio rises from 0.75 to 0.87. The between effects in the rst three models show that on average counties with higher gender wage ratios have lower levels of CSA but not signi cantly so.
Additional within effects show that, increases in IPV are positively and signi cantly associated with CSA by biological fathers, mothers' partners, and family members. The between coe cient of IPV directed towards females is also positive and signi cant in models 1, 2, and 3. This is consistent with prior research that shows that IPV and child abuse tend to co-occur. The between coe cients of secular violence is positive and signi cant in all models except for mother's partners, while the within coe cient is signi cant in all models. This indicates that children living in areas with higher rates of overall violence are more vulnerable to sexual exploitation and increases in violence in a community are associated with an increase in CSA.
The results of the primary speci cation show that as the gender wage gap narrows, CSA perpetrated by mother's partners declines signi cantly. However, there are several threats to the validity of these ndings. For example, x ̅ jc can still be correlated with µ jc due to unobserved time-varying confounders that may have been omitted (Bell & Jones, 2015;Gunasekara et al., 2014). If the signi cance of the relationship between wage ratio and CSA by mothers' partners were simply a result of an in uential omitted variable, one might expect to see a similar in uence exerted upon the wage ratio coe cients for sexual abuse perpetrated by biological fathers and/or family members, but that is not the case. Nonetheless, we re-estimate the model with lagged dependent variables to check if any time varying effects that are not included in the main speci cation are potentially biasing the results. It is important to note that inclusion of a lagged dependent variable leads to bias as it violates the assumptions of the random component of the model being independent of explanatory variables. Since µ jc affects y jct−1 , inclusion of the lagged dependent variable as an explanatory factor creates correlation between the independent variables and the error term. As such the results presented in model 1 of Table 3 are strictly meant to be evaluated as a check for omitted variable bias. As expected, both the within and between coe cients of the lagged dependent variable are signi cant. Their inclusion shrinks the within coe cient of wage ratio from 2.178 to 1.88 but remains signi cant at 5%. Standard errors in parentheses *** p < 0.01, ** p < 0.05, * p < 0.1 Notes: Estimates are based on a random effect multi-level negative binomial model where outcome variable is aggregated county-year measure of police reported sexual assaults perpetrated against children under 18 by mothers' romantic partners. Sexual assault includes forcible rape, forcible sodomy, sexual assault with an object, forcible fondling. The main variable of interest is the ratio of female and male wages. County speci c means of independent variables are included to control for xed effects. Within effects represent the change in demeaned independent variables over time.
There is evidence that models with link functions other than identity do not reliably partition out the within and between variance when subject speci c means are non-linearly related to the error terms (Bell et al., 2019;Brumback et al., 2010). When this happens, estimates can be inconsistent. Although biases are usually small (Goetgeluk & Vansteelandt, 2008), it is worth checking the possibility of non-linearity given the attenuation in statistical signi cance of wage ratio. We re-estimate the models by including polynomial terms of the county speci c means of the independent variables. We also substitute the demeaned variables with the original variables; therefore, the county speci c means provide the contextual effect in this speci cation (Allison, 2014). The main idea is that if the coe cients are not very different from the main speci cation, it is indicative that bias is not a signi cant cause of concern. Model 2 of Table 3 presents the results of the alternate speci cation. Despite the inclusion of the polynomial terms the effect of wage ratio on child sexual abuse perpetrated by mother's romantic partners retains the negative and signi cant relationship. The coe cient of wage ratio remains signi cant at a 1% level and similar in size to the main speci cation. Model 3 shows that pooled results from 25 multiply imputed models yield results that are consistent with the main model.
Finally, to con rm the effect is driven by intra-household bargaining, we re-estimate the models with total wages instead of the female/male wage ratio as the main independent variable. Results in model 4 demonstrate that total wages have no effect on child sexual abuse. This is consistent with previous studies that have analyzed the impact of exogenous changes in macro-economic factors and found that it is the gender speci c improvements that leads to a reduction in violence against women rather than a general improvement in overall conditions (Aizer, 2010;Anderberg et al., 2016). As a last check, we calculate rates of CSA perpetrated by mother's romantic partners per 100,000 and estimate xed effects model as well as a traditional mixed effects model with random intercepts for counties and state xed effects. Results (in appendix) are robust to the alternate speci cations.

Impact of Employment on Child Sexual Abuse
To distinguish the causal impact of difference forms of economic empowerment on bargaining power, we reestimate the child sexual abuse model using the predicted employment rate as the main explanatory variable. Since it is the difference between the economic opportunities favoring men and women determines bargaining power (Anderberg et al., 2016), therefore we also operationalize the predicted employment rate as a ratio. Table 3 present the results of effect of employment on child sexual abuse.
Over time as the employment gap narrows, CSA exhibits an insigni cant decline in model 1, 2, and 4. This insigni cance supports that bargaining mechanism that suggests that wages and not employment increase bargaining power. Model 1 and 2 in Table 4 shows that on average counties with higher female employment rates have higher levels of CSA by biological fathers and mothers' partners, but the effect is not signi cant. Previous studies that have found signi cant positive effects of gender speci c employment on child maltreatment attribute it to increased exposure to abusive adults as mother increase the time contribution to paid work (Lindo et al., 2018). shows that as improvement in economic prospects increase female bargaining power, not only do women face a lower risk of violence within relationships, but it is also easier for them to leave abusive partnerships. We argue that this effect extends to protect children from abusive individuals and provide evidence of a causal relationship between the gender wage gap and police reported CSA. We compare this effect across several different relationship categories which should not be impacted by changes in bargaining power. The results show no evidence of a decline in CSA perpetrated by strangers and family members in response to changes in gender speci c wages. The ndings are robust to sensitivity checks and provide empirical evidence that suggests that bargaining effect is indeed driving the reduction in CSA. This is consistent with previous literature that shows that child outcomes improve when mothers have more bargaining power and provide an additional rationale for gender wage parity. While it is outside the scope of the current study to analyze these speci c mechanisms, it is di cult to conceive of a process whereby female autonomy and empowerment will lead to lower reporting mechanistically and result in an arti cial relationship.
Our ndings identify an important policy tool that can mitigate the burden of adverse childhood experiences. Mothers can play a signi cant role in primary prevention and be instrumental in inhibiting victimization of children. This is important because despite being one of the top preventable risk factors in the US burden of disease, CSA prevention is hampered by the fact that preemptive identi cation of prospective victims is challenging and resource intensive.
Interventions aimed at education and disclosure alone are not su cient and subsequent criminal justice actions to apprehend and prosecute perpetrators do not undo the lifetime consequences of trauma borne by the victims.
Endowing mothers with the agency and capacity to be protective barriers can not only address the gaps in existing strategies but also have important spillover bene ts operationalized through child wellbeing. It is important to note that closing the gender wage gap has no impact on CSA perpetrated by biological fathers. This may be due to limitations in the bargaining mechanism earlier and such a relationship may be better analyzed in the context of child custody laws.
We acknowledge that there are several limitations to this study. First, the data is anonymized, therefore, prevalence and incidence cannot be analyzed separately. Second, NIBRS is unlikely to capture the true incidence of child abuse and likely to suffer from underreporting problems. However, this is also true for alternate sources of child abuse data (Fallon et al., 2010). Despite these limitations, NIBRS data provides some distinct advantages through identi cation of the gender and relationship between the victim and offender and allowing for longitudinal analysis and is less likely to suffer from de nitional variations that can impact other administrative data sources (Adhia, 2018).
Our results also show that different measures of improvements in women's economic status are not equivalent in their protective effects and this distinction has important policy implications. As demonstrated, safety and well-being is achieved through good well-paying jobs rather than being merely employed. In addition to the direct and protective effect, closing the gender wage gap also has important spillover bene ts. Larger effects transmitted via children's well-being and their future productivity in the labor force can be substantial and should be considered explicitly in policy decisions. Although our study provides novel evidence on the relationship between CSA and macro-economic factors, it is merely highlighting a new path of inquiry. Future research should explore the relationship between macro-economic factors and CSA using multiple data sources and build on this initial evidence further. Scholars should also take into consideration the distinction between pertinent measures of bargaining power due to important policy implications.