This study estimates the associations of income with both (self-reported) child protective services (CPS) involvement and parenting behaviors that proxy for child abuse and neglect risk among unmarried families. Our primary strategy follows the instrumental variables (IV) approach employed by

A large and longstanding literature documents that low-income, poverty, and other markers of socioeconomic disadvantage are associated with increased risk of child abuse and neglect (

We use an instrumental variables (IV) strategy to estimate the effect of income on child maltreatment. Our approach, which closely follows that of

Our data are drawn from the Fragile Families and Child Wellbeing Study (FFCW), an urban, population-based birth cohort that has been followed from a focal child’s birth through age nine. We limit our analysis sample to families for whom the EITC is relevant: unmarried families with gross incomes below $45,000. Our child maltreatment measures consist of both (self-reported) child protective services (CPS) involvement and behaviorally approximated measures of child abuse and child neglect. We find that an exogenous increase in income is associated with a modest reduction in behaviorally-approximated child neglect and relatively large reduction in CPS involvement, particularly among low-income single-mother families.

The EITC is a refundable federal tax credit that supplements the earnings of low-wage workers. The credit amount varies by earnings, marital status, and number of children, ranging in 2012 from a maximum of almost $500 for a single adult to a nearly $6,000 for a family with three or more children (

To date, there have been no micro-level studies of links between the EITC and child maltreatment. More generally, there have been no rigorous studies of the causal role of income on child maltreatment, with two potential exceptions.

Our data are drawn from FFCW, a longitudinal cohort study of 4,898 children born between 1998 and 2000, in 20 U.S. cities with populations greater than 200,000. FFCW sampled nonmarital births with a 3:1 ratio to marital births. As such, FFCW parents are disproportionately likely to be low-income, have limited educational attainment, be of minority race/ethnicity, be unmarried, and become involved with CPS, relative to the U.S. population. Families were interviewed at the birth of the focal child and when the child was age 1, 3, 5 and 9.

We use observations from the age 3, 5, and 9 interviews, which results in a possible sample of 14,694 family-wave observations of 4,898 families. We first excluded 6,154 observations due to missing data.^{1} We then excluded families in which the mother was married at the age-3 interview (2,741 family-wave observations) and families with an adjusted gross income (AGI) of more than $45,000 (in nominal dollars) in any year of observation (1,759 observations), because such families would be well beyond the eligibility cutoff for the EITC. This resulted in a sample of 4,040 family-wave observations of 1,600 families.

The documented benefits of the EITC are most prominent for single-mother families and for families with two or more children (^{2} Notably, the types of families that are most likely to be eligible for and who benefit most from the EITC—low-income, single-mother, and larger families—are also at greatest risk for child maltreatment (

We operationalize child maltreatment both via behaviorally-approximated measures of child abuse and neglect, and with mothers’ self-reports that they had been investigated by CPS. The behaviorally-approximated measures included subsets of the Parent-Child Conflict Tactic Scales (

Child neglect consists of parental actions or inactions that place a child in situations or environments in which there is a foreseeable risk of harm as a result of inadequate supervision, food, shelter, medical care, emotional support, or other material or psychological necessities. We assess neglect via 11 indicators: (1) the child witnessed domestic violence; (2) the mother reported being too drunk or high to care for the child; (3) the mother reported using hard drugs; (4) the mother reported currently using non-prescribed drugs several days per week or more; (5) the mother reported earning income from illegal activities such as drug sales or prostitution; (6) the mother reported leaving the child unsupervised (alone) when she should not have; (7) the mother was unable to ensure that the child received the food he or she needed; (8) the mother was unable to get the child to the doctor or hospital when needed; (9) the family’s electricity or heat was shut off for non-payment; (10) the family experienced homelessness; and (11) the family experienced housing-related doubling up for financial reasons. We code child neglect equal to one if the sum of the 11 items falls in the top quartile of FFCW sample values, and zero otherwise. For both abuse and neglect, we estimated supplemental analyses using greater than one-half of a standard deviation (SD) above the sample mean as a maltreatment threshold, as well as a z-scored transformation of the continuous measures.

Note that none of our behaviorally-approximated measures necessarily meet statutory definitions of maltreatment. However, they reflect conditions that commonly bring families to the attention of CPS. For example, exposure to domestic violence and parental drug abuse are cited in 29% and 20% of CPS cases (

We also mothers reports that their family was investigated by CPS. At ages 5 and 9, the focal child’s primary caregiver (generally mother) was asked whether the family had been contacted by CPS since the focal child’s birth (in the age 5 interview) or since the prior interview (in the age 9 interview). Mothers who answered in the affirmative were asked to provide the date of their most recent CPS contact. We attributed CPS involvement to the interview wave that immediately succeeded the CPS contact date. Consequently, we are likely underestimating CPS involvement at wave 3, given we only know the date of most recent contact at waves 4 and 5.

Relying on self-reported CPS involvement is cause for concern given that there may be systematic bias in reporting. Unfortunately, because no existing national, longitudinal survey includes both income data and administrative data on CPS involvement, self-reports are commonly used in population-based studies (^{3}

A final concern is that CPS investigations are likely to underestimate maltreatment, given that a substantial portion of maltreatment is never reported (

Our primary predictor is post-tax and transfer family income. We began with the FFCW constructed measure of total household income reported by the mother.^{4} We then subtracted unearned income (e.g., government benefits, child support) to create a measure of household earnings.^{5} Finally, we used our derived earnings data and other income sources and amounts to calculate tax liabilities and credits using TAXSIM version 9.3 (National Bureau of Economic Research, 2015). TAXSIM generates estimates of state and federal tax liabilities or refunds due. The total (state and federal) tax liability (or refund) is then deducted from (added to) total household income to calculate post-tax and transfer (net) income.

TAXSIM also produces the combined state and federal EITC amount for which a family is eligible, given the tax year, their income, filing status (married or unmarried), number of dependents, and state of residence. This amount, which serves as the exogenous source of variation in family income (instrument) in our IV models, assumes full take-up of the EITC, though prior estimates suggest that the take-up rate for the EITC among eligible families is about 80 to 87% (

Although the largest EITC expansions occurred in the 1990s, there is considerable variation across states and over time during our observation period.

We control for a number of static and time-variant characteristics. Static characteristics include race/ethnicity, maternal education, and number of biological children in the household (at the age-3 interview). Time variant characteristics include family structure (married, cohabiting, single mother), age of the youngest child in the household, the mother’s age, whether the mother reported no household income, the average of lagged and current household income, and census tract unemployment and public assistance receipt rates. We use the average of lagged and current household income, rather than simply lagged household income, given the considerable amount of time (2 to 4 years) between FFCW data collection waves.^{6} All models also control for wave of observation and either region or state of observation.

We first present results from IV regressions in which the potential EITC benefit available to a family is used to instrument income (our preferred specification). The appropriateness of this approach relies on three assumptions: (1) the available EITC benefit is predictive of variation in net income; (2) the EITC benefit only affects maltreatment through its effect on income; and (3) the EITC benefit is uncorrelated with the error term. The first assumption is easily tested using weak identification tests, which demonstrate the EITC is a strong instrument.^{7} The second is justified because the primary purpose of the EITC is to encourage work through wage supplementation and it provides no (direct) non-monetary benefits, thus making it improbable that it would belong in the structural equation. The third assumption is more difficult to substantiate. It is possible that states with more generous EITCs differ from states with smaller or no EITCs on characteristics associated with maltreatment rates. Similarly, changes over time in EITC benefits may co-occur with changes in unobserved local conditions, which may affect the likelihood of maltreatment. We address this potential problem through the inclusion of either region or state dummies, as well as by controlling for the census tract unemployment rate and public assistance receipt rates (we also include wave dummies in all models).

Even after accounting for possible confounding effects of time and location, variation in EITC amount is still partly a function of three family characteristics: pretax earnings, marital status, and number of dependents, each of which is likely to be correlated with unobserved family characteristics. To address this, we follow the strategy used by

We estimated pooled and fixed-effects two-stage least squares regressions. The first stage model, in OLS form, is:

The validity of our IV strategy is dependent on “controlling flexibly for pretax income with the control function” (

We next present results from a series of robustness checks. We first estimated pooled cross-sectional OLS regressions and OLS regressions with family-specific fixed-effects to assess the association between net income and CPS involvement. The pooled OLS model, with standard errors clustered at the family level, is of the basic form:

Second, we present results from reduced form models in which we regressed each outcome on the maximum EITC potentially available to the family in a given state and year, rather than on family income. The reduced-form strategy allows us to examine whether there is a direct association of the generosity of the EITC to which a family is subject with the likelihood that the family engages in maltreatment. This model, in OLS estimation, takes the form:

Next, we present results from regressions using a control function that provides information about the direction and magnitude of bias in our OLS estimates. Consider the equation:

Descriptive statistics are presented in

Our first-stage IV results are presented in

The second-stage results (

^{8} Our estimates support the hypothesis that the benefits of the EITC are most prominent for single-mother and larger families. Indeed, the link between income and both behaviorally-approximated neglect and CPS involvement is particularly strong for to these groups. Specifically, it is negative and at least marginally significant for all of the IV models for single mothers and several of the IV models for families with multiple children. In terms of effect size, we find, for example, a $1,000 increase in income to be associated with roughly a 1.0 to 1.2 percentage point (3% to 4%) decrease in behaviorally-approximated neglect and a .58 to .70 percentage point (8% to 10%) decrease in CPS involvement among low-income single-mother families.^{9}

The OLS estimates when family-specific fixed effects are included are smaller and non-significant. Nearly all of the reduced form estimates are negative, suggesting that EITC generosity is inversely associated with maltreatment. These estimates are considerably larger than those from the linear probability models (with and without fixed effects). At the same time, only the neglect estimates for models that do not include family fixed effects attain (marginal) statistical significance. The control function results are consistent with those from the reduced form models, although the coefficients are smaller in magnitude. The coefficients in both the reduced form and control function models are larger than those in the OLS models (without the inclusion of fixed-effects), again suggesting that the OLS coefficients are downwardly biased.

We find that, at least among single-mother families and, to a slightly lesser extent, families with greater number of children, our (preferred) IV specification produces larger and more frequently significant estimates of the effect of income on behaviorally-approximated neglect and CPS involvement than models that less rigorously address selection. Indeed, the IV results for single-mother families suggest significant, small to modest decreases in behaviorally-approximated neglect and modestly large decreases in CPS involvement per a $1000 exogenous increase in income, whereas estimates from the more naive models suggests smaller declines. This may be the case for three reasons. First, the OLS estimates may reflect greater attenuation bias due to measurement error in income. Second, the link between income and child maltreatment may be strongest among relatively lower-income families such that the local average treatment effect produced by our IV strategy is most relevant to such families. Finally, permanent increases in income are thought to have larger influences on family wellbeing than temporary shocks. As such, if EITC expansions reflect relatively permanent income increases rather than temporary income shocks, the IV estimates should be larger than the OLS estimates. We find no evidence of a causal link between income and child abuse.

The general pattern of our results is suggestive of a causal link between income and both child neglect and CPS involvement, at least among single-mother and possibly larger families, which benefit most from the EITC. Moreover, the absence of statistical significance from many of the second stage IV results does not necessarily indicate a lack of a causal relation. The IV strategy is primarily intended to detect bias in the size and direction of the coefficients produced by more naïve models. Indeed, because the variance of the IV estimator is larger than that of the OLS estimator (as the former uses only a portion of the variance in the instrumented variable) the method tends to produce large second stage standard errors; this “is the price paid for avoiding the asymptotic bias of OLS” (

Several caveats should be considered when interpreting out results. First, the generalizability of our findings is limited to relatively disadvantaged urban families whose incomes are potentially affected by EITC benefit generosity. Second, whereas there is adequate EITC variation across states and over time to support our identification strategy, many of the largest EITC expansions occurred in the 1990s, before the FFCW study began. We cannot be certain that the same results would be found using data from earlier time periods. Finally, because our measure of CPS involvement is self-reported, it may be subject to social desirability (and, therefore, underreporting) bias as well as faulty or incomplete recollection of events. In addition, CPS-investigation was only measured at the age 5 and age 9 interviews and, at each time point, dates were provided only for the most recent investigation. Thus, we likely underestimate of CPS investigations, and particularly recurrent and early contacts.

Additional research is needed to achieve a more complete understanding of whether links between income and child maltreatment are causal and, thereby, whether economic support policies may reduce maltreatment and CPS involvement. Such research should also focus on the mechanisms through which income may influence maltreatment risk. Given the high public and private cost of child maltreatment, the extensive body of literature documenting that low-income families are disproportionately likely to come to the attention of CPS, and the efficiency associated with direct cash transfers like the EITC, such research is crucial to informing policy. It is well known that, in addition to being disproportionately low income, families at risk of maltreatment and CPS involvement are disproportionately characterized by a host of other risk factors, including poor parenting skills and knowledge of child development, substance abuse, mental health problems, criminal justice involvement, cognitive impairments, poor health, and residence in disadvantaged neighborhoods. Many of these problems are relatively intractable; they are difficult to ameliorate and treatment is often prolonged and expensive (if even available), and many families fail to take-up or comply with treatment. As such, if a causal link between income and maltreatment exists—which is cautiously suggested by our results—then economic support may be an additional tool for preventing child maltreatment.

The Fragile Families and Child Wellbeing Study is funded by NICHD grant numbers R01HD36916, R01HD39135, and R01HD40421, as well as a consortium of private foundations and other government agencies. This research was supported by funding from the Institute for Research on Poverty and the Waisman Center (NICHD grant number P30 HD03352) at the University of Wisconsin-Madison, Population Research Center, (R24 Center Grant) 5 R24 HD042849 NICHD and Training Program in Population Studies 5 T32 HD007081, NICHD at the University of Texas at Austin, and Population Research Center (R24 Center Grant) 2 P2C HD058486 at Columbia University School of Social Work. The authors are listed alphabetically.

Specifically, 46% of excluded family-wave observations resulted from a family not being interviewed at a given wave and 42% from missing data on the CPS or behaviorally-approximated maltreatment measures; the remaining exclusions were due to missing income data.

We also tested two additional sample selection criteria: (1) including limiting the sample to families with AGI below 130% of poverty (

Notably, the majority of CPS investigations include allegations that are not able to be substantiated by a preponderance of the evidence. As such, investigations, rather than substantiated cases of maltreatment are widely used in child maltreatment studies because the decision to substantiate often reflects factors unrelated to the actual maltreatment allegations (

In the FFCW age-3 through age-9 interviews, respondents were asked to provide an exact dollar amount of household income. Those that were unable or unwilling were asked to provide a range. Approximately 90% of respondents provided household income data in one of these two forms. The FFCW study team then imputed household income dollar amounts for respondents who reported income in range format based on other respondents who provided income in the same range but via detailed income amount. They then imputed dollar amounts for those with who did not report income in either format. Both imputations included the following covariates: relationship status, age, race/ethnicity, immigrant, employed last year, earnings, total adults in the household, and received welfare in the last year. For a detailed description of the FFCW constructed income variables, see

Although the FFCW data contain separate measures of earnings, this item is only asked with regard to the respondent. Earnings data for partners are only available if the mother’s current partner is the biological father of the focal child; even then, these data are often incomplete. Thus, we determined that subtracting nontaxable income from total income was a superior approach to income based on only those earnings reported.

We also conducted our analyses using only lagged income. The results do not change.

For all IV results, we present the Kleibergen-Paap

IV results for cohabiting families and families with only one child at baseline (age 3) are presented in

We also estimated supplemental models using alternative specifications of the behaviorally-approximated abuse and neglect measures, including dichotomous measures that a family scored more than half of a standard deviation above the sample mean for abuse or neglect, and continuous measures of the abuse and neglect indices (standardized to have a mean of 0 and standard deviation of 1). These results (see

Full sample | Complete case sample | Analysis sample | |
---|---|---|---|

CPS investigation | 4.1% | 5.7% | 7.5% |

Abuse (continuous) | 5.13 | 5.23 | 6.21 |

Neglect (continuous) | .43 | .42 | .54 |

Net income | 4.02 | 4.20 | 2.69 |

EITC | 1.35 | 1.35 | 1.98 |

Lagged pretax income | 42.52 | 42.53 | 18.92 |

Married | 29.2% | 32.1% | .00% |

White | 21.7% | 22.3% | 11.6% |

Black | 47.2% | 5.2% | 64.4% |

Hispanic | 27.2% | 24.4% | 22.4% |

Other race | 3.9% | 3.1% | 1.61% |

Less than HS | 34.7% | 32.2% | 44.9% |

HS only | 3.3% | 31.2% | 35.5% |

More than HS | 35.0% | 36.6% | 19.6% |

No. Children | 2.158 | 2.304 | 2.41 |

Single | 51.4% | 40.3% | 59.8% |

Cohabiting | 20.0% | 24.8% | 33.0% |

Married | 28.6% | 34.9% | 7.2% |

Age of youngest child | 3.13 | 2.22 | 2.28 |

No. adults in household | 2.00 | 1.99 | 1.83 |

Age of mother | 3.99 | 3.91 | 29.63 |

Northeast | 41.4% | 41.9% | 42.9% |

South | 19.6% | 18.8% | 16.4% |

Midwest | 25.6% | 29.1% | 32.5% |

California | 13.4% | 1.2% | 8.19% |

Age 3 interview | 33.3% | 32.7% | 32.4% |

Age 5 interview | 33.3% | 33.1% | 33.7% |

Age 9 interview | 33.3% | 34.3% | 33.9% |

Unemployment rate | .10 | .10 | .12 |

Public assistance rate | .07 | .07 | .09 |

Note: Means (and standard deviations) or percent presented.

Abuse | Neglect | CPS Investigation | |
---|---|---|---|

Percent | 33.45 | 34.44 | 6.59 |

Model 3: All controls | .0373 | −.0367 | −.0338 |

Model 4: Add state fixed effects | .0562 | −.0346 | −.0344 |

Model 5: With family fixed effects | .1218 | .0464 | −.0452 |

Model 3: All controls | −.0558 | −.0871 | −.1018 |

F-statistic (first stage) | 240.97 | 240.97 | 240.97 |

Model 4: Add state fixed effects | −.0086 | −.0758 | −.0991 |

F-statistic (first stage) | 231.94 | 231.94 | 231.94 |

Model 5: With family fixed effects | .1992 | .0825 | −.0749 |

F-statistic (first stage) | 131.85 | 131.85 | 131.85 |

Percent | 35.72 | 37.28 | 6.71 |

Model 3: All controls | −.0510 | −.2641 | −.0379 |

Model 4: Add state fixed effects | −.0426 | −.2591 | −.0332 |

(ln income estimate presented) | (.1280) | (.1230) | (.0610) |

Model 5: With family fixed effects | .1530 | −.2086 | −.0709 |

Model 3: All controls | −.1315 | −.3141 | −.1018 |

F-statistic (first stage) | 231.43 | 231.43 | 231.43 |

Model 4: Add state fixed effects | −.0949 | −.3035 | −.0968 |

F-statistic (first stage) | 223.50 | 223.50 | 223.50 |

Model 5: With family fixed effects | .1351 | −.1994 | −.0983 |

F-statistic (first stage) | 123.30 | 123.30 | 123.30 |

Note: Standard errors in parentheses. Standard errors for the LP estimates are clustered by family. Robust standard errors are used for the fixed effects estimates. Model 3 includes all time constant and time varying covariates as well as the average of lagged and current income, Model 4 replaces region fixed-effects with state fixed effects, and Model 5 includes family-specific fixed effects. The first stage F statistics are from the Kleibergen-Paap weak identification test, for which the critical values are 16.38, 8.96, 6.66, and 5.53 (corresponding to 10%, 15%, 20% and 25% maximum relative bias, respectively;

p<.10

p<.05

p<.01

p<.001

Abuse | Neglect | CPS Investigation | |
---|---|---|---|

Percent | 33.99 | 35.68 | 7.96 |

Model 3: All controls | −.0051 | −.0083 | −.0008 |

Model 4: Add state fixed effects | −.0039 | −.0087 | −.0010 |

Model 5: With family fixed effects | −.0008 | −.0001 | −.0024 |

Model 3: All controls | −.0117 | −.0065 | −.0032 |

F-statistic (first stage) | 57.87 | 57.87 | 57.87 |

Model 4: Add state fixed effects | −.0088 | −.0070 | −.0034 |

F-statistic (first stage) | 53.52 | 53.52 | 53.52 |

Model 5: With family fixed effects | .0029 | .0035 | −.0020 |

F-statistic (first stage) | 17.43 | 17.43 | 17.43 |

Percent | 35.52 | 37.67 | 8.37 |

Model 3: All controls | −.0056 | −.0166 | −.0017 |

Model 4: Add state fixed effects | −.0044 | −.0167 | −.0016 |

Model 5: With family fixed effects | −.0005 | −.0093 | −.0070 |

(.0078) | (.0083) | (.0049) | |

Model 3: All controls | −.0121 | −.0164 | −.0039 |

F-statistic (first stage) | 289.71 | 289.71 | 289.71 |

Model 4: Add state fixed effects | −.0092 | −.0164 | −.0039 |

F-statistic (first stage) | 272.86 | 272.86 | 272.86 |

Model 5: With family fixed effects | −.0009 | −.0079 | −.0053 |

F-statistic (first stage) | 38.39 | 38.39 | 38.39 |

Note: 3,657 family-wave observations of 1,515 families. Standard errors in parentheses. Standard errors for the LP estimates are clustered by family. Robust standard errors are used for the fixed effects estimates. Model 3 includes all time constant and time varying covariates as well as the average of lagged and current income, Model 4 replaces region fixed-effects with state fixed effects, and Model 5 includes family-specific fixed effects. The first stage F statistics are from the Kleibergen-Paap weak identification test, for which the critical values are 16.38, 8.96, 6.66, and 5.53 (corresponding to 10%, 15%, 20% and 25% maximum relative bias, respectively;

p<.10

p<.05

p<.01

p<.001

Abuse | Neglect | CPS Investigation | |
---|---|---|---|

Percent | 31.39 | 31.73 | 7.20 |

Model 3: All controls | −.0014 | .0141 | −.0008 |

F-statistic (first stage) | 44.75 | 44.75 | 44.75 |

Model 4: Add state fixed effects | −.0013 | .0145 | −.0018 |

F-statistic (first stage) | 44.05 | 44.05 | 44.05 |

Model 5: With family fixed effects | .0066 | .0370 | .0125 |

F-statistic (first stage) | 21.88 | 21.88 | 21.88 |

Percent | 33.11 | 35.19 | 4.66 |

Model 3: All controls | .0056 | .0098 | .0019 |

F-statistic (first stage) | 10.49 | 10.49 | 10.49 |

Model 4: Add state fixed effects | .0093 | .0126 | .0016 |

F-statistic (first stage) | 8.79 | 8.79 | 8.79 |

Model 5: With family fixed effects | 0.1229 | 0.0490 | 0.0880 |

F-statistic (first stage) | 0.08 | 0.08 | 0.08 |

Note: Standard errors in parentheses. Standard errors for the LP estimates are clustered by family. Robust standard errors are used for the fixed effects estimates. Model 3 includes all time constant and time varying covariates as well as the average of lagged and current income, Model 4 replaces region fixed-effects with state fixed effects, and Model 5 includes family-specific fixed effects. The first stage F statistics are from the Kleibergen-Paap weak identification test for instrumental variables. All IV models families meet the critical value of 16.38 (corresponding to a 10% maximum relative bias;

p<.10

p<.05

p<.01

p<.001

Abuse | Neglect | CPS Investigation | |
---|---|---|---|

Percent | 35.97 | 38.30 | 7.69 |

Model 3: All controls | −0.0068 | −0.0129 | −0.0048 |

F-statistic (first stage) | 114.32 | 114.32 | 114.32 |

Model 4: Add state fixed effects | −0.0049 | −0.0132 | −0.0047 |

F-statistic (first stage) | 136.78 | 136.78 | 136.78 |

Model 5: With family fixed effects | 0.0054 | −0.0112 | −0.0054 |

F-statistic (first stage) | 68.10 | 68.10 | 68.10 |

Percent | 36.11 | 39.43 | 6.95 |

Model 3: All controls | −0.0095 | −0.0157 | −0.0062 |

F-statistic (first stage) | 94.24 | 94.24 | 94.24 |

Model 4: Add state fixed effects | −0.0083 | −0.0160 | −0.0062 |

F-statistic (first stage) | 112.74 | 112.74 | 112.74 |

Model 5: With family fixed effects | 0.0059 | −0.0082 | −0.0060 |

F-statistic (first stage) | 37.08 | 37.08 | 37.08 |

Percent | 36.45 | 38.34 | 7.57 |

Model 3: All controls | −0.0078 | −0.0130 | −0.0043 |

F-statistic (first stage) | 106.73 | 106.73 | 106.73 |

Model 4: Add state fixed effects | −0.0058 | −0.0131 | −0.0041 |

F-statistic (first stage) | 102.82 | 102.82 | 102.82 |

Model 5: With family fixed effects | 0.0043 | −0.0103 | −0.0055 |

F-statistic (first stage) | 66.31 | 66.31 | 66.31 |

Percent | 36.68 | 39.40 | 6.76 |

Model 3: All controls | −0.0110 | −0.0160 | −0.0058 |

F-statistic (first stage) | 87.19 | 87.19 | 87.19 |

Model 4: Add state fixed effects | −0.0095 | −0.0162 | −0.0056 |

F-statistic (first stage) | 85.10 | 85.10 | 85.10 |

Model 5: With family fixed effects | 0.0040 | −0.0075 | −0.0064 |

F-statistic (first stage) | 37.19 | 37.19 | 37.19 |

Percent | 37.09 | 39.95 | 6.68 |

Model 3: All controls | −0.0139 | −0.0165 | −0.0069 |

F-statistic (first stage) | 62.50 | 62.50 | 62.50 |

Model 4: Add state fixed effects | −0.0126 | −0.0167 | −0.0068 |

F-statistic (first stage) | 60.22 | 60.22 | 60.22 |

Model 5: With family fixed effects | 0.0056 | −0.0103 | −0.0078 |

F-statistic (first stage) | 23.75 | 23.75 | 23.75 |

Model 3: All controls | −0.0085 | −0.0144 | −0.0071 |

F-statistic (first stage) | 113.18 | 113.18 | 113.18 |

Model 4: Add state fixed effects | −0.0067 | −0.0144 | −0.0071 |

F-statistic (first stage) | 109.77 | 109.77 | 109.77 |

Model 5: With family fixed effects | 0.0040 | −0.0086 | −0.0061 |

F-statistic (first stage) | 68.66 | 68.66 | 68.66 |

Percent | 36.08 | 37.89 | 7.78 |

Model 3: All controls | −0.0067 | −0.0129 | −0.0052 |

F-statistic (first stage) | 34.56 | 34.56 | 34.56 |

Model 4: Add state fixed effects | −0.0044 | −0.0127 | −0.0053 |

F-statistic (first stage) | 30.25 | 30.25 | 30.25 |

Model 5: With family fixed effects | 0.0044 | −0.0128 | −0.0057 |

F-statistic (first stage) | 10.92 | 10.92 | 10.92 |

Percent | 37.85 | 39.79 | 6.74 |

Model 3: All controls | −0.0110 | −0.0165 | −0.0063 |

F-statistic (first stage) | 79.04 | 79.04 | 79.04 |

Model 4: Add state fixed effects | −0.0095 | −0.0164 | −0.0062 |

F-statistic (first stage) | 62.55 | 62.55 | 62.55 |

Model 5: With family fixed effects | 0.0090 | −0.0107 | −0.0071 |

F-statistic (first stage) | 20.41 | 20.41 | 20.41 |

Note: Standard errors in parentheses. Standard errors for the LP estimates are clustered by family. Robust standard errors are used for the fixed effects estimates. Model 3 includes all time constant and time varying covariates as well as the average of lagged and current income, Model 4 replaces region fixed-effects with state fixed effects, and Model 5 includes family-specific fixed effects. The first stage F statistics are from the Kleibergen-Paap weak identification test for instrumental variables. All IV models families meet the critical value of 16.38 (corresponding to a 10% maximum relative bias;

p<.10

p<.05

p<.01

p<.001

Abuse .50 SD threshold | Neglect .50 SD threshold | |
---|---|---|

Percent | 17.15 | 35.72 |

Model 3: All controls | −.0056 | −.0049 |

F-statistic (first stage) | 222.69 | 222.69 |

Model 4: Add state fixed effects | −.0043 | −.0050 |

F-statistic (first stage) | 215.78 | 215.78 |

Model 5: With family fixed effects | −.0003 | −.0000 |

F-statistic (first stage) | 141.04 | 141.04 |

Percent | 18.21 | 37.97 |

Model 3: All controls | −.0086 | −.0122 |

F-statistic (first stage) | 194.72 | 194.72 |

Model 4: Add state fixed effects | −.0033 | −.0105 |

F-statistic (first stage) | 225.29 | 225.29 |

Model 5: With family fixed effects | −.0033 | −.0103 |

F-statistic (first stage) | 138.65 | 138.65 |

Note: 4,040 family-wave observations of 1,750 families. Standard errors in parentheses. Standard errors for the LP estimates are clustered by family. Robust standard errors are used for the fixed effects estimates. Model 3 includes all time constant and time varying covariates as well as the average of lagged and current income, Model 4 replaces region fixed-effects with state fixed effects, and Model 5 includes family-specific fixed effects. The first stage F statistics are from the Kleibergen-Paap weak identification test, for which the critical values are 16.38, 8.96, 6.66, and 5.53 (corresponding to 10%, 15%, 20% and 25% maximum relative bias, respectively;

p<.10

p<.05

p<.01

p<.001

Abuse | Neglect | |
---|---|---|

Mean | .037 | .070 |

(SD) | (1.047) | (1.073) |

Model 3: All controls | −.0139 | .0073 |

F-statistic (first stage) | 222.69 | 222.69 |

Model 4: Add state fixed effects | −.0095 | .0052 |

F-statistic (first stage) | 215.78 | 215.78 |

Model 5: With family fixed effects | .0071 | .0225 |

F-statistic (first stage) | 141.04 | 141.04 |

Mean | .063 | .100 |

(SD) | (1.052) | (1.081) |

Model 3: All controls | −.0215 | −.0080 |

F-statistic (first stage) | 194.72 | 194.72 |

Model 4: Add state fixed effects | −.0060 | −.0145 |

F-statistic (first stage) | 225.29 | 225.29 |

Model 5: With family fixed effects | −.0011 | −.0008 |

F-statistic (first stage) | 138.65 | 138.65 |

Note: Standard errors in parentheses. Standard errors for the LP estimates are clustered by family. Robust standard errors are used for the fixed effects estimates. Model 3 includes all time constant and time varying covariates as well as the average of lagged and current income, Model 4 replaces region fixed-effects with state fixed effects, and Model 5 includes family-specific fixed effects. The first stage F statistics are from the Kleibergen-Paap weak identification test, for which the critical values are 16.38, 8.96, 6.66, and 5.53 (corresponding to 10%, 15%, 20% and 25% maximum relative bias, respectively;

p<.10

p<.05

p<.01

p<.001

Maximum Federal and State EITC Benefits by Year

2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | |
---|---|---|---|---|---|---|---|---|---|---|

1 child | $2,353 | $2,428 | $2,506 | $2,547 | $2,604 | $2,662 | $2,747 | $2,853 | $2,917 | $3,043 |

2 children | $3,888 | $4,008 | $4,140 | $4,204 | $4,300 | $4,400 | $4,536 | $4,716 | $4,824 | $5,028 |

3 children | $3,888 | $4,008 | $4,140 | $4,204 | $4,300 | $4,400 | $4,536 | $4,716 | $4,824 | $5,657 |

CA | – | – | – | – | – | – | – | – | – | – |

TX | – | – | – | – | – | – | – | – | – | – |

MD | 15% | 16% | 16% | 18% | 20% | 20% | 20% | 20% | 25% | 25% |

MI | – | – | – | – | – | – | – | – | 10% | 20% |

NJ | 10% | 15% | 18% | 20% | 20% | 20% | 20% | 20% | 23% | 25% |

PA | – | – | – | – | – | – | – | – | – | – |

VA | – | – | – | – | – | – | 20% | 20% | 20% | 20% |

IN | – | – | – | 6% | 6% | 6% | 6% | 6% | 6% | 9% |

NY | 23% | 25% | 28% | 30% | 30% | 30% | 30% | 30% | 30% | 30% |

MA | 10% | 15% | 15% | 15% | 15% | 15% | 15% | 15% | 15% | 15% |

TN | – | – | – | – | – | – | – | – | – | – |

IL | 5% | 5% | 5% | 5% | 5% | 5% | 5% | 5% | 5% | 5% |

FL | – | – | – | – | – | – | – | – | – | – |

OH | – | – | – | – | – | – | – | – | – | – |

WI – 1 child | 4% | 4% | 4% | 4% | 4% | 4% | 4% | 4% | 4% | 4% |

WI – 2 children | 14% | 14% | 14% | 14% | 14% | 14% | 14% | 14% | 14% | 14% |

WI – 3 children | 43% | 43% | 43% | 43% | 43% | 43% | 43% | 43% | 43% | 43% |

The Maryland EITC is non-refundable.

Simulated Total (State and Federal) EITC for Single Filers with 2 Children by State, Year, and Earnings

$15,000
| $30,000
| |||||
---|---|---|---|---|---|---|

State | 2001 EITC | 2005 EITC | 2009 EITC | 2001 EITC | 2005 EITC | 2009 EITC |

No State EITC | 4,855 | 4,833 | 5,028 | 1,877 | 1,840 | 2,168 |

MD | 7,879 | 8,042 | 8,690 | 2,815 | 2,760 | 3,252 |

MI | 4,855 | 4,833 | 6,034 | 1,877 | 1,840 | 2,602 |

NJ | 5,584 | 5,800 | 6,285 | 1,877 | 1,840 | 2,710 |

VA | 4,855 | 4,833 | 6,034 | 1,877 | 1,840 | 2,602 |

IN | 4,855 | 5,123 | 5,481 | 1,877 | 1,950 | 2,363 |

NY | 6,011 | 6,231 | 6,489 | 2,297 | 2,365 | 2,818 |

MA | 5,584 | 5,558 | 5,782 | 2,158 | 2,116 | 2,493 |

IL | 5,087 | 5,075 | 5,279 | 1,971 | 1,932 | 2,276 |

WI | 5,535 | 5,510 | 5,732 | 2,139 | 2,097 | 2,472 |

Note: Earnings and EITC amounts are in 2009 dollars.

Descriptive statistics

No CPS | CPS | ||
---|---|---|---|

Maltreatment measures (top quartile): | |||

Abuse | 0.327 | 0.485 | |

Neglect | 0.348 | 0.468 | |

Income and potential EITC benefit (in thousands): | |||

Income | 20.812 | 19.142 | |

Potential EITC benefit (instrument) | 1.984 | 1.930 | |

Time constant covariates: | |||

White | 0.102 | 0.159 | |

Black | 0.647 | 0.595 | |

Hispanic | 0.224 | 0.223 | |

Other race | 0.016 | 0.020 | |

Less than HS education | 0.450 | 0.429 | |

HS education | 0.354 | 0.352 | |

More than HS education | 0.195 | 0.216 | |

Number of children in the home at child age 3 | 2.374 | 2.910 | |

South | 0.159 | 0.219 | |

Midwest | 0.324 | 0.339 | |

Northeast | 0.431 | 0.402 | |

West (California) | 0.085 | 0.040 | |

Time varying covariates: | |||

Married | .073 | .059 | |

Cohabiting | .332 | .306 | |

Single | .595 | .635 | |

Age of youngest child | 2.275 | 2.369 | |

Number of adults in the home | 1.840 | 1.747 | |

Number of children in the home | 2.612 | 3.216 | |

Mother’s age | 29.607 | 29.870 | |

No income | 0.015 | 0.010 | |

Average of lagged and current income | 19.091 | 16.852 | |

Unemployment rate | 0.121 | 0.120 | |

Public assistance rate | 0.091 | 0.091 | |

Wave 3 | 0.339 | 0.143 | |

Wave 4 | 0.323 | 0.508 | |

Wave 5 | 0.338 | 0.349 | |

Percent of full sample | 92.55 | 7.45 | |

Observations | 3,739 | 301 |

Note: 4,040 family-wave observations of 1,750 families. Proportion or mean (and standard deviation) presented.

p<.10,

p<.05,

p<.01,

p<.001.

First-stage IV results

Model 3: | Model 4: | Model 5: | |
---|---|---|---|

Simulated EITC benefit | 1.023 | 1.030 | .936 |

(.082) | (.083) | (.125) | |

Kleibergen-Paap weak identification test ( | 222.69 | 215.78 | 141.04 |

Note: 4,040 family-wave observations of 1,750 families. Standard errors in parentheses. Standard errors for the LP estimates are clustered by family. Robust standard errors are used for the fixed effects estimates. Model 3 includes all time constant and time varying covariates as well as the average of lagged and current income, Model 4 replaces region fixed-effects with state fixed effects, and Model 5 includes family-specific fixed effects. For these models, the values of the Kleibergen-Paap weak identification test all exceed the critical value of 16.38 (corresponding to a 10% maximum relative bias;

p<.10

p<.05

p<.01

p<.001

Second-stage IV results

Abuse | Neglect | CPS Investigation | |
---|---|---|---|

Percent | 33.91 | 35.72 | 7.45 |

Model 3: All controls | −.0054 | −.0049 | −.0045 |

Model 4: Add state fixed effects | −.0037 | −.0050 | −.0045 |

Model 5: With family fixed effects | .0053 | −.0000 | −.0027 |

Note: 4,040 family-wave observations of 1,750 families. Standard errors in parentheses. Standard errors for the LP estimates are clustered by family. Robust standard errors are used for the fixed effects estimates. Model 3 includes all time constant and time varying covariates as well as the average of lagged and current income, Model 4 replaces region fixed-effects with state fixed effects, and Model 5 includes family-specific fixed effects.

p<.10

p<.05

p<.01

p<.001

IV results for single-mother families and families with two or more children at age 3 (baseline)

Abuse | Neglect | CPS Investigation | |
---|---|---|---|

Percent | 35.34 | 37.97 | 7.59 |

Model 3: All controls | −.0069 | −.0122 | −.0058 |

F-statistic (first stage) | 194.72 | 194.72 | 194.72 |

Model 4: Add state fixed effects | −.0048 | −.0124 | −.0058 |

F-statistic (first stage) | 186.07 | 186.07 | 186.07 |

Model 5: With family fixed effects | .0050 | −.0103 | −.0070 |

F-statistic (first stage) | 138.65 | 138.65 | 138.65 |

Percent | 34.25 | 35.94 | 8.63 |

Model 3: All controls | −.0087 | −.0065 | −.0063 |

F-statistic (first stage) | 120.14 | 120.14 | 120.14 |

Model 4: Add state fixed effects | −.0075 | −.0073 | −.0062 |

F-statistic (first stage) | 144.10 | 144.10 | 144.10 |

Model 5: With family fixed effects | .0032 | −.0007 | −.0037 |

F-statistic (first stage) | 69.40 | 69.40 | 69.40 |

Note: Standard errors in parentheses. Standard errors for the LP estimates are clustered by family. Robust standard errors are used for the fixed effects estimates. Model 3 includes all time constant and time varying covariates as well as the average of lagged and current income, Model 4 replaces region fixed-effects with state fixed effects, and Model 5 includes family-specific fixed effects. The first stage F statistics are from the Kleibergen-Paap weak identification test for instrumental variables. All IV models families meet the critical value of 16.38 (corresponding to a 10% maximum relative bias;

p<.10

p<.05

p<.01

p<.001

OLS, fixed-effects, reduced form, and control function regression results

Abuse | Neglect | CPS Investigation | |
---|---|---|---|

Percent | 33.91 | 35.72 | 7.45 |

Model 1: income only | −.0003 | −.0035 | −.0007 |

Model 2: Add covariates | .0003 | −.0034 | −.0008 |

Model 3: Add lagged income | .0001 | −.0031 | −.0001 |

Model 4: Add state fixed effects | .0001 | −.0031 | −.0002 |

Model 5: All controls | −.0006 | −.0015 | −.0003 |

Model 3: All controls | −.0016 | −.0081 | −.0020 |

Model 4: Add state fixed effects | −.0008 | −.0081 | −.0021 |

Model 5: With family fixed effects | .0030 | −.0015 | −.0014 |

Model 3: All controls | −.0012 | −.0058 | −.0014 |

Model 4: Add state fixed effects | −.0006 | −.0060 | −.0016 |

Model 5: With family fixed effects | .0025 | −.0012 | −.0012 |

Note: 4,040 family-wave observations of 1,750 families. Standard errors in parentheses. Standard errors for the LP estimates are clustered by family. Robust standard errors are used for the fixed effects estimates. Model 1 contains no covariates, Model 2 controls for all time constant and time varying covariates, Model 3 adds the average of lagged and current income, Model 4 replaces region fixed-effects with state fixed effects, and Model 5 includes family-specific fixed effects.

p<.10

p<.05

p<.01

p<.001