Police violence and the health of black infants.

Analysis of 3.9 million birth records reveal spillover effects of police killings on the health of black infants.


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Supplementary Text Table S1. Sample characteristics for black infants. Table S2. Sample characteristics for white infants. Table S3. Sample characteristics for Hispanic infants. Table S4. Results from 36 DD models. Table S5. Results from 36 DD models with sibling fixed-effect. Table S6. Effect of exposure to police killing of unarmed blacks on birth weight of black infants for distances below 1 km. Table S7. Sensitivity analysis for various definitions of trimester. Table S8. Sensitivity analysis for different definitions of exposure to police killings before and after birth. Table S9. Effect of exposure to police killing of unarmed blacks during pregnancy on residential mobility for black mothers. Table S10. 2SLS models for effect of police killings of unarmed blacks during pregnancy within 1 km on birth weight of black infants. Fig. S1. Police killings in California, 2005-2017. Fig. S2. Effect of maternal exposure to police killings of unarmed blacks before, during, and after pregnancy on the gestational age of black infants. Fig. S3. Effect of maternal exposure to police killings within 1.5 km on gestational age in weeks by race/ethnicity of infant and characteristic of police killing. Fig. S4. Effect of maternal exposure to police killings within 1.5 km on low birth weight in weeks by race/ethnicity of infant and characteristic of police killing. Fig. S5. Effect of maternal exposure to police killings within 1.5 km on premature birth by race/ethnicity of infant and characteristic of police killing. Second, paid researchers coded the type of incident in order to restrict the cases to "intentional or purposeful police killing" and "unintentional police killing but result of extremely reckless, reckless or negligent use of force". This coding is based on the following definition of police killings as "any interaction with the police where the officer uses force and the person dies during or immediately after the interaction. This includes cases that result in death as a consequence of being shot, beaten, restrained, pepper sprayed, tasered, or otherwise harmed by police officers, whether on-duty or off-duty. … This includes acts where one or more police officers set in motion a chain of events that leads to the death of a suspect or another individual if the original act involved the use of police force. These cases might capture high speed chases or instances where a police officer kills a bystander when shooting at a suspect. The definition excludes (a) suicides, (b) accidents caused by suspects themselves (e.g. a fleeing suspect who causes a deadly car crash), and (c) police-caused accidents unrelated to the use of force (e.g. a car crash under normal traffic conditions that is not related to the vehicular pursuit of a suspect)." Out of the 3,022 cases in the Fatal Encounters database, 2,025 cases were classified as "Intentional or purposeful" or "Unintentional but result of extremely reckless, reckless or negligent use of force". The remaining cases were excluded from the database.
Excluded cases include duplicates, an incident in which an off-duty police officer shot and killed his wife during a domestic dispute, several cases in which the suspect kills bystanders during a car chase, and several cases in which the deaths are accidental or self-inflicted. The analysis further restricts police killings to 1,891 incidents involving black, Hispanic or white victims.
Third, the coding procedure verified and completed missing information for individual victims on the following variables: victim's race, date and geographic location of the incident. While the Fatal Encounters database is comprehensive and well-maintained, there are occasional errors and cases with missing information. Most important, information on victim race is missing for about 17.4% of all cases in California and considered unreliable for others. To address this problem, this study used two independent coders from Amazon Mechanical Turk to verify and complete the information for all cases. Each coder received the victim's name, date of the incident, and the state in which it occurred. They were asked to collect information on the race of the victim, the involved police agencies, and the city in which the incident occurred from newspaper sources. A student research assistant cross-validated all cases for which the information from Fatal Encounters and our MTurk coders were not identical.
This cross-validation and the comparison between the two independent coders strengthens the quality and accuracy of the data verification process.
As part of this coding and verification process, coders added a variable "armed/unarmed" to the database. The information is based on the best available public information usually from newspaper sources or in some cases video material. In many cases, newspapers rely on police information, which is not always reliable. Despite these problems, newspaper sources are the only available information.
Finally, this study used the Google Geocoding API to convert the address of the incident into geographic coordinates (latitude and longitude).
The result of this procedure is a comprehensive database of all officer-involved killings in California between January 2005 and December 2017. Figure S1 shows the geographic distribution of police killings in California from 2005 to 2017 by race. Police killings are concentrated in urban centers like Los Angeles, San Diego and Fresno but many cases are spread throughout the state across 50 of the 58 counties in California. Most police killings involve black (21%), white (34%) or Hispanic (45%) victims. Over 30% involve unarmed victims.
A potential limitation of the data is that it undercounts police killings in earlier years considering that large parts of the data collection are based on newspaper and online sources. Indeed, the average number of cases per year is 131.6 from 2005 to 2011 compared to 161.7 from 2012 to 2017 -an almost 23% increase. Considering that the Fatal Encounter-based data used in this article are the best available data source on police killings over this period, it is impossible to distinguish real change in police killings from undercount in earlier years. The potential undercount could have opposing implications for the results reported here. On the one hand, an undercount of less severe cases in earlier periods might imply that the reported estimates overestimate the effect of police killings, considering that the police killing data in early years is biased towards cases that receive substantial news coverage. On the other hand, omitted police killings essentially imply measurement error in the treatment variable, which biases the effects towards zero so that the reported estimates might underestimate the true effect. To partly address this concern, I repeat the main analysis for the effect of police killings of unarmed blacks on the birth weight of black infants with additional interaction terms between the treatment indicators and a continuous year variable (not pre-registered). This model examines whether the size of the police killing effect changes over time and therefore addresses some of the concerns about underreporting of police killings in earlier years. The size of the interaction terms for exposure during the first and second trimester is consistently small and statistically insignificant (p-values above 0.46). This finding indicates that the size of the police killings effect does not change over time alleviating some of the concerns about changes in the reporting of police killings over the years.

Post-Treatment Selection Bias
Conditioning on posttreatment variables either by controlling for, or by sub-setting data based on variables measured after the treatment can bias estimates of causal effects (43).
This post-treatment selection bias is a potential concern for the results presented here.
Cases might select out of the treatment group because of residential mobility, or they might select out of live birth through miscarriages, abortions or reduced fertility. If this selection is related to the treatment indicator "exposure to police killings", the results presented here might be biased. For example, a family might decide to move after a local policing killing. Because birth records only include the residential address at birth, this selective mobility leads to measurement error in the treatment indicator. Similarly, stress related to local police killings might induce miscarriages or influence decisions about abortions so that pregnant women who are exposed to the treatment select out of the sample. This section discusses both potential biases in detail, presents supporting evidence, and sensitivity analysis to address the concern. None of the analysis in this section are part of the pre-registered analysis plan.

Residential Mobility
Parents might decide to move after a local policing killing. Because birth records only include the residential address at birth, this selective mobility leads to measurement error in the treatment indicator. Previous research suggests that 12% of subjects move at least once during pregnancy with most moves within the same neighborhood and over short distances (44). However, it remains unclear whether residential mobility during pregnancy is related to local police killings. Two additional analyses address this potential problem. Both analyses use data on siblings to take advantage of at least two observed addresses for the first and second child. The analyses focus on exposure to police killings of unarmed blacks among black mothers as the subgroup most affected by local police killings.
The first analysis examines whether exposure to police killings effects residential mobility. For this purpose, the sample is restricted to siblings and the level of analysis is a sibling pair. The outcome is defined as change in census tract between the first and second child. The treatment indicator is defined as exposure to police killing of unarmed blacks during pregnancy with the second child based on the address from the first birth. The results are presented in table S9. They show the effect of exposure to police killing of unarmed blacks during pregnancy on residential mobility for black infants by distance to the incident (1, 2 and 3km) and for two model specification without the control variables used in the main model and with the same set of control variables. In addition, the models include a variable that measures the age difference between the first and second child in years. The results show no discernable effect of exposure to police killings of unarmed blacks on residential mobility. The effect estimates are small and statistically insignificant with inconsistent signs across model specifications. This finding indicates that local police killings are unrelated to residential mobility during pregnancy alleviating concerns about post-treatment selection bias.
The second sensitivity analysis is based on the sibling model described above and uses an instrumental variable approach to correct for measurement error in the treatment indicator. Focusing on mothers with at least two births in the dataset, the instruments for exposure during the first, second and third trimester (as well as the terms for exposure before and after pregnancy) use the address from the birth record of the firstborn child to measure exposure during all pregnancies. For example, the instrument measures exposure to policing killings during the second pregnancy by determining whether a policing killing occurred in the first, second or third trimester in proximity to the residential address from the first birth record. In many cases, of course, the addresses are the same so that the treatment and instrument are the same as well.
However, the key difference to the treatment indicator is that the instrument assumes that the mother never moved. For older siblings, this instrumental variable is unaffected by any measurement error introduced through residential mobility.
The model includes the same set of control variables and fixed effect terms for mother, census tract and year-month as the main sibling analysis. Results from the first stage regression show that the instruments are highly correlated with the treatment indicator with partial F-statistics well above 10,000 (p < 0.000), which is far higher than the commonly used threshold of 10. Table S10 presents the results from the two-stage least squares (2SLS), instrumental variable regression together with the same results presented in the main text of the article. The findings are remarkably consistent across the sibling model presented in the main text and the 2SLS sibling model. This finding suggests that post-treatment bias related to residential mobility or residential mobility in general is not a concern for the findings presented here.

Selection out of Live Births
The second potential post-treatment selection bias is based on selection out of live births through early terminations of pregnancy (miscarriage and induced abortion) or reduced fertility, which are not recorded in birth records. In 2011, only 67% percent of pregnancies resulted in live births (45). Of the remaining pregnancies, 18% resulted in abortions and 15% ended in miscarriage (3). Stress related to local police killings might increase the likelihood of miscarriages, influence decisions about abortions or reduce fertility. Indeed, previous research indicates that population stressors can reduce fertility and live births particularly for male fetuses (46-48). This sub-setting of the data based on post-treatment events amounts to potential post-treatment selection bias. I explore this possibility by examining changes in the number of births to black mothers following police killings of unarmed blacks in different time periods after the incidents.
For example, a decline in births to black mothers in the 6-9 months after a police killing would indicate an increase in early terminations of pregnancy due to miscarriage or induced abortions. A change in births 10 or more months after an incident, however, would suggest reduced fertility possibly related to stress or intentional decisions about the timing of conception.
To model these changes in births, I use a Difference-in-Difference (DD) approach based on data on the census tract-month level. The dependent variable is the number of births to black mothers in census tract j and month t. Additional analysis focus on the number of male births instead of all births considering that previous research found larger effects of population stressors on male fetuses. The main independent variable is a binary indicator for police killings of an unarmed black person in census tract j and month t together with three 3 lead and 12 lagged terms. The lead terms make it possible to assess the plausibility of the DD approach. The lagged terms allow me to estimate the effect of police killings over different time periods after the incident. The model includes a census tract fixed effect term to adjust for stable differences in the number of births across areas, and a month-year effect that captures differences in births across months that are constant over all areas such as seasonal shifts or changes in economic condition. In addition, the model includes a county-specific linear time trend. The core assumption of this approach is that in the absence of police killings, the change in births in affected areas would have been the same as the change in control areas. An alternative specification focuses on quarters instead of month to increase the count of births (with 2 lead and 4 lagged terms). Tables S1 to S10  Table S6. Effect of exposure to police killing of unarmed blacks on birth weight of black infants for distances below 1 km. Control variables include a linear county-specific trend, child's gender, proximity to any police killing and fixed effect terms for census tract, year-month and mother's id for the sibling model. The number of cases is 246,018 for the Difference-in-Difference model and 196,211 for the sibling model. *P < 0.05, **P < 0.01, ***P < 0.001 Exposed before pregnancy Exposed during pregnancy   Exposed before pregnancy Exposed during pregnancy show the effect of maternal exposure to police killings of unarmed blacks during pregnancy on the birth weight of black infants. The analysis uses 3 instead of 6 months periods for the time periods before and after police killings. Control variables are listed in note to Fig. 1. The number of cases is 246,018 for the Difference-in-Difference (DD) model and 196,211 for the DD model with sibling fixed effects (Sib. Model). *P < 0.05, **P < 0.01, ***P < 0.001 Exposed before pregnancy Exposed during pregnancy  Table S9. Effect of exposure to police killing of unarmed blacks during pregnancy on residential mobility for black mothers. The sample is restricted to siblings and the level of analysis is a sibling pair. The outcome is defined as change in census tract between the first and second child. The treatment indicator is defined as exposure to police killing of unarmed blacks during pregnancy for the second child based on address from the first birth. *P < 0.05, **P < 0.01, ***P < 0.001

Within 1km
Within 2km  Table S10. 2SLS models for effect of police killings of unarmed blacks during pregnancy within 1 km on birth weight of black infants. The model specification is based on the sibling analysis in the main text but instruments the treatment indicators with exposure to police killings based on the residential address from the birth record of the first-born child. Results from the first stage regression show that the instruments are highly correlated with the treatment indicator with partial F-statistics well above 10,000 (p < 0.000). Control are listed in Fig. 1 Observations 196,118 196,118 196,118 196,118 Figures S1 to S6