Human capital in the inner city

Abstract

Twenty-six percent of black males in the USA report seeing someone shot at before turning 12. This paper investigates how black young males alter their behavior when living in violent neighborhoods, using the nationally representative National Longitudinal Survey of Youth 1997 to quantitatively characterize the “code of the street” from the sociology literature. Black and white young males are equally likely to engage in violent behavior, conditional on reported exposure to violence. Education and labor market outcomes are worse when reporting exposure, unconditionally and controlling for observables. Mediators documented in the ethnography are quantitatively important in the estimated structural model.

Appendices

Appendix 1: Derivation of the likelihood function

Denote the standard normal CDF and pdf, respectively, by $\Phi$ and $\phi$. To construct the likelihood function of the dynamic selection model, begin by considering the conditional likelihood. Conditional on type, we can express

$$\begin{aligned} Pr(\overline{D}_i=1 | \tau _i = \tau )&= \,\Phi \left( \beta X_i + \xi ^D_{\tau } \right) . \end{aligned}$$

We can also write the probability of graduation at age 23, $Pr(G_i | \tau _i = \tau )$, as

$$\begin{aligned} Pr\left( G_i =1 | \tau _i = \tau \right) =&\Phi \Big ( \beta ^G X_i + \gamma ^G_{v,1} K_v(18) + \gamma ^G_{v,2} K^2_v(18) + \gamma ^G_{nv,1} K_{nv}(18) \nonumber \\&+ \gamma ^G_{nv,2} K^2_{nv}(18) + \overline{\gamma }^G \, \overline{D_i} \, \mathbf {1} \{ a > 18 \} + \xi ^{G}_i \Big ). \end{aligned}$$

Hours worked contribute either

$$\begin{aligned} Pr(W_i = 0 | \tau _i = \tau ) =\,&1-\Phi \Big ( \big [\beta ^W X_i + \gamma ^W_{v,1} K_v(18) + \gamma ^W_{v,2} K^2_v(18) + \gamma ^W_{nv,1} K_{nv}(18)\\ \nonumber&+ \gamma ^W_{nv,2} K^2_{nv}(18)+ \overline{\gamma }^W \, \overline{D_i} \, \mathbf {1} \{ a> 18 \} + \gamma ^W \, G_i + \xi ^{W}_i \big ]/\sigma _W \Big ), \text {or} \\ Pr(W_i = w | \tau _i = \tau ) =\,&\frac{1}{\sigma _W} \phi \Big ( \big \{w - \big [\beta ^W X_i + \gamma ^W_{v,1} K_v(a) + \gamma ^W_{v,2} K^2_v(a) + \gamma ^W_{nv,1} K_{nv}(a) \\ \nonumber&+\gamma ^W_{nv,2} K^2_{nv}(a) + \overline{\gamma }^W \, \overline{D_i} \, \mathbf {1} \{ a > 18 \} + \gamma ^W \, G_i + \xi ^{W}_i \big ] \big \}/\sigma _W \Big ), \end{aligned}$$

so that the contribution to the likelihood of age 23 weekly hours worked is

$$\begin{aligned} Pr(W_i | \tau _i = \tau ) = \mathbf {1}\{W_i = 0\} Pr(W_i = 0 | \tau _i = \tau ) + \mathbf {1}\{W_i > 0\} Pr(W_i = w | \tau _i = \tau ). \end{aligned}$$

Define $\mathbf {S}_{i}(a)=(S_{v, i}(a), S_{nv, i}(a))$, $\mathbf {K}_{i}(a)=(K_{v, i}(a), K_{nv, i}(a))$, and

$$\begin{aligned} \mu ^{v}(X_i, \mathbf {K}_i(a), \tau _i = \tau , a) =\,&\beta ^{v} X_i + \gamma ^{v}_{v} K_v(a) + \gamma ^{v}_{v,2} K_v^2(a) + \gamma ^{v}_{nv,1} K_{nv}(a)\\ \nonumber&+ \gamma ^{v}_{nv,2} K^2_{nv}(a) + \overline{\gamma }^{v} \, \overline{D_i} \, \mathbf {1} \{ a> 18 \} + \xi ^{S_{v}}_i + \lambda ^{v}(a) \\ \mu ^{nv}(X_i, \mathbf {K}_i(a), \tau _i = \tau , a) =\,&\beta ^{nv} X_i + \gamma ^{nv}_{v} K_v(a) + \gamma ^{nv}_{v,2} K_v^2(a) + \gamma ^{nv}_{nv,1} K_{nv}(a) \\ \nonumber&+ \gamma ^{nv}_{nv,2} K^2_{nv}(a) + \overline{\gamma }^{nv} \, \overline{D_i} \, \mathbf {1} \{ a > 18 \} + \xi ^{S_{nv}}_i + \lambda ^{nv}(a). \end{aligned}$$

Then where $\Phi _2(x ; m, \Sigma )$ is the cumulative distribution function of a bivariate normal distribution at x with mean m and covariance matrix $\Sigma$,³⁰

$$\begin{aligned} Pr(\mathbf {S}_{i}(a) =(1,1) | \tau _i = \tau )&=\, \Phi _2 \left( \left[ \begin{array}{c} \mu ^{v}(X_i, \mathbf {K}_i(a), \tau _i = \tau , a) \\ \mu ^{nv}(X_i, \mathbf {K}_i(a), \tau _i = \tau , a) \\ \end{array} \right] ; \left[ \begin{array}{c} 0\\ 0 \\ \end{array} \right] , \left[ \begin{array}{cc} 1 &{} \rho ^{S} \\ \rho ^{S} &{} 1 \\ \end{array} \right] \right) \\ Pr(\mathbf {S}_{i}(a) =(0,1) | \tau _i = \tau )&= \Phi _2 \left( \left[ \begin{array}{c} -\mu ^{v}(X_i, \mathbf {K}_i(a), \tau _i = \tau , a) \\ \mu ^{nv}(X_i, \mathbf {K}_i(a), \tau _i = \tau , a) \\ \end{array} \right] ; \left[ \begin{array}{c} 0\\ 0 \\ \end{array} \right] , \left[ \begin{array}{cc} 1 &{} -\rho ^{S} \\ -\rho ^{S} &{} 1 \\ \end{array} \right] \right) \\ Pr(\mathbf {S}_{i}(a) =(1,0) | \tau _i = \tau )&= \Phi _2 \left( \left[ \begin{array}{c} \mu ^{v}(X_i, \mathbf {K}_i(a), \tau _i = \tau , a) \\ -\mu ^{nv}(X_i, \mathbf {K}_i(a), \tau _i = \tau , a) \\ \end{array} \right] ; \left[ \begin{array}{c} 0\\ 0 \\ \end{array} \right] , \left[ \begin{array}{cc} 1 &{} -\rho ^{S} \\ -\rho ^{S} &{} 1 \\ \end{array} \right] \right) \\ Pr(\mathbf {S}_{i}(a) =(0,0) | \tau _i = \tau )&= \Phi _2 \left( \left[ \begin{array}{c} -\mu ^{v}(X_i, \mathbf {K}_i(a), \tau _i = \tau , a) \\ -\mu ^{nv}(X_i, \mathbf {K}_i(a), \tau _i = \tau , a) \\ \end{array} \right] ; \left[ \begin{array}{c} 0\\ 0 \\ \end{array} \right] , \left[ \begin{array}{cc} 1 &{} \rho ^{S} \\ \rho ^{S} &{} 1 \\ \end{array} \right] \right) . \end{aligned}$$

Note that the estimated model constrains time trends in street behavior to cross at a particular age, so that:

$$\begin{aligned} \lambda ^{v}_{4}&= \frac{\lambda ^{v}_{1} - \lambda ^{v}_{3}}{16} + \lambda ^{v}_{2} \\ \lambda ^{nv}_{4}&= \frac{\lambda ^{nv}_{1} - \lambda ^{nv}_{3}}{14} + \lambda ^{nv}_{2}. \end{aligned}$$

Writing an individual’s outcome as $\mathcal {O}_i = (D_i, \mathbf {S}_{i}(12), \dots , \mathbf {S}_{i}(23), G_i, W_i)$ and defining $\pi _{\tau } \equiv Pr(\tau _i = \tau )$, we can write

$$\begin{aligned}&Pr(\mathcal {O}_i | \tau _i=\tau ) = Pr(D_i | \tau _i = \tau ) Pr(\mathbf {S}_{i}(12) | \tau _i = \tau ) \cdots \\&Pr(\mathbf {S}_{i}(23) | \tau _i = \tau ) Pr(G_i | \tau _i = \tau ) Pr(W_i | \tau _i = \tau ), \end{aligned}$$

and

$$\begin{aligned} Pr(\mathcal {O}_i) = Pr(\mathcal {O}_i | \tau _i=1) \pi _1 + \cdots + Pr(\mathcal {O}_i | \tau _i=T) \pi _T. \end{aligned}$$

The estimated model conditions type probabilities on initial exposure to violence ($Pr(\tau | \underline{D}=0)$ and $Pr(\tau | \underline{D}=1)$). The log-likelihood function is $\mathcal {LL} = \sum _i ln\left( Pr(\mathcal {O}_i) \right) .$

Appendix 2: Measuring exposure to violence and ecometrics

The self-reported data on exposure to violence used in the analysis are consistent with related administrative data, such as the Centers for Disease Control and Prevention (CDC)/National Center for Health Statistics (NCHS) individual-level measures of homicide death rates displayed in the text. County-level administrative crime data from the Federal Bureau of Investigation’s Uniform Crime Reporting (UCR) Program also relate large racial gaps in exposure to violence. At age 16 the average homicide rate per 100,000 residents in NLSY97 black males’ county of residence was 11.2, again more than twice the average for NLSY97 white males, 5.2. On average, black males lived in counties at age 16 with 193 additional assaults per 100,000 residents compared to their white counterparts (517 vs 324).

Prominent researchers in the neighborhood effects literature have proposed directing attention to “ecometrics” or using tools from the psychometric literature to improve the quality of neighborhood-level measures (Sampson 2012, p. 60). Relatedly, an important topic that has received little analysis in the empirical neighborhood effects literature is the appropriate definition of neighborhood (Durlauf 2004). In this Appendix, I provide preliminary ecometric evidence on the importance of the definition of “neighborhood” in measuring exposure to violence, which is broadly consistent with the results in Damm and Dustmann (2014) that different measures can provide very different information.

We might define neighborhoods as counties: This is the finest geographic partition available for the NLSY97, and there is ample variation in homicide or violent assault rates across counties even in the same metro area. If we were to define neighborhoods in this way, we would interpret the empirical evidence as falsifying Anderson’s theory applying to an empirically large share of black young males, as there is no correlation between this measure of exposure to violence and street behavior. In contrast, if we measure exposure to violence using the self-reported variable in the NLSY97 asking whether respondents have seen someone shot, we find the strong correlations displayed in the text.

1.1 UCR county-level measures of exposure to violence

An alternative measure of exposure to violence to the one used in the analysis in the paper would be constructed using homicide and assault rates in combination with data on county of residence from the NLSY97 Geocode File. I construct such a variable using crime data that come from the Federal Bureau of Investigation’s Uniform Crime Reporting (UCR) Program by way of the National Archive of Criminal Justice Data (NACJD), a project of the Inter-university Consortium for Political and Social Research (ICPSR).³¹

I use the county-level detailed arrest and offense files for the years 1997 until 2007, such as US DoJ (1997), to create county-level homicide and assault rates. These variables are considered missing if they have been imputed based on less than 6 months of data for the year. The homicide (assault) rate is calculated as the number of homicides (assaults) reported in a county divided by the county population of agencies reporting crimes. Following convention, this rate is then multiplied by 100,000 to be expressed as the annual homicide (assault) rate per 100,000 individuals. Using the Federal Information Processing Standards (FIPS) state and county codes in which NLSY97 respondents report residing, these county-level homicide and assault rates are then assigned to individuals for the period beginning in the previous year.

1.2 Descriptive statistics

Surprisingly, street behaviors appear independent of the violence in a respondent’s county of residence, regardless of whether it is measured by the homicide or assault rate. Figure 13a, c shows rates of street behavior after dividing black males in the NLSY97 into county homicide rate quartiles, and Fig. 13b, d does the same by assault rate quartiles. We can see that respondents are no more likely to engage in street behaviors when residing in more violent counties than when living in less violent counties. Street behaviors of white males follow similar patterns that are also uncorrelated with violence in a respondent’s county of residence.

Fig. 13

Street behavior of black males by violence in county of residence. a By county homicide rate quartile. b By county assault rate quartile. c By county homicide rate quartile. d By county assault rate quartile

One fact making these data especially surprising is that there is substantial variation in homicide rates between counties, even within the same metropolitan statistical areas (MSAs). Figure 14 shows such variation between 1997 and 2007 between counties in the same MSA. For example, the homicide rate in St. Charles, Missouri, was 1.15 per 100,000 in 2007, compared with 39.92 in St. Louis City. The homicide rate in Montgomery County, Maryland, was 2.80 per 100,000 in 1997, compared with 56.90 in the District of Columbia. Even among less extreme examples, there is considerable variation in homicide rates between counties.

There is also significant variation in the homicide rate between the counties of residence of African-American males in the NLSY97. Figure 15a shows that while the homicide rate of counties in which NLSY97 males lived decreased between 1997 and 2007, it is clear that African-American males still lived in much more violent counties in 2007 than white males did in 1997. The 75th percentile county-level homicide rate for white males was 8.5 in 1997 and 7.5 in 2007. For black males in the NLSY97, the 75th percentiles for 1997 and 2007 were, respectively, 15.5 and 14.3. Figure 15b shows similar patterns when we look by age of respondents in the NLSY97.

Fig. 14

Homicide rates in select MSAs (by county). a Washington, DC. b New Orleans, LA. c Cleveland, OH. d Detroit, MI. e Philadelphia, PA. f St. Louis, MO. g Atlanta, GA. h Kansas City, MO/KS. i Indianapolis, IN. j Columbus, OH. k San Francisco, CA. l Newark, NJ

Fig. 15

Homicide rates in NLSY97 males’ county of residence. a Males in the NLSY97 by year. b Males in the NLSY97 by age

Fig. 16

Distribution of homicide rate by census tract in Cleveland City, Ohio

1.3 Interpretation and ecometrics

If we believed that county-level crime variables accurately measure the neighborhood violence to which individuals were exposed, these data would be interpreted as empirical evidence falsifying Anderson’s theory applying to an empirically large share of black young males. This highlights the importance of ecometrics, because another explanation for the surprising results in Fig. 13 is that county-level homicide or assault rates do not accurately measure the violence to which youth are exposed. This analysis adopts the second interpretation, using two key justifications.

First, consider the following evidence from Cleveland, Ohio, on the variation in homicide rates between census tracts within the same county. Figure 16 shows data from the Northeast Ohio Community and Neighborhood Data for Organizing (NEO CANDO) illustrating that homicide rates exhibit tremendous variation between census tracts in Cleveland City, only one municipality of the 58 located within Cuyahoga County, Ohio. In 1990 the 90th percentile homicide rate per 100,000 residents for census tracts in Cleveland City was 116, and in 2000 it was 43. Since county of residence is the finest geographic partition available for the NLSY97 data, this evidence from the NEO CANDO data set suggests this partition could be too coarse to accurately measure the violence to which youth are exposed in their neighborhoods.

Second, the individual-level measures of exposure to violence self-reported in the NSLY97 exhibit patterns consistent with Anderson’s theory. These variables are then used to measure exposure to violence in the analysis, since it is plausible that these variables are more accurate measures and since they are consistent with the qualitative evidence documented by urban ethnographers (Table 12).

Table 12 NLSY97 males’ neighborhood and school characteristics, by race (%)

Appendix 3: The self-administered section of the NLSY97 questionnaire

The Introduction to the self-administered section of the NLSY97 questionnaire is as follows (Taken from page 210 of NLSY97 2000):

“(INTERVIEWER: IT IS NOW TIME TO ADMINISTER THE AUDIO CASI SECTION OF THE INTERVIEW. PLEASE INSERT THE HEADPHONES INTO THE LAPTOP AND THEN READ THIS INTRODUCTION TO THE RESPONDENT:)

This part of the interview is different from the previous parts. In the previous parts I read you the questions and recorded your answers. For this section you will hear the question through the headphones while you read the question on the computer screen. Let me show you how this works. We have several practice questions. The first practice question asks you if you like chocolate ice cream.

(INTERVIEWER: TURN LAPTOP AROUND AND HAND RESPONDENT THE HEADPHONES.)”