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# August, 2014

## RACE ON POLICING: Conclusions

The coefficients obtained are again substantively large. Carrying out the same thought experiment as the preceding section (reallocating police from random assignment to maximizing own-race policing holding the number and composition of the police force constant), property crime is predicted to decline by 22.5 percent and violent crime is essentially unchanged (up by 0.2 percent). As noted earlier, this is likely to be an upper bound on the actual gains that could be realized from reallocating police by race more.

Table 5 presents a sensitivity analysis of the results for crime rates using the same set of alternative specifications employed in Table 3. The coefficients reported in Table 5 are differences between own-race and cross-race policing (e.g. in column 1, the value reported is white police on white crime minus non-white police on white crime). A negative coefficient implies that own-race police are more effective in reducing crime. For property crime, 18 of the 20 coefficients are negative and 8 of these are statistically significant at the .05 level. For violent crime, the results continue to be mixed, with own-race policing generally appearing beneficial with whites but not with non-whites.

## RACE ON POLICING: Estimating the Relationship 2

In interpreting Table 4, it is important to bear in mind the caveat that a direct measure of crime by race is not available. Identification of the model is based on the assumption that in cities with large minority populations, a greater fraction of a minority police officer’s dealings with criminals will be with minorities, and similarly for white officers in cities with a larger white population share. By using interaction terms, it is possible to separately identify the differential impact that police of each race have on crime committed by race.

If 62 is more negative than 0j, then this suggests that an additional non-white officer is associated with a greater reduction in white crime than an additional white officer. As an informal check on the validity of this indirect approach, we also report estimates using arrest rates as the dependent variable. For arrests, we do have breakdowns by race. Thus, we can compare the results of the indirect approach to those from the direct estimation in the preceding section. To the extent that similar results are obtained, our confidence in the indirect approach increases.

## RACE ON POLICING: Estimating the Relationship

Under the assumption that the composition of the fire department captures important omitted factors of a city’s situation, these variables should be included as controls, not used as instruments. The final row of the table adds the firefighter variables as regressors. The coefficients are similar to those from the baseline specification, suggesting that firefighter composition is not capturing important omitted factors so.

Summarizing Table 3, over four-fifths of the coefficients presented are negative. All 37 of the coefficients that are statistically significant at the .05 level carry a negative sign. The only column for which a statistically significant negative sign is never obtained is for non-white drug arrests.

## RACE ON POLICING: Results of Estimation 4

Table 3 presents a range of alternative specifications as a means of gauging the sensitivity of our estimates. The columns of Table 3 match those of Table 2. Each row represents a different specification. Only the differences in the own-race and cross-race arrest coefficients are reported (i.e. for odd columns the coefficient on white police minus the coefficient on black police, and for even columns the reverse). A negative value in Table 3 means that arrests are lower with own-race policing than with cross-race policing. The 72 entries in Table 3 (9 rows by 8 columns) represent coefficients from 72 different regressions. Coefficients that are statistically significant at the .05 level are highlighted in boldface.

## RACE ON POLICING: Results of Estimation 3

This variable would not be expected to directly affect white arrests and with one exception is not statistically significant in the odd columns. City population is negatively related to arrest rates across all eight specifications. This result is consistent with both Glaeser and Sacerdote (1997) which documents lower probabilities of arrest in big cities, and Cullen and Levitt (1998) which finds that rising crime rates are associated with urban flight. All else equal, therefore, cities with rising populations tend to have falling crime rates itat on.

Arrest rates are generally lower when a Black mayor holds office and, somewhat surprisingly, when unemployment rates are high. Income per capita appears to be positively related to drug arrests, but is not statistically significantly related to any of the other categories. State age shares do not carry a consistent sign (the omitted category is the percent of the population over age 45). This is not particularly surprising given the limited variation in these measures that remains once city and year effects have been removed.

## RACE ON POLICING: Results of Estimation 2

Comparing the coefficients in the top two rows of the first column, the addition of white police is associated with a statistically insignificant 0.13 increase in the number of white total arrests per capita, whereas additional non-white officers are associated with a statistically significant increase of 18.5 arrests of white suspects. Our primary interest is in the difference between these two coefficients, rather than the levels themselves. Therefore, the bottom row of the table reports the p-value from a t-test of the null hypothesis that the impact of white and non-white officers is the same. This hypothesis of equality is rejected.

The pattern of coefficients in the second column, corresponding to total arrests of nonwhites, is the reverse of that in the first column. Non-white arrests are positively related to the addition of more white officers, but appear to decline with the addition of non-white officers.

## RACE ON POLICING: Results of Estimation

The set of covariates included in the regressions is constrained by the lack of data available on an annual basis at the city level. While some variables, such as city population and the presence of a black mayor, are available annually for cities, in other cases compromises must be made. We attempt to deal with these data limitations in three ways. First, where annual data for larger geographic areas exist, we use the most disaggregated data series available. Thus, SMSA-level unemployment rates, state per capita income, and state measures of the age distribution are included as regressors. Second, where city-level measures are critical, as with the percent black, we linearly interpolate between decennial censuses.

Finally, as a substitute for effective covariates, we include year dummies, city-fixed effects, and, in some specifications, region-year interactions using the nine U. S. census regions. These variables absorb much of the variation in the data, particularly for demographic and socio-economic factors which tend to change slowly over time. For instance, year and city dummies alone eliminate over 95 percent of the variation in the demographic variables and over 90 percent of the variation in per capita income. To the extent that other (unmeasured) demographic and socio-economic factors exhibit a similar pattern, the use of these indicator variables will reduce any omitted-variable bias from this source.

## RACE ON POLICING: Data Sources and Estimation Approach

The data set used in this paper is a panel of data containing the 134 U.S. cities with population greater than 100,000 as of the year 1975. Panel data, with city-fixed effects and time dummies included as controls, are less likely to be adversely affected by unobserved heterogeneity than would cross-sectional data from cities in a given year. The limiting factor on our sample is data on the racial composition of municipal police forces, taken from the EEO-4 survey of governments conducted annually by EEOC since 1973. Working in concert with the technical staff of EEOC, we have obtained access to data for the years 1977, 1981, 1984, 1986, 1989, and 1993. For each department of the local government, the racial and gender composition of the work staff is reported by functional category (e.g. protective services, officials and administrators, administrative support, professionals).

Although greater detail on race is available in the data, we limit our analysis in this paper to the broad classifications of white and non-white. The primary motivation for doing so is concern over lack of comparability of the definition of Hispanic across data sources. In some specifications, cities with Hispanic populations greater than ten percent using the Census definition are eliminated as a check on the sensitivity of the results read more.

## RACE ON POLICING: A Stylized Model 3

Having laid out the elements of the model, it is now possible to examine the impact of changes in the number of officers on the measures of interest, and in particular, focus on the differential impacts of white and non-white police. Because the number of arrests is the crime measure for which the best data are available by race, we focus the analysis on equation 5. Taking the partial derivative of equation 5 with respect to both non-white and white police yields

increase in the number of non-white officers compared to white officers. Four factors help to determine this relationship, corresponding to the four terms in equation 6. The first term reflects the fact that reductions in crime, ceteris paribus, will lead to fewer arrests. Thus, if police of one race are more effective in deterring crime by criminals of race i, then adding police of that race may result in fewer arrests. The second term captures changes in reporting behavior of victims; if more crimes are reported when there are more minority police, then the presence of minority police will be associated with more arrests. The third and fourth terms represent the direct changes in arrests due to differential true arrest and false arrests per crime across officers of different races. In the empirical section that follows, variants on equation 6 will be estimated.