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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.

If race-specific estimates of criminal activity were available, one would also want to directly estimate the relationship between crime by race and the racial composition of the police force.

Unfortunately, data on the race of the offender is only available when a crime is solved by arrest. Often the victim does not observe the race of the criminal in crimes such as auto theft or burglary. For those crimes where a victim does identify the race of the suspect, this information is not systematically collected and reported in the available data sets.

There is, however, an indirect means of estimating a race-specific crime impact if one is willing to impose assumptions about the way white and non-white officers are assigned to patrol beats (which in turn dictates the distribution of arrest opportunities). Our baseline assumption is that white and non-white officers are randomly assigned to neighborhoods.11 If this is the case, then white and non-white officers would each expect to face the same distribution of arrest opportunities. Denote the efficiency with which crimes committed by criminals of race i are reduced with each additional officer of race j as Д,, Allowing crime rates to may systematically differ across race by a proportion y, and assuming у is constant over time for a given city, the total impact of police on crime can be modeled as follows:

where Crime is total crime in the city and year, White is the fraction of the population that is white, and the subscripts w and n correspond to white and non-white respectively. All other variables are as defined above. Adding in the appropriate control variables and an error term, equation 8 can be estimated with a city-level panel using only aggregate crime data, but will provide separate estimates of the relative impact of white and minority police on white crime (Pww and Pw„) and on minority crime ((3nw and (3nn). payday loans no credit check