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An econometric model of stop rates in E&W

Using data provided by the UK government on police stops, discussed earlier, one could compute the stop rate per 1,000 persons for each ethnicity in each Area for each year of the period 2006-07 through 2017-18. Consequently, for each of the 8,000 stop rates recorded, there was an associated ethnicity, Area, and year. These stop rates constituted the dependent variable, У, of the analysis and this took values Ykrt for k = 1, . . . , 16, r = 1, • • ■, 42, t = 1,. . ., 12.

It was hypothesised that Y was a function of three determining variables - ethnicity (E), Area (A), and year (T). The novelty about the econometric equation, estimated by Ordinary Least Squares (OLS), was that the ethnicity and the area variables were allowed to interact so that the estimated equation was as follows:

This meant that the stop rate of a particular ethnicity k (say, Black Caribbean) depended not just on the value of k but also on the value of r (i.e., the area in which ethnic group was located). So, for example, the stop rate associated with Black Caribbeans living under the jurisdiction of the West Midlands police force could be different from that for Black Caribbeans living under the jurisdiction of the Metropolitan police force. Within the context of this “interaction” model, it was then possible to test whether interethnic differences in stop rates were significantly different within areas and whether inter-area differences in stop rates were significantly different within ethnicities.

Following the suggestion in Long and Freese (2014), the results from estimating equation (5.5) as an OLS regression model are presented in the form of the predicted stop rates (PSR) computed from the estimated coefficients. These were computed using the method of “recycled predictions”, as described in Long and Freese (2014, chapter 4) and in the STATA manual.14

Suppose, using the regression estimates, one computes the mean stop rates for each of the 16 ethnic groups as uk,k = l,... ,16. Since the regression line passes through the mean, the ok will be the sample means. The difference between these mean stop rates will not, however, reflect differences in stop rates between the ethnic groups which can be ascribed entirely to differences in ethnicity. This is because the mean stop rates, ak, conflate differences in ethnicities with differences in the spatial distribution of the ethnic groups. The fact that the stop rate for Black Caribbeans, BC, is four times that for British Whites, aBW, may be partly due to ethnic differences but it may, in part, also be due to the fact that, compared to British Whites, a larger proportion of Black Caribbeans live under the jurisdiction of the Metropolitan Area, where the overall stop rate is high. Computing the mean stop rates over the ethnic groups will not neutralise these spatial differences and, hence, differences between the ak cannot be wholly attributable - although, undoubtedly, some part may be - to differences in ethnicity.

The method of “recycled predictions” isolates the effect of ethnicity on the predicted stop rate. In order to compute these rates, hypothetical scenarios are constructed in which it is assumed that all the (nearly 8,000) stops are of persons from ethnic group k, where k successively takes values from 1 to 16 (i.e., runs the gamut of ethnicities); the mean stop rate is then computed for each of these scenarios and denoted uk, k = 1, . . ., 16. Since the values of the area variables are unchanged between these hypothetical scenarios, the only difference between them is the ethnicity of the persons stopped.15 Consequently, the difference between aBC and am, would be entirely due to differences in ethnicity between Black Caribbeans and British Whites since other relevant differences between them would have been neutralised.

In essence, therefore, in evaluating the effect of two characteristics X and У on a particular outcome, the method of “recycled predictions” compares outcomes under two scenarios: first, “all have the characteristic X” scenario and, then, “all have the characteristic Y” scenario, with the values of the other variables unchanged between the scenarios. The difference between the two outcomes is then entirely due to the differences in the attribute represented by X and У. The stop rates computed from these hypothetical scenarios (dk) are, hereafter, referred to as the PSR for the different ethnic groups, and they are to be distinguished from the groups’ sample stop rates (dk).

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