In Chapter 4 we derived two measures of the index of racial segregation in subsidized low-income housing, Ixpha(assign) and Ixpha(admit), and argued that the two estimates jointly capture the racial composition of individual housing projects and the allocation of units among racial groups. The first index, Ixpha(assign), measures the assignment by racial group of households on the waiting list to available units. The second index, Ixpha(admit), measures the access by racial group of households in need of housing assistance to the PHA's facilities. The first index was calculated by averaging the deviation (DIFFxj(assign)) of the observed proportion of tenants from racial group X in individual projects from the expected proportion derived from the PHA's waiting list. The second index was calculated by averaging the difference (DIFFxj(admit)) between the observed share of racial group X among all tenant households and the expected share derived from the underlying demand for housing assistance (see Chapter 4 and the discussion there).
In estimating Ixpha(assign) and Ixpha(admit) simplifying assumptions were made which could result in lower or higher calculated values of segregation. Indeed, the estimate I'xpha(admit), for example, assumes that the need for low-income housing in a PHA is proportional to the racial composition of the general population. However, as other studies have shown, the racial composition of the PHA's population is not always the best predictor of the racial composi