GEOGRAPHIC AREAS USED IN THE ANALYSIS
The analysis was done separately for metropolitan and nonmetropolitan areas. BLS reported at least some data for 400 metropolitan statistical areas (MSAs), but data on wages or RSEs for at least one of the three selected occupations were missing for 21 areas, leaving data for 379 MSAs in the analysis. BLS reported data for 172 nonmetropolitan areas, but data on wages or RSEs for at least one of the selected occupations were missing for four areas, leaving data for 168 nonmetropolitan areas in the analysis. Each nonmetropolitan area was contained within a single state, but many states contained more than one nonmetropolitan area (for example, northeast Alabama nonmetropolitan area, northwest Alabama nonmetropolitan area, southeast Alabama nonmetropolitan area, and southwest Alabama nonmetropolitan area). RTI analyzed data for these nonmetropolitan areas individually and did not aggregate them into a single statewide nonmetropolitan area. RTI’s analysis likely overstates the RSEs of single statewide nonmetropolitan areas.
CALCULATION OF RSE FOR EACH AREA
The RSE for each area was calculated according to the following derivation:
Let a1, a2, and a3 be the weights of the components in the index, where component 1 is registered nurses; component 2 is nursing aides; and component 3 is administrative support occupations.
The weights are as follows:
a1 = 0.56, a2 = 0.15, and a3 = 0.29.
Let y1, y2, y3 = estimated mean wages for the components (in a certain area).
The index value (Y; weighted average wage) is defined as Y = (a1· y1 + a2 · y2 + a3 · y3).
Let s1, s2, s3 = standard errors (SEs) for y1, y2, and y3 respectively. The SEs (s) were calculated from the BLS-reported RSEs as s1 = (RSE1 · y1), s2 = (RSE2 · y2), and s3 = (RSE3 · y3).
Let c be the sampling correlation between pairs of y variables, which is unknown. For this simulation, it was assumed that c is equal to 0.5 (extremes values are 0 and 1).
Now, the squared SE of Y, denoted V, can be calculated for each area, using the national employment weights a1, a2, and a3; the assumed sampling correlation c; and the BLS-reported SEs s1, s2, and s3.
Then, the RSE for each area is calculated as .