How Well Have Rural and Small Metropolitan Labor Markets Absorbed Welfare Recipients?. Sensitivity Of Changes In Wages ANd Employment To Alternative Elasticity Assumptions

04/01/2001

The elasticity assumptions were instrumental in determining the size of the demand and supply shifts from the employment and wage data that we collected. Therefore, we used alternative labor demand and labor supply elasticities to test the sensitivity of our results to the elasticity assumptions. In the report, we used a supply elasticity of 0.3 and a demand elasticity of 0.4. We used three sets of alternative elasticity assumptions to conduct the sensitivity analysis. We incremented the assumed elasticities by 0.1, we decremented the assumed elasticities by 0.1, and we used a supply elasticity of zero.

Exhibits D.1 and D.2 present the decomposition of the change in employment into the change due to the demand shift and the change due to the supply shift under the three different elasticity assumptions. Change in employment due to the shift in demand and shift in supply was not sensitive to small changes in the elasticity assumptions where elasticities were incremented or decremented by 0.1, but was sensitive to large changes in the elasticity assumptions. With a supply elasticity of zero, all the change in employment was due to the shift in supply; the shift in demand had no effect on employment. The average percent change in employment attributable to supply increased from 2.1 percent to 5.6 percent in the 1996 to 1998 period. However, we did not believe that a supply elasticity of zero was plausible. Therefore, we felt confident that the employment findings were robust to the elasticity assumptions.

Exhibits D.3 and D.4 present the decomposition of the change in wages into the change due to the demand shift and the change due to the supply shift under the three different elasticity assumptions. We found that the decomposition of the change in wages was more sensitive to the elasticity assumptions than the decomposition of the change in employment. The decomposition depended on the sum of the demand and supply elasticities. A higher sum decreased the percentage change in wages attributable to the shift in demand (or supply). The change in wages became smaller, because the demand and supply curves were more elastic; i.e., they were more responsive to changes in wages. A smaller change in wages was needed to bring about a change in employment. Hence, when we incremented the elasticity assumptions by 0.1, the percentage change in wages attributable to demand decreased from 9 to 7 percent. The reverse was true for a lower sum of the demand and supply elasticities. When we decremented the elasticity assumptions by 0.1, the percentage change in wages attributable to demand increased from 9 to 12 percent. A supply elasticity of zero increased the percentage change in wages attributable to demand to 16 percent; however, as discussed above, we do not believe this elasticity assumption was plausible.

Based on the sensitivity analysis, we concluded that our employment findings were robust to the alternative elasticity assumptions, but our wage findings were not. However, our basic findings are not affected much by reasonable changes in the elasticities as a result of the small size of the increase in employment due to welfare reform relative to the low-skill labor market.

Exhibit D.1
Percent Change in Employment, 1993-1996
Region Overall Demand=0.3
Supply=0.4
Demand=0.4
Supply=0.5
Demand=0.2
Supply=0.3
Demand=0.3
Supply=0
Demand Supply Demand Supply Demand Supply Demand Supply
Decatur and Florence, Alabama 9.2 5.1 4.1 5.0 4.3 5.4 3.8 0.0 9.2
Rural Mississippi 13.5 7.9 5.6 7.7 5.7 8.2 5.2 0.0 13.5
Joplin, Missouri 10.8 7.3 3.5 7.5 3.3 7.3 3.5 0.0 10.8
Southeast Missouri 9.3 5.4 3.9 5.2 4.0 5.6 3.7 0.0 9.3
Jamestown, New York 1.9 0.6 1.3 0.4 1.4 0.8 1.1 0.0 1.9
North Country, New York -0.3 -0.2 0.0 -0.2 0.0 -0.2 -0.1 0.0 -0.3
Medford-Ashland, Oregon 12.8 7.0 5.8 6.7 6.1 7.5 5.3 0.0 12.8
Central Oregon 14.0 7.4 6.7 7.0 7.1 8.0 6.1 0.0 14.0
Florence, South Carolina 8.1 4.6 3.6 4.4 3.7 4.8 3.3 0.0 8.1
Vermont 7.4 3.9 3.5 3.7 3.8 4.2 3.2 0.0 7.4
Eau Claire, Wisconsin 15.5 8.6 6.9 8.3 7.2 9.1 6.4 0.0 15.5
Wausau, Wisconsin 8.6 5.1 3.5 5.0 3.6 5.3 3.3 0.0 8.6
Average 9.2 5.2 4.0 5.1 4.2 5.5 3.7 0.0 9.2
United States 8.7 5.0 3.8 4.8 3.9 5.2 3.5 0.0 8.7
Source: Lewin calculations using ES-202, NISP, OES, and BLS education and training requirements data.
Exhibit D.2
Percent Change in Employment, 1996-1998
Region Overall Demand=0.3
Supply=0.4
Demand=0.4
Supply=0.5
Demand=0.2
Supply=0.3
Demand=0.3
Supply=0
Demand Supply Demand Supply Demand Supply Demand Supply
Decatur and Florence, Alabama 2.5 1.6 0.9 1.6 0.9 1.6 0.9 0.0 2.5
Rural Mississippi 6.8 4.2 2.6 4.2 2.6 4.3 2.5 0.0 6.8
Joplin, Missouri 7.9 4.8 3.2 4.7 3.2 4.9 3.0 0.0 7.9
Southeast Missouri 4.8 2.9 1.9 2.8 1.9 3.0 1.8 0.0 4.8
Jamestown, New York 2.5 1.9 0.6 2.0 0.4 1.8 0.6 0.0 2.5
North Country, New York 4.5 3.0 1.6 3.0 1.5 3.0 1.5 0.0 4.5
Medford-Ashland, Oregon 8.1 5.0 3.1 4.9 3.1 5.1 3.0 0.0 8.1
Central Oregon 7.5 4.6 2.9 4.5 3.0 4.7 2.8 0.0 7.5
Florence, South Carolina 6.4 3.8 2.6 3.7 2.7 3.9 2.5 0.0 6.4
Vermont 5.0 3.3 1.7 3.3 1.6 3.3 1.7 0.0 5.0
Eau Claire, Wisconsin 4.4 3.6 0.8 3.8 0.6 3.4 1.0 0.0 4.4
Wausau, Wisconsin 7.4 4.5 2.8 4.5 2.9 4.7 2.7 0.0 7.4
Average 5.6 3.6 2.1 3.6 2.0 3.6 2.0 0.0 5.6
United States 7.1 4.7 2.4 4.8 2.3 4.7 2.4 0.0 7.1
Source: Lewin calculations using ES-202, NISP, OES, and BLS education and training requirements data.
Exhibit D.3
Percent Change in Wages, 1993-1996
Region Overall Demand=0.3
Supply=0.4
Demand=0.4
Supply=0.5
Demand=0.2
Supply=0.3
Demand=0.3
Supply=0
Demand Supply Demand Supply Demand Supply Demand Supply
Decatur and Florence, Alabama -0.8 12.8 -13.7 9.9 -10.7 18.1 -19.0 22.5 -23.1
Rural Mississippi 1.2 19.7 -18.6 15.5 -14.3 27.4 -26.2 34.5 -33.7
Joplin, Missouri 6.6 18.2 -11.6 14.9 -8.3 24.2 -17.6 31.9 -26.9
Southeast Missouri 0.4 13.4 -13.0 10.5 -10.1 18.7 -18.3 23.5 -23.2
Jamestown, New York -2.7 1.5 -4.2 0.9 -3.6 2.6 -5.4 2.6 -4.7
North Country, New York -0.4 -0.6 0.1 -0.5 0.1 -0.7 0.3 -1.0 0.7
Medford-Ashland, Oregon -1.8 17.5 -19.3 13.4 -15.2 24.8 -26.7 30.6 -32.0
Central Oregon -3.8 18.4 -22.2 13.9 -17.7 26.6 -30.3 32.3 -35.1
Florence, South Carolina -0.5 11.4 -11.9 8.8 -9.3 16.1 -16.5 20.0 -20.3
Vermont -2.0 9.8 -11.8 7.4 -9.4 14.1 -16.1 17.1 -18.6
Eau Claire, Wisconsin -1.5 21.5 -22.9 16.5 -18.0 30.3 -31.8 37.5 -38.6
Wausau, Wisconsin 1.0 12.8 -11.8 10.0 -9.0 17.7 -16.7 22.3 -21.6
Average -0.4 13.0 -13.4 10.1 -10.5 18.3 -18.7 22.8 -23.1
United States -0.1 12.5 -12.5 9.7 -9.8 17.5 -17.5 21.8 -21.9
Source: Lewin calculations using ES-202, NISP, OES, and BLS education and training requirements data.
Exhibit D.4
Percent Change in Wages, 1996-1998
Region Overall Demand=0.3
Supply=0.4
Demand=0.4
Supply=0.5
Demand=0.2
Supply=0.3
Demand=0.3
Supply=0
Demand Supply Demand Supply Demand Supply Demand Supply
Decatur and Florence, Alabama 1.1 4.1 -3.0 3.3 -2.2 5.5 -4.4 7.1 -6.3
Rural Mississippi 1.9 10.6 -8.7 8.5 -6.5 14.4 -12.5 18.5 -17.1
Joplin, Missouri 1.4 11.9 -10.5 9.4 -8.0 16.4 -15.0 20.9 -19.8
Southeast Missouri 0.8 7.2 -6.4 5.7 -4.9 9.9 -9.1 12.5 -11.9
Jamestown, New York 3.0 4.8 -1.8 4.1 -1.1 6.1 -3.2 8.4 -6.2
North Country, New York 2.3 7.5 -5.2 6.1 -3.8 10.0 -7.7 13.0 -11.3
Medford-Ashland, Oregon 2.1 12.4 -10.3 9.9 -7.8 17.0 -14.9 21.8 -20.2
Central Oregon 1.7 11.4 -9.8 9.1 -7.4 15.7 -14.0 20.0 -18.7
Florence, South Carolina 0.6 9.4 -8.7 7.4 -6.7 13.0 -12.4 16.4 -15.9
Vermont 2.5 8.2 -5.7 6.6 -4.1 10.9 -8.4 14.3 -12.4
Eau Claire, Wisconsin 6.2 9.0 -2.8 7.7 -1.5 11.3 -5.1 15.7 -11.1
Wausau, Wisconsin 1.9 11.3 -9.5 9.0 -7.2 15.5 -13.6 19.9 -18.5
Average 2.1 9.0 -6.9 7.2 -5.1 12.1 -10.0 15.7 -14.1
United States 3.8 11.8 -7.9 9.6 -5.7 15.7 -11.9 20.6 -17.7
Source: Lewin calculations using ES-202, NISP, OES, and BLS education and training requirements data.