The pull of the economy is modeled as a demand shift an increase in the demand for low-skill labor at any wage level (i.e., an outward shift in the demand curve). The push of welfare reform is modeled as a supply shift an increase in the supply of low-skill labor at any wage level (i.e., an outward shift in the supply curve). Both shifts are positive, i.e., they involve an increase in demand and an increase in supply at every wage.
The shifts can be illustrated on a standard labor demand/labor supply diagram (Exhibit 4.1). LS0 is the labor supply curve before welfare reform, and LS1 is the labor supply curve after welfare reform. LD0 is the labor demand curve before economic expansion, and LD1 is the labor demand curve after economic expansion.
The demand shift from LD0 to LD1 and the movement along LS0 from Point A to Point B represent the pull of the economy. It is important to note that the pull of the economy does not shift the supply curve. Employment increases from E0 to EB. The number of welfare recipients pulled into employment is less than this amount, because some who are pulled into employment by the expansion are not welfare recipients.
Symmetrically, the supply curve shift from LS0 to LS1 and the movement along LD1 from Point B to Point C represents the push of welfare reform. As a result, employment increases from EB to E1. As drawn, the new equilibrium is at a lower wage than the initial equilibrium the upward pressure of economic expansion on wages is more than offset by the downward pressure of welfare reform. Under such a scenario, some individuals who are working in the initial equilibrium will not be willing to work in the new equilibrium, because of the lower wage. These workers are displaced by welfare reform. In the diagram, they are represented by the horizontal distance from EV to E0. The number of new workers is represented by the distance from EV to E1, and is exactly equal to the size of the shift in the supply curve.
It is important to keep in mind that the supply curve represents the supply of workers from two populations adults who are in the group targeted by welfare programs and all other low-skill, working-age adults. Thus, the increased employment due to the pull of the economy that is represented in Exhibit 4.1 exceeds the number of welfare recipients who are drawn into employment by the economic expansion. Similarly, the workers displaced by welfare reform in Exhibit 4.1 might include some who are in the target group for welfare programs, and some of these might even enter welfare as a result.(32)
Points A and C represent initial and final equilibrium outcomes, before and after welfare reform (supply shift) and economic expansion (demand shift). The percentage changes in employment and wages between these two points can be expressed formally by the following equations, which show the effects of the demand and supply shifts on wages and employment.(33)
(i) % D employment = ( es * % D demand + ed * % D supply) / ( ed + es)
(ii) % D wage = (% D demand - % D supply) / ( ed + es)
- ed is the absolute value of the elasticity of demand the absolute value of the percentage change in employment associated with a one percent increase in the wage rate along the demand curve (the value is positive);
- es is the elasticity of supply the percentage change in employment associated with a one percent increase in the wage rate along the supply curve (the value is positive);
- % D wage is the percentage change in the equilibrium wage;
- % D employment is the percentage change in equilibrium employment;
- % D demand is the percentage change in labor demanded at a given wage level (i.e., the size of the horizontal shift of the demand curve, expressed in percent); and
- % D supply is the percentage change in labor supplied at a given wage level (i.e., the size of the horizontal shift of the supply curve, expressed in percent).
We observe the initial (pre-reform) equilibrium point (Point A) and final (post-reform) equilibrium point (Point C) in the data collected (discussed in Section II.A below). These data give us the following information.
- Employment at Point A;
- Wages at Point A;
- Employment at Point C; and
- Wages at Point C
This information can be used along with information about the shapes of the supply and demand curves to obtain Point B in Exhibit 4.1. Point B is the wage and employment combination that would have been attained as a result of the economic expansion in the absence of welfare reform. The wage and employment information described above defines Points A and C (equilibrium outcomes before and after welfare reform).
Using the elasticity assumptions (that is, the value of the percentage change in employment associated with the percentage change in wages), we can draw labor demand and labor supply curves that pass through Points A and C. The intersection of the demand curve passing through Point C (LD1) and the supply curve passing through Point A (LS0) is Point B. Points A and C, along with the elasticity assumptions, are sufficient to produce the entire figure. We can also use this information to calculate other information of interest (e.g., the size of the shifts in the demand and supply curves, and the number of displaced workers).
The only remaining unknowns in the equations (i) and (ii) are the magnitudes of the demand and supply shifts (% D demand and % D supply). Because we have two equations and two unknowns, we can solve these two equations for % D demand and % D supply (see below). We can then use the equations to estimate the effects of the demand and supply shifts independently; that is, we can produce counterfactuals for the impact of economic expansion on employment and wages in the low-skill market, as well as counterfactuals for the impact of welfare reform on the same outcomes.
Solving equations (i) and (ii) for % D demand and % D supply, we get the magnitudes of the demand and supply shifts (equations (iii) and (iv)).
(iii) % D demand = % D employment + ed * % D wage
(iv) % D supply = % D employment - es * % D wage
Equations (i) through (iv) apply to small shifts in the supply and demand curves, but provide reasonable approximations for larger shifts if the elasticities of supply and demand are reasonably constant; they are exact if elasticities are constant. Constant elasticity functions are often used to represent supply and demand curves in the applied economics literature. We make use of elasticity estimates from the literature and the above relationships in our analysis.
The wage and employment equations can be used to analyze the impact of the supply shift alone (let % D demand be zero), or the demand shift alone (let % D supply be zero); that is, given the shift to the demand curve or the supply curve, and given the elasticities, we can use the equations to predict the impact on employment and wages. The percentage of workers displaced by an increase in supply can be derived from (iv).
(v) % displacement = % D supply - % D employment = - es * % D wage