How Well Have Rural and Small Metropolitan Labor Markets Absorbed Welfare Recipients?. Downward Wage Rigidity


The above discussion assumes that the responsiveness of wage adjustments to shifts in either curve are symmetric: in percentage terms, the effects of a positive shift in a curve on wages and employment are equal, but opposite in sign, to the effects of a negative shift of the same size. Economists have long argued, however, that institutional factors, such as the minimum wage and union contracts, result in asymmetric responses to demand shifts. More specifically, a downward shift in demand, induced by a recession or some other factor, might have very little negative impact on wages, but result in large reductions in employment, while an outward shift in demand of equivalent size, starting from the same point, results in higher wages and small increases in employment.

This phenomenon is very relevant for our analysis because many low-skill workers receive wages that are close to the minimum wage and because the starting point of our analysis, 1993, is near the beginning of a recovery from a major recession. If unemployment in an area in 1993 is still high relative to historical values, then the number of low-skill workers who are willing to work at current wage rates might be substantially higher than the number who are employed, and outward demand shifts are likely to increase employment, with little effect on wages, while outward supply shifts might simply result in greater unemployment, with little effect on employment or wages.

This is illustrated in Exhibit 4.3, in a stylized fashion. The initial supply curve is kinked; it is horizontal at wage level W0, to the left of Point B, then follows the upward sloping LS0. W0 represents a peak wage from the most recent expansionary period. The demand curve that generated that wage rate (i.e., pre-recession peak demand) is represented by LD-1, and peak employment is E-1. The initial demand curve LD0 passes through the horizontal portion of the initial supply curve at E0 (Point A).

Exhibit 4.3
Demand and Supply for Low-Skill Labor in the Presence of Downward Wage Rigidity

Demand and Supply for Low-Skill Labor in the Presence of Downward Wage Rigidity

Consider first an outward shift in demand (LD1), holding supply constant. The wage remains constant until the demand curve shifts past the previous peak demand curve at Point B, then rises along LS0 to Point C, where LD1 intersects LS0. This scenario can be used to illustrate what happens if we ignore the kinked supply curve in the analysis. Suppose we, mistakenly, assume that the initial supply curve is LS*  which also passes through LD0 at Point A, but is not kinked. The employment and wage change generated by the fixed kinked supply curve and the shift in demand is identical to what would be observed if LS* was the initial supply curve and supply shifted from LS* to LS0 as demand shifted from LD0 to LD1 (Point C). Thus, if we ignored the kinked nature of the hypothetical true supply curve, we could easily mistake an increase in employment and wages that is due solely to a demand shift as the result of both a shift in demand and a smaller shift in supply. The size of the false supply shift is the horizontal distance from Point A to Point B. In this stylized model, this is identical to the drop in employment from peak pre-recession employment, E-1, to E0. While the increase in employment from E0 to E1 is entirely due to the demand shift, the analysis would attribute part of the change to the false supply shift  represented by the distance between E1 and E*.

Next, consider an outward shift in supply, to LS1, holding demand constant, again starting at Point A. As the wage rate is already at the pre-expansion peak, it cannot decline further. There is no increase in employment, because demand does not shift. The number of persons seeking jobs at the existing wage rate is E3 (Point D), and E3 E1 workers are unemployed. Hence, under this stylized scenario, the push of welfare reform would just increase unemployment without increasing employment or depressing wages. This scenario further illustrates what happens if the analysis were to ignore the kinked supply curve. It would appear that the shift in supply due to welfare push was the horizontal distance from LS* to LS1, greater than the horizontal distance which represents the actual shift, from LS0 to LS1, again by amount E-1 E0.

The analysis becomes more complex if there is both a demand and a supply shift, because the order in which they shift matters. If supply shifts first, to LS1, then demand shifts to LD1, the wage rate stays constant and employment expands to E2; E3 E2 workers are unemployed. If, instead, demand shift firsts, then supply, wages increase to W1, employment increases to E1, and the shift in supply has no impact on wages or employment, but results in unemployment of E4 E1.

In a less stylized version of the above example, the supply curve would be more elastic at wage rates below previous peaks, and less elastic at higher wage rates. Such a supply curve would yield findings that are qualitatively similar to the stylized version presented above, with outward shifts in supply generating only modest wage reductions and outward shifts in demand generating only modest increases up to the point where demand passes the previous peak, and more pronounced increases thereafter.

In the decomposition of employment and wage changes into changes due to welfare push and changes due to the economy, we do not attempt to model kinks in the supply curve like those that appear in this stylized example, because we do not have a sound empirical basis for differentiating between the supply elasticity for low-skill workers during the early recovery from a recession and the elasticity as economic expansion passes the earlier peak. Instead, we use a constant elasticity model with an elasticity based on findings in the literature. The analysis of the kinked supply curve, above, is very important, however, in helping us interpret the findings.