A change in the structure of unemployment compensation

3. A change in the structure of unemployment compensation

Changes in the level or structure of unemployment compensation have an impact on the aggregate employment schedule F and on the shirking constraint C . The consequences of changes in the parameter x, x s b s , b e , b, are given by Ž . Ž . d Nrd x s F C y C F rD and dwrd x s F C y C F rD, where D s w x w x x N x N C F y C F - 0. The derivatives of the shirking constraint C and the aggre- w N N w gate employment schedule F with respect to b e are: qÕ X b e Ž . e e C s ye s y - 0 6 Ž . b b 2 1 y q Ž . t f Y en q f X qÕ X b e Ž . Ž . e e F s yt n e s - 0 7 Ž . Y b e b 2 2 1 y q f e Ž . Therefore, a rise in benefits b e for those workers who have lost their position for exogenous reasons shifts the shirking constraint and the aggregate employment schedule to the right in the wage-employment space. These shifts imply more employment. d N e e t e wn q n Ž . b ww e w s y e d b e t e wn q n y e w Ž . N ww e w ww e w f Y en q f X q f Y ene Ž . ww w X e s qÕ b 8 Ž . Ž . 2 1 y q D Ž . Moreover, it can be shown that wages decrease. 4 dw t n e e e q e e 1 y t n e qÕ X b e Ž . Ž . e N b b e N s s - 0 9 Ž . e d b D 2 1 y q D Ž . In its effects on the employees’ behaviour, the increase in b e is tantamount to a reduction in the probability of being fired for exogenous reasons. This implies a less pronounced decline in the utility which an employee incurs when losing the job for no fault of his or her own. Therefore, the expected utility of not being fired for shirking increases, even if part of it derives from unemployment benefits b e . Effort rises for a given wage and, thus, induces a reduction in unemployment. The beneficial employment consequences of a rise in the benefit level b e for non- 4 Ž Y X . If the restriction on technology f enq f 0 is dropped and replaced by the requirement that the Ž . aggregate employment schedule is downward sloping at the equilibrium F 0 , the above results N with respect to wages will not be affected. The employment prediction will continue to hold if Ž Ž .. Ž .Ž . 1qh 1qu 0, where h s d e rdw wr e is the elasticity of marginal effort with respect to w w wages, and u is the inverse of the elasticity of the marginal product with respect to effort, Ž X .Ž X . 1ru s d f rd e er f . shirkers result from an increase in the attractiveness of the no-shirking option, for given levels of wages and employment. The employment effect is independent of relative benefits, that is, employment will also expand with a rise in b e if b e - b s . Moreover, if the benefit office is not only able to restrict unemployment compen- sation for shirkers to a level 0 - b s F b e , but can completely deny shirkers any benefits, such that b s s 0 applies, an increase in unemployment compensation b s b e will unambiguously raise employment and effort, while wages will fall. In Ž . contrast to the assertion of Atkinson 1995, 197 ‘‘that the existence of unemploy- ment insurance does not affect the incentive to shirk’’, it might even reduce this incentive. The reduction in the wage owing to a rise in b e is the consequence of two opposing effects: since effort rises with b e , employment per firm and aggregate employment increase. This tends to drive up wages. However, the increase in benefits for non-shirkers allows the firm to reduce the efficiency wage for a given level of unemployment. This negative wage effect dominates in the present Ž . framework since marginal effort is independent of aggregate employment e s 0 wN and, therefore, the downward shift of the shirking constraint in the wage-employ- ment space is unambiguously more pronounced than the upward movement of the aggregate employment schedule. An increase in benefits b s which a former employee receives due to being fired because srhe shirked, raises wages and lowers employment since C s 0 and b F s 0. Furthermore, a lump-sum, across-the-board rise in unemployment com- b e s Ž pensation b, b s b s b , also raises wages and reduces employment C 0, b . 5 F 0 . This result reflects the predominant finding for efficiency wage models b that a higher uniform benefit level has adverse employment consequences since shirking becomes more attractive. 6 Moreover, a simultaneous increase in b e and b s is likely to have the same qualitative though not quantitative consequences as higher benefits solely for shirkers will have. This is the case because b e enters the Ž . s effort function only with a probability qr 1 y q , while b has an impact on effort Ž . e s with the higher probability 1r 1 y q . Unless the increase in b and b is 5 The assumption of bs b e s b s 0 is the most convenient way of analysing an across the board Ž . w Ž . Ž . Ž . Ž Ž rise in benefits. The effort function is then given by e w, b,u, q s 0.5 Õ w y Õ b y 1y u r u 1y ..x q . 6 Ž . Ž . Ž . See, for example, Shapiro and Stiglitz 1984 , Pisauro 1991 , Carter 1992 , or Drago and Ž . Ž . Ž . Heywood 1992 . Bull 1985 and Shapiro and Stiglitz 1985 briefly discuss the impact of differential Ž . benefits for shirkers and non-shirkers in the context of the Shapiro and Stiglitz 1984 model in which, however, shirking never occurs in equilibrium. In contrast to the usual results, in adverse selection models, lower unemployment benefits might increase search by low-quality workers relative to that of high-quality ones such that the incentives to pay efficiency wages rise. Hence, unemployment can Ž . increase if benefits are lowered Stiglitz, 1986, 188 . In multi-sector fair-wage efficiency models, higher unemployment compensation can also raise employment since the movement of labour across Ž sectors might invalidate the adverse incentive effects of higher benefits Agell and Lundborg, 1992; . Albert and Meckl, 1997 . extremely disproportionate or the marginal utilities from obtaining b s and b e strongly diverge, the rise in b s will dominate the increase in b e .

4. The role of the benefit office