Employment Fluctuations with Equilibrium Wage Stickiness

Transcription

1 Employment Fluctuations with Equilibrium Wage Stickiness Robert Hall (AER, 2005) presented by Tomás Rodríguez Martínez Universidad Carlos III de Madrid 1 / 20

2 A bit of historical context Around the 2000s the labor market friction models started by Diamond (1982), Mortensen (1985) and Pissarides (1985) were well established. The model has plenty of appealing features: It describes the labor market in a very intuitive way. Analytically tractable and it generates easy and useful comparable statics. Can be easily adapted to study many labor market issues. However, Shimer (2005), argues that the model fails quantitatively in two important dimensions. It cannot generate plausible fluctuations of unemployment and vacancies given a productivity shock. 2 / 20

3 The Shimer s Puzzle In the data: sd(ln p) = 0.02 and sd(ln θ) = Therefore, one would need an implied elasticity of d ln θ/d ln p 20! But in the model the two variables basically move one-to-one. Shimer gets an elasticity of Acemoglu, assuming that Hosio s condition holds, get an implied elasticity of the model of 1.03! And even if we decrease worker s bargaining power to zero (the lower bound) we cannot go very far: 1.39 On the other hand, the wage responds more than one to one... 3 / 20

4 Hall (2005) Introduction The idea of this paper is that part of this problem comes from the fact that wages respond too strongly. Solution: Depart from Nash Bargaining and use Sticky wages instead. This paper provides the quantitative results of DMP with sticky wages. With sticky wages Hall gets an elasticity of 94!. With the same calibration, Nash Bargaining gives us / 20

5 Introduction The idea is simple: In the Nash Bargaining DMP, wages are determined as a share over the surplus (or bargaining set) of the match. The bargaining set is bounded by the reservation wage of the firm and worker. The business cycle shifts these reservation wages and the equilibrium wages, given the bargaining parameters. But in principle any wage inside the bargaining set is valid. 5 / 20

6 Introduction Hall fixes the wage to be the same at all states. Now the cycles shift the boundaries of the bargaining set but not the equilibrium wage. In bad times the equilibrium wage is too high firms receive less of the surplus of the match. They anticipate this mechanism and post less vacancies stronger downward effect on unemployment! 6 / 20

7 Evidence The data supports this mechanism: vacancies are strongly countercyclical. 7 / 20

8 Model Standard DMP model. Tightness: x = v/u and matching technology: φ(x) = ωx α. Finding job probability: φ(x). Filling vacancy probability: ρ(x) = φ(x)/x. Exogenous and fixed separation rate: δ. Outside option λ and productivity z s. 8 / 20

9 Equilibrium The values associated with the state s: U s = λ + βe s [φ(x s )(w s + V s ) + (1 φ(x s ))U s ] (1) V s = βe s [(1 δ)(w s + V s ) + δu s ] (2) J s = z s = β(1 δ)e s (J s w s ) (3) 0 = k + βρ(x)e s (J s w s ) (4) 9 / 20

10 Equilibrium Conditional on the state contingent w s we can define the bargaining set using the reservation wages. The worker s reservation wage: w s = U s V s. The employer s reservation wage: w s = J s. The Bargaining set: B s = [w s, w s ]. Any wage within this set will result in retention of a match and will benefit both employer and worker. 10 / 20

11 Equilibrium In the symmetric Nash bargain problem the wage is just w s = w s + w s 2 Here the wage will be determined using the Nash demand-game auction. Workers propose wage w L and firms propose wage w H. If w L w H a match is formed with w = κw L + (1 κ)w H. This auction game has the property that any w = w L = w H B s is a Nash equilibrium. 11 / 20

12 Equilibrium A wage rule w s is an equilibrium if it results in a solution to the value functions with w s B. There is a rich space of equilibria (including the Nash bargain). We will consider a class of constant wages: w s = w s. PROPOSITION: A constant wage is an equilibrium of the model if: λ w min s [1 β(1 δ)j s ]. The fixed wage could be easily adapted to a nonstationarity environment s.t. z t = z P t z M t w t = wz P t. 12 / 20

13 Calibration Similar to Shimer s. Parameters Solve the Nash Bargain DMP, set the fixed the wage to the median productivity state (z 3 = 1) and solve the Fixed wage DMP. Equilibrium wage is founded to be w = / 20

14 Properties of the Model The fixed wage DMP has a stronger response in vacancy creation. That arises because in the good times all the surplus from the extra productivity goes to the firms which creates an additional incentive for them to post more vacancies. In the bad times firms react negatively as they have to buffer all the bad shock themselves. Remember that: u s = δ δ + φ(x s ). Therefore, the jump in the vacancies impacts unemployment through job creation. 14 / 20

15 Properties of the Model Fixed Wage 15 / 20

16 Properties of the Model Nash Bargain 16 / 20

17 Comparison to Shimer s Shimer s calibration with bargaining implied an elasticity of 1.7, Hall gets 1.8. The elasticity of the fixed wage model is much higher: 94. That s actually higher than that data, but that could be because not all the wages are literally fixed. Other type of wages could be considered: smoothed wages, adaptive wages / 20

18 Is this the end of the story? At that time the literature have accepted that the wage setting mechanism should be changed. Shimer itself argued that this should be the way to go. Others begun to work on how to endogenize wage rigidity: Menzio (2005), Kennan (2006). However, Hagendorn and Manovskii (2008) have taken another route: The problem is in how the model is typically calibrated. 18 / 20

19 Is this the end of the story? Hagendorn and Manovskii (2008) argued that we have to view the DMP as a linear approximation of a much nonlinear and richer model. In that model the outside option should be closer to the productivity level λ = z z is too low! Also, the vacancy cost should vary in the BC. Using the elasticity of wages and the average tightness they pin down both the outside option and the bargaining weight. The bargaining weight is lower than the usual ( 0.05) but the outside option higher ( 0.95). Their implied elasticity: d ln θ/d ln p / 20

20 Thank you! 20 / 20

21 Appendix 1 Calibration 21 / 20