Heterogeneous wage setting

Even though a standard approach in the recent literature, introducing wage rigidity for each and every worker is not supported by the facts, as pointed out by Haefke, Sonntag, and van Rens (2008) and Pissarides (2009). When disaggregating the rigid aggregate wage series, the authors find that this rigidity is mostly due to noncyclical wages for

16Of course, to be able to continue the analysis, Blanchard and Gal´ı (2010) introduce sticky prices such that monetary policy is effective in this setting.

workers in ongoing job relationships, whereas wages for new hires are highly cyclical.

The latter, in turn, is consistent with employing Nash bargaining to determine wages.

Accordingly, the authors conclude that wage rigidity cannot be the answer to the unemployment volatility puzzle, which typically serves as a rationale for introducing those rigidities.

Taking these findings as a starting point, in this section, I investigate the im-plications of introducing a wage setting mechanism into the presented model which is consistent with empirical evidence. In particular, heterogeneous wage setting is employed when considering the decentralized economy. In this setup, I distinguish between two kinds of workers: those who are in ongoing job relationships and those who were hired in the current period, i.e., newly hired workers. Contrary to Blan-chard and Gal´ı (2010) who use a rigid wage for every worker, in my setup only workers in ongoing job relationships earn this rigid wage. New hires bargain over the wage for the current period, modeled here by employing the generalized Nash solution. It should be noted that this is just a slight change to the framework of Blanchard and Gal´ı (2010), since I use the same type of rigid wage as in their model. It applies, however, only to workers in ongoing jobs. Nevertheless, since the overwhelming part of the labor force is in ongoing jobs, it is just a very small fraction of workers who are affected by the changes in the wage determination mechanism.¹⁷ Moreover, the economy-wide average wage is still rigid.

First, consider the representative firm’s problem given the wage, W_t^a(i), where a indicates that this is the average real wage the representative firm pays. It is just the wage sum divided by the number of workers employed by the individual firm. Thus,

W_t^a(i) = (1−δ)Nt−1(i)W_t^o+Ht(i)W_tⁿ

N_t(i) (2.12)

= (1−δ)N_t−1(i)

Nt(i) ΘA^1−γ_t + H_t(i)

Nt(i)W_tⁿ , (2.13) where W_t^o = ΘA^1−γ_t is the rigid wage for ongoing jobs specified as in Blanchard and Gal´ı (2010), and W_tⁿ is the wage for new hires, to be determined in a separate step by Nash bargaining. Furthermore, the number of workers in ongoing job relationships is (1−δ)Nt−1(i), i.e., last period’s non-separated worker, and new hires are given by

17For empirical evidence on the US, see Haefke, Sonntag, and van Rens (2008), for instance.

Ht(i). Since all firms are identical, it is possible to write W_t^a(i) = W_t^a∀i.

In this setup with flexible prices and monopolistic competition, the representative firm maximizes its value

{Pt+kmax(i)}^∞_k=0Et

" _∞ X

k=0

Qt,t+k(Pt+k(i)Yt+k(i)−Pt+kW_t+k^a Nt+k(i)−Pt+kGt+kHt+k(i))

# , (2.14) by setting the price of its differentiated good,P_t(i), optimally each period, subject to the production function and demand given by

Yt(i) =

Pt(i) Pt

−ε

(Ct+GtHt) ∀t. (2.15) In addition, the time path for the aggregate price index Pt = hR1

0 Pt(i)^1−εdii_1−ε¹ , the average real wageW_t^a, cost per hireGt, and the stochastic discount factor for nominal payoffsQt,t+k≡β^{k C}_C ^t

t+k

Pt

Pt+k are taken as given.

Solving this problem leads to the usual optimal price setting rule in such an envi-ronment, i.e., relative prices are set as a markup over real marginal cost

Pt(i) Pt

=MM Ct ∀t, (2.16)

where the optimal markup is given byM ≡ _ε−1^ε , and real marginal cost are obtained as

M Ct = W_tⁿ At

+Bx^α_t −β(1−δ)Et

C_t Ct+1

A_t+1 At

W_t+1ⁿ

At+1 −ΘA^−γ_t+1+Bx^α_t+1

. (2.17) This is just the respective costs less expected savings of hiring a worker now instead of next period. The former consist of this period’s (Nash) wage and hiring costs, each normalized by productivity. The latter depend on next period’s expected hiring costs and the expected difference between the wage for a newly hired worker and the ongoing wage, again normalized by productivity.

Furthermore, symmetry of the equilibrium implies Pt(i) = Pt ∀i, and thus due to equation (2.16)

M Ct= 1

M ∀t. (2.18)

Finally, plugging this equilibrium condition for real marginal cost into equation (2.17) leads to

W_tⁿ At

= 1

M−Bx^α_t +β(1−δ)Et

Ct

Ct+1

At+1

At

W_t+1ⁿ

At+1 −ΘA^−γ_t+1+Bx^α_t+1

. (2.19) These conditions are derived under the assumption that wages, and in particular the wage for new hires, are taken as given. In order to specify the equilibrium, I have to assume a wage determination scheme for the newly hired workers, leading to an expression for the process ofW_tⁿ, which can be combined with the preceding equation.

In accordance with the high cyclicality of wages for new hires, I use the generalized Nash solution. To derive the wage schedule, first consider the household side. The (real) value of a newly hired worker to the household at timet is given by

Vt^N =W_tⁿ−CtχN_t^φ+βEt

Ct

Ct+1

δ(1−xt+1)Vt+1^U + (1−δ)Vt+1^O +δxt+1Vt+1^N

. (2.20) This is just the (Nash) wage minus the marginal rate of substitution plus the dis-counted expected continuation values. With respect to the latter, conditional on being employed in period t, δ(1−xt+1) is the probability of being separated and not rehired in the next period, thus becoming unemployed. With probability (1−δ) a worker is not separated, i.e., she is in an ongoing job in the next period, and δxt+1 is the probability of being separated but hired again in t+ 1, i.e., being a newly hired worker. Similarly, the value of a worker in an ongoing job to the household at time t results as

Vt^O = ΘA^1−γ_t −CtχN_t^φ+βEt

Ct

Ct+1

δ(1−xt+1)Vt+1^U + (1−δ)Vt+1^O +δxt+1Vt+1^N

. (2.21) The preceding expression has the same structure as the one for the value of a newly hired worker except that the Nash wage is replaced by the rigid wage for workers in ongoing jobs. Finally, the value of an unemployed member to the household at time

t is given by

Vt^U =βEt

Ct

Ct+1

xt+1Vt+1^N + (1−xt+1)Vt+1^U

, (2.22)

where unemployment income is set to zero, and the probability of being employed, and thus newly hired, in the next period conditional on being unemployed in the current period is the job-finding rate next period, xt+1. From these expressions it is possible to calculate the household’s surplus from a newly created job, Vt^N − Vt^U.

Concerning the firm side, and as in Blanchard and Gal´ı (2010), the surplus of that agent from a newly created job is simply Vt^J = Gt. This is due to the fact that the hiring cost are the marginal cost the firm has to pay when it chooses to substitute a newly hired worker for another one.

Employing the usual sharing rule,Vt^N− Vt^U =ϑVt^J, whereϑindicates the worker’s relative bargaining weight,¹⁸ results in the following expression for the wage:

W_tⁿ

A_t −β(1−δ)Et

Ct

C_t+1 At+1

A_t W_t+1ⁿ

A_t+1

= (2.23)

ϑBx^α_t + CtχN_t^φ

A_t −β(1−δ)Et

Ct

C_t+1 At+1

A_t ϑ(1−xt+1)Bx^α_t+1+ ΘA^−γ_t+1 .

Combining this with the equilibrium condition (2.19), leads to

χC_tN_t^φ At

= 1

M −(1 +ϑ)Bx^α_t +β(1−δ)Et

C_t Ct+1

A_t+1 At

B(x^α_t+1+ϑx^α_t+1(1−xt+1))

, (2.24) which together with the equation describing the evolution of newly hired workers (2.6), the definition of labor market tightness (2.8), the aggregate resource constraint C_t=A_t(N_t−Bx^α_tH_t), and an exogenous process for A_t characterizes the equilibrium under heterogeneous wage setting.

The important thing to note here is that this is the same equilibrium as in Blan-chard and Gal´ı’s (2010) setting with Nash bargaining for every worker and not only for

18Alternatively, the optimality condition can be written as (1−ζ) Vt^N− Vt^U

= ζVt^J, where ζ ∈ (0,1) such that ϑ = _1−ζ^ζ ∈ (0,∞). ζ indicates the share of the joint surplus going to the household.

new hires, i.e., equation (2.11). Consequently, as in their setup and also as in the con-strained efficient allocation, the equilibrium features a constant unemployment level.

This, in turn, implies that the short-run inflation unemployment trade-off, obtained with a rigid wage for every worker,disappears,even though the economy-wide average wage is rigid if γ >0. The latter can be seen from the expression for the equilibrium average wage, which results as

W_t^a = ΘA^1−γ_t +δA_t

"

1 1−β(1−δ)

1

M−(1−β(1−δ))B(x^∗)^α

−Θ X∞

i=0

βⁱ(1−δ)ⁱEt(A^−γ_t+i)

#

, (2.25)

where x^∗ is the (constant) equilibrium job-finding rate. For γ = 0 the average wage moves one for one with productivity. If γ > 0, however, this one-for-one relation breaks down and the average wage is rigid. The preceding equation (2.25) is obtained by plugging in the equilibrium Nash bargained wage for the new hires into equation (2.13). This equilibrium Nash wage, in turn, results when combining the equilibrium condition (2.24) and the wage schedule (2.23), yielding

W_tⁿ At

= 1

1−β(1−δ) 1

M−(1−β(1−δ))B(x^∗)^α

−Θ X∞

i=1

βⁱ(1−δ)ⁱE_t(A^−γ_t+i). (2.26) The first term of this expression is the expected discounted Nash wage from pe-riod t into the infinite future, where the term in parenthesis is the equilibrium Nash bargained wage in a setup where every worker gets the Nash wage, normalized by pro-ductivity. The second term just subtracts the expected discounted future rigid wage starting from period t+ 1, normalized by productivity.¹⁹ Consequently, in expected discounted value terms an individual worker gets the same wage sum over the course of her tenure at a firm in this setup as in the framework with Nash bargaining for every worker in every period. Thus, since what matters for hiring incentives and thus employment fluctuations is the permanent wage and not how the stream of wage pay-ments is distributed over the duration of the job, it comes as no surprise that the same

19Depending on the stochastic process for productivity, even the Nash wage could be rigid to some degree in this setup.

equilibrium arises in the case with heterogeneous wages as in the case with general Nash bargaining.²⁰ Moreover, as a result, the expected labor costs for an individual worker over the course of her tenure at an individual firm normalized by productivity corresponds to the first term of expression (2.26), which is constant. Hence, expected labor costs move one for one with productivity, eliminating all potential hiring incen-tives, which in turn leads to an unchanged employment level in response to technology shocks.

In sum, introducing a form of wage rigidity which is consistent with empirical evidence leaves the monetary authority with a single target. It can exclusively focus on inflation with no concern whatsoever for employment stabilization. Furthermore, since wage rigidity cannot be a valid answer to the unemployment volatility puzzle, the question remains what other mechanisms can account for the observed fluctuations in unemployment and what are the implications for monetary policy. The following section sheds light on this issue.

Im Dokument Essays in Econometrics and Macroeconomics (Seite 83-89)