M. Alper Cenesiz Universidade do Porto & Luıs Guimaraes Queen’s University, Belfast Eesti Pank January 25, 2019

1. Income Effects and the
Cyclicality of Job Search Effort
Alper C¸ enesiz
Universidade do Porto
&
Lu´ıs Guimar˜aes
Queen’s University, Belfast
Eesti Pank
January 25, 2019
C¸ enesiz and Guimar˜aes, 2019 – p. 1/20

2. Overview I
• The cyclicality of job search effort is crucial for labor market dynamics:
– (For theory) If procyclical, it helps to overcome the Shimer critique (Gomme and
Lkhagvasuren, JME, 2015).
– (For data) If countercyclical, it results in less unemployment rates during
recessions (Mukoyama et al., AEJ-M, 2018).
• Evidence: job search effort is not procylical:
– Acyclical in DeLoach and Kurt, JLR (2013), Leyva (2017), and Shimer (2004);
– Countercyclical in Mukoyama, et al. (2018);
– (Indirectly) countercyclical in Ahn and Shao (2017), Faberman and Kudlyak
(2016), and Hornstein and Kudlyak (2016).
C¸ enesiz and Guimar˜aes, 2019 – p. 2/20

3. Overview II
• The workhorse for macro labor research is the matching framework (aka DMP model,
Diamond 1982, Mortensen 1982, and Pissarides 1985).
• But, at odds with the evidence, the canonical matching model predicts procyclical
search effort.
• Question: Can introducing income effects (IE) reconcile theory with evidence?
• (Before the answer) Why IE?
– Negative relation between wealth and search effort, (DeLoach and Kurt, 2013 and
Mukoyama, et al., 2018).
– In Faberman and Kudlyak (2016), if IE dominate substitution effect, those with
lowest return to search exert higher effort.
C¸ enesiz and Guimar˜aes, 2019 – p. 3/20

4. Overview III:
• To obtain acyclical/countercylical effort, we introduce income effects (IE):
– By making use of the CRRA utility specification.
• By controlling households’ attitude towards risk, we control the magnitude of IE.
• IE dictate qualitative and quantitative predictions of the model.
C¸ enesiz and Guimar˜aes, 2019 – p. 4/20

5. The Model
• An RBC model with macthing frictions.
• Time is discrete and denoted by t.
• There are two actors: a representative household and a representative firm.
• The representative household consists of employed and unemployed workers.
• Exogenous labor force participation: ut + nt = some constant.
• Every period, a δ fraction of jobs is exogenously destroyed.
C¸ enesiz and Guimar˜aes, 2019 – p. 5/20

6. Employment and Matching
• The law of motion of employment:
nt+1 = (1 − δ)nt + mt. (1)
• Matching function:
mt = σvη
t (¯etut)1−η
. (2)
• Using θt ≡ vt/ut notation, the job-finding and -filling probabilities per ¯et:
f(¯et, θt) = σ (θt/¯et)η
, (3)
µ(¯et, θt) = σ (θt/¯et)η−1
. (4)
• nt: employed workers, mt: matches, vt: vacancies, ¯et: average search effort, ut:
unemployed workers, θt: labor market tightness, f(): prob. of finding a job, µ(): prob.
of filling a vacancy
C¸ enesiz and Guimar˜aes, 2019 – p. 6/20

7. The Household I
• The optimization problem is
Vt = max
{ct,et}
c1−γ
t − 1
1 − γ
−
ψ
ζ
eζ
t ut − χnt + βEtVt+1 ,
subject to
ct ≤ wtnt + dt,
nt+1 ≤ (1 − δ)nt + f(¯et, θt)utet.
• ct: consumption, et: effort, ut:unemployed, nt: employed, wt: wage, dt: dividend
income, f(): prob. of finding a job
C¸ enesiz and Guimar˜aes, 2019 – p. 7/20

8. The Household II
• The first-order condition for effort is
ψeζ−1
t = βf(¯et, θt)EtVn,t+1, (5)
where Vn,t:
Vn,t = wtc−γ
t + ψeζ
t /ζ − χ + (1 − δ − etf(¯et, θt))βEtVn,t+1. (6)
• Vn,t: value of an additional worker for the household, ct: consumption, et: effort,
ut:unemployed, nt: employed, wt: wage, dt: dividend income, f(): prob. of finding a
job.
C¸ enesiz and Guimar˜aes, 2019 – p. 8/20

9. The Firm I
• The firm produces a homogeneous good with the technology
yt = ztnt, (7)
• The optimization problem is
Jt = max
vt
ztnt − wtnt − κvt + βEt (ct+1/ct)−γ
Jt+1 ,
subject to
nt+1 = (1 − δ)nt + µ(¯et, θt)vt.
• yt: output, zt: TFP, nt: employed workers, wt: wage, vt: vacancies, ct: consumption,
µ(): prob. of filling a vacancy.
C¸ enesiz and Guimar˜aes, 2019 – p. 9/20

10. The Firm II
• The optimal choice of vt implies the free-entry condition:
βEt (ct+1/ct)−γ
Jn,t+1 µ(¯et, θt) = κ, (8)
where
Jn,t = zt − wt + (1 − δ)βEt (ct+1/ct)−γ
Jn,t+1 . (9)
• Jn,t: Value of a worker for the firm, zt: TFP, nt: employed workers, wt: wage, vt:
vacancies, ct: consumption, µ(): prob. of filling a vacancy.
C¸ enesiz and Guimar˜aes, 2019 – p. 10/20

11. The Wage
• Workers and firms bargain over wages such that the bargained wage maximizes the
Nash product:
wt = arg max Vn,t/c−γ
t
φ
Jn,t
1−φ
, (10)
• The equilibrium wage is
wt = φ zt + etf(¯et, θt)
κ
µ(¯et, θt)
+ (1 − φ) χ −
ψ
ζ
eζ
t
1
c−γ
t
. (11)
• wt: wage, Vn,t: Value of a worker for the housefold, Jn,t: Value of a worker for the
firm, ct: consumption, zt: TFP, et: effort, f(): prob. of finding a job, µ(): prob. of filling
a vacancy.
C¸ enesiz and Guimar˜aes, 2019 – p. 11/20

12. Closing the Model
• In equilibrium: ¯et = et.
• Resource Constraint:
yt = ct + κvt. (12)
• Law of motion of productivity:
log zt+1 = ρ log zt + εt+1; εt+1 ∼ NIID(0, σ2
ε), (13)
C¸ enesiz and Guimar˜aes, 2019 – p. 12/20

13. Benchmark Calibration
Discount factor: β = 0.996
Rate of job destruction: δ = 0.036
Matching function elasticity: η = 0.5
Workers’ bargaining power: φ = 0.5
Convexity of effort disutility: ζ = 2
Relative risk aversion: γ ∈ [0, 4]
Autocorrelation of productivity: 0.98
Standard deviation of productivity shock: 0.005
χ, ψ, σ, and κ pinned down by steady-state targets n = 0.943, θ = 0.72, e = 1, κv = 0.01y.
C¸ enesiz and Guimar˜aes, 2019 – p. 13/20

14. Impulse responses to a productivity increase
0 50 100 150 200 250 300
-15
-10
-5
0
5
10
15 Labor Market Tightness
γ=0 γ=1 γ=4
0 50 100 150 200 250 300
-8
-6
-4
-2
0
2
4
6
8 Unemployment
0 50 100 150 200 250 300
-8
-6
-4
-2
0
2
4
6 Job Search Effort
The horizontal axis measures time in months. The vertical axis measures the
logarithmic/percentage deviation from the steady state. The impulse is a 1% increase in
productivity.
C¸ enesiz and Guimar˜aes, 2019 – p. 14/20

15. Cumulative responses to a productivity increase
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0.5 1.5 2.5 3.51 2 3 4
Unemployment
Labor Market Tightness
Job Search Effort
The horizontal axis measures the degree of income effects, γ ∈ [0, 4]. The vertical axis
measures the 8-year cumulative responses. The impulse is a 0.5% increase in productivity.
C¸ enesiz and Guimar˜aes, 2019 – p. 15/20

16. Endogenous vs Exogenous Effort
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0.5 1.5 2.5 3.51 2 3 4
Unemployment
Endogenous Effort
Exogenous Effort
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0.5 1.5 2.5 3.51 2 3 4
Labor Market Tightness
The horizontal axis measures the degree of income effects, γ ∈ [0, 4]. The vertical axis
measures the 8-year cumulative responses. The impulse is a 0.5% increase in productivity.
C¸ enesiz and Guimar˜aes, 2019 – p. 16/20

17. Sensitivity Analysis
γ = 0 γ = 1 γ = 4
θ u e θ u e θ u e
Benchmark 2.35 -1.66 1.17 0.19 -0.08 -0.01 -2.20 1.67 -1.34
vµ(e, θ)H = 0.005y 2.83 -1.90 1.21 0.25 -0.11 -0.02 -2.35 1.71 -1.27
vµ(e, θ)H = 0.0075y 3.23 -2.11 1.24 0.30 -0.13 -0.02 -2.46 1.73 -1.23
φ = 0.05 24.39 -17.21 12.19 0.11 -0.02 -0.05 -3.59 2.60 -1.93
vκ = 0.002y 11.75 -8.29 5.87 0.12 -0.04 -0.05 -3.25 2.36 -1.77
ρ = 0.99 2.67 -1.81 1.17 0.47 -0.20 -0.05 -2.01 1.61 -1.41
ρ = 1 26.65 -13.09 1.17 23.32 -9.76 -2.58 18.81 -5.24 -7.67
b = 0.4 2.35 -1.66 1.17 0.98 -0.63 0.37 -1.09 0.92 -0.87
Model with Capital 2.35 -1.66 1.17 0.92 -0.59 0.34 -0.77 0.68 -0.69
8-year cumulative responses. The impulse is a 0.5% increase in productivity.
C¸ enesiz and Guimar˜aes, 2019 – p. 17/20

18. The Case χ = 0
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
2 5 10 20
Unemployment
Labor Market Tightness
Job Search Effort
The horizontal axis measures the degree of income effects, γ ∈ [0, 20]. The vertical axis
measures the 8-year cumulative responses. The impulse is a 0.5% increase in productivity.
C¸ enesiz and Guimar˜aes, 2019 – p. 18/20

19. Summary
• Income effects dictate the behavior of the model.
• One of three possibilities emerges:
1. If income effects are absent or low, effort is procyclical.
2. If income effects are moderate, the Shimer (2005) critique is acute.
3. If income effects are high, unemployment is procyclical.
Thank you very much!
C¸ enesiz and Guimar˜aes, 2019 – p. 19/20

20. Two Intuitive Equations
• The equilibrium condition for effort simplifies to (in log-linear terms)
ζˆet = ˆθt − γˆct. (14)
• The equilibrium wage equation simplifies to (in log-linear terms)
ˆwt =
φ
w
zˆzt +
(ζ − 1)κθ
ζ
ˆθt +
(1 − φ)γχcγ
w
ˆct. (15)
C¸ enesiz and Guimar˜aes, 2019 – p. 20/20