A Contribution to the Empirics of
Reservation Wages
Alan B. Krueger
Princeton University & NBER
and
Andreas I. Mueller
Columbia University & NBER & IZA
RAND Corporation
December 15, 2014
Background
• Sequence of reservation wages over spell of unemployment
central to search theory (e.g., Mortensen, 1977).
• Long tradition of looking at reservation wages across
workers with different unemployment durations (e.g.,
Kasper, 1967; Feldstein and Poterba, 1984). But are those
with low reservation wages the first to exit unemployment?
Could bias against finding a downward gradient.
• Shimer and Werning (2007) look at empirical elasticity of the
reservation wage with respect to UI benefits and, based on
Feldstein and Poterba’s estimates, conclude it may improve
welfare to raise UI benefits.
2
Our Research
• High-frequency longitudinal data on reservation wages
from survey of 6,000 UI recipients in NJ.
• Uses repeated information of self-reported reservation
wages over unemployment spell to overcome potential
bias associated with previous cross-sectional
comparisons.
• Calibration exercise for what to expect.
• Evidence on efficacy of reservation wages in predicting
job acceptance/rejection.
• Assess whether benefits set optimally.
3
Main Conclusions
• Reservation wage starts out too high and declines too
slowly, on average, compared to calibration, perhaps
because of over confidence or anchoring.
• Reservation wage only falls for older workers and those
with personal savings.
• Reservation wage in relation to offered wage helps
predict job acceptance and rejection.
• Little evidence UI affects reservation wage. Can’t reject
null hypothesis that UI benefits were set optimally.
4
Outline
1. Calibrated Search Model
2. Survey of Unemployed Workers in NJ
3. Replicate Previous Cross-Sectional Analyses
4. Reservation Wages Over Unemployment Spell
5. Evidence from Job Offers and Acceptances
6. Implications for Optimal Level of UI Benefits
7. Conclusion
5
Search Model
Value function U(.) of unemployed worker:
𝑈 𝑡 = 𝑢(𝑏 𝑡 ) + 𝛽 max 𝑈 𝑡 − 1 + 𝛼
𝑅
𝑊 𝑥, 𝑚 = 0 − 𝑈 𝑡 − 1 𝑑𝐹 𝑥
𝑅
Where R=reservation wage, α= constant arrival rate of job offers, T =
maximum duration of benefits, t = remaining duration of unemployment
benefit, u(.) = flow utility function, β = discount factor, m=number of months
employed, and W(x,m=0)= value of starting a job. Need m>6 to re-qualify for
UI.
Next introduce qualifying period for UI benefits.
6
Search Model II
𝑊 𝑤, 𝑚 = u 𝑤 + 𝛽 1 −  𝑊 𝑤, 𝑚 + 1 + U 0 +𝛼𝑒 1 − 
𝑊 𝑤, 𝑚 = u(𝑤) + 𝛽 1 −  𝑊 𝑤, 𝑚 + U T +𝛼𝑒 1 − 
𝑤
𝑊 𝑥, 𝑚 + 1 − 𝑊 𝑤, 𝑚 + 1 𝑑𝐹 𝑥
𝑤
𝑊 𝑥, 𝑚 − 𝑊 𝑤, 𝑚 𝑑𝐹 𝑥
𝑊 𝑅 𝑡 , 𝑚 = 0 = 𝑈(𝑡)
7
Key Calibration Assumptions
•
•
•
•
•
•
•
•
•
•
Benefits last 99 weeks
No saving so consumption equals benefit
Consumption at layoff is set to match average duration of 7 months
Assume 31.3% drop in consumption at UI exhaustion (consistent
with Low, Meghir and Pistaferri (2010) and Gruber (1997))
CRRA Utility with coefficient of 2
5% annual discount rate
Offer arrival rate (α) of 0.3 per month for unemployed and 0.1 for
employed
Standard deviation of log offered wages of 0.24
Exogenous separation probability (δ) of .02 per month
m>6 months to re-qualify for UI
8
Calibrated Model
Decline of reservation
wages over 23 months of UI
eligibility in NJ
Reservation wage if
unlimited UI
Reservation wage if no UI
0.21% decline per week
Note: Difference between blue and
red lines is approximately the
effect of UI on reservation wage.
9
Other Factors that Could Affect
Reservation Wages
•
•
•
•
•
Search intensity
Consume out of personal savings as well
Personal savings and spouse’s income
Learning about potential wage offer distribution
Psychological toll of unemployment likely rises with duration
unemployed
Let’s go to the data.
10
Survey Design
• Start with universe of UI recipients in NJ in late September 2009
• Stratified random sample (n=63,813)
-- Strata consisted of duration of unemployment (0-2, 10-12, …,
40-42, 50-53, 60-69, 70-79 weeks) and email address on file
-- Over sampled long term unemployed & those with email addresses
• NJ LWD sent letter inviting participation in early October 2009
• Web survey – administered by Cornell Survey Research Institute
• Entry Survey -- Offered $20 for participation or $40 if wait 12
weeks (46% took latter)
• 12 weekly surveys, starting with week of entry survey
• Extended Survey: Additional 12 weeks of interviews for those with 60+
weeks of unemployment to start
• Low response rate (10% on entry; 40% thereafter), but can create weights
from administrative data and compare sample and universe
11
Bonus Table: Descriptive Statistics for Universe, Stratified Sample, and Respondents
12
UI Weekly Exit Rate by UI Duration
13
The Ratio of the Weekly Wage in 2010
To the Previous Weekly Wage
Notes: Both the weekly wage in 2010 and the previous wage are from administrative data. The previous
weekly wage is computed from earnings in the base year, which are used to compute the
unemployment benefits, whereas the weekly wage in 2010 is computed from NJ wage records (and thus
earnings from other states are omitted). Weights are used to adjust for sampling probability and non14
response.
15
Unemployment Rate in New Jersey and U.S., Seasonally Adjusted, 2008-10
16
17
18
Sample and Data
• Restrict sample
– Age 20-65
– Did not accept job in previous week
– Did not work in previous week
• Administrative data on weekly UI benefit rate;
earnings on prior job; and earnings in 2010 if
re-employed in NJ.
• Reservation wage ratio =
19
In 12% of cases, the
reservation wage was within
5% of the previous wage
20
Cross-Sectional Analysis
21
Reservation Wages over
Unemployment Spell
22
Reservation Wages over
Unemployment Spell
Little visible evidence of tendency for reservation wage to decline
over the spell of unemployment.
23
Reservation wage is relatively stable in weeks before UI
exhaustion.
24
Fixed effects estimates indicate statistically insignificant and small
change in reservation wage ratio over spell of unemployment.
Sizable decline for older workers with savings. No apparent effect
25
of UI benefits exhausting or elapsing.
26
Estimates for subsample looking for full-time work are still small,
but statistically significant. Still driven by those with savings and
older workers.
27
Other Job Features
• Unemployed workers only slightly more willing to
accept jobs requiring a longer commute as duration
of unemployment rises.
• Unemployed workers reduce their occupational
aspirations over the spell of unemployment, with the
magnitude of the effect slightly stronger than the
reservation wage estimates.
28
29
30
Validating Reservation Wages
• Survey contains information on job offers and acceptances, and
offered wage.
• Use reservation wage from prior interview.
• Information on 1,499 job offers
– 61.6% accepted
– 16.6% rejected
– 21.8% undecided
• Using administrative data can track UI exits in following month
(and stayed off UI)
– 45.7% of those who accepted an offer exited UI
– 5.3% of those who rejected an offer exited UI
– 26.0% of those who were undecided exited UI
31
Likelihood of Accepting Offer
Reservation wage has some predictive power for likelihood of
accepting or rejecting an offer. Also, some noise in hours, which
affects hourly reservation wage.
32
33
34
What explains the shape of the
acceptance function?
1. Measurement error in offered wages and
reservation wages
2. Non-wage amenities and other job
characteristics
35
36
What explains mass point at
W=R?
• The mass point is not affected if we:
– lag the reservation wage 4 weeks instead of 1 week
– exclude those who expect to be recalled to their
previous employer
• Some unemployed may search in markets with
tight dispersion of potential wages
• Employers may know the worker’s reservation
wage and capture the entire surplus (Diamond
paradox)
37
38
Why no bias comparing cross-section and panel? Simulation
suggests small part of the variability.
39
Offer Acceptance
From previous table we can see unemployed workers are:
• More likely to accept jobs that pay better
• Less likely the higher the reservation wage
• More likely to accept part time jobs
And that:
• Value of offered wage has predictive power conditional on whether the
wage exceeds the reservation wage
• Binary indicator of whether reservation wage exceeds the offered wage is
a strong predictor of job acceptance or rejection
• Reservation wage captures more info than previous wage
• Savings and unemployment duration do not predict acceptance
conditional on reservation wage
40
41
Optimal UI Benefits
• Relate analysis to Shimer and Werning (2007)
∗ ∗
𝜀
(𝑏
,𝜏 )
𝑢𝑟 ,𝑏
∗ ∗
∗ ∗
• 𝑅𝑏 (𝑏 , 𝜏 ) = 𝑢𝑟(𝑏 , 𝜏 ) 1 +
1 − 𝑢𝑟(𝑏 ∗ , 𝜏 ∗ )
• Formula implies that if pre-tax reservation wage is
sufficiently responsive to the level of UI benefits,
then it is welfare increasing to raise UI benefits
Where 𝑅𝑏 (𝑏 ∗ , 𝜏 ∗ ) is the responsiveness of pre-tax reserva wage to the unemployment benefit, 𝑢𝑟(𝑏 ∗ , 𝜏 ∗ )is the
∗ ∗
unemployment rate, and 𝜀𝑢𝑟 ,𝑏 (𝑏 , 𝜏 ) is the elasticity of the unemployment rate w.r.t. the level of UI benefits.
42
Estimating the Right Hand Side
• Meyer (1990): 1% increase UI reduces job
finding hazard by .88.
• Average unemployment rate in NJ 9.6%
∗ ∗
𝜀
(𝑏
, 𝜏 ) = 0.8
• 𝑢𝑟 ,𝑏
• Right hand side= .18 (slightly higher than
Shimer and Werning)
43
Calibrated Model
Decline of reservation
wages over 23 months of UI
eligibility in NJ
Reservation wage if
unlimited UI
Reservation wage if no UI
Note: Difference between blue and
red lines is approximately the
effect of UI on reservation wage.
44
45
Conclusion
• Reservation wages decline at a modest rate over the spell of
unemployment
– Decline driven by older individuals and those with non-negligible
savings.
– Suggests people treat time-limited government social insurance
benefits differently than personal savings
• Unemployment insurance only has limited impact on reservation
wages -- Challenge for Shimer and Werning (2007)
• Importance of lagged reservation for job acceptance encouraging for
research on self-reported reservation wages
• Why reported reservation wage starts out too high and declines too
slowly is a challenge for search theory
• Can interventions that alter the reservation wage lead to a faster
return to work?
46