a contribution to the empirics of reservation wages alan b. krueger princeton university & nber...

A Contribution to the Empirics ofReservation Wages

Alan B. KruegerPrinceton University & NBER

and

Andreas I. MuellerColumbia University & NBER & IZA

RAND CorporationDecember 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.

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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.

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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. Conclusion5

Search Model

Value function U(.) of unemployed worker:

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.

𝑈ሺ𝑡ሻ= 𝑢(𝑏ሺ𝑡ሻ) + 𝛽max𝑅 ቊ𝑈ሺ𝑡− 1ሻ+ 𝛼න ൫𝑊ሺ𝑥,𝑚= 0ሻ− 𝑈ሺ𝑡− 1ሻ൯𝑑𝐹𝑅 ሺ𝑥ሻቋ

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•

Search Model II

𝑊ሺ𝑤,𝑚ሻ= uሺ𝑤ሻ+ 𝛽ቂሺ1− ሻ𝑊ሺ𝑤,𝑚+ 1ሻ+ Uሺ0ሻ+𝛼𝑒ሺ1− ሻ ൫𝑊ሺ𝑥,𝑚+ 1ሻ− 𝑊ሺ𝑤,𝑚+ 1ሻ൯𝑑𝐹𝑤 ሺ𝑥ሻቃ

𝑊ሺ𝑤,𝑚ഥሻ= u(𝑤) + 𝛽ቂሺ1− ሻ𝑊ሺ𝑤,𝑚ഥሻ+ UሺTሻ+𝛼𝑒ሺ1− ሻ ൫𝑊ሺ𝑥,𝑚ഥሻ− 𝑊ሺ𝑤,𝑚ഥሻ൯𝑑𝐹𝑤 ሺ𝑥ሻቃ

𝑊ሺ𝑅ሺ𝑡ሻ,𝑚= 0ሻ= 𝑈(𝑡)

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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

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Calibrated Model

Decline of reservation wages over 23 months of UI eligibility in NJ

Reservation wage if unlimited UI

Reservation wage if no UI

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Note: Difference between blue and red lines is approximately the effect of UI on reservation wage.

0.21% decline per week

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.

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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

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Bonus Table: Descriptive Statistics for Universe, Stratified Sample, and Respondents

UI Weekly Exit Rate by UI Duration

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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 non-response. 14

The Ratio of the Weekly Wage in 2010To the Previous Weekly Wage

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Unemployment Rate in New Jersey and U.S., Seasonally Adjusted, 2008-10

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Sample and Data

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• 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 =

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In 12% of cases, the reservation wage was within5% of the previous wage

Cross-Sectional Analysis

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Reservation Wages over Unemployment Spell

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Little visible evidence of tendency for reservation wage to decline over the spell of unemployment.

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Reservation Wages over Unemployment Spell

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 of UI benefits exhausting or elapsing. 25

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Estimates for subsample looking for full-time work are still small, but statistically significant. Still driven by those with savings and older workers.

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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.

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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

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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

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What explains the shape of the acceptance function?

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1. Measurement error in offered wages and reservation wages

2. Non-wage amenities and other job characteristics

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What explains mass point at W=R?

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• 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)

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Why no bias comparing cross-section and panel? Simulation suggests small part of the variability.

Offer AcceptanceFrom 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

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Optimal UI Benefits

• Relate analysis to Shimer and Werning (2007)

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• 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 is the responsiveness of pre-tax reserva wage to the unemployment benefit, is the unemployment rate, and is the elasticity of the unemployment rate w.r.t. the level of UI benefits.

𝑅𝑏(𝑏∗,𝜏∗) = 𝑢𝑟(𝑏∗,𝜏∗)൬1+ 𝜀𝑢𝑟,𝑏(𝑏∗,𝜏∗)1− 𝑢𝑟(𝑏∗,𝜏∗)൰

𝑅𝑏(𝑏∗,𝜏∗) 𝜀𝑢𝑟,𝑏(𝑏∗,𝜏∗) 𝑢𝑟(𝑏∗,𝜏∗)

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Estimating the Right Hand Side

• Meyer (1990): 1% increase UI reduces job finding hazard by .88.

• Average unemployment rate in NJ 9.6%

• = 0.8

• Right hand side= .18 (slightly higher than Shimer and Werning)

𝜀𝑢𝑟,𝑏(𝑏∗,𝜏∗)

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Calibrated Model

Decline of reservation wages over 23 months of UI eligibility in NJ

Reservation wage if unlimited UI

Reservation wage if no UI

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Note: Difference between blue and red lines is approximately the effect of UI on reservation wage.

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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