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Royal Economic Society Sargan Lecture Michael Keane Labor Supply: Estimating the Roles of Human Capital and the Extensive Margin Chair: James Banks
Royal Economic Society
Royal Economic Society
Labour Supply: the Roles of Human Capital and the Extensive Margin Michael P. Keane University of Oxford Royal Economic Society Sargan Lecture March 30, 2015
Labour Supply is Important For many reasons, for example: • (1) Optimal Tax rates are Lower to the extent that Labour Supply Elasticities are Larger • (2) Macro models require labour supply elasticity in a certain range to explain the data • (3) Can differences in tax rates explain differences in hours worked across countries? • And so on….
The Labour Supply Literature • Until recently, there was a clear consensus in the economics profession that labor supply elasticities are small: • Saez, Slemrod and Giertz (JEL, 2012): “…the profession has settled on a value … for [the compensated elasticity] close to zero … This implies that the efficiency cost of taxing labor income … is bound to be low …”
The Labour Supply Literature • Classic papers estimating the Frisch elasticity of inter-temporal substitution: • MaCurdy (JPE, 1981) – 0.15 • Browning, Deaton and Irish (1985) – 0.09 • Altonji (JPE,1986) – 0.17 • Blundell and Walker (1986) – 0.03 As Frisch > Hicks > Marshall, this implies the Hicks (compensated) elasticity is small as well.
Challenging Conventional Wisdom • Recently the consensus has started to break down, for two main reasons: • (1) Models with Human Capital generate much larger elasticity estimates • (2) Accounting for the “ extensive margin ,” – including participation and retirement – also leads to larger elasticities
The Human Capital Argument: • Most existing estimates of labour supply elasticities are biased downward… • Because they treat wages as exogenous – ignoring the fact that work experience builds human capital • See Imai and Keane (IER, 2004), Keane (JEL, 2011), Keane-Rogerson (JEL, 2012)
Why are Elasticity Estimates So Small? • Hours vs. Wages over the Life-Cycle (Men): Wage Hours, Wages Hours Age • Given this pattern, and assuming exogenous wages , the elasticity must be very small
The Problem with Most Prior Work: Assumes Wage = Price of Time • But the after-tax wage is not the price of time • If you work more hours (today) you get both: 1.The after-tax wage rate (today) 2.The increase in future earnings due to the human capital gained from work experience • “ Effective Wage ” = After-Tax Wage + Human Capital Gained by Working • Heckman (‘76 ), Shaw (‘89), Imai - Keane (‘04)
The Effective Wage Rate • Effective Wage over the life-cycle: Effective wage = Wage Wage + HC return Wage HC return Age • It is much flatter than the measured wage
Labor Supply and the Effective Wage • Hours vs. Effective Wage over the Life-Cycle Wage, Effective Wage Hours Hours Age • Hours look very responsive to effective wage
Imai-Keane model predictions • Imai-Keane (IER, 2004) extended the basic life-cycle model to include human capital • Intuitively, their approach can be interpreted as regressing hours on the effective wage • It generates a compensated elasticity with respect to (unanticipated) permanent tax changes of 0.70 . • Comparison: Chetty (ECMA, 2012) pools estimates from many existing studies, most based on short-run effects of tax reforms, and obtains a Hicks elasticity of 0.58 .
How Elasticities Vary with Age • With Human Capital labour supply elasticities are no longer fixed parameters. • Elasticities grow strongly with age: • Young people are less responsive to the wage rate, as human capital concerns are important for them. • According to the Imai-Keane model: • Hicks = 0.45 at ages 30-40 • Hicks = 1.45 at age 55.
Human Capital and Long Run Tax Effects • If work experience builds human capital it implies effect of taxes on labour supply will grow over time: • Consider the effect of a permanent 1 point tax rate increase in the Imai-Keane model, on labour supply over the whole life:
Permanent Tax Increase 1% - Compensated Age Labour Supply Change in Change in Elasticity Wage Rate After-Tax Wage 25 -1.00% -0.54 30 -0.58 -0.08% -1.08% 35 -0.14% -1.14% -0.64 40 -0.76 -0.20% -1.20% 45 -1.02 -0.26% -1.26% 50 -0.40% -1.40% -1.58 55 -2.66 -0.72% -1.72% 60 -3.86 -1.50% -2.50% 65 -5.84 -2.32% -3.32%
Effect of Permanent Tax Changes • The effect of a tax increase grows over time • It slows down the rate of human capital accumulation, creating a “ snowball ” effect on after-tax wages • Seeing a small short-run effect may trick us into thinking elasticities are small
The Extensive Margin Argument • Much prior work on labour supply looks only at employed men. • Labour Supply can be very responsive on the participation margin, even if work hours are not very responsive for the employed. • What matters is the density of workers who are close to their reservation wage
The Extensive Margin Argument • People who are likely to be close to indifferent between working and not working: • The Young (Low wages) • The Old (Declining Health and Wages) • Married Women with Kids (High value of home production)
The Extensive Margin Argument Some key papers in this literature: • French (RES, 2005) • Change and Kim (IER, 2006) • Rogerson and Wallenius (JET, 2009) • Erosa, Fuster, Kambourov (RES, forthcoming )
Contrasting effects of Human capital vs Extensive margin • Extensive margin model implies high elasticities for the Old and Young • Human capital model implies elastic labor supply for the Old • But it implies small elasticities the Young – The Young are not very concerned about the current wage, as it is just a fraction of their “effective wage,” which also includes human capital investment returns
Integrating the Two Ideas “Labour Supply: the Roles of Human Capital and the Extensive Margin” by Michael Keane (Oxford) Nada Wasi (Michigan) March 2015
Model Structure • We develop a model that includes: – Human Capital (Learning by Doing) – Discrete Choice of Hours – Job Offer probabilities – A Realistic Specification of the US Social Security System (Retirement Benefits) – Private Pensions and Health Expenditure – Saving and Bequests – Progressive taxes
Model Structure • Choice Set – Consumption ( C t ) – Work Hours ( h t ) ϵ [0, 500, 1000, 1500, 2000, 2500] – Whether to apply for social security benefit • Ages 62 to 74 only • Must start to collect at 75 • Annual decision period, where: – t =16, 18 or 22 is school leaving age • Corresponding to HS dropout, HS grad or college – t = 91 is the terminal period
Model Structure high dropout school college a 1 0.303 0.275 0.244 1.508 1.522 1.495 a 2 0.00025 0.000173 0.000168 b
Wage Process • k t = Human Capital at age t • 𝑙 𝑢+1 = 𝑙 𝑢 , ℎ 𝑢 , 𝑢 𝜁 𝑢+1 • ln 𝑙 𝑢 , ℎ 𝑢 , 𝑢 = 𝜇 0 + 𝜇 1 𝑚𝑜𝑙 𝑢 + 𝜇 2 max ℎ 𝑢 − ℎ, 0 + 𝜇 3 max (ℎ 𝑢 − ℎ ) 2 , 0 +𝜇 4 𝑢 − 18 + 𝜇 5 (𝑢 − 18) 2 • Both Hours and Age can increase wages, nesting the Basic Life-Cycle Model 1 2 𝜏 2 , 𝜏 • Wage shock: log 𝜁 𝑢 ~𝑂 − • 𝑥 𝑢 = 𝑙 𝑢 𝑗𝑔 ℎ 𝑢 ≥ 1500 85𝑙 𝑗𝑔 ℎ < 1500
Wage Process dropout high school college λ 0 0.167689 0.177828 0.197579 λ 1 0.917578 0.920000 0.918083 λ 2 0.003932 0.004794 0.005809 λ 3 -0.000091 -0.000090 -0.000091 λ 4 0.000126 0.000125 0.000300 λ 5 -0.000005 -0.000005 -0.000006 σ 0.1 0.09 0.1 𝒊 50 50 50 • The return to work experience ( λ 2 ) is greater for more educated workers
Fixed Cost of Work
Job Offer Probabilities • Important so Elasticities are not distorted by ignoring involuntary/frictional unemployment • Logit with latent index L t where: • All parameters differ by education level • Offer probs differ in flexible way with age (notches at 23,30,40,50,59) and lagged work ( P t-1 )
Job Offer Probabilities Dropout High School College m 1 1.58 2.16 2.38 m 2 0.10 0.07 0.00 m 3 -0.02 -0.02 -0.02 m 4 -0.06 -0.06 -0.06 m 5 -0.08 -0.08 -0.08 m 6 -0.008 -0.04 -0.03 m 7 -0.07 -0.06 -0.06 • Offer probs higher for more educated types • From age 16 to 23 offer probabilities rise substantially for the lower education types • Note: Preliminary – we have not let many of these parameters differ by type yet
Social Security Benefits • People are eligible to start collecting SS “retirement benefits” at 62 • They can delay, with (roughly) actuarially fair adjustments, until age 70 • One can keep working while receiving SS benefits, so “claiming SS” and “retirement” are two distinct decisions
Social Security Benefits
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