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Royal Economic Society

Royal Economic Society

Royal Economic Society

John Moore President 2015-17

Royal Economic Society

Sargan Prize

Presented by Sir Richard Blundell

Royal Economic Society

Sargan Prize Koen JOCHMANS

Royal Economic Society

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

• f 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):
• Given this pattern, and assuming exogenous

wages, the elasticity must be very small

Age

Hours, Wages Hours Wage

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:
• It is much flatter than the measured wage

Wage Age Effective wage = Wage + HC return Wage HC return

Labor Supply and the Effective Wage

• Hours vs. Effective Wage over the Life-Cycle
• Hours look very responsive to effective wage

Wage, Hours Age Hours 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,

• n labour supply over the whole life:

Permanent Tax Increase 1% - Compensated

Age Labour Supply Elasticity Change in Wage Rate Change in After-Tax Wage 25

• 0.54
• 1.00%

30

• 0.58
• 0.08%
• 1.08%

35

• 0.64
• 0.14%
• 1.14%

40

• 0.76
• 0.20%
• 1.20%

45

• 1.02
• 0.26%
• 1.26%

50

• 1.58
• 0.40%
• 1.40%

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

• n 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
• nly 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 (Ct) – Work Hours (ht) 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

dropout high school college a1 0.303 0.275 0.244 a2 1.508 1.522 1.495 b 0.00025 0.000173 0.000168

Wage Process

• kt = Human Capital at age t
• 𝑙𝑢+1 = 𝑕 𝑙𝑢, ℎ𝑢, 𝑢 𝜁𝑢+1
• ln 𝑕 𝑙𝑢, ℎ𝑢, 𝑢 = 𝜇0 + 𝜇1𝑚𝑜𝑙𝑢

+ 𝜇2 max ℎ𝑢 − ℎ, 0 + 𝜇3 max (ℎ𝑢 − ℎ )2, 0 +𝜇4 𝑢 − 18 + 𝜇5(𝑢 − 18)2

• Both Hours and Age can increase wages, nesting

the Basic Life-Cycle Model

• Wage shock: log 𝜁𝑢 ~𝑂 −

1 2 𝜏2, 𝜏

• 𝑥𝑢 = 𝑙𝑢

𝑗𝑔 ℎ𝑢 ≥ 1500 85𝑙 𝑗𝑔 ℎ < 1500

Wage Process

• The return to work experience (λ2) is

greater for more educated workers

dropout high school college λ0 0.167689 0.177828 0.197579 λ1 0.917578 0.920000 0.918083 λ2 0.003932 0.004794 0.005809 λ3

• 0.000091
• 0.000090
• 0.000091

λ4 0.000126 0.000125 0.000300 λ5

• 0.000005
• 0.000005
• 0.000006

σ 0.1 0.09 0.1 𝒊 50 50 50

Fixed Cost of Work

Job Offer Probabilities

• Important so Elasticities are not distorted by

ignoring involuntary/frictional unemployment

• Logit with latent index Lt 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 (Pt-1)

Job Offer Probabilities

• 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

Dropout High School College m1 1.58 2.16 2.38 m2 0.10 0.07 0.00 m3

• 0.02
• 0.02
• 0.02

m4

• 0.06
• 0.06
• 0.06

m5

• 0.08
• 0.08
• 0.08

m6

• 0.008
• 0.04
• 0.03

m7

• 0.07
• 0.06
• 0.06

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

Social Security Benefits

• Actual benefits (SSInc) are obtained by

applying a highly progressive tax structure to AIME (3 brackets, 10%, 68%, 85%)

• “PIA” = 0.90 of AIME up to $9.8k

+0.32 of AIME from $9.8k to $44.9k +0.15 of AIME over $44.9k

• SSinc = f(PIA, age retired)
• There are details like a “tax” on earnings

while receiving SS that is rebated later (known as the “earnings test”)

Private Pensions

Progressive Taxation

Medical Costs, Survival, UB

• Medical expenditure is a quadratic in age,

with a kink at 65 (when Medicare begins)

• Survival probabilities taken from National

Vital Statistics Reports (Dec 2002) for Males

• There is an “unemployment benefit” (UB)

received by anyone with ht = 0, ht-1 >0 and SSt =0

• UB is currently set at ≈ $2500 (Note this is

net of any non-pecuniary job benefits)

Asset Accumulation

Bequests

State Variables

• Assets (At)
• Human Capital (kt)
• Accumulated SS benefit (AIMEt)
• Lagged participation (Pt-1)

Starting at 55:

• Lagged Pension (Pent-1)

Starting at 62:

• Lagged SS status (SSt-1)
• Age of Claiming SS (AgeSS)

Note: State space gets very big at age 62!!

Solution and Estimation

• We solve the DP problem using grids for

Assets, Human Capital and AIME

• We fit the model to CPS, HRS and CEX data
• n male household heads (or spouse of head)
• The CPS data is from 1996-2005:
• Oldest people born in 1922-1926

– Aged 70-74 in 1996

• Youngest people born in 1985-1989

– Aged age 16-20 in 2005

Solution and Estimation

• Estimation is by Method of Moments (MOM)
• Moments we fit …..

– CPS (1996-2005): Participation, Hours, Wage – CEX (2002-2006): Consumption/ 𝐺𝑏𝑛𝑗𝑚𝑧 𝑇𝑗𝑨𝑓 – HRS (1992-2012): Age of Claiming SS

• Exogenous processes: Medical Costs (MEPS, 1996-2009), Private

Pensions HRS (1992-2010)

Assessment of Model Fit

• Model has not quite converged, but the fit

looks quite good.

• We plot:

– Employment (Participation) – Hours Conditional on Employment – Total Hours (Un-conditional) – Median Full-Time Wage – Consumption

• By Age and Education Level

20 25 30 35 40 45 50 55 60 65 70 500 1000 1500 2000 2500 Age Annual hours worked

Average hours (unconditional on work)

Dropout (model) dropout (CPS) High school (model) High school (CPS) College (model) College (CPS)

20 25 30 35 40 45 50 55 60 65 70 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Age %employed

Labor force participation

Dropout (model) dropout (CPS) High school (model) High school (CPS) College (model) College (CPS)

20 25 30 35 40 45 50 55 60 65 70 500 1000 1500 2000 2500 Age Annual hours worked

Average hours conditional on employment

Dropout (model) dropout (CPS) High school (model) High school (CPS) College (model) College (CPS)

20 25 30 35 40 45 50 55 60 65 70 5 10 15 20 25 30 Age Hourly wage (1999 dollars)

Median full-time wage

Dropout (model) dropout (CPS) High school (model) High school (CPS) College (model) College (CPS)

20 30 40 50 60 70 80 90 0.5 1 1.5 2 2.5 3 3.5 4 4.5x 10

4

Age Average annual consumption (1999 dollars)

Average consumption

Dropout (model) dropout (CEX) High school (model) High school (CEX) College (model) College (CEX)

Labour Supply Elasticities

(predicted by the model)

• Frisch Elasticity by Age:
• Elasticity of Lifetime Hours wrt Permanent Tax

Age Dropout HS College 20 1.42 1.06

• 25

1.16 0.25 0.12 30 0.67 0.74 1.13 40 0.69 1.09 0.96 50 0.95 0.99 0.73 60 1.00 0.94 0.87 Dropout HS College

Hicks 0.62 0.66 0.73 Marshall 0.20 0.20 0.17

20 30 40 50 60 70

• 0.5

0.5 1 1.5 2 2.5 3

Hicks elasticities

Age Negative value of elasticities Dropout High school College

Age Elasticity

Extensive Margin Model Human Capital Model

Pure HC vs. Extensive Margin Model Predictions

20 30 40 50 60 70

• 0.5

0.5 1 1.5 2 2.5 3

Marshallian elasticities

Age Negative value of elasticities Dropout High school College

25 30 35 40 45 50 55 60 65 70

• 0.5

0.5 1 1.5 2 2.5 3 Age Negative value of elasticities

Hicks and Marshallian elasticities: College

Hicks elasticity Marshallian elasticity

20 30 40 50 60 70

• 0.5

0.5 1 1.5 2 2.5 3 Age Negative value of elasticities

Hicks and Marshallian elasticities: High school

Hicks elasticity Marshallian elasticity

20 30 40 50 60 70

• 0.5

0.5 1 1.5 2 2.5 3 Age Negative value of elasticities

Hicks and Marshallian elasticities: Dropout

Hicks elasticity Marshallian elasticity

Summary

• We added many important features to the basic

Imai-Keane (2004) life-cycle labor supply model:

– Corner Solutions – Retirement Behaviour – Search Frictions (Job Offer probabilities) – Progressive taxation

• Despite these extensions, the main message

is the same:

• Accounting for human capital leads to much

higher labour supply elasticities than earlier consensus would suggest.

Summary

• The Hicks elasticity of lifetime hours is

about 0.60 to 0.70, which is much higher than was typically found in earlier work (that ignored human capital).

• As a result, the welfare cost of taxation of

earnings is likely to be higher than previously thought.

Summary

• Economists should pay more attention to

how taxes alter incentives to acquire human capital

• If labour is a form of capital, arguments for

preferential tax treatment of returns to physical capital may no longer hold

Thank You!

Royal Economic Society