2. Introduction to Labor Supply
Labor facts
Men: labor force participation rates declined from 80% in 1900 to 72% in 2009.
Women: labor force participation rates rose from 21% in 1900 to 59% in 2009.
Hours worked fell from 40 to 34 per week during the same time period.

3. Measuring the Labor Force
Current population survey (CPS)
Labor Force = Employed + Unemployed
LF = E + U
Size of LF does not tell us about “intensity” of work.
Labor Force Participation Rate
LFPR = LF/P
P = civilian adult population 16 years or older not in institutions.

4. Measuring the Labor Force
Current population survey (CPS)
Employment-Population Ratio (percent of population that is employed).
EPR = E/P
Unemployment Rate
UR = U/LF

5. Measuring the Labor Force
Labor force measurement relies on subjectivity and likely understates the effects of a recession.
Hidden unemployed: persons who have given up in their search for work and have therefore left the labor force.
The employment rate (E/P) can be a better measure of fluctuations in economic activity than the unemployment rate.

6. Labor Force Participation Facts
Labor force participation (LFP) is greatest for all groups during the ages of 25 to 55.
LFP increases with education.
LFP has decreased for men over the age of 65 from 63% in 1900 to under 22% by 2009.

7. Labor Force Participation Facts
More women than men work part-time.
More men who are high school drop outs work than women who are high school drop outs.
White men have higher participation rates and hours of work than black men.

8. Average weekly hours of work of production workers, 1900-2010

9. Labor Force Participation Rates by Gender US, 1950–2010

10. Participation rate in Taiwan
by gender

11. Trend of participation rate
It is common that participation rate for men has been decreasing over time, while women’s participation rate has been increasing.
One limitation of the participation rate as a labor supply index is that it does not illustrate hours worked or full time / part time works. These distinctions are particularly important for females.

12. Participation rates in various countries
From 吳聰敏 《經濟學原理》 下

13. Participation rates in various countries
Women’s participation rate differs significantly across countries.
Variation in men’s participation rate is relatively small.

14. Reasons for not participating
Taiwan

15. Reasons for not participating
One limitation of unemployment rate is that it does not suggest the number or the proportion of discouraged workers.
In the case of Taiwan, we cannot observe any sharp jump in the number of non-participating individuals during recession periods and

16. Unemployment Rates for the Civilian Labor Force, US 1946–2009

17. Unemployment rate in Taiwan
by gender

18. Unemployment rate in various countries
From 吳聰敏 《經濟學原理》 下

19. Unemployment and Long-Term Unemployment, Selected European and North American Countries, 2007

20. Employment Distribution by Major Nonfarm Sector US, 1954–2010

21. Nominal and Real Hourly Earnings, U. S
Nominal and Real Hourly Earnings, U.S. Nonsupervisory Workers in the Private Sector, US, 1980–2009

22. Relationship among Wages, Earnings, Compensation, and Income

23. Static Labor Supply Model
Designed to describe how individuals make decisions about whether to work, and how much to work
Useful for discussing responses to changes in labor market conditions or policies
Stood the test of time – discussion goes back to 1930

24. Setup: Preferences
Preferences for leisure (time spent not working), and consumption (of items purchased)
Individuals maximize utility: max U(C,L,X)
Where C is consumption, L is leisure (any time spend not working), and X are individual attributes (such as number of children, family and cultural background)

25. Preferences assumed to take ‘usual’ form: quasi-concave
Preferences assumed to take ‘usual’ form: quasi-concave. This means both leisure and consumption exhibit diminishing marginal returns
Utility
Consumption
Utility
Leisure

26. These preferences lead to indifference curves with diminishing marginal rates of substitution
U=U*(L,C,X)
MRS= = slope of indiff curve
Consumption
Leisure

27. Setup: Constraints Let’s discuss model in terms of hours per week
Suppose the maximum number of hours available to work / week is 80: T = 80
Individuals earn w for each hour worked
Individuals can buy C for $1 per unit
Individuals have some income, even without working

28. The Budget Constraints
C = Y + w(T-L) (or) C +wL= Y + wT
C is consumption
Y is non-market income
W is hourly wage rate
T is maximum time (= 80)
H is hours worked
Y + wT = ‘full income’
How much you could consume if you worked as much as possible
H=(T-L)<=T
Can’t work more than 80 hours / week

29. On a Graph:
C =Y + w(T-L)
wT+Y
slope = -w Y
Leisure T

30. Full-time / Part-time Y T 40 60 w40+Y w20+Y wT+Y slope = -w Y Leisure
C =1(H=40)wH + Y, or
1(H=20)wH + Y, or Y
C =Y + w(T-L) Y T 40 60
w40+Y
w20+Y
wT+Y
slope = -w Y
Leisure T

31. Tax on wage income Leisure T slope = -w(1-taxrate) Y wT+Y slope = -w Y
C =Y+w(1-taxrate)(T-L )
C =Y + w(T-L)
Leisure T
slope = -w(1-taxrate) Y
w(1-taxrate)T+Y
wT+Y
slope = -w Y
Leisure T

32. Welfare Leisure T Y wT+Y welf Y Leisure T C =Y + w(T-L) slope = -wT
slope = -w Y
wT+Y
slope = -w
welf Y
Leisure T

33. Labour Costs (e.g. Daycare, transportation)
C =Y + w(T-L)
slope = -w Y
Y+LC
wT+Y
slope = -w Y
Leisure T

34. Kinks (e.g. Overtime) T Y 40 wT+Y Y Leisure T C =Y + w(T-L)T
slope = -wnt Y
slope = -wot 40
wT+Y
slope = -w Y
Leisure T

35. Solving the Model

36. Equilibrium of Nonparticipant
Slope=-W
Market Wage less than
the reservation wage
Income
Slope= -WR R R’ Y
A=E0
Corner Solution
Leisure

37. Equilibrium of a Participant
Income
Market wage exceeds the
reservation wage l0
W0h0+YN E0
Interior Solution R R’
Indifference curve tangent
To budget constraint YN T
Leisure

38. An Increase in Nonlabour Income on Supply leads to an increase in leisure if leisure is a normal good
C =Y1 + w(T-L)
C = Y2 + w(T-L) 35 T Y2
wT+Y1 Y1 40 T

39. An Increase in Nonlabour Income on Supply leads to an increase in leisure if leisure is an inferior good
C =Y1 + w(T-L)
C = Y2 + w(T-L) 45 T Y2
wT+Y1 Y1 40 T

40. The Effect of an Increase in Nonlabour Income on Labour Supply
Normal goods ­ income leads to ­ consumption of leisure (decrease in labour supply)
Inferior goods ­income leads to ¯ consumption of leisure (increase in labour supply)
Typically we assume leisure is a normal good

41. 3 things happen when an individual’s wage increases from w1 to w2
The ‘cost’ of leisure rises, relative to consumption: incentive to work more (substitution effect)
At previous wealth level, Y+w1T, the total amount of consumption or leisure that can be purchased is lower at new ‘costs’: C+w2L (1st income effect)
New wage increases wealth to Y+w2T, increasing wealth (2nd income effect)

42. 1) The substitution effect: L1 to L2
C +w1L=Y +w1 (T-L)
U = U1
C +w2L=(Y+sub) +w1 (T-L)
U = U1
New Optimal L, after all adjustments L2
wT+Y1 L1 T L1 T

43. 2) The 1st Income Effect: L2 to L3 (hold wealth constant)
C +w2L=(Y+sub) +w1 (T-L)
U = U1
C +w2L=Y +w1 (T-L)
1st Inc.
Effect L3 L2 L1 T L2 L1 T

44. 3) The 2nd Income Effect: L3 to L4 (the endowment effect)
C +w2L=Y +w1 (T-L)
C +w2L=Y +w2 (T-L) L4
2nd Inc.
Effect L3 L2 L1 T L3 L2 L1 T

45. 3 things happen when an individual’s wage increases from w1 to w2
The ‘cost’ of leisure rises, relative to consumption: incentive to work more (substitution effect)
At previous wealth level expressed as consumption, Y+w1T, the total amount of consumption or leisure that can be purchased is lower at new ‘costs’: C+w2L (1st income effect)
New wage increases wealth to Y+w2T, increasing wealth (2nd income effect)

46. The Slutsky Equation Describes Substitution Effect and Combined Income Effect
Sub.Effect
1st Inc.Effect
2nd Inc.Effect

47. The Slutsky Equation
Sub.Effect
Combined Inc.Effect

48. If Leisure Normal Good: The Slutsky Equation implies individuals are more likely to reduce work for those working lots, and vice versa L1 L2 T L2 L1 T

49. To Summarize so far:
Changes to an individual’s leisure/income budget constraint affect the relative cost of leisure versus consumption and/or overall potential income
Leisure is typically assumed a normal good
The size of the overall income effect depends on how much an individual works before the change
You should become completely familiar with drawing labour supply budget constraints under particular assumptions and anticipating large or small changes in labor supply from changes in these assumptions

50. Who are the unemployed?
Model assumes individuals choose freely a combination of consumption and leisure, given wage rate
Individual faces only one wage, that never changes
All unemployment is voluntary

51. What if only options are part-time work, or nothing?
Wants to work Lj
Ex. of
Someone under-employed
Involuntary unemployed
Can only work Lx
At least better than LA

52. What if only options are full-time work or nothing?
Can only work Lx
Ex. of
Someone over-employed
Wants to work LK
At least better than LA

53. What is involuntary unemployment?
Involuntary unemployment occurs when a person is willing to work at the prevailing wage yet is unemployed. Involuntary unemployment is distinguished from voluntary unemployment, where workers choose not to work because their reservation wage is higher than the prevailing wage.
Orley Ashenfelter’s view:
“A worker is involuntarily unemployed if she has identical preferences and skills as other workers and yet is unable to find the number of hours work that others have both chosen and managed to find”.

54. Labor Supply Curve
Relationship between hours worked and the wage rate.
At wages slightly above the reservation wage, the labor supply curve is positively sloped (the substitution effect dominates the income effect).
If the income effect begins to dominate the substitution, hours of work decline as the wage rate increases (a negatively sloped labor supply curve).

55. The Backward Bending Labor Supply Curve
Hours of Work
Wage Rate ($) 40 20 30 10 25

56. Labor Supply Elasticity
The labor supply elasticity (σ) measures responsiveness in hours worked to changes in the wage rate.
σ = Percent change in hours worked divided by the percent change in wage rate.
Labor supply elasticity less than 1 is inelastic as hours of work respond proportionally less than the change in wages.
Labor supply elasticity greater than 1 is elastic as hours of work respond proportionally more than the change in wages.

57. Estimating Labour Supply Responses, take 1
Typical model:
hoursi = B0 + B1wi + B2Xi + ei
But a $2 change in the wage rate might be a large change for some and a small change for others.
Better way…

58. Labour Supply elasticity measures the percentage change in time worked from a percentage change in wages

59. Estimating Labor Supply Responses, take 2

60. Is there omitted variables bias?

61. Problems with estimating supply elasticity
Unobserved skills, locations, tastes…
These factors could be related both to wages and hours
Can’t take log of 0
Another threat is “simultaneous bias”.

62. A more useful approach:

63. One example of natural experiment
In 1986, a reform of personal income tax system in the United States reduce tax rates from 50% to 28% for families with taxable incomes over $170,000.
The change was sudden.
The IE and SE combined is ambiguous.
One study compared labor supply increases, from 1984 to 1990, for married women in the 99th and 90th percentiles.

65. One example of natural experiment
It found that the labor force participation rate for women in the 99th percentile rose by 19.4 percent and that, if working, their hours of work rose by 12.7 percent during that period.
In contrast, both labor force participation and hours of work for women at the 90th percentile rose only by about 6.5 percent.

66. Policy Application: The Earned-Income Tax Credit
The EITC should increase labor force participation of nonworkers of targeted groups.
The EITC encourages some non-workers to start working and never encourages a worker to quit working.
The EITC produces an income effect.
Hours worked should change.

67. Application: Earned Income Tax Credit (EITC)
The EITC program makes income tax credits available to low-income families with at least one worker.
A tax credit of $1 reduces a person’s income taxes by $1, and in the case of the EITC, if the tax credit for which workers qualify exceeds their total income tax liability, the government will mail them a check for the difference.
Thus, the EITC functions as an earnings subsidy, and because the subsidy goes only to those who work, the EITC is seen by many as an income maintenance program that preserves work incentives.
In the US, it is now the largest cash subsidy program directed at low-income households with children.

68. The EITC and the Budget Line
Hours of Leisure
Consumption ($)
110
10,350
13,520
14,490
17,660
33,178 E J H G F
Net wage is 40% above the actual wage
Net wage equals the actual wage
Net wage is 21.06% below the actual wage

69. Estimating the effect of EITC
Eissa and Liebman – QJE 1996
The EITC tops off work for low income individuals, up to a certain amount
Substantial expansion of EITC for single women with children in 1986

70. 1986 change affected single parents only
Single moms with incomes between 11,000 and 15,432 became eligible for first time
15,432
11,000
6,500
5,000 L

71. Estimate average labor supply effect from introducing program

72. Can we simply compare average hours before and after?
Average Hours worked
Difference
Single Mothers
EITC before 86 reforms
EITC after 86 reforms
Any factors that lead to change in hours will be attributed to reform change

73. Estimate effect from ‘difference in the differences’
Alternative approach: compare change in hours for one group affected by reform and change in hours for another group not affected by reform
Difference after change
Average Hours worked
Single women, no children
Difference before change
Single Mothers
EITC before 86 reforms
EITC after 86 reforms
Estimate effect from ‘difference in the differences’
Since hours worked increased for group not affected by the same amount, estimate no effect from reform.

74. What Eissa and Liebman Find

75. Main Findings
EITC reforms increased single parent’s labor supply by 2.8 percentage points, and more for those with less than high school education
No evidence that reforms decreased hours worked among single parents already working

76. Application: (Un)Employment Insurance in Canada
Must have worked minimum 420 – 700 hours in same job (12 to 20 weeks at 35 hours per week)
Can receive EI from 14 weeks to 45 weeks, depending on unemp. rate in region
Basic benefit rate is 55% of average insured earnings, up to maximum $413 per week ($21,476 annual rate). This amount is taxable income.

77. Other points Can’t get EI if voluntarily quit job without just cause
Can’t get EI if fired from job
If start new, long-term job (PT or FT), must notify by law, and payments stop
Otherwise, payments end after 45 weeks, or EI maximum amount eligible paid

78. Graphical Analysis of UI
Assume wage $500 per week
UI is 55% of previous annualized earnings, no maximum
Must work at least 10 weeks to qualify
Ignore contributions for now

79. Budget constraint with UI
$26,000
slope = -225
slope = -500 Y
52 weeks 42

80. New Optimization with UI for someone working
Sub. Effect induces less work
$26,000
Supply would go down if leisure normal good
slope = -225
slope = -500 Y 42
52 weeks

81. New Optimization with UI for someone not working
UI induces some to work b/c earn more money for same hours worked
$26,000
slope = -500 Y 42
52 weeks 22

82. Some problems with this analysis
Can’t choose whether receive UI or not – must be laid off by employer
This creates incentive to co-ordinate with employer – pay me less and lay me off over and over again (increases utility)
Does not take into account costs – UI contributions about 3% of salary for employer and 3% for employee

83. Labor Supply over the Life Cycle
Wage rates change over the worker’s life (over the life cycle).
Wages are low when young.
Wages rise with time and peak around age 50.
Wages decline or remain stable after age 50.
The changes in wages over the life cycle are “evolutionary” wage changes that alter the price of leisure.

84. Theoretical Issues of Evolutionary Wages
A person will work more hours when wages are higher (i.e., the substitution effect tends to dominate the income effect).
The profile of hours of work over the life cycle will have the same shape as the age-earnings profile.
Intertemporal substitution hypothesis: people substitute their time over the life cycle to take advantages of changes in the price of leisure.

85. The Life Cycle Path of Wages and Hours for a Typical Worker
Wage Rate 50
Hours of work

86. Hours of Work over the Life Cycle for Two Workers with Different Wage Paths
Joe’s wage exceeds Jack’s at every age. Although both Joe and Jack work more hours when the wage is high, Joe works more hours than Jack if the substitution effect dominates. If the income effect dominates, Joe works fewer hours than Jack.

87. Labor Force Participation Rates over the Life Cycle in 2010

88. Hours of Work over the Life Cycle in 2010 (need figure 2-21)

89. Labor Supply Over the Business Cycle
Added-worker effect.
So-called “secondary” workers currently out of the labor market are affected by a recession because the main breadwinner becomes unemployed or faces a wage cut.
A secondary worker may choose to enter the labor force during these bad times
The labor force participation rate of secondary workers (i.e., the added worker effect) is counter-cyclical.

90. Labor Supply Over the Business Cycle
Discouraged worker effect.
Unemployed workers find it very difficult to find jobs during a recession, so they give up searching.
Discouraged workers exit the labor force during bad times.
The labor force participation rate of discouraged workers is pro-cyclical.

91. Labor Supply Over the Business Cycle
The discouraged worker effect dominates the added-worker effect, especially during recessions.
The Labor Force Participation Rate is procyclical

92. Retirement
Lifetime income is higher the longer a worker puts off retirement.
If pension benefits are constant, wage increases have a substitution and income effect, so lifetime income might not be altered.
An increase in pension benefits reduces the price of retirement, increasing the demand for leisure and encouraging the worker to retire earlier.

93. The Impact of the Social Security Earnings Test on Hours of Work
The Social Security earnings test (which taxed retirees when they earned more than $17,000 per year) generated the budget “line” that affects behavior in varying ways.
The repeal of the earnings test moved retirees to another budget line, as a result:
One retiree would not change his hours of work.
A second retiree would reduce his hours.
A third retiree might increase or decrease his hours, depending on whether substitution or income effects dominate.

94. The Impact of the Social Security Earnings Test on Hours of Work
Conclusions:
(1) Overall, the theory suggests that elimination of the Social Security earnings test is unlikely to substantially increase labor supply among retirees.
(2) The empirical evidence confirms the theoretical explanations: the labor supply effects of the repeal tended to be small.