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Labor supply

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  1. Labor supply

  2. Trends of participation rate • Women’s, especially married women’s, participation rate has been increasing in the past 6 decades. • Men’s participation rate, however, has been increasing. • Trends are shared by high income countries.

  3. Table 6.1 Labor Force Participation Rates of Females in the United States over 16 Years of Age, by Marital Status, 1900–2008 (Percentage)

  4. Trends of participation rate • Women’s, especially married women’s, participation rate has been increasing in the past 6 decades. • Men’s participation rate, however, has been increasing. • Trends are shared by high income countries.

  5. Table 6.2 Labor Force Participation Rates for Males in the United States, by Age, 1900–2008 (percentage)

  6. Trends of participation rate • Women’s, especially married women’s, participation rate has been increasing in the past 6 decades. • Men’s participation rate, however, has been increasing. • Trends are shared by high income countries.

  7. Table 6.3 Labor Force Participation Rates of Women and Older Men, Selected Countries, 1965–2008 (Percentage)

  8. Participation rate in Taiwan by gender

  9. 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 labour market conditions or policies • Stood the test of time – discussion goes back to 1930

  10. 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)

  11. Utility 0 Consumption Preferences assumed to take ‘usual’ form: quasi-concave. This means both leisure and consumption exhibit diminishing marginal returns Utility 0 Leisure

  12. MRS= = -slope of indiff curve U=U*(L,C,X) These preferences lead to indifference curves with diminishing marginal rates of substitution Consumption 0 Leisure

  13. 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

  14. 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 • Can’t work more than 80 hours / week

  15. On a Graph: C =Y + w(T-L) wT+Y slope = -w Y Leisure T 0

  16. w40+Y w20+Y Y 40 60 T 0 Full-time / Part-time C =1(H=40)wH + Y, or 1(H=20)wH + Y, or Y C =Y + w(T-L) wT+Y slope = -w Y Leisure T 0

  17. slope = -w(1-taxrate) w(1-taxrate)T+Y Y Leisure T 0 Tax on wage income C =Y+w(1-taxrate)(T-L ) C =Y + w(T-L) wT+Y slope = -w Y Leisure T 0

  18. slope = -w Y Leisure T 0 Welfare C =Y + w(T-L) wT+Y slope = -w welf Y Leisure T 0

  19. slope = -w Y Y+LC 0 Labour Costs (e.g. Daycare, transportation) C =Y + w(T-L) wT+Y slope = -w Y Leisure T 0

  20. slope = -wot slope = -wnt Y 40 T 0 Kinks (e.g. Overtime) C =Y + w(T-L) wT+Y slope = -w Y Leisure T 0

  21. Solving the Model

  22. U1 U2 Slope=-W R Slope= -WR Corner Solution A=E0 Y R’ T Equilibrium of Nonparticipant U0 Market Wage less than the reservation wage Income 0 Leisure

  23. U2 U1 U0 Interior Solution E0 Indifference curve tangent To budget constraint W0h0+YN R R’ l0 Equilibrium of a Participant Income Market wage exceeds the reservation wage YN T 0 Leisure

  24. Y2 35 T 0 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) wT+Y1 Y1 40 T 0

  25. Y2 45 T 0 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) wT+Y1 Y1 40 T 0

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

  27. 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)

  28. New Optimal L, after all adjustments L2 1) The substitution effect: L1 to L2 C +w1L=Y +w1 (T-L) U = U1 C +w2L=(Y+sub) +w1 (T-L) U = U1 wT+Y1 L1 T 0 L1 T 0

  29. 1st Inc. Effect L3 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) L2 L1 T L2 L1 T 0 0

  30. 2nd Inc. Effect L4 3) The 2nd Income Effect: L3 to L4 (the endowment effect) C +w2L=Y +w1 (T-L) C +w2L=Y +w2 (T-L) L3 L2 L1 T L3 L2 L1 T 0 0

  31. 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)

  32. The Slutsky Equation Describes Substitution Effect and Combined Income Effect Sub.Effect 1stInc.Effect 2ndInc.Effect

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

  34. If Leisure Normal Good:The Slutsky Equation implies individuals are more likely chance to reduce work for those working lots, and vice versa L1 L2 T 0 L2 L1 T 0

  35. 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

  36. 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

  37. 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

  38. 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

  39. What is involuntary unemployment? • If there is always someone out there willing to pay 50 cents if you shine their shoes, can you ever be involuntarily unemployed? • OrleyAshenfelter’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”.

  40. Why is unemployment viewed as a social concern? • Outcomes unequal: some able to choose optimal leisure/consumption bundle, others not • “Why don’t you accept the work available at lower wage rates?” • “Why don’t all other similarly situated workers have to do the same?” • It is this constraint on choice in the labor supply model imposed on some, but not all similar workers that defines involuntary unemployment

  41. You are offered w2 : your utility would be higher if you were offered w1 40 0 Involuntary unemployment Other workers with same preferences and skills offered w1 40w1 40w2 40 0 0 0

  42. What’s missing in this discussion? • Why would some workers with same skills be offered one wage, and others a different wage? • Perfect competition suggests differential should go away • We will come back to this later… (for now, consider reading Ashenfelter (1978)

  43. 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…

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

  45. Estimating Labour Supply Responses, take 2

  46. Is there omitted variables bias?

  47. 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

  48. A more useful approach:

  49. Labor supply model