week 2 slides 1

• Labor supply decisions can be understood through microeconomic and labor economic theory.
• A simple model of individual labor supply is introduced with three applications:
  • Labor supply in hours worked, measured at the intensive margin, describes how many hours a worker chooses.
  • Labor supply in work (or not), measured at the extensive margin, describes when a person decides to work or quit.
  • Labor supply in intertemporal substitution, measured dynamically, describes whether a person works more tomorrow than today.
• Important variables include:
  • Number of hours worked (H).
  • Work for pay (0/1).
  • Wage rates (W).

Rules, Preferences, and Utility

• Individuals gain utility from consuming goods (C) and leisure (L).
• A utility function U(C, L) indicates how much utility individuals receive from different combinations of C and L, with U increasing in both C and L.
• Utility function is well-behaved: indifference curves slope downward and don't intersect, increasing away from the origin.
• Indifference curve slope is marginal rate of substitution, measuring how much consumption a worker will forego for an extra hour of leisure.
• The slope gets flatter when a worker has less goods to consume and more time to devote to leisure, also known as a diminishing marginal rate of substitution.
• MUL and MUc represent the marginal utility of leisure and consumption, respectively.
  • MU₁ measures how utility changes with one more hour of leisure activities.
  • MUc measures how utility changes with one more dollar spent on consumption.
• The marginal rate of substitution (MRS) in consumption is: MRS = MUL / MUC

Prices

• Individuals buy consumer goods; the price for consumer goods is P (normalized to 1).
• Individuals buy leisure time against a price.
• Every hour an individual does not work is defined as a leisure hour.
• Leisure is another good that can be bought by not working.
• An individual receives an hourly wage (W) for every hour worked.
• Leisure price is the value of a working hour foregone (W).
• Both prices are exogenously determined (by assumption) and taken as given by the individual worker.

Budget and Time Constraints

• Individuals face a budget constraint and are assumed to spend their total income on consumer goods: PC = V + WH
  • Individuals have access to two income sources: labor income from work (WH), and non-labor income (V) unrelated to hours worked.
• Individuals face a day time constraint.
• T represents the maximum available time and each hour not worked is defined as leisure: T=H+L
• In many empirical applications on weekly labor supply T is often set at either 168 or 112.

Constraints

• The two previous constraints combined: PC = V + WH leads to PC = V + W(T – L) and PC + WL = V + WT
• V + WT, often coined full income, is all the income available if a person worked all the time.
• V + WT is exogenous and determined outside the model.
• C and L are endogenous and determined inside the model.
• The traditional two goods C and L can be bought at prices P and W.
• In the C – L plane, budget constraint slope transforms from PC + WL = V + WT to C = −(W/P)L + (V + WT)/P yielding ΔC/ΔL = -W/P.

Worker Choices

• Workers have preferences for C and L (represented by utility function).
• Workers face limitation in choosing C and L (imposed by budget constraint).
• Workers choose that combination of C and L to maximize utility given constraint.

Utility Maximization

• Utility maximizing workers choose a combination od C and L where the indifference curve and budget constraint are tangent to each other.
• At the point of tangency, slopes of the indifference curve and budget line match.
• The slope of the indifference curve: MUL∆L + MUc∆C =0 results in ΔC/ΔL = MUL / MUC.
• The slope of the budget line can be calculated using PC + WL = V + WT = ΔC/ΔL = -W/P.
• The first order condition is written as [MUL / MUC] = W / P with L=L*,C=C*.
• Individuals equate marginal benefit to marginal cost.
• An individual continues to buy consumption goods and leisure until the ratio of the marginal benefits of 2 goods equals the rate of the marginal costs (W/P).
• FOC gives us the optimal labor supply analytical H*(W, P, V,T).

Comparative Statics

• H*(W, P, V, T), allows us to predict worker's labor supply when either non-labor income or wages changes.
• Two questions:
  • How do hours of work change when non-labor income increases?
  • How do hours of work change when income increases?
• No clear cut answer, labor supply might fall or rise.

Non-Labor Income

• Leisure consumption will rise with income if leisure is a normal good, implying less hours of work.
• Leisure consumption will fall with non-labor income if leisure is an inferior good, implying more hours of work.
• Leisure is often assumed to be a normal good.

Wage Changes

• There is no clear cut answer: labor supply may again fall or rise.
• Higher wages mean more return to work, raising the price of leisure.
• Those with more expensive leisure will consume more goods and demand less leisure which means that workers will work more, which is the substitution effect.
• Since leisure is a normal good, higher incomes raise individuals’ labor income, leisure demand will rise, implying less hours of work, also known as income effect.
• The net effect comes down to:
  • If the substitution effect is greater than the income effect, an increase in wages leads to a rise in labor supply.
  • If the income effect is larger than the substitution effect, an increase in wages leads to a fall in labor supply.

Estimating Labor Supply Functions (Cobb-Douglas)

• Estimating the labor supply function, assuming it is analytically possible
  • Utility U(C, L) = ẞc In C + ẞ₁ In L, where βc + BL = 1
  • Budget line PC + WL = TW + V
• Estimate the marginal utility of leisure and consumption.
  • MUL = BL/L and MUc = ẞc/C
• Derive first order conditions such as the tangency condition
• Substitute this into the budget constraint
• Most labor supply studies estimate a version of the following model: Yi = αο + α₁W + α₂V + εi
• Only well-measured random variation in W₁ and V₁, the key labor supply parameters are identified.
• For most men, the labor supply elasticity is negative (income effect dominates substitution effect);
• For most women, the labor supply elasticity is positive (substitution effect dominates income effect);
• For most men and women, the income effect is negative (as seen in the lottery studies).

The Decision to work

• The wage offer must be above an individuals reservation wage for them to want to work.
• There is some reservation wage (WR) at play for the worker to start working.
• If wage offer is below, the worker refuses to work, therefore if W < WR, the worker works zero hours.
• If wage offer is above reservation wage, the worker works at that wage, therefore if W > WR, the worker works, where hours decided depend on marginal benefits and costs.
• A worker's reservation wage is determined by the slope of the indifference curve where a worker is indifferent between working and not working,
  • MUL / MUC = WR/P

Comparative Statics

• Wage offer encourages working, when high enough to exceed reservation wage, thus working occurs.
• More working discourages non-working, therefore people rather stick to reservation wages.

Testing Labor Supply Models

• EITC is a natural experiment.
• A good experiment to see what happens to changes budget constraint to workers.
• Eissa and Liebman evaluate the 1986 EITC reform that made EITC more generous.
  • steeper phase-in rate from 11 to 14 percent
  • higher maximum credit for wider earnings window
  • lower phase-out rate from 12 to 10 percent
• Eissa and Liebman distinguish two groups: treatment group and control group.
  • KIDS = 1, having children (treatment group) while KIDS = 0, being childless (control group)
• They identify two periods: before and after the EITC reform
  • POST = 1 is set for after the reform years, and POST = 0 for before the reform
  • There is the EITC treatment, if, and only if, in treatment group
  • KIDS × POST = 1 describes mothers are treated, only after the reform; KIDS × POST = 0 is for when mothers before, all childless women before and after
• A simple difference-in-differences setup (DD)
  • DD identifies labor supply response if the common/parallel trend assumption holds.

EITC Predictions

• At extensive margin, the EITC encourages non-working mothers to work.
• At intensive margin, the EITC encourages most working mothers to work less.
• In the phase-in region, an increased wage means most mothers work more.
• During constant tax credit, most mothers work less (income effect).
• Phase-out means lower wage means mothers work less (substitution and income effects each other).
• Outside credit region, some work less (to get credit).