Labor Economics: Supply, Demand, and Market Equilibrium
Labor Economics
Lecture 1 (Ch1)
Labor Supply
Definitions of Unemployment and Other Statistics
In the Current Population Survey, people aged 16 and greater are classified into the following three categories:
- Employed: In the reference week, the person must work at least one hour with pay, or work at least 15 hours in a non-paid job (family farm, etc.).
- Unemployed: The person is on temporary layoff from a job, or has no job but is actively seeking a job.
- Out of the labor force: Neither employed nor unemployed. (This includes students, homemakers, people who stopped looking for a job because it is too difficult to find one, etc.)
Given the above definitions, we define:
- In the labor force = Either employed or unemployed.
- Labor force participation rate = LF/P
- Unemployment rate = U/LF
- Employment rate = E/P
Some Issues with These Statistics
- Labor force participation rate: This does not consider the intensity of work.
- Unemployment rate: If an unemployed worker gives up looking for a job, this person will be considered out of the labor force, thus not counted as unemployed (hidden unemployed). The unemployment rate may understate the true depth of a recession.
- Employment rate: This statistic mixes unemployed workers with those who have no intention to work, such as retirees or students.
The Model of Labor-Leisure Choice
If you work a lot, you will earn a lot of money, but you will have little time for leisure. If you spend all of your time on leisure, you will earn no money.
So, this is the trade-off that dictates your labor supply decision.
Consider you consume two goods:
- Leisure (L) & other goods (C)
For simplicity, let us define leisure as the time you are not working (and not sleeping).
Your utility can be expressed as
U = f(C, L)
The Indifference Curve
The combination of C and L that keeps the utility constant:
- Downward sloping
- A higher indifference curve indicates higher utility
- We assume it is convex to the origin
Shapes of Indifference Curves
The Budget Constraint
C = wh + V ———————(1)
Where C is the consumption of goods other than leisure, w is the hourly wage rate, h is the hours worked, and V is the non-labor income (such as a spouse’s income).
Since leisure is defined as the time you are not working, we have
h = T – L ———————————(2)
Where T is the total hours available, and L is the hours of leisure you take.
Combining (1) and (2), we have:
C = w(T – L) + V
So
C = (wT + V) – wL —————————(3)
Graphing the Budget Constraint
The Hours of Work Decision
Consider the following example:
- W = $10 per hour
- T = 110 hours (non-sleeping time per week)
- V = $100
You choose the combination of C and L on the budget line that maximizes utility.
What Happens to Hours of Work When Non-Labor Income Changes?
We assume that leisure is a normal good. Thus, when non-labor income increases, the consumption of leisure increases, and the hours worked decreases.
What Happens to the Labor Supply if the Wage Rate Changes?
We can better understand the change in the consumption bundle in two steps:
- In case (a), the substitution effect is not large enough to dominate the income effect, so the change in wage increases leisure (and decreases the hours worked).
- In case (b), the substitution effect is large enough to dominate the income effect, so the change in wage decreases leisure (and increases the hours worked).
So, whether an increase in wage increases hours worked or not depends on the relative size of income effects and substitution effects.
To Work or Not to Work
What Happens if the Wage Rate Changes?
Labor Supply Curve
This is a curve that shows the relationship between hours worked and the wage rate.
At wages slightly above the reservation wage, we assume the labor supply curve is positively sloped (the substitution effect dominates the income effect).
If the income effect begins to dominate the substitution effect, we assume hours of work decline as the wage rate increases (a negatively sloped labor supply curve).
The Backward Bending Labor Supply Curve
Labor Supply Elasticity
We can estimate the labor supply elasticity by estimating:
Log(h) = β0 + β1log(w) + β(other variables) + error
Past studies indicate that the elasticity for labor supply of men is negative, and is about -0.1.
Past studies indicate that the elasticity for labor supply of women is positive, and is about 0.2 (though the estimate varies considerably among studies).
Labor Supply of Women
What Explains the Increase in Female Labor Force Participation?
According to the theory of work-leisure choice, an increase in wage rate will increase labor force participation.
The theory also predicts that a decrease in reservation wage increases labor force participation.
What would have decreased women’s reservation wage?
- A decrease in the number of children. This may reduce the reservation wage, thus increasing female labor force participation (although the direction of the causality can run in both ways).
- The power of washing machines! (and vacuum cleaners)
- The “three Jingi (godly instruments)” of 1950s in Japan.
There is strong evidence that these time-saving technologies have increased women’s labor force participation considerably.
Reference: Greenwood, Jeremy, Ananth Seshadri, and Mehmet Yorukoglu, “Engines of Liberation,” Review of Economic Studies, (2004)
- A greater supply of better men (a new type, who will be better husbands)!
The presence of men who cooperate and are productive in housework makes investing in market skills more attractive for women.
Such men are increasing (believe it or not), and there is some evidence for it.
Reference: RAQUEL FERNA´NDEZ, ALESSANDRA FOGLI, and CLAUDIA OLIVETTI, “MOTHERS AND SONS: PREFERENCE FORMATION AND FEMALE LABOR FORCE DYNAMICS” Quarterly Journal of Economics, Nov, 2004
Policy Application: Welfare Programs and Work Incentives
There are various welfare programs:
- Aid to Families with Dependent Children
- Temporary Assistance for Needy Families
- Supplemental Nutrition Assistance Program (the Food Stamps)
- and so on.
There are critics of these welfare programs, and most of the critics were motivated by the conjecture that they foster dependency on public assistance.
Thus, it is important to understand the nature of work disincentive effects of such programs.
A Hypothetical Example: A Take-It-or-Leave-It Cash Grant
Consider a hypothetical example of a welfare program, where the government pays a person a cash grant of $300 per week as long as this person is unemployed. Once this person finds a job, he loses this cash grant.
Exercise: Draw the budget constraint of a person, assuming the following.
- If the person finds a job, his hourly wage will be $10 per hour (i.e., w=10)
- The weekly time-endowment (i.e., non-sleeping time) is 110 hours (i.e., T=110)
- Non-labor income is zero (i.e., V=0).
Answer
The Effect of This Cash Grant on Labor Supply
If there were no grant, the person would work some hours.
But in the presence of the grant, the person will not work at all.
Thus, there is a clear work disincentive effect of this type of grant.
Exercise
How can the above welfare program be improved in a way that encourages the person to work, and at the same time be able to assist the person financially?
Some Answers
One idea is the phase-out scheme, in which the amount of grant is gradually reduced as the person starts to earn income, instead of suddenly eliminating the grant.
Another idea is to give an ‘earned income tax credit’. This scheme will provide a grant in which the amount is equal to some percentage of the earned income. This scheme will be discussed later in this handout.
The Phase-Out Scheme
Now, consider the following phase-out scheme.
A person is given a cash grant of $300 if the person is unemployed. If the person finds a job, then the amount of grant is reduced by 50 cents for each dollar earned in the job.
Exercise: Draw the budget constraint for this person. Assume T=110, w=$10, and V=0
Answer
Thus, for the first 60 hours of work per week, the income increases by $5 for each hour he works.
Thus, this particular phase-out scheme is equivalent to taxing earnings at a tax rate of 50%.
When he works 60 hours per week, the grant is completely eliminated, so the budget constraint becomes the same as the original one.
Exercise: Then, what are the effects of the phase-out grant scheme on labor supply?
Answer: The Effect of Phase-Out Scheme Grant on Labor Supply
So, in this example, the person supplies fewer hours in the presence of the phase-out grant scheme.
But, is the effect always negative (decrease labor supply)?
In fact, the effect is always negative (but less so than the take-it-or-leave-it grant).
(Explanation of the previous slide) If you draw the line parallel to the original budget constraint, you get point C. Point C should be to the right of point A, since leisure is a normal good. And, this point should be to the left of point B because the original budget line is steeper than the budget line with the phase-out grant. This means that point B is always to the right of point A, which means that the person always works less in the presence of the phase-out grant.
Of course, if the person’s utility-maximizing hours worked is greater than 60 in the absence of this phase-out grant, this person will be unaffected by the phase-out grant.
Many Welfare Programs Use the Phase-Out Scheme.
- Aid to Families with Dependent Children (AFDC) in the USA (until 1996)
The amount of this grant varies across states. The amount is reduced by 67 cents for each dollar earned in the labor market.
The median amount of grant in 1994 was $366.
The empirical effects of AFDC on labor supply vary among studies, ranging between a 10% to 50% reduction in hours worked.
In 1996, this program was replaced by the Temporary Assistance for Needy Families.
- Seikatsu hogo seido (Income assistance program) in Japan.
This program first computes the ‘minimum living income’ (Saitei seikatu hi) depending on the location of residency, the number of dependents, etc.
Then, if the household income falls short of the minimum living income, the government provides a grant equal to the difference between the minimum living income and the actual household income.
For example, consider a single mother with two children (2 years old and 4 years old). Then, the minimum monthly living income is 215,110 yen. And if her monthly income is 120,000 yen, then she will get 95,110 yen from the government.
This also means that, if her income increases by 1 yen, the amount of grant will be reduced by 1 yen.
Thus, the rate of phase-out is extreme: it is equivalent to taxing her income at 100%. In fact, the budget constraint for this person is almost equivalent to a take-it-or-leave-it grant.
There are very few studies estimating the work disincentive effects of this grant (so this may be a good thesis topic).
The Earned Income Tax Credit
Another idea to assist economically disadvantaged persons while minimizing the work disincentive effect is the Earned Income Tax Credit.
This has actually been implemented in the US since 1975, and is currently the largest cash-benefit program in the US.
The actual Earned Income Tax Credit is the following.
- It is given to households with children.
- For convenience, consider a single-mother-household with children. She is given 40% of tax credits (i.e., each dollar she earns, she gets 40 cents of assistance from the government) as long as her annual earning is less than $11,000.
- This means she can get a maximum of $4,400.
- If her annual earning reaches $11,000, the maximum amount is held constant until her annual earning reaches $14,370.
- Once her annual earning reaches $14,370, each additional dollar earned in the labor market reduces the grant by 21.06 cents.
Exercise:
Exercise: Draw a budget line under the Earned Income Tax Credit scheme. Assume T = 110hours*52weeks, w=$10, V=0.
The Effect of the Earned Income Tax Credit on Labor Supply
The effects are different depending on the shape of the indifference curve.
There are several possibilities, which are listed below.
The Empirical Effects of the Earned Income Tax Credit on Labor Supply?
First of all, how would you estimate such an effect?
Answer
If you have a control group, then you can apply the Difference-in-Difference estimator.
For example, let (work)it be the dummy variable indicating if the person is working at time t. Let (After)it be the dummy indicating the period after the Earned Income Tax Credit was implemented, and (Treat)i be the treatment group dummy.
Then you can estimate
(Work)it = β0 + β1(Treat) + β2(After)
+β3(Control)(After)+e
Then, β3 will show the effect of EITC on labor force participation.
Eissa and Liebman “Labor supply response to the Earned Income Tax Credit” (Quarterly Journal of Economics 1996, vol.11) estimated the effects that the 1986 expansion in the EITC had on female labor supply using the difference-in-difference approach.
The control group is single women without children. The treatment group is single women with children.
TAX EXEMPTION
Taxable income ＝ Salary － Tax exemption
Tax exemption Amount of tax
Currently, various tax exemptions are given, depending on the household’s circumstances.
THE SPOUSAL TAX EXEMPTION SYSTEM IN JAPAN
Consider a household where the husband is the primary income earner, and the wife is the secondary income earner (which is typical in Japan)
When the wife’s income is below a certain threshold, the husband is given a tax exemption.
This system is to reduce the tax burden for a household where the wife is dependent on the husband’s income.
PROBLEMS WITH EXEMPTION FOR SPOUSES HAVE BEEN POINTED OUT
The spousal tax exemption system may cause a work disincentive for married women.
It is widely believed that married women are attempting to maintain their income within the threshold where their husband can claim the spousal tax exemption.
Because of this possibility, there has been pressure to reduce or eliminate the spousal tax exemption.
- The Tax Commission (Seihu Zeisei Chousa Kai) recommended in 2003 to reduce the amount of the spousal tax exemption.
- The possible work disincentive effect was one of the reasons.
- In 2004, the government considerably reduced the spousal tax exemption (this will be discussed later).
- In 2008, the Tax Commission proposed to entirely eliminate the spousal tax exemption. This was not implemented, however.
THE PURPOSE OF THE LECTURE
- Understand the Japanese spousal tax exemption system, and how it might cause work disincentive effects.
- Discuss the empirical evidence of the actual effects of the spousal tax exemption.
THE SPOUSAL TAX EXEMPTION SYSTEM IN JAPAN
Currently there are two spousal tax exemptions in Japan.
- The Exemption for Spouses
- The Special Exemption for Spouses (Introduced in 1987)
This system has experienced several changes in the past.
The best way to understand is to follow the history of this system.
The Exemption for Spouses (Until 1986, this was the only spousal exemption.)
THE WIFE’S BUDGET CONSTRAINT UNDER THE EXEMPTION FOR SPOUSES IN 1986
Consider a household where the husband’s income is 1000man yen
There are several tax exemptions that this husband can claim
Employee tax exemption ＝２１0man yen
The basic tax exemption ＝３5man yen
Social Security payment deduction ≈ ８５man yen
Spousal Tax Exemption ＝ The amount depends on the wife’s income
Then, the husband’s taxable income
＝ １０００－（２１０＋３５＋８５＋Spousal tax exemption）
＝ ６７０－Spousal Tax Exemption
- When the wife’s income <>１００man yen, the Exemption for Spouses= 35man yen
The husband’s taxable income＝ ６７０－３５＝６３５
- When the wife’s income>100man yen, the Exemption for Spouses = 0
The husband’s taxable income＝ ６７０－０＝６７０
LET’S COMPUTE THE AMOUNT OF TAX THE HUSBAND PAYS
GRAPHING THE WIFE’S BUDGET CONSTRAINT
Wife’s budget constraint
After tax household Income = Wife’s after tax income
+ Non labor income
EXERCISE
Assume the wife’s before tax wage rate is 1000 yen per hour, and the husband’s before tax annual income is 1000man yen. Given the spousal tax exemption, and income tax schedule, draw her budget constraint. Assume the annual time endowment is 5720 hours (110hours*52 weeks).
Note that, a worker can claim the employee tax deduction (65man yen) and the basic tax deduction (35man yen). Thus, she will not pay her income tax until her income exceeds 100man yen.
(Employee tax deduction will increase as her income increases, but it stays flat until her income is 162.5man. We ignore prefectural taxes and other things to make the matter simple.)
When the wife’s before tax income exceeds 100man yen, the household income suddenly drops by about 10man yen.
Due to this drop, the possibility that wife will stop working at the income equal to 100man yen was pointed out.
In fact, the income distribution of married women had a significant cluster at income equal to 100man yen.
This cluster of the data was the famous 100man yen ceiling.
EXERCISE
Propose a modification to the spousal tax exemption schedule that would have less work disincentive effects.
THE INTRODUCTION OF THE SPECIAL SPOUSAL EXEMPTION (IN １９８７)
In order to solve the problem of the sudden drop in the after tax household income, the Special Exemption for Spouses was introduced in 1987.
The total amount of exemption is reduced gradually as the wife’s income increases.
This solves the problem of the sudden drop in the after tax household income. See next slides:
HOW THE INTRODUCTION OF THE SPECIAL EXEMPTION FOR SPOUSES CHANGED THE WIFE’S BUDGET CONSTRAINT?
Now, let’s draw the budget constraint for a married woman after the introduction of the Special Exemption for Spouses.
We continue to assume:
- The wife’s wage rate is 1000yen per hour
- The husband’s income is 1000man yen annually.
COMPUTING THE AFTER TAX HOUSEHOLD INCOME
THE CHANGES IN SPOUSAL TAX EXEMPTION SYSTEM AFTER 1987
There have been several changes
- 1995: The amounts of exemptions were slightly increased. Also, the threshold income where the Exemption for Spouses was cut was changed to 103man yen.
After this reform, 100man yen ceiling began to be called the103man yen ceiling.
- 2004: The added-on part of the Special Exemption for Spouses was eliminated.
１９９５年 THE CHANGE IN SPOUSAL TAX EXEMPTION SCHEDULE
Amount of both the Exemption for Spouses (ES), and the Special Exemption for Spouses (SES) were slightly increased.
The threshold income where the ES is cut was changed to 103man yen
２００４年 SPECIAL EXEMPTION FOR SPOUSES WAS SIGNIFICANTLY REDUCED
The Added-on part of the Special Exemption for Spouses were eliminated
2004~PRESENT. THIS IS THE CURRENT SPOUSAL TAX EXEMPTION SCHEDULE.
LET’S TALK ABOUT THE EFFECTS OF SPOUSAL EXEMPTION SYSTEM ON THE MARRIED WOMEN’S LABOR SUPPLY
Theoretically, the spousal tax exemption system will cause work disincentive effects.
The graph in the next slide illustrates the work disincentive effects (for the case of the spousal tax exemption schedule between 1995 to 2003).
THE EFFECTS OF SPOUSAL TAX EXEMPTION SCHEDULE (1987~2003)
Spousal exemption will increase the amount of leisure, and consequently reduces the hours worked.
Thus, even if the problem of the sudden drop in household income was solved, the spousal exemption schedule always has work disincentive effects (though the work disincentive effects would be smaller than if there were the sudden drop).
Now, let us take a look at the income distribution of married working women over time.
MARRIED WOMEN’S INCOME DISTRIBUTION
1993~1994 data (From Japanese Panel Survey of Consumers)
Even if the problem of sudden drop in the household income at 100man yen was solved a long time ago, there still is a cluster of women at income around 100man yen.
SOME STUDIES ESTIMATING THE WORK DISINCENTIVE EFFECTS OF SPOUSAL TAX EXEMPTIONS
- Kantani (1997): 35% reduction in hours worked
- Akabayashi (2006): 5.5% reduction in hours worked.
- Takahashi (2010): 4% reduction in hours worked among the married women who are in income between 70man to 103man. The segment choice probabilities are extremely small, thus, the overall effect is very small.
- Sakata & McKenzie （２００６）: 2004 elimination of the add-on part of the Special Exemption for Spouses did not increase hours worked. But it had some effect on the labor force participation of married women.
WHY IS THERE STILL A CLUSTER OF WOMEN AT 100MAN YEN?
There is no sudden drop in household constraint after 1987.
Why is there still a cluster of married women at income equal to 100man yen?
Possibility 1:
Husbands often received a fringe benefit from his company, called spousal allowance. This allowance is suddenly cut when the wife’s income exceeds 103man yen. This creates an incentive for wives to stop working at 103man yen.
This is possible. However, if this is the case, then we will not be able to claim that the spousal tax exemption is responsible for the 103man yen ceiling.
Possibility 2： When the wife’s income exceeds 130man yen, the wife should start paying her National Pension Plan premium of about 13man per year. This causes a drop in the budget constraint.
Possibility 3: Part-time jobs often have hours restrictions (about 25 hours per week). When you work as much as possible with this constraint, your income will be about 100man yen.
For example, if wage rate is 800yen and if you work 25 hours per week for 50 weeks, the annual income will be 800yen*25hours*50weeks =100man yen.
Thus, the possibility that married women face only two options, 25 hours per week job (part time job), or 40 hours per week job (full time job), may be the cause of 100man yen ceiling.
Reference (Sorry that many of them are in Japanese)
- Akabayashi, Hideo, 2006. The Labor Supply of Married Women and Spousal Tax Deductions in Japan. Review of Economics of the Household, Issue 4, pp. 349-378.
- Kantani, Takayuki, 1997. Josei Roudou no Tayouka to Kadai. (Diversification and Policy Issues of Female Workers.) Financial Review, December, pp. 29-49, (in Japanese)
- Sakata and McKenzie 坂田圭・コリン・マッケンジー（２００６）「配偶者特別控除の廃止は有配偶女性の労働供給を促進したか」、樋口美雄編『日本の家計行動のダイナミズム』慶應義塾大学出版会
- Takahashi (2010):高橋新吾（２０１１）「配偶者控除及び社会保障制度が日本の既婚女性に及ぼす労働抑制効果の測定」日本労働研究雑誌、No.605, Dec. 2010, pp. 28-43 (English version posted on the folder)
Labor Economics
Lecture 3
Labor Demand
THE PRODUCTION FUNCTION
q=f(E,K)
Where E is the amount of labor employed and K is the amount of capital.
Short run: the period in which the amount of some inputs (in this case K) cannot be changed.
Long run: The period long enough for the amount of all inputs to be changed.
We describe how the labor demand curve is derived.
We first describe the case for the short run, then the long run case will be described later.
DERIVING THE SHORT RUN LABOR DEMAND CURVE FOR A FIRM
In the short run, capital is fixed.
We assume that an individual firm is too small to affect the output price, the price of labor (wage), and the price of capital (k).
We assume that the production function has a particular shape, described in the following slides.