Changing 4. Economic Roles and the Family, and Modeling Female Labor Supply
Ronald Lee Econ/Demog 175 January 28, 2010
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Readings for next Tuesday
Kristin Mammen and Christina Paxson (2000) Womens Work and Economic Development Journal of Economic Perspectives v.14 ,n.4 pp.141-151; 158-164. (pp.125-143 in Reader). Claudia Goldin (2006) The Quiet Revolution that Transformed Womens Employment, Education, and Family American Economic Review 96(2):1-21. The Ely Lecture.
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Readings for next Thursday
Michael J. Brien and Michelle E. Sheran (2003) The Economics of Marriage and Household Formation in Shoshana A. GrossbardShechtman ed. Marriage and the Economy (Cambridge University Press) pp.37-54. Evelyn L. Lehrer (2003) The Economics of Divorce in Shoshana A. Grossbard-Shechtman ed. Marriage and the Economy (Cambridge University Press) pp.55-74.
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4. Lecture Plan
1. The Evolution of the Family 2. Models of labor supply
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Announcements
For PS1, make sure you calculate the percentages for the population pyramid relative to the whole population. For example, you should not calculate the number of males at a given age relative to the total male population. Do it relative to the whole population of both sexes.
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Turn on your clickers at start of each class.
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Q1. In a stable population:
A. the size of each age group is constant over time. B. Each age group is the same percent of the total population size. C. The populations of Germany and Japan are declining, so they cannot be stable populations. D. All of the above E. None of the above.
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I. The Evolution of the Family
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Background for iClicker survey question
First generation immigrants are people who live in the US but were born in other countries. Second generation immigrants are people who were born in the US (and therefore are US citizens, and not immigrants at all) whose parents were born in another country. (Lets say, at least one parent). All others are third or higher generation immigrants. Which are you? I am 1.5, my mother was an immigrant.
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Q2.1 How many people including yourself were in your household when you were growing up, say at age 10 or so?
Only first generation immigrants answer.
A. B. C. D. E. 2 3 4 5 6+
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Q2.2 How many people including yourself were in your household when you were growing up, say at age 10 or so?
Only second generation immigrants answer.
A. B. C. D. E. 2 3 4 5 6+
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Q2.3 How many people including yourself were in your household when you were growing up, say at age 10 or so?
Only Third Plus generation immigrants answer (that is, all who have not yet).
A. B. C. D. E. 2 3 4 5 6+
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Theories of changing family life: Introduction
There have been vast changes in family life over recent centuries.
Some of you have experienced both traditional and modern families Others only US family life, but even here, huge changes in recent decades.
Here try to understand
Nature and function of traditional family How and why it has changed Where family life is headed next
Industrialization has brought sweeping changes, many of which have affected the vitality and centrality of the family. Leads into section on economics of marriage and fertility
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Traditional family (ignore diversity, search for common themes)
Features of preindustrial family It was extended including grandparents, aunts, uncles, cousins, etc. as well as parents and their children. Center of economic production
Agricultural production by family members Important productive activities in the home: processing food, making clothes, fetching firewood and water, etc. Kids began working at young ages, began to produce what they consumed around ages 10 to 15.
Training
Before formal education, training was provided within family, with occupations passed down from parent to child Before formal educational degrees, the family certified members as suitable for jobs.
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Features of Traditional family (cont.: 2)
Insurance functions
Family shared economic successes of individual members, buffered failure Helped if sick, disabled, crop failure, etc. Health insurance Old age support
Physical security
Without police, judges, courts, protection of life and property was through household size and kin
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Features of Traditional family (cont.: 3)
Monitoring of members behavior
Because of insurance function, family had to monitor its members to guard against shirking, faking. Because family reputation was so important, family had to monitor the behavior of its members. Consequently there was little privacy
Childbearing and rearing took maybe 30 years of adult life for women (say 18 to 48); reproduction was central.
Pregnant Breastfeeding Caring for young kids In first reading at start of course, I estimated that women spent about 70% of adult life bearing and rearing young children.
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Important Theoretical Concept: Gains to marriage
Combined Utility of two people married, minus sum of separate utilities if single. Sources of gains:
Specialization and division of labor in the household different economic roles. Sex, companionship, love. Bearing and rearing children. Efficiency in living arrangement, returns to scale: roommates get you same.
Preindustrial family had large gains to marriage because
Household was so important as locus of both production and consumption specialization, division of labor, and returns to scale were all so important.
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Here is an illustration of the costs of living alone. This household consists of a man about 50 years old. He has been married several times, but all of his wives left him after brief periods. He owns a small amount of land, which, with the exception of several small adjacent plots, he leases to sharecroppers. Figure 1 presents a record of his activities during two days in late December. Figure 1. Time allocation of man who lives alone in Char Gopalpur from Mead Cain (1977) Economic Activities of Children in a Village in Bangladesh Population and Development Review p.205 You wont be able to see the details, but you can see the difference between housework and Ronald Lee, UC Berkeley, 2010 18 productive work.
Mead Cain, on the man who lives alone in a Bangladeshi Village.
Of 25.3 waking hours, 19.5 (77 percent) were occupied by work. Of the working hours, 18.2 (93 percent) consisted of housework, including cooking, drying, winnowing and husking paddy, sweeping, fetching water, and washing dishes and utensils. Women or young children would normally perform these tasks, thus permitting the household head and other able males to cultivate the family land and engage in other income-producing work. In the case of the man who lives alone, however, the demands of necessary housework exhaust his time, forcing him to lease his land to sharecroppers. Cain (1978) Population and Development Review, p.204.
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So what changes brought us from that world to the one we live in now?
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Fundamental causal drivers of change
Shift of locus of production from household to factories and offices, reduces economic functions of family, makes children incompatible with work. Changing technology of home production and consumption makes it easy to run a household with only one person, unlike in old days. Growth in earning power of women
Raises LFP (labor force participation) Reduces fertility This in turn frees time for more work outside home, etc. Reduces gains to marriage
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Fundamental causal drivers of change (cont.: 2)
insurance markets and public programs replace familial risk spreading function. financial markets permit self insurance, easier provision for old age greater geographic and occupational mobility weakens extended family Growing prosperity raises the demand for privacy, living alone
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Fundamental causal drivers of change (cont.: 3)
Public education reduces childrens dependence on their families, reduces participation in economic activities at home Growth of welfare state
Pensions lead to earlier retirement and less co-residence with kids. Pensions and financial markets reduce need for children for old age support Need based welfare programs reduce gains to marriage Also reduces losses for women due to divorce All this leads further to less marriage, more divorce, lower fertility
Contraceptive technology (developed in response to demand)
Makes it possible for women to plan births carefully This may have far reachingBerkeley, 2010 Goldin article for next Ronald Lee, UC effects; see 23 class.
Positive feedback, and enhancers of family change
Divorce becomes less stigmatized as it becomes more common. Women need less time for childrearing, more for market labor, therefore invest more in market skills.
Reduces gains to marriage increases cost of kids, reducing fert still farther.
As divorce becomes more common, women begin to strategize, to cover their bets by developing a potential occupation. Reduces gains to marriage.
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Resulting changes in demographic behavior from all this
Less and later marriage. More divorce Lower fertility More fertility outside of marriage Smaller households, more living alone, less elder coresidence Weakened ties among family members, who need each other less (e.g. elderly parents do not count on their adult children; grandparents do not co-reside with their grandchildren; children do not count on their parents for finding them a job; familial insurance no longer needed).
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Q3. The example of the man in Bangladesh who lived alone shows:
A. He has a large potential gain from marriage because then he could achieve economies of scale and division of labor in home production. B. If he were married, then his wife could do the home production and he could do the agricultural work on his fields, so he would be better off. C. Both of above; A and B say pretty much the same thing.
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Q1. Comparing China to the US which statement is true?
A. Fertility is higher China in and life expectancy is lower. B. Fertility is lower in China and mortality is higher. C. Fertility and mortality are both lower in China. D. Fertility and mortality are both higher in China.
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II. Model of Labor Supply
Labor-leisure model in household setting. We should think of leisure here as actually mostly home production. So household gets utility from the leisure of the stay-home spouse, here assumed to be the wife.
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Consider economic choice of how much wife works in labor market
If she works more, household income is greater, but she has less time for home production. Utility depends on both. We assume the household chooses an amount of leisure for her that maximizes its utility. Who makes the decision? The wife? The husband? Joint?
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Pindyck and Rubinfeld is valuable background reading for this section.
They develop the labor supply model for an individual, and have some discussion of the household labor supply.
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Standard model of womens labor supply (implicit in Mammen-Paxson reading)
Assumptions
Family income comes from husbands earnings, wifes earnings, and asset income. Family income from all sources other than wifes work is constant,
Husband always works full time at fixed wage other family income also constant (e.g. from assets)
All family income is consumed. Household (family) utility depends on
Total family consumption Wifes leisure or time for home production
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The standard model of labor supply
Notation
1. Y = family income not from wifes work (husbands labor earnings plus asset income) 2. w = wifes potential wage per hour of work 3. T = total discretionary time for wife (e.g. 14 hours/day) 4. L = wifes leisure or home production time. 5. C = consumption of market goods by the household.
Assume that C = total income; no saving or dissaving.
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The standard model of labor supply (cont.)
Algebra Labor supply of wife is T-L Earnings of wife are w(T-L) Total family income is Y + w(T-L) C = Y + w(T-L) Utility: u(C,L) (depends on both household consumption C and on wifes leisure or home production time L)
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Utility
We will assume that household utility has some important properties
More consumption yields more utility (positive marginal utility, dU/dC>0) Same for wifes leisure: positive marginal utility The more the household already consumes, the less does additional consumption raise utility (diminishing marginal utility of consumption), and same for leisure.
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We could assume some specific math expression for the relation of utility to C and L. For example:
U(C,L) = C+L (but this does not have diminishing marginal utility; the gain to utility is always the same no matter how high is consumption) U(C,L) = square root of C*L (this does have diminishing marg utility) U(C,L) = a*ln(c) + b*ln(L) Or many others.
Instead we will use diagrams of indifference curves that show combinations of C and L that yield equal utility.
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Indifference map of utility
C=cons
L = leisure
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Indifference map of utility
Every point on the graph corresponds to some level of C and L.
C=cons
The contours connect all the combinations of C and L that yield the same utility. The contours (indifference curves, because a person would be indifferent between any combinations on the curve) could be calculated from some given utility function, but here I just drew them freehand.
L = leisure
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Indifference map of utility
These indifference curves have some important properties.
C=cons
They cannot cross, because that would mean that a person was indifferent about having more or less of both C and L, which contradicts the assumption that it is always better to have more of one. For the same reason, they must always decline going to the right, and rise going to the left.
L = leisure
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Indifference map of utility
Indifference curves farther from the origin (to the right and up) have higher utility.
C=cons
L = leisure
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Q2. The sex ratio declines at older ages in China, from about 1.0 at age 70 to about .4 at age 90. The main reason is: A. Women marry men who are a few years older, on average. B. Men of these generations migrated to the US. C. Men of these generations died in earlier wars. D. Women live longer then men, on average, as in most other countries.
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The next few slides are intentionally blank frames, to use in class.
Vertical axis is total family income Horizontal axis is wifes leisure (left to right, ending at T), and wifes supply of labor (right to left, starting at T) If wife works full time, income is Y + wT If wife stays home full time, income is Y Slope of budget constraint is -w each additional hour of leisure she takes reduces family income by w. At optimal labor-leisure choice, the utility the family gets from w more dollars of consumption just equals the utility it gets from one more hour of wifes leisure or home production.
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The effect of higher wage for women
For a woman who is initially supplying some labor to the market, a higher wage has two effects
Family income rises, because she would earn more for the same hours The price of leisure rises, since the family now has to forego more consumption for each hour she stays home. The net effect could be either an increase or a decrease in hours of labor. Could be backward bending labor supply curve.
For a woman initially supplying no labor, there is only a substitution effect, bringing her closer to supplying labor to the market.
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Similar analysis applies to male labor supply
Because males labor earnings are typically a higher share of family income, when his wage rises, the income effect is relatively larger than for a female, so the backward bending outcome (reduced labor supply) is far more likely for males than for females.
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Labor supply elasticities from Pindyck and Rubinfeld Reading
Hshld Type Heads hrs wrt hds w 2-earner with kids -.002 Spouses hrs wrt spouses w -.086 -.028 Heads hrs wrt spouses w -.004 -.059
2 earner -.107 with no kids
The first and third columns of estimates indicate that both head and spouse supply is bckwrd bndg.
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The following slides just repeat what I have already done in class; you can use them to review. Note that the decomposition into income and substitution effects is done differently in class, and in these following slides.
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The budget constraint for the household
C=Y+ w(T-L)
C* Y
Each additional hour in market work adds w to consumption, but reduces her leisure or home production by 1 hour. The slope of the budget constraint here is w.
0 Leisure, L
L* Labor = T - l
T
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Ronald Lee, UC Berkeley, 2010
Choice of optimal hours of leisure (home production time) and labor market work (L and T-L) by a wife whose household has Y other income. C=Y+ w(T-L) Each additional hour in market work adds w to consumption, but reduces her leisure or home production by 1 hour. The slope of the budget constraint here is w. Household has this much income regardless of wifes decision 0 Leisure, L L* Labor = T - L T
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C* Y
Ronald Lee, UC Berkeley, 2010
Now suppose that non-wife income, Y, is higher. The budget constraint will shift higher, but keeps the same slope because her wage, w, has not changed. C=Y+ w(T-L) Wifes leisure, or the goods she produces at home, is a normal good, so with higher income and no change in prices, the household chooses more of her home time (leisure) and less of her market work. The red lines show this new optimum.
C3* C* Y
0 Leisure, L
L*
L3*
T
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Labor = T - L
Now suppose that the wifes potential wage is higher, say w2>w. Now the budget constraint is the same if she does not work at all, but otherwise it rotates upward. If she works full time, taking 0 leisure, household income and consumption is w2*T + Y.
C2* C* Y
0 Leisure, L
L2* L* Labor = T - L
T
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Ronald Lee, UC Berkeley, 2010
We can decompose the change into an income effect and a price or substitution effect. (In lecture I will do this in the opposite order, showing the substitution effect on the original indifference curve. You can do it either way, and for tiny changes the result will be the same. Draw a hypothetical new budget constraint parallel to the old one, so it has the original slope, but shift it upwards until it is tangent thethe new optimum. A is to original indifference curve. C is the new optimum. C C2* C* A Y B B is the hypothetical optimum if income rose enough to reach the higher indifference curve, but the slope of the budget constraint did not change. The change from A to B is the income effect. The change from B to C is the price effect or substitution effect.
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0 Leisure, L
L* L2* Labor = T - L
T
Ronald Lee, UC Berkeley, 2010
The income effect is positive: the wifes leisure (or the things she produces at home) is a normal good, so with no change in prices and higher income, the household will choose more of the wifes leisure and thus less of her market work. The price effect is negative: higher wages make leisure more costly, so if income is unchanged, the couple will choose less leisure and more consumption. The way I drew the indifference curves, the price effect is greater than the income effect, so the wife takes less leisure and does more market work when the wage is higher.
C C2* C* A Y B
0 Leisure, L
Theory alone cannot tell us T which way this will go; it is equally possible that the Labor = T - L 2010 Ronald Lee, UC Berkeley, 55 income effect would be bigger. L* L2*
This is an empirical question: what do the data tell us? When the income effect is greater, so higher wages lead to less labor supplied to the market, we say there is a backward bending labor supply curve.
C C2* C* A Y B
This diagram and theory is referred to in the Mammen and Paxson reading which we will discuss next. It is important. Learn it for the midterm.
0 Leisure, L
L* L2* Labor = T - L
T
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Ronald Lee, UC Berkeley, 2010