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Microeconomic models of fertility (1):

“the cost of time”

Economic DemographyDemog/Econ c175

Prof. Ryan EdwardsMarch 12, 2020

3/12/20 11:38 AM demog/econ c175

Congratulations!

• You’ve joined me in Zoom, or you’re doing your learning in another mode that works for you

• I was very impressed with your ability to adapt and complete the take-home midterm exam

• In particular, thank you to students who patrolled Piazza after hours and answered other students’ questions in ways that 100% fit the Honor Code

• We are grateful and impressed

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If Zoom deteriorates

• You could go “audio only”

• (See my 3/11 bCourses announcement)

+1 669-900-6833 US (San Jose)

Meeting ID: 832 316 511

3/12/20 11:38 AM demog/econ c175 3

Have a question? You can “raise your hand”

3/12/20 11:47 AM demog/econ c175 4

Perspectives on distance learning

• A key part of economics is “humans adapt”

– That doesn’t mean shocks don’t have costs

– But just like Solow after an earthquake, we will come roaring back!

• Using videoconferencing effectively is a increasingly valuable tool

– As a worker, you might use it to communicate with remote workers, and you might be remote too

– You might use videoconferencing to stay in touch with family so that you can move to where a new job is

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My Grandma turned 100!• We celebrated her birthday on Zoom!

• She grew up poor and motherless in a state where currently, Deaths of Despair are high and increasing

• She fought and prevailed, and she sent her kids to college and beyond

• She is among the 1.5% of her 1920 birth cohort to reach age 100

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But let’s be honest

• Snippet of a lit review on distance learning by Joshua Goodman (J Labor Econ, 2019)

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And that’s when instructors really know what they’re doing!

• Zoom is a familiar tool to me and the GSI’s

• Teaching large classes is also familiar

• Doing both together: The idiom is “can I walk and chew gum at the same time?”

• We’ll see! Have suggestions? Let me know, maybe Piazza is best

3/12/20 11:38 AM demog/econ c175 8

Help us help you

• It’s a time to try new things• Try to proactively reach out to us so that we can

help• Together let’s give new meaning to the “Co” in

COVID-19– Cooperation– Coordination

• Use videoconferencing. Practice makes perfect

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One last perspective: Externalities

• Imagine everyone could own and monitor their personal environment

• Sick folks could be charged a price for bringing a virus inside, and they would stay away if the price was too high

• Sound goofy?

• At least now we know that invisible germs cause disease, but we still can’t detect them quickly

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You are helping internalize a very costly externality

• Just like with global climate change, the actions of some people in a pandemic affect outcomes for others, but there is no market to price those actions

• We need and have institutions to address this big market imperfection

• Some institutions are clearly working a little better or more quickly than others

• See? Economics is everywhere (so are challenges)

3/12/20 11:38 AM demog/econ c175 11

Changes in C175 in Spring 2020 (1/2)

• Participation– No more iClickers for now– I’m exploring other polling options– I plan to mute users during class presentation

and then I will monitor chat for questions

3/12/20 11:38 AM demog/econ c175 12

Changes in C175 in Spring 2020 (2/2)

• Office hours for me– We’ll try shared videoconference – Anybody interest can join, nobody muted – Click the link in my entry in the Office Hours

Schedule

• Office hours for GSI’s– TBD

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Current events

• WHO declares COVID-19 a pandemic, meaning affecting global populations

• Trump bans travel from Europe (Schengen) for 30 days, officially closing the barn door after the cow has gotten out

• San Francisco has banned gatherings of 1,000+; WA state counties, 250+

• NBA has postponed its season indefinitely

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What in the world?• Health care delivery systems — especially hospitals, the

old model — are not designed to have the capacity to accept a huge bulge of cases

• Why? It would be tremendously wasteful in normal times

• Risks seem to be chiefly for the elderly and those with underlying health conditions, especially respiratory conditions

• If you’re inconvenienced, that’s no fun. Moves by UC Berkeley & others aim to slow the spread of COVID-19 and give hospitals a better chance to treat the sick

3/12/20 11:38 AM demog/econ c175 15

Some perspective• In 2009, the H1N1 swine flu pandemic was bad, especially

for developing countries. Not super bad for the U.S.

• The 1918 “Spanish” flu —

– Peaked in Fall 1918

– Might have actually begun in Kansas in early Spring 1918

– Was called “Spanish” because Spain had been neutral in WWI, and so its media wasn’t censored

– Today, it is a blessing that our media is actually reporting events, but it is also sobering in the 24hr news cycle

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Big pictures: Where we have been in C175

• Maybe best summarized by the 2018 Nobel prizes

– Human population and density are important for understanding knowledge and development

– Capital is important but probably not supremely

– Climate change is the Ultimate Challenge for Economics

• It’s caused by human populations and CO2

• When carbon isn’t priced right, big problems happen; what will we do?

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Next parts of C175• The economics of family, marriage, and fertility

• Immigration– Economics: motivations, winners, losers

– Fiscal impacts: do immigrants absorb more benefits than they pay in taxes, or the reverse? Or are they just like natives?

• Health and mortality

– Some basic health economics: healthy choices, constraints, etc.

– By this time in the course, surely some more on epidemics!

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Fertility & Family• Why do families choose the number of children they do?

– Sometimes there are biological constraints (but won’t be our focus)

– There are most definitely budget constraints

– And there are preferences

• Why do spouses choose their partners?

– What is happening with marriage here and abroad? Does it matter?

• Throughout: women’s work and the changing economy here and abroad

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The big questions about fertility

• Big Puzzle: If kids are “normal” goods, why has fertility fallen as incomes have climbed?

• A big problem in socio-biology: why doesn’t social/economic success produce more offspring?

• Two kinds of questions:– Temporal– Cross-sectional (within a society & between societies)

• Additional motivation: what will happen in the future?

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Trends in U.S. fertility: down, down, BOOM, down

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Differential fertility: between educational levels of women

• Total Fertility Rate for everyone is 4.0

• A very strong educational gradient

• (Note: TFR is a period measure and has some caveats.)

0

1

2

3

4

5

6

No Edu

c

Primary

Seconda

ryHigh

er

TFR

Zimbabwe 1999

3/12/20 11:38 AM demog/econ c175

Between states in India

233/12/20 11:38 AM demog/econ c175

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Microeconomic models

• Today and next time: work and wages

• Next time: the financial and opportunity costs of childbearing

– Together, these create the “shadow price” of children

– “Shadow” because markets don’t record the full price, only the explicit financial part

• Later: Gary Becker’s quantity-quality tradeoff model

3/12/20 11:38 AM demog/econ c175

Econ 100A and C175 and the fine print

• In Econ 100A (Hal Varian’s Intermediate Microeconomics) you learn and draw income and substitution effects

• We will too. They are powerful theoretical tools, even if these effects may sometimes point in different directions

• Sadly, there are at least 2 ways of decomposing price changes into income and substitution effects, and you might have seen the other one

• We are going to do what Varian calls the “Hicks substitution effect,” which also appears in Wikipedia

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Some background about income and substitution effects

• It turns out that the interest rate is the price of current spending

– If the interest rate is higher, your wealth will be worth more if you keep it (or save it) rather than spend it

– If the interest rate is lower, the reverse is true, and spending now is cheaper vis-à-vis its opportunity cost (spending later)

• What happens to current spending when the price of current spending falls?

• Well, the Federal Reserve just cut the federal funds ratetarget, a key interest rate, by 0.50% on March 3, 2020

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Not so fast?• If you’re like me, the substitution effect of a price change might be

the most intuitive

• A drop in the interest rate, the price of current spending, should have a substitution effect that shifts demand away from the future and toward the current

• But at the microeconomic level, there is also an income effect associated with every change in a price

• If the interest rate falls, net savers with lots of wealth will feel poorer and might spend less now — working against the substitution effect

• The Fed’s monetary policy looks like it does because of the aggregaterelationship across many savers, spenders, importers and exporters, and across many firms that borrow funds

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Learning objectives here• Understand income and substitution effects

– Sometimes they “stack” and push demand in the same direction

– And sometimes they work against each other, and the outcome is an empirical question

– This takes a lot of practice

• Use income and substitution effects to think rigorously about fertility choice when important stuff changes

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An indifference curve shows combinations of goods that the consumer deems equivalent

• Enjoyment of most goods is subject to diminishing marginal utility

• The more movies I see or popcorn I eat, the happier I am

• Because this is true for both goods, then my internal tradeoff between movies and popcorn favors the good I have least of

• When I have lots of movies, I’d give up a lot of movies for a little popcorn and still be be on U0 29

popcorn

movies

U0

Lots of movies, not much popcorn

Not many movies, whole lotta popcorn

Giving up lots of movies

For a little popcorn

Giving up a few movies

For a lotta popcorn

The consumer’s objective is to maximize utility subject to a budget constraint

• More of both goods raises well-being unambiguously, from U0 to U1, a higher indifference curve that’s parallel to U0

• Choices are constrained by the budget, which states that cash to spend (Y) equals prices times quantities

• Y = p1X1 + p2X2

• Holding Y and prices fixed, this is a line with slope –p1/p2

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good X2

good X1

U0U1

Yp2

Yp1

rise over run = (–Y/p2) / (Y/p1) = –p1/p2

The highest possible utility occurs where the indifference curve is tangent to the budget

• For normal goods with some complementarity between them, the tangency will typically occur somewhere around the middle of the budget constraint

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good X2

good X1

U0U1

Yp2

Yp1

U–1

Let’s be precise about indifference curves

• Indifference curves are kind of picky things to draw right

• They should have a steep then gentle slope, like a Black Diamond ski trail all the way down to the chalet

• They can’t bend up like this, because that would imply that that past the inflection point, you’re suddenly not helped with more of both X1

and X2

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good X2

good X1

Ugood

Ubad

Giving you more X1 and more X2 but you’re not happier?

Let’s be more precise about indifference curves

• Many of you know this well: Indifference curves can NEVER cross each other

• Think about a topological map with elevations —

• Those curves can never hit each other, because it would mean that two elevations are the same!

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good X2

good X1

U0

U1

THEY CAN’T CROSS!!

300 ft200 ft

200 ft

300 ft

Bermuda Triangle of weirdness

A much more subtle point: Curvature is important• Suppose we drew

indifference curves that were like straight lines!

• Preferences that look like this exhibit “strong substitutability” (or weak complementarity) between X1 and X2

• If you give the consumer a little more X2 even with no more X1, utility rises,

U0 to U1

• Consumer doesn’t care if X1 and X2 arrive together; they don’t have to “go together”

• Examples: Miller Lite vs. Coors LightFat Slice pizza vs. Blondie’s pizza

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good X2

good X1

U0U1

Lots of X2 and not much X1

More equal X1 and X2, just as good

What about the other extreme in curvature?

• Preferences that exhibit strong complementarity between X1 and X2 look like right-angle axes

• Technically called “Leontief” after Nobelist

• It means that if you give the consumer a little more X1 but no more X2, you might as well have done nothing

• Consumer doesn’t care about more X2 without more X1 because they must “go together”

• Think: Baseball and beer. Both good, but more baseball without more beer? Not better

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good X2

good X1

U0

U1

Lots of X2 and not much X1

Throwing away a bunch of useless X2, just as good

With indifference curves, it’s easy to draw them sort of like this accidentally, especially on an exam

• On exams, students sometimes draw indifference curves that look a lot like these

• When there is strong complementarity in preferences like this,

• i.e., when the indifference curves look a lot like L’s,

• Changes in budget constraints might not have large effects!

• All of these budgets have different relative prices between X1 and X2, but strong complementarity means the optimal point is unchanging!

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good X2

good X1

U0

U1

Lots of X2 and not much X1

Throwing away a bunch of useless X2, just as good

What if good X2 isn’t actually a good?

• Then we’ll get “half of Leontief,” where the indifference curves are either vertical or horizontal

• With preferences like these, the consumer will always choose a “corner solution” because X2 isn’t a good

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good X2

good X1

U0 U1

Lots of X2 and not much X1

Throwing away a bunch of useless X2, just as good

Highest indifference curve is reached in the corner

A “real world” policy implication of this theory• Poverty isn’t good. What should we do about it?

• Why don’t we transfer money to poor people

Option 1: We give money to everyone in poverty

Option 2: We subsidize wages for everyone in poverty

• If we think that spending time working is good for ultimately escaping poverty, which option is better if we admit that working isn’t fun?

• Option 2 creates a substitution effect incentivizing work. Both have income effects disincentivizing it (with more funds, buy more leisure)

• We might say, “Option 2 is less bad for work”38

Gary Becker (1981) identifies women’s wages as the key variable in the rise of women’s work

39

As women’s wages rose in the U.S. after 1950,

So too did women’s labor force participation — in particular, marriedwomen’s participation, which leaves less time for children

Hoffman and Averett show us the different trends for men and women

40

And they show us trends by marital status & kids

41

Labor Force Participation and Fraction with Young Children for 33- to 37-year-old married, college graduate women 42

Goldin (2006) shows us work and young kids, once moving in opposite directions, but no more!

Why would women’s wages affect participation, fertility, etc.?

• To examine this, we explore a model from labor economics, altered to show us the labor supply decisions

• We’re going to pretend it’s the 1960s and 70s, and we’re talking about women in marital unions

• The decision-maker is technically the household

• We assume the husband always works (and actually brings in income!)

• The question this model answers is: How much does the wife work in the labor market versus work at home

43

A model of female labor supply• Assume each household has a man and a woman

• Man works maximum effort, does no housework, earns income Y

• The woman faces a market wage w per unit of time and can trade some portion of her total time, T, for market wages

• The time the woman does not spent working is “leisure” or home production like childcare, housework, H

• The labor supplied by the woman is T – H

• The earnings of the woman are w(T – H)

• Total household income is Y + w(T – H) equals total consumption C

• The goods here are C and H

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A budget constraint and preferences over home production and consumption

• Here, the goods are (1) total household consumption, equal to income, and (2) the woman’s “leisure” or home production

• Women’s work time is all time not spent in home production

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Total household consumption, C

Home production, H

The budget constraint has a kink• The man’s income is

available regardless of the woman’s working, so at H = T, the household gets Y

• The woman can trade time for income at the wage rate, w

• The household has standard preferences over woman’s leisure and income

• Woman’s labor supply, T – H*, is determined by the tangency

46T

Slope = –w

Y U0

H*

T – H*

C*

Total household consumption, C

Home production, H

What if there were an increase in the man’s wages?

• This just shifts the budget constraint upward without changing the slope, since Y is the only thing that changes

• We call this a pure income effect, maybe for obvious reasons!

• With more income, you can buy more of each good: consumption and leisure both rise at the same time

47T

Y U0

U1

H*H**

Y’C*

C**

Total household consumption, C

Home production, H

Is this fully realistic?• We are assuming that “leisure” is a normal good: demand for leisure

rises with income

• Is this really true, when leisure is bluntly defined as all the woman’s time not spent engaged in market work?

• Not if leisure time isn’t really leisure but home production

• If you had more income, would you spend more time raising your kids and washing the dishes? Maybe, maybe not

• You might instead substitute market goods that you can purchase with your income for that home production!

• But let’s stick with our story and follow it through 48

What if there were an increase in the woman’s wage?

• If w increases, then the budget constraint pivots up

• There is a new optimality point, but where is it in relation to the old?

• There are income and substitution effects at work on the demands for leisure and consumption

• How do we decompose the total effect into these components?

49T

Y U0

U1

H*H***

C*

C***

Total household consumption, C

Home production, H

Decompose the change into level versus slope effects

• Think about the effect of the change in the wage, w, which is the relative price of H

• Holding utility constant at U0, the change in w, here a parallel dashed blue line, slides us in a northwest direction on the indifference curve

• That shows us the substitution effect

• The income effect then moves us from Hs and Csto the new optimal point at H*** and C***

50T

Y U0

U1

H*H***

C*

C***

Hs

Cs

Income effectSubstitution effect

Total household consumption, C

Home production, H

What can we say about H*** and C*** versus H* and C*?

• In the case of H, we can’t be sure which way we’ve gone, since the income and substitution effects operate in different directions!

• The way I have drawn it, the substitution effect outweighs the income effect, and leisure falls — female work rises

• For consumption,income and substitution effects operate in the same direction: toward an increase

51T

Y U0

U1C*

C***

Cs

Income effectSubstitution effect

Total household consumption, C

Home production, HH*H***Hs

What if the woman is not working but her wage rises?• In many societies during

early stages of industrialization, women are not working in the labor market

• That is, they’re located at the kink

• At that point, an increase in the female wage has “only a substitution effect” on leisure, which increases work

• Why? At the kink, there’s no income from work!

• Technically, a discrete jump to H’ will also have an income effect that partially offsets the increase in work

52T

YU0

U1

Substitution effect

C’

H’ H*

C*

Income effect

Total household consumption, C

Home production, H

What have we found?• Increases in male wages should probably be associated with decreased female

labor supply, other things equal

• Increases in female wages could increase or decrease work, depending on whether the substitution effect dominates the income effect

• So ultimately the effect of female wages on female labor supply is an empirical question

• What’s a real world example of these issues? The Earned Income Tax Credit is a transfer to working parents with kids

– It’s like a wage subsidy, or an increase in the wage, but whose?

– For married moms, the EITC may decrease female labor supply because it’s like a pure income effect through male wages

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