Rebirth after Disaster: Models of Post-Pandemic Fertility

Rebirth after Disaster:Models of Post-Pandemic Fertility and Marriage

Joshua R. GoldsteinUC Berkeley

Talk for “Demographic Aspects of the COVID-19 Pandemicand its Consequences”

Monday, November 30, 2020

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Thanks

I Paola Di Giulio and Wittgenstein Centre for the invitation

I Ron Lee, Tom Cassidy, and Nathan Seltzer for many usefuldiscussions

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Agenda

I Some examples from present and pastI Models?

1. Descriptive (“rescheduling” vs. “postponement”)2. Demographic dynamics (revisiting Lee’s moving target)3. Contagious behavior (revisiting Hernes)

I Conclusions and possible directions

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Some examples from the past and present

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Sweden and the Spanish Flu

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1914 1916 1918 1920 1922 1924

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0010

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1500

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Year, month

Bir

ths

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Swedish Birth Counts (from HMD)

Immediate boom, which lasts 5 / 35

Historical Bust and Bounce of US Marriages

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1910 1915 1920 1925

7580

8590

Year

Mar

riage

s pe

r 10

00 u

nmar

ried

wom

enU.S. Marriage Rate

Delayed boom, which also lasts 6 / 35

What is happening today?

I We don’t know births, yet.

I But we can see weddings

Marriages in my childhood home (Lane County, Oregon).

Jan Feb Mar Apr May Jun Jul Aug Sept

2019 86 82 115 112 163 267 259 284 266

2020 95 114 90 78 126 153 156 275 166

Big declines, on the order of 40 percent.

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Our questions for demography after the pandemic

I Will there be a baby and/or wedding “boom”?

I Will cohorts “recuperate”?

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Our questions for demography after the pandemic

I Will there be a baby and/or wedding “boom”?

I Will cohorts “recuperate”?

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Our scaled-back questions that we hope models can anwer

I Under what conditions might there be a boom or bounce?

I What dynamics or assumptions would we need for cohorts torecuperate?

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1. Descriptive Models

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“Rescheduling” (What non-demographers imagine)

x

age /

x x x x x x x

period totals

1 1 1 1 0 2 1 1

What does this assume?

I All births occur, just later than planned.

I Instant return to “old normal”.

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“Rescheduling” (What non-demographers imagine)

x

age /

x x x x x x x

period totals

1 1 1 1 0 2 1 1

What does this assume?

I All births occur, just later than planned.

I Instant return to “old normal”.

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“Rescheduling” (What non-demographers imagine)

x

age /

x x x x x x x

period totals

1 1 1 1 0 2 1 1

What does this assume?

I All births occur, just later than planned.

I Instant return to “old normal”.

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“Postponement” (What demographers like Bongaarts andFeeney imagine)

x x x

age /

x x x x

period totals

1 1 1 1 0 1 1 1

What does this assume?

I All births occur, just later than planned.

I We stay at the “new normal”

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“Postponement” (What demographers like Bongaarts andFeeney imagine)

x x x

age /

x x x x

period totals

1 1 1 1 0 1 1 1

What does this assume?

I All births occur, just later than planned.

I We stay at the “new normal”

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2. Models that combine demography and behavior

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Ron Lee’s “moving target”

Ingredients:

I Cohorts have a target family size

I Unfulfilled fertility happens at a constant rate

I Birth timing and period level is an output of model, not aninput.

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An equation relating flow of births to stock of children

fertility = rate × (unachieved family size target)

fx = α × (T − Fx)

= 0.3 × (2.0 − 1.0)

fx birth rate x years after onset of childbearing

α rate at which unachieved desires are achieved,constant by duration

T desired family size target (Ron lets T vary by period).

Fx children already born

Innovation: to model epidemic, we let α vary by period.

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A simple example of a cohort α = 1/2, T = 1

period

3 1/16

duration 2 1/8

1 1/4

0 1/2

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Filling in the Lexis surface

period

3 1/16 1/16 1/16 1/16

duration 2 1/8 1/8 1/8 1/8

1 1/4 1/4 1/4 1/4

0 1/2 1/2 1/2 1/2

--- --- --- ---

total 1 1 1 1

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Recovery after a zero-fertility year

period

3 1/16 0 1/8 1/8

duration 2 1/8 0 1/4 1/4

1 1/4 0 1/2 1/4

0 1/2 0 1/2 1/2

--- --- --- ---

total 1 0 3/2 5/4 ...

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A simulated boom, after 15% decline with no change intarget

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(a) A boom

Years (relative to shock)

Ann

ual B

irth

s

−5 0 5 10

0.8

0.9

1.0

1.1

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●New target = 1

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No boom, but return to previous level, if target declinesjust slightly

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(a) A boom

Years (relative to shock)

Ann

ual B

irth

s

−5 0 5 10

0.8

0.9

1.0

1.1

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●New target = 1

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(b) A bounce

Years (relative to shock)

Ann

ual B

irth

s

−5 0 5 10

0.8

0.9

1.0

1.1

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New target = 0.99

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Even a small decline in target can overwhelm rebound

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(a) A boom

Years (relative to shock)

Ann

ual B

irth

s

−5 0 5 10

0.8

0.9

1.0

1.1

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●New target = 1

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(b) A bounce

Years (relative to shock)

Ann

ual B

irth

s

−5 0 5 10

0.8

0.9

1.0

1.1

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New target = 0.99

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(c) A whimper

Years (relative to shock)

Ann

ual B

irth

s

−5 0 5 10

0.8

0.9

1.0

1.1

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New target = 0.95

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A larger decline in target can make fertility continue to fall

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(a) A boom

Years (relative to shock)

Ann

ual B

irth

s

−5 0 5 10

0.8

0.9

1.0

1.1

●

●● ● ● ● ● ● ● ● ●

●

●New target = 1

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●

● ● ● ● ● ● ● ● ● ● ● ●

(b) A bounce

Years (relative to shock)

Ann

ual B

irth

s

−5 0 5 10

0.8

0.9

1.0

1.1

●

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●

New target = 0.99

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(c) A whimper

Years (relative to shock)

Ann

ual B

irth

s

−5 0 5 10

0.8

0.9

1.0

1.1

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New target = 0.95

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(c) A thud

Years (relative to shock)

Ann

ual B

irth

s

−5 0 5 10

0.8

0.9

1.0

1.1

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New target = 0.9

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Moving Target Model, preliminary conclusions

I Super simple model, but still creates complicated dynamics

I Even small changes in target have very large effects

I Perhaps, boom after Spanish Flu in Sweden consistent withno change in target.

I Covid today? Target expected to decline, making boomunlikely. (Recovery, whimper or thud?)

I But, who knows? Maybe Trump’s demise and pandemic’s endwill bring a new spring? And targets will increase.

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Moving Target Model, preliminary conclusions

I Super simple model, but still creates complicated dynamics

I Even small changes in target have very large effects

I Perhaps, boom after Spanish Flu in Sweden consistent withno change in target.

I Covid today? Target expected to decline, making boomunlikely. (Recovery, whimper or thud?)

I But, who knows? Maybe Trump’s demise and pandemic’s endwill bring a new spring? And targets will increase.

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3. Diffusion models for behavioral change

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Endogenous targets?

Can we have the target as an output of a model, rather than aninput?

Yes. “Social contagion” or “social diffusion” modelsproduce eventual cohort levels as an output.

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Endogenous targets?

Can we have the target as an output of a model, rather than aninput? Yes. “Social contagion” or “social diffusion” modelsproduce eventual cohort levels as an output.

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Hernes modeled marriage as a social contagion

I No target

I We just “seed” the behavior, and it spreads as cohort ages

I Age effect

marriages = unmarried · marriage rate (contagion, age)

px = (1 − Px) · a(Px)e−bx

px are marrages aged x

Px are cumulative marrages by age x

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A sample Hernes schedule

20 25 30 35 40 45

0.00

0.02

0.04

0.06

Age

Proportion marrying at each age

20 25 30 35 40 45

0.0

0.2

0.4

0.6

0.8

1.0

Age

Cumulative proportion

Can ask what happens if a shock occurs . . .. 27 / 35

A big shock, e.g., for cohort born in year 2000

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20 25 30 35 40 45

0.00

0.02

0.04

0.06

Age

Proportion marrying at each age (with big shock)

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20 25 30 35 40 45

0.0

0.2

0.4

0.6

0.8

1.0

Age

Cumulative proportion (with big shock)

No boom, only some recuperation. (endogenous target) 28 / 35

A Bust and Boom in Period Marriages

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−10 0 10 20 30

0.6

0.7

0.8

0.9

1.0

period

Tota

l 1st

Mar

riage

Rat

eSimulated time path of Period Marriage Rate

As cohorts tend to bust and recuperate in rough synchrony 29 / 35

Two specific conclusions

1. Lee model suggests period birth rebound will depend verystrongly on what happens to target.

2. Hernes model suggests period partnership rebound couldhappen even if cohorts don’t recuperate.

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Broader lessons

I Unpredictability: anything goes right after the pandemic ends

I Patience: even short-lived shock could reverberate for years

I Lagged effects even stronger in real world – epidemic won’tsuddenly end for everyone at the same time(e.g., Great Recession)

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Future theoretical directions

I Extension: cohort diffusion across whole of Lexis surface?

I Mathematics: perturbation analysis of differential equations?

I Two-stage process: entrance into childbearing (“marriage”),and then fertility?

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Leontine’s harsh tweet

A gentler conclusion: empirical work and formal work arecomplementary. Models can help us work through our thinking andpoint us to what we want to measure.

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Measurement Coda: The return of fertility intentions?

I A high frequency birth intentions barometer?

I Extending to cohabitations and marriage?

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Thank you

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