Consequences of the Demographic Transition

Economic DemographyDemog/Econ c175

Prof. Ryan EdwardsSpring 2020

3/2/2020

13/3/20 12:19 PM demog/econ c175

Announcements

• Lab 6 will be due this Friday by midnight

• Today is Super Tuesday! Don’t forget to vote

3/3/20 12:19 PM demog/econ c175 2

COVID-19• If you’re like me, you’re amazed at:

– The rapid pace of developments

– The lack of centralized messaging by our government and media

• Latest(?) news– 6 deaths in WA state, 1 confirmed case in Alameda County, a

health care worker in Solano County

– CDC is ramping up testing; previous standards allowed little

• The UC Berkeley EVC/Provost Paul Alivisatos is on it

• We need to think about potential changes to C175

3/3/20 12:19 PM demog/econ c175 3

Preparedness & Plans• I think instruction can continue regardless. We are all

committed to getting you your units & training

• Tech is awesome. Zoom can handle many hundreds of users on videoconference– Regular class meetings would become Zoom videoconference

– Sections would become Zoom, or video, or online chat

– Office hours would become Zoom or chat

• If we need to, the midterm would become a take-home with Honor Code as usual (if we did: sadly, no questions)

• We will keep you updated3/3/20 12:19 PM demog/econ c175 4

Questions?

3/3/20 12:19 PM demog/econ c175 5

Otherwise…

• Next meeting: in-class review– Good strategy: look at 2019 midterm and formulate

questions

– I’ll have nothing prepared for Thu, please bring Qs

• One week from today: midterm exam in class

• Then new instruction on Thu 3/12 and Tue 3/17 and Thu 3/19

• Then Spring Break week

3/3/20 12:19 PM demog/econ c175 6

Agenda• How to study for the Midterm exam• Social Security & OADR– Transitional windfalls and costs

– Rates of return

– The US case (and abroad)

• Demographic Transition– Some facts

– Impact on age structure

73/3/20 12:19 PM demog/econ c175

Priorities for studying

1. Lecture (slides, videos, any discussion), Section, Office Hours

2. Labs3. Required readings4. Other readings to help understand 1 & 2.5. Ask questions on Piazza, in office hours,

during in-class review

83/3/20 12:19 PM demog/econ c175

More on Social Security (PAYGO pensions)

demog/econ c175 93/3/20 12:19 PM

10

PAYGO identity• PAYGO short for pay-as-you-go:

annual outflows = annual inflows

• If workers (!") and old-folks (!#)Benefits(this year)= Taxes(this year)

$ !% = ' ( !)where t = tax rate; y = earnings per worker; and $ = benefits per retiree

• Rearranging the PAYGO Identity:

' = $( ×

!#!)

tax rate = (“replacement rate”) ´ (“old age dependency ratio”)

3/3/20 12:19 PM demog/econ c175

Recall OADRs from earlier: Up 33% in the U.S. by 2040

Country OADR in 2020

OADR in 2040

OADR in 2060

U.S. 0.28 0.39 0.45

China 0.19 0.42 0.58

Japan 0.52 0.71 0.83

3/3/20 12:19 PM demog/econ c175 11

OADR = pop aged 65+ / pop aged 20-64. Source: UN Pop WPP 2019

12

PAYGO identity! = #

$ ×&'&(

• Suppose the OADR )*)+

were to rise by 33%

• If you wanted to maintain the same replacement rate ,-

• Then the PAYGO tax rate would have to rise by 33%

• Currently the Social Security payroll tax rate is 12.4% (said to be “shared equally” between workers and employers). An increase of 33% would produce a payroll tax rate of 16.5%

3/3/20 12:19 PM demog/econ c175

13

iq12.1. Suppose the OADR !"!#

rises by 10%. What must happen

to the replacement rate $% if the tax rate remains the same?

& = () ×

+,+-

A. Rises by 10%

B. Falls by 10%

C. Remain the same

3/3/20 12:19 PM demog/econ c175

14

iq12.1. Suppose the OADR !"!#

falls by 20%. What must happen

to the tax rate if the replacement rate $% remains the same?

& = () ×

+,+-

A. Rises by 20%

B. Falls by 20%

C. Remain the same

3/3/20 12:19 PM demog/econ c175

Implicit rate of return• To simplify, imagine that all taxes are paid at age 40 and all

benefits received at age 70

• Then, implicit return on PAYGO contribution

rP = log(benefit * chance still alive / tax) / time

e.g., in our generational doubling example from last time:Benefit = 8 = 14 – 6; tax = 4; survival 1.0; time was 30 years:

rP = log(8 * 1.0 / 4) / 30 = 2.3%

153/3/20 12:19 PM demog/econ c175

Estimated rates of return based on history of taxes and benefits and survival

Ch. 32: Social Security 2287

Table 1Redistribution across cohorts in the US Social Security system (OASI) a

Birth cohort Internal rate of return(%)

Aggregate lifetime net intercohort transfer evaluatedin 1989 (billions of 1989 dollars)

1876 36.5 12.1

1900 11.9 112.0

1925 4.8 99.6

1950 2.2 14.0

1975 1.9 !8.0

2000 1.7 !15.2

a Source: Leimer (1994). Intercohort transfer calculation uses 2% real discount rate.

equal to the growth of the wage base. In practice, repeated benefit expansions over timehave created a series of initial generations all receiving benefits that were many timeshigher than tax payments. Thus, in the USA, workers who paid payroll tax rates of 2to 5% during their working years have been beneficiaries of payroll tax rates of 10 to12% in their retirement years 68. Table 1 shows internal rates of return and lifetime nettransfers from Social Security for successive birth cohorts taken from Leimer (1994).The internal rate of return, i, is the return that equalizes the present discounted valueof the total OASI taxes paid and benefits received for the cohort:

0 =age = max age!

age = 0

benefitsage ! taxesage(1 + i)age

.

The net transfers received by the cohort are the present discounted value of benefitsreceived minus taxes paid using a real discount rate, in this case 2%. We see thatwhereas the cohort that was born in 1900 received a rate of return of nearly 12% onits payroll taxes, a person born in 2000 can expect to receive only a 1.7% return onhis or her taxes 69. Similarly, while the accumulated (to 1989) value of the benefitsreceived by members of the cohort born in 1925 was $100 billion more than the taxesthe cohort members paid, future cohorts will receive substantially less in benefits thanthey pay in.

68 See Burkhauser and Warlick (1981), Moffitt (1984), Duggan, Gillingham and Greenlees (1993),Steuerle and Bakija (1994), and Caldwell et al. (1998).69 The numbers shown assume no change in Social Security tax or benefit rules in the future. Leimer(1994) contains additional results under various assumptions for how Social Security’s long run deficitis eliminated.

Source: Feldstein

Note: assumes PAYGO balance in future,Accounts for inflation,Mixes rich and poor

163/3/20 12:19 PM demog/econ c175

Is 2% a good deal?

• Something like you would earn on a risk free investment like treasury bills

• Less than stock market average• BUT insures against many risks– Annuity against longevity risks (dying too early,

too late)– Poor timing of the market (e.g., retiring in 2008)– Individual variation in investments

173/3/20 12:19 PM demog/econ c175

Trust fund

Scheduled spending and revenue Trust fund balance

Currently trust fund invests in treasury debt, some proposeto diversify into stocks (controversial)

183/3/20 12:19 PM demog/econ c175

What happens when trust fund runs out?

193/3/20 12:19 PM demog/econ c175

For other countries , a different story

• Demography is less favorable

• Benefits are higher

203/3/20 12:19 PM demog/econ c175

21

Examples for industrial nations, OADR projected to 2050

Country Earnings replacement rate

Old Age Dependency Ratio

Implied payroll tax rate

France .91 .55 .50

Italy .75 .58 .44

Spain .63 .60 .38

Japan .54 .59 .32

US .41 .41 .17Ron Lee’s calculations from data in Gruber and Wise.

3/3/20 12:19 PM demog/econ c175

The Demographic Transition

A story of changing birth and death rates

demog/econ c175 223/3/20 12:19 PM

Puzzle of the demographic transition

• The Demographic Transition seems obvious today– Birth and death rates used to be high, now both low

• Put ourselves in the position of 1970s– World population growth accelerating

– Energy prices skyrocketing

– Environmental worries

– Economic slowdown

• Less obvious then probably!

3/3/20 12:19 PM demog/econ c175 23

24

Idealized description• Pre-transition

– High fertility, high mortality

– mortality fluctuating due to random shocks

• Transition– Mortality falls first, fertility decline lags– Result is “transitional growth”

• Post-transition – Fertility finally falls

– Fluctuations in growth are due to fertility

– Sub-replacement demography?

3/3/20 12:19 PM demog/econ c175

25

Thumbnail sketch of the demographic transition

Crude Birth Rate

CrudeDeath Rate

R

Time Time

Crude Growth Rate (R)

Note crude rates are per capita (e.g., CBR = births / population)

3/3/20 12:19 PM demog/econ c175

Demographic Transition in Sweden and Mexico (Crude Rates)

Sources: B.R. Mitchell, European Historical Statistics 1750-1970 (1976): table B6; Council of Europe, Recent Demographic Developments in Europe 2001 (2001): tables T3.1 and T4.1; CELADE, Boletin demografico 69 (2002): tables 4 and 7; Francisco Alba-Hernandez, La poblacion de Mexico (1976): 14; and UN Population Division, World Population Prospects: The 2002 Revision (2003): 326.

0

10

20

30

40

50

60

1775 1800 1825 1850 1875 1900 1925 1950 1975 2000

SwedenBirth Rate

Death Rate

MexicoBirth Rate

Death Rate

Births/Deaths per 1,000

1950

Source: PRBdemog/econ c175

27

Transition statistics• Pre-transition

– TFR greater than 6

– life expectancy about 40 to 50

– Korea (1950): CBR – CDR = .037 - .032 = .005

• Transitional growth– crude growth rates reach 1-2% in historical Europe, 3-4% in Africa

– Iraq (1985): CBR – CDR = 42/1000 – 8/1000 = .034

• Post-transition– TFR about 2

– life expectancy 70 or 80

– Belgium (1984): CBR – CDR = .012 - .011 = .001

3/3/20 12:19 PM demog/econ c175

Population growth rates over the course of the demographic transition

approaching 3 percent for the Less and Least Developed Countries. After fertilitybegins to decline, the trajectories slope diagonally down toward the right, recross-ing contours toward lower rates of population growth. Europe briefly attains1.5 percent population growth, but then fertility plunges, a decline picked up after1950 by the group, ending with population decline at 1 percent annually. However,the actual European population growth rate is very near zero: slightly higher thanhypothetical steady-state growth rate due to changes in the age distribution and inimmigration. All three groups are projected to approach the zero-growth contourby 2050, the More Developed Countries from below and the Less and LeastDeveloped Countries from above.

There has been rapid global convergence in fertility and mortality amongnations over the past 50 years, although important differences remain. This con-vergence of fertility and mortality is in marked contrast to per capita GDP, whichhas tended to diverge between high-income and low-income countries during thistime. Today, the median individual lives in a country with a total fertility rate of2.3—barely above the 2.1 fertility rate of the United States—and a median lifeexpectancy at birth of 68 years compared to 77 years for the United States (Wilson,2001).

Actual trends in population growth rates can be seen over a longer time periodin Figure 4. Data before 1950 for the Less Developed Countries (which here

Figure 4Population Growth Rates, 1750–2150

Source: The population growth rates are calculated as instantaneous (exp(rt)) rates based onpopulation data. The data for 1750–1950 are taken from Tables 1 and 2 of United Nations (1999)and for 1950–2150 are taken from United Nations (2000).

178 Journal of Economic Perspectives

demog/econ c175 283/3/20 12:19 PM

Consequences of the Demographic Transition

Not just population size, also age structure

demog/econ c175 293/3/20 12:19 PM

Life cycle profiles of income and consumption

Dependency ratios are “shortcut” statistics, easier and quicker to read They reveal the ratios of those in dependent ages (<15 & >65) to those of working ages

Dependency measures

• Old-Age Dependency Ratio (OADR)OADR = Pop aged 65+ / Pop aged 15-65

• Youth Dependency Ratio (YDR)YDR = Pop aged < 15 / Pop aged 15-65

• Total Dependency Ratio = YDR + OADR

Example: Vietnam’s age-structure during DT

• When is dependency the lowest?

• What is growth rate in 1950? In 2075?

• Why so many kids in 1975?

• Is fertility sub-replacement in 2000?

1950

2075

2000

20502025

1975

A Classic Demographic Transition:India 1900-2100 (Lee, 2003)

● YDR increases before it decreases

● OADR increases long after● A window of low-dependency

(“demographic dividend”)est. + 0.5% per capita gdp

growth per year

3/3/20 12:19 PM demog/econ c175 33

Optimal Population Growth Rates

343/3/20 12:19 PM demog/econ c175

Three sides of the story

• Population growth is …– Good because there are more workers per elderly

– Bad because there are more children per worker

– Bad because of capital dilution; saving is costly

353/3/20 12:19 PM demog/econ c175

Lee-Mason et al. (2014)

Look at current age-profiles of consumption and production (private and public) to measure effect of age-structure

Use Solow framework to model capital

Calculate optimal fertility

363/3/20 12:19 PM demog/econ c175

Optimal Long-run Total Fertility RatesPublic (age-structureonly)

Public & Private(age –structure only)

Consumption (+ capital effects)

Observed today

Low income countries

1.1 1.8 1.2 4.0

Middle income countries

3.0 2.0 1.5 2.1

High income countries

2.9 2.3 1.8 1.7

Public is higher because child costs born by parentsStriking result is that low fertility (< 2) is "optimal"

Source: Lee et al 2014

373/3/20 12:19 PM demog/econ c175

Optimal fertility conclusions• Moderately low fertility might be something to aim for, not be

scared of ...

• Why?

– Both kids and elderly are expensive. Stable pyramid, increase in one cancelled out by decrease in other.

– Capital deepening (Solow effect) makes slow population growth attractive

• Caveats

– Age-schedules are exogenous and fixed, and that’s not fully realistic

– Technology growth is exogenous, but Romer/Boserup say it’s a function of population!

383/3/20 12:19 PM demog/econ c175