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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
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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?
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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
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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
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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
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More on Social Security (PAYGO pensions)
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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”)
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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
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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%
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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
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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
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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%
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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
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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
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Trust fund
Scheduled spending and revenue Trust fund balance
Currently trust fund invests in treasury debt, some proposeto diversify into stocks (controversial)
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What happens when trust fund runs out?
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For other countries , a different story
• Demography is less favorable
• Benefits are higher
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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.
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The Demographic Transition
A story of changing birth and death rates
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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!
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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?
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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)
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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
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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
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Consequences of the Demographic Transition
Not just population size, also age structure
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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
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Optimal Population Growth Rates
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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
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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
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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
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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!
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