Empirical Models

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Empirical Models

• David Canning
• Harvard University

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I. Effects of Fertility Redcution
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Economic Stories for Fertility Reduction

• Technological change has increased the returns to
  education/ lowered cost of education.
• Falling child mortality has reduced the
  insurance demand for children and reduced
  wasted educational costs.
• Falling contribution of children to household
  finances with urbanization.
• Rising value of time (higher wages and human
  capital) children are time expensive.

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Desired Fertility and Actual Fertility

• Economic theory concentrates on changes in
  desired fertility.
• Desired fertility may vary between male and
  female partners. Household bargaining model
  versus unitary household.
• Actual Fertility may differ from desired
  fertility role of contraception

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Empirical Effects of Low Fertility

• Fertility is chosen. May be a consequence of
  female work decisions and desired education of
  children
• We want to find structural effect of lower
  fertility. Evidence for this requires exogenous
  change in fertility.

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Instruments for FertilitySex Ratio

• Sex ratio of previous births is random and
  affects future fertility.
• Son preference
• Mixed sex preference
• Problem sex ratio may affect household income
  (dowries) and desired investment in kids giving
  direct effect of child health and education
  investments.
• Randomness?

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Instruments for FertilityTwins

• Twins are random. Increase family size more
  than planned.
• Problem twins are less healthy than average due
  to sharing of mothers resources during fetal
  development. Timing/spacing of births may have
  effects on resource availability.
• Randomness?

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Instruments for FertilityAbortion Laws

• Abortion laws affect fertility
• About 26 of pregnancies end in abortion
• Large fertility effect e.g. US state laws
• Abortion laws may be endogenous
• Control for country fixed effects, time trend and
  country x time trend effects.
• Precise timing may be exogenous
• Some reversals of trend to more liberal laws.

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Data

• Female Labor Market Participation (ILO 2007)
• By cohort (15-19, 20-25,,60-64)
• 1950-2000
• 97 countries
• Fertility (WDI 2006)
• Total fertility rate
• Abortion Index (United Nations Population
  Division 2002)
• Abortion Health Index physical and mental health
  of the mother, rape, fetal impairment
• Abortion Availability Index economic hardship,
  on request

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Empirical Specification
Estimated Equation
Pijt female labor force participation of age
group i, country j, year t kjt capital stock
per working age person urbanjt population
living in urban area () fschooljt average
years of schooling for females gt15 years of
age mschooljt average years of schooling for
males gt15 years of age
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Female Labor Force Participation (25-29)
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First Stage Regressions
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Age Group Specific Fertility Effects
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Total Dynamic Effect of Fertility Decline
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SIMULATION

• Economy with
• no technological progress
• constant survival schedule
• Constant education rates
• Investigate the effect of fertility reduction
• Calibrate to South Korea education/survival/fertil
  ity

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Simulation Framework I

• Production Function
• Physical Capital Stock
• Parameterization

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Simulation Framework II

• Demographic Structure
• Human Capital

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Specific Example South Korea
1960 2000
Fertility (TFR) 5.6 1.2
Life Expectancy at birth 55.2 76.8
Female Labor Market Participation (25-29) 26.3 55.7
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Fertility and Female Labor Market Participation -
Korea
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Simulation Scenarios

• Baseline Initial steady state 1960.
• Add actual fertility reductions
• Solow model population effect on capital labor
  ratio
• Age Structure Demographic Change with fixed
  cohort specific participation rates
• Age Structure plus Female Labor Supply

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Results
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Korea Simulated Demographic Structure
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Korea Demographics and Workers per Capita
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Simulation Results Summary

• Demographic transition has important effects on
  long term per capita income. The magnitude of
  these effects can be sizeable and depends on
• Aging and old age labor force participation
• The magnitude of the female labor supply response
  to fertility declines.

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Conclusions

• Empirical results suggest that the decline in
  fertility leads to a significant increase in
  female labor force participation
• This increase in female labor force participation
  compounds the positive long term growth effects
  induced by the demographic transition
• The magnitude of this effect depends on the
  participation behavior of the 65 age group the
  focus of our complementary study

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II. Heath and Life Span Effects
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Health and Life Span Effects

• Value of Health/Lifespan Improvements
• Health and Worker Productivity
• Life spans and life cycle behavior
• retirement
• Consumption/savings
• Institutions
• Health lifespan and education

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Value of Health Improvements

• Welfare Gain from Lifespan Improvement
• Value of life span gain in money units.
• Vale of a statistical life
• What money gain would give the same welfare
  benefit as the gain in life expectancy?

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Individual Utility

• Life time welfare
• Budget constraint

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Indirect Utility

• Assuming
• Annuity of 1 for life has value

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Equivalent Variation

• Survival rates rise from S0 to S1 while income
  rises from y0 to y1
• The equivalent variation e (rise in annual
  income) of the health improvement solves
• Or

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Approximation of EV

• Using a Taylor series expansion
• The equivalent variation depends on the
  discounted growth in survival and the level of
  income

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Value of Life Span Increases

• We can estimate the equivalent variation if we
  know the age specific survival function before
  and after, the level of income and the shape of
  the utility function.
• The utility function needs to be determined both
  in terms of its slope ( higher order terms may be
  important as well) and its intercept notice we
  implicitly take the utility of being dead to be
  zero.
• U(c) is the utility of being alive and having
  consumption c. We can find the intercept from
  value of life studies.

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Health and Full Income

• Health adds directly to welfare as well as acting
  as an input into production.
• Value of Life studies put a high monetary
  valuation on small risks of death.
• Over 50 of welfare gain in US from 1900 has been
  lifespan (Nordhaus).
• Calibration of utility function as in Becker,
  Philipson and Soares (2005).

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Health and Worker Productivity

• Issues
• No consensus on how to define health
• Health status indicators have large measurement
  errors.
• Effect is bi-directional we cannot infer
  causality from correlation.

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Measuring Health CapitalMultiple Indicators of
Health

• Self assessed health status
• Morbidity Rates
• Physical function limitations
• Physical growth outcomes

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Health Human Capital

• We are interested in health that comes as a
  result of health and other investments
  controlled health.
• Uncontrolled health , e.g. due to genetic
  differences will affect productivity but is not
  health capital.
• Compare with IQ and schooling as human capital.
• Ideally we would measure the effect of a health
  input on health status and then trace out the
  effect of the improved health status on
  productivity but this is rare.

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Feedbacks from Income to Health

• Model has three functions which occur
  simultaneously.
• Health is a function of health and other inputs
  (including shocks).
• People decide, based on their income, on inputs
  and activities that affect health.
• Health affects productivity and income

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Analytical Framework

• Health production function
• Health H
• Health inputs l
• Exogenous health factors (genetic etc.) g usually
  unobserved
• Random error e1

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Input determination

• The level of inputs depends on household
  characteristics, such as wage earnings W, and the
  availability of inputs X
• We solve out for the effect of current health
  h on input demands.

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Productivity

• Wages W depend on health H, education E, other
  factors Z and an error term

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Estimation Problems

• We have measurement error in health biases
  results downwards.
• Health affect wages but wages also affect health
  via their effect on health inputs we have
  reverse causality.
• We only want the human capital element of
  healths contribution to wages, not the genetic
  component.

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Problems can be overcome using an instrumental
variable

• Suppose instead of health we use predicted health
  based on the local availability of health
  services and factors that can used as policies to
  affect health.
• This removes measurement error
• This removes the reverse causality since the
  predicted health is independent of an
  individuals wage.
• The predicted health measure is pure controlled
  health and does not include any individual
  specific uncontrolled health.

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Empirical Results on Wages Determinants

• All these variables are instrumented- for example
  by local food prices or distance to a health
  facility when young
• Calories important (below 2000 kcal).
• Proteins important
• BMI important
• Height important
• Days ill/working days lost important

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Lifespan, Retirement, and Saving

• Mis-match between time path of labor income and
  consumption.
• Cash and in kind transfers within the household
  and between generations through bequests.
• Transfers through the social security system.
• Private Saving/borrowing.

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Savings Rates
Source PWT6.1
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Micro to Macro

• Macro focus on age structure effects.
• In micro data savings rates vary by age with a
  peak at around 55 but these age effects on
  household savings are modest.
• Most of the savings boom in East Asia was due to
  higher savings at every age with only a modest
  contribution from age structure effects.
• Accounting effects of demographic change can only
  explain a small fraction of variation in savings.
• We need to explain changes in saving behavior at
  each age.

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Savings Booms

• Increase in individual savings due to
  improvements in health and longevity?
• Major alternative theory is habit formation in
  consumption.
• Effect of new financial institutions is also
  possible

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Why Longevity Could Raise Savings Rates

• Possible Arguments
• Unhealthy life span increase.
• Effect of longer lifespan on compounding when
  interest rates and income growth are positive.
• Effect on returns to saving. Without annuities,
  a high mortality rate reduces effective returns.
• Our Argument
• Social security system incentives restrict labor
  supply of the elderly and effectively limit the
  retirement age.

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Critique Compression of Morbidity

• If longer life spans are associated with healthy
  aging (compression of morbidity), optimal
  response is to extend the working life with
  little impact on savings rates.
• We can regard a longer life as stretching time,
  which stretches the retirement age but does not
  affect savings rates.
• The empirical effect of longevity on savings
  lacks a theoretical foundation.

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National Life Expectancy and Health, 2000
H Healthy life expectancy LLife expectancy H
-7.062 0.979 L (0.615) (0.010) R2
0.982
Data from World Health Report 2001
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Data for 2000, from World Health Report 2001
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Hypothesis

• Under complete markets the effect of longer life
  spans on savings rates is zero or even negative
• A positive effect of longevity on savings rates
  depends on the presence of institutions that
  prevent or discourage longer working lives.

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Life Cycle Theory

• Maximize lifetime utility with a budget
  constraint

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Assumptions

• Full insurance annuities
• Exogenous health and mortality
• Constant death rate
• Disutility of work rises with age but depends on
  life expectancy compression of morbidity

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Optimal Consumption and Retirement

• Two conditions optimal consumption over time.
• Optimal retirement wage times marginal utility
  of consumption equals the disutility of working.
• General solution defines retirement and
  consumption by an implicit function.

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Figure 1 Retirement and Consumption
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Assume Log Utility

• Use implicit function theorem to find optimal
  retirement and consumption

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Wage Level Effects

• In a model with log utility the wage level does
  not affect the retirement decision income and
  substitution effects balance.
• With a general utility function (CRRA gt 1),
  rising wages promote earlier retirement and a
  lower consumption/wage ratio, i.e., a higher
  savings rate.

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Preliminary Empirical Results Micro

• Use HRS survey. Gives good measures of household
  wealth and subjective survival probabilities for
  individuals.
• Question do people who expect to live longer
  save more and so hold more wealth?
• Problem all current variables depend on wealth.
  Subjective survival probabilities depend on
  wealth and have large measurement error (lots of
  0 or 1 in replies).

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Estimation

• Model current Wealth as depending on
• Inheritances.
• Planned accumulation to date as proxied by a
  function of age, schooling, and height.
• Probability of survival to 75, instrumented with
  parents current age, or age at death.
• Unplanned accumulation to date, the error term.

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Results

• Wealth increases with inheritances.
• Wealth increases with height and education,
  probably reflecting higher income.
• Wealth increases with age in the HRS sample
  (primarily between 40 and 60).
• Instrumented subjective survival probabilities
  have a positive and significant effect on
  wealth holdings. (Passes instrument validity
  test).

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Macro Saving

• Aggregation over cohorts is not stright forward
  depends on the distribution of income.
• Age specific savings rates may rise while average
  savings rates fall when life span increases.
• Zero savings over lifespan means zero saving on
  average in steady state saving is a
  disequilibrium phenomenon.

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Increasing Longevity and Saving
Saving Rate
T
T
0
Age
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Aggregate Savings Rates

• In a stable population, with a fixed life
  expectancy, net life cycle savings are zero.
• A rise in life expectancy with a fixed age
  structure increases aggregate savings the saving
  of the young and middle aged for retirement is
  larger than the dis-saving of the older
  generation.
• This saving boom is temporary it disappears when
  the age structure adjusts to a stable structure
  given the higher lifetimes.

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Table 5 Effects on Steady-State Saving Rate
Effect on Steady-State Saving Rate (percentage points)
Old/ Working Age Ratio rises by 0.01 -1.336 (4.07)
Life expectancy rises by 1 year with universal coverage, mandatory retirement, and a fully funded system 0.424 (2.27)
Life expectancy rises by 1 year with universal coverage, mandatory retirement and a pay-as-you-go system with replacement rate of 0.5 0.003 (0.02)
Life expectancy rises by 1 year with universal coverage, mandatory retirement and a pay-as-you-go system with replacement rate of 1.0 -0.418 (1.90)
Effect of introducing a retirement incentive with life expectancy at 66 years. 2.489 (2.23)
Effect of introducing a retirement incentive with life expectancy at 81 years. 3.055 (3.48)
Effect of moving from a pay-as-you-go system (replacement rate 1.0) to a fully funded system with life expectancy 66 years. 0.005 (0.16)
Effect of moving from a pay-as-you-go system (replacement rate 1.0) to a fully funded system with life expectancy 81 years. 13.148 (2.93)
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Health and Education

• Health and cognitive development
• Incentive effects from longer working life
• Lower depreciation of human capital
• Heath and education complementarities
• Fewer working days lost

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III. The Demographic Dividend
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Evidence

• 1986 NAS report
• The report was revisionist (Kelley 2001) as
  opposed to other population-alarmist reports.
• Little evidence of effects at country level

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Environment and Population

• CO2 Emissions rise with population but are more
  elastic with respect to income
• Log CO21.12 Log Pop 1.48 Log Y
• (0.01) (0.03)
• R2 0.897
• Panel data (5 year)1960-2000 time dummies
  included
• Major threat is rising incomes in India and China
• Acid rain and ozone deletion have had an
  effective global institutional response.
• Global institutional response to global warming
  has been weak.

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Capital and Land Effects

• Free movement of capital prevents declinei n
  capital/labor ratios.
• Effects may be large if capital markets are
  closed/imperfect.
• Land effects may be large in agricultural
  societies.
• But land shortage may spur industrialization.

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Components of Population Growth

• Kelly and Schmidt 1995
• While growth of population numbers does not
  matter, components do matter.
• Population growth birth rate- death rate. High
  birth and death rates both seem to have a
  negative effect on growth.
• Lagged (15 year) birth rate sometimes positive
• handout

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Importance and Problems

• Components of population growth may matter even
  if pop growth is neutral on average.
• Fixed effects estimators are biased
• Does not distinguish behavioral effects from
  accounting effects

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Age Structure Effects
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Age Structure Effects(continued)
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Estimating Equation

• Working age pop growth
• Population growth

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Constraints

• Equation is derived from an identity.
• Some parameters are fixed by the identity
• Coefficients on log initial participation rate p
  and and working age share of pop c should be
  equal size and opposite to coefficient on initial
  income.
• Coefficients on participation rate growth, work
  age pop growth and pop growth should be 1, 1, -1.
• Why estimate these?

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1 2 3
OLS 2SLS 2SLS
log working age over total pop 0.257 (0.118) 0.284 (0.125) 0.180 (0.143)
log participation rate -0.186 (0.058) -0.166 (0.058) -0.164 (0.062)
growth of participation rate -0.570 (0.302) -0.280 (0.527) -0.212 (0.560)
growth of working age over total pop 0.789 (0.329) 1.222 (0.575) -0.793 (0.973)
growth of working age ratio times openness 3.328 (1.184)
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Estimation versus identity

• Identity should be found by estimator if model is
  correct
• Difference between estimate and identity reflects
  mis-specification.
• Model may not adjust fully for changes in labor
  quality when labor quantity is changing rapidly.
• Identity assumes full employment of resources.

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Demographic Dividend is not Automatic

• Depends on effective policies in other areas
• Education
• Labor market
• Trade
• Governance
• Macroeconomic management
• Latin America provides example of "unreaped
  dividend"

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Case Study Ireland

• Rapid Economic Growth 1990s
• Celtic Tiger
• Approaching East Asian Growth Miracle rates.

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Sub-Saharan Africas population
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East Asia's Population
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Ireland's Population
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Why this rapid demographic change in Ireland?

• Mortality rates at European norms.
• Fertility rates high by European standards until
  1979.
• Rapid fertility decline after 1979.
• High levels of migration.

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Family Planning in Ireland

• 1969 The Fertility Guidance Company Ltd. is
  formed (predecessor of the IFPA)
• 1973 Irish Supreme Court legalizes the
  importation of contraceptives for personal use
• 1979 Health (Family Planning) Act becomes law
  sale of contraceptives legalized for family
  planning (with prescription)
• 1985 Amendment to 1979 law makes contra-ceptives
  available to those over 18 without prescription.

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Migration in Ireland

• Relatively large fluctuations endogenous
  response to economic performance
• Sizable impacts on age structure
• Out-migration mainly among 15-24 year olds
• In-migration mainly among 35-44 year olds, plus
  their children

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Ireland Conclusion

• Demographic change has promoted economic
  performance in Ireland.
• Fertility decline was abetted by the family
  planning movement in Ireland and the legalization
  of contraception.
• The policy environment in Ireland favored capture
  of the demographic dividend.
• Ireland's natural demographic dividend is now at
  its peak.

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Questions

• Age structure effects accounting versus
  behavior.
• Conditions that interact with effects of the
  demographic dividend.
• Link from fertility and mortality to age
  structure formal demography.
• Importance of Migration.

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Demographic Accounting

• Age structure effects are accounting to some
  extent.
• Assume age specific behavior remains the same and
  examine the effect of age structure changes
• But there are also behavioral effects

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Mortality Rates

• Declines in age specific mortality rates change
  age structure.
• Mortality decline leads to increase in longevity
  may have life cycle effects.
• Mortality decline also linked to morbidity
  decline healthier people.

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Birth Rates

• Changes in the birth rate affects age structure
• Birth rates changes are usually linked to female
  labor supply.
• Labor supply and fertility jointly determined
  (not one causes the other).
• Lower fertility may be linked to higher levels of
  investment in human capital.

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Policy Interaction

• What policies are most important for making use
  of the extra labor supply that comes from the
  demographic transition?
• Labor market, openness, etc.
• Ireland and many good features.

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Explanations for Irelands Growth

• EU membership and subsidies
• Increased trade and FDI, partly due to tax
  incentives
• Delayed convergence
• Good macroeconomic management
• Social contract between government, trade unions,
  and employers
• Education expansion in the 1970s.
• (Transfer pricing)

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Age Structure and Fertility

• Can we rewrite of growth age structure identity
  in terms of fertility and mortality rates?
• Clearly lagged birth and death rates matter for
  current age structure
• Simple relationship?

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Migration

• Migration is clearly endogenous
• Responds to domestic and international
  opportunities.
• Primarily movements of working age population.
• Loss mitigated by remittances.
• Welfare criteria especially unclear with
  migration.

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The End