Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability Dynamic Population Structure with Stochastic Mortality and Fertility Rates Yu Lin, Xiaoming Liu The University of Western Ontario July 19, 2012 Dynamic Population Structure with Stochastic
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Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Dynamic Population Structure with StochasticMortality and Fertility Rates
Yu Lin, Xiaoming LiuThe University of Western Ontario
July 19, 2012
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Objectives
Propose a population structure model based on the Lesliematrix, validate the model with U.S. population data
Predict future population structure and explore the impacton the future labour force stability
Investigate the impact of a DC pension system on the laborforce stability, based on the predicted population structure
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Objectives
Propose a population structure model based on the Lesliematrix, validate the model with U.S. population data
Predict future population structure and explore the impacton the future labour force stability
Investigate the impact of a DC pension system on the laborforce stability, based on the predicted population structure
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Objectives
Propose a population structure model based on the Lesliematrix, validate the model with U.S. population data
Predict future population structure and explore the impacton the future labour force stability
Investigate the impact of a DC pension system on the laborforce stability, based on the predicted population structure
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Leslie Matrix
nx: Population size of each age group x
sx: Survival probability for x, (nx+1)t+1 = sx(nx)t
fx: Total birth rate among those who are at age group xAt time t+ 1, the population of the new born is
(n0)t+1 =
ω−1∑x=0
fx(nx)t
n0n1n2. . .nω−1
t+1
=
f0 f1 f2 . . . fw−2 fω−1
s0 0 0 . . . 0 00 s1 0 . . . 0 0
. . .0 0 0 . . . Sω−2 0
n0n1n2. . .nω−1
t
This can be written as, nt+1 = Lnt.Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Leslie Matrix
Historical data not satisfy the stable growth rate assumption
Leslie Model modification
nt+1 = Lnt
⇓
nt+1 = Ltnt
Population is divided into five-year age groups and projectedevery five years
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Leslie Matrix
Historical data not satisfy the stable growth rate assumption
Leslie Model modification
nt+1 = Lnt
⇓
nt+1 = Ltnt
Population is divided into five-year age groups and projectedevery five years
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Leslie Matrix
Historical data not satisfy the stable growth rate assumption
Leslie Model modification
nt+1 = Lnt
⇓
nt+1 = Ltnt
Population is divided into five-year age groups and projectedevery five years
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Projected Population Structure
Figure: Projected Population Size in 1955 and 1995
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Projected Population Structure
Figure: Projected and Observed Population Size in 1995
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
The Impact of Immigration Population
nx is the current population size for age group x;n is the total population size for all ages;tx is the immigration population for age group x;t is the total immigration population size.Assumption: Immigration population has the same agedistribution as the original population
tx/t = nx/n
After immigration, the population percentage for age group x is,
nx + txn+ t
=nx + nxt/n
n+ t=
(nxn+ nxt)/n
n+ t=nxn
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Projected Population Structure
Figure: Projected and Observed Population Percentage in 1995
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Lee-Carter Model
logmx,t = ax + bxkt + εx,t
kt+1 = kt + c+ et, et ∼ N(0, σ2)
mx,t describes the observed central death rate at age x in year t;ax describes the age pattern of mortality averaged over time;bx describes the deviations from the averaged pattern when ktvaries;kt describes the variation in the level of mortality over time.
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Fertility Forecasting Using Lee-Carter Model
(a) Before log Transformation (b) After log Transformation
Figure: Fertility Rates by Age of Mother from 1976-2006
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Fertility Forecasting (Comparison)
Figure: Projected and Observed Population Percentage in 1995
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Fertility Forecasting (Comparison)
Figure: Projected and Observed Population Percentage in 2005
Dynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability
Future Population Structure Prediction
Figure: Predicted Population Percentage in future yearsDynamic Population Structure with Stochastic Mortality and Fertility Rates
Population Structure Mortality and Fertility Forecasting Impact on Labour Force Stability