Mortality convergence across industrialized countries. Paris - - PowerPoint PPT Presentation

Mortality convergence across industrialized countries.

Paris Seminar in Demographic Economics H´ ector Pifarr´ e i Arolas (with Hippolyte d’Albis and Loesse Jacques Esso)

Toulouse School of Economics

December 3, 2013

Question

The question: Has there been convergence in mortality patterns across industrialized countries since 1960?

Question

◮ In particular, we study the convergence of the distributions of

ages-at-death extracted from the period life tables.

Ages-at-death distribution, US 2009

500 1000 1500 2000 2500 3000 3500 4000 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103 106 109 Number of deaths

Ages-at-death distribution

US 2009

.

Ages-at-death distribution, US and Japan 1960

500 1000 1500 2000 2500 3000 3500 4000 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103 106 109 Number of deaths

Ages-at-death distribution

US 1960 Japan 1960

Ages-at-death distribution, US 1960 and 2009

500 1000 1500 2000 2500 3000 3500 4000 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103 106 109 Number of deaths

Ages-at-death distribution

US 2009 US 1960

Motivation

◮ Why do we care?

◮ Important for the assessment of welfare convergence between

countries (Becker et al., 2005).

◮ It can be used to improve demographic projections (Li and Lee,

2005).

Motivation

Currently, two different approaches:

◮ Study convergence of certain moments of the distribution: life

expectancy, inequality / dispersion (Wilson, 2001 and Peltzman, 2009).

◮ Assess convergence considering the whole distribution (Edwards and

Tuljapurkar, 2005). This is our approach

Roadmap

◮ Methods: Kullback Leibler divergence ◮ General trends

◮ Western and Eastern countries (and EU)

◮ Explaining the trends ◮ Convergence clubs ◮ Conclusions

Methods

◮ The problem: to find a measure of dissimilarity between two

distributions

Methods

500 1000 1500 2000 2500 3000 3500 4000 4500 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103 106 109 Number of deaths

Ages-at-death distribution

US 2009 Japan 2009

.

Methods

◮ We use a measure of dissimilarity between distributions, the

Kullback-Leibler divergence (KLD) (Kullback and Leibler, 1951; also used in Edwards and Tuljapurkar,2005)

◮ For two discrete probability distributions, the divergence of P from Q

is given by KLD (Q P) =

i ln

• Pi

Qi

• Pi

◮ wherePi, Qi are the probability masses in i = 1, ..., N

Methods

◮ Our concept of convergence: any group of countries converges in

mortality if the dissimilarities across their ages-at-death distributions are reduced

◮ We compute the sum of KLDs each year from individual

distributions to the period’s average distribution

◮ It is a shortcut to compute the sum of pairwise KLD between all the

countries in the sample.

Data

◮ We use data from the Human Mortality Database (mortality.org). ◮ Our full sample has 35 countries (and regions)

Australia, Austria, Belgium, Bulgaria, Belarus, Canada, Switzerland, Czech Republic, East Germany, West Germany Denmark, Spain, Estonia, Finland, Civil France, Northern Ireland, United Kingdom, Scotland, Hungary, Ireland, Iceland, Italy, Japan, Lithuania, Luxemburg, Latvia, Netherlands, Norway, Poland, Portugal, Russia, Slovakia, Sweden, Ukraine, USA

General trends

◮ There has been a clear process of divergence in both mortality at

age 0 and adult mortality.

General trends

General trends

◮ However, the overall trend is the result of the interaction of different

trends for different groups

◮ For example, western and eastern countries have marked differences.

General trends

General trends

General trends

◮ However, within Western countires, the EU has converged.

General trends

General trends

Explaining the trends

◮ We study separately western and easter countries to unveil the forces

behind the trends in KLD. Australia, Austria, Belgium, Canada, Switzerland, West Germany, Denmark, Spain, Finland, France, Northern Ireland, Scotland, Ireland, Iceland, UK, Italy, Japan, Luxemburg, Netherlands, Norway, Portugal, Sweden, USA Bulgary, Belarus, Czech Republic, East Germany, Estonia, Hungary, Latvia, Poland, Russia, Slovakia, Ukraine

Explaining the trends

◮ For normal distributions, it is possible to compute the KLD as a

function means and variances (Roberts and Penny, 2002). KLD (Q P) = 1

2 ln

• σ2

P

σ2

Q

• + 1

2 µ2

Q+µ2 p+σQ−2µQµP

µ2

p

− 1

2 ◮ Age-at-death distributions aren’t statistically normal, but this allows

to interpret the contributions of mean and variance to overall trend.

Explaining the trends

◮ A caveat: the effect of changes in the variance is not straightforward. ◮ When comparing two normal distributions (P with respect to Q), the

term

• σ2

P − σ2 Q

• −
• µ2

Q + µ2 p − 2µQ

• ⋚ 0

◮ determines the sign of ∂KLD ∂σ2

P .

◮ When the means are different, a decrease in the variance may

increase the KLD.

Explaining the trends (Western countries)

60 65 70 75 80 85 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Years

Life expectancy, age 0

Australia Austria Belgium Canada Switzerland West Germany Denmark Spain Finland France Northern Ireland Scotland Ireland Iceland UK Italy Japan Luxemburg Netherlands Norway Portugal Sweden USA 60 62 64 66 68 70 72 74 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Years

Life expectancy, age 10

Australia Austria Belgium Canada Switzerland West Germany Denmark Spain Finland France Northern Ireland Scotland Ireland Iceland UK Italy Japan Luxemburg Netherlands Norway Portugal Sweden USA

Explaining the trends (Western countries)

Median absolute deviation, means age 0

year MAD 1960 1970 1980 1990 2000 1.2 1.4 1.6 1.8 2.0 2.2

Median absolute deviation, means age 10

year MAD 1960 1970 1980 1990 2000 1.0 1.2 1.4 1.6 1.8

Explaining the trends (Western countries)

Variances, age 0

Variances, age 10

Australia Austria Belgium Canada Switzerland West Germany Denmark Spain Finland France Northern Ireland Scotland Ireland Iceland UK Italy Japan Luxemburg Netherlands Norway Portugal Sweden USA

Explaining the trends (Western countries)

Median absolute deviation, variances age 0

year MAD 1960 1970 1980 1990 2000 10 20 30 40 50

Median absolute deviation, variances age 10

year MAD 1960 1970 1980 1990 2000 8 10 12 14 16 18 20

Explaining the trends (Western countries)

◮ We compare the values for the KLD holding constant variances. ◮ At age 0, convergence has been driven mostly by reductions in infant

mortality.

◮ The dispersion of life expectancies has slightly decreased and there

has been a strong convergence in variances.

◮ At age 10, the variance has greatly contributed to the dissimilarities.

◮ There is increased dispersion in life expectancies and the variance

has increased slightly too.

Explaining the trends (Eastern countries)

60 65 70 75 80 85 Years

Life expectancy, age 0

Bulgary Belarus Czech Republic East Germany Estonia Hungary Latvia Poland Russia Slovakia Ukraine 50 55 60 65 70 75 Years

Life expectancy, age 10

Bulgary Belarus Czech Republic East Germany Estonia Hungary Latvia Poland Russia Slovakia Ukraine

Explaining the trends (Eastern countries)

Explaining the trends (Eastern countries)

160 210 260 310 360 410 460 510 560 Years

Variance, age 0

Bulgary Belarus Czech Republic East Germany Estonia Hungary Latvia Poland Russia Slovakia Ukraine 120 170 220 270 320 370 Years

Variance, age 10

Bulgary Belarus Czech Republic East Germany Estonia Hungary Latvia Poland Russia Slovakia Ukraine

Explaining the trends (Eastern countries)

Explaining the trends (Eastern countries)

◮ At both age 0 and age 10, divergence has been driven increasing

disparities in life expectancy

◮ Increases in the dispersion of variances have actually contributed

negatively to the KLD.

Convergence clubs (Western countries)

◮ There exist subgroups of countries that converge (e.g. EU vs rest of

capitalist countries).

◮ Are there any clubs of convergence within the sample of western

countries?

Convergence clubs (Western countries)

Convergence clubs (Western countries)

Convergence clubs (Western countries)

◮ There are several countries that change drastically their mean and

variance coordinates (e.g. Japan, Denmark).

◮ We move from countries being distributed along the axis where we

have low variance and high means to increasing disparities.

Convergence clubs (Eastern countries)

◮ How about for Eastern countries?

Convergence clubs (Eastern countries)

Convergence clubs (Easternn countries)

Convergence clubs (Eastern countries)

◮ In the case of Eastern countries, the pattern is reversed.

Conclusions and Next Steps

◮ We have reassessed the mortality convergence hypothesis with a

different definition of convergence.

◮ We find that although there isn’t convergence for the whole sample,

there exist subgroups or convergence clubs (e.g. EU).

◮ Our resultsnegate the basic hypothesis of previous works: there isn’t

evidence of a common steady state across countries.

◮ Next steps include investigating the set of variables that defines a

convergence club and the stability over time of the clubs.

◮ In particular, our preliminary analysis seems to indicate a strong

effect of political federations.

◮ Thanks for coming!