of childbearing in low-fertility countries Nan Li and Patrick Gerland, United Nations * Abstract In most developed countries, total fertility reached below-replacement level and stopped changing notably. Contrary to the almost stationary fertility level, the mean age of childbearing () is increasing markedly, reflecting a more general postponement transition that may correspond to fundamental shifts for society (Lee and Goldstein, 003, Billari, 005). The postponement of childbearing, however, includes changes in fertility at all reproductive ages, which are more complicated than the increase of. Using the idea of the Lee-Carter (99) method that deals with mortality, we show that the changes in the age pattern of fertility can be well described by a single variable, which leads to simple ways of projection. We discuss some application issues using the data from Italy, and describe a condition under which the model is epected to work well for other countries. The model and its estimations Most fertility studies deal with age-specific fertility rate (ASFR), which sums to total fertility (TF) over the reproductive ages. To model the age pattern of fertility, we focus on the proportionate ASFR, which is ASFR/TF, and sums to over the reproductive ages. Denote the proportionate ASFR at age and time t by Fp(,, and denote the overtime average of Fp(, by a(, the model can be written as Fp (, a( + b( k(. () where b( is the rate of change by age groups and k( is the overall time trend. One may see immediately that the right-hand side is identical to the Lee-Carter (99) model. In fact, what we really borrowed from the Lee-Carter method is the idea, which is * Population Estimates and Projection Section, United Nations Population Division, Dept. of Economic and Social Affairs, United Nations, New York, NY 007, USA. The views epressed in this paper are those of the authors and do not necessarily reflect those of the United Nations. Its contents has not been formally edited and cleared by the United Nations.
to convert the task of dealing with a group of variables (Fp(, at different ages) to that of handling a single variable k(. Parameters b( and variable k( in model () can be estimated in various ways, and we discuss two below. The first estimation is obtained using the ordinary least squares (OLS). To see this, let b( =. () Thus, k( is the difference between the observed at time t and the given by a(: Fp(, a( = k( b( = k(. (3) Since k( is known, b( is solvable using OLS to minimise t [ Fp(, a( b( k( ] with constrain (): Fp(, k( t b( = k (. (4) t An advantage of the first estimation is that the model is identical to the observed value at any time. The disadvantage of first estimation is, however, that the difference between the observed and model Fp(, has no constraint on valid bounds. The second estimation is obtained using the singular value decomposition (SVD), which provides the values of b( and k( that minimises t [ Fp(, a( b( k( ] (see, Lee and Carter, 99). For their convenience, Lee and Carter scaled the b( to sum to over all. For our convenience, we scale the b( as in (), so that k( is the difference between the model at time t and the given by a(. The advantage of the second estimation is that the sum of the squared difference between the observed and model Fp(, is minimised. A disadvantage of the second estimation, however, is that there are differences between the observed and model values of, which is zero using the first estimation.
Some application issues Denote by Fpm(, the model value of Fp(,. The eplanation ratio, which indicates the proportion of the variance of Fp(, eplained by Fpm(,, is defined as [ Fp(, Fpm(, ] t R = [ Fp(, a( ]. (5) t Using the data on Fp(, in Table, we have R=0.85 (SVD) and R=0.75 (OLS). Table. Italian proportionate ASFR 5-9 0-4 5-9 -34 35-39 40-44 45-49 950-955 0.033 0.5 0. 0.6 0.6 7 0.005 955-960 0.037 0.4 0.3 0.3 0.4 8 0.004 960-965 0.34 0.3 0.3 0.4 4 0.003 965-970 0 0.57 0.37 0.0 0.7 0.036 0.003 970-975 3 0.78 0.3 0.0 0.03 0.03 0.00 975-980 9 0.0 0.33 0.94 6 0.003 980-985 5 0.8 0.347 4 0.00 985-990 0.038 0.37 0.363 0.48 0.096 0.09 0.000 990-995 0.03 0.85 0.354 0.9 0.9 0.0 0.000 995-000 0.09 0.44 0.37 0.36 0.47 0.00 000-005 0.0 0.34 0.95 0.337 0.7 0.034 0.000 Sources: UNSD and Eurostat Thus, as we epect, SVD worked better than OLS did in terms of describing Fp(,. On the other hand, as is shown in the third panel of Figure, SVD cannot perfectly fit the (, which is described eactly by OLS. Therefore, which estimation to use depends on which variable, Fp(, or Mac(, is more important to the user. 3
Why does the model work well? Putting in the continuous version, () yields [ Fp(, a( ] { [ Fp(, a( ] d dt [ Fp(, a( ] k( d dt d dt [ Fp(, a( ]} 0. k(, Thus, the condition for () to work well is that the rates of change in [Fp(,-a(] are similar at different ages. In fact, the changes of age pattern of fertility that we concern are two rotations. The first rotation is caused by the reduction of childbearing at older ages, in which [Fp(,-a(] rises at younger and drops at older ages. And the second rotation is due to postponing childbearing, in which [Fp(,-a(] drops at younger and rises at older ages. When such rotations take place at the rates that are similar over ages, (6) holds. Therefore, we may epect () to work well not only for the data of Italy, but also those when the rotations take place evenly over age. Turning to projection, the above model will yield a maimum, namely m, older than which the model will produce negative values for Fp(, at some (6) 4
younger ages. This is because that b( is negative at younger ages, which will make Fp(, negative when k( rises to a certain level Km: a( Km = min[ ], b( < 0. (7) b( Since k( differs with ( by a constant According to () and (), the maimum is written as m = a( + Km. (8) a (, Km leads to the m. Using data in 950-005, the m is estimated as 3.0 by SVD, or 3. by OLS. Given the model (SVD) values of ( and m as eample, there are various simple ways to project future (. Among these, the one shown in the third panel is perhaps the simplest, in which the ( converges to m eponentially at the pace measured from its last two values. When ( is projected, so are the Fp(, using (), as can be seen in the last panel of Figure. When the m given by (8) looks too small to be plausible, for eample of many East European countries, we suggest use a plausible maimum that may be taken from other countries, and replace the subsequent negative values of the projected Fp(, at a certain by its last positive value. By doing so, we projected a more plausible trajectory for the, and stopped following the modelled projection of Fp(, when it becomes negative. 5
References Lee, R. D. and L. Carter. 99. Modelling and Forecasting the Time Series of U.S. Mortality. Journal of the American Statistical Association 87: 659 7. Lee, R. and J.R. Goldstein. 003. Rescaling the life cycle: Longevity and proportionality. Population and Development Review, 9: 83-07. Billari, F. 005. Partnership, childbearing and parenting: Trends of the 990s. In The new demographic regime: Population challenges and policy responses. United Nations: New York and Geneva. 6
0/7/009 Modelling and projecting the postponement of childbearing in low-fertility countries Nan Li & Patrick Gerland IUSSP 009 Marrakech, Morocco ( Oct. 009) Session 64: Timing of fertility and family transitions in Europe United Nations Population Division Estimates and Projection Section Outline Background Data Estimation and forecasting model Results and findings The views and opinions epressed in this slides are those of the author and do not necessarily represent those of the United Nations. The contents has not been formally edited and cleared by the United Nations. The designations employed and the material in these slides do not imply the epression of any opinion whatsoever on the part of the Secretariat of the United Nations concerning the legal status of any country, territory or area or of its authorities, or concerning the delimitation of its frontiers or boundaries IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org)
0/7/009. Issue: Total fertility vs. Mean Age of Childbearing (980-007) keeps rising while TF stagnates below replacement level or fluctuates toward replacement level Italy: Covariance [TF,]=-0.09.6 Western Europe Italy (980-005): Covariance[TF,] =-0.09 3.4 TF. 6 980 985 990 995 000 005 00 IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org)
.5.8.6.4..8.6.4. 980 985 990 995 000 005 00 6 Austria (980-007): Covariance[TF,] =-0.07 980 985 990 995 000 005 00 6.9.8.7.6.5 980 985 990 995 000 005 00 7.5.5 Finland (980-007): Covariance[TF,] =0.03 980 985 990 995 000 005 00 4 Czech Republic (980-007): Covariance[TF,] =-0.46.5.5 Bulgaria (980-007): Covariance[TF,] =-0.8 980 985 990 995 000 005 00 3 9.5 Denmark (980-007): Covariance[TF,] =0.5 980 985 990 995 000 005 00 5.6.4..8 980 985 990 995 000 005 00 6 6 6 4 Iceland (980-007): Covariance[TF,] =-.5 35.4..8.6.4 Hungary (980-007): Covariance[TF,] =-0. 980 985 990 995 000 005 00 0.8.6.4..8.6.4 9.5 9.5 7.5 7 6.5. 980 985 990 995 000 005 00 7 9 7.8 France (980-007): Covariance[TF,] =0.0.6 980 985 990 995 000 005 00 6.5.5 980 985 990 995 000 005 00 Estonia (989-007): Covariance[TF,] =- Ireland (986-007): Covariance[TF,] =-. 980 985 990 995 000 005 00 5 5..8.6.4. 980 985 990 995 000 005 00 6 9.5 7.5 7 6.5 6 5.5.95.9.85.8.75 Poland (990-007): Covariance[TF,] =-0.9 3.7.8.6.4.5.5 980 985 990 995 000 005 00 Luembourg (980-007): Covariance[TF,] =0.07. 980 985 990 995 000 005 00 6 Norway (980-007): Covariance[TF,] =.65 980 985 990 995 000 005 00 6.5.5.5.5 7.5 7 6.5 Lithuania (980-007): Covariance[TF,] =- 9.5 9.5 7.5 7 3 9.5 9.5 7.5 980 985 990 995 000 005 00 5.5.5.8.75.7.65.6.55.5 Netherlands (980-007): Covariance[TF,] =.45 980 985 990 995 000 005 00 7.5..8.6 Sweden (980-007): Covariance[TF,] =-0.03.4 980 985 990 995 000 005 00 7 Slovakia (980-007): Covariance[TF,] =-0.38 980 985 990 995 000 005 00 4 7 6 6 3 3.5 9.5 9.5 3 9.6.5.4 3 9 Switzerland (980-007): Covariance[TF,] =-.3 980 985 990 995 000 005 00 6.85.8.75.7.65 United Kingdom (980-005): Covariance[TF,] =-0.0.6 980 985 990 995 000 005 00 7 Slovenia (98-007): Covariance[TF,] =-0.5 980 985 990 995 000 005 00 5 Romania (980-007): Covariance[TF,] =- 980 985 990 995 000 005 00 4 6 3 9.5 9.5 7.5 0/7/009 Southern Europe Greece: Covariance [TF,]=-0. Spain: Covariance [TF,]=-0. Greece (980-007): Covariance[TF,] =-0. Spain (980-007): Covariance[TF,] =-0. Portugal: Covariance [TF,]=-0.4 Portugal (980-007): Covariance[TF,] =-0.4 Austria Cov=-0.07 Western Europe Denmark France Luembourg Netherlands Switzerland Cov=0.0 Cov= Cov=0.5 Cov=0.07 Cov=- Northern Europe Finland Iceland Ireland Norway Sweden U.K. Cov=- Cov=0.03 Cov=- Cov= Cov=-0.03 East-Central Europe Czech Rep. Hungary Poland Slovakia Slovenia Cov=-0.46 Cov=-0.9 Cov=-0.38 Cov=-0.5 Cov=-0.0 Cov=-0. Eastern Europe Bulgaria Estonia Lithuania Romania Cov=-0.8 Cov=- Cov=- Cov=- IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 3
0/7/009. Data Data sources Eurostat database (http://europa.eu/estatref/download/everybody) 5 countries with annual fertility rates by single age for the last 5 years or more. Western Europe: Austria, Denmark, France métropolitaine, Luembourg (Grand-Duché), Netherlands, Switzerland. Northern Europe: Finland, Iceland, Ireland, Norway, Sweden, United Kingdom 3. Southern Europe: Greece, Italy, Portugal, Spain 4. East-Central Europe: Czech Republic, Hungary, Poland, Slovakia, Slovenia 5. Eastern Europe: Bulgaria, Estonia, Lithuania, Romania IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 4
0/7/009 3. Model and estimation strategy Age pattern of fertility modelling F(, = age-specific fertility rate at age and time t TF ( t ) 50 5 F (, t ) Fp(, = proportionate age-specific fertility rate at age and time t F (, Fp (, TF ( with 50 5 Fp (, Italy: Fp(, 0.09 980 (=7.6) 005 (=.8) 0.07 0.03 0.0 0.0 0.00 5 0 5 35 40 45 50 IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 5
0/7/009 Age pattern of fertility modelling Fp (, a( b( k ( Identical to Lee, R. D. and L. Carter. 99. Modelling and Forecasting the Time Series of U.S. Mortality. Journal of the American Statistical Association 87: 659 7. a( = over-time average of Fp(, b( = rate of change by age groups k( = overall time trend a( = average (pas age pattern IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 6
0/7/009 Two ways to estimate b( and k( () Ordinary Least Squares (OLS) rescaling b( to get b ( k( = difference between observed at time t and given by a( Fp (, a ( k ( b ( k ( and b( t Fp (, t ) k ( t ) t k ( t ) Solved by minimizing t [ Fp (, a( under constraint that b( k ( ] b ( Two ways to estimate b( and k( () Singular Value Decomposition (SVD) by minimizing: [ Fp (, a( b( k ( ] t rescaling b( to get b ( k( = difference between the model at time t and the given by a( IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 7
( Fp(, b( k( Modelling and projecting the postponement 0/7/009 A.Italy (980-005): Rate of change by age b( B.Italy (980-005): Time Trend k( 0.0 b(.5 k( 0.005 0.5 0 0-0.5-0.005 - OLS SVD -0.0 OLS -.5 SVD - 5 0 5 35 40 45 50-980 985 990 995 000 005 Age Year t C.Italy (980-005): Mean Age of Childbearing ( D.Italy: ASFR density distribution PASFR( 3.5 3 3.5 (005) =.8 0. 0.09 Fp(, 980 005 050 (OLS proj.) 050 (SVD proj.) 3 Maimum : 0.07 m: OLS=3.5 SVD=3.5.5 9.5 9.5 OLS SVD Observed OLS Proj. mac050=3.4 SVD Proj. mac050=3.3 7.5 980 990 000 00 00 0 040 050 Year t 0.03 0.0 0.0 0 5 0 5 35 40 45 50 Age OLS vs. SVD: Pros and cons () OLS: best to fit, but estimates of b( and k( done sequentially, and difference between the observed and model Fp(, has no constraint on valid bounds () SVD: best to fit overall age pattern, estimates of b( and k( done simultaneously with constraints on valid bounds but differences between observed and model values of IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 8
0/7/009 Goodness of fit Eplanation Ratio (R) = proportion of the variance of Fp(, eplained by Fpm(, which is the model value of Fp(, [ Fp (, t ) Fpm (, t )] R t [ Fp (, t ) a ( ] t Maimum m = age limit at which the model will produce negative values for Fp(, at younger ages because b( < 0 at younger ages and k( rises to a certain level Km: Km min[ a( ], b( b( Since k( differs with ( by a constant Km leads to 0 a ( m a ( Km IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 9
0/7/009 K( projection from 005-07 to 050 Only k( term in model is time dependent and needs to be projected Since k( = difference between the model at time t and the given by a( Project ( to converge toward m eponentially using trend for past 0 years. 4. Results and Findings IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 0
0/7/009 Model fitting performance () very good fit for most countries (>80% or even 90% variance eplained) () SVD fit outperforms OLS fit Country minyear mayear CovTfMac R(OLS) R(SVD) Western Europe Austria 980 007-0.07 0.93 0.93 Denmark 980 007 0.5 0.96 0.97 France 980 007 0.0 0.94 0.95 Luembourg 980 007 0.07 0.79 0.80 Netherlands 980 007 0.95 0.96 Switzerland 980 007-0.9 0.9 Northern Europe Finland 980 007 0.03 0.88 0.89 Iceland 980 007-0.8 0.8 Ireland 986 007-0.85 0.89 Norway 980 007 0.97 0.97 Sweden 980 007-0.03 0.96 0.97 United Kingdom 980 005-0.0 0.94 0.96 Southern Europe Greece 980 007-0. 0.9 0.9 Italy 980 005-0.09 0.93 0.93 Portugal 980 007-0.4 0.89 0.90 Spain 980 007-0. 0.85 0.86 East-Central Europe Czech Republic 980 007-0.46 0.95 0.95 Hungary 980 007-0. 0.93 0.93 Poland 990 007-0.9 0.97 0.98 Slovenia 98 007-0.5 0.93 0.93 Slovakia 980 007-0.38 0.96 0.96 Eastern Europe Bulgaria 980 007-0.8 0.9 0.95 Estonia 989 007-0.95 0.95 Lithuania 980 007-0.70 0.77 Romania 980 007-0.8 0.89 a( = average age pattern of fertility 0.09 A. Western Europe Austria (=7.6) 0.09 B. Northern Europe Finland (=9) 0.09 C. Southern Europe 0.07 Switzerland (=9.3) Denmark (=.8) France (=.7) Luembourg (=.7) Netherlands (=9.5) 0.07 Ireland (=.4) Iceland (=.) Norway (=.5) Sweden (=9.) United Kingdom (=) 0.07 Spain (=9.6) Greece (=7.9) Italy (=9.4) Portugal (=) 0.03 0.03 0.03 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.00 5 0 5 35 40 45 50 5 0 5 35 40 45 50 0.00 5 0 5 35 40 45 50 D. East-Central Europe E. Eastern Europe 0.09 0.07 Czech Republic (=6) Hungary (=6.4) Poland (=7.3) Slovenia (=7.) Slovakia (=6) 0.09 0.07 Bulgaria (=4.5) Estonia (=6.6) Lithuania (=6.6) Romania (=5.6) 0.03 0.03 0.0 0.0 0.0 0.0 0.00 5 0 5 35 40 45 50 0.00 5 0 5 35 40 45 50 IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org)
0/7/009 b( = rate of change by age A. Western Europe B. Northern Europe C. Southern Europe 0.0 0.006 0.00-0.004 5 0 5 35 40 45 50 Austria -0.009 Switzerland - Denmark France -0.09 Luembourg Netherlands - 0.0 0.006 0.00-0.004 5 0 5 35 40 45 50 Finland -0.009 Ireland - Iceland Norway -0.09 Sweden - United Kingdom 0.0 0.006 0.00-0.004 5 0 5 35 40 45 50-0.009 Spain Greece - Italy -0.09 Portugal - D. East-Central Europe E. Eastern Europe 0.0 0.006 0.00-0.004 5 0 5 35 40 45 50 0.0 0.006 0.00-0.004 5 0 5 35 40 45 50-0.009 - -0.09 Czech Republic Hungary Poland Slovenia -0.009 - -0.09 Bulgaria Estonia Lithuania Romania - Slovakia - k( = overall time trend A. Western Europe B. Northern Europe C. Southern Europe 4.05 3.05.05 Austria Switzerland Denmark France Luembourg Netherlands 4.05 3.05.05 Finland Ireland Iceland Norway Sweden United Kingdom 4.05 3.05.05.05.05.05 Spain Greece -0.95-0.95-0.95 Italy Portugal -.95 980 990 000 00 00 0 040 050 -.95 980 990 000 00 00 0 040 050 -.95 980 990 000 00 00 0 040 050 D. East-Central Europe E. Eastern Europe 4.05 3.05 4.05 3.05.05.05 Czech Republic Hungary Poland -0.95 Slovenia Slovakia -.95 980 990 000 00 00 0 040 050.05.05-0.95 Bulgaria Estonia Lithuania Romania -.95 980 990 000 00 00 0 040 050 IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org)
0/7/009 Mean Age of Childbearing ( 33 3 3 A. Western Europe 33 3 3 B. Northern Europe 33 3 3 C. Southern Europe 9 Austria Switzerland 7 Denmark 6 France Luembourg 5 Netherlands 4 3 980 990 000 00 00 0 040 050 9 Finland 7 Ireland Iceland 6 Norway 5 Sweden 4 United Kingdom 3 980 990 000 00 00 0 040 050 9 Spain 7 Greece 6 Italy 5 Portugal 4 3 980 990 000 00 00 0 040 050 33 D. East-Central Europe 33 E. Eastern Europe 3 3 9 Czech Republic 7 Hungary 6 Poland 5 Slovenia 4 Slovakia 3 980 990 000 00 00 0 040 050 3 3 9 7 6 5 4 Bulgaria Estonia Lithuania Romania 3 980 990 000 00 00 0 040 050 Mean Age of Childbearing Maimum Mean Age Decennial Modal Age Median Age Country 005 050 Increase 005 050 005 050 Western Europe Austria.9 9.0.7 0.4.7..4.0 Denmark 3.7.3 3.5 0.3 9.9.8 9.6.8 France 3.7 9.7 3.0 0.3 9.. 9.0. Luembourg 3.7 9.8 3.5 0.4.0 3.9 9.3 3. Netherlands 3.7.6 3. 0..8 3.4..7 Switzerland 33..6 3.7 0.5.8 3.5. 3. Northern Europe Finland 3.4 9.9 3. 0.3 9.7.9 9.4.5 Iceland 3.0 9.4.9 0.3.8 9.9.6.0 Ireland 3.0 3. 3.9 0. 3.8 33.8 3.3 3.5 Norway 3.4 9.8 3. 0.3 9.7.7 9..5 Sweden 3..5 3.0 0.3.5 3.5.0 3.3 United Kingdom 3.8 9..6 0.3.4 3.6.7 3. Southern Europe Greece.9 9.9.9 0. 9.6.3 9.. Italy 3.5 3.0 3.3 0.3 3.0 3.0.4 3.7 Portugal. 9.3. 0. 9.7.5.9 9.8 Spain 3.4.9 3.4 0. 3.5 3.0.7 3. East-Central Europe Czech Republic.6.6.6 0.4. 9.0 7.9.9 Hungary.3.5.3 0.4.5 9.5.0 9.5 Poland 9.8. 9.8 0.3 7.4.9 7.4.9 Slovenia 3.3 9.4 3. 0.4.6 9.5.5 9.3 Slovakia 9.5 7.7 9.6 0.4 7.4 9.0 7.0 9.0 Eastern Europe Bulgaria 7.8 6. 7.7 0.4 5.5.0 5. 7.4 Estonia.0..3 0.5 7.3 9. 7.4 9.5 Lithuania 9.3 7.6 9.3 0.4 6.3.0 6.7.3 Romania.3 6.7. 0.3 6.3.5 6.0 7.9 IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 3
p(90)-p(0 p(90)-p(0 p(90)-p(0 p(90)-p(0 p(90)-p(0 0/7/009 38 36 34 3 6 Dispersion of the fertility age distributions Italy 4 Mean Mode p(0) 38 0 Median p(90) 36 8 34 980 990 000 00 00 0 040 050 3 p(90) = Age for upper 90 percentile p(0) = Age for lower 0 percentile 6 4 0 Mean Mode p(0) Median p(90) Czech Republic 8 980 990 000 00 00 0 040 050 Median age vs. p(90)-p(0) age dispersion 8 7 6 5 4 3 0 9 8 A. Western Europe Austria Switzerland Denmark France Luembourg Netherlands 3 4 5 6 7 9 3 3 33 Median 8 7 6 5 4 3 0 9 8 D. East-Central Europe 8 7 6 5 4 3 0 9 8 Finland Ireland Iceland Norway Sweden United Kingdom B. Northern Europe 3 4 5 6 7 9 3 3 33 Median Czech Republic Hungary Poland 980 050 Slovenia Slovakia 3 4 5 6 7 9 3 3 33 Median 8 7 6 5 4 3 0 9 8 8 7 6 5 4 3 0 9 8 Spain Greece Italy Portugal C. Southern Europe 3 4 5 6 7 9 3 3 33 Median E. Eastern Europe Bulgaria Estonia Lithuania Romania 3 4 5 6 7 9 3 3 33 Median IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 4
Fp(, 0/7/009 Projected age pattern in 050 A. Western Europe B. Northern Europe C. Southern Europe 0.0 Austria Switzerland Denmark France Luembourg Netherlands 0.0 Finland Ireland Iceland Norway Sweden United Kingdom 0.0 Spain Greece Italy Portugal 0.0 0.0 0.0 0.00 0.00 0.00 5 0 5 35 40 45 50 5 0 5 35 40 45 50 5 0 5 35 40 45 50 0.0 D. East-Central Europe Czech Republic Hungary Poland Slovenia Slovakia 0.0 E. Eastern Europe Emerging of bi-modal age distributions Bulgaria Estonia Lithuania Romania 0.0 0.0 0.00 5 0 5 35 40 45 50 0.00 5 0 5 35 40 45 50 0. 0.09 Emerging of bi-modal age distributions United Kingdom 980 005 050 (OLS proj.) 050 (SVD proj.) 0.07 0.03 0.0 0.0 0 5 0 5 35 40 45 50 Age IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 5
( Fp(, b( k( Modelling and projecting the postponement 0/7/009 b( = rate of change by age B. Northern Europe 0.0 0.006 0.00-0.004 5 0 5 35 40 45 50-0.009 B. Northern Europe - -0.09 - Ireland United Kingdom Lack of decline (or even increase) in fertility under age 0 in UK, Ireland, Slovakia, Bulgaria, Romania, etc. 0.0 0.006 0.00-0.004 5 0 5 35 40 45 50-0.009 - -0.09 - Finland Ireland Iceland Norway Sweden United Kingdom Challenges with East-Central Europe and Eastern Europe A.Czech Republic (980-007): Rate of change by age b( B.Czech Republic (980-007): Time Trend k( 3.5 OLS 0.0 3 SVD.5 0.005 0.5-0.005 0.5-0.0 OLS 0 - b( < 0 SVD -0.5 - -0.0 5 0 5 35 40 45 50 Age -.5 980 985 990 995 000 005 Year t C.Czech Republic (980-007): Mean Age of Childbearing ( D.Czech Republic: ASFR density distribution PASFR( 0. 0.09 980 007 9 7 6 5 (007) =.8 Maimum : m: OLS=9.6 SVD=9.5 artificial stagnation OLS SVD Observed 0.07 0.03 0.0 050 (OLS proj.) 050 (SVD proj.) Fp(, < 0 due to b( < 0 OLS Proj. mac050=9.6 0.0 SVD Proj. mac050=9.5 4 980 990 000 00 00 0 040 050 Year t 0 5 0 5 35 40 45 50 Age IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 6
b( ( ( Fp(, k( Fp(, 0/7/009 Additional constraints If m <= latest observed or implausibly low, compute m using eperience from other countries m = latest * ratio from all countries (ecept Central & Eastern Europe) of [average(m) / average(latest )] = latest *.05 Replace subsequent negative values of the projected Fp(, at a certain by its last positive value. -0.0 Eample: Czech Republic 5 0 5 35 40 45 50 0.0 0.005 9 0-0.005 7-0.0-6 Age A.Czech Republic (980-007): Rate of change by age b( C.Czech Republic (980-007): Mean Age of Childbearing ( (007) =.8 Maimum : m: OLS=9.6 SVD=9.5. Unconstraint OLS OLS SVD SVD - Observed 5 0 5 35 40 45 50 OLS Proj. mac050=9.6 Age SVD Proj. mac050=9.5 4 980 990 000 00 00 0 040 050 Year t -.5 980 985 990 995 000 005 3.5 3.5 0. 0.09.5 0.07 0.5 0-0.5 0.03 - OLS Year t B.Czech Republic (980-007): Time Trend k( SVD D.Czech Republic: ASFR density distribution PASFR( 980 007 050 (OLS proj.) 050 (SVD proj.) 0.0 -.5 980 985 990 995 000 005 0.0 Year t 0 5 0 5 35 40 45 50 Age 3 C.Czech Republic (980-007): Mean Age of Childbearing ( 0. D.Czech Republic: ASFR density distribution PASFR( 9 (007) =.8 Maimum : (input=.6) m: OLS=9.6 SVD=9.5 0.09 0.07 980 007 050 (OLS proj.) 050 (SVD proj.) 7. Constraint Constraint: OLS = min(pasfr)>=0 SVD = min(pasfr)>=0 6 5 OLS SVD Observed OLS Proj. mac050=.6 SVD Proj. mac050=.6 4 980 990 000 00 00 0 040 050 Year t 0.03 0.0 0.0 0 5 0 5 35 40 45 50 Age IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 7
0/7/009 Mean age in 050 Sensitivity analysis Country n=0 n=5 n=5 Western Europe Austria.7.7.6 Denmark 3.5 3.5 3.5 How much does the length of the reference period matters to project k(? -> use the latest 0, 5,, 5 years? France 3.0 3. 3. Luembourg 3.5 3.5 3.4 Netherlands 3. 3.4 3.5 Switzerland 3.7 3.6 3.5 Northern Europe Finland 3. 3. 3. Iceland.9.7.8 Ireland 3.9 3.9 Norway 3. 3. 3. Sweden 3.0 3.0 3.8 United Kingdom.6.7.7 Southern Europe Greece.9.9.9 Italy 3.3 3.3 3.3 Portugal...0 Spain 3.4 3. 3.0 East-Central Europe Czech Republic.6.5.4 Hungary.3.. Poland 9.8 9.7 Slovenia 3. 3. 3. Slovakia 9.6 9.6 9.4 Eastern Europe Bulgaria 7.7 7.7 7.5 Estonia.3.3 Lithuania 9.3 9.3 9.0 Romania.. 7.9 4.05 3.05.05 Netherlands: trend in Austria Switzerland Denmark France Luembourg Netherlands k( Western Europe.05-0.95 -.95 980 990 000 00 00 0 040 9 050 33 3 3 7 6 5 4 ( Western Europe Austria Switzerland Denmark France Luembourg Netherlands 3 980 990 000 00 00 0 040 050 IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 8
0/7/009.05.55.05 0.55-0.45 Netherlands: trend in k( k( Netherlands k( observed -0.95 k( projected with n=0 k( projected with n=5 -.45 k( projected with n=5 0.0 -.95 0.09 980 990 000 00 00 0 040 050 0.07 0.03 0.0 0.0 Sensitivity of the length of period of reference used to project trend in k( n= 0, 5,, 5 on age pattern of fertility in 050 Limited effect, overall very robust Age-Specific Fertility Pattern 007 n=0,050 n=5,050 n=5,050 0.00 5 0 5 35 40 45 50 Conclusion Overall approach robust and fleible to project fertility age patterns for below-replacement countries SVD fitting performs better than OLS to find b( and k( High consistency within and between regions for future age patterns of fertility Identification of special cases:. Adolescent fertility not declining in some countries potentially leading to future bi-modal age distributions ;. Special case of Central and Eastern Europe postponing childbearing through very pronounced declines at younger and rises at older ages requiring additional projection constraints. IUSSP 009 - Session 64 - Nan Li (li3@un.org) & Patrick Gerland (gerland@un.org) 9