sex ratio at birth by vietnamese region estimation and

Sex Ratio at Birth by Vietnamese RegionEstimation and Projection, a Bayesian modeling

approach

Fengqing Chao

Statistics Program, King Abdullah University of Science and Technology(KAUST)

Session 56 Time Series ModelingENAR Spring Meeting (virtual)

Mar 16th, 2021

March 16, 2021

Introduction Data Method Results Summary

Background

Sex Ratio at Birth (SRB)

SRB: ratio of male to female births.

An important indicator:

For population estimation and projection.To assess the prenatal gender equality.

SRB imbalance

The biological/natural SRB fluctuates within a narrow bandbetween 1.03–1.07 (i.e. 103 to 107 male births per 100 femalebirths).

Since 1970, observed SRB in some Asian and EasternEuropean countries are much higher than the natural level.

Fengqing Chao Mar 2021 ENAR


Background

SRB imbalance (cont.)

The imbalanced (usually upward inflated) SRB is due to thecoexistence of 3 main factors:

1 Strong son preference at population level.2 Sex determine and abortion technology is accessible and

affordable.3 Family size is getting smaller over time.

On national level, Chao et al. PNAS 2019 reports 12 placeswith SRB inflation:

Albania; Armenia; Azerbaijan; China; Georgia; Hong Kong;India; Republic of Korea; Montenegro; Taiwan; Tunisia;Vietnam.



Background

Vietnam demography and SRB imbalance

Great heterogeneity of Vietnamese culture across regions:

North: strict patrilineal family system, influenced by China.South: less acute need for a male child felt by couples, due tothe Khmer culture and bilateral kinship sytem.

SRB imbalance in Vietnam began in 2001 (later than mostAsian countries).

Important to estimate and project SRB and assess the SRBimbalance by Vietnam sub-national region.



Objectives

Estimate and project SRBfor six Vietnam regionsduring 1980–2050.

Identify Vietnam regionswith imbalanced SRB.

Preprint: Chao F, GuilmotoCZ, Ombao H. SocArXiv,2021.doi:10.31235/osf.io/9xrbk.

Vietnamese regions and provinces matching

4

6

3

1

2

5

Da nang

Haiphong

Hanoi

Hue

Thanh Pho Ho Chi Minh (Saigon)

1: Northern Midlands andMountain Areas2: Red River Delta3: Northern Central Area andCentral Coastal Area4: Central Highlands

5: South East

6: Mekong River Delta

300 km

N



Data

We compiled an extensive database for Vietnam regional SRBfrom surveys and censuses.

526 SRB observations.

Reference year: 1972–2019.

More than 2,933,093 births records are included in thedatabase.1

1Number of births in some data sources are unknown. The total number isthe sum of known numbers.



Data quality model

We assume the ith observed SRB yi follows a normal distributionon the log-scale. For i ∈ 1, · · · , 526,

log(yi )|Θr [i ],t[i ], ω ∼ N (log(Θr [i ],t[i ]), v2i + ω2),

where

i indexes all the SRB observations across regions over time.

yi : the ith observed SRB from region r [i ] in year t[i ].

Θr ,t : the true SRB for Vietnamese region r in year t.

v2i : known stochastic/sampling variance.

ω2: unknown non-sampling error variance (assign a vagueprior to ω).



Model for Θr ,t

Θr ,t , the true SRB, is modeled as:

Θr ,t = bΦr ,t + δrαr ,t ,

where

b: the SRB baseline level for the entire Vietnam fixed at1.063, based on Chao et al. PNAS 2019.

Φr ,t : capture the natural fluctuations of SRB within eachregion over time.

δr : region-specific binary identifier of the sex ratio transition.

αr ,t : region-specific SRB imbalance process.



Model for Θr ,t

Φr ,t follows an AR(1) times series model on the log scale tocapture the natural fluctuations of SRB within each region overtime:

log(Φr ,t) ∼ N (0, (1− ρ2)/σ2ε ), if t = 1980,

log(Φr ,t) = ρ log(Φr ,t−1) + εr ,t , if t ∈ 1981, · · · , 2050,

εr ,ti.i.d.∼ N (0, σ2ε ),

where ρ = 0.9 and σε = 0.004 based on Chao et al. PNAS 2019.



Model for Θr ,t

δr is the binary identifier of the sex ratio transition, following aBernoulli distribution:

δr |πr ∼ B(πr ), for r ∈ 1, · · · , 6,logit(πr )|µπ, σπ ∼ N (µπ, σ

2π), for r ∈ 1, · · · , 6.

Vague priors are assigned to µπ and σπ.



Model for Θr ,t

SRB imbalance process αr ,t is modeled with a trapezoid functionwith hierarchical structure.

Sex ratio transition model

Year

α r,t

γ0,r γ1,r γ2,r γ3,r

0

ξr

λ1,r λ2,r λ3,r

γ0,r : starting year ofinflation period.

λ1,r , λ2,r , λ3,r : periodlengths of increase,stagnation and decrease ofinflation.

ξr : the maximum value thatthe adjustment factor couldreach.



Model for Θr ,t

The sex ratio transition process Ωc,t for country c year t ismodeled as:

αr ,t =

(ξr/λ1,r )(t − γr ), γ0,r < t < γ1,r

ξr , γ1,r < t < γ2,rξc − (ξc/λ3,r )(t − γ2,r ), γ2,r < t < γ3,r

0, t < γ0,r or t > γ3,r

,

where γ1,r , γ2,r , γ3,r can be expressed by γ0,r , λ1,r , λ2,r , λ3,r .Hierarchical distribution and informative priors are assigned to thefollowing regional-level parameters:

γ0,r |σγ ∼ t3(2001, σ2γ),

ξr ∼ N (µξ, σ2ξ )T (0, ),

λm,r ∼ N (µλm, σ2λm)T (0, ), for m ∈ 1, 2, 3.

Means and variances of the ξr and λ’s follows the national level ofthe Vietnam SRB inflation process, based on Chao et al. AOAS2021 (forthcoming).



SRB estimates by Vietnam regions

1.04 1.06 1.08 1.10 1.12 1.14 1.16

Sex Ratio at Birth

Central Highlands

Mekong River Delta

Northern Central Area andCentral Coastal Area

South East

Northern Midlands andMountain Areas

Red River Delta

198020002018



Vietnamese regional estimates and projections

Region with imbalanced SRB

1980 1990 2000 2010 2020 2030 2040 20500.9

1.0

1.1

1.2

1.3

Red River Delta

Sex

Rat

io a

t Bir

th

Regional SRBNational baseline

2000 2034

Annual PCFPS (2006)Annual PCFPS (2008)Annual PCFPS (2009)Annual PCFPS (2010)Annual PCFPS (2011)Annual PCFPS (2012)Annual PCFPS (2013)Annual PCFPS (2014)Annual PCFPS (2015)Annual PCFPS (2016)Annual PCFPS (2017)Annual PCFPS (2018)Annual PCFPS (2019)Census (1989)Census (1999)Census (2009)Census (2019)DHS (1997)DHS (2002)Intercensal Survey (2014)MICS (2013−14)Surveys of Birth (2007)Surveys of Birth (2008)



Summary

Conclusion

We estimate and project SRB by Vietnamese region during1980–2050.

We identify regions with imbalanced SRB.

Co-authors

Christophe Z. Guilmoto, CEPED/IRD, Universite de Paris.

Hernando Ombao, Statistics Program, KAUST.

For more details, refer to our preprint:Chao, F., Guilmoto, C. Z., Ombao, H. (2021). Sex ratio at birthin Vietnam among six subnational regions during 1990–2050,estimation and probabilistic projection using a Bayesian hierarchicaltime series model. SocArXiv, doi:10.31235/osf.io/9xrbk.


https://doi.org/10.31235/osf.io/9xrbk

https://doi.org/10.31235/osf.io/9xrbk


References

Chao, F., Gerland, P., Cook, A. R., Alkema, L. (2019). Systematic assessmentof the sex ratio at birth for all countries and estimation of national imbalancesand regional reference levels. Proceedings of the National Academy ofSciences, 116(19), 9303-9311.

Chao, F., Guilmoto, C. Z., Ombao, H. (2021). Sex ratio at birth in Vietnamamong six subnational regions during 1990–2050, estimation and probabilisticprojection using a Bayesian hierarchical time series model. SocArXiv,doi:10.31235/osf.io/9xrbk.

Chao, F., Gerland, P., Cook, A. R., Alkema, L. (2021, forthcoming). Global

estimation and scenario-based projections of sex ratio at birth and missing

female births using a Bayesian hierarchical time series mixture model. Annals

of Applied Statistics, arXiv:2006.07101.


sex ratio at birth by vietnamese region estimation and

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