Page 61 - IJPS-8-2

International Journal of
Population Studies Projecting sex ratio at birth in Pakistan

observations) and simulation exercises (appendix for levels and trends in the SRB observations. To ensure that
details). The validation and simulation results suggest the probability parameter π lies in the interval [0, 1], we
p
good calibration and predictive power of the model. use the logit transformed π follows a hierarchical normal
p
2
The remainder of this section overviews the SRB distribution with a global mean and variance µ and ,
π

Bayesian model. respectively. δ follows a Bernoulli distribution:
p
π δ ( π ∼ | B {1,p ∈ ), for , },k
2.2.1. Bayesian model for provincial SRB estimation p p p
and projection ( π )| µσ ∼logit π , π ( µ σ, π 2 ) , for p ∈  {1, , }.k
p
π
The model for the SRB in Pakistan province is based on the
model described previously by Chao et al. (2021a, b). In this Vague priors are assigned to the parameters related to
study, we made a few modifications to the model to better the indicator that detects sex ratio transitions:
address the data quality and availability of provincial SRBs inverselogit

 01,,
in Pakistan. Subnational SRB models have been applied
 02,.
to other culturally and demographically heterogeneous

countries with son preference such as Nepal (Chao, et al., α refers to the province-specific SRB imbalance
p,t
2022) and Vietnam (Chao et al., 2021c). process. The process is assumed to be non-negative and is
The outcome of interest Θ , the SRB in Pakistan modeled by a trapezoidal function representing the three
p,t
province p in year t is modeled as follows: consecutive stages (increase, stagnation, and decrease)
of the sex ratio transition. The trapezoidal function
Θ , pt = Φb , pt +δ α , pt , specification of α is motivated by the patterns of national-
p
p,t
level SRB observations in countries with strong statistical
b = 1.056 is the SRB baseline level for the entire son preference to capture the three-stage transition process
Pakistan. The Pakistan SRB baseline b is estimated based (Chao et al., 2021a). The trapezoidal functional form for
on national SRB observations in Pakistan before the α can capture the shape of the observed SRB transition
reference year 1970 (Chao et al., 2019a, b). p ∈ {1,…,k} process according to Chao et al. (2021c) for those countries.
p,t
is the province index where k = 7. t ∈{0,…,h} is the time α is modeled as:
index where t = 0 refers to the year 1980 and t = h refers p,t
to the year 2050. α , pt = ( ξ / λ 1p )( −t 0p ) , if t 0p << t 1p
t
t
p
Φ follows an AR (1) time series model on the log scale, α = ξ , if t <<t t
p,t
which captures the natural fluctuations of SRB in each , pt p 1p 2p
(
province over time. The values of ρ and σ (ρ = 0.9) and α = ξ −ξ / λ )( −t t ) , if t < <t t
∈
σ = 0.004) were not estimated but were borrowed from a , pt p p 3p 2p 2p 3p
∈
>
previous study (Chao et al., 2019a,b), which robustly α , pt = 0, if < t t ort t 3p
0p
estimated the parameters from an extensive national SRB
database. We assume that log (Φ ) is causal and weakly Where,
p,t
stationary AR (1) process with parameters ρ and σ , and t t ,
∈
hence, log (Φ p,t–s ) is uncorrelated with ∈ for all s>0. The 1 p 0 p 1 p
p,t
unconditional variance at t = 0 is expressed as / 1 t 2 p t ,
2
2
1
p
p
2

for log (Φ ). Φ is modeled as follows: t t .
p,t
p,t
2
log ( Φ , pt ) ∼  ( 0, σ / ( −ρ1 2 )) , if t = 0, 3 p 2 p 3 p

The start year of the SRB inflation t is modeled by a
0p
( Φ log , pt ) = ρ ( Φ log , pt −1 ) +  , pt if ∈, t {1, , },h continuous uniform prior distribution with a lower bound
ε pt, ii d. .. N 0 , ε . at the year 1980 and an upper bound at the year 2050,
2
respectively. For p ∈ {1,…,k}, we have:
δ is the binary identifier of the sex ratio transition at t 0p ∼  ( )
0, .h
p
the provincial level with only two possible values 1 and 0.
δ = 1 indicates an SRB imbalance in province p, whereas The province-specific period lengths of the three
p
δ = 0 indicates no imbalance in province p. The provincial stages of the SRB inflation (λ , and λ ) are assigned
3p
p
1p
sex ratio transition identifier parameter δ is meant to with informative priors. The means of prior distributions
p
detect whether the transition process exists based on the are taken from a systematic study (Chao et al., 2021a)
Volume 8 Issue 2 (2022) 55 https://doi.org/10.36922/ijps.v8i2.332