Levels and trends in the sex ratio at birth and missing female births for 29 states and union territories in India 1990–2016: A Bayesian modeling study

Fengqing Chao; Ajit Kumar Yadav

doi:10.3934/fods.2019008

Article Contents

2019, Volume 1, Issue 2: 177-196. Doi: 10.3934/fods.2019008

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Levels and trends in the sex ratio at birth and missing female births for 29 states and union territories in India 1990–2016: A Bayesian modeling study

Fengqing Chao^1, , and
Ajit Kumar Yadav^2,

1.
Institute of Policy Studies, Lee Kuan Yew School of Public Policy, National University of Singapore, 1C Cluny Road, House 5259599, Singapore
2.
International Institute for Population Sciences, Govandi Station Road, Mumbai, Maharashtra 400088, India

^* Corresponding author: Fengqing Chao
^* Corresponding author: Fengqing Chao

Published: June 2019

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Abstract

The sex ratio at birth (SRB) has risen in India and reaches well beyond the levels under normal circumstances since the 1970s. The lasting imbalanced SRB has resulted in much more males than females in India. A population with severely distorted sex ratio is more likely to have prolonged struggle for stability and sustainability. It is crucial to estimate SRB and its imbalance for India on state level and assess the uncertainty around estimates. We develop a Bayesian model to estimate SRB in India from 1990 to 2016 for 29 states and union territories. Our analyses are based on a comprehensive database on state-level SRB with data from the sample registration system, census and Demographic and Health Surveys. The SRB varies greatly across Indian states and union territories in 2016: ranging from 1.026 (95% uncertainty interval [0.971; 1.087]) in Mizoram to 1.181 [1.143; 1.128] in Haryana. We identify 18 states and union territories with imbalanced SRB during 1990–2016, resulting in 14.9 [13.2; 16.5] million of missing female births in India. Uttar Pradesh has the largest share of the missing female births among all states and union territories, taking up to 32.8% [29.5%; 36.3%] of the total number.

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Mathematics Subject Classification: Primary: 62H12; Secondary: 91D20.

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Figure 1. SRB point estimates and uncertainty for all Indian states/union territories in 1990 and 2016. States/union territories are ordered by decreasing point estimates of SRB for the year 2016. Dots are point estimates. Horizontal lines are 95% uncertainty intervals. The vertical line indicates the SRB baseline level for the whole India at 1.053

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Figure 2. SRB point estimates in 1990 and 2016 for 29 states and union territories in India. Top: SRB in 1990. Bottom: SRB in 2016. State and union territory names are: Andhra Pradesh (AP); Arunachal Pradesh (AR); Assam (AS); Bihar (BH); Chhattisgarh (CH); Delhi (DL); Goa (GO); Gujarat (GJ); Haryana (HR); Himachal Pradesh (HP); Jammu and Kashmir (JK); Jharkhand (JH); Karnataka (KA); Kerala (KE); Madhya Pradesh (MP); Maharashtra (MH); Manipur (MN); Meghalaya (MG); Mizoram (MZ); Nagaland (NA); Orissa (OR); Punjab (PJ); Rajasthan (RJ); Sikkim (SK); Tamil Nadu (TN); Telangana (TG); Tripura (TR); Uttar Pradesh (UP); Uttarakhand (UT); West Bengal (WB). In 1990, TG is estimated together with AP. In 2016, TG is not estimated

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Table 1. Observations by source type. The series periods are in brackets after the series names, they refer to the periods when the fieldwork of the surveys are conducted. The total number of observations are the sum of observations from the 29 Indian states and union territories. DHS: Demographic and Health Surveys. SRS: Sample Registration System

Data Source Type	Series Name (Series Period)	Total # Obs. (Range # Obs. per state/union territory)
Census	Census (2011)	29 (1–1)
DHS		598 (4–55)
	DHS (1992–1993)	101 (1–11)
	DHS (1998–1999)	107 (1–12)
	DHS (2005–2006)	100 (1–11)
	DHS (2015–2016)	290 (1–21)
SRS	SRS	310 (3–17)
Total		937 (5–73)

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Table 2. SRB results by Indian state/union territory. Point estimates and 95% uncertainty intervals (where apply) for (ⅰ) SRB in 1990 and 2016; (ⅱ) change of SRB between 1990 and 2016; (ⅲ) the year in which the maximum SRB is (only for states/union territories identified with imbalanced SRB during 1990–2016); and (ⅳ) the maximum SRB during observation period (only for states/union territories identified with imbalanced SRB during 1990–2016). Numbers in brackets are 95% uncertainty intervals. ¶: SRB in 1990 is significantly different from national SRB baseline value 1.053. §: SRB in 2016 is significantly different from national SRB baseline value 1.053. States/union territories are in alphabetic order

State/Union Territory	SRB			Maximum SRB
State/Union Territory	1990	2016	change 1990–2016	Year	Value
Andhra Pradesh§	1.054[1.013; 1.095]	1.089[1.056; 1.123]	0.035[-0.018; 0.087]	2015	1.089[1.061; 1.117]
Arunachal Pradesh	1.058[0.987; 1.131]	1.047[0.991; 1.107]	-0.010[-0.087; 0.063]
Assam§	1.063[1.018; 1.107]	1.089[1.057; 1.124]	0.027[-0.029; 0.083]	2015	1.090[1.061; 1.121]
Bihar§	1.074[1.036; 1.112]	1.098[1.068; 1.128]	0.023[-0.024; 0.072]	2002	1.134[1.116; 1.153]
Chhattisgarh	1.038[0.985; 1.094]	1.035[1.001; 1.070]	-0.003[-0.067; 0.060]
Delhi¶§	1.148[1.084; 1.215]	1.142[1.101; 1.184]	-0.006[-0.082; 0.067]	2003	1.160[1.125; 1.197]
Goa	1.065[0.993; 1.139]	1.068[1.008; 1.130]	0.003[-0.075; 0.077]
Gujarat¶§	1.114[1.068; 1.159]	1.140[1.108; 1.173]	0.026[-0.029; 0.083]	2000	1.161[1.136; 1.186]
Haryana¶§	1.181[1.130; 1.233]	1.181[1.143; 1.217]	-0.000[-0.064; 0.063]	2000	1.226[1.199; 1.255]
Himachal Pradesh¶	1.116[1.062; 1.173]	1.087[1.048; 1.128]	-0.029[-0.097; 0.037]	2001	1.137[1.104; 1.172]
Jammu and Kashmir¶§	1.150[1.087; 1.215]	1.128[1.091; 1.166]	-0.021[-0.096; 0.049]	2003	1.171[1.137; 1.207]
Jharkhand§	1.094[1.037; 1.152]	1.092[1.057; 1.127]	-0.002[-0.070; 0.063]	1999	1.101[1.061; 1.142]
Karnataka	1.059[1.020; 1.101]	1.061[1.033; 1.091]	0.002[-0.049; 0.052]	2004	1.075[1.056; 1.095]
Kerala	1.062[1.018; 1.106]	1.038[1.006; 1.069]	-0.025[-0.080; 0.029]	2002	1.085[1.063; 1.109]
Madhya Pradesh§	1.086[1.047; 1.127]	1.086[1.056; 1.115]	-0.001[-0.051; 0.047]	1999	1.092[1.071; 1.115]
Maharashtra	1.079[1.037; 1.122]	1.103[1.053; 1.154]	0.024[-0.040; 0.087]	2011	1.111[1.073; 1.150]
Manipur	1.056[0.989; 1.132]	1.062[1.006; 1.121]	0.005[-0.070; 0.080]
Meghalaya	1.053[0.986; 1.123]	1.043[0.988; 1.100]	-0.009[-0.084; 0.063]
Mizoram	1.032[0.963; 1.107]	1.026[0.971; 1.087]	-0.005[-0.080; 0.067]
Nagaland	1.054[0.986; 1.125]	1.051[0.994; 1.110]	-0.003[-0.080; 0.070]
Orissa	1.072[1.031; 1.115]	1.058[1.028; 1.089]	-0.014[-0.066; 0.037]
Punjab¶§	1.210[1.157; 1.264]	1.156[1.115; 1.194]	-0.054[-0.119; 0.008]	2000	1.250[1.218; 1.282]
Rajasthan¶§	1.133[1.092; 1.175]	1.140[1.108; 1.173]	0.007[-0.044; 0.058]	2004	1.161[1.141; 1.182]
Sikkim	1.050[0.971; 1.132]	1.048[0.984; 1.117]	-0.001[-0.079; 0.072]
Tamil Nadu	1.056[1.014; 1.096]	1.083[1.052; 1.114]	0.027[-0.024; 0.080]	2015	1.083[1.058; 1.109]
Tripura	1.053[0.987; 1.122]	1.046[0.991; 1.105]	-0.007[-0.081; 0.068]
Uttar Pradesh¶§	1.105[1.073; 1.138]	1.131[1.104; 1.160]	0.026[-0.016; 0.069]	2002	1.152[1.136; 1.169]
Uttarakhand§	1.118[1.047; 1.190]	1.152[1.116; 1.189]	0.034[-0.043; 0.109]	2015	1.154[1.123; 1.186]
West Bengal	1.052[1.013; 1.091]	1.059[1.030; 1.088]	0.007[-0.042; 0.056]

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Table 3. Results for number of missing female births, for 18 Indian state/union territories with imbalanced SRB. Point estimates and 95% uncertainty intervals for (ⅰ) the average annual number of missing female births (AMFB) in thousands for periods 1990–2000 and 2001–2016; (ⅱ) the cumulative number of missing female births (CMFB) in thousands for period 1990–2016; (ⅲ) the proportion of state-level CMFB to the national CMFB for periods 1990–2000, 2001–2016 and 1990–2016. Numbers in brackets are 95% uncertainty intervals. Proportions may not sum up to 100% due to rounding. States/union territories are ordered alphabetically

India & State/Union Territory	Average AMFB (, 000)		CMFB (, 000)	Proportion of National CMFB (%)
India & State/Union Territory	1990–2000	2001–2016	1990–2016	1990–2000	2001–2016	1990–2016
India	461[378; 544]	612[551; 672]	14,861[13,239; 16,465]	100	100	100
Andhra Pradesh	2[-16; 22]	21[12; 29]	359[85; 632]	0.6[0.0; 4.5]	3.4[2.0; 4.7]	2.4[0.6; 4.1]
Assam	2[-7; 11]	8[3; 13]	146[14; 279]	0.4[0.0; 2.2]	1.3[0.5; 2.0]	1.0[0.1; 1.9]
Bihar	45[21; 68]	67[54; 80]	1,567[1,202; 1,918]	9.8[4.8; 14.3]	10.9[9.0; 12.9]	10.6[8.4; 12.6]
Delhi	10[5; 15]	12[9; 14]	295[213; 379]	2.1[1.1; 3.3]	1.9[1.5; 2.4]	2.0[1.4; 2.6]
Gujarat	41[26; 56]	46[39; 53]	1,187[974; 1,402]	9.0[5.8; 12.3]	7.5[6.4; 8.7]	8.0[6.6; 9.4]
Haryana	32[25; 38]	33[30; 37]	885[778; 990]	6.9[5.3; 9.0]	5.4[4.8; 6.2]	6.0[5.2; 6.8]
Himachal Pradesh	4[2; 6]	3[2; 4]	88[52; 125]	0.9[0.4; 1.4]	0.4[0.3; 0.6]	0.6[0.3; 0.8]
Jammu and Kashmir	8[4; 11]	9[7; 11]	234[176; 292]	1.7[0.9; 2.6]	1.5[1.2; 1.8]	1.6[1.2; 2.0]
Jharkhand	12[0; 24]	14[7; 20]	352[156; 550]	2.6[0.0; 5.2]	2.2[1.2; 3.3]	2.4[1.1; 3.6]
Karnataka	5[-8; 18]	6[0; 12]	145[-41; 334]	1.1[0.0; 3.9]	0.9[0.0; 1.9]	1.0[0.0; 2.2]
Kerala	5[-3; 12]	0[-3; 3]	52[-56; 156]	1.0[0.0; 2.6]	0.0[0.0; 0.5]	0.3[0.0; 1.0]
Madhya Pradesh	27[8; 46]	28[18; 38]	742[470; 1,031]	5.9[1.9; 9.8]	4.6[3.1; 6.0]	5.0[3.3; 6.7]
Maharashtra	26[-2; 54]	43[15; 71]	975[318; 1,613]	5.6[0.0; 11.2]	7.0[2.6; 11.1]	6.5[2.3; 10.4]
Punjab	35[29; 42]	29[25; 32]	846[746; 949]	7.7[6.0; 9.8]	4.7[4.1; 5.3]	5.7[5.0; 6.6]
Rajasthan	56[39; 73]	71[62; 80]	1,755[1,495; 2,004]	12.1[8.5; 16.1]	11.6[10.2; 13.2]	11.8[10.2; 13.6]
Tamil Nadu	4[-10; 18]	9[3; 15]	191[-13; 382]	0.9[0.0; 3.7]	1.5[0.5; 2.5]	1.3[0.0; 2.5]
Uttar Pradesh	142[101; 184]	207[185; 229]	4,873[4,262; 5,498]	30.9[23.6; 38.1]	33.8[30.9; 37.0]	32.8[29.5; 36.3]
Uttarakhand	5[1; 8]	7[5; 9]	160[86; 234]	1.0[0.1; 1.8]	1.1[0.8; 1.5]	1.1[0.6; 1.6]

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Table 4. Validation results for left-out observations. Error is defined as the difference between a left-out observation and the posterior median of its predictive distribution

Median error	0.005
Median absolute error	0.035
Below 95% prediction interval (%)	0.4
Above 95% prediction interval (%)	0.3
Expected (%)	2.5
Below 80% prediction interval (%)	3.0
Above 80% prediction interval (%)	2.8
Expected (%)	10

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Table 5. Differences in SRB estimates in selected observation years based on training set and full dataset. Error is defined as the differences between an estimate based on full dataset and training set. The proportions refer to the proportions (%) of states/union territories in which the median SRB estimates based on the full dataset fall below or above their respective 95% and 80% uncertainty intervals based on the training set

	1995	2005	2015
Median error	0.003	-0.001	0.003
Median absolute error	0.003	0.002	0.003
Below 95% uncertainty interval (%)	0	0	0
Above 95% uncertainty interval (%)	0	0	0
Expected proportions (%)	≤2.5	≤2.5	≤2.5
Below 80% uncertainty interval (%)	0	0	0
Above 80% uncertainty interval (%)	0	0	0
Expected proportions (%)	≤10	≤10	≤10

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Table 6. Notation summary

Symbol	Description
$ i $	Indicator for observation, $ i = 1, \ldots, n $, where $ n=937 $.
$ t $	Indicator for year, $ t=0, \ldots, h $. $ t=0 $ refers to year 1990 and $ t=h $ refers to year 2016.
$ s $	Indicator for Indian state/union territory, $ s = 1, \ldots, k $, where $ k=29 $.
$ y $	Indicator for data source type, $ y = 1, \cdots, z $, where $ z=2 $.
$ \mathcal{I}_1 $	$ \mathcal{I}_1 = \left\{i= 1, \cdots, n \| y[i] = \text{SRS}\right\} $ denotes the set of indexes for SRS observations.
$ \mathcal{I}_2 $	$ \mathcal{I}_2 = \left\{i = 1, \cdots, n \| y[i] \neq \text{SRS}\right\} $ refers to the set of indexes for non-SRS observations.
$ v_i $	The $ i $-th SRB observation on log-scale.
$ \delta_i $	The $ i $-th error term for $ v_i $.
$ \sigma_i^2 $	The $ i $-th stochastic variance (if data is SRS) or sampling variance (if data is non-SRS) for $ v_i $.
$ \omega_y^2 $	The non-sampling variance parameters with non-SRS data source type for $ y = 1, \cdots, z $.
$ V_{s, t} $	The model fitting for the true SRB for state/union territory $ s $ in year $ t $ on log-scale.
$ P_{s, t} $	The difference between $ V_{s, t} $ and $ a0 $ for state/union territory $ s $ in year $ t $.
$ a0 $	The baseline level parameter of SRB for the whole India on the log-scale.
$ \rho $	Autoregressive parameter in AR(1) time series model for $ P_{s, t} $.
$ \sigma_\epsilon^2 $	Variance of distortion parameter in AR(1) time series model for $ P_{s, t} $.
$ b_s $	The state-specific level parameters for $ s = 1, \cdots, k $ in AR(1) time series model for $ P_{s, t} $.
$ \sigma_b^2 $	The variance parameter for $ b_s $.

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