Levels and trends in the sex ratio at birth and missing female births for 29 states and union territories in India 1990

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June 2019, 1(2): 177-196. doi: 10.3934/fods.2019008

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

Published June 2019

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.

Keywords: Bayesian hierarchical model, sex ratio at birth, missing female births, India, subnational estimation.

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

Citation: Fengqing Chao, Ajit Kumar Yadav. 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. Foundations of Data Science, 2019, 1 (2) : 177-196. doi: 10.3934/fods.2019008

References:

[1]	L. Alkema, F. Chao, D. You, P. Jon and C. C. Sawyer, Sawyer, National, regional, and global sex ratios of infant, child, and under-5 mortality and identification of countries with outlying ratios: a systematic assessment, The Lancet Global Health, 2 (2014), e521-e530. doi: 10.1016/S2214-109X(14)70280-3. Google Scholar
[2]	L. Alkema and J. New, Global estimation of child mortality using a Bayesian B-spline bias-reduction model, The Annals of Applied Statistics, 8 (2014), 2122-2149. doi: 10.1214/14-AOAS768. Google Scholar
[3]	G. N. Allahbadia, The 50 million missing women, Journal of Assisted Reproduction and Genetics, 19 (2002), 411-416. Google Scholar
[4]	G. Aravamudan, Disappearing Daughters: The Tragedy of Female Foeticide, Penguin Books, New Delhi, 2007.Google Scholar
[5]	I. Attané and C. Z. Guilmoto, Watering the Neighbour's Garden: The Growing Demographic Female Deficit in Asia, Committee for International Cooperation in National Research in Demography, Paris, 2007.Google Scholar
[6]	J. Banister, Shortage of girls in China today, Journal of Population Research, 21 (2004), 19-45. doi: 10.1007/BF03032209. Google Scholar
[7]	S. Basten and G. Verropoulou, "Maternity migration" and the increased sex ratio at birth in Hong Kong SAR, Population Studies, 67 (2013), 323-334. doi: 10.1080/00324728.2013.826372. Google Scholar
[8]	J. Bongaarts, The implementation of preferences for male offspring, Population and Development Review, 39 (2013), 185-208. doi: 10.1111/j.1728-4457.2013.00588.x. Google Scholar
[9]	J. Bongaarts and C. Z. Guilmoto, How many more missing women? Excess female mortality and prenatal sex selection, 1970–2050, Population and Development Review, 41 (2015), 241-269. doi: 10.1111/j.1728-4457.2015.00046.x. Google Scholar
[10]	Y. Cai and W. Lavely, China's missing girls: Numerical estimates and effects on population growth, China Review, 3 (2003), 13-29. Google Scholar
[11]	A. Chahnazarian, Determinants of the sex ratio at birth: Review of recent literature, Biodemography and Social Biology, 35 (1988), 214-235. doi: 10.1080/19485565.1988.9988703. Google Scholar
[12]	F. Chao, P. Gerland, A. R. Cook and L. Alkema, Systematic assessment of the sex ratio at birth for all countries and estimation of national imbalances and regional reference levels, Proceedings of the National Academy of Sciences, 116 (2019), 9303-9311. doi: 10.1073/pnas.1812593116. Google Scholar
[13]	F. Chao, D. You, P. Jon, L. Hug and L. Alkema, National and regional under-5 mortality rate by economic status for low-income and middle-income countries: a systematic assessment, The Lancet Global Health, 6 (2018), e535-e547. doi: 10.1016/S2214-109X(18)30059-7. Google Scholar
[14]	M. Das Gupta, Z. Jiang, B. Li, Z. Xie, W. Chung and H. Bae, Why is son preference so persistent in East and South Asia? A cross-country study of China, India and the Republic of Korea, The Journal of Development Studies, 40 (2003), 153-187. doi: 10.1596/1813-9450-2942. Google Scholar
[15]	G. Duthé, F. Meslé and J. Vallin, High sex ratios at birth in the Caucasus: Modern technology to satisfy old desires, Population and Development Review, 38 (2012), 487-501. doi: 10.1111/j.1728-4457.2012.00513.x. Google Scholar
[16]	B. Efron, The Jackknife, the Bootstrap, and other Resampling Plans, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1982. Google Scholar
[17]	M. D. Frost, M. Puri and P. R. A. Hinde, Falling sex ratios and emerging evidence of sex-selective abortion in Nepal: evidence from nationally representative survey data, BMJ open, 3 (2013), e002612. doi: 10.1136/bmjopen-2013-002612. Google Scholar
[18]	A. Gelman and D. B. Rubin, Inference from iterative simulation using multiple sequences, Statistical Science, 7 (1992), 457-472. doi: 10.1214/ss/1177011136. Google Scholar
[19]	S. M. George, Millions of missing girls: From fetal sexing to high technology sex selection in India, Prenatal Diagnosis, 26 (2006), 604-609. doi: 10.1002/pd.1475. Google Scholar
[20]	S. M. George, Sex selection/determination in India: Contemporary developments, Reproductive Health Matters, 10 (2002), 190-192. doi: 10.1016/S0968-8080(02)00034-4. Google Scholar
[21]	D. Goodkind, Sex-selective Abortion, Reproductive Rights, and the Greater Locus of Gender Discrimination in Family Formation: Cairo's Unresolved Questions, University of Michigan, Population Studies Center, 1997.Google Scholar
[22]	D. Goodkind, Child underreporting, fertility, and sex ratio imbalance in China, Demography, 48 (2011), 291-316. doi: 10.1007/s13524-010-0007-y. Google Scholar
[23]	C. Z. Guilmoto, Sex Imbalances at Birth: Current Trends, Consequences and Policy Implications, UNFPA Asia and Pacific Regional Office, Bangkok, Thailand, 2012.Google Scholar
[24]	C. Z. Guilmoto, The sex ratio transition in Asia, Population and Development Review, 35 (2009), 519-549. doi: 10.1111/j.1728-4457.2009.00295.x. Google Scholar
[25]	C. Z. Guilmoto, Skewed sex ratios at birth and future marriage squeeze in China and India, 2005–2100, Demography, 49 (2012), 77-100. doi: 10.1007/s13524-011-0083-7. Google Scholar
[26]	C. Z. Guilmoto, Son preference, sex selection, and kinship in Vietnam, Population and Development Review, 38 (2012), 31-54. doi: 10.1111/j.1728-4457.2012.00471.x. Google Scholar
[27]	C. Z. Guilmoto, X. Hoàng and T. N. Van, Recent increase in sex ratio at birth in Viet Nam, PLoS One, 4 (2009), e4624. doi: 10.1371/journal.pone.0004624. Google Scholar
[28]	C. Z. Guilmoto and Q. Ren, Socio-economic differentials in Birth Masculinity in China, Development and Change, 42 (2011), 1269-1296. doi: 10.1111/j.1467-7660.2011.01733.x. Google Scholar
[29]	T. Hesketh and J. Min, The effects of artificial gender imbalance: Science & Society Series on Sex and Science, EMBO reports, 13 (2012), 487-492. doi: 10.1038/embor.2012.62. Google Scholar
[30]	V. M. Hudson and A. M. Den Boer, Bare Branches: The Security Implications of Asia's Surplus Male Population, MIT Press, Cambridge, Mass, 2004. Google Scholar
[31]	P. Jha, M. A. Kesler, R. Kumar, F. Ram, U. Ram, L. Aleksandrowicz, D. G. Bassani, S. Chandra and J. K. Banthia, Trends in selective abortions of girls in India: analysis of nationally representative birth histories from 1990 to 2005 and census data from 1991 to 2011, The Lancet, 377 (2011), 1921-1928. doi: 10.1016/S0140-6736(11)60649-1. Google Scholar
[32]	P. Jha, R. Kumar, P. Vasa, N. Dhingra, D. Thiruchelvam and R. Moineddin, Low male-to-female sex ratio of children born in India: national survey of 1$\cdot$1 million households, The Lancet, 367 (2006), 211-218. doi: 10.1016/S0140-6736(06)67930-0. Google Scholar
[33]	R. Kaur, S. S. Bhalla, M. K. Agarwal and P. Ramakrishnan, Sex Ratio at Birth – The Role of Gender, Class and Education, United Nations Population Fund, New Delhi, 2017.Google Scholar
[34]	Lancet India Correspondent, Misuse of amniocentesis, The Lancet, 321 (1983), 812-813. Google Scholar
[35]	S. Li, Imbalanced sex ratio at birth and comprehensive intervention in China, in 4th Asia Pacific Conference on Reproductive and Sexual Health and Rights (Hyderabad, India, Oct 29-31, 2007), United Nations Population Fund, 2007.Google Scholar
[36]	T. Lin, The decline of son preference and rise of gender indifference in Taiwan since 1990, Demographic Research, 20 (2009), 377-402. doi: 10.4054/DemRes.2009.20.16. Google Scholar
[37]	K. Madan and M. H. Breuning, Impact of prenatal technologies on the sex ratio in India: An overview, Genetics in Medicine, 16 (2014), 425-432. doi: 10.1038/gim.2013.172. Google Scholar
[38]	F. Meslé, J. Vallin and I. Badurashvili, A sharp increase in sex ratio at birth in the Caucasus. Why? How?, in Watering the neighbour's garden: The growing demographic female deficit in Asia (eds. I. Attané and C. Z. Guilmoto), Committee for International Cooperation in National Research in Demography, (2007), 73–88.Google Scholar
[39]	N. Oomman and B. R. Ganatra, Sex selection: The systematic elimination of girls, Reproductive Health Matters, 10 (2002), 184-188. doi: 10.1016/S0968-8080(02)00029-0. Google Scholar
[40]	C. B. Park and N. H. Cho, Consequences of son preference in a low-fertility society: Imbalance of the sex ratio at birth in Korea, Population and Development Review, 21 (1995), 59-84. doi: 10.2307/2137413. Google Scholar
[41]	M. Plummer, Rjags: Bayesian Graphical Models Using MCMC, 2011. Available from: http://CRAN.R-project.org/package=rjags.Google Scholar
[42]	M. Plummer, JAGS: A program for analysis of bayesian graphical models using gibbs sampling, in Proceedings of the 3rd International Workshop on Distributed Statistical Computing, Vienna, Austria, (2003)Available from: http://mcmc-jags.sourceforge.net/.Google Scholar
[43]	M. Plummer, N. Best, K. Cowles and K. Vines, CODA: Convergence Diagnosis and Output Analysis for MCMC, R News, 6 (2006), 7-11. Available from: https://cran.r-project.org/package=coda.Google Scholar
[44]	R. Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2018. Available from: https://www.R-project.org/.Google Scholar
[45]	T. K. Roy and A. Chattopadhyay, Daughter discrimination and future sex ratio at birth in India, Asian Population Studies, 8 (2012), 281-299. doi: 10.1080/17441730.2012.714669. Google Scholar
[46]	K. C. Samir, M. Wurzer, M. Speringer and W. Lutz, Future population and human capital in heterogeneous India, Proceedings of the National Academy of Sciences, 115 (2018), 8328-8333. doi: 10.1073/pnas.1722359115. Google Scholar
[47]	A. Sen, Missing women, British Medical Journal, 304 (1992), 587-588. doi: 10.1136/bmj.304.6827.587. Google Scholar
[48]	B. R. Sharma, N. Gupta and N. Relhan, Misuse of prenatal diagnostic technology for sex-selected abortions and its consequences in India, Public Health, 121 (2007), 854-860. doi: 10.1016/j.puhe.2007.03.004. Google Scholar
[49]	O. P. Sharma and C. Haub, Sex ratio at birth begins to improve in India, Population Reference Bureau, 2008. Available from: http://www.prb.org/Publications/Articles/2008/indiasexratio.aspx.Google Scholar
[50]	Y. Su and M. Yajima, R2jags: A Package for Running Jags from R, 2015. Available from: http://CRAN.R-project.org/package=R2jags.Google Scholar
[51]	S. L. Tandon and R. Sharma, Female foeticide and infanticide in India: an analysis of crimes against girl children, International Journal of Criminal Justice Sciences, 1 (2006), 1-10. Google Scholar

show all references

References:

[1]	L. Alkema, F. Chao, D. You, P. Jon and C. C. Sawyer, Sawyer, National, regional, and global sex ratios of infant, child, and under-5 mortality and identification of countries with outlying ratios: a systematic assessment, The Lancet Global Health, 2 (2014), e521-e530. doi: 10.1016/S2214-109X(14)70280-3. Google Scholar
[2]	L. Alkema and J. New, Global estimation of child mortality using a Bayesian B-spline bias-reduction model, The Annals of Applied Statistics, 8 (2014), 2122-2149. doi: 10.1214/14-AOAS768. Google Scholar
[3]	G. N. Allahbadia, The 50 million missing women, Journal of Assisted Reproduction and Genetics, 19 (2002), 411-416. Google Scholar
[4]	G. Aravamudan, Disappearing Daughters: The Tragedy of Female Foeticide, Penguin Books, New Delhi, 2007.Google Scholar
[5]	I. Attané and C. Z. Guilmoto, Watering the Neighbour's Garden: The Growing Demographic Female Deficit in Asia, Committee for International Cooperation in National Research in Demography, Paris, 2007.Google Scholar
[6]	J. Banister, Shortage of girls in China today, Journal of Population Research, 21 (2004), 19-45. doi: 10.1007/BF03032209. Google Scholar
[7]	S. Basten and G. Verropoulou, "Maternity migration" and the increased sex ratio at birth in Hong Kong SAR, Population Studies, 67 (2013), 323-334. doi: 10.1080/00324728.2013.826372. Google Scholar
[8]	J. Bongaarts, The implementation of preferences for male offspring, Population and Development Review, 39 (2013), 185-208. doi: 10.1111/j.1728-4457.2013.00588.x. Google Scholar
[9]	J. Bongaarts and C. Z. Guilmoto, How many more missing women? Excess female mortality and prenatal sex selection, 1970–2050, Population and Development Review, 41 (2015), 241-269. doi: 10.1111/j.1728-4457.2015.00046.x. Google Scholar
[10]	Y. Cai and W. Lavely, China's missing girls: Numerical estimates and effects on population growth, China Review, 3 (2003), 13-29. Google Scholar
[11]	A. Chahnazarian, Determinants of the sex ratio at birth: Review of recent literature, Biodemography and Social Biology, 35 (1988), 214-235. doi: 10.1080/19485565.1988.9988703. Google Scholar
[12]	F. Chao, P. Gerland, A. R. Cook and L. Alkema, Systematic assessment of the sex ratio at birth for all countries and estimation of national imbalances and regional reference levels, Proceedings of the National Academy of Sciences, 116 (2019), 9303-9311. doi: 10.1073/pnas.1812593116. Google Scholar
[13]	F. Chao, D. You, P. Jon, L. Hug and L. Alkema, National and regional under-5 mortality rate by economic status for low-income and middle-income countries: a systematic assessment, The Lancet Global Health, 6 (2018), e535-e547. doi: 10.1016/S2214-109X(18)30059-7. Google Scholar
[14]	M. Das Gupta, Z. Jiang, B. Li, Z. Xie, W. Chung and H. Bae, Why is son preference so persistent in East and South Asia? A cross-country study of China, India and the Republic of Korea, The Journal of Development Studies, 40 (2003), 153-187. doi: 10.1596/1813-9450-2942. Google Scholar
[15]	G. Duthé, F. Meslé and J. Vallin, High sex ratios at birth in the Caucasus: Modern technology to satisfy old desires, Population and Development Review, 38 (2012), 487-501. doi: 10.1111/j.1728-4457.2012.00513.x. Google Scholar
[16]	B. Efron, The Jackknife, the Bootstrap, and other Resampling Plans, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1982. Google Scholar
[17]	M. D. Frost, M. Puri and P. R. A. Hinde, Falling sex ratios and emerging evidence of sex-selective abortion in Nepal: evidence from nationally representative survey data, BMJ open, 3 (2013), e002612. doi: 10.1136/bmjopen-2013-002612. Google Scholar
[18]	A. Gelman and D. B. Rubin, Inference from iterative simulation using multiple sequences, Statistical Science, 7 (1992), 457-472. doi: 10.1214/ss/1177011136. Google Scholar
[19]	S. M. George, Millions of missing girls: From fetal sexing to high technology sex selection in India, Prenatal Diagnosis, 26 (2006), 604-609. doi: 10.1002/pd.1475. Google Scholar
[20]	S. M. George, Sex selection/determination in India: Contemporary developments, Reproductive Health Matters, 10 (2002), 190-192. doi: 10.1016/S0968-8080(02)00034-4. Google Scholar
[21]	D. Goodkind, Sex-selective Abortion, Reproductive Rights, and the Greater Locus of Gender Discrimination in Family Formation: Cairo's Unresolved Questions, University of Michigan, Population Studies Center, 1997.Google Scholar
[22]	D. Goodkind, Child underreporting, fertility, and sex ratio imbalance in China, Demography, 48 (2011), 291-316. doi: 10.1007/s13524-010-0007-y. Google Scholar
[23]	C. Z. Guilmoto, Sex Imbalances at Birth: Current Trends, Consequences and Policy Implications, UNFPA Asia and Pacific Regional Office, Bangkok, Thailand, 2012.Google Scholar
[24]	C. Z. Guilmoto, The sex ratio transition in Asia, Population and Development Review, 35 (2009), 519-549. doi: 10.1111/j.1728-4457.2009.00295.x. Google Scholar
[25]	C. Z. Guilmoto, Skewed sex ratios at birth and future marriage squeeze in China and India, 2005–2100, Demography, 49 (2012), 77-100. doi: 10.1007/s13524-011-0083-7. Google Scholar
[26]	C. Z. Guilmoto, Son preference, sex selection, and kinship in Vietnam, Population and Development Review, 38 (2012), 31-54. doi: 10.1111/j.1728-4457.2012.00471.x. Google Scholar
[27]	C. Z. Guilmoto, X. Hoàng and T. N. Van, Recent increase in sex ratio at birth in Viet Nam, PLoS One, 4 (2009), e4624. doi: 10.1371/journal.pone.0004624. Google Scholar
[28]	C. Z. Guilmoto and Q. Ren, Socio-economic differentials in Birth Masculinity in China, Development and Change, 42 (2011), 1269-1296. doi: 10.1111/j.1467-7660.2011.01733.x. Google Scholar
[29]	T. Hesketh and J. Min, The effects of artificial gender imbalance: Science & Society Series on Sex and Science, EMBO reports, 13 (2012), 487-492. doi: 10.1038/embor.2012.62. Google Scholar
[30]	V. M. Hudson and A. M. Den Boer, Bare Branches: The Security Implications of Asia's Surplus Male Population, MIT Press, Cambridge, Mass, 2004. Google Scholar
[31]	P. Jha, M. A. Kesler, R. Kumar, F. Ram, U. Ram, L. Aleksandrowicz, D. G. Bassani, S. Chandra and J. K. Banthia, Trends in selective abortions of girls in India: analysis of nationally representative birth histories from 1990 to 2005 and census data from 1991 to 2011, The Lancet, 377 (2011), 1921-1928. doi: 10.1016/S0140-6736(11)60649-1. Google Scholar
[32]	P. Jha, R. Kumar, P. Vasa, N. Dhingra, D. Thiruchelvam and R. Moineddin, Low male-to-female sex ratio of children born in India: national survey of 1$\cdot$1 million households, The Lancet, 367 (2006), 211-218. doi: 10.1016/S0140-6736(06)67930-0. Google Scholar
[33]	R. Kaur, S. S. Bhalla, M. K. Agarwal and P. Ramakrishnan, Sex Ratio at Birth – The Role of Gender, Class and Education, United Nations Population Fund, New Delhi, 2017.Google Scholar
[34]	Lancet India Correspondent, Misuse of amniocentesis, The Lancet, 321 (1983), 812-813. Google Scholar
[35]	S. Li, Imbalanced sex ratio at birth and comprehensive intervention in China, in 4th Asia Pacific Conference on Reproductive and Sexual Health and Rights (Hyderabad, India, Oct 29-31, 2007), United Nations Population Fund, 2007.Google Scholar
[36]	T. Lin, The decline of son preference and rise of gender indifference in Taiwan since 1990, Demographic Research, 20 (2009), 377-402. doi: 10.4054/DemRes.2009.20.16. Google Scholar
[37]	K. Madan and M. H. Breuning, Impact of prenatal technologies on the sex ratio in India: An overview, Genetics in Medicine, 16 (2014), 425-432. doi: 10.1038/gim.2013.172. Google Scholar
[38]	F. Meslé, J. Vallin and I. Badurashvili, A sharp increase in sex ratio at birth in the Caucasus. Why? How?, in Watering the neighbour's garden: The growing demographic female deficit in Asia (eds. I. Attané and C. Z. Guilmoto), Committee for International Cooperation in National Research in Demography, (2007), 73–88.Google Scholar
[39]	N. Oomman and B. R. Ganatra, Sex selection: The systematic elimination of girls, Reproductive Health Matters, 10 (2002), 184-188. doi: 10.1016/S0968-8080(02)00029-0. Google Scholar
[40]	C. B. Park and N. H. Cho, Consequences of son preference in a low-fertility society: Imbalance of the sex ratio at birth in Korea, Population and Development Review, 21 (1995), 59-84. doi: 10.2307/2137413. Google Scholar
[41]	M. Plummer, Rjags: Bayesian Graphical Models Using MCMC, 2011. Available from: http://CRAN.R-project.org/package=rjags.Google Scholar
[42]	M. Plummer, JAGS: A program for analysis of bayesian graphical models using gibbs sampling, in Proceedings of the 3rd International Workshop on Distributed Statistical Computing, Vienna, Austria, (2003)Available from: http://mcmc-jags.sourceforge.net/.Google Scholar
[43]	M. Plummer, N. Best, K. Cowles and K. Vines, CODA: Convergence Diagnosis and Output Analysis for MCMC, R News, 6 (2006), 7-11. Available from: https://cran.r-project.org/package=coda.Google Scholar
[44]	R. Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2018. Available from: https://www.R-project.org/.Google Scholar
[45]	T. K. Roy and A. Chattopadhyay, Daughter discrimination and future sex ratio at birth in India, Asian Population Studies, 8 (2012), 281-299. doi: 10.1080/17441730.2012.714669. Google Scholar
[46]	K. C. Samir, M. Wurzer, M. Speringer and W. Lutz, Future population and human capital in heterogeneous India, Proceedings of the National Academy of Sciences, 115 (2018), 8328-8333. doi: 10.1073/pnas.1722359115. Google Scholar
[47]	A. Sen, Missing women, British Medical Journal, 304 (1992), 587-588. doi: 10.1136/bmj.304.6827.587. Google Scholar
[48]	B. R. Sharma, N. Gupta and N. Relhan, Misuse of prenatal diagnostic technology for sex-selected abortions and its consequences in India, Public Health, 121 (2007), 854-860. doi: 10.1016/j.puhe.2007.03.004. Google Scholar
[49]	O. P. Sharma and C. Haub, Sex ratio at birth begins to improve in India, Population Reference Bureau, 2008. Available from: http://www.prb.org/Publications/Articles/2008/indiasexratio.aspx.Google Scholar
[50]	Y. Su and M. Yajima, R2jags: A Package for Running Jags from R, 2015. Available from: http://CRAN.R-project.org/package=R2jags.Google Scholar
[51]	S. L. Tandon and R. Sharma, Female foeticide and infanticide in India: an analysis of crimes against girl children, International Journal of Criminal Justice Sciences, 1 (2006), 1-10. Google Scholar

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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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)

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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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]

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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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]

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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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

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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	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

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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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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American Institute of Mathematical Sciences