Experiments in modeling recent Indian fertility pattern

Abstract

Modelling is a well-established concept for understanding the typical shape and pattern of age-specific fertility. The distribution of India’s age-specific fertility rate (ASFR) is unimodal and positively skewed and is distinct from the ASFR of the developed countries. The existing models (P-K model, Gompertz model, Skew-normal model and G-P model considered here) that were developed, based on the experiences of the developed countries, failed to fit the single-year age-specific fertility pattern for India as a whole and for the six selected states. Our study has proposed four flexible models, to capture the diverse age pattern of fertility, observed in the Indian states. The proposed models were compared in three ways; among themselves, with the original models and with the popular Hadwiger model. The parameters of these proposed models were estimated through the Non-Linear Least Squares Method. To find the model with best fit, we used the corrected version of Akaike’s Information Criterion (AICc). Optimization of the four original models was successfully done. When the model was fitted to the empirical data of the 4th round of the National Family Health Survey conducted in 2015–2016, the results of this study showed that all the four proposed models outperform their corresponding original models and the Hadwiger model. When comparison among the proposed models was done, the Modified Gompertz Model provided the best fit for India, Uttar Pradesh and Gujarat. Whereas, the Modified P-K model gave the best fit for West Bengal, Tripura and Karnataka. The Modified G-P model is the most suitable model for Punjab. Although our proposed models illustrated the fitting of ASFR for India as a whole and the selected six states only, it provides an important tool for the policymakers and the government authorities to project fertility rates and to understand the fertility transitions in India and various other states.

A Partition Theorem for a Randomly Selected Large Population

“…Cases of a given large population or subpopulation showing oscillatory behaviour of transitioning from a stationary to a non-stationary state or vice versa were earlier given in Rao and Carey (2019). The theory and partition methods described could be used in insect demography (Unnikrishnan and Gadagkar 2020;Chi et al 2019;Tasnin et al 2021), plant sciences (Mohammadi-Tabar et al 2015;Chalmandrier et al 2021), or other research areas where age-and aging-based stratification is done, for example Mondal et al (2016), Ning et al (2017) and Srivastava et al (2021). With many countries in the world approaching or at replacement levels but often with widely varying if not unstable age distributions, the partitioning theory outlined here has the potential to provide new metrics on age structure in particular, and on overall population dynamics in general.…”

Predictions of Malaysia Age-Specific Fertility Rates using the Lee-Carter and the Functional Data Approaches

“…In literature, there are a variety of parametric fertility models used to explain the behavior of the fertility patterns by age. The class of these polynomials models includes widely recognized models such as the Hadwiger model, Hadwiger mixture model, Coale-Trussell model Beta and Gamma models, Pearson Type curve models, the scaled Weibull model, logistic model, Skew logistic model and Gompertz model [3]. These parametric models have their advantages and work as best fit under different patterns for given age groups.…”