Abstract Projection of future population for a country by age and - PDF document

Probabilistic Approach of Population Projection for India and States Anurag Verma 1* , Abhinav Singh 2 , P.S. Pundir 2 1. Dept. of Community Medicine, IMS, BHU, Varanasi, India 2. Dept. of Statistics, University of Allahabad, Allahabad, India * presenting author , e-mail :-imsbhuanurag@gmail.com Abstract Projection of future population for a country by age and sex, are widely used for policy development, planning and research. They are mostly done deterministically, but there is a widespread need for probabilistic projections. In this paper we propose a Bayesian method for probabilistic population projections for India. The total fertility rate (TFR) and life expectancies at birth are projected probabilistically using Gompertz and logistic growth models respectively under Bayesian paradigm. The estimates obtained from proposed two models combined using cohort-component method to obtain age-specific projection of the population by sex. The analysis has been made using Markov Chain Monte Carlo (MCMC) technique with the software OpenBUGS. Convergence diagnostics techniques available with the OpenBUGS software have been applied to ensure the convergence of the chains necessary for implementation of MCMC. The method is illustrated by making 40- year projection using Indian data for the period 1971-2011. The study will provide probabilistic point estimates of parameter as well as the projection along with highest posterior density (HPD) interval, which is derived from population number and vital events, includes age specific death rates, life expectancies, age specific birth rate, total fertility rates and dependency ratio. Keywords: Demography, Probabilistic Population Projection, Bayesian Approach, Posterior Distribution Introduction Population Growth has become one of the most important problems in the world [1]. The idea of the future population is achieved with the help of projection. The demand of precise projected figures is always requisite for government personals, actuaries, for their social, 1 | P a g e

economic planning purposes. The size of the population and the growth of a country directly affect the state of the economy, politics, culture, education and the environment, etc. In this country, and determine the cost of exploring natural sources no one wants to wait until these resources are depleted because of the population explosion. Therefore, the study of population projection has been started earlier [2-4]. Currently, there are two main approaches in statistics, such as the Frequentist and the Bayesian approach for data analysis [5]. The utilization of Bayesian approach in the field of data analysis is moderately new and has discovered mass support throughout the previous two decades to persons belonging to various disciplines. Probably the main reason behind the growing support is its flexibility and generality that allows it to deal with the complex situation. In addition, the Bayesian method is typically preferred by the classical method in estimate parameters causing intractable from of the likelihood function [5]. Difficult situation can be handled by BUGS (Bayesian analysis using Gibbs Sampling) software for its flexibility and overall approach [6]. This study is based on a Bayesian way of data analysis. Bayesian method, uncertainty in model choice is incorporated through averaging techniques. Here the resulting predictive distributions from Bayesian forecasting models have two main advantages over those obtained using more traditional stochastic models. First, uncertainties in the data, the model parameters and model choice are explicitly represented using probabilistic distributions. As a result, more realistic probabilistic population forecasts are obtained. Second, Bayesian models formally allow the incorporation of expert opinion including uncertainty into the forecasts [7, 8]. Most population projection are currently done deterministically, using the cohort component method [9, 10], this is an age and sex-structured version of the basic demographic identity that the population of a country at the next time point is equal to the population at the current time point, plus the number of births minus the number of deaths, plus the number of immigrants minus the number of emmigrants. It was formulated in matrix form by Leslie [11]. Population Projection are currently produced by many organization, including national and local governments and private companies. The main organizations that have produced population projection for all states including India is Registrar General of India. I n India’s current method (RGI, 2006) [12] does not yield an assessment of uncertainty about future population. 2 | P a g e

Standard population projection methods are deterministic, meaning that they yield a single projected value for each quantity of interest. However, Probabilistic projection that gives a probability distribution of each quantity of interest and hence convey uncertainty about the projections are widely desired [13-14]. In the recent past, researcher developed alternative methods which allowed for probabilistic population projection, aimed for probabilistic interpretation of each demographic factor of interest. Alho and Spencer (1985), Alho (1990) ,Cohen (1986, 1988), Pflanumer (1988), Lee (1992) and Lee and Tuljapurkar (1994),Allho (1999),Keilman (2002) show a probabilistic population projection. The comparison of deterministic and probabilistic method can be found by Lee(1998), Alho& Spencer (2006) and Stillwell&Clarke (2011). In this study expand on the work of Rahul(2007) up on is suggestion to integrate statistical and demographic methodology in performing age-specific population projection. The aim of the study is to improve current methodology in population projection for making probabilistic population projection using cohort component method under Bayesian approach for India and States. The total fertility rate and female and male life expectancies at birth are projected probabilistically using Bayesian models estimated via Markov Chain Monte Carlo under WinBUGS software using Indian population data. These are then converted to age- specific rates and combined with a Cohort Component Projection model. This yields Probabilistic projections of any population quantity of interest, the method is illustrated for four Indian state of different demographic stages, continents and sizes. In India’s current projection method dose not yield an assessment of uncertainty about future population quantities. It is somewhat subjective because the model used have been selected by the analyst from a small number of predetermined possibilities rather than estimated from the data. It is also somewhat rigid in that the set of model used is small and may not cover a full range of realistic future possibilities. To address these issues, we will develop a Bayesian probabilistic population projection method. This involves building Bayesian models to project the fertility and mortality rate, each of which produces a large number of possible future trajectories from the posterior predictive distribution. These are then input to the cohort component projection method to provide a posterior predictive distribution of any future population quantity of interest. 3 | P a g e