Probabilistic demography developed with Bayesian dynamic linear models: Testing and projections for Puerto Rico

Abstract

Demography was mainly deterministic until few years ago. Bayesian methodology for Demography was proposed by Raftery and colleagues to primarily include a measure of uncertainty in the United Nations projections. Raftery's Bayesian approach is linked to Box and Jenkins' ARMA models with hierarchical structures. However, to model cases like Puerto Rico, where there is high emigration and low sustained fertility, a different assessment could be considered.<br /> <br /> We propose a set of methodological and practical innovations in Demography with Dynamic Linear Models (DLMs) to strengthen projections for Puerto Rico. As our first methodological innovation, a DLM representation of ARMA models to model net migration rates for Puerto Rico was used. Migration is greatly influenced by climatic, economic and environmental factors. The nature and structure of DLMs could provide a better way to capture drastic changes in this demographic indicator. We develop an approximation of the empirical Bayes factor to perform tests between <em>DLMARMA</em>(1,1) and <em>DLMARMA</em>(1,0) models based on Rodriguez and Pericchi's work on 2001 . In addition, we developed a hierarchical AR(1) dynamic linear model (HDLM) to project net migration rates for seven US states that have reported negative net migration during 15 years. In this model, we also incorporate a <em>Scaled Beta</em>2 distribution for the scaling parameters instead of the criticized Inverse Gamma distribution.<br /> <br /> We also introduce another way to project the Total Fertility Rate (TFR) for Puerto Rico. We propose a TFR model only for 17 countries with TFR less than 1.5, based on Raftery's work. This change is adopted due to the dramatic descending behavior of the TFR of Puerto Rico in recent years. In fact, some researchers have expressed that the assumption that all countries will once again reach or oscillate around the replacement level TFR=2.1 seems unlikely.<br /> <br /> Subsequently, we generate our own probabilistic population projections for Puerto Rico by 2050. The median population for 2050 is expected to be 2,283,400 people with (2,110,000 , 2,488,500) a 95% probability interval.