Using Functional Principal Components Analysis (FPCA) to improve deterministic household projections in Brazil

Household projection has been gaining increasingly attention in the literature. Applications are considerable relevant on studies concerning social housing demand family formation and environmental issues such as consumption of water energy and durable goods. Most of the Brazilian household projection experiences uses Headship Rate Method and assumes that the headship rates will be constant over time not considering sex or household type differences. The objective of this study is to propose a new alternative approach for headship rates forecasting that avoid constant rate scenarios in household projections. Instead of the scenario-based approach the new approach will use confidence intervals of the stochastic forecasting to build high low and medium variants. The results will be compared with PNAD observation from 2019. The model for projecting headship rates proposed here follows the Functional Principal Components Analysis (FPCA) (Booth et al 2014) based on Lee-Carter (1992) approach which uses the SVD decomposition to decompose the log of a defined rate into three effects: a general mean pattern an effect of change at each age and other effect of change over time.