Dynamic Econometric Models: A State‐Space Formulation

In the area of econometrics, the investigation and characterization of processes that retain memory for the past are often of interest. This work overcomes collinearity problems that arise in distributed lag formulations by modeling these effects as structural elements within nonlinear dynamic models using transfer functions. Our main contribution lies in performing sequential Bayesian inference for nonlinear dynamic models, providing an efficient computational solution based on analytical approximations. The scalability offered by the proposed sequential method is particularly relevant in the econometric context, where long time series or multiple levels of disaggregation are often encountered. The proposed models incorporate stochastic volatility, achieved through the use of discount factors. An extensive simulation investigation validates the inferential approximation. The results of the proposed sequential and analytical approximation are compared with the inference obtained through Hamiltonian Monte Carlo in a particular application to real‐world consumption data. The results show that the sequential approach produces results that are largely comparable while requiring a significantly shorter amount of computing time. Using the proposed Bayesian state‐space framework and a thorough examination of the Phillips curve, a case study is developed focusing on the relationship between inflation and the output gap in the Brazilian scenario. We conclude with a substantial contribution, based on an innovative approach that preserves Bayesian sequential inference and offers a joint model for inflation and the output gap, with dynamic predictive structures assigned to the means, precisions, and correlation between both economic indicators.