Deterministic and stochastic macrodynamic models for developing economies' policies : an analysis of the Brazilian economy

This work verifies the interactions between fiscal and monetary policies in Brazil, involving real GDP, the Interest index, Inflation index, real Exchange rate, and actual public debt, using empirical data from January 1998 to December 2018 to calibrate the model. In the analyses, we employ macrodynamic deterministic and stochastic models of differential equations to examine the interconnection of the endogenous variables and the stability of Brazilian economic policy. In the stochastic model, we introduced stochastic perturbations in the uncontrollable coefficients and additive random walks affecting the endogenous variables. Shocks imposed on the structured dynamic model showed that stochastic innovations propagate more strongly in the monetary variables: inflation, interest rates, and exchange rates. We have also established forecasts for endogenous variables from January 2019 to December 2026 and conducted backtest analyses using the empirical data observed for the endogenous variables from January 2019 to December 2023. The forecast estimations were demonstrated to be satisfactory.