Non-Gaussian score-driven conditionally heteroskedastic models with a macroeconomic application

Abstract

We contribute to the literature on empirical macroeconomic models with time-varying conditional moments, by introducing a heteroskedastic score-driven model with Student’s t-distributed innovations, named the heteroskedastic score-driven $t$ -QVAR (quasi-vector autoregressive) model. The $t$ -QVAR model is a robust nonlinear extension of the VARMA (VAR moving average) model. As an illustration, we apply the heteroskedastic $t$ -QVAR model to a dynamic stochastic general equilibrium model, for which we estimate Gaussian-ABCD and $t$ -ABCD representations. We use data on economic output, inflation, interest rate, government spending, aggregate productivity, and consumption of the USA for the period of 1954 Q3 to 2022 Q1. Due to the robustness of the heteroskedastic $t$ -QVAR model, even including the period of the coronavirus disease of 2019 (COVID-19) pandemic and the start of the Russian invasion of Ukraine, we find a superior statistical performance, lower policy-relevant dynamic effects, and a higher estimation precision of the impulse response function for US gross domestic product growth and US inflation rate, for the heteroskedastic score-driven $t$ -ABCD representation rather than for the homoskedastic Gaussian-ABCD representation.