A first-order approximation technique is not suited to handle issues such as welfare comparison, time-varying variance. Following Schmitt-Grohe and Uribe [1], in this paper, we derive a second-order approximation to estimate the dynamic stochastic equilibrium model with stochastic volatility, to capture the different impacts of the level shocks and the volatility shocks. Furthermore, the paper presents an application of standard quantitative New Keynesian business cycle model, and the results shows the negative effects of stochastic volatility shocks. Furthermore, the paper presents an application of standard quantitative New Keynesian business cycle model, and the empirical results find that the level shocks have positive effects on consumption, investment and output, while the volatility shocks have negative effects on consumption, investment and output.
Consumption-Habits in a New Keynesian Business Cycle Model