Essays on quantitative macroeconomic theory

This doctoral dissertation consists of four self-contained chapters. Chapter 1 argues that since public debt helps the private sector to insure idiosyncratic risk, it is relevant for inflation dynamics due to its effects on interest rates. I study this channel using a quantitative Heterogeneous Agent New Keynesian (HANK) model. Once properly calibrated, my framework suggests the mechanism to be important for explaining the post-2022 “last mile” inflation in the US. Chapter 2 develops a rich HANK model with Seach-and-Matching (SaM) frictions on the labor market. With the framework, we revisit the question whether unemployment risk-driven precautionary saving is making economic downturns worse. We find the impact to be moderate and highlight its dependence on model assumptions requiring better discipline. In Chapter 3, I find that hybrid perturbation, a relatively simple numerical method, is useful for analyzing business cycle models with SaM-frictions. I show that it can accurately solve a well-known benchmark model and may thus be an alternative to global solution methods.