Heterogeneous-Agent New Keynesian models (HANK)---which replace the representative household by a whole distribution of households---are the about to become the new state-off-the-art model of modern monetary economics because they allow for more realistic consumption patterns of households and a rich description of income and wealth distributions. This PhD thesis contributes to the ongoing advancements in the HANK literature in three ways. First, it employs empirically realistic, medium-sized state-of-the-art HANK models to analyze the macroeconomic and distributional impact of contemporary policy issues such as climate change. This thesis shows that the macroeconomic impact of higher carbon prices is similar than those of carbon shocks: they increase inflation and decreases economic activity. Nevertheless, higher carbon prices can be welfare-beneficial if the government pays back the increased revenue from higher carbon prices as lump-sum transfers to households. Second, it deepens our understanding of the interplay between (systematic) monetary and fiscal policy within this framework. It shows that, compared to independent monetary policies, a monetary union does not redistribute the impact of business cycle shocks vertically, that is, between households of different wealth and income brackets. It does, however, redistribute horizontally across countries, that is, between households within the same wealth and income brackets. For the euro area, this redistribution is strongest at the tails of the distribution. In addition, it shows that by using distortionary taxes and adjusting the government debt level, fiscal policy can be a perfect substitute for monetary policy when the latter is constrained by the effective lower bound, an exchange rate peg, or a monetary union. Third, this thesis connects HANK models with the fast-growing field of behavioral macroeconomics by integrating empirically supported behavioral elements. It develops a HANK model in which households’ expectations underreact to aggregate news as is robustly found in survey data. This behavioral HANK model then matches four recent important empirical findings in the monetary economics literature that previously could not be reconciled within one model. It also shows that incorporating them all into a single model matters greatly for the business cycle implications of monetary policy as, for example, after supply shocks, inflation increases much more strongly. In addition, this thesis shows that allowing for empirically documented heterogeneity in cognitive skills and overconfidence thereon enhances the empirical fit of HANK models to match the wealth distribution and the distribution of marginal propensity to consume. Key to this result is that overconfident households underestimate their precautionary savings motive, thereby oftentimes ending up hand-to-mouth, as they also do in the data.
