This thesis is composed of three independent chapters, but all centered around the broader topic of how macroeconomic policies interact with various aspects of household heterogeneity. Monetary Policy and Inequality under Labor Market Frictions and Capital-Skill Complementarity We provide a new channel through which monetary policy has distributional consequences at business cycle frequencies. We show that an unexpected monetary easing increases labor income inequality between high and less-skilled workers. In particular, this effect is prominent in sectors intensive in less-skilled labor, that exhibit high degree of capital-skill complementarity (CSC) and are subject to matching inefficiencies. To rationalize these findings we build a New Keynesian DSGE model with asymmetric search and matching (SAM) frictions across the two types of workers and CSC in the production function. We show that CSC on its own introduces a dynamic demand amplification mechanism: the increase in high-skilled employment after a monetary expansion makes complementary capital more productive, encouraging a further rise in investment demand and creating a multiplier effect. SAM asymmetries magnify this channel. Monetary-Fiscal Interactions and Redistribution in Small Open Economies Ballooning public debts in the wake of the covid-19 pandemic can present monetary-fiscal policies with a dilemma if and when neutral real interest rates rise, which might arrive sooner in emerging markets: policymakers can stabilize debts either by relying on fiscal adjustments (AM-PF) or by tolerating higher inflation (PM-AF). The choice between these policy mixes affects the efficacy of the fiscal expansion already today and can interact with the distributive properties of the stimulus across heterogeneous households. To study this, I build a two agent New Keynesian (TANK) small open economy model with monetary-fiscal interactions. Targeting fiscal transfers more towards high-MPC agents increases the output multiplier of a fiscal stimulus, while raising the degree of deficitfinancing for these transfers also helps. However, precise targeting is much more important under the AM-PF regime than the question of financing, while the opposite is the case with a PM-AF policy mix: then deficit-spending is crucial for the size of the multiplier, and targeting matters less. Under the PM-AF regime fiscal stimulus entails a real exchange rate depreciation which might offset "import leakage" by stimulating net exports, if the share of hand-to-mouth households is low and trade is price elastic enough. Therefore, a PM-AF policy mix might break the Mundell-Fleming prediction that open economies have smaller fiscal multipliers relative to closed economies. Weak Wage Recovery and Precautionary Motives after a Credit Crunch During the economic recovery following the financial crisis many advanced economies saw subdued wage dynamics, in spite of falling unemployment and an increasingly tight labour market. We propose a mechanism which can account for this puzzle and work against usual aggregate demand channels. In a heterogeneous agent model with incomplete markets we endogenize uninsurable idiosyncratic risk through search-and-matching (SAM) frictions in the labour market. In this setting, apart from the usual precautionary saving behaviour, households can self-insure also by settling for lower wages in order to secure a job and thereby avoid becoming borrowing constrained. This channel is especially pronounced for asset-poor agents, already close to the constraint. We introduce a credit crunch into this framework modelled as a gradual tightening of the borrowing constraint (and utilizing a continuous time approach, known as HACT). The perfect foresight transition dynamics feature falling wages despite a tightening labour market and expanding employment. As households suddenly find themselves closer to the borrowing constraint, the increased precautionary motive drives them to accept lower wages in the bargaining process, while firms respond to this by posting more vacancies, leading to a tighter labour market and falling unemployment. If the household deleveraging pressure is persistent enough after the credit crunch, it can explain the weak wage recovery in spite of already stronger aggregate demand.