This thesis investigates how central bank policies affect the economy. The core of central banking is of course monetary policy. However, more recently, central banks have also introduced a wider range of regulatory policies to ensure financial stability. I investigate how these policies affect the economy with a particular focus on inflation expectations, capital (re-)allocation, and bank stress tests. In the first chapter I investigate the conduct of monetary policy in a model with an endogenous degree of expectations anchoring. The anchoring of inflation expectations is a central tenet of monetary policy making. Most central banks in advanced economies try to anchor private long-term inflation expectations to their inflation target. I use an estimated New Keynesian model with endogenous forecast switching to replicate the time-varying excess sensitivity of long-term inflation expectations to inflation surprises as well as the resulting movements of long-term inflation expectations. In this model, de-anchoring leads to increased inflation volatility and can cause deflationary spirals when the zero lower bound (ZLB) is binding. This can be prevented by an asymmetric monetary policy rule which responds more aggressively to below-target inflation. Price Level Targeting, on the other hand can increase the risk of deflationary spirals near the ZLB. In the second chapter, written jointly with Carl-Wolfram Horn, we analyse the effect of monetary policy on mergers and acquisitions (M&A) activity in the U.S. Even though there exists a popular narrative that monetary policy is a key driver of M&A activity, little academic research has been conducted to establish how monetary policy in fact affects M&A activity. We confirm the predictions of a stylised model with frictional financial markets by showing that contractionary monetary policy significantly decreases M&A activity, especially for financially constrained firms. We furthermore investigate the effect of monetary policy on deal quality, measured as the abnormal stock returns for the acquiring firm. We find that contractionary monetary policy reduces beneficial capital reallocation by reducing M&A activity, but the marginal transaction is of higher quality as fewer constrained firms engage in M&A. In the third chapter, written jointly with Natalie Kessler, we study stress tests, a prominent tool employed by central banks around the world such as the Federal Reserve in their role as financial regulator to enhance financial stability. This constitutes a de facto constraint on balance sheets: equity must be sufficient to maintain current lending also tomorrow, even after absorbing severe loan losses. We study the effects of such forward looking constraints in a representative bank model. More severe stress tests scenarios lead to lower dividends, higher equity levels, and universally lower, albeit less volatile, lending. Subsequently, we calibrate our model to U.S. banks to compute the optimal, state-dependent severity of stress tests. Finally, we compare stress tests with several policy alternatives, such as the Covid-19 dividend ban, the counter-cyclical capital buffer (CCyB), and the dividend prudential target (DPT): while the first two perform well as complementary policies, a DPT is not welfare-improving for a supervisor seeking stable lending levels.