The financial crisis of 2007-2009 drew attention to the essential role of banks for the macroeconomy and to the importance of having a resilient financial sector. A vulnerability in the financial sector spills over to the real economy and can drive it into a deep recession. Following the financial crisis, policy makers have issued rules and regulations aimed at strengthening the banks. My dissertation considers some of those measures, namely bank liquidity regulation and deposit insurance, and tries to assess their effectiveness in stabilizing the financial sector and the economy in general. The first chapter (joint with Prof. Luisa Lambertini) develops a model with regulated banks and a hedge fund to analyze the behavior of wholesale funding and the macroeconomic consequences of liquidity regulation. Banks raise deposits and subordinated wholesale funding from the hedge fund. Wholesale funding amplifies shocks: it is curtailed in economic downturns to avoid leveraging up and risk-taking by banks, further depressing credit and economic activity. By making banks safer, liquidity regulation increases wholesale funding and bank loans at the steady state. However, flat liquidity regulation requiring banks to hold a constant fraction of liquid assets can have unintended consequences and increase macroeconomic volatility. Our model further shows that cyclically adjusted regulation stabilizes the response of the economy to shocks. We also provide empirical evidence suggesting that liquidity helps contain the contraction in wholesale funding and loans during times of funding stress. The second chapter explores the macroeconomic and welfare implications of harmonizing or joining deposit insurance in the Eurozone. I develop a two-country model to represent the core and periphery countries in the Eurozone. The model features fragile banks that can be subject to endogenous and costly runs. The two countries are financially integrated through an international interbank market. I introduce deposit insurance and compare different insurance regimes in steady state and along the business cycle. The model emphasizes that financial integration implies co-movement in asset prices and the transmission of shocks across the border. I find that when deposit insurance has lower coverage in the periphery than in the core, financial stability is undermined in both regions due to higher asset price volatility and a higher probability of deposit runs. Hence, either harmonizing or joining deposit insurance leads to substantial welfare benefits for both countries. In the third chapter, I develop a macroeconomic model with multiple equilibria and bank runs to analyze deposit insurance. A bank run is a sunspot equilibrium, and it is caused by a self-fulfilling panic of all depositors. The model features a unique no-run equilibrium when macroeconomic conditions are good, but an unexpected negative shock may open up the possibility of a run equilibrium. A bank run is a rare but costly event that drives the economy in a long and severe recession. I analyze the introduction and build-up of a deposit insurance fund and show that it reduces the cost and probability of bank runs. The dynamic simulation of the model reveals that deposit insurance diminishes macroeconomic and financial instability following a technological shock.