This dissertation includes three chapters discussing the importance of bank heterogeneity in monetary policy implementation using tools such as changes in the interest on reserve and the discount window on bank lending. The first two chapters focus on the implications of differences in government regulation, while the third chapter focuses on market competition. The first chapter assesses the effects of a policy reform changing the relative return of holding reserves on the reserves held by U.S. branches of foreign banks compared to conventional domestic banks, using difference-in-differences regression analysis. The second chapter studies the implications of dispersion in the relative return of holding reserves using a liquidity mismatch banking model with different sectors that can trade reserves in an over-the-counter market for federal funds. The model is used to study the effects of changes to regulation, policy rates, and other market conditions on the distribution of reserves across sectors and the federal funds rate. The third chapter documents changes in competition in the loan and deposit market over the last two decades and considers the implications for monetary policy tools using regression analysis compared to simulations of a Dynamic Stochastic General Equilibrium model.Chapter 1, titled DEPOSIT INSURANCE AND PORTFOLIO DESIGN OF BANKS, reviews the distinct response of U.S. branches of foreign banks to the monetary policy of interest on reserve balances following a policy reform in 2011. The Federal Deposit Insurance Corporation (FDIC) reform changed the relative return of holding reserves for U.S. branches of foreign banks (foreign banks for short) compared to conventional domestic banks (domestic banks for short). The data show higher excess reserves held by foreign banks following this policy change. A fixed-effects model is used to measure the effect of a change in the FDIC policy on excess reserves held by each sector. A difference-in-difference comparison suggests a difference of 0.16 in reserves to assets of domestic banks compared to foreign banks following the policy change and a more considerable gap of around 0.25 for banks with average assets holdings in the top 15 percentile. Furthermore, the event study confirms that these larger banks widely capture the impact of policy. The next chapter, Chapter 2, titled BANK PORTFOLIO CHOICE AND MONETARY POLICY TRANSMISSION IN THE FACE OF A NEW FEDERAL FUNDS MARKET, studies the implications of differences in regulation of banks for monetary policy. The chapter presents an equilibrium model in the framework of Bianchi and Bigio (2022) to include two types of bank branches instead of one; domestic banks must hold deposit insurance, while U.S. branches of foreign banks cannot. Deposit insurance allows for a more stable funding source but attaches a higher balance-sheet cost. Calibration finds consistent predictions that explain the higher excess reserves and the sequential credit supply of foreign branches. Moreover, findings suggest that foreign branches are more responsive to monetary policy tools, such as interest on reserves, because their funding source is associated with higher volatility in deposit withdrawals. The monetary policy of changes to the corridor rates in the model is the same across all banks. Still, because U.S. branches of foreign banks face different tradeoffs than U.S domestic banks, monetary policy affects each sector differently. Chapter 3, titled CHANNELS OF MONETARY POLICY WITH IMPERFECT COMPETITION IN THE BANKING SECTOR, uses a relatively new measure of market power proposed by Boone (2008) to estimate the implications of market power on the pass-through of monetary policy for two monetary policy channels. The lending channel and the deposits channel. Data suggest that market power is high in the deposit market and somewhat high in the loan market, with an incline in competition in both sectors in the last two decades preceding 2001. The paper evaluates monetary policy pass-through to deposit and lending rates given the competition across banks using a Dynamic Stochastic General Equilibrium (DSGE) model with sticky prices. The central assumption of the model is that the pass-through depends on competition across banks. It includes banks with imperfectly competitive markups for loans to firms, markdowns of deposit rates to consumers, and a monetary policy authority that can either change the federal funds rate or the spread between the federal funds rate and the rate paid on excess reserves. The model estimations align with the empirical evidence suggesting banks will compensate on loan spreads to avoid the contraction in lending caused by higher policy rates, while deposits will fluctuate less, and therefore spreads may increase when market rates increase. / Economics