University of Southern California Dissertations and Theses

The changing policy environment and banks' financial decisions

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The changing policy environment and banks' financial decisions

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Content THE CHANGING POLICY ENVIRONMENT AND BANKS' FINANCIAL DECISIONS by Vivian Wong A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY BUSINESS ADMINISTRATION August 2021 Copyright 2021 Vivian Wong Contents List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Chapter 1 Explaining Post-Crisis Bank Balance Sheet Developments 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 Household Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.2 Bank Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3.3 Combined Government Central Bank . . . . . . . . . . . . . . . . . . 21 1.3.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.4 Quantitative Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.4.1 Target Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.4.2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.4.4 Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.5 Comparative Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1.5.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 1.6 Deposit Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 1.6.1 A Shift in Demand for Deposits . . . . . . . . . . . . . . . . . . . . . 44 1.6.2 Greater Deposit Demand and Key Bank Ratios . . . . . . . . . . . . 52 ii 1.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Chapter 2 Quantitative Easing and Bank Regulations 64 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.2.1 Household-Nonnancial Firm . . . . . . . . . . . . . . . . . . . . . . 67 2.2.2 Bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.2.3 Central Bank Government . . . . . . . . . . . . . . . . . . . . . . . . 80 2.2.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2.2.5 Nonstochastic Steady State . . . . . . . . . . . . . . . . . . . . . . . 83 2.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 2.3.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 2.4 Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 2.4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 2.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 References 105 Appendix A Bank Balance Sheet Developments, by Asset Size 111 Appendix B Equations 116 B.1 Derivatives for Potential Regulatory Costs . . . . . . . . . . . . . . . . . . . 116 B.2 Nonstochastic Steady State Details . . . . . . . . . . . . . . . . . . . . . . . 119 B.2.1 Chapter 1: Baseline Model . . . . . . . . . . . . . . . . . . . . . . . . 119 B.2.2 Chapter 2: Extended Model with Government Bonds . . . . . . . . . 123 Appendix C Calibration 127 C.1 Full Results and Robustness Checks . . . . . . . . . . . . . . . . . . . . . . . 127 iii Appendix D Counterfactual Details 135 D.1 For Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 D.2 For Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Appendix E Comparative Statics Details 139 E.1 Balance Sheet Changes for Each Parameter . . . . . . . . . . . . . . . . . . . 139 E.1.1 Required Capital Ratio (') . . . . . . . . . . . . . . . . . . . . . . . 139 E.1.2 Cost of Capital Shortfall () . . . . . . . . . . . . . . . . . . . . . . . 140 E.1.3 Required Liquidity Coverage Ratio ( ) . . . . . . . . . . . . . . . . . 140 E.1.4 Costs of LCR Shortfall () . . . . . . . . . . . . . . . . . . . . . . . . 141 E.1.5 Interest on Reserves (r f ) . . . . . . . . . . . . . . . . . . . . . . . . . 141 E.1.6 Housing Preference ( ) . . . . . . . . . . . . . . . . . . . . . . . . . . 142 E.1.7 Weight of Deposits in Household Utility () . . . . . . . . . . . . . . 144 E.1.8 Government Mortgage Supply (M G ) . . . . . . . . . . . . . . . . . . 145 E.1.9 Average Household Income (W ) . . . . . . . . . . . . . . . . . . . . . 147 Appendix F Demand for Deposits: Alternative Specications and Robustness Checks148 F.1 The Fed Funds Rate Dierential, In ation, and Specication Tests. . . . . . 148 F.2 Stock Market Investment and Deposits . . . . . . . . . . . . . . . . . . . . . 151 iv List of Tables 1.1 Summary of Target and Model Moments . . . . . . . . . . . . . . . . . . . . 25 1.2 Summary of Inputted Parameters Used in Calibration . . . . . . . . . . . . . 27 1.3 Model Calibration Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.4 Results of Counterfactual Exercises . . . . . . . . . . . . . . . . . . . . . . . 40 1.5 Balance Sheet Responses to Regulatory and Macroeconomic Forces . . . . . 41 1.6 Mean value of holdings for families holding debt (thousands of 2016 dollars) 46 1.7 Mean value of holdings for families holding asset (thousands of 2016 dollars) 46 1.8 Reasons respondents gave as most important for their families' saving . . . . 46 1.9 Deposits Coverage in Panel Data (SOD) versus FDIC QBS . . . . . . . . . . 49 1.10 Summary Statistics for Full Sample Used in Arellano-Bond Estimation . . . 50 1.11 Naive OLS and Fixed-eects Regressions . . . . . . . . . . . . . . . . . . . . 53 1.12 Arellano-Bond Estimation of Deposit Demand (2000-2015) . . . . . . . . . . 54 1.13 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 1.14 The Relationship between Cash and Deposits Ratio . . . . . . . . . . . . . . 56 1.15 Relationship between Cash Ratio and Deposits Ratio: Role of Capital Buers 58 1.16 Relationship between Cash Ratio and Deposits Ratio: Role of Capital Buers (cont.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 1.17 Relationship between Cash Ratio and Deposits Ratio: Interacting Capital Buers with Deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.18 Relationship between Mortgage ratio and Deposits Ratio: Role of Capital Buers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 v 1.19 Relationship between Mortgage Ratio and Deposits Ratio: Role of Capital Buers (cont.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 1.20 Relationship between Mortgages Ratio on Deposits Ratio with Interaction Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.1 Household-Nonnancial Firm Balance Sheet . . . . . . . . . . . . . . . . . . 68 2.2 Bank Balance Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 2.3 Central Bank Government Balance Sheet . . . . . . . . . . . . . . . . . . . . 80 2.4 Summary of Target and Model Moments . . . . . . . . . . . . . . . . . . . . 86 2.5 Moment Targets for Calibration for Each QE End-date . . . . . . . . . . . . 88 2.6 Summary of Inputted Parameters Used in Calibration . . . . . . . . . . . . . 89 2.7 Calibration Results: Balance Sheets . . . . . . . . . . . . . . . . . . . . . . . 93 2.8 Properties of Dierent Assets . . . . . . . . . . . . . . . . . . . . . . . . . . 95 2.9 Calibration Results: Interest Rate Dierentials . . . . . . . . . . . . . . . . . 96 2.10 Parameters Used in Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . 97 2.11 Counterfactual Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 2.12 Counterfactual Results: Interaction Eects . . . . . . . . . . . . . . . . . . . 103 C.1 Full Model Calibration Results . . . . . . . . . . . . . . . . . . . . . . . . . . 131 C.2 Full Model Calibration Results, Removing Crisis Years from Data . . . . . . 132 C.3 Full Model Calibration Results, Required Reserves Removed from Cash . . . 133 C.4 Full Model Calibration Results, Changing Average Household Income . . . . 134 D.1 Parameter Inputs for Counterfactual Scenarios . . . . . . . . . . . . . . . . . 136 D.2 Parameter Inputs for Counterfactual Scenarios in Part One . . . . . . . . . . 137 D.3 Parameter Inputs for Counterfactual Scenarios in Part Two . . . . . . . . . . 138 E.1 Balance Sheet Response to Changing ' . . . . . . . . . . . . . . . . . . . . . 139 E.2 Balance Sheet Response to Changing . . . . . . . . . . . . . . . . . . . . . 140 vi E.3 Balance Sheet Response to Changing . . . . . . . . . . . . . . . . . . . . . 141 E.4 Balance Sheet Response to Changing . . . . . . . . . . . . . . . . . . . . . 141 E.5 Balance Sheet Response to Changing r f . . . . . . . . . . . . . . . . . . . . 142 E.6 Balance Sheet Response to Changing r f (cont.) . . . . . . . . . . . . . . . . 143 E.7 Balance Sheet Response to Changing . . . . . . . . . . . . . . . . . . . . . 143 E.8 Balance Sheet Response to Changing . . . . . . . . . . . . . . . . . . . . . 145 E.9 Balance Sheet Response to Changing (cont.) . . . . . . . . . . . . . . . . . 145 E.10 Balance Sheet Response to Changing M G . . . . . . . . . . . . . . . . . . . . 146 E.11 Balance Sheet Response to Changing M G (cont.) . . . . . . . . . . . . . . . 146 E.12 Balance Sheet Response to Changing W . . . . . . . . . . . . . . . . . . . . 147 E.13 Balance Sheet Response to Changing W (cont.) . . . . . . . . . . . . . . . . 147 F.1 Arellano-Bond Estimation of Deposit Demand, Modied Instruments (2000-2015)149 F.2 Arellano-Bond Estimation of Deposit Demand, Modied Instruments Excluding High In ation Counties (2000-2015) . . . . . . . . . . . . . . . . . . . . . . . 150 F.3 Arellano-Bond Estimations of Deposit Demand with Stock Returns (2000-2015)153 vii List of Figures 1.1 Selected Bank Balance Sheet Ratios, 1997:Q1-2017:Q3 . . . . . . . . . . . . 2 1.2 Fed Funds Rate, Jan.1997 to Dec.2017 . . . . . . . . . . . . . . . . . . . . . 4 1.3 S&P/Case-Shiller US National Home Price Index, Jan.1997 to Dec.2017 . . . 5 1.4 Bank Liabilities Composition in Shares, 1997 to 2017 . . . . . . . . . . . . . 16 1.5 Potential Costs Associated with Capital Regulation . . . . . . . . . . . . . . 18 1.6 Mortgage Market Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.7 Shares of Mortgage Liabilities Outstanding, by Entity, 1997 to 2017 . . . . . 30 1.8 Bank Asset Composition in Shares, 1997 to 2017 . . . . . . . . . . . . . . . . 31 1.9 Interest Rate on Cash, by BHC, 2000 to 2017 . . . . . . . . . . . . . . . . . 32 1.10 Interest Rate on Loans Backed by Real Estate, By BHC, 2000 to 2017 . . . . 33 1.11 Returns on Bank Assets, by Type, 1997 to 2017 . . . . . . . . . . . . . . . . 34 1.12 Counterfactual Results: Key Ratios . . . . . . . . . . . . . . . . . . . . . . . 40 1.13 Comparative Statics Results: Key Ratios . . . . . . . . . . . . . . . . . . . . 43 1.14 Credit Limit and Balance for Credit Cards and HELOC . . . . . . . . . . . 45 2.1 Federal Reserve Bank Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 2.2 Treasuries Holdings of Dierent Sectors . . . . . . . . . . . . . . . . . . . . . 84 2.3 Deposits Holdings of Dierent Sectors . . . . . . . . . . . . . . . . . . . . . . 85 2.4 Treasuries as Share of Liquid Assets for Household-Nonnancial Firm Sector 85 2.5 Counterfactual Results: Balance Sheet . . . . . . . . . . . . . . . . . . . . . 100 2.6 Counterfactual Results: Interest Rate Dierentials . . . . . . . . . . . . . . . 101 A.1 Cash as Share of Total Assets, by Asset Size . . . . . . . . . . . . . . . . . . 112 viii A.2 Leverage, by Asset Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 A.3 Loans Backed by Real Estate as Share of Total Assets, by Asset Size . . . . 113 A.4 Share of Total Industry Assets, by Asset Size . . . . . . . . . . . . . . . . . . 114 ix Abstract In Chapter 1, I investigate the potential forces driving major bank balance sheet developments in the years following the 2007-2008 nancial crisis. The share of cash as a percentage of banks' total assets has more than doubled over the last decade while residential mortgage loans have shrunk. Meanwhile, bank leverage has plunged and remained muted for the last 10 years. These developments are often attributed to changes in post-crisis banking regulation, but it is dicult to pinpoint how regulation shapes bank behavior in the presence of other macroeconomic factors. Using a general equilibrium model, I assess the capacity of three factors to explain the trends: post-crisis bank regulations, monetary policy, and changes to household preferences. The model suggests greater demand for bank deposits by households is an important contributor to the rise in cash on bank balance sheets post-crisis. In empirical analysis, I explore the positive relationship between demand for bank deposits and banks' cash ratios to test the model's implications. In Chapter 2, I evaluate the impact of quantitative easing (QE) on interest rates and bank and household-nonnancial rm balance sheets in the post-crisis period. Because bank regulation, household-rm preferences, and QE in uence the composition of balance sheets, the three factors must be modeled jointly to understand their combined and separate eects. Extending the general equilibrium framework from Chapter 1, I analyze the eectiveness of the portfolio rebalancing channel of QE in the presence of changing household-rm preferences and capital or liquidity regulations. The model highlights that stricter liquidity rules limit the ability of QE to encourage more lending by banks. Greater household-rm demand for deposits also amplify changes in interest rate spreads created by QE. The quantitative results emphasize the importance of considering bank regulations and liquidity preferences when policymakers use QE to target specic interest rate or bank balance sheet goals, as uctuations in either of the two factors can make ne-tuning of policy dicult. x Chapter 1 Explaining Post-Crisis Bank Balance Sheet Developments 1.1 Introduction As Figure 1.1 highlights, the share of cash in total assets of US depository institutions have roughly doubled since 2009 while reductions in leverage continued and then plateaued. Loans secured by real estate have dramatically fallen, driven by sharp declines in family residential mortgages. 1 What are the forces underlying these trends? How large of a role does banking regulation play? Understanding how regulation aects the composition of bank balance sheets is important because changes in banks' assets and liabilities are linked to credit provision to dierent sectors. By altering banks' decisionmaking process, policies targeted at banks also in uence the broader economy. New rules instated after the 2007-2008 nancial crisis are often credited for making banks and the nancial system safer, but it is not clear how the rules interact with one another or with other economic forces. I investigate the eects of capital and liquidity-based regulations together with movements in macroeconomic factors using a general equilibrium model with banks. The model considers the bank's portfolio problem in the face of household decisions and regulatory constraints. The bank receives deposits from households and can lend or hold cash as reserves at the central bank. Two types of lending occur. First, mortgages are made to households that yield a return dependent on the probability of default and the value of the home used as collateral. In each period, the household experiences a shock to preferences 1 For a discussion on variation between banks of dierent asset sizes, see the Appendix. 1 Figure 1.1: Selected Bank Balance Sheet Ratios, 1997:Q1-2017:Q3 Source: FDIC Quarterly Banking Prole. 2 that changes their demand for housing and determines the price of houses. Given the house price, the household chooses whether to move to a new home, how much to save at the bank, and the size of the mortgage to take out from the bank. Second, banks make other loans to the household which pay a constant return. For simplicity, I assume that other loans are exogenous, while mortgages are endogenous and determined in the general equilibrium. Regulatory constraints consist of a minimum ratio of equity to risk-weighted assets and a liquidity coverage ratio. Reserves help fulll the requirements, but earn little return. Mortgages earn a higher return, but lower regulatory ratios. When regulatory ratios approach minimum stipulated levels, the bank increases the likelihood of incurring a shortfall and facing penalties imposed by the regulator and investors. Thus, the bank faces a tradeo between compliance risk and return. To maximize shareholder value, the bank wants to hold all assets as higher paying mortgages rather than cash. Yet, if it holds too little cash, the bank may realize large regulatory costs. Changes in macroprudential rules and the economic environment are captured by separate parameters to represent dierent elements that can aect the bank's optimization choice. I consider four major changes that occurred around the nancial crisis. First, regulators raised bank capital requirements starting in 2013 as part of a new Basel III framework to mitigate risk. Second, a Liquidity Coverage Ratio (LCR) was introduced in 2015 to make banks resilient to sudden cash out ows. Third, the Federal Reserve lowered interest rates precipitously from around ve percent in 2007 to less than half of a percent in 2009 and kept rates low until early 2016 (see Figure 1.2). Lastly, housing prices rose over the early 2000s to a peak in July 2006 and then fell until early 2012 (see Figure 1.3). Using aggregated balance sheet data on FDIC-insured depository institutions, I calibrate key model parameters to pre-crisis (2000-2007) and post-crisis (2009-2016) conditions. Analyzing changes in parameters over the two periods, I isolate potential drivers of the shift away from real estate loans to a larger share of cash in total assets. Through counterfactual analyses, I quantify how important each of the four major changes is in shaping bank 3 Figure 1.2: Fed Funds Rate, Jan.1997 to Dec.2017 Source: Federal Reserve. behavior. Quantitative exercises show that a combination of changes in the interest rate (monetary policy), household demand, and tighter regulations can account for the evolution of cash holdings, Tier1 capital ratios, mortgage share of total assets, and leverage in the data. Counterfactual exercises highlight that capital and liquidity requirements aect dierent sides of the balance sheet. In the model, the bank responds to higher capital rules by cutting deposit funding and shrinking the entire balance sheet. To meet higher liquidity coverage ratios, the bank raises the share of reserves in total assets and reduces the share of mortgages, which sometimes increases leverage. The results emphasize how the combination of lower interest rates with stronger household demand for savings and houses is essential to temper the bank's sharp reduction of risk-weighted assets, allowing leverage to remain fairly constant in the post-crisis period while cash holdings continue to climb. Importantly, the model suggest a greater role for household deposit demand in facilitating 4 Figure 1.3: S&P/Case-Shiller US National Home Price Index, Jan.1997 to Dec.2017 Source: S&P Dow Jones Indices LLC. the rise of cash on bank balance sheets, hitherto unexplored. 2 I document a rise in deposit demand using a money demand estimation and oer proof for the positive relationship between greater deposit demand and the buildup of cash ratios through panel data analysis. Linkages derived from the empirical exercise, though suggestive in nature, support mechanisms proposed by the model about how changes in household demand interact with constraints placed by capital regulation to shape the composition of bank balance sheets. My paper connects three lines of literature spanning household nance, banking, and macro- prudential policy to understand bank decisionmaking through the lens of portfolio composition. 2 Standard analyses of macroprudential policy focus on equity and do not study the share of cash in total assets. Zhu (2008) and De Nicol o et al (2012) are two prominent models cited in the literature on capital regulation and bank nancial decisions. Zhu employs a model where the balance sheet consists of loans, deposits, and equity, where equity serves as the main tool to meet capital requirements. De Nicol o et al similarly only consider loans, bonds, deposits, and equity in the bank's balance sheet. Recent work by Mankart et al (2020) incorporates a liquid asset into the balance sheet that functions like cash in my model to meet regulatory constraints. However, the focus of Mankart and co-authors is to evaluate how dierent regulations in uence aggregate loan supply and bank failures, not balance sheet composition. 5 There is extensive theoretical work on how housing aects investment and consumption decisions of consumers. Portfolio selection models outline how investors choose dierent asset mixes when they own a house and are subject to house price risk. 3 General equilibrium models trace out how house prices drive uctuations in aggregate consumption. 4 However, the models examine the household optimization problem in great detail and contain little to no treatment of banks' balance sheet choices. Like household portfolio models, I incorporate house ownership, mortgages, and house prices into my model, but I allow the bank's choices about capital structure and asset holdings in uence the bank-household lending relationship. In a similar vein, I include insights from household portfolio literature into the theoretical structure commonly used in banking and macroprudential analyses. Most general equilibrium models separate lenders from borrowers, with banks channeling deposits from household to rms. 5 In contrast, within my model setup, households are both debtors and savers, which is consistent with household portfolio data. 6 My setup also allows me to analyze interactions between household and bank balance sheets. Understanding how household savings aects regulatory constraints is particularly interesting given policymakers' re-examination of bank leverage limits because of large deposit in ows during the coronavirus pandemic. 7 Liquidity 3 Grossman and Laroque (1991) introduce an illiquid durable good into a standard consumption-based asset pricing model to show that transactions costs associated with buying and selling houses can change investors' degree of risk aversion. Flavin and Yamashita (2002) look at how demand for housing and mortgage nance imposes a constraint on the consumer's optimal mean-variance ecient portfolio. Cocco (2004) and Yao and Zhang (2005) study how house ownership reduces stock market participation among lower nancial net-worth individuals and relative to individuals renting housing. 4 Iacoviello (2004) provides a structural model explaining consumption dynamics as a function of utility derived from housing, housing prices, and borrowing constraints tied to home collateral values. Aoki et al (2004) explains in his model how transmission of monetary policy shocks to consumption is determined by the relative ease with which households can borrow against their home equity. 5 Dynamic general equilibrium models used to study macroprudential rules, such as Covas ad Driscoll (2014), have workers as savers and entrepreneurs as borrowers. Traditional business cycle models, like that used in Begenau (2018) to analyze the eects of capital requirements on bank lending, also have households as suppliers of savings and rms as loan takers. 6 For example, Telyukova (2013) discusses how households hold low-return cash despite having outstanding credit card balances with high interest rates (the \credit card debt puzzle") and provides a theoretical model based on households' needs for liquidity as an explanation. 7 The Supplementary Leverage Ratio Interim Final Rule approved on May 2020 allowed temporary exclusion of US Treasuries and Federal Reserve Bank deposits from the supplementary leverage ratio denominator to accommodate in ows of deposits stemming from ight to liquid assets behavior which expanded balance sheets and pushed up leverage ratios at banks. See https://www.occ.gov/news-issuances/federal-register/2020/85fr32980.pdf for further details. 6 and capital rules were designed to address funding out ows from banks, so most analyses do not explore implications of deposit demand by households in their models. The structure of the chapter is as follows. Section 2 explains the regulatory environment and discusses why the model is needed. Section 3 describes the model. Section 4 presents a calibration of the model and counterfactual exercises using aggregated balance sheet data. Section 5 covers the comparative statics of key model parameters and Section 6 explores the results from the comparative statics exercise using empirical analysis. Section 7 concludes. 1.2 Background The Basel III Accord dramatically increased capital-based rules for banks in the wake of the nancial crisis. According to Basel III guidelines endorsed in the US on September 2010, banks must hold more safe assets to satisfy higher capital ratios, a Supplemental Leverage Ratio (SLR), a Liquidity Coverage Ratio (LCR), and enhanced capital buer rules. The SLR necessitates that banks increase the quantity of capital held against on-balance and o-balance sheet exposures. It is essentially a leverage ratio constraint placed on the bank. Basel III Supplementary Leverage Ratio rules dictate a minimum leverage ratio of 3%, with US implementation of the rules setting the minimum at 5% for systemically important banks. The LCR requires banks to hold sucient high quality liquid assets to survive a signicant stress scenario lasting 30 days. 8 New capital rules dictate a capital conservation buer of 2.5% of risk-weighted assets plus a countercyclical buer of 2.5% during credit booms on top of a new minimum capital requirement of 6% of risk-weighted assets. In sum, the quantity and quality of capital banks need at hand has grown. Larger cash reserves and capital buers are meant to make banks more resilient against 8 A signicant stress scenario could include any combination of the following: a run on deposits, loss of unsecured wholesale funding capacity, loss of short-term nancing, out ows from the bank due to downgrades in the bank's credit rating, market events that induce large collateral haircuts and increased liquidity needs, unscheduled drawdown of commited credit facilities provided to clients, and the potential need to buy back debt or honor non-contractual obligations to mitigate reputational risk. For additional details, please see http://www.bis.org/publ/bcbs238.pdf 7 adverse shocks, but if higher regulatory capital is a drag on lending, economic growth suers. As adjustments to capital rules in the last year by the Federal Reserve, and the Trump Administration's review of Dodd Frank suggests, there is uncertainty about whether regulatory reforms have gone too far and if the nancial system is too burdened to support healthy risk-taking and economic growth. Moreover, overnight repo market turmoil in September 2019 further highlights concerns that new regulations are limiting banks' ability to provide liquidity to markets. There is a general consensus about how banks reacted to the Liquidity Coverage Ratio (LCR) that came into full eect on January 2017. Ihrig et al (2017) document that large banks accumulated reserve balances beginning in 2014 to comply with the requirement, then shifted towards holding more Treasuries and government-sponsored entity (GSE)-backed MBS. On the lending side, Gete and Reher (2017) show that tighter lending standards induced by higher liquidity and capital requirements on large banks have led to increased mortgage application denial rates, particularly among low income and minority borrowers. However, it is unclear how macroprudential capital rules aect bank behavior or whether the rules successfully promote safer decisionmaking by banks. Increasing the required quantity of safe assets held against risky assets generally decreases loan growth and generates less risky balance sheets. 9 However, there is evidence that stricter capital-based rules may not prevent crises and can exacerbate risk-taking. 10 The empirical studies do not 9 Aiyar, Calomiris, and Wieladek (2014) explain intuitively how capital requirements raise costs of issuing loans, causing banks to reduce lending and pass on the costs to borrowers in the form of higher interest rates. Corbae and D'Erasmo (2014) and Giordana and Schumacher (2013) both explicitly model a complex banking sector within a general equilibrium framework and arm that aggregate loan supply falls in response to a rise in capital requirements. Bridges et al (2014), using a 1990-2011 sample of UK banks, supplies evidence for banks cutting a large portion of commercial real estate loans, a slightly smaller portion of corporate lending, and a minimal fraction of household secured nance. Juelsrud and Wold (2018) present evidence from Norway that banks raise capital ratios in reaction to Basel III rules by reducing risk-weighted assets, supplying more credit to the corporate sector relative to the household sector. Noss and Toano (2014), using aggregate data on UK banks and a rough measure of capital requirements, estimate that banking lending may contract by as much as 4.5% to a 1% increase in macroprudential capital requirements during an economic boom. Francis and Osborne (2009) place the drop at around 0.8%, while a study by the Macroeconomic Assessment Group (MAG) attached to Basel and the Financial Stability Board (FSB) estimate a range of 0.7% to 2.1% if the 1% increase in capital requirements is phased in over a two year period. 10 Jord a et al. (2017) show empirically that higher captial buers do not prevent nancial crises using historical data for advanced economies. Gale (2010) discusses how, in theory, feedback eects can lead banks 8 provide a clear guide about what rules guide banks' balance sheet decisions when faced with new macroprudential regulation. Additionally, the interaction between household borrowing-savings choices with asset allocation decisions of the bank is not explored in standard analyses. Given the drop in the federal funds rate after the nancial crisis and the incremental implementation of Basel III, a theoretical framework is needed to understand the channels through which macroprudential tools function. I propose a model to analyze bank balance sheet choices in the context of new regulatory rules and macroeconomic factors to isolate the mechanisms driving bank behavior post-crisis. 1.3 The Model There are three sectors in the economy: the household sector, the bank sector, and a combined government central bank. First, I describe the household sector and the bank sector along with the regulatory rules considered in the model. Second, I introduce the role of the government central bank. Then I dene the equilibrium and solve for the nonstochastic steady state with some baseline parameters to characterize how the optimal choices of households and banks jointly determine the composition of bank balance sheets. 1.3.1 Household Sector Time is discrete and the horizon innite. A representative household receives utility from consumption, C t , the size of the house they own, H t , and savings, S t : log(C t ) + t log(H t ) + t log(S t ) to reach for yield and take on more risk given higher capital requirements. Cohen and Scatigna (2016) document an increase in risky assets along with capital among global banks in emerging markets in response to post-crisis regulation. Uluc and Wieladek (2016) show that, in the UK, rising microprudential capital requirements lead to risk-shifting towards mortgage loans to higher risk borrowers at the individual bank level. 9 Household income consists of a xed wage,W t , and dividends from bank equity,D t . Income not spent is saved at the bank in the form of deposits, so savings, S t , earn interest r s t . Households derive utility from deposits because of their liquidity properties. As discussed in Begenau (2018), this gives rise to a convenience yield on deposits whereby households want to hold deposits even with little to no return on their investment (when r s t is close to zero). Said dierently, households not only value deposits as an asset for consumption smoothing, but also value the short term nature of deposits that allows them to withdraw funds at any time. The parameter t captures the degree of liquidity preference and thus the size of the convenience yield. In comparison, housing is an illiquid form of savings that is not as easy to adjust. To extract liquidity from the house they own, the household must take out a mortgage, M t , with interest rate r m t from the bank. 11 The household has preference shock, t , which changes their demand for housing. 12 Total housing supply in the economy is xed, at H, so changes in the household's demand for housing aects the price of the house, P t , exposing them to house price risk. 13 Maintenance costs that must be paid each period also uctuate with the house price, P t H t . Timing is as follows: • The household enters the period with the house they own, H t , a mortgage of size M t , and savings, S t , from the previous period. 11 As a simplication, mortgages, M t , encapsulate all loans backed back real estate on the bank balance sheet. Included are loans backed by single family and multi-family residential properties, farmland, nonfarm nonresidential property, home equity loans, and loans for construction and development. Additionally, I abstract from the heterogeneity of loan terms for dierent real estate collateral by having a single loan type that is the simple xed-rate mortgage loan for a house. Changes in household demand for residential housing will drive changes in M t , which captures the essence of the fourth panel in Figure 1.1. 12 The form of the utility function with a housing demand shock is similar to that found in Liu, Wang, and Zha (2013). As the authors explain, the housing demand shock can be thought of as a reduced form representation of shocks not captured in the model, like idiosyncratic liquidity shocks or collateral constraints on borrowing that in uence housing demand. Since the household here is subject to a collateral constraint, the house demand shock is meant to capture changes in home services production technology, like that suggested by Iacoviello and Neri (2010). The housing preference shock relies on an underlying assumption that utility depends on the services households receive from housing and there are time-varying shocks to the technology needed to produce services from housing stock. 13 Essentially, prices adjust indirectly via t to allow the housing market to clear and match demand for housing with supply in equilibrium. 10 • Housing preference shock, t , and degree of liquidity preference, t , are realized, price, P t , is revealed, wages, W t , and dividends, D t , are received. • The household chooses current consumption,C t , next period housing,H t+1 , mortgage, M t+1 , and savings, S t+1 . If the household moves to a new house, they must pay the dierence in the value of the houses P t (H t+1 H t ). Households also have other loans from the bank each period, L t , with interest r l t . 14 To keep the model tractable, these loans are assumed to be exogenously chosen. Budget Constraint The household's budget constraint is W t +D t + M t+1 (1 +r m t ) + L t+1 (1 +r l t ) +S t =C t +T t + S t+1 (1 +r s t ) +M t +L t +P t (H t+1 H t ) +P t H t (1.1) On the left-hand side is the household's source of funds from current income, next period borrowing, and current savings. On the right-hand side is the household's use of funds. They include consumption, tax payments to the government, next period savings, current borrowing, and housing costs. Collateral Constraint Because the household can potentially default on the mortgage loan, the house serves as collateral for the loan. The bank imposes a loan-to-value limit on the size of the mortgage 14 This simplication of the household's portfolio is used to capture the non-mortgage related assets on bank balance sheets, including commercial and industrial loans, loans to individuals, securities, other loans, Fed funds sold, and reverse repurchase agreements. Fed funds purchased and repurchase agreements are subtracted from L t because interbank borrowing is not considered in the model. 11 given to the household based on the value of the house. M t+1 E t (P t+1 )H t+1 (1.2) Since the loan size is based on the expected future value of the house (the house price is not known when the mortgage is made), the mortgage can be interpreted as the culmination of a rst lien mortgage and any equity loans or lines of credit. 15 The Household's Problem The household maximizes lifetime utility derived from consumption, savings, and the house they own, subject to its budget constraint (equation (1.1)) and the collateral constraint (equation (1.2)). Dene the value function U(S t ;H t ;M t ) = max Ct;S t+1 ;M t+1 ;H t+1 flog(C t )+ t log(H t )+ t log(S t )+ h E t [U(S t+1 ;H t+1 ;M t+1 )]g: In recursive form, the household solves the Lagrangian L(S t ;H t ;M t ) =U(S t ;H t ;M t ) + 1;t W t +D t + M t+1 (1 +r m t ) + L t+1 (1 +r l t ) +S t 1;t C t +T t + S t+1 (1 +r s t ) +M t +L t +P t (H t+1 H t ) +P t H t + 2;t P t+1 H t+1 M t+1 Optimal Choices When deciding how much to borrow, how much to save, and how to allocate spending between consumption and housing, the household faces several tradeos. In the intertemporal dimension, the household decides whether to consume now or save to have more resources 15 As in Cocco (2004), I assume the household can costlessly renegotiate their desired level of debt to keep the model simple. 12 to spend in the future. In the intratemporal dimension, the household must choose between utility gained from consumption, enjoyment of a bigger home, or the benets of having liquid savings at hand. Taking the derivative with respect to consumption, C t , savings, S t+1 , size of the mortgage, M t+1 , and housing, H t+1 , we have the rst-order conditions that capture the optimal choices made by the household. Consumption. The household's choice of consumption is described by 1;t = 1 C t (1.3) Consumption is chosen so that the marginal utility gained from an additional unit of consumption is equal to the value of an additional dollar in the household's budget that the household must give up. Savings. Household savings is determined by h E t t S t+1 + 1 C t+1 (1 +r s t ) = 1 C t (1.4) When deciding how much to save, the household weighs the expected discounted marginal utility of future savings and consumption against the incremental loss in utility from foregone consumption today. Mortgage. The decision about borrowing to buy a house depends on the value of an additional dollar in home equity, expressed as 2;t = 1 C t 1 (1 +r m t ) h E t 1 C t+1 (1.5) Home equity is equal to the dierence in the value of the house less the value of the mortgage, ( P t+1 H t+1 M t+1 ). For a given house worthP t+1 H t+1 , when the household increases the size 13 of their mortgage loan, they reduce home equity and their potential to borrow more against the value of their home in the future. Equation (1.5) links the cost of reducing home equity by an additional dollar today to the dierence in the marginal utility gained from one unit of borrowing today (discounted by the cost of borrowing) and the discounted expected loss in marginal utility from forgone consumption tomorrow. The greater the dierence between marginal utility gained from borrowing today and utility cost of repayment tomorrow, the more valuable is additional borrowing. 16 Housing. The choice to move and buy a new home is characterized by 2;t P t+1 + h E t t H t+1 + P t+1 C t+1 = P t C t + h E t P t+1 C t+1 (1.6) On the left-hand side are the household's marginal benets, consisting of utility from additional equity available to borrow from today and the expected increase in utility from owning the new home and extra consumption tomorrow. On the right-hand side are the marginal costs associated with acquiring a new house plus the expected future maintenance costs, expressed in utility terms. 1.3.2 Bank Sector Setup A representative bank takes deposits, S t , from households and can invest in mortgages, M bt , and other loans, L t , to households or hold the deposits in the form of reserves at the 16 Slackness conditions apply, so 2;t ( P t+1 H t+1 M t+1 ) = 0. Either 2;t = 0 and P t+1 H t+1 >M t+1 , or 2;t > 0 and P t+1 H t+1 =M t+1 . Additional equity is only valuable when the loan-to-value limit is binding. 14 central bank. 17 The price of deposits isq s t = 1 (1+r s t +) . 18 The portion of deposits held in other loans to households, L t , earns interest rate r l t . Income from mortgages is characterized by y t =z t M bt , wherez t is the gross return on investment and M bt is the amount of investment. Letting denote the probability of household default 19 and denote the recovery rate on the value of the foreclosed home, andM t is the total mortgages demanded by households,z t equals M bt Mt P t H t + (1)(1 +r m t )M bt M bt Central bank reserves,F t , earn a gross return of (1+r f t ), and act as a buer against potential liquidity shocks. The bank pays dividends of D t each period. For simplicity, I assume other loans,L t , are exogenous while mortgages,M bt , are endogen -ously determined. Potential Regulatory Costs The bank is subject to a capital constraint and a Liquidity Coverage Ratio (LCR). When the bank's capital ratio or LCR approaches the minimum regulatory benchmark, the bank increases its risks of potentially incurring a shortfall, whether in stress tests scenarios or in actual liquidity crises. Given that the bank's capital condition is public knowledge, the larger the distance between the bank's regulatory ratios and minimum required levels, the lower is the expected regulatory burden and negative market reaction faced by the bank. Furthermore, banks revealed during the September 2019 overnight repo market freeze 17 To match the asset side of the balance sheet, deposits here include subordinated debt, other borrowed money, and other liabilities. Fed funds purchased and repurchase agreements are not included, as there is no interbank market in the model. In the data, deposits drive most of the change in the non-equity portion of total liabilities (less Fed funds purchases and repurchase agreements) from 2000 to 2018 (see Figure 1.4). Thus, I treat the entirety of non-equity as if they are deposits in the model and only consider the decisions behind changes in deposits in the bank and household's problem. 18 is the unit cost of intermediation as proposed by Phillipon (2015). The constant per unit cost is akin to overhead costs associated with provision of deposit services that are not paid to the depositors. 19 I don't explicitly modeling the strategic default choice of the household and instead use to capture the costs of default in reduced form. Default can be interpreted as a price wedge that causes banks to charge higher interest rates for mortgage provision. Alternatively, can also capture the provisions for mortgage related loan and lease losses banks must deduct from assets, which is like a cost for mortgage lending. 15 Figure 1.4: Bank Liabilities Composition in Shares, 1997 to 2017 Source: FDIC Quarterly Banking Prole. that incurring daylight overdrafts entail immeasurable costs, so buers are always positive. These dynamics are captured parsimoniously by a convex cost that increases as the bank's regulatory ratio falls. 20 . 20 The potential costs I have in mind include direct costs of heightened regulatory scrutiny or intervention in bank operations, cuts in dividend payouts imposed as penalties by regulators, reductions in the market evaluation of the rm, and increases in the price of additional external funding. Banks that fail the Dodd-Frank Act Stress Tests (DFAST) or the Comprehensive Capital Analysis and Review (CCAR) conducted by the Federal Reserve are barred from increasing shareholder payouts through dividends or share buybacks. Under Basel III, banks that experience a shortfall in their LCR are subject to enhanced reporting commensurate with the size and duration of the shortfall and regulatory supervisors could also require a bank to reduce its exposure to liquidity risk, strengthen its overall liquidity risk management, or improve its contingency funding plan. Neretina et al (2015) provide evidence that DFAST and CCARs aect the CDS spreads of banks. Flannery et al (2017) and Fernandes, Igan, and Pinheiro (2017) suggest that investors are attentive to bank stress tests and trade based on the results, which impacts banks' average returns. The formulation of regulation as a convex adjustment cost mirrors the setup in Furne (2001), Pari es et al (2011) and Roger and Vl cek (2011) though the functional form is dierent. 16 Capital Requirement. The capital requirement is calculated as shareholder's equity divided by risk-weighted assets: F t+1 +M bt+1 +L t+1 S t+1 ! mt M bt+1 +! lt L t+1 Taking the required ratio to be equal to ' t , the potential regulatory cost related to capital ratios is: 8 > > < > > : F t+1 +M bt+1 +L t+1 S t+1 !mM bt+1 +! lt L t+1 ' t 2 ; if F t+1 +M bt+1 +L t+1 S t+1 !mtM bt+1 +! lt L t+1 >' t 1; otherwise (1.7) Liquidity Coverage Ratio. The mandated liquidity coverage ratio must be met each period. Regulators assign runo rates to the bank's deposits, t , and outstanding unused credit lines, t , to calculate potential cash out ows due to negative shocks, taking into account potential osetting cash in ows from mortgage payments. 21 High quality liquid assets in the bank's possession, comprised of reserves (F t+1 ) and a portion of other loans ( lt L t+1 ), must be equal or greater than some multiple of net cash out ows ( t 1). Thus, the potential regulatory costs associated with LCR are: 8 > > < > > : F t+1 + lt L t+1 + 1 2 r m t+1 M bt+1 tS t+1 +tM bt+1 t 2 ; if F t+1 + lt L t+1 + 1 2 r m t+1 M bt+1 tS t+1 +tM bt+1 > t 1; otherwise (1.8) Figure 1.5 illustrates the general shape of potential regulatory costs as a function of the bank's distance from the minimum requirement, using the capital ratio as an example. 21 Deposits that can be withdrawn quickly have a minimum runo rate of 10%. Commitments for mortgages primarily secured by a rst or subsequent lien on a one-to-four family property that can be drawn upon within 30 calendar days of a calculation date have a runo rate of 10% applied to the undrawn portion. Committed credit and liquidity facilities to retail and small business customers are assigned a runo of 5% of undrawn portions. Retail and business customer in ows equal to 50% of contracted amounts can be used to oset cash out ows. 17 Figure 1.5: Potential Costs Associated with Capital Regulation To simplify notation, let t+1 = F t+1 +M bt+1 +L t+1 S t+1 ! mt M bt+1 +! lt L t+1 ' t 2 + F t+1 + lt L t+1 + 1 2 r m t+1 M bt+1 t S t+1 + t M bt+1 t 2 Derivatives taken with respect to variablei are denoted as i;t+1 . Reserves reduce regulatory costs ( F;t+1 < 0), while deposits increase regulatory costs ( S;t+1 > 0). The eect of mortgages is less clear, since mortgages both add to capital requirements and partially oset liquidity out ows, but they generally reduce regulatory costs ( Mb;t+1 < 0). For more details, please see the Appendix. Budget Constraint The bank's budget constraint is z t M bt +(1 +r l t )L t +q s t S t+1 +F t =S t +D t + t+1 +M bt+1 +L t+1 +q f t F t+1 (1.9) 18 where q f t = 1 (1+r f t ) is the price of reserves. On the left-hand side is the bank's source of funds, comprised of revenue from investment, z t M bt + (1 +r l t )L t , the value of deposits issued next period, q s t S t+1 , and reserves, F t . Funds are used to repay deposits, S t , pay dividends, D t , pay expected regulatory costs, t+1 , to lend,M bt+1 +L t+1 , or are allocated to reserves next period (adjusted for the rate of return), q f t F t+1 . The Bank's Optimization Problem The goal of the bank is to maximize its value, which is the present value of dividend payments to households. The problem of the bank in recursive form is V (z t ;P t ;S t ;M bt ;F t ) = max S t+1 ;M bt+1 ;F t+1 fD t + b E t V (z t+1 ;P t+1 ;S t+1 ;M bt+1 ;F t+1 )g s.t. (1:9) The bank's problem mirrors a rm's equity value maximization problem, with constant returns to scale production technology, convex regulatory costs, and a borrowing constraint. Optimal Balance Sheet Choices When deciding the relative amounts of deposits, reserves, and mortgages to hold, the bank faces a tradeo between risk and return. Assets with higher returns are more desirable for generating dividends, but the gains must be weighed against the risks of experiencing costly regulatory shortfalls. Taking the rst-order conditions from the optimization problem for deposits, S t+1 , reserves, F t+1 , and mortgages, M bt+1 , we obtain the conditions that characterize the optimal decisions of the bank. Deposits. Because deposits are a liability for the bank, deposits are equivalent to borrowing. When deciding how much to borrow, the bank considers the marginal benet of an additional 19 unit of borrowing versus the marginal cost, expressed as q s t = b + S;t+1 (1.10) The marginal benet to the bank is the value of one dollar today, weighted by the rate of return paid to depositors, q s t . Marginal costs of borrowing (shown on the right-hand side of equation (1.10)) include the discounted value of the one dollar the bank must return to the depositor tomorrow plus the cost of additional capital the bank must hold to meet regulatory liquidity and capital rules for one additional unit of borrowing. Deposits reduce the liquidity coverage ratio, F t+1 +M bt+1 +L t+1 S t+1 !mtM bt+1 +! lt L t+1 , and capital ratio, F t+1 + lt L t+1 + 1 2 r m t+1 M bt+1 tS t+1 +tM bt+1 , which increases the bank's risk of incurring a shortfall and facing penalties, so the bank must consider the capital costs of borrowing when deciding on the optimal share of deposits on its balance sheet. Reserves. The bank's choice about reserves is characterized by b F;t+1 =q f t (1.11) Reserves are chosen so that the marginal benets of additional funds tomorrow and reduction in potential regulatory costs (since reserves increase regulatory liquidity and capital ratios) are equal to the marginal cost of reserves. Mortgages. Mortgages are determined by b E t (1)(1 +r m t+1 ) + P t+1 H t+1 M t+1 Mb;t+1 = 1 (1.12) An additional dollar made in mortgages brings the bank an expected return based on the probability of default, , the interest rate charged, r m t+1 , and the value of the home used as collateral adjusted for the size of the total mortgage taken against the home, P t+1 H t+1 M t+1 . 20 Mortgages partially reduce the bank's required regulatory ratios and increase the potential regulatory costs faced by the bank. The second term in equation (1.12) is the net marginal benet from one unit of mortgages in terms of regulatory liquidity and capital costs. For each extra unit of mortgages, the bank can use its net interest revenue to raise additional deposits, which relax constraints placed on borrowing by the liquidity ratio requirement. However, for one extra unit of mortgages, the bank reduces its liquidity ratio by the risk weight in the denominator of the required ratio, which it must oset by holding additional reserves. The net marginal benet of one unit of mortgages in terms of regulatory capital costs is F t+1 +M pt+1 +L t+1 S t+1 !mtM bt+1 +! lt L t+1 . Increasing mortgages by one unit raises bank equity, (F t+1 + M pt+1 +L t+1 S t+1 ), and enables the bank to raise additional deposits. At the same time, the capital ratio is reduced by ! mt , so the bank needs to hold extra reserves to oset the increase in mortgages, leading to a net marginal benet of ! mt (S t+1 F t+1 L t+1 ). Marginal benets must be equal to the price of one unit of mortgages made, which is one. 1.3.3 Combined Government Central Bank The government central bank collects taxes from households, intervenes in the mortgage market, and issues reserves to the banking sector. Let the total value of mortgages extended to households be M t , equal to the sum of mortgages intermediated by the bank sector, M bt , and by the government, M gt (see Figure 1.6). The government intervenes in the mortgage market by supplying mortgages, M gt , to achieve an equilibrium price of (1 +r m t ). 22 22 I use this assumption to capture, in a simple way, how US government-sponsored enterprises, like the Federal Home Loan Banks, Freddie Mae, and Fannie Mac, reduce the cost of mortgage-nancing for households through the purchase and securitization of mortgages. 21 Figure 1.6: Mortgage Market Equilibrium For a set interest rate level, r f t , the central bank issues reserves, F t . 23 The chosen level of reserves must satisfy the budget constraint: (1 +r m t )M gt+1 + (1 +r f t )F t =T t +F t+1 +z t M gt (1.13) where z t : Mgt Mt P t H t + (1)(1 +r m t )M gt M gt The government central bank does not maximize an objective function and just maintains a balanced budget embodied in equation (1.13). 1.3.4 Equilibrium Denition Let X be a vector of state variables containing housing preference parameter, t , the weight of deposits in household utility, t , house size,H t , government mortgage supply,M gt , 23 The interest rate on reserves, r f is determined by many factors, like unemployment and in ation, that are outside of the model. I incorporate interest rate policy in a reduce-form way by dening r f t as an exogenous variable. 22 the central bank's interest rate on reserves, r f t , amount of other loans, L t , and interest on other loans,r l t . LetK be a vector containing variables describing the regulatory environment: minimum capital ratio,' t , risk-weights on mortgages and other loans,! mt and! lt , minimum LCR, t , out ow rates on deposits and mortgages, t and t , and other loans qualifying as high quality liquid assets, lt . Denote the set of policy functions for the household as f H : 8 > > > > > > > < > > > > > > > : C(X;W t ) consumption S H (X;W t ) savings demand M H (X;W t ) mortgage demand H H (X;W t ) housing demand 9 > > > > > > > = > > > > > > > ; Denote the set of policy functions for the bank as f B : 8 > > > > < > > > > : S B (X;K;z t ) deposit supply M B (X;K;z t ) mortgage supply F B (X;K;z t ) reserves demand 9 > > > > = > > > > ; Denote the set of policy functions for the government central bank as f G : F G (X;z t ) reserves supply An equilibrium consists of f H , f B , f G , a dynamic process for t , house price, P t , interest rates r s t and r m t such that: 1. Household policy functions f H satisfy equations (1.3)-(1.5) given P t , r s t , and r m t . 2. Bank policy functions f B satisfy equations (1.10)-(1.12) given P t , r s t , and r m t . 3. Government central bank policy functions f G satisfy its budget constraint: (1 +r m t )M gt + (1 +r f t )F t =T t +F t+1 +z t M gt 23 4. Markets clear: • Mortgages: M B +M G =M H • Reserves: F B =F G =F • Housing: H H =H • Savings: S H =S B =S Nonstochastic Steady State Setting the housing preference shock t = , I solve for the nonstochastic steady state of the model. The set of equations describing the steady state can be found in the Appendix. 1.4 Quantitative Exercises I calibrate model parameters to re ect the macroeconomic and regulatory environment, household characteristics, interest rates, and the structure of the housing market before and after the nancial crisis. To focus on the main channels of interest, I specically try to match balance sheet and regulatory ratios in the data with model moments determined by capital and liquidity regulation, monetary policy, and household preference parameters. I then examine the evolution of model parameters implied by the change in moments from pre- to post-crisis to understand which channels are more important. 1.4.1 Target Moments The two time periods considered are pre-crisis dened as 2000 to 2007 and post-crisis from 2009 to 2016. I choose years relatively close to the peak of the nancial crisis and use six year periods on either side just to balance the observations. Because I want to explain the drop in leverage and accumulation of cash holdings by banks after the nancial crisis, my rst two targets are the cash to total assets ratio and 24 Table 1.1: Summary of Target and Model Moments Data moment Data source Model moment cash total assets FDIC Quarterly Banking Prole F F +M B +L assets assets - liabilities FDIC Quarterly Banking Prole F +M B +L F +M B +LS Tier1 risk-weighted assets ratio FDIC Quarterly Banking Prole F +M B +LS !mM B +! l L liquidity coverage ratio Basel 3 assessment reports F + l L+ 1 2 r m M B S+M B average sales price of house sold in US average square footage of house US Census P MZM own rate Federal Reserve r s return on equity FDIC banking ratios 1 b book leverage. To quantify the perceived costs of regulatory noncompliance, and , I include banks' actual liquidity coverage and Tier 1 capital ratios as targets. Given the large movements in interest rates and housing prices that occurred from 2000 to 2012, I also want to match the interest rate on deposits and the price per square foot for housing to estimate housing preferences, , and utility from deposits, . To pin down the discount factor, b , which aects the range of interest rates on deposits, r s , that the model can accommodate, my last target is the return on bank equity. Table 1.1 summarizes the target moments and corresponding model moments. Balance sheet data come from the FDIC Quarterly Banking Prole (QBP). The QBP provides aggregated nancial results of all FDIC-insured institutions, encompassing national and state banks, federal savings associations, and thrifts (all of whom are subject to Basel III capital rules). 24 The cash ratio, row one in Table 1.1, is calculated as \cash and due from depository institutions" divided by total assets. 25 Leverage, row two in Table 1.1, is total assets divided by equity. 24 A weekly or monthly series is also available from the Federal Reserve H.8 "Assets and Liabilities of Commercial Banks in the United States" report, but it is based on a smaller core sample of 875 domestically chartered banks and foreign-related institutions, so it is not used. 25 Cash is line item RCFD0010 or RCON0010 from Schedule RC-A in the FFIEC 031 and 041 Call Reports, which includes cash items in process of collection, unposted debits, currency and coin, balances due from US depository institutions, balances due from banks in foreign countries and foreign central banks, and balances due from Federal Reserve Banks. 25 Regulatory ratios are taken from FDIC QBP data and Basel 3 assessment reports. The Tier1 risk-weighted assets ratio is line item \Tier 1 risk based capital ratio (PCA denition)" for all institutions in FDIC QBP bank ratios data. The liquidity coverage ratio comes from two dierent sources. For the period 2000 to 2007, in lieu of an actual liquidity coverage ratio, I use the average LCR calculated for Group 1 banks (internationally active banks with Tier 1 capital greater than three billion Euros) based on December 31, 2009 data as reported in the Basel Committee on Banking Supervision (BCBS) December 2010 Comprehensive Quantitative Impact Study. 26 Group 1 banks in the Study totaled 91 banks, including 13 US banks, and had an average LCR of 83%. For the period of 2009 to 2016, I use a measure of the LCR for US banks from the BCBS July 2017 Assessment of Basel III LCR regulations report. The average LCR for all internationally active bank holding companies in the US was estimated at 110.5% based on September 30, 2016 data. 27 To obtain the average price per square foot of houses sold in the US, I rely on the Characteristics of New Housing tables from the US Census Survey of Construction (SOC). 28 The average square footage is from the table \Median and Average Square Feet of Floor Area in New Single-Family Houses Completed", which provides data on square footage at annual frequency for the entire US and broad subregions. The average sales price is taken from the series \Average Sales Price of Houses Sold for the United States" (APSUS) retrieved from FRED, which derives from new residential sales data from the US Census and Department of Housing and Urban Development. The MZM own rate is from FRED. MZM is a measure of money stock equal to M2 minus small-denomination time deposits, plus institutional money market mutual funds. M2 consists of savings deposits (including money market deposit accounts), small-denomination 26 see https://www.bis.org/publ/bcbs186.pdf 27 see https://www.bis.org/bcbs/publ/d409.pdf 28 The SOC is a national sample survey of new houses selected from building permits and a canvassing of areas not requiring permits. Builders or owners of the houses selected are interviewed for information including start, sale, and completion dates, and more than 40 physical and nancial characteristics of the houses. The characteristics are collected throughout the construction process, thus the highest response rate is associated with completed homes. The overall national sampling rate is about 1 in 50 new houses, although this varies considerably by individual survey location based on activity. 26 Table 1.2: Summary of Inputted Parameters Used in Calibration Both periods Pre-Crisis (2000-2007) Post-Crisis (2009-2016) Parameter Value Parameter Value Parameter Value W $86,000 H 2,377 H 2,550 0.010 ' 0.040 ' 0.060 0.800 0.018 0.016 0.020 l 0.013 l 0.028 0.650 r f 0.034 r f 0.002 h 0.935 0.032 0.029 ! l 1.000 M G $105,000 M G $148,000 L $152,000 L $190,000 r l 0.067 r l 0.045 0.705 1.000 time deposits (time deposits of less than $100,000), and balances in retail money market mutual funds. Basically, the MZM own rate captures the return on very liquid, short-term, money holdings of households. Return on equity is calculated from the FDIC QBP \Annual Income and Expense of FDIC- insured Commercial Banks and Savings Institutions" table. The numerator is net operating income. The denominator is average total equity capital over four quarters of the previous year, from FDIC QBP balance sheet data. I also construct an alternative measure using the last quarter of every year, but it does not materially change the number. 1.4.2 Setup To isolate the mechanisms behind capital and liquidity regulation, monetary policy, and household preferences, I calibrate other parameters of the model by inputting values directly from the data. Table 1.2 provides the full list of parameters. In the left panel of Table 1.2 are the parameters set constant for both time periods in the analysis. The rst is household wage, W , which I equate to average annual household income in the 2017 US Census, rounded to the nearest thousand, of $86,000 (see row one). The subsequent rows pertain to the housing market structure. I assume that one percent 27 of mortgages are defaulted on with = 0:01. Following general lending standards, the maximum loan-to-value ratio for a mortgage, , is 80 percent. Maintenance costs, , is two percent of home value, calculated as the sum of 2018 US average annual utility bills, homeowner's insurance, HVAC, and house cleaning costs, from Zillow, divided by the average sales price of a house from 2000 to 2018, from FRED. Foreclosure sale recovery value, , is taken from Guren et al (2017) and equals 65 percent. The household discount factor, h , is kept constant at 0.935. To satisfy slackness conditions of the model, h must be less than or equal to 1 (1+r m ) , so I set h just below the pre-crisis value of 1 (1+r m ) , 0.937. The last parameter kept constant is the risk weight assigned to other loans in the calculation of the Tier 1 capital ratio,! l , set to 1. I keep the risk weight on other loans constant so I can solve for the risk weight on mortgages, ! m , that corresponds to the actual Tier 1 capital ratio in the data. 29 I also input parameters for the size of a house, the regulatory environment, interest rates, other bank assets, and government mortgage supply based on averages for each sub-period (see the middle and right panels of Table 1.2). House size, H, is equal to average square footage from the US Census SOC, aforementioned in Section 4.1. Average house size increases from 2,377 square feet pre-crisis to 2,550 post-crisis. The regulatory environment is described by statutory benchmarks for capital and liquidity ratios, and actual holdings of risk-weighted assets. The capital requirement, an equity to risk-weighted assets ratio, ', was raised from 0.04 pre-crisis to 0.06 post-crisis under Basel III. The required liquidity coverage ratio (LCR), , equals 1 for the post-crisis period (last row in the right panel of Table 1.2). The portion of mortgage loans that count as out ows for the LCR, , is calculated as ten percent of the ratio of unused credit lines to total loans backed by real estate, taken from FDIC QBP balance sheet data. remains fairly low in both periods, around 0.02. The portion of other loans that count as high quality liquid assets in the LCR, l , is the share of Treasury securities divided by total assets less mortgages and 29 Alternatively, I can keep the risk weight on mortgages constant and solve for the risk weight on other loans. The choice is not crucial to the calibration, since I am interested in nding some weight combination in the model that satises the Tier 1 ratio and am not targeting the risk weights themselves. 28 cash, also from FDIC QBP. Banks' holdings of Treasury securities increased over the two periods, with the ratio more than doubling from 0.013 to 0.028. Inputted rates includer f and. Interest rate on reserves,r f , is the Fed funds rate, which falls from 3.4 percent pre-crisis to 0.2 post-crisis. Noninterest cost per unit of deposits, , is calculated by dividing total annual noninterest expense by the average of previous year's total assets. Noninterest expense comes from annual bank income and expense data from the FDIC QBP, while total assets come from quarterly balance sheet data. stays fairly constant around 0.03 in both periods. For government mortgage supply, M G , I use the share of total outstanding one to four family residential mortgage liabilities held by US government sponsored entities. The data is from the Flow of Funds Table L128 on home mortgage liabilities. Figure 1.7 shows the share over time held by government sponsored agencies (Fannie Mae and Freddie Mac) as mortgage loans, securitizations, and in agency- and GSE-backed mortgage pools. The share averages 50 percent pre-crisis and 60 percent post-crisis. Growth in the government share of residentital mortgages outstanding stems from restructuring of GSEs under the Housing and Economic Recovery Act (HERA) in September 2008 and subsequent relaxation of qualifying criteria for conforming loans. 30 To re ect the growth in government subsidization of mortgages through direct ownership and securitization (and capture the growth in nonbank lending resulting from government actions) over the two periods, M G , is set at $105,000 pre-crisis and then $148,000 post-crisis, assuming average loan size of around $200,000 pre-crisis and considering the average size of mortgages in 2017 was about $247,000 according to National Statistics for New Fixed-Rate Fully Amortizing Residential Mortgages in the US from the Federal Housing Finance Agency (FHFA) National Mortgage Database (NMDB). 30 HERA permitted Fannie and Freddie to purchase higher balance loans, raising conforming loan limits up to $417,000 or 125% LTV beginning on January 1, 2009 (Congressional Budget Oce). In 2014 and 2015, Fannie Mae and Freddie Mac began accepting mortgages with only 3% downpayment, and eliminated many borrower income and geographic constraints, which made it easier to issue conforming loans (Shoemaker 2019). By making government guarantee of GSE obligations explicit, HERA increased investor demand for agency- and GSE-backed mortgages. These government reforms are linked to growth in nonbank activity in the conventional mortgage market. Nonbanks typically follow an originate-to-distribute model, so stand to benet from improvements in secondary market liquidity (Gete and Reher (2020)). Additionally, expansion of loan eligibility for GSE guarantees and purchases arguably allowed nonbanks in the post-crisis period to operate with looser underwriting standards than depository institutations and expand market share (Shoemaker 2019). 29 Figure 1.7: Shares of Mortgage Liabilities Outstanding, by Entity, 1997 to 2017 Source: Flow of funds. The amount of other loans,L, is based on asset shares in the bank's balance sheet. L is meant to represent other assets not captured by mortgages, M B , and cash,F , in the model. Empirically, other assets comprise of total assets less loans backed by real estate and cash. Figure 1.8 presents the composition of banks' assets by category, as a share of total assets, excluding Fed funds purchased and repurchase agreements. The teal line, cash and due from depository institutions, grows quickly beginning from the rst quarter of 2009. Loans backed by real estate rise over the early-2000s and then gradually decline starting in 2006. The share of other assets, shown in red, is comparably more stable around 55 to 60 percent of total assets. To mimick the evolution of other assets, I choose the value ofL to constitute 57 percent of total assets pre-crisis and 59 percent of total assets post-crisis (where total assets equalsF +M B +L). The resulting inputs are $152,000 for pre-crisis and $190,000 for post-crisis. I derive the interest rate on other loans,r L , using a weighted average calculation. Given the cash to total assets ratio, loans backed by real estate as a share of total assets, and average 30 Figure 1.8: Bank Asset Composition in Shares, 1997 to 2017 Source: FDIC Quarterly Banking Prole. yield on earning assets from the FDIC QBP, I can extract the interest rate on other loans by making two assumptions. The rst assumption is that the average interest rate banks earn on loans backed by real estate is the 30-year xed rate mortgage rate. The second assumption is that banks, on average, receive the Fed funds rate on cash. Figures 1.9 and 1.10 display interest rates on cash and loans backed by real estate, collected from 10-K's and earnings reports of the largest US bank holding companies (BHCs), whose bank subsidiaries constitute roughly half the banking sector's assets. 31 The black lines in Figures 1.9 and 1.10 are the Fed funds rate and 30-year xed rate mortgage rate, respectively. In both graphs, individual BHC colored lines straddle the black line fairly consistently, suggesting my assumptions about average returns on cash and loans backed by real estate are reasonable. 31 BHCs operate in many sectors outside of traditional banking, but their bank subsidiaries tend to be the largest sources of interest rate revenue, so data from BHCs serves as a close approximation for bank interest rates. 31 Figure 1.9: Interest Rate on Cash, by BHC, 2000 to 2017 Source: FDIC Quarterly Banking Prole, FRED, BHC 10-K's and Earnings Reports I obtain interest rate on other loans by solving for r L in the following equation average yield on earning assets = cash total assets r Fed funds + other loans total assets r L + loans backed by real estate total assets r 30 year xed-rate mortgage Time series forr L , and other interest rate components of the weighted average equation are plotted in Figure 1.11 at an annual frequency. The average for r L is 0.067 pre-crisis and 0.045 post-crisis. To implement the calibration, I rst solve for parameters of the model that match data moments for the post-crisis period, 2009 to 2016. In addition to the full set of choice variables for the household and bank, market clearing prices and interest rates, I also solve for regulatory factors. Regulatory parameters include perceived costs of the capital requirement, , the cost of the liquidity requirement, , and the out ow rate of deposits during a stress 32 Figure 1.10: Interest Rate on Loans Backed by Real Estate, By BHC, 2000 to 2017 Source: FDIC Quarterly Banking Prole, FRED, BHC 10-K's and Earnings Reports scenario, . After I obtain the solution for the post-crisis period, I then solve for model parameters in the pre-crisis period. Assuming perceived costs of noncompliance with liquidity rules is the same in both periods, I use for the post-crisis period, 0.749, as the value for in the pre-crisis period to solve for the required liquidity coverage ratio, . 1.4.3 Results Table 1.3 summarizes the model parameters obtained from the calibration exercise. Comparing the values for the pre-crisis, on the left-hand side, with values for the post-crisis period, on the right-hand side, I can describe bank behavior that is consistent with the empirical targets. Regulatory changes, macroeonomic movements in prices, and associated adjustments in bank or household balance sheets will be discussed in turn. 33 Figure 1.11: Returns on Bank Assets, by Type, 1997 to 2017 Source: FDIC Quarterly Banking Prole, FRED, author's own calculations Table 1.3: Model Calibration Results Pre-crisis (2000-2007) Post-crisis (2009-2016) Parameter Key Ratios Parameter Key Ratios 0.67 LCR 0.83 1.00 LCR 1.11 ' 0.04 Tier 1 0.10 ' 0.06 Tier 1 0.13 0.34 P 109 0.33 P 121 0.18 r s 0.02 0.30 r s 0.00 leverage 9.74 leverage 8.63 F 13,144 cash 0.05 F 33,586 cash 0.10 M B 101,478 mortgage 0.38 M B 99,140 mortgage 0.31 S 239,240 deposit 0.90 S 285,316 deposit 0.88 C 66,982 C 65,144 M H 206,478 M H 247,140 PH 258,097 PH 308,925 34 The rst two rows of Table 1.3 re ect the implementation of the LCR and the increase in Tier 1 RWA ratios after the crisis. The minimum required LCR ratio, , increases from 67 to 100 percent and the stipulated minimum Tier 1 ratio,', rises from 4 percent to 6 percent of risk-weighted assets. The bank's actual LCR rises from 83 percent to 111 percent and Tier 1 ratios move from 10 to 13 percent. To meet the new capital and liquidity requirements, the bank sharply reduces leverage, from 9.74 to 8.63 times equity (see row one in the lower panel). To attain lower levels of leverage, the bank doubles the share of assets allocated to cash and decreases the share of mortgages by roughly seven percent (see rows two and three in the lower panel). Additionally, the bank slightly shrinks deposit funding from 90 to 88 percent of total assets. Because the growth in assets is heavily weighted towards cash,F , the bank is able to expand total assets and deposits, S, even while meeting more stringent regulatory ratios. Turning to macroeconomic factors, house prices, P , rose in the post-crisis period while interest rates on savings,r s , fell precipitously (see rows three and four in the top panel). Two elements in the model are relevant for the housing price. The rst is the value of additional borrowing capacity, 2 , which depends on the dierence between the value of borrowed funds today and the household discount rate ( 1 (1+r m ) h ). The second is preference shocks to demand for housing, . From pre- to post-crisis, the value of borrowed funds today, 1 (1+r m ) , rises from 0.938 to 0.958 while the discount rate, h , remains constant at 0.935 (see Table C.1 for more details). Because the value households gain from borrowing a dollar today grows larger compared to the current value of the dollar they pay back tomorrow, households demand more housing. The post-crisis increase in house demand due to changes in relative borrowing costs account for a large portion of the rise in P. As a result, , remains fairly stable across pre and post-crisis periods. Matching the decline in interest rates, r s , to zero, the utility weight of deposits, , grows by 25 percent as households need to derive greater value from cash holdings in order to supply more deposits to banks despite receiving no return on savings. Consumption, C, falls as households accumulate savings and houses 35 (see row four in the lower panel). Combining the changes in the household portfolio with those of the bank, I can characterize the housing market. With the interest rate paid on deposits, r s , at roughly zero, the bank enjoys a signicant reduction in the cost of funds in the later period. With lower cost of funds, the bank still extends a large amount of mortgages, M B , and coupled with stronger household demand for houses, enables households to borrow more against the value of the house (see M H , total household demand for mortgages, and the value of the house, PH, in the last two rows of Table 1.3). Thus, even though the bank reduces its exposure to mortgages relative to other assets in response to regulatory rules, the lower interest rate environment and stronger housing demand allows households to increase their mortgage borrowing. A more detailed discussion of all the model parameters can be found in the Appendix, as well as the full results. Two potential concerns arise concerning the rise in household savings and larger share of reserves in banks' total assets post-crisis. Given the negative shock from the nancial crisis, the buildup of savings by both households and banks could be largely a byproduct of precautionary savings during the onset of the Great Recession from 2007 to 2009. For bank reserves, the post-crisis results could be heavily in uenced by the policy change on October 1, 2008, when the Federal Reserve began paying interest on required and excess reserves. Using the Fed funds rate as the return on reserves for the analysis across sub-periods could understate the size of changes in bank's remuneration on reserves and incentives to hold reserves. The general results discussed here are robust to excluding crisis years from the data and removing required reserves from the denition of cash. Calibration results taking into account these considerations are also in the Appendix. 1.4.4 Counterfactuals To gauge the relative importance of regulatory changes, interest rate movements, and shifts in household preferences, I perform counterfactual exercises to elucidate the mechanisms 36 behind changes in bank balance sheets since 2009. The starting point of my analysis is the model solution for the pre-crisis period. Using parameter values obtained in the calibration for the pre-crisis period, I solve the model for household and bank choice variables (consumption, savings, mortgages, reserves), taxes, per unit price of housing, and interest rates (for deposits and mortgages). From the solution, I calculate key balance sheet ratios, such as the bank's LCR, capital ratio, leverage, deposits as a share of total assets, cash ratio, reserves to deposits, and the share of mortgages in total assets. I do the same using post-crisis parameter values and obtain a benchmark for comparison. Then, I test four counterfactual scenarios. First, I consider what happens when all post-crisis changes occur except for the interest rate decline. Second, I look at how the post-crisis solution changes if I remove increases in household demand for deposits and houses. Third, I exclude the regulatory changes to stipulated capital ratios and the LCR in the post-crisis period. Lastly, I remove the expansion of government subsidies for mortgages. Table 1.4 presents the results of the counterfactual experiments. In the rst two columns are the benchmark model solutions for the pre- and post-crisis period, which I refer to as actuals. In the next four columns are the solutions for each of the counterfactual exercises. For scenario one, I hold the interest rate on reserves constant at its pre-crisis level while setting all other parameters to their post-crisis values. Comparing the post-crisis values in column two of Table 1.4 with the values in the third column, the model still replicates many of the post-crisis changes. In particular, the model is able to match the interest rate on mortgages, r m , and reproduce elevated regulatory ratios and reserves. The LCR of 1.432 overshoots the actual of 1.105, but the capital ratio is very close to 0.127. Ratios of reserves to total assets, F/(F+M B +L), and reserves to deposits, F/S, are quite high, in the range of 0.14 while acutal post-crisis ratios are closer to 0.10. However, without the change in interest rates, the share of mortgages in total assets, M B /(F+M B +L), declines a bit too much while deposits, S, grow, keeping leverage high. The exercise suggests that a sharp drop in interest rates is necessary to induce the bank to shift assets shares away from reserves 37 towards mortgages to reduce reserve ratios and increase the risk prole of its balance sheet. For the second scenario, I keep parameters for housing preference shock, , and weight of deposits in household utility, , at pre-crisis values (see column four of Table D.1 for details on parameter inputs) so that regulatory and interest rate changes occur without changes in household demand for deposits and houses. As the fourth column of Table 1.4 highlights, the combination of interest rate declines and increase regulation can achieve levels of LCR, capital, equity, savings to total assets, and reserves ratios that move in the same direction as actuals. However, capital ratios are too high and the decline in leverage and mortgage share, M B /(F+M B +L) is too steep andr m doesn't fall. Also, there is muted growth in deposits, S, so deposit interest rates,r s , remain elevated. The second counterfactual points to a need for greater household demand for deposits (since barely changes) to expand the bank balance sheet and counteract the contraction in mortgage lending due to stricter regulation. The third scenario examines how the balance sheet evolves when interest rates fall and household demand increases, but there are no hikes in required regulatory ratios. I estimate the model using all post-crisis parameter values excluding those corresponding to the LCR, , and the Tier 1 capital ratio,', which I keep at pre-crisis values of 0.674 and 0.04 respectively (colored in blue in column ve of Table D.1). Comparing the fth column in Table 1.4 with the second column, regulatory ratios are too low and leverage is too high. Two key balance sheet components also move in the wrong direction. The mortgages, M B , and deposits to total assets, S/(F+M B +L), increase relative to the pre-crisis baseline when they should fall. This emphasizes how heightened regulation forces the bank to reduce deposit liabilities, accumulate reserves, and dampen the growth of mortgages on the balance sheet. In the last scenario, I keep the government supply of mortgages,M G , constant to simulate what bank balance sheets would look like without greater government involvement in the mortgage market post-crisis. Almost all balance sheet ratios obtained without the increased government mortgage subsidy (in the last column of Table 1.4) are within a hundredth of a decimal point of the actuals (in column two). Only leverage and the share of mortgages 38 in total assets are noticeably dierent. Without greater government subsidization, interest rates on mortgages,r m , do not decrease as sharply compared to pre-crisis levels, so the bank has greater incentive to supply mortgages. Indeed, the level of mortgages, M B , obtained in the counterfactual, is 130,552, rising from pre-crisis levels of 101,478 rather than declining to below 100,000 as in actuals. To fund the mortgages, there is accompanying growth in deposits, S. The bank's greater demand for deposits drives interest rates on deposits, r s , up relative to the actual post-crisis rate. Thus, expanded government presence in mortgage markets functions primarily to drive down mortgage rates and reduce bank mortgage supply. Figure 1.12 summarizes the changes in key balance sheet ratios from pre- to post-crisis periods obtained through the counterfactual exercises. For comparison, the actual changes in the data are shown in blue. The orange bar represents results from the counterfactual where interest rates are held constant, the yellow bar is for outcomes without household demand changes, the purple bar is the model without regulatory ratio hikes, and the green bar is without the government mortgage subsidy increase. The left panel illustrates that even in the absence of stricter banking regulation, cash ratios rise in the post-crisis period with changes in interest rates and household demand factors (the purple bar). Comparing outcomes in mortgages to total assets ratios across the counterfactual scenarios (middle panel), the importance of heightened regulation or government supply in dampening mortgage loan growth and the countervailing forces from interest rates and household demand is evident. In terms of leverage ratios, the right panel emphasizes role of regulatory hikes in reducing bank leverage. 1.5 Comparative Statics A comparative statics exercise provides further insights about the importance of dierent factors for the bank's equilibrium choice of reserves, F, deposits, S, and mortgages, M. The exercise also illustrates how regulatory ratios and leverage change as the bank's balance 39 Figure 1.12: Counterfactual Results: Key Ratios Table 1.4: Results of Counterfactual Exercises Actuals Post-crisis Counterfactuals Pre-crisis Post-crisis No interest No HH No reg. No gov. (2000-2007) (2009-2016) rate decline pref. change ratio hikes subsidy rise LCR ratio 0.830 1.105 1.432 1.096 0.780 1.096 Capital Ratio 0.105 0.127 0.126 0.154 0.106 0.129 Equity/TA 0.103 0.116 0.110 0.141 0.100 0.118 Leverage 9.737 8.627 9.059 7.099 9.952 8.445 S/(F+M B +L) 0.897 0.884 0.890 0.859 0.900 0.882 F/(F+M B +L) 0.049 0.104 0.144 0.095 0.068 0.103 F/S 0.055 0.118 0.161 0.111 0.075 0.117 M/(F+M B +L) 0.381 0.307 0.294 0.223 0.332 0.365 r s 0.019 0.002 0.006 0.020 0.002 0.007 r m 0.067 0.044 0.043 0.062 0.042 0.049 C 66,982 65,144 64,857 65,427 65,271 66,105 S 239,240 285,316 300,381 239,476 284,833 315,041 M B 101,478 99,140 99,176 62,175 105,152 130,552 F 13,144 33,586 48,475 26,569 21,499 36,804 T 718 397 2,006 412 374 309 D 4,879 3,883 3,878 943 3,825 3,375 P 109 121 121 103 124 115 40 Table 1.5: Balance Sheet Responses to Regulatory and Macroeconomic Forces Parameter Description Leverage Cash Capital LCR Mortgage ratio ratio ratio share ' Required capital ratio fall fall rise rise fall increase Costs of capital shortfall fall fall rise rise fall increase Required LCR rise rise rise rise fall increase Costs of LCR shortfall rise rise rise rise fall increase r f Interest rate on reserves fall fall rise fall fall decrease 0:28 Deposit demand rise rise fall rise rise increase > 0:28 Deposit demand rise rise rise rise fall increase sheet composition changes. I consider the major changes that occurred over the period before and after the nancial crisis highlighted by the counterfactual exercise: a rise in capital requirements, implementation of the liquidity coverage ratio, a drop in interest rates, and increased demand for deposits. To understand how each change in uences the bank's behavior, I separately vary parameters associated with regulatory costs, interest rates, and household preferences to see how the bank's balance sheet diers from the pre-crisis calibration of the model. 1.5.1 Results The comparative statics exercise conrms the general channels outlined by the counter- factual scenarios and also reveals nuances in the eects of the forces considered in the model. First, increases in all regulatory parameters (', , , ) induce build up of capital and reduction in mortgage shares (see the rst four rows of Table 1.5). However, the eect on the cash ratio and leverage is not as uniform. Tightening required Tier 1 capital ratios (') triggers deleveraging but also reductions in the share of cash in total assets, as the bank 41 raises equity by shrinking the entire balance sheet. On the other hand, as rows three and four illustrate, raising liquidity requirements (through or) leads the bank to bolster cash ratios but also increase leverage by expanding deposit liabilities. Essentially, capital ratios encourage banks to replace deposit funding with equity, while the LCR instills a preference for holding cash assets over mortgages but does not inhibit the bank's ability to leverage. Second, reductions in the interest rate on reserves,r f , are linked to lower cash ratios and a smaller share of mortgages in total assets (see row ve of Table 1.5). With lower interest rates on reserves, the bank reduces the share of assets held in reserves, lowering its capacity to accumulate deposits and risk-weighted assets. Leverage falls, the LCR buer shrinks, and the fall in deposit funding slightly outpaces the shrinkage of assets. Compared to regulatory forces, however, the impact of interest rates on the balance sheet is relatively small. Third, the evolution of mortgage shares in total assets and capital ratios due to a change in household demand for deposits, unlike cases discussed so far, is not monotonic. For values of less than or equal to 0.28, greater demand for deposits is associated with a falling capital ratio and a rise in the share of mortgages in total assets (see row six of Table 1.5). Further increases in beyond 0.28 yield a rising capital ratio and falling mortgage share. From Table 1.3, grows from around 0.18 pre-crisis to 0.30 post-crisis, so greater demand for deposits pushes the bank to increase both mortgage assets and deposit funding. Lastly, by varying parameter values equally in percentage terms, I highlight the relative magnitudes of eects on key balance sheet ratios due to each parameter. Figure 1.13 presents the results of reducing interest rates on reserves, increasing deposits demand, raising required Tier 1, LCR, and government mortgage supply from pre-crisis values by 25 percent in turn. General eects of the parameters mirror those discussed above, but the graphs indicate a striking implication of the model. The eect of greater deposit demand on the cash ratio is noticeably stronger than changes derived from other parameters, only second to regulation (see rst panel). Additionally, deposit demand is the strongest force counteracting the fall in mortgage shares due to greater government supply and stricter LCR requirements. Further 42 Figure 1.13: Comparative Statics Results: Key Ratios analysis of the deposit demand parameter, , in the Appendix, suggests that interaction between deposit demand by households and the bank's desire to maintain a capital buer is crucial in determining key balance sheet ratios. Thus, I conduct an empirical analysis of household demand for deposits in the next section. 1.6 Deposit Demand The model suggests greater deposit demand by households is a key element facilitating the rise in cash on bank balance sheets. Additionally, a bank's desire to maintain a capital buer determines its reaction to stronger deposit demand. More demand for deposits reduces the cost of funds, so the bank expands the share of mortgages in its total assets to capitalize on higher returns and the capital buer begins to erode. If the capital buer drops too quickly, potential regulatory costs skyrocket, forcing the bank to cut lending and accumulate cash. To 43 test the mechanism outlined by the model, I rst document the rise in deposit demand, then provide evidence for a positive relationship between deposits and cash ratios, and illustrate how household demand interacts with capital regulation to shape banks' balance sheets. 1.6.1 A Shift in Demand for Deposits One implication of the calibration results is that households have an increased appetite for deposits in the period following the nancial crisis. Anecdotal evidence suggests greater household demand for deposits may stem from reduced access to credit post-crisis. Historical trends outlined in the 2017 Survey of Consumer Finance (SCF) roughly support such a story. Survey results summarized in Table 1.6 point to a general reduction in real values of mortgage loans, home equity lines of credit, credit card balances, and other residential debt of households from pre- to post-2009. The nancial press likewise paints a picture of banks limiting credit to households around the time of the crisis. 32 Research by Gilchrist and Zakraj sek (2011) show that unused loan commitments were cut immediately at the onset of the crisis in 2007 as banks became concerned about credit risk. Consumer credit panel data from the Federal Reserve Bank of New York in Figure 1.14 illustrate shrinkage of credit card and HELOC limits from 2009:Q1 through at least 2013:Q1 even as credit card balances stayed constant or grew over the same period, corroborating the story described above. An additional explanation for greater demand for deposits is heightened risk perception by households after the crisis. The SCF reports a rise in the mean value of transactional accounts accompanied with heightened importance placed on liquidity needs by households after 2009 (see Table 1.7 and Table 1.8). 33 Bayer et al (2019) document that demand for liquidity increases when uncertainty increases. Households faced greater income risk following the Great Recession, fueling a ight to liquidity assets. 32 A New York Times article published in October 2008 notes how major banks and credit card companies cut inactive accounts, reduced credit limits for consumers across all credit scores, tightened lending standards for cards, and dramatically curtailed marketing of new credit cards upon realizing large consumer loan losses in 2008 and in anticipation of more delinquencies related to the economic downtown (Dash 2008). 33 Transactional accounts include savings, checkings, and money market deposit accounts, money market funds, and call or cash accounts at brokerages and prepaid debit cards. 44 Figure 1.14: Credit Limit and Balance for Credit Cards and HELOC Source: FRB New York Consumer Credit Panel, Quarterly Report on Household Debt & Credit (Aug 2020) In reduced form, incorporates the eects of both the credit access and risk perception channels discussed above. From a modeling perspective, the rise in captures an exogenous shift in household's demand for deposits that is unaccounted for by interest rate movements, house price uctuations, and developments in the mortgage market considered in the model. To quantify the shift in household demand for deposits, I use a conventional money demand framework. Money demand models propose a long run relationship between real money balances, income, and interest rates. A typical money demand equation is described by: (mp) t = 0 + 1 y t + 2 w t + 3 R t + 4 r t + 5 own t + 6 t (1.14) where (mp) t is log real money balances, y t is log real income, w t is log real wealth, R t is a nominal long term interest rate, r t is a nominal short term interest rate, own t is the 45 Table 1.6: Mean value of holdings for families holding debt (thousands of 2016 dollars) Type of debt 2001 2004 2007 2010 2013 2016 Secured by residential property: Mortgages 123.9 155.0 173.1 167.8 161.3 159.5 HELOC 35.3 50.6 45.4 60.3 49.4 49.8 Other residential debt 100.3 212.0 205.3 198.5 160.9 160.6 Lines of credit not secured by real estate 24.4 46.5 28.7 54.3 36.3 55.7 Credit card balances 5.6 6.5 8.5 7.8 5.9 5.7 Education loans 18.5 21.2 24.9 28.3 29.8 34.2 Vehicle loans 15.2 17.2 16.9 15.7 15.0 17.2 Other installment loans 14.7 23.8 17.1 16.4 16.4 15.4 Other 23.9 21.7 17.9 18.5 15.1 26.8 Table 1.7: Mean value of holdings for families holding asset (thousands of 2016 dollars) Type of nancial asset 2001 2004 2007 2010 2013 2016 Transaction accounts 32.1 34.5 30.6 35.8 37.4 40.2 Certicates of deposit 50.7 69.8 64.4 80.3 66.5 75.6 Bonds 394.6 695.7 665.0 679.8 599.8 771.0 Stocks 260.5 203.9 255.7 231.8 303.5 327.8 Pooled investment funds (excluding money market funds) 177.2 234.0 358.5 429.5 477.3 775.9 Retirement accounts 141.9 156.5 170.6 189.2 207.5 228.9 Table 1.8: Reasons respondents gave as most important for their families' saving Reason 2001 2004 2007 2010 2013 2016 Education 10.9 11.6 8.4 8.2 8.6 7.2 For the family 5.1 4.7 5.5 5.7 6.3 6.9 Buying own home 4.2 5.0 4.2 3.2 3.1 4.1 Purchases 9.5 7.7 10.0 11.5 9.1 12.1 Retirement 32.1 34.7 34.0 30.1 30.5 30.3 Liquidity 31.2 30.0 32.0 35.2 35.8 36.2 Investments 1.0 1.5 1.6 1.2 1.4 1.8 No particular reason 1.1 0.7 1.1 1.4 1.2 0.6 When asked for a reason, reported do not save 4.9 4.0 3.3 3.5 4.1 0.8 46 return on money balances, and t is the nominal annualized in ation rate (see Dreger and Wolters (2015) for a discussion of the standard model and variants). Higher real income, y, is associated with higher real money balances, while higher returns on alternative assets, R or r, tend to reduce money demand. Drawing on Nagel (2016), I modify equation (1.14) to instead consider the relative return dierentials between similarly liquid assets over deposits given close substitutability between Treasuries and deposits. Additionally, because houses are an alternative form of savings for households in my model, I use house value as a measure of wealth rather than a broader measure of nancial wealth. The basic deposit demand relationship I want to estimate is (mp) t = 0 + 1 y t + 2 real house wealth t + 3 (R t own t ) + 4 (r t own t ) + 5 t (1.15) where (mp) t is log real deposits. Data Because the demand for deposits is aected by income and wealth, variation along these two dimensions should be accounted for when estimating the long term relationship outlined by equation (1.15). In the absence of individual level data that allows me to control for individual-specic characteristics, I use county level data and assume that household wealth and income diers primarily based on the county of residence. Deposit data comes from the FDIC Summary of Deposits (SOD), which contains information on US branch level deposits for all FDIC institutions at an annual frequency from 1998 to 2016. Data are aggregated to the county level by adding together deposits for each bank in a given county. Table 1.9 provides a comparison of coverage between the SOD used here and the FDIC QBP used in the calibration of the model. 960 non-US branches were dropped. The resulting level of SOD deposits used in the panel regression contains information on 47 roughly 80 percent of all deposits at FDIC-insured institutions. 34 Measures of income and house wealth are from the BEA and Zillow. Log real income, y it , is the natural log of county level nominal gross domestic product (GDP) less the natural log of the GDP de ator calculated from the BEA's county and metropolitan area statistical tables, which begin from 2001. Real house wealth, w it , is the natural log of median home value in a county measured by Zillow's home value index for all homes less the natural log of the GDP de ator. Interest rate data is from RateWatch and FRED. For each year, own it is the average interest rate paid on deposits in county i, with all branches taking equal weight in the calculation. Ratewatch county-level interest rate data are from 1998 to 2015. The long term interest rate,R t , is the Treasury 10-year constant maturity yield and the short term interest rate, r t , is the eective Fed funds rate downloaded from FRED. In ation, it , is measured by the growth rate of the county-level GDP de ator from the BEA's county and metropolitan area statistical tables. Table 1.10 summarizes the variables used in the analysis. The resulting panel contains 37,263 total county-quarter observations for deposits. Raw SOD data at the branch level from 1998 to 2015 contains roughly 1.6 million observations. Merging in RateWatch data, which is missing interest rates for a number of counties across all years, reduces the number of observations by 96,181 and total deposits of 3,920 billion. On average, deposits are reduced by around 215 billion each year relative to the original SOD data. After merging in Zillow home values and BEA county level statistics, I aggregate the branch level data to the county level and arrive at a total of 44,794 observations. Since Arellano-Bond requires at least 3 years of data, I drop counties that have less than 3 years of data for the full set of deposits, real income, house wealth, in ation, and interest dierential variables. This reduces the total 34 The main reason for this dierence is because total deposits taken from FDIC QBP includes foreign (non-US) oce deposits, while SOD considers domestic (US) oce deposits, including insured US branches of foreign banks. Additionally, during the cleaning process, counties for which there was no RateWatch data were dropped and counties with less than 3 years of data for RHS variables in equation (1.15) were removed (see discussion in the last paragraph). For comparison, in 2015, total deposits in the raw SOD data is 10,629 billion, which is fairly close to FDIC QBP second quarter domestic oce deposits of 10,589 billion. 48 Table 1.9: Deposits Coverage in Panel Data (SOD) versus FDIC QBS Panel total branch deposits FDIC total deposits Panel coverage (billions USD) (% of FDIC total) 2000 3,670 4,690 78 2001 4,030 5,020 80 2002 4,300 5,254 82 2003 4,800 5,850 82 2004 5,120 6,290 81 2005 5,560 6,821 82 2006 6,070 7,505 81 2007 6,310 8,036 79 2008 6,630 8,573 77 2009 7,160 9,021 79 2010 7,320 9,141 80 2011 7,860 9,766 80 2012 8,530 10,323 83 2013 9,040 10,781 84 2014 9,700 11,490 84 2015 10,200 11,932 85 observations by 7,531 and an average of roughly 150 billion deposits per year, for a total reduction in deposits of 2,779 billion. Empirical Approach The deposit demand relationship I want to estimate at the county level is (mp) it = 0 D post-2008 + 1 (mp) it1 + 2 y it + 3 w it + 4 (R t own it )+ 5 (r t own it )+ 6 it + i + it (1.16) I include a lag of real deposits, (mp) t1 , because there is persistence in the time series. D post-2008 is a dummy variable equal to 1 for post-crisis years and 0 otherwise. The coecient of interest is 0 , which should be positive if there is an exogenous shift in deposit demand in the post-crisis period, given the long term relationship between deposits, interest rates, income, and housing wealth. 49 Table 1.10: Summary Statistics for Full Sample Used in Arellano-Bond Estimation Variable Mean Std. Dev. Min Max Observations deposits (million, $) 3,033 17,120 16.183 919,943 37,263 gdp (million, $) 6,426 23,629 30.602 689,496 31,253 real gdp (million, $) 6,914 24,990 40.065 653,885 31,253 ln(real deposits) 8.95 1.37 5.10 15.94 31,253 ln(real income) 14.33 1.48 10.60 20.30 31,253 ln(real house wealth) 7.16 0.52 5.33 9.23 25,707 in ation (%) 2.30 3.70 -54.76 52.02 29,190 fed funds -return on deposits (%) 0.09 0.78 -3.34 4.09 37,263 tres10 -return on deposits (%) 1.75 0.77 -0.83 3.92 37,263 return on deposits (%) 2.14 1.69 0.01 6.59 37,263 Note: Counties with extreme levels of in ation include counties like those in Texas (De Witt, Dimmit, Karnes, Martin, Reagan) and Doddridge, WV for 2015 and Brooks, TX for 2003, which are fairly small counties with large contributions from oil and gas extraction to GDP. Because we have a short panel with a maximum time period of 15 years, the county-level xed eect will be imprecisely measured using OLS. If a xed eects model is used, the disturbance term i + it will be correlated with the lagged value of real deposit demand, (mp) it1 , leading to biased estimates of the county xed eect (see Arellano Bond (1991)). Instead, an Arellano-Bond estimator is more appropriate. The Arellano-Bond approach estimates equation (1.16) in rst dierences using GMM and instruments for terms that may be correlated with the disturbances: (mp) it = 0 + 1 (mp) it1 + 2 y it + 3 w it + 4 (R t own it ) + 5 (r t own it ) + 6 it + it (1.17) Results To establish some reasonable bounds for the coecient estimates of our model, I rst run OLS and a xed eects estimation of equation (1.16), with a time trend, year xed eects, and robust standard errors clustered by county for both approaches. 35 Generally, the OLS estimate of (mp) it1 is likely to be biased upwards, while the xed eects estimate tends 35 One lag of each RHS variable is included as control variables. 50 to be biased downward, so from Table 1.11, we have an upper bound of 0.96 and a lower bound of 0.73 for (mp) it1 to compare Arellano Bond estimates against. Of note, the coecient on the post-2008 dummy is around 0.03 (see second row) and is signicant even in the presence of a time trend (year in the last row). These initial rough estimates suggest there is a shift in demand for deposits post-2008 and, in analyses to follow, I will focus on whether this result holds. The results of the Arellano-Bond estimation are in Table 1.12. Column 1 is the baseline model estimating equation (1.16) with an additional one lag of each RHS variable and three lags of log real income, y, to control for autocorrelation. Coecients are reported for the level variables and subsequent columns contain results for the baseline model with dierent instruments used in the GMM dierenced equation. For the baseline, I assume that in ation is exogenous while all other explanatory variables are endogenous. To estimate coecients for endogenous RHS variables, the second and later lags of the variable are used as instruments in the dierenced equation. As an example, to estimate the coecient for (R t own it ) in equation (1.17), observations (R t2 +own it2 +) serve as instruments. The third lag and later were used for the fed funds spread because coecient estimates were more within the bounds of values in Table 1.11 compared to using second lags and later. Lags four and onward are used as instruments for y in the dierenced equation because three lags of y are included in the baseline. As a check, the coecient estimate for (mp) it1 of 0.828 in row one column one of Table 1.12 is between 0.960 (for OLS) and 0.733 (xed-eects) estimates in Table 1.11. The coecient for the post-2008 dummy is around 0.04 (second to last row in Table 1.12), slightly outside the bounds we saw in Table 1.11, but not wildly o. Due to the proliferation of instruments, it is important to to check the robustness of results to dierent numbers of instruments used. The total time period for the sample is 15 years, so the maximum lag length is around 13 if we start from the second lag. As we move to the left from column two to column ve in Table 1.12, I reduce the maximum lag length. The number of instruments shrinks from 500 in the baseline to 259 in the last model variant. 51 Movement of coecient estimates across the columns is fairly minimal, except for the last column, where estimates fory,w, and the time trend (year) are noticably dierent. However, in all specications, the coecient attached toD post-2008 is positive and signicant, indicating support for a post-crisis shift in demand for deposits as suggested by the theoretical results in sections 4 and 5. 1.6.2 Greater Deposit Demand and Key Bank Ratios The comparative statics results point to a positive relationship between more demand for deposits from households and higher cash to total asset ratios for banks. To characterize the relationship between deposit demand and bank cash ratios, I look at the relationship between changes in the ratios of deposits and cash to total assets on bank balance sheets. The results here are purely suggestive, as changes in deposit ratios may not be a good proxy for changes in demand for deposits and all variables in the regressions are endogenous. Data For the analysis, I use FR Y-9C, Call Report data consolidated at the level of the bank holding company (BHC). The data are quarterly and span years 2000 to 2018, with a total of around 89,000 observations. Cash is total cash and due from depository institutions, Schedule HC, line 1 (the sum of BHCK0081, BHCK0395, and BHCK0397). Deposits correspond to Schedule HC, line 13, the sum of BHDM6636, BHDM6631, BHDM6636, and BHDM6631. Mortgages are loans backed by real estate from Schedule HC-C, line 1 (BHCK1410). The cash, deposits, and mortgage ratios are just their levels divided by total assets from Schedule HC, line 12(BHCK2170). To calculate capital buers, I consider banks' Tier 1 risk-weighted assets ratio (RWA). The Tier 1 RWA ratio is from Part 1 of Schedule HC-R, line 26, Tier 1 capital (BHCK8274 prior to 2015 and BHCA8274 from 2015 onward) divided by line 46, risk-weighted assets (BHCKA223 prior to 2015 and BHCAA223 from 2015 onward). Buers are equal to the 52 Table 1.11: Naive OLS and Fixed-eects Regressions Dependent variable: (mp) OLS FE (mp) t1 0.960 0.733 (23.32) (16.80) D post2008 0.0289 0.0334 (6.59) (8.07) y 0.131 0.116 (8.11) (7.92) y t1 -0.114 -0.00456 (-7.10) (-0.41) w 0.235 0.213 (17.27) (14.47) w t1 -0.225 -0.125 (-16.81) (-7.76) fedfunds -0.00736 -0.00459 (-5.29) (-3.51) fedfunds t1 0.00819 0.00349 (5.38) (2.23) 10-yr tres. -0.0138 -0.0116 (-11.82) (-10.34) 10-yr tres. t1 0.00139 0.000867 (1.09) (0.75) in ation -0.00783 -0.00734 (-31.91) (-27.39) year -0.00577 -0.00395 (-11.98) (-8.26) N 22,074 22,074 t statistics in parentheses robust standard errors clustered at the county level (2,209 groups) p< 0:05, p< 0:01, p< 0:001 53 Table 1.12: Arellano-Bond Estimation of Deposit Demand (2000-2015) Dependent variable: (mp) Two-step, specic GMM-instruments for lagged RHS vars for fed funds 3+ 3-11 3-9 3-7 3-6 for y 4+ 4-11 4-9 4-7 4-6 other RHS 2+ 2-11 2-9 2-7 2-6 (mp) t1 0.828 0.822 0.810 0.815 0.845 (0.033) (0.035) (0.035) (0.036) (0.035) D post2008 0.044 0.041 0.041 0.041 0.043 (0.006) (0.006) (0.006) (0.005) (0.005) w 0.257 0.258 0.266 0.250 0.291 (0.036) (0.036) (0.037) (0.035) (0.034) 10-yr tres. -0.013 -0.013 -0.013 -0.011 -0.012 (0.002) (0.002) (0.002) (0.002) (0.002) in ation -0.007 -0.007 -0.007 -0.007 -0.007 (0.001) (0.001) (0.001) (0.001) (0.001) fed funds -0.008 -0.009 -0.009 -0.008 -0.007 (0.002) (0.002) (0.002) (0.002) (0.002) y 0.124 0.130 0.119 0.128 0.087 (0.035) (0.040) (0.042) (0.029) (0.047) year -0.0038 -0.0037 -0.0038 -0.0034 -0.0028 (0.0007) (0.0008) (0.0008) (0.0008) (0.0009) Lags of y 3 3 3 3 3 N 18,565 18,565 18,565 18,565 18,565 N instruments 500 454 397 312 259 Windmeijer corrected robust standard errors in parentheses Assumed in ation is exogenous p< 0:05, p< 0:01, p< 0:001 54 Table 1.13: Summary Statistics Variable Obs Mean Std. Dev. Min Max capital buer 74,489 0.0835 0.0414 -0.016 0.293 log(cash) 74,573 0.0176 0.3569 -2.700 2.784 log(mortgages) 72,804 0.0192 0.0586 -3.471 2.160 cash ratio 72,997 0.0003 0.0193 -0.322 0.323 deposits ratio 72,997 0.0001 0.0198 -0.234 0.271 mortgage ratio 74,573 0.0016 0.0197 -0.343 0.384 capital buer 72,929 -0.0001 0.0105 -0.354 0.315 Tier 1 RWA ratio less 0.04 for years up through 2009 and the Tier 1 RWA ratio less 0.06 from 2010. To minimize the in uence of outliers, I winsorize the data at the one percent level based on the cross-sectional distribution of capital buers. Because the analysis is conducted using growth rates, I also conne my analysis to banks with four consecutive quarters of available data. Table 1.13 summarizes the resulting sample and variables considered in the regressions. Empirical Approach and Results I run the following set of panel regressions to examine the link between cash and deposits: cash ratio it = i + 1 deposit ratio it +QTR t + it (1.18) cash ratio = i + 1 deposit ratio + 2 capital buer +QTR t + it (1.19) cash ratio = i + 1 deposit ratio + 2 capital buer + 3 capital buer deposit ratio +QTR t + it (1.20) The baseline, equation (1.18) considers the change in the cash ratio related to changes in the deposit ratio at the BHC level, controlling for BHC xed eects ( i ) and quarter xed eects (QTR t ). I then add in the change in capital buers (equation (1.19)) and interaction term for changes in deposits and buers (equation (1.20)) to gauge how capital 55 Table 1.14: The Relationship between Cash and Deposits Ratio dependent variable: cash ratio variable (18) (18) robust (19) (20) deposit ratio 0.090*** 0.090*** 0.095*** 0.095*** capital buer 0.163*** 0.163*** capital buer deposit ratio -0.174 N 72,997 72,997 65,560 65,560 Bank FE Yes Yes Yes Yes Time FE Yes Yes Yes Yes R 2 0.042 0.042 0.047 0.047 adjusted R 2 0.012 0.041 0.046 0.046 legend * p< 0:05 ** p< 0:01 *** p< 0:001 buers in uence the deposits-cash relationship. Table 1.14 presents the results of the panel regression with bank and time xed eects for equations (1.18) through (1.20). The rst row highlights that the change in banks' cash ratio and the change in the deposit to total assets ratio exhibit a positive relationship. The positive relationship holds even when controlling for changes in the capital buer. In the last row, for equation (1.20), the interaction term is negative, suggesting larger capital buers lead to smaller increases in the cash ratio given increases in deposits. Based on the mechanism outlined by the theoretical model, the size of a bank's capital buer determines whether the bank responds to greater deposit demand by accumulating cash (and reducing mortgages) or by increasing mortgages (and cutting cash) as a share of total assets. To test the channel, I sort banks into quartile and decile buckets based on the size of their capital buer and examine how cash ratios and mortgage ratios of the least and most capitalized banks respond to changes in deposit ratios. Following the setup in Kashyap and Stein (2000), I add four lags of the growth in cash, the contemporaneous capital buer, and lagged capital buer to the equation (1.18). I then sort banks into quartile and decile buckets based on the cross sectional distribution of capital buers in the entire sample. Tables 1.15 and 1.16 summarize the results obtained by estimating banks in the rst and last quartile or decile buckets separately. Comparing the size of the coecient for deposit ratio between the left and right columns of both tables, there 56 is a positive response of changes in cash ratios for banks in the bottom and top of the capital buer distribution. In Table 1.16, the eect on cash ratios is slightly weaker for the top decile bucket compared to the lowest decile bucket. Table 1.17 elaborates on the dierence, with the coecient on the interaction term of (deposit ratio quartile or decile rank) indicating a generally weaker response in the growth rate of cash for banks in higher quartiles versus the lowest quartile (and decile) 36 . The regression results are consistent with the characterization of banks building up less cash in total assets when capital buers are high than when their buers are low. A similar exercise is undertaken to analyze the relationship between capital buers and movements in the mortgage to total assets ratio due to growth in deposit ratios. Tables 1.18 and 1.19 highlight how banks with the smallest buers reduce the share of mortgage loans in total assets, while banks with the largest buers will instead grow the mortgage share. Table 1.20 shows that, just as the theoretical model claims, when deposit ratios climb, banks will accumulate more mortgages when capital buers are high compared to when buers are low. Thus, reduced form associations between deposit growth and changes in cash or mortgage ratios in total assets lend support to the mechanisms laid out by the theoretical analysis. 36 Sorting banks into quartile and decile buckets based on the cross-sectional distribution of capital buers each year (instead of based on the entire sample) produces similar regression results. 57 Table 1.15: Relationship between Cash Ratio and Deposits Ratio: Role of Capital Buers 25 percentile 75 percentile cash ratio t1 -0.386 (0.023) -0.361 (0.024) cash ratio t2 -0.287 (0.021) -0.216 (0.032) cash ratio t3 -0.231 (0.016) -0.147 (0.021) cash ratio t4 -0.007 (0.019) 0.058 (0.020) capital buer 0.113 (0.037) 0.268 (0.035) capital buer t1 -0.183 (0.032) -0.260 (0.034) deposit ratio 0.086 (0.012) 0.099 (0.015) N 14,864 14,867 Bank FE Yes Yes Time FE Yes Yes R 2 0.21 0.20 adj. R 2 0.20 0.20 Table 1.16: Relationship between Cash Ratio and Deposits Ratio: Role of Capital Buers (cont.) 10 percentile 90 percentile cash ratio t1 -0.386 (0.031) -0.412 (0.030) cash ratio t2 -0.318 (0.030) -0.229 (0.049) cash ratio t3 -0.269 (0.026) -0.116 (0.032) cash ratio t4 0.006 (0.032) 0.064 + (0.037) capital buer 0.100 (0.066) 0.265 (0.048) capital buer t1 -0.146 (0.051) -0.276 (0.049) deposit ratio 0.107 (0.018) 0.104 (0.027) N 5,772 5,755 Bank FE Yes Yes Time FE Yes Yes R 2 0.24 0.25 adj. R 2 0.23 0.24 Cluster-robust standard errors in parentheses + p< 0:10, p< 0:05 58 Table 1.17: Relationship between Cash Ratio and Deposits Ratio: Interacting Capital Buers with Deposits Base: 25 percentile Base: 10th percentile cash ratio t1 -0.355 (0.013) -0.355 (0.013) cash ratio t2 -0.216 (0.014) -0.216 (0.014) cash ratio t3 -0.153 (0.010) -0.153 (0.010) cash ratio t4 0.050 (0.011) 0.050 (0.011) capital buer 0.202 (0.018) 0.203 (0.018) capital buer t1 -0.216 (0.018) -0.217 (0.018) deposit ratio 0.098 (0.011) 0.125 (0.017) deposit ratio quartile 2 -0.028 (0.013) deposit ratio quartile 3 -0.016 (0.015) deposit ratio top quartile 0.003 (0.018) deposit ratio decile 2 -0.037 + (0.021) deposit ratio decile 3 -0.039 + (0.023) deposit ratio decile 4 -0.070 (0.021) deposit ratio decile 5 -0.061 (0.021) deposit ratio decile 6 -0.051 (0.022) deposit ratio decile 7 -0.028 (0.022) deposit ratio decile 8 -0.045 + (0.027) deposit ratio decile 9 -0.029 (0.026) deposit ratio top decile -0.016 (0.030) N 60,733 60,733 Bank FE Yes Yes Time FE Yes Yes R 2 0.18 0.18 adj. R 2 0.18 0.18 Cluster-robust standard errors in parentheses + p< 0:10, p< 0:05 59 Table 1.18: Relationship between Mortgage ratio and Deposits Ratio: Role of Capital Buers 25 percentile 75 percentile mortgage ratio t1 -0.132 (0.019) -0.063 (0.014) mortgage ratio t2 -0.077 (0.013) -0.039 (0.014) mortgage ratio t3 -0.073 (0.015) -0.044 (0.013) mortgage ratio t4 0.053 (0.015) 0.099 (0.018) capital buer -0.145 (0.044) -0.207 (0.022) capital buer t1 0.185 (0.040) 0.199 (0.022) deposit ratio -0.051 (0.015) 0.037 (0.024) N 15,210 15,094 Bank FE Yes Yes Time FE Yes Yes R 2 0.07 0.07 adj. R 2 0.06 0.07 Table 1.19: Relationship between Mortgage Ratio and Deposits Ratio: Role of Capital Buers (cont.) 10 percentile 90 percentile mortgage ratio t1 -0.186 (0.032) -0.087 (0.024) mortgage ratio t2 -0.118 (0.019) -0.027 (0.018) mortgage ratio t3 -0.119 (0.028) -0.030 (0.019) mortgage ratio t4 0.063 (0.025) 0.112 (0.022) capital buer -0.145 + (0.076) -0.193 (0.028) capital buer t1 0.159 (0.065) 0.187 (0.028) deposit ratio -0.062 (0.019) 0.043 (0.028) N 5,917 5,827 Bank FE Yes Yes Time FE Yes Yes R 2 0.10 0.10 adj. R 2 0.09 0.09 Cluster-robust standard errors in parentheses + p< 0:10, p< 0:05 60 Table 1.20: Relationship between Mortgages Ratio on Deposits Ratio with Interaction Terms Base: 25 percentile Base: 10th percentile mortgage ratio t1 -0.075 (0.004) -0.075 (0.004) mortgage ratio t2 -0.035 (0.004) -0.035 (0.004) mortgage ratio t3 -0.034 (0.004) -0.034 (0.004) mortgage ratio t4 0.084 (0.004) 0.084 (0.004) capital buer -0.224 (0.009) -0.223 (0.009) capital buer t1 0.216 (0.009) 0.215 (0.009) deposit ratio -0.054 (0.007) -0.046 (0.012) deposit ratio quartile 2 0.034 (0.011) deposit ratio quartile 3 0.047 (0.011) deposit ratio top quartile 0.091 (0.011) deposit ratio decile 2 -0.040 (0.016) deposit ratio decile 3 0.021 (0.017) deposit ratio decile 4 0.013 (0.017) deposit ratio decile 5 0.057 (0.017) deposit ratio decile 6 0.035 (0.017) deposit ratio decile 7 0.051 (0.017) deposit ratio decile 8 0.048 (0.018) deposit ratio decile 9 0.081 (0.018) deposit ratio top decile 0.091 (0.018) N 62,085 62,085 Bank FE Yes Yes Time FE Yes Yes R 2 0.06 0.06 adj. R 2 0.03 0.03 Cluster-robust standard errors in parentheses + p< 0:10, p< 0:05 61 1.7 Conclusion Using a general equilibrium model where a bank makes balance sheet decisions subject to regulatory constraints and household choices, I illustrate how monetary policy combines with changes in household demand and stricter regulation to explain the post-crisis composition of bank assets. Falling interest rates on reserves induce the bank to reduce the share of liquid assets on its balance sheets and dampens the bank's demand for deposits. Higher capital and liquidity requirements also reduce the bank's appetite for accumulating deposit liabilities, but push the bank in the opposite direction for assets, stimulating its demand for reserves at the expense of mortgages. Growth in household demand for savings, meanwhile, stymie the sharp contractions in mortgage lending stemming from stricter bank regulation. Together, these four forces cause bank leverage to atline and cash ratios to continue their precipitous climb in the post-crisis period. Moreover, the model implies that monetary policy, capital rules, and the LCR work through dierent channels. Capital rules mainly constrain expansion of the balance sheet by restricting growth of deposit liabilities. The LCR prompts banks to reshue their assets towards greater cash holdings. Larger cash holdings should decrease the risk prole of the bank, however, compliance with the LCR does not preclude increases in leverage. Monetary policy functions mainly by changing the bank's willingness to amass reserves. Looser policy tends to counteract stronger bank regulation, while tighter policy complements the goals of stricter bank rules. Comparative statics exercises emphasize the importance of rising household demand for deposits for post-crisis changes in bank balance sheets. The model suggests growth in household demand for deposits interacts with the banks' incentives to maintain capital buers to allow the balance sheet to expand even as leverage falls. Reduced form regressions suggest a positive link between household deposit demand and larger shares of cash in bank's total assets, providing support for the model's nding that stricter regulation is not the sole driver of the rise in cash holdings post-crisis. 62 Because the empirical analysis of mechanisms outlined by the model are not causal, the conclusions that can be drawn from the regression results are tentative at best. Exploiting the cross-sectional variation of banks' exposure to deposit shocks and heterogeneity in capital buers to illustrate how changes in household demand interact with capital regulation to shape banks' balance sheets would be the aim of future work. 63 Chapter 2 Quantitative Easing and Bank Regulations 2.1 Introduction As Figure 2.1 highlights, from 2009 to 2017, the Federal Reserve roughly tripled its balanced sheet through purchases of securities as part of quantitative easing (QE). What was the eect of quantitative easing on bank and household-nonnancial rm balance sheets and interest rates? How do regulations interact with QE to modify responses to the Fed's actions? Two theoretical channels are discussed by models of unconventional monetary policy to explain how large scale asset purchases (LSAPs) aect asset prices and the macroeconomy. The rst is the signaling channel, whereby the central bank uses forward guidance and LSAPs to modify expectations about the path of future short-term rates. Portfolio rebalancing is the second channel, which broadly aects risk factors, like duration, liquidity, and safety premiums linked to the term premium of dierent assets. 1 Typically, models of the portfolio rebalancing channel use preferred habitat preferences or nancial frictions to explain how LSAPs move asset prices by changing the relative supply and demand of dierent assets. Financial regulations function through the same channel. Capital and liquidity rules impose on banks a ranking of assets based on risk weights and eligibiity criteria for treatment as high quality liquid instruments. By explicitly assigning values to dierent assets, regulation modies the preferred habit preferences of banks and distorts the demand for certain desireable assets. Inability to substitute freely between assets of dierent regulatory grades places constraints on banks that pass through to asset prices. 1 See Bhattarai and Neely (2016) for a detailed discussion of the components of the term premium and Papadamou et al (2020) for an overview of the empirical literature documenting the eects of US QE. 64 Figure 2.1: Federal Reserve Bank Assets Source: Federal Reserve Statistical Release H.4.1 In the current low interest rate environment, QE is the main tool used by central banks to adjust economic activity. If QE relies on the portfolio rebalancing channel to shape long term rates, then it is important to evaluate how regulation in uences this channel to better calibrate policy. Building on the framework developed in Chapter 1, I analyze the eects of QE on bank and household-rm sector balance sheets to understand how the portfolio rebalance channel works in the presence of bank capital and liquidity regulations. I expand the set of assets held by household-rm and bank sectors to include bonds, in addition to houses and reserves. Unconventional monetary policy enters the model in the form of bond purchases by the central bank, separate from its ability to set the interest rate on reserves. Interest rate dierentials play a key role in the analysis. The rate spread between bonds and reserves captures a liquidity premium associated with LCR regulation that aects banks. The dierence between the interest rate on bonds and deposits measures a liquidity premium 65 on the part of the household-rm but also includes a high quality asset premium coming from bank liquidity regulation. Interest rates on mortgages versus reserves measure default risk, with an added regulatory tax from capital and LCR concerns. Changes in household-rm preferences and bank demand for dierent assets will drive the relative rate spreads, with nancial regulations aecting mainly banks and QE aecting the portfolio choices of both sectors. Quantitative easing took place in three phases. QE1 began in 2008q4 and ended in 2010q1. QE2 spanned 2010q2 to 2011q2. QE3 started in 2012q3 and purchases were wound down in 2014q4. To measure the in uence of QE on bank and household-rm choices, I calibrate model parameters to key bank and household-rm balance sheet ratios and interest rates at the end of each round of QE (2010q1, 2011q2, and 2014q4). Calibration to the three end dates provides a benchmark and changes in model parameters illustrate what portfolio changes occurred between the dates. To assess the eect of QE, I run a counterfactual exercise. First, beginning from the model calibration in 2011q2, I increases the central bank's holdings of government bonds to the cumulative scale of bond purchases that occurred under QE3. Comparing the outcomes in interest rate dierentials and bank or household-rm ratios, I quantify the eect of QE3. To understand how QE3 interacts with regulatory factors and household-rm preferences, I run a second group of scenarios where I pair QE3 with parameter sets linked to stronger capital requirements, liquidity regulation, and household-rm demand for housing and liquidity. The counterfactual results emphasize that stricter liquidity regulation limits the ability of QE to encourage banks to divert assets away from government bonds and towards riskier investments, like mortgage loans. Additionally, liquidity preferences of household-rms that tilt towards greater deposit holdings amplify the changes in interest rate spreads created by QE. The model suggests that bank regulation and uctuations in liquidity demanded by the household-rm sector have the potential to greatly enhance or even unravel the eectiveness of the portfolio rebalancing channel of QE. 66 The structure of the chapter is as follows. Section 2 describes the model. Section 3 presents a calibration of the model using balance sheet data of the aggregated bank sector, liquid asset holdings of the household-nonnancial rm sector, and information on central bank assets. Section 4 covers counterfactual exercises that quantify the eect of QE3 in isolation and in unison with developments in bank regulation and household-rm preferences. Section 5 concludes. 2.2 The Model Mirroring the setup in Chapter 1, there is a bank sector and a combined government central bank. Dierent from Chapter 1, the third sector in the economy fuses the household with nonnancial rms to capture a broader portion of the economy that directly interacts with banks. First, I describe the household-rm sector and the bank sector along with the regulatory rules considered in the model. Second, I introduce the role of the government central bank. Given the similarities with the theoretical framework in Chapter 1, I focus on elements that are new in the model and only brie y discuss aspects that are unchanged from Chapter 1. 2.2.1 Household-Nonnancial Firm An innitely lived representative household-nonnancial rm receives utility from consumption, C t , housing, H t , deposits, S t , and government bonds, B t : log(C t ) + t log(H t ) + t log(S t ) + t log(B t Deposits and bonds enter the utility function to capture liquidity preferences of household-rm, with a dierent weight, t , given to bonds because bonds must rst be sold before they can be used to purchase goods and services. Deposits, S t , earn interest rate r s t , and bonds, B t , provide interest of r b t . Since bonds are less liquid than deposits the household-rm must be 67 Table 2.1: Household-Nonnancial Firm Balance Sheet Assets Liabilities Deposits (S t ) Mortgage (M t ) Gov. Bonds (B t ) Other Loans (L t ) House (H t ) compensated more in terms of return, so r b t is larger than r s t . The household-rm's assets consist of deposits at the bank, holdings of government bonds, and the house it owns. In terms of liabilities, the household-rm has a mortgage it uses to extract liquidity from its house, and other loans from the bank. 2 Table 2.1 summarizes the balance sheet of the household-rm sector. Budget Constraint The household-rm's budget constraint is W t +D t + M t+1 (1 +r m t ) + L t+1 (1 +r l t ) +S t +B t = C t +T t + S t+1 (1 +r s t ) + B t+1 (1 +r B t ) +M t +L t +P t (H t+1 H t ) +P t H t (2.1) On the rst line is the household-rm's sources of funds. Income,W t , comes from exogenous wages paid to the household and nonnancial rm prots. D t are dividends from the banking sector. The current value of future borrowing from mortgages and other loans, M t+1 (1+r m t ) + L t+1 (1+r l t ) , supplement current savings, S t , and bond holdings, B t . On the second line is the household-rm's use of funds. Funds are used for consumption, to pay for taxes, invest in deposits or bonds tomorrow, repay mortgage and other loans, and pay housing costs. 2 The setup follows that in Chapter 1, where other loans are exogenous, while mortgages are determined in the general equilibrium. Other loans include non-mortgage, non-cash related assets on bank balance sheets, like commercial and industrial loans, loans to individuals, securities, other loans, Fed funds sold, and reverse repurchase agreements. 68 The Household-Nonnancial Firm's Problem The household-rm's objective is to maximize lifetime utility subject to its budget constraint (equation (2.1)) and borrowing constraint on mortgages (equation (1.2)). Dene the value function U(S t ;H t ;M t ;B t ) = max Ct;S t+1 ;M t+1 ;H t+1 ;B t+1 flog(C t )+ t log(H t )+ t log(S t )+ t log(B t )+ h E t [U(S t+1 ;H t+1 ;M t+1 ;B t+1 )]g: In recursive form, the household solves the Lagrangian L(S t ;H t ;M t ;B t ) =U(S t ;H t ;M t ;B t ) + 1;t W t +D t + M t+1 (1 +r m t ) + L t+1 (1 +r l t ) +S t +B t 1;t C t +T t + S t+1 (1 +r s t ) + B t+1 (1 +r B t ) +M t +L t +P t (H t+1 H t ) +P t H t + 2;t P t+1 H t+1 M t+1 Optimal Choices The household-rm's decisions about how to allocate its savings amongst deposits, housing, and bonds, or how much to save versus borrow in uence the relative prices of dierent assets. Taking the derivative of the Lagrangian with respect to consumption, C t , savings,S t+1 , size of the mortgage, M t+1 , and housing, H t+1 , yields rst-order conditions that relate optimal choices made by the household-rm to interest rates. Deposits. From the household-rm side, the interest rate on deposits is determined by H E t t+1 C t S t+1 + C t C t+1 = 1 (1 +r s t ) (2.2) On the left is the expected marginal utility today from savings tomorrow, H E t t+1 S t+1 + 1 C t+1 , divided by the marginal utility cost today of foregone consumption, 1 Ct . As the marginal 69 benets of deferring consumption to the future through deposits grow, the interest rate on deposits, r s t , falls. Greater liquidity preferences increase utility that the household-rm derives from additional deposits, so rising t+1 reduces the amount of interest needed as compensation . As the household-rm grows more patient ( H gets larger), marginal utility from future consumption is valued more and r s t shrinks as well. Bonds. The relationship for bonds is almost identical to that of deposits. H E t t+1 C t B t+1 + C t C t+1 = 1 (1 +r b t ) (2.3) Equation (2.3) outlines how the interest rate on bonds is driven by the ratio of future marginal utility from bond investment to the marginal utility cost of foregone consumption today. The interest rate on bonds, r b t , likewise, declines in response to stronger liquidity preferences, t+1 , and more patience on the part of the household-rm, represented by the size of H . Housing. The household-rm's choice to buy more housing has a direct eect on the interest rate on mortgages through the value of additional home equity: 2;t P t+1 = P t C t h E t t+1 H t+1 + P t+1 C t+1 (1) (2.4) With an extra unit of housing, the household-rm gains more room to borrow equal to P t+1 , which I refer to as additional home equity. 2;t is the shadow price of additional borrowing, or how much the household-rm values an extra dollar in mortgage loans. 3 Thus, 2;t P t+1 is the value of additional home equity in terms of greater borrowing capacity. Equation (2.4) denes greater borrowing capacity in marginal utility terms, found on the right-hand side. 3 Slackness conditions require that either 2;t > 0 and the household-rm has reached its collateral limit on mortgage borrowing (i.e.,M t+1 = P t+1 H t+1 ), or 2;t = 0 andM t+1 < P t+1 H t+1 . The discussion about additional home equity only pertains only to the rst case, where the household-rm borrows a mortgage up to the collateral limit. 70 For the household-rm to buy another unit of housing, the value of additional home equity must oset the additional utility cost of housing, Pt Ct , minus the expected future marginal utility from housing taking into account maintenance costs ( h E t t+1 H t+1 + P t+1 C t+1 (1) ). For a given house price,P t+1 , as the household-rm values housing more ( t+1 grows), the value of additional borrowing capacity, 2;t , falls. Mortgages. The value of additional mortgage borrowing capacity, 2;t , from the housing decision aects the interest rate on mortgages in the following way: C t 2;t + H E t C t C t+1 = 1 (1 +r m t ) (2.5) The ratio between the marginal utility cost and the marginal utility benet of mortgage borrowing (the left-hand side of equation (2.5)) determines the size of the interest rate on mortgages. Borrowing another dollar in mortgages reduces utility by the value of additional borrowing capacity and the repayment of one unit consumption tomorrow ( 2;t + H E t 1 C t+1 . The household-rm gains marginal utility from more consumption today through its borrowing ( 1 Ct ). If the household-rm values additional borrowing capacity less, marginal utility costs are lower for a given level of marginal benet, and the household-rm is willing to pay more to borrow, which drives r m t up. Interest Rate Dierentials From the household-rm problem, two sets of interest rate dierentials arise. The rst is the relationship between interest on deposits, r s t , and bonds, r b t . Subtracting equation (2.2) from (2.3): C t H E t t+1 B t+1 t+1 S t+1 = 1 (1 +r b t ) 1 1 +r s t Depending on the relative levels of bond or deposit holdings and the strength of liquidity preferences for one asset or the other, the spread betweenr b t andr s t varies in size and sign. If 71 the marginal utility from deposits outweighs the marginal utility from bonds ( t+1 B t+1 < t+1 S t+1 ), then bonds will command a premium over deposits (r b t > r s t ). If marginal utility of bonds is larger ( t+1 B t+1 > t+1 S t+1 ), interest paid on deposits must be greater than interest on bonds (r b t <r s t ). The second relationship is between interest on mortgages,r m t and bonds,r b t . Subtracting equation (2.3) from equation (2.5) yields: C t 2;t H E t t+1 B t+1 = 1 1 +r m t 1 (1 +r b t ) If the value of additional borrowing capacity is greater than the expected marginal utility gained from investing in bonds ( 2;t H E t t+1 B t+1 > 0), there will be a positive spread between mortgages and bond rates (r m t <r b t ). If the household-rm values expected marginal utility from bonds more than additional borrowing capacity ( 2;t H E t t+1 B t+1 < 0), the mortgage rate will be higher than the bond rate (r m t > r b t ). Household-rm demand for housing relative to bonds drives the dierential between the two assets, but the equilibrium rates will also depend on behavior of the bank sector. 2.2.2 Bank A representative bank chooses the composition of its balance sheet to maximize the discounted value of dividends. Table 2.2 summarizes the bank balance sheet. On the assets side are reserves, bonds, mortgages, and other loans. Liabilities consist of deposits from the household-rm. 4 The bank pays r s t + t on deposits, S t . 5 Reserves, F t , earn a gross return 4 To match the asset side of the balance sheet, deposits here include subordinated debt, other borrowed money, and other liabilities. Fed funds purchased and repurchase agreements are not included, as there is no interbank market in the model. In the data, deposits drive most of the change in the non-equity portion of total liabilities (less Fed funds purchases and repurchase agreements) from 2000 to 2018 (see Figure 1.4). Thus, I treat the entirety of non-equity as if they are deposits in the model and only consider the decisions behind changes in deposits in the bank and household's problem. 5 t is the unit cost of intermediation as proposed by Phillipon (2015). Here, the constant per unit cost is like a deadweight loss associated with provision of deposit services that are not paid to the household-nonnancial rm sector. 72 Table 2.2: Bank Balance Sheet Assets Liabilities Reserves (F t ) Deposits (S t ) Bonds (B t ) Mortgage (M b;t ) Other Loans (L t ) of (1 +r f t ) and bonds, B t , earn (1 +r b t ). The gross return on mortgages is z t , equal to (1)(1 +r m t ) + P t H t M t ; where is the average expected idiosyncratic default rate on mortgages, is the recovery rate on the value of a foreclosed home, and M t is the total mortgages demanded by the household-rm. 6 z t is less than (1 +r m t ) and re ects the reduction in return that arises from loan loss reserves the bank must set aside for each dollar invested in mortgages. Other loans, L t , earn interest rate r l t . I assume other loans, L t , are exogenous while mortgages, M b;t , are endogenously determined. Potential Regulatory Costs Uncertainty faced by the bank is captured by compliance risk. The bank is subject to a minimum capital requirement, ' t , measured by the ratio of equity to risk-weighted assets and a minimum liquidity coverage ratio (LCR), t , equal to the amount of liquid assets covering liability out ows. Equity to risk-weighted assets is dened as F t+1 +M b;t+1 +B t+1 +L t+1 S t+1 ! m;t M b;t+1 +! l;t L t+1 ; (2.6) 6 I don't explicitly modeling the strategic default choice of the household and instead use to capture the costs of default in reduced form. can be interpreted as a price wedge that causes banks to charge higher interest rates for mortgage provision. 73 where! m;t and! l;t are the risk weights assigned to mortgages and other loans, respectively. The LCR is calculated as F t+1 + t B t+1 t S t+1 + t M b;t+1 (2.7) Mortgages, M b;t+1 , and deposits, S t+1 , in the denominator, contribute to out ows that the bank must cover with reserves, F t+1 , or bonds, B t+1 . t is the fraction of deposits that ow out of the bank during a stress event, while t is the drawdown on committed credit lines related to mortgage loans (expressed as a fraction of total mortgages). Because banks must rst sell bonds to turn them into cash, bonds enter into the LCR at a discount of t < 1 and are less useful than reserves for meeting the liquidity requirement. t distinguishes bonds from reserves and allows for dierential pricing of the two assets. Falling below minimum ratios triggers regulatory intervention that impacts dividends, so the risk lies in whether the bank can satisfy the required ratio. The farther away the bank's actual ratios are from the minimum, the lower is the expected cost. Potential regulatory costs associated with the capital requirement are: 8 > > < > > : F t+1 +M b;t+1 +B t+1 +L t+1 S t+1 !m;tM b;t+1 +! l;t L t+1 ' t 2 ; if F t+1 +M b;t+1 +B t+1 +L t+1 S t+1 !m;tM b;t+1 +! l;t L t+1 >' t 1; otherwise The potential regulatory costs associated with the LCR are: 8 > > < > > : F t+1 +tB t+1 tS t+1 +tM b;t+1 t 2 ; if F t+1 +tB t+1 tS t+1 +tM b;t+1 > t 1; otherwise (2.8) 74 Budget Constraint The bank's budget constraint is M b;t +L t +F t +B t + S t+1 (1 +r s t + t ) =S t +D t + M b;t+1 (z t ) + L t+1 (1 +r l t ) + F t+1 (1 +r f t ) + B t+1 (1 +r b t ) + F t+1 +M b;t+1 +B t+1 +L t+1 S t+1 ! m;t M b;t+1 +! l;t L t+1 ' t 2 | {z } Capital Requirement Costs + F t+1 + t B t+1 t S t+1 + t M b;t+1 t 2 | {z } Liquidity Requirement Costs (2.9) On the left-hand side are the bank's sources of funds from current assets (M b;t +L t +F t +B t ) and deposit borrowing. Funds are used to repay current deposits, S t , and dividends, D t , to invest in mortgages, loans, reserves, and bonds, and pay regulatory costs. The Bank's Problem The bank's objective is to maximize the discounted present value of dividends,D t , subject to its budget constraint. The problem of the bank in recursive form is V (z t ;P t ;S t ;M b;t ;F t ;B t ) max S t+1 ;M b;t+1 ;F t+1 ;B t+1 fD t + b E t V (z t+1 ;P t+1 ;S t+1 ;M b;t+1 ;F t+1 ;B t+1 )g s.t. (2:9) Optimal Choices The bank's demand for deposit funding and allocation of investment amongst mortgages, reserves, and bonds interact with the choices of the household-rm to determine the relative prices of dierent assets. Derivatives of the objective function with respect to deposits, mortgages, reserves, and bonds lay out the relationships between interest rates and prot seeking behavior versus regulatory considerations faced by the bank. Deposits. Funding from household-rm deposits creates interest expense for the bank. The price of deposits is driven by two concerns: required return on equity and regulatory 75 costs (the left-hand side of equation (2.10)). b + 2 t ( t S t+1 + t M b;t+1 )(F t+1 + t B t+1 ) (F t+1 + t B t+1 t t M b;t+1 t t S t+1 ) 3 + 2 (! m;t M b;t+1 +! l;t L t+1 ) 2 (F t+1 +B t+1 + (1' t ! m;t )M b;t+1 + (1' t ! l;t )L t+1 S t+1 ) 3 = 1 (1 +r s t + t ) (2.10) Required return is captured by the bank's discount factor, b , which equals the inverse of one plus the return on equity. The more impatient investors are, the higher the bank's cost of equity capital are, since investors would require higher return on their investment. To meet the higher return on investment (smaller b ), the bank increases leverage by borrowing more today, so it is willing to pay greater interest on deposits, r s t . Costs imposed by liquidity and capital regulation are the second and third terms of the left-hand side of equation (2.10). A detailed discussion of marginal regulatory costs with respect to deposits is in Appendix B.1, so I only summarize the main ideas here. Additional deposits add to dollar out ow the bank must cover using high quality liquid assets (reserves, F t+1 , or bonds,B t+1 ). Reserve and bonds provide less return than mortgages or other loans, so diverting investment to high quality liquid assets (HQLA) reduce bank revenues. The higher is the out ow rate placed on deposits by regulators, represented by t , and the larger the buer required (), the greater the amount of HQLA the bank must raise per unit of additional deposits. The bank is then unwilling to accumulate more deposits and the interest rate, r s t falls. The logic is the same for capital costs, with lower interest rates on deposits associated with a heavier burden of capital requirements, measured by the size of . Intermediation costs, t on the right-hand side of equation (2.10), eat away at the banks' interest margin. Intermediation costs are indirectly passed on to the household-rm in the form of lower interest paid on deposits, r s t . Mortgages. Provision of mortgages generates interest income but tightens the bank's regulatory constraints. When choosing the optimal allocation of mortgage loans, the bank 76 equates the two opposing factors, as in equation (2.11). b 2 t ( t S t+1 + t M b;t+1 )(F t+1 + t B t+1 ) (F t+1 + t B t+1 t t M b;t+1 t t S t+1 ) 3 2 (! m;t M b;t+1 +! l;t L t+1 )[! m;t (F t+1 +B t+1 +L t+1 S t+1 )! l;t L t+1 ] (F t+1 +B t+1 + (1' t ! m;t )M b;t+1 + (1' t ! l;t )L t+1 S t+1 ) 3 = 1 h (1)(1 +r m t ) + PtHt Mt i (2.11) On the left-hand side are marginal costs from required return on equity ( b ), liquidity regulation, and capital regulation. In the second term, t is the out ow rate on mortgages arising from drawdowns of unused committed credit lines. When increasing mortgages by one unit, out ows ( t S t+1 + t M b;t+1 ) rise, and the bank must raise HQLA equal to t (F t+1 + t B t+1 ), which increases the LCR by t(F t+1 +tB t+1 ) (tS t+1 +tM b;t+1 ) 2 . Scaling the change in the bank's LCR ratio by the marginal change in regulatory costs from LCR changes, F t+1 +tB t+1 tS t+1 +tM b;t+1 t 3 , provides the increase in regulatory costs from an additional unit of mortgages. As the out ow rate on mortgages, t , rises, or the required LCR buer, , increases, the interest rate on mortgages, r m t , grows because the bank requires greater compensation to cover liquidity costs. The third term on the left-hand side of equation (2.11) is the marginal change in capital costs from additional mortgage investment. Mortgages cause risk-weighted assets,! m;t M b;t+1 + ! l;t L t+1 , to rise. At the same time, the bank must raise equity equal to ! m;t (F t+1 +M b;t+1 + B t+1 +L t+1 S t+1 ) to oset the rise in risk-weighted assets. This yields a net increase in capital coverage of (! m;t (F t+1 +M b;t+1 +B t+1 +L t+1 S t+1 ))! m;t M b;t+1 ! l;t L t+1 , which equals [! m;t (F t+1 +B t+1 +L t+1 S t+1 )! l;t L t+1 ]. If the necessary growth in bank equity is larger than the rise in risk-weighted assets triggered by additional mortgage investment ([! m;t (F t+1 +B t+1 +L t+1 S t+1 )! l;t L t+1 ]> 0), mortgages eat into bank equity and increase capital costs. The return on mortgages, r m t , would need to be higher given the associated capital costs. Conversely, if risk-weighted assets rise faster than amount of equity to be raised per additional mortgage ([! m;t (F t+1 +B t+1 +L t+1 S t+1 )! l;t L t+1 ]< 0), mortgages 77 reduce capital costs and the bank would require a lower interest rate on mortgages. On the right-hand side of equation (2.11), the return on mortgages depends on . Given that households do not default on mortgages in equilibrium, , measures the additional interest banks charge households due to loan loss provisioning rules requiring banks to set aside reserves per dollar of mortgage loans based on average expected (historical) default rates. Loan loss reserves are a contra-asset that reduces the value of mortgage loans and bank earnings. As expected default rates,, rise, gross return (1)(1 +r m t ) + PtHt Mt falls, and banks raise r m t to meet the required return dened by the left-hand side. Reserves. Reserves held at the central bank are risk free and the most liquid of all the bank's assets. An additional benet of reserves is that they reduce capital and liquidity costs. The marginal benets of reserves are tied to the interest rate through equation (2.12) below. b + 2 ( t S t+1 + t M b;t+1 ) 2 (F t+1 + t B t+1 t t M b;t+1 t t S t+1 ) 3 + 2 (! m;t M b;t+1 +! l;t L t+1 ) 2 (F t+1 +B t+1 + (1' t ! m;t )M b;t+1 + (1' t ! l;t )L t+1 S t+1 ) 3 = 1 (1 +r f t ) (2.12) Given the regulatory benets of reserves, the bank will accept a lower gross return, 1 +r f t , on those assets. Since one unit of reserves increases the capital ratio by 1 !m;tM b;t+1 +! l;t L t+1 , higher risk weights on mortgages,! m;t , or on other loans,! l;t , attribute even larger marginal regulatory benets to reserves and drive r f t down. The same holds for LCR out ow rates attached to deposits, t , and mortgages, t , or higher required buers (for capital this is larger and for liquidity this is a bigger ). Alternatively, if r f t is xed, the bank will hold more reserves, F t+1 for the same level of r f t than before the regulatory changes. 78 Bonds. Government bonds are similar to reserves for the bank, but are less liquid and thus less advantageous for regulatory purposes. b + 2 t ( t S t+1 + t M b;t+1 ) 2 (F t+1 + t B t+1 t t M b;t+1 t t S t+1 ) 3 + 2 (! m;t M b;t+1 +! l;t L t+1 ) 2 (F t+1 +B t+1 + (1' t ! m;t )M b;t+1 + (1' t ! l;t )L t+1 S t+1 ) 3 = 1 (1 +r b t ) (2.13) Equation (2.13) outlines the relationship between the marginal benets of holding bonds and the interest rate received, r b t . Equation (2.13) looks exactly the same as (2.12) aside from the t in term two on the left-hand side because bonds reduce liquidity costs by less than reserves. t plays a role in distinguishing interest paid on bonds from the interest on reserves. Interest Rate Dierentials The relationship between interest rate on bonds and reserves is derived by subtracting equation (2.13) from (2.12): 2 ( t S t+1 + t M b;t+1 ) 2 (F t+1 + t B t+1 t t M b;t+1 t t S t+1 ) 3 2 t ( t S t+1 + t M b;t+1 ) 2 (F t+1 + t B t+1 t t M b;t+1 t t S t+1 ) 3 = 1 (1 +r f t ) 1 (1 +r b t ) This simplies to 2 ( t S t+1 + t M b;t+1 ) 2 (F t+1 + t B t+1 t t M b;t+1 t t S t+1 ) 3 | {z } (sign depends on LCR ratio) (1 t ) = 1 (1 +r f t ) 1 (1 +r b t ) If bank's LCR ratio and t 1, then 1 (1+r f t ) 1 (1+r b t ) and r f t r b t Because bonds are not fully counted as HQLA in the LCR, t < 1 and there will be a liquidity premium associated with reserves over bonds (r f t r b t ) proportional to the size of t . 79 Table 2.3: Central Bank Government Balance Sheet Government Central Bank Assets Liabilities Assets Liabilities Mortgages (M g;t ) Bonds (B S t ) Bonds (B CB t ) Reserves (F t ) 2.2.3 Central Bank Government Table 2.3 summarizes the combined central bank government balance sheet. The government intervenes in the mortgage market by supplying mortgages, M g;t , to reduce the interest rate on mortgages r m t paid by households. 7 Bonds, B S t are issued by the government and also held by the central bank, yielding net issuance of B S t B CB t . The central bank holds bonds to back reserve liabilities due to the bank sector. Budget constraint The central bank government collects taxes,T t , from the household-rm sector to satisfy the following budget constraint M g;t +T t + F t+1 (1 +r f t ) + (B S t+1 B CB t+1 ) (1 +r b t ) = M g;t+1 (z t ) +F t + (B S t B CB t ); (2.14) where z t = (1)(1 +r m t ) + PtHt Mt . z t < (1 +r m t ) re ects the reduction in return arising from loan loss reserves the government must set aside for each dollar invested in mortgages. captures the average expected idiosyncratic default rate on mortgages. The supply of government bonds is determined outside the model. Monetary policy occurs through two channels: 1. The interest rate on reserves,r f t , is exogenously determined. The central bank supplies any amount of F t at the given rate. 7 M g;t is exogenously determined based on the extent of government ownership of total outstanding mortgages. 80 2. The central bank conducts quantitative easing by choosing the size of its government bond holdings,B CB t , which aects the net supply of bonds in the system (B S t B CB t ). 2.2.4 Equilibrium Denition Let X be a vector of state variables containing housing preference parameter, t , the weight of deposits in household-rm utility, t , the weight of government bonds in utility, t , house size, H t , government mortgage supply, M gt , government bond supply, B S t , the central bank's interest rate on reserves,r f t , amount of other loans,L t , interest on other loans,r l t , and intermediation costs, t . Let K be a vector containing variables describing the regulatory environment: minimum capital ratio, ' t , risk-weights on mortgages and other loans, ! m;t and ! l;t , minimum LCR, t , out ow rates on deposits and mortgages, t and t , and the share of government bonds that qualies as high quality liquid assets, t . Denote the set of policy functions for the household-rm as f H : 8 > > > > > > > > > > < > > > > > > > > > > : C(X;W t ) consumption S H (X;W t ) savings demand B H (X;W t ) bond demand M H (X;W t ) mortgage demand H H (X;W t ) housing demand 9 > > > > > > > > > > = > > > > > > > > > > ; Denote the set of policy functions for the bank as f B : 8 > > > > > > > < > > > > > > > : S B (X;K;z t ) deposit supply M B (X;K;z t ) mortgage supply F B (X;K;z t ) reserves demand B B (X;K;z t ) bond demand 9 > > > > > > > = > > > > > > > ; 81 Denote the set of policy functions for the government central bank as f G : 8 > < > : F G (X;z t ) reserves supply B CB (X;z t ) bond holdings 9 > = > ; An equilibrium consists of f H , f B , f G , a dynamic process for house price, P t , interest rates r s t , r b t , and r m t such that: 1. Household-rm policy functions f H satisfy equations (2.2)-(2.5) given P t , r s t , r b t , and r m t . 2. Bank policy functions f B satisfy equations (2.10)-(2.13) given P t , r s t , r b t , and r m t . 3. Government central bank policy functions f G satisfy its budget constraint in equation (2.14). 4. Markets clear: • Mortgages: M B t+1 +M G t+1 =M H t+1 . 8 • Other loans: L H t+1 =L B t+1 . • Housing: H =H t+1 . 9 • Reserves: F t+1 =B CB t+1 • Bonds: B = B S t+1 = B CB t+1 +B H t+1 +B Banks t+1 . The interest rate on bonds, r b t is determined in equilibrium and allows the bond market to clear. • Deposits: S H t+1 =S B t+1 . 10 The aggregate resource constraint W t + S B t+1 (1+r s t +t) + M H t+1 (1+r m t ) = C t + M B t+1 zt + M G t+1 zt +P t (H t+1 H t )+P t H t + F t+1 +M b;t+1 +B t+1 +L t+1 S t+1 !m;tM b;t+1 +! l;t L t+1 ' t 2 + F t+1 +tB t+1 tS t+1 +tM b;t+1 t 2 + S H t+1 (1+r s t ) holds as a result of preceding market clearing conditions being fullled. 8 Extra payment by household of ((1 +r m t )z t )M H t+1 is the markup due to loan loss provisioning. 9 Housing supply is xed exogenously and price of housing,P t+1 , adjusts to match supply with household demand. 10 t S H t+1 is the reduction in prots for the bank from intermediation costs. 82 2.2.5 Nonstochastic Steady State Setting household-rm preference parameters and regulatory parameters to xed constants, I solve for the nonstochastic steady state of the model. The set of equations describing the steady state can be found in the Appendix. 2.3 Calibration To calibrate the model, I match developments in both household-nonnancial-rm and bank sector balance sheets. In Chapter 1, the model suggested household preferences helped explain the buildup in cash on bank balance sheets in the post-crisis period, so the condition of the household-nonnancial-rm must be included. Additionally, because LSAPs occur in the secondary market for securities, quantitative easing aects the distribution of securities between banks and other economic actors. Moreover, empirical evidence points to the household-nonnancial-rm sector as one of the main sellers of securities to the Fed. Thus, I begin with an overview of the liquid asset held by the household, nonnancial rm, and bank sectors and then focus on describing the changes that occur between each quantitative easing program before turning to targeted data moments. Figure 2.2 highlights that Treasury securities as a share of total assets have been growing for banks, while roughly declining for households and nonnancial rms from 2010 to 2017. Vertical lines mark the beginning of each QE episode. QE1 began in 2008q4 with a focus on easing mortgage market conditions and resulted in total purchases of $600 billion agency debt and mortgage-backed securities and $300 billion Treasuries by the end of 2010q1 (Ennis and Wolman (2012)). QE2 focused on Treasury securities, increasing the Federal Reserve's holdings of Treasuries from roughly $775 billion in 2010q2 to $1.62 trillion in 2011q2 (see Figure 2.1). QE3 further increased Treasury holdings starting in 2012q3 and ended in 2014q4 with total purchases of around $800 billion according to Table 5 of the Federal Reserve's H.4.1 statistical release. The decline in household and nonnancial rm Treasury holdings 83 Figure 2.2: Treasuries Holdings of Dierent Sectors Source: Flow of Funds, FDIC Quarterly Banking Statistics as a share of total assets seems to coincide with the start of QE2 in Figure 2.2. As Carpenter et al (2015) document, the ultimate sellers of Treasuries during LSAPs were households, so QE2 could be the reason. Meanwhile, shares of deposits in total assets have been on the rise since after the nancial crisis, around the start of QE1, for both households and nonnancial rms (see Figure 2.3). Figure 2.4 combines household and nonnancial rms' holdings of deposits and Treasuries together as a measure of liquid assets, underlining that the share of Treasuries in liquid assets jumped sharply at the onset of QE1, then fell from a post-crisis peak in 2010q2 and has uctuated around eight to ten percent from 2010 to 2017. How did QE shape these shifts in balance sheet composition and how were interest rate dierentials related to the changes? 2.3.1 Setup To analyze the changes in household-rm and bank balance sheet composition potentially related to QE, I rst generate benchmarks by matching key model parameters to the re ect 84 Figure 2.3: Deposits Holdings of Dierent Sectors Source: Flow of Funds Figure 2.4: Treasuries as Share of Liquid Assets for Household-Nonnancial Firm Sector Source: Flow of Funds 85 Table 2.4: Summary of Target and Model Moments Data moment Data source Model moment cash total assets FDIC Quarterly Banking Prole F F +M B +B B +L assets assets - liabilities FDIC Quarterly Banking Prole F +M B +L F +M B +B B +LS Tier1 risk-weighted assets ratio FDIC Quarterly Banking Prole F +M B +B B +LS !mM B +! l L liquidity coverage ratio Basel 3 assessment reports F +tB B S+M B average sales price of house sold in US average square footage of house US Census P MZM own rate Federal Reserve r s return on equity FDIC banking ratios 1 b return on Treasuries US Treasury r b Treasuries, as a share FDIC Quarterly Banking Prole B B (F +M B +B B +L) of bank total assets Treasuries, as a share of Flow of Funds B H (B H +S) household-rm liquid assets the conditions at the end of each QE phase (201q1, 2011q2, and 2014q4). Data targets include the same key balance sheet ratios as in Chapter 1, Section 1.4.1, plus the share of Treasury securities held by the two sectors. Table 2.4 summarizes the targeted empirical measures and corresponding model moments. The rst target is the cash to total assets ratio of the bank, which will pin down total reserves, F , in the model and the amount of bonds held by the central bank B CB . 11 Bank leverage determines the level of deposits, S, and the savings of the household-rm. Since perceived costs of capital and liquidity regulation ( and ) play an important role in the bank's pricing of deposits and dierent assets, I include banks' actual liquidity coverage and Tier 1 capital ratios as targets. Matching the interest rate on deposits and the price per 11 I must assume that the central bank controls the total amount of reserves held by the bank sector, which simplies the analysis, but may be imprecise because FDIC-insured depository institutions covered in Call Report data do not hold all of the reserves in the nancial system. Other entities that can hold reserves include credit unions and uninsured foreign banking oces (FBOs) in the US. Based on their analysis of the distribution of reserves, Ennis and Wolman (2012) observe that foreign-related institutions played a signicant role in determining how the banking system absorbed the changes in aggregate reserves, with FBOs holding more than 40 percent of total reserves in 2011q2. 86 square foot for housing allows me to quantify preference parameters, , and utility from deposits, . The bank's required return on equity aects the pricing of all assets, so I use the average return on equity in the data to obtain a realistic discount factor, b . The interest rate on government bonds, r b , identies , the household-rm liquidity preference for Treasuries. The share of Treasuries in total assets of the bank and Treasuries as a share of household-rm liquid assets together with the cash ratio in row one determine the total supply of government bonds in the model, B S =B CB +B B +B H . 12 A detailed explanation of data sources and variable denitions for the rst ve target moments can be found in Chapter 1, Section 1.4.1, so I only discuss Treasury related moments next. The interest rate on government bonds, r b , is the average interest rate on Treasuries, calculated by the US Treasury based on aggregate interest payments divided by the total debt outstanding at the time of record. I use the interest series for Total Marketable Treasuries, which includes Treasury Bills, Notes, and Bonds where ownership can be transferred from one person or entity to another and the securities can also be traded on the secondary market. I assume the household-rm and bank sectors hold Treasuries of dierent maturities in the same distribution as the composition of total marketable debt in the economy. Treasuries as a share of bank total assets comes from aggregated FDIC-insured depository institution balance sheet data found in the FDIC Quarterly Banking Prole and correspond to in the sum of US Treasury securities available-for-sale (at fair value), RCON1287, and US Treasury securities held-to-maturity (at amortized cost), RCON0211, divided by total assets, RCON2170, in the FFIEC 041 Call Reports. Treasuries as a share of household-rm liquid assets is calculated from Flow of Funds Tables L.102, for Nonnancial Business, and L.101, for Households. Nonnancial business includes nonnancial corporate and nonnancial noncorporate business sectors. Households include domestic hedge funds, private equity funds, personal trusts, and nonprot organizations. For liquid assets, I sum 12 There are many holders of Treasury securities outside of household-rms and banks, so directly using data on the level of total outstanding Treasuries as B S would make the model unsolvable or require unrealistically high values attached to the amount of bonds held by either the bank or household-rm sectors as a share of their assets in the model. 87 Table 2.5: Moment Targets for Calibration for Each QE End-date Date moment 2010q1 2011q2 2014q4 cash ratio 0.09 0.10 0.13 leverage 8.71 8.42 8.75 Tier1 ratio 0.120 0.131 0.129 LCR 1.105 1.105 1.105 house price, P 115 108 139 MZM own rate 0.003 0.002 0.001 return on equity 1.055 1.076 1.091 return on Treasuries 0.025 0.024 0.020 Bank tres/total assets 0.012 0.012 0.027 HH-rm tres/liquid assets 0.112 0.090 0.075 up checkable deposits and currency, total time and savings deposits, and Treasury securities assets from both tables. Table 2.5 presents the empirical values of the targets for each quarter of interest in the calibration. Of note, the LCR is constant because it is set to the average post-crisis value in Basel 3 assessment reports given the absence of quarterly data. The cash ratio, return on Treasuries and savings (MZM), and share of Treasuries in bank's total assets are relatively unchanged between 2010q1 and 2011q2. The largest dierence between the two periods is that leverage, house price, and the household-rm's Treasuries to liquid assets share are lower in 2011q2, while Tier 1 and return on bank equity grow. Between 2011q2 and 2014q4, cash ratios, leverage, house price, and return on bank equity are much higher. Interest rates on savings and Treasuries fall slightly from 2011q2 levels. Treasury shares move the most. The household-rm's share of Tresauries in liquid assets continue to fall noticably and the bank's share of Treasuries in total assets more than doubles. I calibrate other parameters of the model by inputting values directly from data. The approach is identical to Chapter 1, Section 1.4.2, but the values dier slightly, given the dierent points in time considered. Table 2.6 provides the full list of parameters. I will highlight where input values dier substantially from those in Table 1.2 in turn. In the left panel of Table 2.6 are the parameters set constant for all periods in the analysis. 88 Table 2.6: Summary of Inputted Parameters Used in Calibration For All Periods: For Dierent QE End-dates: Parameter Value Parameter 2010q1 2011q2 2014q4 ' 0.06 0.0149 0.0149 0.0172 1.00 W 86,000 88,000 100,000 0.01 H 2,392 2,480 2,657 0.80 r f 0.0025 0.0025 0.0025 0.02 0.0294 0.0296 0.0272 0.65 M G 121,670 126,898 187,916 ! l 1.00 L 174,000 160,000 228,000 r l 0.0548 0.04495 0.0390 QE happens post-crisis, so required regulatory minimums for the capital ratio, ', and the LCR, , are unchanged. The default rate on mortgages, , maximum LTV ratio, , house maintenance costs, , foreclosure recovery rate, , and the risk-weight on other loans in the capital ratio, ! l , are unchanged from Section 1.4.2. Dierent from Chapter 1, the model here has a household-rm sector, so wages, W , includes nonnancial rm prots. Data come from the BEA's income statistics. I rst add together compensation of employees and proprietor's income from Table 2.1, Personal Income and Its Disposition, with nonnancial corporate prots with inventory valuation adjustments from Table 6.16D., Corporate Prots by Industry. Then I divide the sum by the number of US households, from the annual US Census Current Population Survey, to obtain per household nominal income for each year, rounded to the nearest thousand. Wages grow slowly from 2010q1 to 2011q2 and reach around $100,000 in 2014q4. The interest rate on reserves, r f , is now the interest rate on excess reserves (IOER) from the Federal Reserve, rather than the fed funds rate, since IOER begins in 2008 and is available for all three QE end-dates. IOER remained set at 0.25 percent in the post-crisis period, so QE was carried out in the absence of changes in the short-term risk-free rate. is the per unit intermediation cost attached to deposits. Intermediation costs for the bank are relatively constant, though they fall in 2014q4. 89 The portion of mortgage loans that count as out ows for the LCR, , average square footage of housing, H, the interest rate on other loans, r l t , the level of other loans, L, and government supply of mortgages, M G , follow the same treatment as in Section 1.4.2, with slightly diferent values. Government supply of mortgages, M G , is inputted to re ect the share of total outstanding one to four family residential mortgage liabilities held by US government sponsored entities. M G is chosen so that the ratio of M G to M H is 0.55 in 2010q1, 0.59 in 2011q2, and 0.64 in 2014q4 to re ect the growing presence of the government in the mortgage market (see footnote 30 in Section 1.4.2). Other loans, L, are set to match the average share of non-mortgage, non-cash, non-Treasury assets in the bank's total assets in the post-crisis period, which equals 0.57. House size, H, government mortgages, M G , other bank loans, L, and LCR out ows from mortgage loans,, grow over the QE end-dates, while the interest rate on other loans, r l steadily falls. To implement the calibration, I solve for parameters of the model to match data moments for each of the QE end-dates separately. In addition to the full set of choice variables for the household-rm and bank, market clearing quantities, prices, and interest rates, I also solve for regulatory factors. Regulatory parameters, including perceived costs of the capital requirement, , the cost of the liquidity requirement, , the out ow rate of deposits in the LCR, , and the risk-weight on mortgages, ! m , in uence the pricing of assets by the bank. Of direct relevance to interest rate dierentials, the percentage of Treasuries that count towards HQLA, , will solve to match the spread between bonds and reserves, r b r f . On the household-rm side, solution values for liquidity preferences, and , will be consistent with the dierence in interest rates on bonds and deposits,r b r s , while utility from housing, , embodies the in uence of house prices on mortgage rates, r m . These parameters will be the focus of analysis on the calibration results. 90 2.3.2 Results Calibration results provide a guide for understanding the dierent factors behind balance sheet adjustments and movements in interest rate dierentials during QE2 and QE3. Quantitative easing in the model is re ected by growth in central bank bond holdings (B CB ), which will drive down the return on bonds since r b adjusts to match bond demand with the reduction in net bond supply (B S B CB ) to clear the market. Rather than discuss the mechanical link between QE and bonds, I delve into changes in the household-rm and bank sectors that can, in reaction to QE or independently, play an equally important role in balance sheet and interest rate determination. Balance Sheets Table 2.7 provides the resulting balance sheet compositions for each QE end-date along with related model parameters. From the end of QE1 to the end of QE2, in the top panel, bank reserves in total assets rose from 8.7 percent to 10 percent, while the share of bonds remained constant and the share of mortgages fell slightly. On the other hand, household-rm bonds in liquid assets fell from 11 to 9 percent. The changes suggest that the household-rm sector was the main seller of Treasuries to the central bank during QE2, rather than banks. To think about why the household-rm would be a heavier seller of Treasuries, I examine the levels of dierent balance sheet components and likely parameters driving their movements. The second panel of Table 2.7 indicates that deposits fell together with bond holdings of the household-rm from 2010q1 to 2011q2, reducing liquid assets. Mortgages also shrank. A rise in consumption accompanied the shift away from liquid assets and loans, which is consistent with the fall in house prices and lower household-rm preferences for all assets shown in the third panel. With the reduction in deposits from the household-rm, the bank balance sheet also shrank. In terms of composition, the bank shifts its assets more heavily towards reserves, cutting holdings of bonds and mortgages. The bank invests more in lower yielding reserve 91 assets because the costs associated with regulatory capital, , are much higher in 2011q2 and the bank needs more reserves to cover higher out ow rates attached to deposits, , to meet the same LCR requirement (see bottom panel of Table 2.7). Regulatory concerns are the main motivator for changes on the bank side during QE2. From 2011q2 to 2014q4, regulatory considerations for the bank continue to grow, leading to climbing reserve and bond ratios at the expense of mortgage shares in total assets. Household-rm holdings of bonds as a share of liquid assets are lower in 2014q4 compared to 2011q2, due to faster growth in deposits compared to bonds. Mortgages demanded by the household-rm are also higher. The growth in deposits and strength in mortgage demand enables the bank to expand mortgages along with reserves and bonds even in the face of the tougher regulatory environment. How the aformentioned factors translate into interest rate movements is discussed next. Interest Rate Dierentials To facilitate the interpretation of the results on interest rate spreads, I rst lay out the properties each investment instrument possesses within the theoretical framework. Table 2.8 summarizes the attributes of dierent assets, borrowing from the setup of Table 1 in Bhattarai and Neely (2016). Each column is a dierent property, and entries indicate parameters relevant for measuring the extent the asset has each property, based on rst order conditions of the model. In the context of the model, liquidity indicates an asset is easily converted into funds for consumption of goods and services by the household-rm. Assets with liquidity properties are bonds and deposits. The size of the liquidity premium is determined by marginal utilities, B H for bonds and S for deposits. Default risk applies to assets that require loss provisioning to account for default rates, which only mortgages have because of . HQLA designates an asset as high quality from the perspective of liquidity regulation, which includes reserves with highest quality of 1 and bonds at < 1. LCR penalty means the asset is assigned an out ow rate in LCR calculations; mortgages have 92 Table 2.7: Calibration Results: Balance Sheets QE1 end QE2 end QE3 end 2010q1 2011q2 2014q4 Balance sheet ratios Bank reserves/total asset ratio 0.087 0.101 0.126 Bank bond/total assets 0.012 0.012 0.027 Bank mortgages/total assets 0.326 0.313 0.272 Household-rm bond/liquid assets 0.112 0.090 0.075 Balance sheet components S : deposits 267,866 245,635 350,846 B H : household-rm bonds 33,863 24,235 28,421 (B H + S): household-rm liquid assets 301,730 269,870 379,268 M H : household-rm mortgages 220,240 214,080 295,520 C: household-rm consumption 72,213 74,781 82,010 F: reserves 26,293 28,092 49,965 B B : bank bonds 3,734 3,466 10,539 M B : bank mortgages 98,570 87,182 107,604 (F+ B B + M B + L): bank total assets 302,598 278,740 396,107 B CB : central bank bonds 26,293 28,092 49,965 B S : bond supply 63,891 55,793 88,925 L: other loans 174,000 160,000 228,000 Household-rm preferences P : house price 115 108 139 : houses 0.257 0.250 0.314 : deposits 0.248 0.222 0.293 : bonds 0.020 0.014 0.017 Bank concerns Tier1 ratio 0.12 0.13 0.13 : capital cost 0.577 1.624 3.031 ! m : mtg. risk weight 1.162 1.066 1.132 LCR 1.105 1.105 1.105 : LCR cost 0.453 0.487 0.828 : Treasury HQLA 0.305 0.346 0.408 : mtg. out ow 0.015 0.015 0.017 : deposit out ow 0.087 0.103 0.135 93 and deposits (an asset for the household-rm) have . Risk-weighted assets in the capital ratio, mortgages, have a direct capital penalty! m . Each row of Table 2.8 provides parameters that directly aect the interest rates paid on the assets, with larger liquidity parameters and higher HQLA properties pushing rates down, while more default risk and greater LCR or capital penalties pushing rates up. Table 2.9 presents the model parameters obtained from calibration. Of note, the interest rate on mortgages over reserves, unlike the other spreads, is a calibrated value that does not re ect an empirical mortgage rate series. Compared to actual data on the average 30-year xed rate mortgage rate minus IOER,r m r s , overstates the stability of spreads. At the end of 2010q1, the 30-year mortgage spread over IOER was 4.75 percent. The spread then fell to 4.40 in 2011q2 and to 3.71 percent in 2014q4. In the calibration results, the spread increases over time, becauser m estimates rise, which runs counter to the actual data. Analyses in this section about the drivers of movements in the mortgage rate and spread over reserves are still valid, with the caveat that they are for the wrong direction of changes in the rates. From the end of QE1 to QE2, the largest change in rate spreads was for mortgages over reserves (r m r s ). As the second panel highlights, the rise in interest rates on mortgages is reason behind the change. Checking the direct factors aecting mortgage pricing from Table 2.8, doesn't change, is constant, and! m actually falls. No direct factors are pushing r m up from 2010q1 to 2011q2. Turning to indirect factors, household-rm preferences (third panel) for houses fell over this period, re ecting the drop in house prices and reduced demand for housing which would push mortgage rates down. For bank concerns in the bottom panel, the bank's discount factor, b , fell because required return on equity (ROE) grew. From the discussion in Section 2.2.2, rising ROE motivates the bank to raise the interest rate charged on mortgages, r m . The scaling factor on capital costs, , also tripled, suggesting a role for tighter capital constraints and, to a lesser degree, changes in ROE driving the mortgage spread. From 2011q2 to 2014q4, bond spreads fall by 0.3 percentage points. The decline in the 94 Table 2.8: Properties of Dierent Assets Liquidity Default risk HQLA LCR penalty Capital penalty Mortgages (M) ! m Gov. bond (B) B H Reserves (F) 1 Deposits (S) S interest rate on bonds, r b , is the biggest contributor to the change. Direct factors aecting bond pricing, B H , S , and , move in opposite directions. Household-rm marginal utility from bonds versus deposits shrinks, translating to a smaller bond liquidity premium, r b r f (see the analysis of interest rate dierentials in Section 2.2.1). is higher in 2014q4, so bonds grow more like reserves in their value as HQLA for banks, which reduces the regulatory liquidity premium on bonds, r b r f . The doubling of regulatory costs for the LCR () further magnies the response of the bond spread to changes in . Changes in the liquidity properties of bonds, derived from bank regulatory concerns and household-rm preferences, are the strongest candidates to explain declining bond premiums over the period. 2.4 Counterfactuals The calibration provides model parameters to match empirical interest rates, but is ignostic about whether QE, household-rm preferences, regulations, or bank concerns drive specic events like bond sales or reduction in spreads. To isolate the eects of QE on balance sheets and interest rate dierentials and quantify how QE interacts with bank regulatory concerns (, , ! m , , ) and household-rm preferences ( , , ), I turn to counterfactual exercises. 2.4.1 Setup I dene QE as purchases of government bonds by the central bank, represented in the model as growing valuesB CB . Indeed, from Table 2.7,B CB increases from 26,293 in 2010q1 95 Table 2.9: Calibration Results: Interest Rate Dierentials QE1 end QE2 end QE3 end 2010q1 2011q2 2014q4 Interest rate spreads r b r f : bonds over reserves 0.023 0.021 0.018 r m r f : mortgages over reserves 0.038 0.041 0.041 r b r s : bonds over deposits 0.022 0.022 0.019 Interest rates r b : bonds 0.025 0.024 0.020 r m : mortgages 0.041 0.044 0.044 r s : deposits 0.003 0.002 0.001 r f : reserves 0.003 0.003 0.003 Household-rm preferences P : house price 115 108 139 : houses 0.257 0.250 0.314 : deposits 0.248 0.222 0.293 S: deposits 267,866 245,635 350,846 : bonds 0.020 0.014 0.017 B H : bonds 33,863 24,235 28,421 Bank concerns b : 1/ROE 0.948 0.930 0.917 : capital cost 0.577 1.624 3.031 ! m : mtg. risk weight 1.162 1.066 1.132 : LCR cost 0.453 0.487 0.828 : Treasury HQLA 0.305 0.346 0.408 : mtg. out ow 0.015 0.015 0.017 : deposit out ow 0.087 0.103 0.135 96 Table 2.10: Parameters Used in Counterfactuals Factor Model parameters QE3 B CB : central bank bond holdings Regulation LCR : costs : Treasury HQLA : deposit out ow Capital : costs ! m : mortgage risk-weight HH-rm preferences House demand Liquidity : for deposits : for bonds to 28,092 in 2011q2 and 49,965 in 2014q4. However, the levels of B CB in the model are magnitudes smaller than actual Treasuries holdings in the Federal Reserve's H.4.1 data, so I quantify each phase of QE as the percentage growth rate of Treasury holdings from the end-date of a previous QE to the end-date of the current QE in question. For QE2, the growth rate of Treasury holdings on the Fed's balance sheet from 2010q1 to 2011q2 is 108 percent. For QE3, the growth rate from 2011q2 to 2014q4 is 52 percent. Because the growth rate of B CB from 2010q1 to 2011q2 (6 percent) is well short of 100 percent, I use 2011q2 as the starting point for the counterfactual exercise, with the aim to evaluate QE3. The counterfactual will have two parts. In the rst part, I estimate the direct eects on balance sheet ratios and interest rate spreads from QE3, regulation, and household-rm preferences separately. In the second part, I pair QE3 with movements in regulatory and preference parameters to evaluate interaction eects. In each counterfactual, I begin with the model solution for 2011q2. Next, I change the value of relevant parameters and resolve the model to obtain new values for balance sheet ratios and interest rate spreads. Looking at the changes in balance sheet and interest rates, I can then quantify the eects of dierent factors. Balance sheet ratios include bank reserves to total assets, bank bonds to total assets, bank mortgages to total assets, and household-rm bond to liquid assets. Interest rate spreads include bonds over reserves (r b r f ), mortgages over reserves (r m r f ), and bonds over deposits (r b r s ). Table 2.10 summarizes the model parameters associated with each factor I want to assess in the counterfactuals. 97 For part one, I run three counterfactual scenarios. First, I consider what happens when the only change that occurs is QE3, which I quantify by increasing the value of central bank bond holdings (B CB ) in 2011q2 by 52 percent. Second, I look at regulatory eects in isolation, by changing LCR and capital parameters from 2011q2 values to their 2014q4 values. For the third counterfactual, I only change household-rm preference parameters. In part two, I run four scenarios. The rst adds parameter changes associated with capital regulation to QE3. The second assesses QE3's interaction with LCR parameters. The third exercise measures the joint eect of QE3 and household-rm demand for housing. For the last counterfactual, I evaluate how household-rm liquidity preferences aect the impact of QE3 on balance sheet ratios and interest rate spreads. 2.4.2 Results Part One When examining the in uence of dierent factors one-by-one, QE3 stands out as the largest force acting on balance sheets. Figure 2.5 provides a visual of the percent changes in bank balance sheet ratios due to each factor. The rst bar in blue indicates the actual change in each ratio from 2011q2 to 2014q4 in the data. The subsequent bars are changes in calculated from the counterfactual exercise, with red-orange corresponding to the eect of QE3, yellow to regulation, and purple to household-rm preferences. The red-orange bar for QE3 is the tallest for all key ratios, except for the household-rm bond ratio, where household-preferences are the most visible factor. QE is the strongest force pushing bank cash ratios up, pulling bank bond ratios down, and pushing bank mortgage shares up. For the share of bonds in total bank assets, regulation and household-rm preferences both push the ratio in the same upward direction. However, for the bank mortgage ratio, regulations and household-rm factors appears to counter each other. The results suggest that QE3 would have triggered a large rebalancing of bank balance sheets away from Treasuries and towards 98 mortgages in the absence of other developments and little to no eect on household-rm liquid assets. Figure 2.6 presents the counterfactual results for interest rate dierentials. The rst bar in blue indicates the actual change in each ratio from 2011q2 to 2014q4 in the data, except for the interest rate spread between mortgages and reserves r m r f , which re ects a calibrated spread that diers from actual data. For the spread between interest rate on bonds and reserves, r b r f , QE3 (in red-orange) almost exactly accounts for the entire reduction found in the data (in blue). In terms of the mortgage-reserves dierential,r m r f , the growth in the spread due to regulation (in yellow) appears to cancel out the downward pressure coming from QE. It is unclear why household-rm preferences (in purple) has no eect on the spread, though. The decline in the dierence between interest rates on bonds and deposits,r b r s , is mostly achieved by regulation alone (the yellow bar is almost equal to the blue bar). However, QE and household-rm preferences cause movements in the opposite direction. Across all categories, regulation appears to dampen interest rate movements due to QE while household-rm preferences seem to add on to QE eects. Table 2.11 summarizes the counterfactual results from part one. The second row of both panels, bank bond ratio for the top and the mortgage-reserves interest rate dierential for the bottom, reiterate how the separate eects from QE, regulation, and preferences do not add up to the changes in the data. Part two of the counterfactual exercise addresses the question about combined eects of various factors. Part Two Table 2.12 summarizes the changes in balance sheet ratios and interest rate spreads produced by counterfactual scenarios that explore interaction eects between QE3 and dierent regulatory or preference parameters. In the rst column are the eects of QE3 alone. The second column is the combined impact of QE plus the rise in capital costs () and mortgage risk-weight (! m ). The third column contains the results from adding to QE the 99 Figure 2.5: Counterfactual Results: Balance Sheet Table 2.11: Counterfactual Results Changes from 2011q2 to 2014q4, % points Data QE3 Regulation HH prefs Balance sheet ratios Bank cash ratio 2.54 6.32 -0.45 -1.99 Bank tres/total assets 1.42 -18.02 8.17 6.17 Bank mortgages/total assets -4.11 7.72 -5.14 7.16 HH-rm tres/liquid assets -1.49 -0.03 -0.23 -1.04 Interest rate spreads r b r f -0.37 -0.38 0.03 -0.04 r m r f 0.00 -0.56 0.48 -0.08 r b r s -0.26 0.15 -0.19 0.01 Note that the value in the Data column is a calibrated model spread. In actual data, r m r f declines by 0.69 percentage points. 100 Figure 2.6: Counterfactual Results: Interest Rate Dierentials NB: The value for r m r f in the Data column is a calibrated model spread. In actual data, r m r f declines by 0.69 percentage points. 101 changes in LCR related parameters. Column four includes household-rm house preference parameter, , with QE. The last column refers to results from the scenario with QE plus changes in liquidity preference parameters of the household-rm. See Table D.3 for a details on the values of the full parameter sets used in each counterfactual. Examining the estimates for balance sheet ratios in the top panel under each scenario, it is clear that rising liquidity regulation has the strongest dampening eect on QE3 for Treasuries and mortgage shares. From Table 2.12 row three, quantitative easing places pressure on the bank to decrease Treasury shares in total assets by 18 percentage points. Liquidity regulation removes more than half the QE drop, bringing the drop down to only around 5 percentage points from 18. The eect is even more stark for the share of mortgages in total bank assets. Rising LCR parameters ip the increase of almost 8 percentage points due to QE into a fall in mortgage share of almost half a percentage point. Tougher LCR rules counter the ability of QE to encourage banks to divert assets towards more risky or higher-yielding investments. For the share of Treasuries in liquid assets of the household-rm, stronger liquidity preferences amplify the impact of QE3. Specically, both demand for deposits and Treasuries grow from 2011q1 to 2014q4, with demand for deposits increasing faster than Treasuries (see third panel of Table 2.9. The shift towards deposits strengthens the reduction of Treasuries by the household-rm, bringing their share in liquid assets down a past a full percentage point compared to only 0.03 under QE. More deposits sought by household-rms apparently do not increase reserves held by banks, as growth the bank's cash ratio is tempered with the change in liquidity preferences. However, deposit demand may cause interest rates to fall much farther than the Fed intends if household-rms amass more deposits in response to LSAPs. Indeed, the last row of the bottom panel of Table 2.12 conrms that greater liquidity preferences magnify the widening of the interest rate dierential between bonds and deposits (r b r s ). QE increases the spread by 0.15 percentage points, mainly by pushing the deposit 102 Table 2.12: Counterfactual Results: Interaction Eects QE3 QE3 QE3 QE3 QE3 +capital + LCR + +liquidity Balance sheet ratios Bank cash ratio 6.32 6.34 5.37 4.40 4.37 Bank tres/total assets -18.02 -18.55 -5.46 -12.70 -11.55 Bank mortgages/total assets 7.72 8.19 -0.33 11.54 10.51 HH-rm tres/liquid assets -0.03 -0.04 -0.22 0.02 -1.09 Interest rate spreads r b r f -0.38 -0.49 -0.16 0.28 -0.99 r m r f -0.56 -0.60 0.07 0.39 -1.45 r b r s 0.15 0.19 -0.10 -0.11 0.37 rate towards zero. Household-rm liquidity preferences more than doubles the spread to 0.37. For the spread between bonds and reserves, or mortgages and reserves, there is a similar eect where liquidity preferences of the household-rm exacerbate changes in interest rate spreads created through QE. 2.5 Conclusion Augmenting the general equilibrium model from Chapter 1 with bonds as an additional asset, I characterize how quantitative easing functions through the portfolio rebalancing channel and how bank regulations contribute to the process of interest rate determination. Using the theoretical framework, I create a simple matching of components of capital and liquidity rules and household-rm preference parameters to attributes of mortgages, bonds, reserves, and deposits that matter for pricing of their interest rates. Larger liquidity preferences and higher HQLA properties attached to an asset reduce rates, while more default risk and greater LCR or capital penalties imposed push rates up. Relative sizes of these components then in uence the spreads between assets. Calibrating the model to the end-dates of QE1, QE2, and QE3, I identify potential drivers of bank's and household-rm's balance sheet choices and establish the size of factors that matter for changes in asset holdings and interest rate dierentials aside from QE. With 103 the assumption that total bank reserves are controlled by central bank bond holdings, I run counterfactuals where QE occurs through bond purchases. By comparing the impact of QE3 to the eects of changes in regulatory and preference factors, I obtain a rough idea of how components work in concert with or in opposition to one another. In a second set of counterfactual scenarios, I pair capital, LCR, and household-rm preference parameters with QE3 to analyze their interaction eects. The counterfactual exercises emphasize the importance of considering bank regulations when using QE to reach well-dened goals for monetary policy. The model highlights that stricter liquidity regulation has a strong dampening eect on the ability of QE to shape bank's Treasuries and mortgage shares. In particular, tougher LCR rules can undo the reach for yield motives QE creates to stimulate a shift away from safe securities towards riskier investments. Furthermore, liquidity preferences of household-rms can potentially exacerbate changes in interest rate spreads created through QE, making it dicult to ne-tune policy. These results suggest that the interplay of nancial rules and QE may be an area that warrants more research. One major limitation of the model is its inability to match the level of interest rates on mortgages and by extension, the interest rate dierential between mortgages and reserves. Aforementioned in Section 2.3.2, the spread of the average 30-year xed mortgage rate over reserves steadily fell from 2010q1 to 2014q4. 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International Journal of Central Banking (2008). 110 Appendix A Bank Balance Sheet Developments, by Asset Size In the introduction, movements in cash as a share of total assets, leverage, and loans backed by real estate were highlighted as examples of balance sheet ratios that have changed dramatically between pre-2009 and post-2009 periods. The data presented in Figure 1 were aggregates. For the cash ratio, total cash and due was summed up across all FDIC-insured depository institutions and divided by the sum of total assets of all banks. Leverage and mortgage ratios were also calculated in a similar manner. This method of calculation places more weight on the balance sheets of larger banks, so re ect the activity of the banks with the largest assets in the sector more than banks of smaller asset sizes. Since small, medium, and large banks tend to have dierent business models and sometimes very dierent customers, the aggregation of balance sheets may mask heterogeneity in how banks have changed in reaction to the post-2009 environment. The variation in post-crisis regulatory rules across size thresholds is another important reason to compare balance sheet changes across banks of dierent sizes. Notably, banks with total assets under $50 billion are not subject to a LCR, while bank with assets between $100 to $250 billion are subject to modied LCR requirements, and those above $250 billion are subject to a full LCR. Capital requirements also vary depending on whether banks are Category II, III, or IV banks, which correspond roughly to assets sizes of over $700 billion, between $250 and 700 billion, $100 to 250 billion, between $50 to 100 billion. I use the Category size thresholds as cutos to examine trends in balance sheets from 2000 to 2016 among the dierent groups. Figure A.1 presents the evolution of cash as a share of total assets. Here, cash and due is summed up among all banks in each size category and divided by the sum of total assets at those same banks. For banks between $50 to 100 billion assets in gold, banks between $100 111 to 250 billion in gray, $250 to 700 billion in turqoise, and above $700 billion in dark blue all, cash as a share of deposits rose from around 3 to 8 percent in 2000 to between 8 to 12 percent after 2009. Meanwhile, for banks below $50 billion, in orange, rose only to slightly, from 4 percent in 2000 to slightly above 4 to 6 percent after 2009. Nonetheless, banks in all asset classes increased the share of cash in total assets in the period from 2010 to 2016. Leverage, measured as total assets divided by equity within each size category, displays a similar pattern across banks. As Figure A.2 highlights, leverage fell from a range between 10 to 15 percent of equity in 2000 to between 5 and 9 percent of equity in 2016. During the run-up to the crisis, in 2006 and 2007, the sector made up of banks with $250 to 700 billion in total assets (in turqoise) accumulated the most leverage, reaching almost 25 percent of equity, while the leverage of all other asset size groups remained below 15 percent. From 2010 to 2016, leverage of banks in the between $250 to 700 billion group fell quite precipitously to converge to lower levels of leverage along with other size categories. Figure A.1: Cash as Share of Total Assets, by Asset Size 112 Figure A.2: Leverage, by Asset Size Figure A.3: Loans Backed by Real Estate as Share of Total Assets, by Asset Size 113 Figure A.4: Share of Total Industry Assets, by Asset Size Unlike cash in total assets and leverage, the change in loans backed by real estate as a share of total assets was not uniform across all banks. In Figure A.3, in contrast to other asset size groups, the share of loans backed by real estate rose for banks with assets below $50 billion, in orange, and banks with assets above $700 billion, in dark blue. For banks with assets between $50 to 100 billion (in gold) and $250 to 700 billion (in turqoise), the share of loans backed by real estate followed a similar pattern, rising from around 20 percent in 2000 to around 35 percent in 2006 and then falling to slightly under 20 percent in 2016. For banks with between $100 to 250 billion, in gray, the ratio remained almost stable at around 20 percent. Thus, aggregate trends from 2000 to 2016 that are consistent across all size groups are the fall in leverage and rise in cash as a share of total assets. To place the dierences in growth of loans backed by real estate in total assets in perspective, it is useful to consider the changes in shares of total industry assets occupied by each asset size category over the 114 same period. Figure A.4 shows how the share of banks above $700 billion in total assets (in dark blue) has been rising since 2002, comprising a little over 50 percent of total assets in the banking sector in 2016. Meanwhile, the share of total industry assets held among banks below $50 billion (in orange) and between $50 to 100 billion in total assets (in gold) has been declining. In the paper, discussion of aggregate trends in the banking sector will mainly re ect changes in banks larger than $100 billion in assets, with movements in banks below $100 billion in assets playing a lesser role given their diminishing share of the industry. Given the focus of the paper is on understand the role of post-crisis regulatory rules which disproportionately aect the larger banks, the emphasis placed on balance sheet changes among banks larger than $100 billion in aggregated data is not an issue. However, the empirical section of the paper explores the in uence of changes in demand for deposits on bank balance sheets distinctly because the analysis is generalizable to all banks. 115 Appendix B Equations B.1 Derivatives for Potential Regulatory Costs t+1 denotes the combined regulatory costs faced by the bank from capital and liquidity rules: F t+1 +M bt+1 +L t+1 S t+1 !mtM bt+1 +! lt L t+1 ' t 2 + F t+1 + l L t+1 + 1 2 r m t+1 M bt+1 tS t+1 +tM bt+1 t 2 The derivative with respect to deposits, S t+1 , is S;t+1 =2 (! mt M bt+1 +! lt L t+1 ) 2 (F t+1 + (1' t ! mt )M bt+1 + (1' t ! lt )L t+1 S t+1 ) 3 + 2 t ( t S t+1 + t M bt+1 )(F t+1 + lt L t+1 + 1 2 r m t+1 M bt+1 ) (F t+1 + lt L t+1 + ( 1 2 r m t+1 t t )M bt+1 t t S t+1 ) 3 The rst term is the increase in capital burden from an additional unit of deposits. By increasing deposit funding, the bank reduces equity (F t+1 +M t+1 +L t+1 S t+1 ) and lowers the capital ratio. This increases regulatory costs by (! mt M bt+1 +! lt L t+1 ) because of the weighting structure. The second term is the marginal increase in liquidity costs. Each dollar increase in deposits adds to the denominator of the LCR F t+1 + lt L t+1 + 1 2 r m t+1 M bt+1 tS t+1 +tM bt+1 , which brings the bank closer to its minimum requirements. To counteract the decline, the bank must raise high quality liquid assets, through reserves,F t+1 , Treasuries, lt L t+1 , or additional mortgage interest revenue, r m t+1 M t+1 . The derivative with respect to reserves, F t+1 , is F;t+1 = 2 (! mt M bt+1 +! lt L t+1 ) 2 (F t+1 + (1' t ! mt )M bt+1 + (1' t ! lt )L t+1 S t+1 ) 3 2 ( t S t+1 + t M bt+1 ) 2 (F t+1 + lt L t+1 + ( 1 2 r m t+1 t t )M bt+1 t t S t+1 ) 3 116 Reserves add to equity, so an additional unit of reserves reduces capital costs by an amount equal to the risk-weighted assets equity is held against, (! mt M bt+1 +! lt L t+1 ) in the numerator of the rst term. Similarly, reserves reduce liquidity costs, so the marginal reduction in regulatory costs associated with an additional unit of reserves is the amount of liability out ows one unit of high quality liquid asset osets, ( t S t+1 + t M bt+1 ) in the numerator of the second expression. The derivative with respect to mortgages, M bt+1 , is Mb;t+1 = 2 (! mt M bt+1 +! lt L t+1 )[! mt (S t+1 F t+1 L t+1 ) +! lt L t+1 ] (F t+1 + (1' t ! mt )M bt+1 + (1' t ! lt )L t+1 S t+1 ) 3 2 ( t S t+1 + t M bt+1 )( 1 2 r m t+1 t S t+1 t F t+1 t lt L t+1 ) (F t+1 + lt L t+1 + ( 1 2 r m t+1 t t )M bt+1 t t S t+1 ) 3 The rst term is the net marginal reduction in regulatory costs of one unit of mortgages related to the capital ratio, F t+1 +M bt+1 +L t+1 S t+1 !mtM bt+1 +! lt L t+1 . Increasing mortgages by one unit raises bank equity, (F t+1 +M pt+1 +L t+1 S t+1 ), and enables the bank to raise additional deposits. At the same time, the capital ratio is reduced by ! mt , so the bank needs extra reserves to oset the increase in mortgages, leading to a net decrease of ! mt (S t+1 F t+1 L t+1 ). If the amount of reserves that needs to be raised is greater than the amount of additional deposits that can be raised, S t+1 <F t+1 +L t+1 , additional mortgages eat into the bank's equity and net marginal capital costs increase with additional mortgages. The second term is the net marginal benet from one unit of mortgages in terms of regulatory liquidity costs. For each extra unit of mortgages, the bank can use its net interest revenue to raise additional deposits, 1 2 r m t+1 t S t+1 , which relax constraints placed on borrowing by the liquidity ratio requirement. However, for one extra unit of mortgages, the bank reduces its liquidity ratio by in the denominator of the required ratio, F t+1 + lt L t+1 + 1 2 r m t+1 M bt+1 tS t+1 +tM bt+1 , which it must oset by holding additional reserves equal to t F t+1 . If the amount of high quality liquid assets that must be raised ( t (F t+1 + lt L t+1 )) is greater than the amount deposits generated from interest revenue ( 1 2 r M t+1 t S t+1 ), net marginal liquidity costs increase with 117 additional mortgages. 118 B.2 Nonstochastic Steady State Details B.2.1 Chapter 1: Baseline Model The set of equations describing the steady state when 2 > 0 and M H = P H are: r s = S h ( C + S) 1 (B.1) P = h H C 1 + h ( 1) 1 1+ r m h (B.2) M H = P H (B.3) C = W + D M H r m 1 + r m L r l (1 + r l ) T + S r s 1 + r s P H (B.4) 1 (1 + r s +) b 2 ( S + M B )( F + l L + 1 2 r m M B ) ( F + l L + ( 1 2 r m ) M B S) 3 2 (! m M B +! l L) 2 ( F + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.5) 1 1 + r f + b + 2 ( S + M B ) 2 ( F + l L + ( 1 2 r m ) M B S) 3 + 2 (! m M B +! l L) 2 ( F + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.6) 2 ( S + M)( 1 2 r m S F l L) ( F + l L + ( 1 2 r m ) M B S) 3 + 2 (! m M B +! l L)[! m ( S F L) +! l L] ( F + (1'! m ) M B + (1'! l ) L S) 3 + b h (1)(1 + r m ) + i 1 = 0 (B.7) 119 D = M B + r l L + [ r m (1 + r m )] M B + ( 1 1 + r s + 1) S + ( r f 1 + r f ) F F + M B + L S ! m M B +! l L ' 2 F + l L + 1 2 r m M B S + M B 2 (B.8) T =(1 + r m ) M G + r f F M G (B.9) M G = M H M B (B.10) 120 The set of equations describing the steady state when 2 = 0 and P H > M H are: r s = S h ( C + S) 1 (B.11) P = h H C 1 + h ( 1) (B.12) 1 (1 + r m ) = h (B.13) C = W + D M H r m 1 + r m L r l (1 + r l ) T + S r s 1 + r s P H (B.14) 1 (1 + r s +) b 2 ( S + M B )( F + l L + 1 2 r m M B ) ( F + l L + ( 1 2 r m ) M B S) 3 2 (! m M B +! l L) 2 ( F + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.15) 1 1 + r f + b + 2 ( S + M B ) 2 ( F + l L + ( 1 2 r m ) M B S) 3 + 2 (! m M B +! l L) 2 ( F + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.16) 2 ( S + M)( 1 2 r m S F l L) ( F + l L + ( 1 2 r m ) M B S) 3 + 2 (! m M B +! l L)[! m ( S F L) +! l L] ( F + (1'! m ) M B + (1'! l ) L S) 3 + b (1)(1 + r m ) + P H M H 1 = 0 (B.17) 121 D = M B M H P H + r l L + [ r m (1 + r m )] M B + ( 1 1 + r s + 1) S + ( r f 1 + r f ) F F + M B + L S ! m M B +! l L ' 2 F + l L + 1 2 r m M B S + M B 2 (B.18) T =(1 + r m ) M G + r f F M G M H P H (B.19) M G = M H M B (B.20) 122 B.2.2 Chapter 2: Extended Model with Government Bonds The set of equations describing the steady state when 2 > 0 and M H = P H are: h C S + 1 1 (1 + r s ) = 0 (B.21) h + C 2 1 (1 + r m ) = 0 (B.22) h C B H + 1 1 (1 + r b ) = 0 (B.23) h C H (1 + h h 2 C) P = 0 (B.24) M H P H = 0 (B.25) W + D + M H (1 + r m ) + L (1 + r l ) + S + B H C T S (1 + r s ) M H L P H B H (1 + r b ) = 0 (B.26) 1 (1 + r s + ) b 2 ( S + M B )( F + B B ) ( F + B B M B S) 3 2 (! m M B +! l L) 2 ( F + B B + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.27) b 1 (1 + r f ) + 2 ( S + M B ) 2 ( F + B B M B S) 3 + 2 (! m M B +! l L) 2 ( F + B B + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.28) 123 b 1 (1 + r b ) + 2 ( S + M B ) 2 ( F + B B M B S) 3 + 2 (! m M B +! l L) 2 ( F + B B + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.29) b 1 h (1)(1 + r m ) + P H M H i 2 ( S + M B )( F + B B ) ( F + B B M B S) 3 + 2 (! m M B +! l L)[! m ( S F B B L) +! l L] ( F + B B + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.30) M B + L + S (1 + r s + ) + F + B B S D M B h (1)(1 + r m ) + P H M H i L (1 + r f ) F (1 + r f ) B B (1 + r b ) F + M B + B B + L S ! m M B +! l L ' 2 F + B B + S + M B 2 = 0 (B.31) M G + T + F (1 + r f ) + ( B S B CB ) (1 + r b ) M G h (1)(1 + r m ) + P H M H i F( B S B CB ) = 0 (B.32) M H M B M G = 0 (B.33) F B CB = 0 (B.34) B S B CB B B B H = 0 (B.35) 124 The set of equations describing the steady state when 2 = 0 and P H > M H are: h C S + 1 1 (1 + r s ) = 0 (B.36) h (1)(1 + r m ) + P H M H + C 2 1 (1 + r m ) = 0 (B.37) h C B H + 1 1 (1 + r b ) = 0 (B.38) h C H (1 + h h 2 C) P = 0 (B.39) 2 = 0 (B.40) W + D + M H (1 + r m ) + L (1 + r l ) + S + B H C T S (1 + r s ) M H L P H B H (1 + r b ) = 0 (B.41) 1 (1 + r s + ) b 2 ( S + M B )( F + B B ) ( F + B B M B S) 3 2 (! m M B +! l L) 2 ( F + B B + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.42) b 1 (1 + r f ) + 2 ( S + M B ) 2 ( F + B B M B S) 3 + 2 (! m M B +! l L) 2 ( F + B B + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.43) 125 b 1 (1 + r b ) + 2 ( S + M B ) 2 ( F + B B M B S) 3 + 2 (! m M B +! l L) 2 ( F + B B + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.44) b 1 h (1)(1 + r m ) + P H M H i 2 ( S + M B )( F + B B ) ( F + B B M B S) 3 + 2 (! m M B +! l L)[! m ( S F B B L) +! l L] ( F + B B + (1'! m ) M B + (1'! l ) L S) 3 = 0 (B.45) M B + L + S (1 + r s + ) + F + B B S D M B h (1)(1 + r m ) + P H M H i L (1 + r f ) F (1 + r f ) B B (1 + r b ) F + M B + B B + L S ! m M B +! l L ' 2 F + B B + S + M B 2 = 0 (B.46) M G + T + F (1 + r f ) + ( B S B CB ) (1 + r b ) M G h (1)(1 + r m ) + P H M H i F( B S B CB ) = 0 (B.47) M H M B M G = 0 (B.48) F B CB = 0 (B.49) B S B CB B B B H = 0 (B.50) 126 Appendix C Calibration C.1 Full Results and Robustness Checks Table C.1 presents the full set of parameters obtained from the baseline calibration exercise. Analyzing the changes in parameters from pre- to post-crisis sheds light on the dierent forces in uencing the bank and household portfolio choices. Beginning with regulatory changes, in the rst row, the required liquidity coverage ratio, , rose from 67 percent to 100 percent. The out ow rate assigned to deposits, , also increased, from around 9 to 13 percent, incentivizing the bank to reduce deposit liabilities and or raise holding of liquid assets. Required Tier 1 ratios rose form 4 to 6 percent. At the same time, risk weights attached to mortgages for the Tier 1 ratio, ! m , fell slightly, as did the perceived costs of capital shortfalls, . Nevertheless, actual bank LCR and Tier 1 ratios rose to 111 percent and 13 percent. The combined changes in regulatory rules encourage the bank to hold more reserves, reduce mortgage lending, and cut deposit funding. Indeed, leverage falls, from 9.74 to 8.63 times equity. To reduce average leverage from 9.7 to around 8.6, the bank cuts the ratio of deposits to total assets by around two percent, decreases the share of mortgages by seven percent, and doubles the share of assets allocated to cash (see rows two through four in the Key Ratios columns of the middle panel of Table C.1). Second, by doubling the ratio of reserves to deposits, F/S, the bank boosts its cash and regulatory ratios in the post-crisis period. This occurs even though interest rates on reserves, r f , drop to zero. On the household side, re ecting the increase in house price, P, demand for houses increases in the post-crisis period. To understand the movement of house preferences, , the 127 change in interest rates on mortgages, r m , must be taken into account. Given the increase in government supply of mortgages post-crisis, r m falls from 6.7 percent to 4.4 percent (see row six in the middle panel of Table C.1). The drop in cost of mortgage loans for households raises the values of borrowed funds today, 1 (1+r m ) , from 0.938 to 0.958. The current value of a dollar the household must repay tomorrow is 1 h , 0.935 in both periods. Because the borrowed funds are worth even more in today's terms than the amount households must repay tomorrow in the post-crisis period (at 0.023 versus 0.003), household demand for borrowing. The large magnitude of changes in the incentives to obtain mortgages are enough to account for the rise in P, so housing preferences, , remain relatively stable over both periods (see row six of Table C.1). To match the growth in deposits levels and fall in interest rates on deposits towards zero percent post-crisis, household demand for deposits rises. The weight of deposits in utility, , rises from 0.178 pre-crisis to 0.294 post-crisis, translating into more savings supplied by the household to the bank. With greater supply, the interest rate on deposits,r s fall. Household consumption, C, falls as a result of the shift towards more housing and savings. Combining the changes in the household portfolio with those of the bank, I can characterize the housing market. With the decline in the interest rate paid on deposits,r s , from about 1.9 to 0.2 percent, the bank enjoys a signicant reduction in the cost of funds in the later period. At the same time, the reduction in return on mortgages dampens the banks willingness to increase supply, leaving mortgages, M B , slightly lower post-crisis. Lower interest rates, coupled with higher house prices, enables households to borrow more with the higher value of the house (see M H , total household demand for mortgages, and the value of the house, PH, in the last two rows of Table C.1). Thus, even though the bank reduces its exposure to mortgages relative to other assets on the balance sheet in response to regulatory rules, the lower interest rate environment and stronger housing demand allows households to increase their mortgage borrowing. Table C.2 presents the full set of model parameters obtained when crisis years (2007 128 through 2009) are removed from the data. In contrast to the baseline case, the housing preference shock, , increases post-crisis, because the growth in housing prices is much larger, from 106 to 123. Growth in household demand for deposits, , is also a bit larger. All other parameters are roughly unchanged. The changes translate into an increase in the bank's supply of mortgages and stronger deposit growth in levels. This suggests that the rise in household demand for deposits is not solely driven by the years surrounding the Great Recession, but is a general trend in the post-crisis years. Table C.3 highlights that removing required reserves from the denition of cash on bank balance sheets has minimal aect on the baseline calibration results. However, removing required reserves from cash addresses the problem of using the Fed funds rate as the interest rate on reserves for both pre- and post-crisis periods. Having both required and excess reserves included in cash, dierential rates need to be applied to cash holdings, depending on the portion allocated to required or excess reserves. From pre- to post-crisis, the return on required reserves needs to jump from zero to less than one percent, while the return on excess reserves would jump from the Fed funds rate to the interest rate paid on excess reserves. With cash in the model, F , dened as cash and due from depository institutions, less required reserves, the Fed funds rate can be used as the uniform return on cash. For the pre-crisis period, before the Fed began paying interest on reserves, banks with excess reserves would lend the funds out in the overnight interbank market, receiving the Fed funds rate. In the post-crisis period, the Fed funds rate serves as a oor for the interest rate on excess reserves (IOER), so using the Fed funds rate as the return on reserves provides a lower bound for interest earned on excess reserves. Table C.4 considers how changes in average household income aect household preference parameter estimates. In the original calibration, household income was held at at $86,000 for both periods. From the 2017 US Census, Table H.6, average real household income in terms of 2017 CPI-U-RS adjusted dollars, fell about one percent from pre ($79,992) to post-crisis ($78,599). Median real income also dropped a bit, averaging $58,577 from 2000 129 to 2007 and $56,377 from 2009 to 2016. On the other hand, nominal incomes rose over the two periods. Given that all values in the model are nominal, I recalibrate the model to have W, average household income, increased from $61,281 from 2000 to 2007 to $73,589 from 2009 to 2016. Due to the growth in income, household consumption levels rise in the post-crisis period relative to the baseline in Table C.1. Demand for housing is also stronger with more income, which reduces the size of the house preference shock, , in the second period required to match the rise in house prices. Otherwise, bank balance sheet dynamics and other changes mirror the baseline case. 130 Table C.1: Full Model Calibration Results Pre-crisis (2000-2007) Post-crisis (2009-2016) Parameter Key Ratios Parameter Key Ratios 0.674 LCR 0.83 1.000 LCR 1.11 0.085 0.125 0.705 0.705 ! m 1.083 Tier 1 0.10 ! m 1.057 Tier 1 0.13 2.264 1.479 0.336 leverage 9.74 0.331 leverage 8.63 0.178 0.294 b 0.886 ROE 1.13 b 0.932 ROE 1.07 S 239,240 S (F +M B +L) 0.90 S 285,316 S (F +M B +L) 0.88 r s 0.019 r s 0.002 F 13,144 F/S 0.05 F 33,586 F/S 0.12 r f 0.034 cash ratio 0.05 r f 0.002 cash ratio 0.10 M B 101,478 M B (F +M B +L) 0.38 M B 99,140 M B (F +M B +L) 0.31 r m 0.067 1 (1+r m ) 0.938 r m 0.044 1 (1+r m ) 0.958 h 0.935 h 0.935 P 109 P 121 C 66,982 C 65,144 H 2,377 H 2,550 T 718 T 397 D 4,879 D 3,883 M H 206,478 M H 247,140 PH 258,097 PH 308,925 131 Table C.2: Full Model Calibration Results, Removing Crisis Years from Data Pre-crisis (2000-2006) Post-crisis (2010-2016) Parameter Key Ratios Parameter Key Ratios 0.676 LCR 0.83 1.000 LCR 1.11 0.088 0.130 0.731 0.731 ! m 1.052 Tier 1 0.10 ! m 1.028 Tier 1 0.13 2.411 2.129 0.326 leverage 9.85 0.344 leverage 8.60 0.179 0.306 b 0.881 ROE 1.14 b 0.923 ROE 1.08 S 234,253 S (F +M B +L) 0.90 S 290,697 S (F +M B +L) 0.88 r s 0.017 r s 0.001 F 13,146 F/S 0.06 F 35,302 F/S 0.12 r f 0.032 cash ratio 0.05 r f 0.002 cash ratio 0.11 M B 95,569 M B (F +M B +L) 0.37 M B 103,663 M B (F +M B +L) 0.32 r m 0.067 1 (1+r m ) 0.938 r m 0.045 1 (1+r m ) 0.957 h 0.935 h 0.935 P 106 P 123 C 67,131 C 64,726 H 2,356 H 2,566 T 688 T 402 D 4,744 D 3,924 M H 200,569 M H 251,663 PH 250,711 PH 314,579 132 Table C.3: Full Model Calibration Results, Required Reserves Removed from Cash Pre-crisis (2000-2007) Post-crisis (2009-2016) Parameter Key Ratios Parameter Key Ratios 0.673 LCR 0.83 1.000 LCR 1.11 0.078 0.116 0.634 0.634 ! m 1.069 Tier 1 0.10 ! m 1.032 Tier 1 0.13 2.221 1.457 0.335 leverage 9.74 0.327 leverage 8.63 0.174 0.284 b 0.886 ROE 1.13 b 0.932 ROE 1.07 S 234,287 S (F +M B +L) 0.90 S 278,012 S (F +M B +L) 0.88 r s 0.019 r s 0.002 F 11,624 F/S 0.05 F 30,324 F/S 0.11 r f 0.034 cash ratio 0.04 r f 0.002 cash ratio 0.10 M B 101,478 M B (F +M B +L) 0.39 M B 99,140 M B (F +M B +L) 0.32 r m 0.066 1 (1+r m ) 0.938 r m 0.043 1 (1+r m ) 0.958 h 0.935 h 0.935 P 109 P 121 C 67,148 C 65,411 H 2,377 H 2,550 T 666 T 391 D 4,794 D 3,836 M H 206,478 M H 247,140 PH 258,097 PH 308,925 133 Table C.4: Full Model Calibration Results, Changing Average Household Income Pre-crisis (2000-2007) Post-crisis (2009-2016) Parameter Key Ratios Parameter Key Ratios 0.674 LCR 0.83 1.000 LCR 1.11 0.085 0.125 0.705 0.705 ! m 1.083 Tier 1 0.10 ! m 1.057 Tier 1 0.13 2.264 1.479 0.533 leverage 9.74 0.409 leverage 8.63 0.283 0.367 b 0.886 ROE 1.13 b 0.932 ROE 1.07 S 239,240 S (F +M B +L) 0.90 S 285,316 S (F +M B +L) 0.88 r s 0.019 r s 0.002 F 13,144 F/S 0.05 F 33,586 F/S 0.12 r f 0.034 cash ratio 0.05 r f 0.002 cash ratio 0.10 M B 101,478 M B (F +M B +L) 0.38 M B 99,140 M B (F +M B +L) 0.31 r m 0.067 1 (1+r m ) 0.938 r m 0.044 1 (1+r m ) 0.958 h 0.935 h 0.935 P 109 P 121 C 42,263 C 52,733 H 2,377 H 2,550 T 718 T 397 D 4,879 D 3,883 M H 206,478 M H 247,140 PH 258,097 PH 308,925 134 Appendix D Counterfactual Details D.1 For Chapter 1 Table D.1 summarizes the dierent parameter values used to obtain solutions for the counter- factual exercises. Values in bold indicate parameters that were unchanged from their values pre-crisis when solving the model. D.2 For Chapter 2 Table D.2 summarizes the dierent parameter values used in the solutions for the counter- factual exercises analyzing dierent factors in isolation. Values in bold indicate parameters that were changed from their values in 2011q2 to their values in 2014q4 when solving the model. Table D.3 summarizes the dierent parameter values used in the solutions for the counter- factual exercises analyzing interactions between factors. Values in bold indicate parameters that were changed from their values in 2011q2 to their values in 2014q4 when solving the model. 135 Table D.1: Parameter Inputs for Counterfactual Scenarios Actuals Counterfactuals Pre-crisis Post-crisis No interest No HH No reg. No gov. (2000-2007) (2009-2016) rate decline pref. changes ratio hikes subsidy rise 0.178 0.294 0.294 0.178 0.294 0.294 0.336 0.331 0.331 0.336 0.331 0.331 b 0.886 0.932 0.932 0.932 0.932 0.932 h 0.935 0.935 0.935 0.935 0.935 0.935 0.010 0.010 0.010 0.010 0.010 0.010 0.800 0.800 0.800 0.800 0.800 0.800 ! m 1.083 1.057 1.057 1.057 1.057 1.057 ! l 1.000 1.000 1.000 1.000 1.000 1.000 0.020 0.020 0.020 0.020 0.020 0.020 0.650 0.650 0.650 0.650 0.650 0.650 l 0.013 0.028 0.028 0.028 0.028 0.028 ' 0.040 0.060 0.060 0.060 0.040 0.060 2.264 1.479 1.479 1.479 1.479 1.479 0.674 1.000 1.000 1.000 0.674 1.000 0.705 0.705 0.705 0.705 0.705 0.705 0.085 0.125 0.125 0.125 0.125 0.125 0.018 0.016 0.016 0.016 0.016 0.016 0.032 0.029 0.029 0.029 0.029 0.029 r f 0.034 0.002 0.034 0.002 0.002 0.002 r l 0.067 0.045 0.045 0.045 0.045 0.045 M G 105,000 148,000 148,000 148,000 148,000 105,000 L 152,000 190,000 190,000 190,000 190,000 190,000 W 86,000 86,000 86,000 86,000 86,000 86,000 H 2,377 2,550 2,550 2,550 2,550 2,550 136 Table D.2: Parameter Inputs for Counterfactual Scenarios in Part One Actuals Counterfactuals 2011q2 2014q4 QE3 eect Regulatory eect HH preferences 0.2215 0.2935 0.2215 0.2215 0.2935 0.0145 0.0168 0.0145 0.0145 0.0168 0.2496 0.3141 0.2496 0.2496 0.3141 0.1026 0.1347 0.1026 0.1347 0.1026 ! m 1.0660 1.1318 1.0660 1.1318 1.0660 b 0.9297 0.9165 0.9297 0.9297 0.9297 0.4868 0.8277 0.4868 0.8277 0.4868 1.6235 3.0311 1.6235 3.0311 1.6235 0.3460 0.4080 0.3460 0.4080 0.3460 h 0.9350 0.9350 0.9350 0.9350 0.9350 0.0100 0.0100 0.0100 0.0100 0.0100 0.8000 0.8000 0.8000 0.8000 0.8000 0.0200 0.0200 0.0200 0.0200 0.0200 0.6500 0.6500 0.6500 0.6500 0.6500 ! l 1.0000 1.0000 1.0000 1.0000 1.0000 ' 0.0600 0.0600 0.0600 0.0600 0.0600 1.0000 1.0000 1.0000 1.0000 1.0000 0.0149 0.0172 0.0149 0.0149 0.0149 0.0296 0.0272 0.0296 0.0296 0.0296 r f 0.0025 0.0025 0.0025 0.0025 0.0025 r l 0.0495 0.0390 0.0495 0.0495 0.0495 B CB 28,092 49,965 42,760 42,760 42,760 M G 126,898 187,916 126,898 126,898 126,898 L 160,000 228,000 160,000 160,000 160,000 W 88,000 100,000 88,000 88,000 88,000 H 2,480 2,657 2,480 2,480 2,480 137 Table D.3: Parameter Inputs for Counterfactual Scenarios in Part Two QE3 QE3 QE3 QE3 QE3 eect + capital + LCR + + liquidity 0.2215 0.2215 0.2215 0.2215 0.2935 0.0145 0.0145 0.0145 0.0145 0.0168 0.2496 0.2496 0.2496 0.3141 0.2496 0.1026 0.1026 0.1347 0.1026 0.1026 ! m 1.0660 1.1318 1.0660 1.0660 1.0660 b 0.9297 0.9297 0.9297 0.9297 0.9297 0.4868 0.4868 0.8277 0.4868 0.4868 1.6235 3.0311 1.6235 1.6235 1.6235 0.3460 0.3460 0.4080 0.3460 0.3460 h 0.9350 0.9350 0.9350 0.9350 0.9350 0.0100 0.0100 0.0100 0.0100 0.0100 0.8000 0.8000 0.8000 0.8000 0.8000 0.0200 0.0200 0.0200 0.0200 0.0200 0.6500 0.6500 0.6500 0.6500 0.6500 ! l 1.0000 1.0000 1.0000 1.0000 1.0000 ' 0.0600 0.0600 0.0600 0.0600 0.0600 1.0000 1.0000 1.0000 1.0000 1.0000 0.0149 0.0149 0.0149 0.0149 0.0149 0.0296 0.0296 0.0296 0.0296 0.0296 r f 0.0025 0.0025 0.0025 0.0025 0.0025 r l 0.0495 0.0495 0.0495 0.0495 0.0495 B CB 42,760 42,760 42,760 42,760 42,760 M G 126,898 126,898 126,898 126,898 126,898 L 160,000 160,000 160,000 160,000 160,000 W 88,000 88,000 88,000 88,000 88,000 H 2,480 2,480 2,480 2,480 2,480 138 Appendix E Comparative Statics Details E.1 Balance Sheet Changes for Each Parameter E.1.1 Required Capital Ratio (') As Table E.1 highlights, increasing the required capital ratio primarily shifts the liability structure of the bank towards more equity and less deposit funding. Asset composition is roughly unchanged, with cash constituting 5 percent of assets and mortgages at 38 percent even though total assets shrink. Due to the reduction in deposit shares, the LCR also grows together with the required capital ratio, leading the LCR buer to rise slightly from 16 percent to 17 percent. Of note, the capital buer does not change as the required capital ratio increases. Table E.1: Balance Sheet Response to Changing ' ' Capital Capital Equity LCR LCR S (TA) F (TA) M (TA) Total Ratio Buer Ratio Buer Assets (TA) 0.04 0.10 0.06 0.10 0.83 0.16 0.90 0.05 0.38 266,622 0.05 0.11 0.06 0.11 0.83 0.16 0.89 0.05 0.38 266,339 0.06 0.12 0.06 0.12 0.84 0.16 0.88 0.05 0.38 266,056 0.07 0.13 0.06 0.13 0.84 0.16 0.87 0.05 0.38 265,775 0.08 0.14 0.06 0.14 0.84 0.17 0.86 0.05 0.38 265,494 0.09 0.15 0.06 0.15 0.84 0.17 0.85 0.05 0.38 265,214 0.10 0.16 0.06 0.16 0.85 0.17 0.84 0.05 0.38 264,936 139 Table E.2: Balance Sheet Response to Changing Capital Capital Equity LCR LCR S (TA) F (TA) M (TA) Total Ratio Buer Ratio Buer Assets (TA) 1.45 0.096 0.056 0.094 0.828 0.154 0.906 0.05 0.38 267,094 1.55 0.097 0.057 0.095 0.828 0.154 0.905 0.05 0.38 267,027 1.65 0.098 0.058 0.096 0.828 0.155 0.904 0.05 0.38 266,964 1.75 0.099 0.059 0.098 0.829 0.155 0.902 0.05 0.38 266,903 1.85 0.100 0.060 0.099 0.829 0.155 0.901 0.05 0.38 266,844 1.95 0.101 0.061 0.100 0.829 0.156 0.900 0.05 0.38 266,788 2.05 0.102 0.062 0.101 0.829 0.156 0.899 0.05 0.38 266,733 2.15 0.103 0.063 0.102 0.830 0.156 0.898 0.05 0.38 266,680 2.25 0.104 0.064 0.103 0.830 0.156 0.897 0.05 0.38 266,629 E.1.2 Cost of Capital Shortfall () Increasing the cost of a capital shortfall creates similar adjustments to the bank balance sheet as changing the required capital ratio, albeit at more muted levels. Table E.2 shows how there are small reductions in the share of deposits in total assets, and small increases in the capital ratio, equity, LCR, capital and LCR buers. In model calibration, mainly controls the size of the capital buer, which has indirect eects on the LCR and LCR buer as well. E.1.3 Required Liquidity Coverage Ratio ( ) Increasing the required LCR primarily changes the composition of total assets. As columns seven through eight of Table E.3 show, the share of cash in total assets rises to about 8 percent while the share of mortgages falls from 38 to 36 percent as we increase the required LCR from 65 to 100 percent. The capital ratio and capital buer change only slightly, while leverage subtly rises as the LCR reaches 100 percent. The LCR buer also falls slightly, but is not as noticable compared to the large reduction in mortgage share. 140 Table E.3: Balance Sheet Response to Changing Capital Capital Leverage LCR LCR S (TA) F (TA) M (TA) Total Ratio Buer Buer Assets (TA) 0.65 0.10 0.06 9.72 0.81 0.16 0.897 0.05 0.38 266,324 0.70 0.10 0.06 9.75 0.86 0.16 0.897 0.05 0.38 266,952 0.75 0.10 0.06 9.79 0.91 0.16 0.898 0.06 0.38 267,583 0.80 0.10 0.06 9.82 0.95 0.15 0.898 0.06 0.37 268,216 0.85 0.10 0.06 9.85 1.00 0.15 0.899 0.06 0.37 268,852 0.90 0.11 0.07 9.89 1.05 0.15 0.899 0.07 0.37 269,491 0.95 0.11 0.07 9.92 1.10 0.15 0.899 0.07 0.37 270,132 1.00 0.11 0.07 9.95 1.15 0.15 0.900 0.08 0.36 270,776 Table E.4: Balance Sheet Response to Changing Capital Capital Leverage LCR LCR S (TA) F (TA) M (TA) Total Ratio Buer Buer Assets (TA) 0.50 0.10 0.06 9.73 0.81 0.14 0.90 0.05 0.38 266,418 0.60 0.10 0.06 9.73 0.82 0.15 0.90 0.05 0.38 266,523 0.70 0.10 0.06 9.74 0.83 0.16 0.90 0.05 0.38 266,617 0.80 0.10 0.06 9.74 0.84 0.16 0.90 0.05 0.38 266,702 0.90 0.10 0.06 9.75 0.84 0.17 0.90 0.05 0.38 266,780 E.1.4 Costs of LCR Shortfall () Increasing the cost of LCR shortfalls primarily increases the LCR bufer and LCR ratio. As Table E.4 highlights, capital ratios and balance sheet compositions do not change in response to larger values of . E.1.5 Interest on Reserves (r f ) As the interest rate on reserves rises, the share of cash in total assets gradually rises, given the higher yield. Comparing the columns of Table E.5, the capital ratio and capital buer are relatively unchanged, with the share of deposits in total assets growing very slightly. The most signicant changes are in leverage and the LCR. Capital ratios remain fairly stable because mortgages, a risk-weighted asset, are increasing along with reserves in total assets. 141 Table E.5: Balance Sheet Response to Changing r f r f Capital Capital Leverage LCR LCR S (TA) F (TA) M (TA) Total Ratio Buer Buer Assets (TA) 0.005 0.11 0.07 9.64 0.79 0.11 0.896 0.045 0.379 264,083 0.010 0.11 0.07 9.66 0.79 0.12 0.896 0.046 0.380 264,463 0.015 0.10 0.06 9.67 0.79 0.12 0.897 0.046 0.380 264,855 0.020 0.10 0.06 9.69 0.80 0.13 0.897 0.047 0.380 265,265 0.025 0.10 0.06 9.70 0.81 0.14 0.897 0.047 0.380 265,698 0.030 0.10 0.06 9.72 0.82 0.14 0.897 0.048 0.381 266,168 0.035 0.10 0.06 9.74 0.83 0.16 0.897 0.049 0.381 266,697 0.040 0.10 0.06 9.77 0.85 0.18 0.898 0.051 0.380 267,339 Meanwhile, both reserves and mortgages both add to liquid assets so the LCR rises. Table E.6 sheds light on the increase in leverage. Starting from reserves, F, higher r f means more attractive yields for the bank, so demand is greater. To pay for the interest on reserves, the central bank must raise taxes, T, which causes household consumption, C, to fall. Higher taxes also somewhat reduces household savings supplied to the bank, evidenced by slow rise in interest paid on savings, r s . The bank gathers more deposits to fund its reserves growth and additional investment in mortgage lending, M, given the spread of mortgage rates, r m , over the cost of deposits, r s , is still large relative to the interest rate spread earned on reserves. Because the supply of mortgages from the bank is higher than the demand for mortgages by households, r m is declining as r f increases, leading to a slight uptake in demand for housing by households re ected in P. Expansion of the bank's balance sheet driven by slightly faster growth in deposits than reserves or mortgages, so leverage rises a bit. E.1.6 Housing Preference ( ) The parameter governs the strength of household's demand for houses, which is re ected in the price of houses and demand for mortgage loans. As the rst two columns of Table E.7 142 Table E.6: Balance Sheet Response to Changing r f (cont.) r f C S M b F T P r s r m Leverage TA 0.005 67,013 236,696 100,125 11,958 327 108 0.018 0.0674 9.64 264,083 0.010 67,010 237,076 100,379 12,084 388 108 0.018 0.0672 9.66 264,463 0.015 67,007 237,469 100,627 12,228 451 108 0.018 0.0671 9.67 264,855 0.020 67,002 237,879 100,867 12,397 515 108 0.018 0.0670 9.69 265,265 0.025 66,997 238,313 101,097 12,601 582 108 0.018 0.0668 9.70 265,698 0.030 66,990 238,784 101,312 12,856 653 109 0.019 0.0667 9.72 266,168 0.035 66,980 239,316 101,501 13,197 729 109 0.019 0.0666 9.74 266,697 0.040 66,967 239,962 101,641 13,697 815 109 0.019 0.0665 9.77 267,339 Table E.7: Balance Sheet Response to Changing Capital Capital Leverage LCR LCR S (TA) F (TA) M (TA) Total Ratio Buer Buer Assets (TA) 0.33 0.10 0.06 9.74 0.83 0.16 0.897 0.050 0.375 264,103 0.34 0.10 0.06 9.73 0.83 0.16 0.897 0.049 0.384 268,018 0.35 0.10 0.06 9.73 0.83 0.15 0.897 0.049 0.392 271,909 0.36 0.10 0.06 9.72 0.82 0.15 0.897 0.048 0.401 275,776 0.37 0.10 0.06 9.72 0.82 0.15 0.897 0.048 0.409 279,619 0.38 0.10 0.06 9.70 0.82 0.14 0.897 0.047 0.413 281,542 0.39 0.10 0.06 9.65 0.81 0.14 0.896 0.047 0.415 282,174 143 demonstrate, increased demand for houses does not in uence capital ratios much. On the other hand, leverage and LCR ratios move considerably, all falling as increases. Shifts in the asset composition of the balance sheet explain the declines in LCR and leverage. As total assets increase, the share of mortgages grows at a much faster pace than reductions in the share of deposits and share of reserves. Since assets are expanding quickly and deposits are shrinking somewhat, equity rises and the leverage ratio falls. Because mortgages contribute to the out ows that banks must hold liquid assets to cover and reducing reserves shrinks liquid assets, the denominator of the LCR grows and the numerator shrinks as increases, lowering the LCR ratio. E.1.7 Weight of Deposits in Household Utility () As the weight of deposits in the utility function increases, the household values savings more and increases deposit balances even while receiving minimal interest,r s (see Table E.8). Because the bank can pay less on deposits, its cost of funds fall and the bank oers more mortgages to take advantage of the growing spread between return on mortgages,r m , and the interest paid on deposits,r s . While increasing mortgages, the bank also increases reserves, F, which drives up taxes, T, and reduces household consumption, C. The reduced consumption somewhat dampens household demand for houses, but the rapid growth in supply lowersr m , so demand for houses still increases on net, re ected in the rising P. Of note, the growth in mortgages stalls and reverses after passes 0.295. To understand the behavior of mortgages, changes in key balance sheet ratios must be taken into account. The rst three columns of Table E.9 illustrate that as the share of deposits and mortgages increases, the capital ratio falls and leverage rises. However, the bank still maintains its capital buer above 5.8 percent as climbs from 0.175 to 0.275. Once the capital buer falls below 5.8 percent, at of 0.295, the bank cuts back on mortgage growth (see column eight) and begins to rebuild its capital. For levels of deposit demand beyond 0.295, the bank dramatically increases the level and share of reserves in total assets 144 Table E.8: Balance Sheet Response to Changing C S M b F T P r s r m 0.175 67,004 238,035 100,367 13,007 714 108 0.019 0.0672 0.195 66,867 245,085 106,838 13,846 739 111 0.015 0.0635 0.215 66,712 252,198 113,270 14,813 768 115 0.012 0.0599 0.235 66,538 259,423 119,611 16,000 806 118 0.009 0.0566 0.255 66,342 266,904 125,735 17,665 860 121 0.006 0.0535 0.275 66,108 275,280 131,120 20,934 969 124 0.003 0.0509 0.295 65,736 287,986 132,967 31,863 1,343 125 0.002 0.0496 0.315 65,243 304,619 131,485 49,843 1,960 124 0.002 0.0495 0.335 64,745 321,410 129,690 68,276 2,593 123 0.002 0.0495 Table E.9: Balance Sheet Response to Changing (cont.) Capital Capital Leverage LCR LCR S (TA) F TA) M (TA) Total Ratio Buer Buer Assets (TA) 0.175 0.105 0.065 9.71 0.83 0.15 0.90 0.049 0.378 265,374 0.195 0.103 0.063 9.88 0.84 0.17 0.90 0.051 0.392 272,684 0.215 0.102 0.062 10.04 0.85 0.18 0.90 0.053 0.404 280,083 0.235 0.100 0.060 10.20 0.88 0.20 0.90 0.056 0.416 287,611 0.255 0.099 0.059 10.37 0.92 0.24 0.90 0.060 0.426 295,400 0.275 0.098 0.058 10.57 1.01 0.34 0.91 0.069 0.431 304,055 0.295 0.097 0.057 10.98 1.37 0.70 0.91 0.101 0.420 316,829 0.315 0.098 0.058 11.61 1.94 1.26 0.91 0.150 0.394 333,328 0.335 0.098 0.058 12.26 2.46 1.79 0.92 0.195 0.371 349,965 accompanying deposit growth. Thus, the capital buer is a binding constraint on mortgage growth and in uences the reallocation of assets on the bank's balance sheet. E.1.8 Government Mortgage Supply (M G ) As government supply of mortgages increases, the interest rate on mortgages, r m , falls, as does the supply of mortgages provided by banks (see columns r m andM b in Table E.10). With lower interest rate on mortgages, household demand for mortgages increases, which is re ected in the growing price of houses, P. The interest rate on deposits, r s , drops as the bank seeks less funding for mortgage loans and shrinks its balance sheet (see column S in 145 Table E.10: Balance Sheet Response to Changing M G M G C S M b F T P r s r m 105,000 66,982 239,240 101,478 13,144 718 109 0.019 0.067 110,000 66,807 235,214 97,103 13,040 726 109 0.018 0.066 115,000 66,638 231,241 92,784 12,938 735 109 0.017 0.065 120,000 66,475 227,323 88,521 12,840 743 110 0.016 0.065 125,000 66,316 223,463 84,318 12,746 752 110 0.016 0.064 130,000 66,164 219,664 80,174 12,657 760 111 0.015 0.063 135,000 66,017 215,926 76,094 12,573 769 111 0.014 0.062 140,000 65,876 212,253 72,077 12,496 778 112 0.013 0.062 145,000 65,742 208,648 68,125 12,426 787 112 0.013 0.061 150,000 65,613 205,112 64,240 12,366 796 113 0.012 0.060 Table E.11: Balance Sheet Response to Changing M G (cont.) M G Capital Capital Leverage LCR LCR S (TA) F (TA) M (TA) Total Ratio Buer Buer Assets (TA) 105,000 0.10 0.06 9.74 0.83 0.16 0.90 0.049 0.381 266,622 110,000 0.10 0.06 9.73 0.83 0.16 0.90 0.050 0.370 262,143 115,000 0.10 0.06 9.73 0.84 0.16 0.90 0.050 0.360 257,722 120,000 0.11 0.07 9.73 0.84 0.17 0.90 0.051 0.349 253,362 125,000 0.11 0.07 9.73 0.84 0.17 0.90 0.051 0.339 249,064 130,000 0.11 0.07 9.73 0.85 0.18 0.90 0.052 0.327 244,831 135,000 0.11 0.07 9.73 0.85 0.18 0.90 0.052 0.316 240,667 140,000 0.11 0.07 9.73 0.86 0.18 0.90 0.053 0.305 236,572 145,000 0.11 0.07 9.73 0.86 0.19 0.90 0.053 0.293 232,551 150,000 0.11 0.07 9.73 0.87 0.20 0.90 0.054 0.281 228,606 Table E.10 and the last column of Table E.11). Turning to Table E.11, in terms of ratios, capital is mostly unchanged, while leverage and LCR ratios rise. The increase in LCR is driven by the increasing share of reserves in total assets (raising the LCR numerator) coupled with the rapid decline in mortgage share (driving the LCR denominator down). The decline deposits slightly outpaces the decline in total assets, so leverage falls somewhat. 146 Table E.12: Balance Sheet Response to Changing W W C S M b F T P r s r m 86,000 66,982 239,240 101,478 13,144 718 109 0.019 0.067 90,000 70,399 250,001 112,676 13,685 736 114 0.018 0.066 94,000 73,813 260,769 123,874 14,226 754 120 0.018 0.066 98,000 77,225 271,544 135,073 14,768 773 126 0.018 0.066 102,000 80,634 282,324 146,271 15,309 791 132 0.018 0.065 106,000 84,041 293,111 157,470 15,851 809 138 0.017 0.065 Table E.13: Balance Sheet Response to Changing W (cont.) W Capital Capital Leverage LCR LCR S (TA) F (TA) M (TA) Total Ratio Buer Buer Assets (TA) 86,000 0.105 0.065 9.74 0.83 0.16 0.897 0.049 0.381 266,622 90,000 0.103 0.063 9.82 0.83 0.15 0.898 0.049 0.405 278,361 94,000 0.103 0.063 9.89 0.83 0.15 0.899 0.049 0.427 290,100 98,000 0.102 0.062 9.96 0.83 0.15 0.900 0.049 0.447 301,840 102,000 0.101 0.061 10.03 0.82 0.15 0.900 0.049 0.466 313,581 106,000 0.100 0.060 10.10 0.82 0.15 0.901 0.049 0.484 325,321 E.1.9 Average Household Income (W) When average household income rises, consumption, C, savings, S, and demand for housing increases. Table E.12, shows how the growth in deposits leads to a decline in the interest rate paid on deposits, r s , which lowers rates charged on mortgage loans, r m , even as mortgage demand is high (re ected in the higher house prices, P). With the extra supply of deposits and greater demand for houses from households, the bank is able to invest in more mortgages, M b , and reserves, F. Taxes on households, T, increase to fund reserves, but the higher taxes do not translate into less consumption because incomes are growing. Table E.13 highlights that as household income grows, the bank balance sheet expands and leverage rises. The LCR is fairly stable, as is the LCR buer, but capital ratios fall because the share of deposits in total assets is growing while the share of reserves stays relatively at and the share of mortgages (which have a higher risk weight) is rapidly increasing. 147 Appendix F Demand for Deposits: Alternative Specications and Robustness Checks F.1 The Fed Funds Rate Dierential, In ation, and Specication Tests. Given the concentrated nature of the US banking industry, where the top ve institutions by size make up roughly half of total sector assets, the ability of banks to set interest rate on deposits is an important factor to consider. Dreschler, Savov, and Schnabl (2017) argue that banks choose deposit rates in response to movements in the fed funds rate to aect the spread, essentially controlling the cost of liquidity for households. In their model, as in mine, households have preferences for liquidity, so demand for deposits responds readily to changes in the liquidity premium. Since I am interested in measuring the shift in demand for deposits, I want to isolate the component of deposit rates driven by supply factors to better measure the demand curve. Table F.1 summarizes results from a specication that considers the in uence of banks over the fed funds spread. Column (1) is the baseline model. The estimated equation modies equation (16) by adding one lag ofy it and replacing (r t own it ) with \ Own rate. The \ Own rate is obtained by regressing deposit rates on the spread between the fed funds rate and deposit rate. I do this to capture the variation in deposit rates that is related to bank's funding costs, to try and control for the portion of deposit rates that may be determined by rate setting bank branches. At the same time, I limit the instrument count to run overidentication 148 Table F.1: Arellano-Bond Estimation of Deposit Demand, Modied Instruments (2000-2015) Dependent variable: lnM =ln(deposits) it ln(gdp de ator) it (1) (2) (3) (4) lnM t1 0.473 (0.0296) -0.003 (0.0554) 0.112 (0.1041) 0.378 (0.0652) t 2 0.107 (0.0915) t 3 -0.014 (0.0552) t 4 -0.057 (0.0874) lnY 0.081 (0.0125) 0.168 (0.0792) 0.095 (0.0715) -0.143 + (0.0758) t 1 0.052 (0.0112) 0.101 (0.0149) 0.087 (0.0194) 0.349 (0.0642) t 2 0.059 (0.0098) 0.039 (0.0177) t 3 0.047 (0.0115) 0.028 (0.0227) t 4 0.027 (0.0583) 0.045 (0.0565) lnW 0.172 (0.0111) -0.119 (0.0600) -0.032 (0.0902) 0.033 (0.0485) t 1 0.232 (0.0456) 0.152 (0.0758) 0.085 + (0.0439) In ation -0.007 (0.0003) -0.010 (0.0013) -0.010 (0.0017) -0.010 (0.0010) t 1 -0.003 (0.0006) -0.004 (0.0011) -0.001 (0.0005) 10yr Tres -0.010 (0.0009) -0.010 (0.0012) -0.010 (0.0019) -0.009 (0.0011) t 1 -0.003 (0.0016) -0.004 (0.0021) -0.000 (0.0014) \ Own rate 0.002 + (0.0009) 0.006 (0.0016) 0.008 (0.0020) 0.008 (0.0026) t 1 -0.005 (0.0015) -0.003 (0.0030) -0.009 (0.0023) Post-2008 0.041 (0.0032) 0.032 (0.0044) 0.035 (0.0086) 0.023 (0.0052) N 22,074 17,319 17,319 18,565 N Instruments 97 27 41 33 Arellano-Bond Test for zero autocorrelation in rst-dierenced errors (H 0 :E( it ; it2 ) = 0) Z-stat -0.00 -0.53 -1.23 0.05 Prob>Z 0.99 0.60 0.22 0.96 Sargan's Test for over-identifying restrictions chi 2 -stat 250.90 27.98 18.18 30.68 Prob>chi 2 0.00 0.01 0.75 0.08 Hansen's Test for over-identifying restrictions chi 2 -stat 220.33 17.91 27.00 25.98 Prob>chi 2 0.00 0.12 0.26 0.21 Dierence-Hansen's Test for exogeneity of instruments (H 0 : instruments are exogenous) chi 2 -stat 35.46 4.79 1.70 8.61 Prob>chi 2 0.00 0.69 0.98 0.20 Windmeijer corrected robust standard errors in parentheses + p< 0:10, p< 0:05 149 Table F.2: Arellano-Bond Estimation of Deposit Demand, Modied Instruments Excluding High In ation Counties (2000-2015) Dependent variable: lnM =ln(deposits) it ln(gdp de ator) it (1) (2) (3) (4) lnM t1 0.474 (0.0330) -0.050 (0.0520) 0.101 (0.1046) 0.435 (0.0658) t 2 0.020 (0.1237) t 3 -0.013 (0.0641) t 4 -0.096 (0.0961) lnY 0.085 (0.0139) 0.085 (0.0719) 0.051 (0.0786) -0.208 (0.0872) t 1 0.025 (0.0118) 0.103 (0.0131) 0.081 (0.0204) 0.297 (0.0939) t 2 0.055 (0.0111) 0.042 (0.0202) t 3 0.044 (0.0094) 0.044 (0.0207) t 4 0.055 (0.0595) 0.101 + (0.0594) lnW 0.140 (0.0105) -0.120 + (0.0663) -0.033 (0.0958) 0.060 (0.0560) t 1 0.214 (0.0472) 0.127 + (0.0733) 0.046 (0.0456) In ation -0.006 (0.0003) -0.011 (0.0022) -0.009 (0.0031) -0.011 (0.0020) t 1 -0.003 (0.0009) -0.003 (0.0016) -0.002 (0.0008) 10yr Treasury -0.011 (0.0012) -0.010 (0.0021) -0.011 (0.0012) t 1 -0.005 (0.0015) -0.006 (0.0019) -0.001 (0.0015) \ Own rate 0.001 (0.0010) 0.007 (0.0019) 0.007 (0.0029) 0.008 (0.0038) t 1 -0.004 (0.0015) -0.001 (0.0029) -0.006 (0.0028) Post-2008 0.036 (0.0032) 0.031 (0.0046) 0.039 (0.0080) 0.025 (0.0062) N 21,405 16,776 16,776 17,999 N Instruments 97 27 41 33 Arellano-Bond Test for zero autocorrelation in rst-dierenced errors (H 0 :E( it ; it2 ) = 0) Z-stat 0.04 -0.55 -0.23 0.19 Prob>Z 0.97 0.58 0.81 0.85 Sargan's Test for over-identifying restrictions chi 2 -stat 280.25 25.09 16.82 35.70 Prob>chi 2 0.00 0.01 0.81 0.02 Hansen's Test for over-identifying restrictions chi 2 -stat 258.54 11.89 24.90 33.31 Prob>chi 2 0.00 0.46 0.35 0.04 Dierence-Hansen's Test for exogeneity of instruments (H 0 : instruments are exogenous) chi 2 -stat 68.78 7.55 7.56 19.34 Prob>chi 2 0.00 0.37 0.37 0.00 Windmeijer corrected robust standard errors in parentheses + p< 0:10, p< 0:05 150 tests and gauge model validity. 1 For the Arellano-Bond estimation, I do not constrain the number of lags used for the GMM dierence estimator of lnM and all RHS variables are taken as exogenous. Columns 2 through 4 are alternative versions of the baseline model in 1, with additional lags to RHS variables and modications to the assumptions used in GMM dierence estimation to obtain a model that passes all specication tests (Arellano-Bond, Sargan, Hansen, and Dierence-Hansen's tests). 2 Of note, throughout, the coecient value for Post-2008 remains consistently positive throughout and is only slightly below the baseline estimate of around 0.4 from Table 1.12 in the specication with 41 instruments that passes all model validity tests. Table F.2 presents the same set of regressions as Table 1.12, excluding counties that exhibit extremely high levels of in ation. In ation matters for deposit demand because higher levels of in ation erode the real value of cash and deposits, and households may respond by drastically cutting holdings of deposits. High in ation would bias predicted deposits demanded downward, potentially pushing up the coecient on the post-2008 dummy given higher actual levels of deposits in the post-crisis period. Removing the high in ation counties, which consist of 79 small counties across Arizona, Colorado, Louisiana, New Mexico, Oklahoma, and Texas, with large oil and gas industries relative to the size of the local economy, does little to alter the results of Table F.1. F.2 Stock Market Investment and Deposits One alternative source of return not considered in the analysis is the stock market. Stock market returns may matter for a couple of reasons. In the theoretical model, households 1 Misspecication and overidentication tests are very sensitive to proliferation of instruments, so provide unreliable results for models with hundreds of instruments like my baseline case in Section 6.1.2. See Roodman (2009) for a more detailed discussion about the problem of too many instruments. 2 (2) uses third and fourth lags for GMM dierence estimator oflnM. The rst lags oflnW , in ation, own rate, the contemporaneous 10-yr Tres rate, and rst through third lags of lnY are assumed to be exogenous. Column (3) uses fth through eighth lags for GMM dierence estimator of lnM, while other instruments match (2). The model in column (4) uses fth through seventh lags for GMM dierence estimator of lnM and other instruments match (2). 151 do not explicitly hold stock, but they do receive dividends as owners of the banks. If stock returns and dividends are high, household wealth increases and this may boost demand for deposits. Another concern is that, as Lin (2018), explains, when the stock market is booming, people tend to move out of deposits and into equity markets. Along those lines, a plausible mechanism driving the upward shift in demand for deposits could be lower stock returns in the post crisis period. To test if this could be an important omitted variable driving results, I obtain gross annual market returns from Ken French's website. 3 I then construct my stock market return dierential at the county level by subtracting from gross annual market returns average interest rates on deposits for each county. There are 33,288 stock return dierential observations, with an average of 6.28 percent, standard deviation of 18.83 percent. The largest dierentials are around 35% in absolute value. Table F.3 replicates the Aerllano-Bond regressions run in columns one through four of Table 1.12 with the new stock market return measure in the estimation. 4 The coecient for stock market return spreads over deposit rates is negative, as expected, but statistically and economically insignicant for all variations of the estimation. Compared to values in Table 1.12, the magnitude of the post-2008 shift in deposit demand is slightly weaker, but still positive and signicant throughout. Also, the size of the coecient for the post-2008 dummy approaches the bounds of the biased OLS and xed eect regressions, suggesting inclusion of stock market returns improves the estimation but does not alter the main results. 3 The original data are from from Ibbotson Associates and are constructed as the value-weight return of all CRSP rms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 or 11 at the beginning of month t, good shares and price data at the beginning of t, and good return data for t. 4 Reducing the maximum number of instruments to the sixth lag aected coecients signicantly, so I do not repeat the same exercise here. 152 Table F.3: Arellano-Bond Estimations of Deposit Demand with Stock Returns (2000-2015) Dependent variable: lnM =ln(deposits) it ln(gdp de ator) it Two-step, specic GMM-instruments for lagged RHS vars for fed funds 3+ 3-11 3-9 3-7 for y 4+ 4-11 4-9 4-7 other RHS 2+ 2-11 2-9 2-7 lnM t1 0.852 (0.0314) 0.845 (0.0341) 0.834 (0.0346) 0.832 (0.0337) lnY 0.166 (0.0371) 0.161 (0.0433) 0.153 (0.0435) 0.162 (0.0363) lnW 0.253 (0.0509) 0.248 (0.0491) 0.260 (0.0513) 0.285 (0.0415) t 1 -0.158 (0.0553) -0.158 (0.0523) -0.154 (0.0560) -0.181 (0.0462) In ation -0.006 (0.0006) -0.006 (0.0006) -0.006 (0.0006) -0.006 (0.0005) t 1 0.001 (0.0003) 0.001 (0.0003) 0.001 (0.0003) 0.001 (0.0003) 10yr Treasury -0.005 + (0.0025) -0.004 (0.0022) -0.004 (0.0023) -0.004 (0.0019) t 1 0.000 (0.0029) -0.001 (0.0031) -0.000 (0.0033) -0.002 (0.0029) Stocks -0.000 (0.0001) -0.000 (0.0001) -0.000 (0.0001) -0.000 (0.0001) t 1 -0.000 (0.0001) -0.000 (0.0001) -0.000 (0.0000) -0.000 (0.0000) Fed funds 0.000 (0.0031) 0.001 (0.0034) 0.001 (0.0038) 0.002 (0.0031) t 1 0.000 (0.0032) 0.000 (0.0030) 0.002 (0.0031) -0.000 (0.0029) Post-2008 0.028 + (0.0147) 0.032 (0.0137) 0.038 (0.0142) 0.040 (0.0126) year -0.002 (0.0015) -0.003 (0.0013) -0.003 (0.0015) -0.003 (0.0014) Lags of lnY 3 3 3 3 N 18,565 18,565 18,565 18,565 N Instruments 500 501 435 289 Windmeijer corrected robust standard errors in parentheses Assumed in ation is exogenous + p< 0:10, p< 0:05 153

Abstract (if available)

Abstract In Chapter 1, I investigate the potential forces driving major bank balance sheet developments in the years following the 2007–2008 financial crisis. The share of cash as a percentage of banks' total assets has more than doubled over the last decade while residential mortgage loans have shrunk. Meanwhile, bank leverage has plunged and remained muted for the last 10 years. These developments are often attributed to changes in post-crisis banking regulation, but it is difficult to pinpoint how regulation shapes bank behavior in the presence of other macroeconomic factors. Using a general equilibrium model, I assess the capacity of three factors to explain the trends: post-crisis bank regulations, monetary policy, and changes to household preferences. The model suggests greater demand for bank deposits by households is an important contributor to the rise in cash on bank balance sheets post-crisis. In empirical analysis, I explore the positive relationship between demand for bank deposits and banks’ cash ratios to test the model’s implications. ❧ In Chapter 2, I evaluate the impact of quantitative easing (QE) on interest rates and bank and household-nonfinancial firm balance sheets in the post-crisis period. Because bank regulation, household-firm preferences, and QE influence the composition of balance sheets, the three factors must be modeled jointly to understand their combined and separate effects. Extending the general equilibrium framework from Chapter 1, I analyze the effectiveness of the portfolio rebalancing channel of QE in the presence of changing household-firm preferences and capital or liquidity regulations. The model highlights that stricter liquidity rules limit the ability of QE to encourage more lending by banks. Greater household-firm demand for deposits also amplify changes in interest rate spreads created by QE. The quantitative results emphasize the importance of considering bank regulations and liquidity preferences when policymakers use QE to target specific interest rate or bank balance sheet goals, as fluctuations in either of the two factors can make fine-tuning of policy difficult.

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Asset Metadata

Creator Wong, Vivian (author)

Core Title The changing policy environment and banks' financial decisions

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Degree Conferral Date 2021-08

Publication Date 07/18/2021

Defense Date 05/18/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag capital requirements,demand for deposits,liquidity requirements,macroprudential policy,OAI-PMH Harvest,quantitative easing

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Quadrini, Vincenzo (committee chair), Hoberg, Gerard (committee member), Ramcharan, Rodney (committee member), Zeke, David (committee member)

Creator Email vivianwo@marshall.usc.edu,vivianwo@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC15602349

Unique identifier UC15602349

Legacy Identifier etd-WongVivian-9769

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Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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