Bank Liquidity and Capital Regulation in General Equilibrium

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Bank Liquidity and Capital Regulation in General Equilibrium Francisco Covas and John C. Driscoll 2014-85 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Bank Liquidity and Capital Regulation in General Equilibrium Francisco Covas∗ John C. Driscoll† September 12, 2014 Abstract Wedevelop anonlinear dynamic general equilibrium model with abanking sectorand useit to study the macroeconomic impact of introducing a minimum liquidity standard for banks on top of existing capital adequacy requirements. The model generates adistribution of bank sizes arising from differences in banks’ ability to generate revenue from loans and from occasionally binding capital and liquidity constraints. Under our baseline calibration, imposing a liquidity requirement would lead to a steady-state decrease of about 3 percent in the amount of loans made, an increase in banks’ holdings of securities of at least 6 percent, a fall in the interest rate on securities of a few basis points, and a decline in output of about 0.3 percent. Our results are sensitive to the supply of safe assets: the larger the supply of such securities, the smaller the macroeconomic impact of introducing a minimum liquidity standard for banks, all else being equal. Finally, we show that relaxing the liquidity requirement under a situation of financial stress dampens the response of output to aggregate shocks. JEL Classification: D52, E13, G21, G28. Keywords: bankregulation,liquidityrequirements,capitalrequirements,incompletemarkets, idiosyncratic risk, macroprudential policy WethankToniAhnert,WilliamBassett,RuiCastro,CarlosGarriga,LucaGuerrieri,MatteoIacoviello,Michael Kiley,NellieLiang,DavidLopez-Salido,AliOzdagli,JaeSim,andseminarparticipantsattheFederalReserveBoard, IBEFA,andUniversityofCalifornia,SantaBarbaraforanumberofvaluablecommentsandsuggestions. ShailyPatel provided excellent research assistance. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of anyone else associated with the Federal Reserve System. This paper previously circulated under the title “The Macroeconomic Impact of Adding Liquidity Regulations to Bank Capital Regulations.” ∗Division of Monetary Affairs, Federal Reserve Board. E-mail: Francisco.B.Covas@frb.gov †Division of Monetary Affairs, Federal Reserve Board. E-mail: John.C.Driscoll@frb.gov

1 Introduction During times of financial stress, such as the recent crisis, financial intermediaries may experience rapid and large withdrawals of funds, motivated by investors’ own funding needs as well as their concernabouttheintermediaries’solvency. Iftheintermediaryeitherdoesnothavesufficientfunds on hand to accommodate the demand for withdrawals, or is (falsely) perceived to not have enough funds, demand for withdrawals may accelerate, leading to a run. In order to reduce the likelihood of such runs, the Basel III regulatory requirements have introduced rules on banks such as the liquidity coverage ratio (LCR) and the net stable funding ratio (NSFR). Roughly speaking, these newregulationsrequirebankstoholdsufficientliquidassetstoaccommodateexpectedwithdrawals of certain types of liabilities over different time intervals. Although such liquidity requirements may reduce the likelihood of bank runs, and of financial crises more generally, they likely come with some cost. By forcing banks to hold a higher fraction of their assets as low-risk, highly liquid securities, these regulations may reduce the quantity and increase the interest rate on bank loans. These regulations may also interact with previously existing regulations such as capital requirements. Since such regulations are new to most countries, it is difficult to do empirical analysis of the effects of their imposition.1 Inthispaper, wedevelopanonlineardynamicgeneralequilibriummodelanduseittostudythe macroeconomic impact of introducing a minimum liquidity standard for banks on top of existing capital adequacy requirements. The liquidity standard requires banks to hold a certain portion of their portfolio in assets that either have a zero or relatively low risk weight. The model generates a distribution of bank size arising from heterogeneity in bank productivity—that is, some banks are able to obtain more revenue from a given quantity of loans made—and from occasionally binding capital and liquidity constraints. Banks also endogenously choose the capital and liquidity “buffers”—the amounts of capital and liquidity above the required minimums. We present partial equilibriumandgeneralequilibriumresultsaswellastransitionaldynamicsbetweensteadystates.2 Our results suggest that under general equilibrium, introducing a minimum liquidity requirementwouldleadtoadeclineinloansbyabout3percentandanincreaseinsecuritiesover6percent in the new steady state on the asset side of banks’ balance sheets. Onthe liability side, deposits are little changed, we observe less dependence on the short-selling of securities and bank equity rises. The introduction of a liquidity standard prevents the most productive banks from fully exploiting their profit opportunities, which reduces the supply of bank loans and increases the cost of funds. As a result, aggregate output declines by about 0.3 percent and consumption drops by about 0.1 1Thereisasubstantialtheoreticalliteratureonthenatureofliquidity,butitsfocusisonthefinancialsectormore broadly. See,forexample,Holmstr¨om and Tirole[1996],Farhi, Golosov, and Tsyvinski[2009],Holmstr¨om and Tirole [2001],Holmstr¨om and Tirole[2011],Brunnermeier and Pedersen[2009],andBolton, Santos, and Scheinkman[2011]. Diamond and Rajan [2011] and Freixas, Martin, and Skeie [2010] discuss the role of liquidity in the banking sector more specifically. 2Ingeneralequilibrium,marketprices—interestratesonloansandsecurities,thereturnoncapital,andthewage rate—are allowed to adjust to their new equilibrium values. 1

percentinthenewsteadystate. Inaddition, theintroductionofaliquidityrequirementinducesthe bank to finance a larger portion of its assets with equity, resulting in a 1 percentage point increase in the capital buffer above the minimum requirement. We also show that our results are somewhat sensitive to the supply of safe assets in our economy. In particular, we study the sensitivity of our results to the availability of securities that are not explicitly modeled in our framework, such as debt securities with the backing of the U.S. Government and central bank reserves that can be drawn in times of stress. Overall, we find that the macroeconomic impact of introducing a liquidity requirement in our economy is mitigated as the availability of safe assets increases. We also analyze the responses in our economy to an increase in capital requirements from 6 to 12 percent. The increase in capital requirements acts as a tax on assets with non-zero riskweights, so bankers’ portfolios become slightly more concentrated in securities, which carry a zero risk-weight. We find that in response to the increase in capital requirements the stock of loans declines by about 1 percent and securities’ holdings increase by about 9 percent. On the liabilities side, bank deposits are little changed, while equity holdings increase over 35 percent. Although the steady state effect of an increase in capital requirements on loans is relatively small, we show that during the transition the short-term impact is considerably stronger with the loan rate increasing 15 basis points and the stock of loans declining close to 4 percent. In our framework, the general equilibrium effects of introducing a liquidity requirement or increasing capital requirements on banks’ holdings of loans and securities are considerably smaller than the partial equilibrium effects. This occurs because the increase in the interest rate on loans and the decrease on the rate of return on securities in the general equilibrium model reduce the degree of substitution from loans to securities. This illustrates the importance of using general equilibriummodelingtoestimatethemacroeconomicimpactofthenewregulations. Thepiecemeal approachofusingmodelsofthebankingsectortoestimatetheimpactofnewregulationsonbanking variables, and then extending those effects to other macroeconomic variables may overstate the impact of the new regulations on the macroeconomy. Finally, we also study the effects of lowering capital and liquidity requirements during a period of financial stress. The introduction of a liquidity standard expands the set of available tools used by central banks and other regulators to conduct macroprudential regulation. Currently, bank stress tests are an important tool in the conduct of macroprudential regulation. Based on the calibration of our model, we find that a reduction in liquidity requirements following a wealth shock to households dampens the response to aggregate output considerably more than an easing of capital requirements. The model developed in this paper is closely related to the papers by Quadrini [2000], Covas [2006] and Angeletos [2007]. These two papers augment the standard model with uninsurable labor income risk, as in Bewley [1986], Imrohoro˘glu [1992], Huggett [1993], and Aiyagari [1994], with an entrepreneurial sector subject to uninsurable investment risk. We expand those models 2

and augment the standard Bewley model with both an entrepreneurial and banking sectors. The bankers in our economy are subject to uninsurable profitability risk and the regulatory capital constraint faced by bankers in our model corresponds to a borrowing constraint faced by workers andentrepreneurs. Themaindifferenceisthatweassumealowerdegreeofriskaversionforbankers and a considerably larger borrowing capacity to enhance the realism of the model. In order to study the response of our economy to changes in regulatory requirements we focus on transitional dynamics between steady states, as in Kitao [2008]. In addition, the problem solved by the banker in our paper is somewhat similar to the problem analyzed by De Nicolo`, Gamba, and Lucchetta [2014], although unlike in that paper our results are obtained under general equilibrium. This paper is also closely related to the literature on the macroeconomic impact of banking frictionsinotherwisestandardmacroeconomicmodels. Van den Heuvel[2008]studiesthewelfarecosts of capital requirements in a general equilibrium model with moral hazard. He and Krishnamurthy [2010] develop a model in which bankers are risk-averse and bank capital plays an important role in the determination of equilibrium prices. Corbae and D’Erasmo [2014] study the quantitative impact of increasing capital requirements in a model of banking industry dynamics. Finally, there is an emerging literature on macro-prudential regulation including the work by Gertler and Karadi [2011],Gertler and Kiyotaki[2011],Kiley and Sim[2011],andGertler, Kiyotaki, and Queralto[2011] which is also important to our work, although that research proceeds from different modeling assumptions.3 More recently, the paper by Adrian and Boyarchenko [2013] also analyze a dynamic stochastic general equilibrium model to study how liquidity and capital regulations affect the supply of safe assets and provides a comparison of capital and liquidity regulation as macroprudential tools. The remainder of the paper proceeds as follows. Section 2 describes the model. Section 3 presents the model calibration. Section 4 discusses the baseline economy and policy experiments and section 5 analyzes the transitional dynamics between steady states. Section 6 discusses the effectiveness of liquidity regulation as a macroprudential tool. Section 7 concludes. 2 The Model We construct a general equilibrium model with agents that face uninsurable risks. We consider three types of agents: (i) workers; (ii) entrepreneurs; and (iii) bankers. Agents are not allowed to change occupations. Workers supply labor to entrepreneurs and face labor productivity shocks which dictate their earning potential. Entrepreneurs can invest in their own technology and face investment risk shocks which determine their potential profitability. Bankers play the role of fi- 3Thereis also anempirical literature ontheroleofcapitalandcapital regulations in thetransmission ofmacroeconomic shocks. See, for example, Peek and Rosengren [1995b], Peek and Rosengren [1995a], Berrospide and Edge [2010], Blum and Hellwig [1995], Concetta Chiuri, Ferri, and Majnoni [2002], Cosimano and Hakura [2011], Francis and Osborne [2009], Hancock and Wilcox [1993], Hancock and Wilcox [1994], Kishan and Opiela [2006], Kishan and Opiela [2000], and Repullo and Suarez [2013]. 3

nancial intermediaries in this economy by accepting deposits from workers and making loans to entrepreneurs. In addition, bankers can also invest in riskless securities. Bankers are subject to revenue shocks that determine their potential profitability. An important feature of the banker’s problem is the presence of occasionally binding capital and liquidity constraints. The model generates real effects of changes in capital and liquidity requirements through two violations of the Modigliani-Miller theorem. First, banks are not indifferent to their form of finance due to both the presence of capital requirements and the absence of outside equity. Second, entrepreneurs are assumed to be dependent on bank loans.4 Workers. As in Aiyagari [1994] workers are heterogeneous with respect to wealth holdings and earnings ability. Since there are idiosyncratic shocks, the variables of the model will differ across workers. To simplify notation, we do not index the variables to indicate this cross-sectional variation. Let cw denote the worker’s consumption in period t, dw denote the deposit holdings and t t aw denote the worker’s asset holdings in the same period, and ǫ is a labor-efficiency process which t t follows a first-order Markov process. Workers choose consumption to maximize expected lifetime utility ∞ E0 β w t u(cw t ,dw t+1 ), Xt=0 subject to the following budget constraint: cw +dw +aw = wǫ +RDdw +Raw, t t+1 t+1 t t t where 0 < β < 1 is the worker’s discount factor, w is the worker’s wage rate, and RD is the gross w rate on deposits and R is gross return on capital. We assume workers are subject to an ad-hoc borrowing constraint; that is aw > a, where a 6 0. The wage rate and the return on capital are t+1 determinedingeneralequilibriumsuchthat laborandcorporatecapitalmarketsclearinthe steady state. Note that we have introduced a demand for deposits by assuming that their holdings bring utility to the worker. However, the deposit rate is assumed to be exogenous since, as described later, bankers take as given the stock of deposits supplied by the workers. Let vw(ǫ,x ) be the optimal value function for a worker with earnings ability ǫ and cash on w hand x .5 The worker’s optimization problem can be specified in terms of the following dynamic w 4Theassumptionofbank-dependencefortheentrepreneurialsectorisinaccordancewiththeliteratureonthecredit channel of monetary policy, which also assumes that some firms, particularly smaller ones, do not have the same amount of access to other forms of finance. See, for, example, Bernanke and Blinder [1988], Peek and Rosengren [2000], Gertler and Gilchrist [1993], Kashyap and Stein [2000], Kashyap and Stein [1994], Driscoll [2004], and Ashcraft [2005]. 5Because the worker’s problem is recursive, the subscript t is omitted in the current period, and a prime denotes the value of the variables one period ahead. 4

programming problem: vw(ǫ,x ) = max u(c ,d′ )+β E[v(ǫ′,x′ )|ǫ], (1) w w w w w cw,d′ w,a′ w s.t. c +d′ +a′ = x , w w w w x′ = wǫ′+RDd′ +Ra′ , w w w a′ > a. w The full list of parameters of the worker’s problem is shown at the top of Table 1. Entrepreneurs. Entrepreneurs are also heterogeneous with respect to wealth holdings and productivityoftheindividual-specifictechnologythattheyoperate. Entrepreneurschooseconsumption to maximize expected lifetime utility ∞ E0 β e tu(ce t ), Xt=0 where 0 < β < 1 is the entrepreneur’s discount factor. Each period, the entrepreneur can invest e in an individual-specific technology (risky investment), or invest its savings in securities. The risky technology available to the entrepreneur is represented by y = z f(k ,l ), t t t t where z denotes productivity, k is the capital stock in the risky investment and l is labor. This t t t investment is risky because the stock of capital is chosen before productivity is observed. The labor input is chosen after observing productivity. The idiosyncratic productivity process follows a first-order Markov process. As is standard, capital depreciates at a fixed rate δ. In addition, the entrepreneur is allowed to borrow to finance consumption and the risky investment. Let be denote the amount borrowed by the entrepreneur and RL denote the gross rate t+1 on bank loans. The loan rate is determined in general equilibrium. Borrowing is constrained, for reasons of moral hazard and adverse selection that are not explicitly modeled, to be no more than a fraction of entrepreneurial capital: be t+1 > −κk t+1, where κ represents the fraction of capital that can be pledged at the bank as collateral. Entrepreneurs that are not borrowing to finance investment can save through a riskless security, denoted by se with a gross return RS which will also be determined in general equilibrium. 5

Under this set of assumptions, the entrepreneur’s budget constraint is as follows: ce t +k t+1+be t+1 +se t+1 = xe t , xe t+1 = z t+1f(k t+1,l t+1)+(1−l t+1)w+(1−δ)k t+1+RLbe t+1 +RSse t+1 , where xe denotes the entrepreneur’s period t wealth. It should be noted that the entrepreneur can t also supply labor to the corporate sector or other entrepreneurial businesses. Let ve(z,x ) be the optimal value function for an entrepreneur with productivity z and wealth e x .6 The entrepreneur’s optimization problem can be specified in terms of the following dynamic e programming problem: ve(z,x ) = max u(c )+β E[v(z′,x′)|z], (2) e e e e ce,k′,b′ e,s′ e s.t. c +k′+s′ +b′ = x , e e e e x′ = π(z′,k′;w)+(1−δ)k′+RLb′ +RSs′, e e e 0 > b′ > −κk′, e s′ > 0, e k′ > 0, where π(z′,k′;w) represents the operating profits of the entrepreneur’s and incorporates the static optimization labor choice. From the properties of the utility and production functions of the entrepreneur, the optimal levels of consumption and the risky investment are always strictly positive. The constraints that may be binding are the choices of bank loans, b′, and security holdings, s′. e e The full list of parameters of the entrepreneur’s problem is shown in the middle panel of Table 1. Bankers. Bankers are heterogeneous with respect to wealth holdings, loan balances, deposit balances and productivity. Bankers choose consumption to maximize expected lifetime utility ∞ E0 β b tu(cb t ), Xt=0 where 0 < β < 1 is the banker’s discount factor. b Bankers hold two types of assets—risky loans (b) and riskless securities (s)—and fund those assets with deposits (d) and equity (e). Loans can also be funded by short-selling securities— implying s can be negative. Each period, the banker chooses the amount of loans it makes to the entrepreneurs, denoted by b t+1. Loans, which are assumed to mature at a rate δ¯, yield both interest and noninterest income 6Because the entrepreneur’s problem is recursive, the subscript t is omitted in the current period, and we let the prime denote the value of the variables one period ahead. 6

(the latter arises, for example, from fees, which in practice are a substantial part of bank income). Banks may differ in their ability to extract net revenue from loans due to (unmodeled) differences in their ability to screen applicants or monitor borrowers, or in market power. For analytical convenience, we represent net revenue in period t from the existing stock of loans b as: t yb = (RL−φ )b +θ g(b ), t b t t t where θ denotes the idiosyncratic productivity of the bank, the function g(b ) exhibits decreasing t t returns to scale, and φ is the cost of operating the loan technology. b The banks also face adjustment costs in changing the quantity of loans, which allows us to capture the relative illiquidity of such assets. The adjustment costs are parametrized by: Ψ(b t+1,δ¯b t ) ≡ ν t b t+1−δ¯b t 2 b t , 2(cid:18) b (cid:19) t where ν t ≡ ν + 1 {bt+1>δ¯bt} +ν−1 {bt+1<δ¯bt} . In our calibration, we will assume that the cost of adjusting the stock of loans downwards is much greater than the cost of adjusting it upwards—reflecting the idea that calling in or selling loans is more costly than originating loans. Net returns from the bank’s securities holdings is given by: ys = RSs , t t which may be negative if the bank is short-selling securities.7 The banker’s budget constraint is written as follows: cb t +b t+1+s t+1+d t+1 = xb t −Ψ(b t+1,δ¯b t ), xb t+1 = (RL−φ b )b t+1+θ t+1g(b t+1)+RSs t+1+RDd t+1. where xb t denotes the banker’s period t wealth and d t+1 the stock of deposits. The bank borrows throughdepositsthatitreceivesfromtheworkers, butcanalsoborrowbysellingsecuritiestoother bankers or entrepreneurs. For simplicity, we assume the share of deposits received by each bank is exogenous and follows a four-state first-order Markov Chain (see the Appendix for further details). However, borrowing from entrepreneurs and other bankers is endogenous and is constrained by capital requirements. Letting e t+1 denote banks’ equity, the capital requirement may be written 7A more realistic formulation would differentiate between securities as asset holdings and wholesale deposits and other types of wholesale funding. This additional realism would come at considerable computational cost, which is why we have pursued the current approach. 7

as: e t+1 > χb t+1, which is equivalent to a risk-based capital requirement, giving a zero risk weight to securities. The capital requirement may in turn be rewritten in terms of securities holdings as (since e t+1 = xb t −Ψ(b t+1,δ¯b t )−cb t ): s t+1 > (χ−1)b t+1−d t+1. We also impose a liquidity requirement, in which we assume that cash on hand—which consists of the return on existing securities holdings and the net revenue from paydowns on existing loans— must be sufficient to satisfy demand for deposit withdrawals under a liquidity stress scenario and interest payments on deposits. This can be represented as: RSs t+1+δ¯b t+1 > (d {s−1,1}+ −RDd t+1), (3) where d represents a decline in the stock of deposits (note that d < 0). Since d follows a {s−1,1}+ t Markov Chain, if in period t the bank is in state s then deposit withdrawals correspond to state {s − 1,1}+. The stringency of the liquidity requirement is given by the assumption about the relative size of the bad deposits realization. It will be calibrated through an assumption of how quickly deposits would run off in a crisis situation.8 Let vb(θ,xb,b,d′) be the optimal value function for a banker with wealth xb, loans b, deposits d′, and productivity θ. The banker’s optimization problem can be specified in terms of the following dynamic programming problem: vb(θ,x ,b,d′) = max u(cb)+β E[vb(x′,b′,d′′,θ′)|θ,d′], (4) b b b cb,b′,s′ s.t. c +b′+s′+d′ = x −Ψ(b′,δ¯b), b b x′ = (RL−φ )b′+θ′g(b′)+RSs′+RDd′, b b e′ > χb′, RSs′+δ¯b′ > (d −RDd′). {s−1,1}+ Corporate sector. In this economy there is also a corporate sector that uses a constant-returnsto-scale Cobb-Douglas production function, which uses the capital and labor or workers and entrepreneurs as inputs. The aggregate technology is represented by: Y = F(K ,L ), t t t 8In the sensitivity analysis section below we also explore the possibility of involuntary drawdowns on loan commitments that are usually observed during financial crisis. For example, according to Santos [2011] the average drawdown rate for nonfinancial borrowers is 23 percent under a one-year horizon, and those are significantly higher during recessions and financial crisis. 8

and aggregate capital, K is assumed to depreciate at rate δ. We introduce the corporate sector t to allow some production to occur without requiring bank loans. In practice, in the U.S. and many other developed economies, firms finance themselves to a greater degree through equity or bond markets or through other nonbank financial intermediaries than they do through bank loans. Without a corporate sector, our model would thus overstate the degree to which regulations on the banking sector affect aggregate output, consumption, and other aggregate variables. To the extent that such regulations are eventually applied to nonbank systemically important financial institutions, our model can be recalibrated so that the share of the economy funded by such systemically important financial institutions increases. Definition 1 summarizes the steady-state equilibrium in this economy. Definition 1 The steady-state equilibrium in this economy is: a value function for the worker, vw(ǫ,xw), for the entrepreneur ve(z,xe), and for the banker, vb(θ,x ,b,d′); the worker’s policy funcb tions{cw(ǫ,xw),dw(ǫ,xw),aw(ǫ,xw)}; theentrepreneur’spolicyfunctions{ce(z,x ),k(z,x ),l(z,x ), e e e be(z,x ),ae(z,x )}; the banker’s policy functions {cb(x ,b,θ,d′),bb(x ,b,θ,d′),s(x ,b,θ,d′), e e b b b d(x ,b,θ,d′)}; a constant cross-sectional distribution of worker’s characteristics, Γ (ǫ,xw) with b w mass η; a constant cross-sectional distribution of entrepreneur’s characteristics, Γ (z,xe) with e mass ν; a constant cross-sectional distribution of banker’s characteristics, Γ (x ,b,θ,d′), with mass b b (1−η−ν); and prices (RD,RL,R,w), such that: 1. Given RD, R, and w, the worker’s policy functions solve the worker’s decision problem (1). 2. Given R, RL, and w, the entrepreneur’s policy functions solve the entrepreneur’s decision problem (2). 3. Given RD, RL, RS, the banker’s policy functions solve the banker’s decision problem (4). 4. The loan, securities, and deposit markets clear: ν bedΓ = (1−η−ν) bbdΓ , (Loan market) e b Z Z S¯ = ν sedΓ +(1−η−ν) sbdΓ , (Securities market) e b Z Z η dwdΓ = (1−η−ν) dbdΓ . (Deposit market) w b Z Z 5. Corporate sector capital and labor are given by: K = η awdΓ w Z L = (η+ν)−ν ldΓ . e Z 9

6. Given K and L, the factor prices are equal to factor marginal productivities: R = 1+F (K,L)−δ, K w = F (K,L). L 7. Given the policy functions of workers, entrepreneurs, and bankers, the probability measures of workers, Γ , entrepreneurs, Γ , and bankers, Γ , are invariant. w e b 3 Calibration The properties of the model can be evaluated only numerically. We assign functional forms and parameters values to obtain the solution of the model and conduct comparative statics exercises. We choose one period in the model to represent one year. Workers’ and entrepreneurs’ problems. The parameters of the workers’ and entrepreneurs’ problems are fairly standard, with the exception of the discount factor of entrepreneurs, which is chosen to match the loan rate. The period utility of the workers is assumed to have the following form: c 1−γw u(c ,d′ ) = ω w +(1−ω)ln(d′ ), e w (cid:18)1−γ (cid:19) w w whereω istherelativeweightonthemarginalutilityofconsumptionanddepositsandγ istherisk w aversion parameter. We set γ to 2, a number often used in representative-agent macroeconomic w models. We set ω equal to 0.97 to match the ratio of banking assets relative to output, since this parameter controls the stock of deposits in our economy. The discount factor of workers is set at 0.96, which is standard. We adopt a constant relative risk-aversion (CRRA) specification for the utility function of entrepreneurs: c 1−γe e u(c ) = . e 1−γ e We set γ to 2, close to that of Quadrini [2000]. The idiosyncratic earnings process of workers is e first-orderMarkovwiththeserialcorrelationparameter, ρ , setto0.80, andtheunconditionalstan- ǫ dard deviation, σ , set to 0.16. Although we lack direct information to calibrate the stochastic pro- ǫ cessforentrepreneurs,wemakethereasonableassumptionthattheprocessshouldbepersistentand consistent with the evidence provided by Hamilton [2000] and Moskowitz and Vissing-Jørgensen [2002] the idiosyncratic risk facing entrepreneurs is larger than the idiosyncratic risk facing workers. Hence, we set the serial correlation of entrepreneurs to 0.70 and the unconditional standard deviation to 0.22. As is standard in the business cycle literature, we choose a depreciation rate δ of 8 percent for 10

Table 1: Parameter Values Under Baseline Calibration Parameter Description Value Workers’ parameters: β Discount factor 0.96 w γ Coefficient of relative risk aversion 2.0 w ω Weight on consumption 0.97 ρ Persistence of earnings risk 0.80 ǫ σ Unconditional s.d. of earnings risk 0.16 ǫ a Borrowing constraint 0.0 η Mass of workers 0.666 w Entrepreneurs’ parameters: β Discount factor 0.95 e γ Coefficient of relative risk aversion 2.0 e ρ Persistence of productivity risk 0.70 z σ Unconditional s.d. of productivity risk 0.22 z κ Borrowing constraint 0.50 α Capital share 0.45 ν Labor share 0.35 δ Depreciation rate 0.08 η Mass of entrepreneurs 0.333 e Bankers’ parameters: β Discount factor 0.95 b γ Coefficient of Relative Risk Aversion 1.0 b χ Capital requirements 0.06 δ¯ Loan maturity 0.24 α Curvature of loan revenues 0.75 b ρ Persistence of shock to loan revenues 0.70 θ σ Unconditional s.d. of shock to loan revenues 0.09 θ ρ Persistence of shock to deposits 0.80 d σ Unconditional s.d. of shock to deposits 0.15 d φ Intermediation cost 0.15 b ν− Adjustment cost for decreasing loans 0.04 ν+ Adjustment cost for increasing loans 0.02 Corporate sector’s parameters: α Capital share 0.36 c δ Depreciation rate 0.08 c the entrepreneurial as well as the corporate sector. The degree of decreasing returns to scale for entrepreneurs is equal to 0.80—slightly less than Cagetti and De Nardi [2006]—with a capital and labor shares of 0.45 and 0.35, respectively. As in Aiyagari [1994] we assume workers are not allowed to have negative assets, and let the maximum leverage ratio of entrepreneurs to be at about 50 11

Table 2: Selected Moments Moment Data Model Tier 1 capital ratio 9.3 12.4 Share of constrained banks 0.2 0.3 Leverage ratio 6.9 7.7 Adjusted return-on-assets 3.4 6.0 Cross-sectional volatility of adjusted return-on-assets 1.3 1.3 % Safe assets held by banks 30.8 38.4 Share of interest income in revenues 0.7 0.2 Share of noninterest expenses 2.9 9.2 Return on securities 2.4 3.3 Loan rate 4.6 4.2 Consumption to output 0.7 0.7 Banking assets to output 0.7 0.6 Safe-to-total assets 0.3 0.3 Memo: Deposit rate 0.6 0.6 % Labor in entrepreneurial sector — 37.6 % Labor in corporate sector — 62.4 % Output of entrepreneurial sector — 48.6 % Output of corporate sector — 44.0 % Output of banking sector — 7.5 Note: Moments are based on sample averages using quarterly observations between 1997:Q1 and 2012:Q3, withtheexceptionofthepercentageofsafeassetsheldbybankswhichisonlyavailablestartingin2001:Q1, andaveragesforshareofinterestincomeinrevenuesandbankingassetstooutputarecalculatedonlyforthe periodafterthefourthquarterof2008wheninvestmentbanksbecamebankholdingcompanies. Theadjusted return on assets is defined as net income excluding income taxes and salaries and employee benefits. The percentageofsafeassetsheldbybanksincludesallassetswithazeroandwitha20percentriskweight. The sampleincludesallbankholdingcompaniesandcommercialbanksthatarenotpartofaBHC,orthatarepart ofaBHCwhichdoesnotfiletheY-9Creport. Theshareofconstrainedbanksisbasedonbanks’responsesin theSeniorLoanOfficerOpinionSurvey. Thesafe-assetshareisobtainedfromGorton, Lewellen, and Metrick [2012]. percent, which corresponds to κ set to 0.5.9 The discount factor of entrepreneurs is chosen to match the average loan rate between 1997 and 2012. Based on bank holding company and call report data the weighted average real interest rate charged on loans of all types was 4.6 percent. By setting β to 0.95 we obtain approximately this e calibration. Bankers’ problem. We divide the set of parameters of the bankers’ problem into two parts: (i) parameters set externally, and (ii) parameters set internally. The parameters set externally are taken directly from outside sources. These include the loan maturity, δ¯, and the capital con- 9Leverage is defined as debt to assets, that is −b/k. At the constraint b = −κk, the maximum leverage in the model is equal to κ=0.50. 12

straint parameter, χ. In addition, we assume the banker has log utility to minimize the amount of precautionary savings induced by the occasionally binding capital constraint. The remaining nine parameters of the banker’s problem are determined so that a set of nine moments in the model are close to a set of nine moments available in the bank holding company and commercial bank call reports. The lower panel in Table 1 reports the parameter values assumed in the parametrization of the banker’s problem. We now describe the parameters set externally. For the capital constraint we assume that the minimumcapitalrequirementinthemodelisequalto6percent,whichcorrespondstotheminimum tier 1 ratio a bank must maintain to be considered well capitalized. Thus, χ equals 0.06. The loan maturity parameter, δ¯, is set to 0.24 so that the average maturity of loans is 4.2 years based on the maturity buckets available on banks’ Call Reports. The parameters set internally—namely the banker’s discount factor, the intermediation cost, the parameters of the banker’s loan technology, the persistence and standard deviation of the shock to deposits, and the adjustment cost parameters—are chosen to match a set of nine moments calculated from regulatory reports. The moments selected are: (i) tier 1 capital ratio, (ii) the fraction of capital constrained banks, (iii) leverage ratio, (iv) adjusted return-on-assets, (v) the cross-sectional volatility of adjusted return on assets, (vi) the share of assets with a zero or 20 percent Basel I risk-weight, (vii) the share of interest income relative to total revenues, (viii) the shareofnoninterestexpenses, and(ix)thereturnonsecurities. TheupperpanelofTable2presents a comparison between the data and the model for this selected set of moments. As discussed above, the supplies of certain types of safe assets such as U.S. Treasury securities, Agency debt and municipal bonds are not directly modeled in our framework. We capture the supply of these assets using the parameter S. As shown in Section 4, our results are somewhat sensitive to the choice of this parameter. Thus, we calibrate the parameter S using the estimates of the share of safe assets provided by Gorton, Lewellen, and Metrick [2012]. Specifically, that paper estimates that during the postwar period the safe-asset share has fluctuated between 30 and 35 percent. In the model we define the safe-asset share as follows. The numerator includes bank deposits, the exogenous amount of safe assets, S, and the amount of borrowing by banks in the securities market. The denominator includes all assets in the economy for each of the three types of agents: workers’ deposits and corporate sector assets; entrepreneurs’ capital and securities; and bankers’ loans and securities. By setting S to 9, we obtain a safe-asset share of 33 percent in our calibrated model. The solution of the model is obtained via computational methods and additional details are provided in the Appendix. 4 Analysis of the Baseline Economy We first present results for apartial equilibriumversionof the model, in which prices (interest rates and wages) are taken as given, in order to gain intuition regarding the different constraints of the 13

Table 3: Bankers’ Wealth Distribution % wealth held by 0−20% 20−40% 40−60% 60−80% 80−100% Low revenue 0.6 0.1 0.1 0.1 0.1 Medium revenue 8.8 12.6 17.1 22.3 34.5 High revenue – – 0.0 0.4 3.3 Note: Allfiguresareinpercent. Thestochasticprocessforthenoninterestincometechnologyisdiscretized into a markov-chain with 5 states. The “low revenue” state corresponds to the first state of the markov chain, the “medium revenue” state to the next three states and the “high revenue” state to the last state. Results are based on the invariant distribution of bankers. In addition to the parameters reported in Table 1,thesteadystatedistributionisobtainedassumingaloanrateof4.2percentandareturnonsecuritiesof 3.3 percent. model. We then present general equilibrium results in which we let all prices adjust. Partial Equilibrium. The macroeconomic effects of the capital and liquidity requirements will depend on the extent to which such requirements are binding. That in turn will depend on the distribution of bankers’ wealth (or net worth). We thus first show information on bankers’ wealth distribution; we next present information on how capital and liquidity constraints vary in the cross-section; we then show how loan and securities holdings vary with net worth, as affected by the capital and liquidity constraints; and we finally present the steady-state effects on our economy of imposing or altering the requirements. Table 3 shows the percentage of wealth held at each quintile and the level of loan productivity. As shown in the table, low productivity bankers in the first quintile of the wealth distribution hold about 0.6 percent of the entire wealth of the banking sector. Conversely, the most productive bankers in the top quintile hold more than 3 percent of the wealth of the banking sector. We did not parametrize the model with the objective of matching the high degree of concentration of banking assets that exists in the U.S. However, as suggested by the results below the impact of the introduction of a minimum liquidity requirement on loan supply would likely be strengthened in a model in which a larger share of assets is held by the top quintile.10 Table 4 shows the share of capital constrained (Panel A) and liquidity constrained (Panel B) bankers in equilibrium. Within each productivity (revenue) level, smaller banks are more likely to be capital constrained than larger banks. For the liquidity constraint we observe the opposite. Larger banks are more likely to be liquidity constrained than smaller banks. Banks that are more productive in terms of loan revenue would like to maximize the share of assets devoted to loans, and therefore hold smaller shares as securities. If the concentration of assets in the top quintile was 10In our calibration the share of wealth held by the top quintile is slightly less than 40 percent. In the data, the average between 1997-2006 was more than 90 percent. 14

Table 4: Share of Bankers with Binding Constraints Panel A: Binding capital constraint 0−20% 20−40% 40−60% 60−80% 80−100% Low revenue 66.4 0.0 0.0 0.0 0.0 Medium revenue 79.2 38.1 7.4 0.0 0.0 High revenue – – 15.6 1.0 0.0 Panel B: Binding liquidity constraint 0−20% 20−40% 40−60% 60−80% 80−100% Low revenue 0.0 0.0 0.0 0.0 0.0 Medium revenue 0.0 4.6 14.6 19.8 20.1 High revenue – – 90.5 99.0 93.7 Note: Each entry in panel A reports the share of bankers with a binding capital constraint in each wealth/loan revenue bucket. Each entry in panel B reports the fraction of agents with a binding liquidity constraint in each wealth/loan revenue bucket. Results are based on the invariant distribution of bankers assuming a loan rate of 4.2 percent and a return on securities of 3.3 percent. higher in the model, the implications of a binding liquidity constraint would be potentially more relevant since larger banks are more likely to be liquidity constrained. Figure 1 plots the policy rules for bank loans and securities as a function of net worth for a bank with the highest revenue shock. The dashed line represents the decision rule of bankers in the absence of a liquidity requirement, while the solid line depicts the banker’s decision rule in the presence of one.11 In the absence of a liquidity requirement, as net worth (and equity) increases from low levels banks initially substitute securities for loans as the capital requirement is relaxed due to the increase in equity. As wealth continues to increase, banks cease to be capital constrained and the choice of loans no longer varies with the bank’s equity. At that point, banks also start to borrow less in the securities market. The presence of a liquidity requirement affects both of these dynamics. The binding nature of the requirement reduces the bank’s ability to invest in loans and borrow by short-selling securities. Note that the effect of the liquidity requirement on the banker’s policy rules is only present when the shock to revenues is sufficiently high, such as the one shown in Figure 1. For lower revenue shocks the region in which the liquidity constraint would bind is above the banker’s optimal loan choice and the policy rules with liquidity requirements overlap with the ones that are only subject to capital requirements. Finally, the presence of a liquidity requirement also makes lending less sensitive to increases in net worth and equity. These effects are reflected in the solution to the partial equilibrium version of the banker’s model, given in Table 5. The first column of the table reports the baseline solution under the 11In both cases, there is a capital requirement. 15

Figure 1: The Effect of the LCR constraint on bankers’ policy rules Loans Securities 650 700 600 650 550 600 500 550 450 500 400 450 350 400 300 350 250 300 No LCR LCR 200 250 100 200 300 400 100 200 300 400 Net worth Net worth Notes: Policy rules for the bankers under the highest revenue state θ = θ¯ 5, average level of deposits d = d¯ 2 and stock of loans l=140. presence of a capital requirement, but not a liquidity requirement. The second column reports the impact of introducing liquidity requirements on model outcomes. The third column reports the model outcomes in response to an increase in the capital requirement from 6 to 12 percent, and the last column reports the impact of simultaneously increasing the capital requirement and imposing a liquidity requirement. The introduction of a liquidity requirement (second column) leads to a substantial increase in the stock of securities and a decrease in the stock of loans, leaving total assets about flat. Although banks’ equity fall somewhat, the more substantial decline in loans boosts the aggregate capital ratio. Though the liquidity requirement only binds for a relatively small share of banks, since these 16

Table 5: Partial Equilibrium Analysis of the Banking Sector Baseline ∆’s relative to Baseline Capital requirements 6% 6% 12% 12% Liquidity requirements No Yes No Yes (1) (2) (3) (4) 1. Securities 10.2% 11.2% 18.1% 2. Loans -5.8% -2.4% -6.6% 3. Assets (=1+2) 0.3% 2.8% 2.9% 4. Equity 3.9% 37.3% 38.2% 5. Liquidity coverage ratio (%) 150.1 158.8 161.3 167.2 6. Liquidity constraint binds (%) — 12.9 — 12.0 7. Capital ratio (%) 12.2 13.5 17.2 18.1 8. Capital constraint binds (%) 26.4 22.0 36.1 32.6 Note: Results are based on the invariant distribution of bankers. The baseline economy is one in which capital requirements are equal to 6 percent (χ=0.06) and there are no liquidity requirements. The rate on loans and the return on securities are set at 3.6 and 1.6 percent, respectively. are the largest banks in our model the effect of imposing a liquidity requirement is quite significant. Anincreaseincapitalrequirementsfrom6to12percent(thirdcolumn)wouldincreasethestock of equity at banks by more than 35 percent, decrease loans over 2 percent, and increase securities holdings by about 11 percent. Higher capital requirements make it more difficult for bankers’ to smooth consumption, thereby increasing the demand to purchase securities which are riskless. The last column of Table 5 combines the increase in capital and liquidity requirements. The overall net impact on equity is positive and both the capital ratio and the liquidity coverage ratio increase significantly relative to the baseline specification. The balance sheet size of banks expands modestly, while loans shrink and securities holdings increase substantially. General Equilibrium. ThefirstcolumnofTable6reportsthebaselinegeneralequilibriumsolution of the full model without a liquidity requirement. In general equilibrium prices (RL,RS,R,w) have to adjust to clear the loan, securities, the asset and the labor markets. In addition, we will be able to make statements about aggregate consumption and output. The second column of Table 6 reports the impact on banking and macroeconomic variables in response to the introduction of a liquidity standard. Securities, loans, assets and equities (rows 1-3 and 5) behave similarly to the partial equilibrium case, though the magnitudes are attenuated. This reduction in magnitude comes from the impact of changes in the loan rate and the return 17

Table 6: General Equilibrium Analysis Baseline ∆’s relative to Baseline Capital requirements 6% 6% 12% 12% Liquidity requirements No Yes No Yes (1) (2) (3) (4) 1. Securities 6.6% 8.9% 13.8% 2. Loans -3.1% -0.8% -3.2% 3. Assets (=1+2) 0.6% 2.9% 3.3% 4. Deposits 0.1% 0.0% 0.1% 5. Equity 7.0% 38.5% 42.4% 6. Liquidity coverage ratio (%) 150.1 155.9 159.4 163.6 7. Liquidity constraint binds (%) — 15.9 — 12.3 8. Capital ratio (%) 12.2 13.5 17.0 18.0 9. Capital constraint binds (%) 26.4 22.7 36.1 31.2 10. Return-on-assets (%) 6.0 6.0 5.9 6.0 11. Loan rate (%) 4.16 4.27 4.20 4.28 12. Return on securities (%) 3.35 3.33 3.32 3.31 13. Output -0.3% -0.1% -0.4% 14. Entrepreneurial sector -0.6% -0.2% -0.7% 15. Corporate sector 0.3% 0.1% 0.4% 16. Consumption -0.1% -0.1% -0.2% Note: Results are based on the invariant distributions of bankers, workers and entrepreneurs. The baseline economy is one in which capital requirements are equal to 6 percent (χ=0.06) and there are no liquidity requirements. For stock variables, the numbers reported in lines 1–5 and 13–16 in columns 2-4 represent percentage changes relative to the baseline specification. on securities. Specifically, the equilibrium loan rate increases 11 basis points in response to the reduction in the supply of loans. This, in turn, makes loans more attractive and dampens the effect of imposing the liquidity requirement on loan supply. In contrast, the equilibrium return on securities falls only slightly—from 3.35 percentage points to 3.33 percentage points—in response to the increase in holdings of securities. The decrease in the riskless return makes securities less attractive to hold, thus, relative to the partial equilibrium case the increase in holdings of securities is reduced in half. Nonetheless, the impact of imposing a minimum liquidity standard on banks on output and consumption is non-negligible. In particular, aggregate output falls about 0.3 percent (0.6 percent in the entrepreneurial sector), and consumption declines about 0.1 percent. 18

The third column of Table 6 reports the general equilibrium results when capital requirements increasefrom6to12percent. Inthiscasetheresultsarealsolesspronouncedrelativetothepartial equilibrium case. Specifically, loans decline less than 1 percent, while securities increase somewhat less relative to the partial equilibrium case. In large part, the increase in demand for securities leads to a small reduction in the equilibrium rate of return on securities (row 12). Although the new steady state level of aggregate output is about flat in response to the increase in capital requirements, consumption still falls in large part because banks need to pay less dividends to sustain the higher capital ratios. Finally, the last column in Table 6 reports the combined effects of an increase in capital and liquidity requirements. The model suggests that a simultaneous increase in capital and liquidity requirements would cause output and consumption to both decline by about 0.4 and 0.2 percent, respectively. Although the decline in output is somewhat modest, there is a sizable redistribution effect of the economy’s production capacity from entrepreneurs (bank dependent borrowers) to the corporate sector. Supply of Safe Assets. We now analyze the comparative statics in our economy when the supply of safe assets—controlled by the parameter S—increases. The availability of safe assets has important implications for the liquidity requirement in our model—as defined in equation (3)— since banks are required to invest a share of their liabilities in liquid assets. In our calibration, the parameter S represents the “exogenous” amount of safe assets available in our economy. This parameter represents liquid assets available in the economy that are not explicitly modeled in our framework, suchasdebtsecuritiesthathavetheexplicitorimplicitbackingoftheU.S.Government orcentralbankreservesthancanbedrawnintimeofstress. Therefore,itisimportanttounderstand how the equilibrium changes in response to an exogenous variation in the supply of safe assets and for reasons not related to the introduction of a liquidity requirement in the banking sector. The left panel of Figure 2 plots the steady state equilibrium in the securities market before the introduction of the liquidity requirement. The supply of securities is positively sloped (the blue line)andcorrespondstothesumofanexogenouscomponent—definedbytheparameterS—andan endogenouscomponentdeterminedbybanksthataresupplyingsafeassetstothemarket(i.e.,those with s′ < 0). The demand for securities by bankers and entrepreneurs is represented by the red solid line and is negatively sloped. The equilibrium in the securities market before the introduction of a liquidity requirement is represented by the dot labeled ‘A’ in the left panel. The dashed lines represent the supply and demand of securities after the introduction of the liquidity requirement. As shown by the blue lines in the left panel, the introduction of the liquidity requirement shifts the supplycurvetotheleftandmakesitveryinelastic. Thishappensbecauseonewayforbankstoease theliquidityrequirementconstraintistoreducetheiramountofborrowinginthesecurities’market, making the supply of securities almost exclusively determined by the parameter S. Meanwhile, the demandforsecuritiesremainsaboutunchangedbecauseanincreaseinbanks’demandforsecurities 19

Figure 2: The Effects of an Increase in the Supply of Safe Assets ) s r+1(/1 = q ,seitiruceS fo ecirP B A Securities ) s r+1(/1 = q ,seitiruceS fo ecirP B’ A’ Securities Note: Thesolidlinesrepresentthedemandandsupplycurvesofsecuritiesbeforetheintroductionofaliquidity requirement. The dashed lines depict the demand and supply curves of securities after the introduction of a liquidity requirement. due tothe introductionoftheLCRisoffsetbythe higherequilibriumloanrate, whichincreasesthe opportunity cost of investing in securities. Thus, the decrease in the supply of securities induced by theintroductionoftheliquidityrequirementreducesitsreturnandthenewsteadystateequilibrium movestopoint‘B’.Althoughbankers’holdingsofsecuritiesincreases,thesumofsecurities’holdings of bankers and entrepreneurs decreases after the introduction of the liquidity requirement. The panel to the right displays the demand and supply curves under a higher level of safe assets. Because the exogenous share of safe assets is now larger, the introduction of the liquidity requirement has a smaller impact on the equilibrium price level of securities (the change from A’ to B’ in the right panel of Figure 2). Specifically, the return on securities declines less relative to the case with a lower level of safe assets. As a result, loans outstanding and aggregate output are also less affected by the introduction of a liquidity requirement. The macroeconomic impact of changes in the supply of safe assets depend importantly on the size of the banking sector and the spread between the loan rate and the return on securities. Overall, the macroeconomic impact of introducingaliquidityrequirementinoureconomyismitigatedastheshareofsafeassetsexogenous to the change in policy increases. This last result has several implications for the design of liquidity requirements. First, in some jurisdictions, the banking sector is large relative to the size of the economy—and therefore also to the supply of domestic government securities. In such countries, allowing foreign securities to serve as safe assets will help reduce the impact of liquidity requirements on the domestic economy. 20

Second, reserves held at the central bank can serve as a potentially large source of safe assets. A number of central banks have greatly increased the supply of such reserves as a consequence of running nontraditional monetary policies at the zero lower bound. Because having a large quantity of reserves can mitigate the macroeconomic effects of introducing a liquidity requirement, maintaining reserves at a high level through the transition period of introducing the requirement may be beneficial. 5 Transitional Dynamics In this section, we illustrate the transitional dynamics of introducing liquidity requirements and compare those to the responses to an increase in capital requirements. In contrast to the results of the previous section, we assume a gradual increase in the liquidity requirement over a three year horizon and describe the responses of all sectors in our economy. In addition, we also compare these responses to the case in which the increase in capital requirements is also done gradually over a three year horizon. Introduction of a liquidity requirement. Figure 3 shows the transitional dynamics of the banking sector in response to the introduction of a liquidity standard. The liquidity standard is increased gradually over a three-year horizon and mimics the transition period under the U.S. LCR proposal.12 Specifically, we assume that in period 1 the economy is in its steady state equilibrium. In period 2, an unanticipated liquidity requirement is announced and implemented at 80 percent, followed by 90 percent in period 3 and reaching 100 percent in period 4. The computational method used to calculate the transitional dynamics is presented in the Appendix. Bankers respond to the introduction of a liquidity standard by decreasing the supply of loans (top right panel) and increasing their holdings of securities (middle right panel). This triggers an increase in the loan rate of approximately 10 basis points in the long run (top left panel) and a decrease in the return of securities of a similar magnitude (middle left panel). The shift in portfolio composition of bankers from loans to securities increases the liquidity coverage ratio (bottom right panel) and also boosts their risk-based capital ratio (bottom left panel). The increase in banks’ risk-based capital ratios is driven in part by the zero risk-weighting of securities. In addition, the liquidity requirement also penalizes banks’ dependence on deposits and borrowing in the securities’ market and as a result it increases their desire to finance with retained earnings. Figure 4 displays the responses of entrepreneurial and aggregate output and consumption. On the entrepreneurial sector, the introduction of the liquidity requirement and subsequent reduction 12October 24, 2013, U.S. regulatory agencies proposed a LCR that would apply to bank holding companies with $250 billion or more in total consolidated assets or $10 billion or more in on-balance-sheet foreign exposure. The proposed LCR establishes a transition period beginning January 1, 2015 with an 80 percent LCR requirement, 90 percent by January 2016 and 100 percent by January 2017. 21

Loan rate 4.3 4.25 4.2 4.15 0 10 20 30 40 Years tnecreP Bank loans 1 0 −1 −2 −3 −4 0 10 20 30 40 ss morf .ved % Years Return on securities 3.4 3.35 3.3 3.25 0 10 20 30 40 tnecreP Bank securities 8 6 4 2 0 0 10 20 30 40 Years ss morf .ved % Years Risk−based capital ratio 14 13.5 13 12.5 12 0 10 20 30 40 tnecreP Liquidity coverage ratio 160 155 150 145 0 10 20 30 40 Years tnecreP Years Figure 3: Introduction of Liquidity Requirements Notes: The horizontal axes contain the number of periods after the change in liquidity requirements. The transitional dynamics assume the new steady state is reached after 60 periods. The hollow dots in the last period indicate the final steady state value. in lending causes both output and consumption to decline (top panels). The reduction in investment in the entrepreneurial sector reduces the demand of labor from entrepreneurs and leads to a reallocation of labor to the corporate sector. Since capital and labor are complements in the corporate sector, this reallocation increases the demand for capital which in turn boosts workers’ holdings of corporate assets and worker consumption in the long run (not shown). However, as shown in the bottom two panels of Figure 4 aggregate output and consumption decline throughout the transition period and fall by about 0.3 and 0.1 percent in the long-run, respectively. Figure 5 compares the transitional dynamics of increasing capital requirements with those of imposing a liquidity requirement. The effects of increasing the liquidity requirement are the same as those presented in Figures 3 and 4. Regarding the increase in capital requirements we assume 22

Entrepreneurial output 0.1 0 −0.1 −0.2 −0.3 −0.4 −0.5 0 10 20 30 40 ss morf .ved % Entrepreneurial consumption 0.1 0 −0.1 −0.2 −0.3 −0.4 0 10 20 30 40 Years ss morf .ved % Years Aggregate output 0 −0.1 −0.2 −0.3 −0.4 0 10 20 30 40 ss morf .ved % Aggregate consumption 0.05 0 −0.05 −0.1 0 10 20 30 40 Years ss morf .ved % Years Figure 4: Introduction of Liquidity Requirements Notes: The horizontal axes contain the number of periods after the change in liquidity requirements. The transitional dynamics assume the new steady state is reached after 60 periods. The hollow dots in the last period indicate the final steady state value. those are unanticipated and rise from 6 to 12 percent over three periods. The effects from imposing a higher capital requirement are different from those of introducing a liquidity requirement since the capital and liquidity constraints bind for a different set of banks and it operates through a different mechanism. Specifically, an increase in capital requirements implies that, for a given level ofprofitabilityrisk, itbecomeshardertosmoothdividendpayoutsforbankers. Asaresult, bankers would like to accumulate more securities (precautionary buffer) and would substitute out of loans into securities. In general equilibrium, bankers’ portfolio reallocation leads to a decrease in the rate of return of securities and an increase in the rate of return of loans. Under our calibration, we find that in response to the increase in capital requirements loan rates increase close to 15 basis points in the near term but subsequently rebound to their baseline 23

value (top left panel). Similarly, outstanding loans on banks’ books fall about 4 percent in the short term but are little changed in the long-run (top right panel). In response to higher capital requirements, the most affected banks are the ones with the lowest levels of equity and the least profitable. As a result, the increase in capital requirements increases their precautionary desire to hold securities which leads to a substantial decrease in the return on those assets (not shown). Consequently,loansbecomerelativelymoreattractiveforbanks,offsettingtheinitialnegativeeffect on lending. In addition, since the supply of loans to bank dependent borrowers is little changed the long-run effects of increasing capital requirements on aggregate output and consumption are relatively small (bottom panels). Comparing effects of imposing liquidity requirements with increasing capital requirements. Figure 5 shows that the evolution of the variables of the model along the transition path are different across the two experiments of imposing a liquidity standard and increasing capital requirements. In the case of the introduction of liquidity requirement, the affected banks are the largest and most profitable. Because banks most affected by the liquidity requirement are not capital constrained, the decline in bank loans in the long run is more pronounced when liquidity requirements are imposed due to the lack of banks’ demand to hold additional assets to minimize fluctuationsindividendpayoutsinresponsetoidiosyncraticrevenueshocks. Moreover,theincrease in capital requirements leads to a higher increase in banks’ liquidity coverage ratios. According to our model, policy makers would be able to increase banks’ holdings of liquid assets more quickly by increasing capital requirements rather than imposing a liquidity requirement (middle panels). We are able to obtain this result in the model because liquid assets have lower risk-weights than loans, which is consistent with what is typically observed in the data. Interestingly, the decline in aggregate consumption in the short-term is considerably more pronounced in the case of more stringent capital requirements as banks accumulate equity by reducing dividend payouts to meet the higher capital requirement (bottom right panel). Sensitivityanalysis. AsshowninTable6,theLCRisabout150percentinthebaselineeconomy. To generate this ratio the model implicitly assumes a 60 percent run-off rate for deposits during a liquidity stress event, which is higher than what is assumed under the U.S. LCR rules. That said, anecdotal evidence based on banks’ earnings reports suggest that banks’ liquidity coverage ratios are between 80 and 120 percent in recent quarters; that is, significantly lower than the aggregate LCR we obtain in our baseline economy. Thus, it is plausible to assume that the LCR ratio generated in the baseline calibration is simply too high, suggesting that the liquidity requirements are unrealistically low in the model. In addition, the results of the comprehensive quantitative impact study BCBS [2010b], estimate that the liquidity coverage ratio for the set of banks included 24

Loan rate 4.3 4.25 4.2 4.15 4.1 0 10 20 30 40 Years tnecreP Bank loans 0 −2 LCR Higher capital −4 0 10 20 30 40 ss morf .ved % Years Risk−based capital 18 16 14 12 0 10 20 30 40 tnecreP Liquidity coverage ratio 165 160 155 150 145 0 10 20 30 40 Years tnecreP Years Aggregate output 0.1 0 −0.1 −0.2 −0.3 −0.4 0 10 20 30 40 ss morf .ved % Aggregate consumption 0.1 0 −0.1 −0.2 −0.3 −0.4 0 10 20 30 40 Years ss morf .ved % Years Figure 5: Comparison of Introducing Liquidity Requirements with Increasing Capital Requirements Notes: Thehorizontalaxescontainthenumberofperiodsafterthechangeinliquidityorcapitalrequirements. The transitional dynamics assume the new steady state is reached after 60 periods. in their sample was 83 percent for Group 1 banks.13 There are a few reasons supporting the idea that under our baseline calibration liquidity requirements aretooloose. First, we donot accuratelymodelloancommitments, sincebank loans by entrepreneurs in the model are fully drawn at origination. According to Santos [2011], the average drawdown rate for non-financial borrowers is about 23 percent over a one year-horizon; drawdowns are significantly higher during recessions and financial crises. As a result, we could model drawdowns of credit facilities during a stress period by also including an outflow assumption on loans to entrepreneurs. 13Group 1 banks are those that have Tier 1 capital in excess of 3 billion of euros, are well diversified, and are internationally active. Of the 91 Group 1 banks included in the quantitative impact study, 13 were U.S. banks. 25

Figure 6 depicts the responses of the variables of the model under different parametrizations of the liquidity standard. In particular, the red dashed lines show the evolution of the variables in the model corresponding to a liquidity coverage ratio of 125 percent in the baseline economy. To attain this calibration we lowered the parameter that controls paydowns on existing loans, δ¯, from 0.24 to 0.10. Relative to the solid blue line, which represents the baseline change in the liquidity standard, the loan rate increases about 20 basis points in the long-run instead of 10 basis points (top left panel). Similarly, holdings of loans on banks’ books declines about 6 percent (top right panel). Aggregate output in the long-run declines by 0.6 percent (bottom left panel). Clearly, increasing the cash outflow assumptions over the stress period would lead to a greater impact of imposing a liquidity standard in the macroeconomy. Discussion. Our model induces a positive correlation between loan revenue and bank size. As shown in Table 4, the liquidity requirement is more likely to bind for larger banks than smaller ones. Because there is a significant concentration of assets among the largest banks, they have a large influence on total loans outstanding in our economy. For this reason, we expect to find a stronger impact of changes in liquidity requirements on the evolution of macroeconomic variables relative to a setup with a representative bank. In addition, the effect of the introduction of liquidity requirements on aggregate output is permanent. This occurs because the liquidity requirement prevents the most productive banks from fully exploiting their profitable opportunities, and the introduction of a liquidity requirement does not lead to a material reduction in the cost of funds to the bank. However, our model only allows for one form of debt finance subject to the same liquidity requirement. If banks have access to other sources of debt finance with longer maturities which are exempted from the liquidity requirement, or have lower outflows assumptions, the impact on loan growth could be mitigated. Discussion of other estimates on the impact of regulatory reform. There are two wellknownstudiesonthemacroeconomicimpactoftheregulatoryreformthatarehelpfultosummarize. First, the Macroeconomic Assessment Group (MAG) produced a reported published by the BCBS [2010a]attheendof2010. Second,theInstituteofInternationalFinanceIIF[2011]—representatives forthebankingindustry—publishesareporteveryyearonthemacroeconomicimpactofregulatory reforms, which was last updated in August of 2013. In the MAG report, it is estimated that a one percentage point increase in minimum capital requirements leads to a decline of 0.19 percent of output relative to the baseline in almost five years. Assuming we can scale up the MAG estimate, then a six percentage point increase in capital requirements leads to a 1.2 percent decrease in output over the same period. The contraction in output provided by the MAG analysis is significantly larger than the estimate suggested by our model. In particular, our calibration suggests that a six percentage point increase in capital requirements leads to a decline of 0.1 percent in aggregate output after 5 years. In the MAG study, the results are based on the assumption that 26

Loan rate 4.4 4.3 4.2 4.1 0 10 20 30 40 Years tnecreP Bank loans 0 −2 −4 Baseline LCR −6 Tighter LCR −8 0 10 20 30 40 ss morf .ved % Years Risk−based capital 15 14 13 12 11 0 10 20 30 40 tnecreP Liquidity coverage ratio 160 150 140 130 0 10 20 30 40 Years tnecreP Years Aggregate output 0 −0.2 −0.4 −0.6 0 10 20 30 40 ss morf .ved % Aggregate consumption 0.1 0 −0.1 −0.2 0 10 20 30 40 Years ss morf .ved % Years Figure 6: Introducing More Stringent Liquidity Requirements Notes: The horizontal axes contain the number of periods after the change in liquidity requirements. The transitional dynamics assume the new steady state is reached after 60 periods. The dashed line represents theliquidityrequirementsdiscussedintheprevioussection,whilethesolidlinerepresentstheintroductionof more stringent liquidity requirements. the Modigliani-Miller proposition holds and the way banking assets are financed does not impact aggregate quantities in the long-run. In our model the Modigliani-Miller proposition does not hold because of capital constraints are bankers are not allowed to raise outside equity, however we have even smaller effects on output due to the portfolio reallocation effect and its impact on the return of securities. ThereportpublishedbytheIIF—agloballobbygroupforthebankingindustry—estimatesthat the combined effect of all regulatory proposals, namely the broad increase in capital requirements, the introduction of a liquidity standard, as well as U.S. specific measures (e.g., Volcker Rule) would lead to a decline of 3.0 percent of GDP after five years. Our combined regulatory changes (6 percentage point increase in capital requirements and the introduction of a liquidity standard) 27

would lead to a decline of 0.4 percent of aggregate output in the long-run. In the IIF study, a key driving force of the results in the increase in loan spreads. In our model the loan rate also increases in response to the more stringent regulatory requirements, albeit by much less. Due to the general equilibrium nature of our model, the bulk of the adjustment occurs through the reallocation of banks’ portfolios as bank dependent borrowers curtail their demand for funds in response to higher loan rates. Because the IIF is based on a partial equilibrium analysis, the impact of the regulatory reform on spreads is probably overstated. 6 Implications for Macroprudential Policy In this section we evaluate the behavior of our model economy in response to an aggregate shock to the wealth of workers subject to different macroprudential policy alternatives. During a stress scenario, regulators may wish to temporarily relax regulations in order to reduce the impact of shocks on the macroeconomy.14 Specifically, we use our model to compare the effects on output of easing liquidity standards against a reduction in capital requirements in response to an aggregate shock. Bank capital stress tests have in recent years become an indispensable part of the toolkit used by central banks and other regulators to conduct macroprudential regulation and supervision. Perhaps liquidity stress tests could also become an important instrument in the implementation of macroprudential regulation. Weintroduceanaggregateshockinoureconomybyconsideringaone-time,two-periodshockto the distribution of workers’ wealth. Specifically, we shock the distribution of wealth of workers by 5 percent in the first period and 3.3 percent in the second period. In addition, we apply the shock in the economy that includes both a capital requirement of 12 percent and the liquidity standard described in equation (3). We consider two types macroprudential policies. The first type relaxes the capital requirement from 12 to 6 percent in the first three periods after the wealth shock occurs and then assumes the capital requirement rises gradually to 12 percent over the next four periods. The macroprudential policy based on the relaxation of the liquidity standard assumes that the LCR is lifted entirely for the first three periods and then rises gradually to 100 percent during the remaining four periods. The shock to the wealth of workers in the first two periods is assumed to be unexpected, but after the shock occurs agents have perfect foresight in terms of both the capital and liquidity regulation policies. Figure 7 plots the response of our economy to the one-time shock to the distribution of workers’ wealth. Asshown inthebaseline case(dash-dotted blueline), aggregate output is2.1percent lower in period 3 after the initial shock in periods 1 and 2. The response in the economy in which capital requirements are relaxed in the first 6 periods is similar, with aggregate output declining 2 percent by period 3. In other words, while the easing of capital requirements helps to dampen the response 14For an overview of macroprudential policies, see Hanson, Kashyap, and Stein [2011]. 28

Aggregate output 0 −0.5 −1 −1.5 −2 −2.5 −2 0 2 4 6 8 10 12 14 Years ss morf .ved % Baseline Relax RBC Relax LCR Relax tighter LCR Figure 7: Aggregate Response of Output to a Wealth Shock Notes: Thehorizontalaxescontainthenumberofperiodsafteranaggregateshockthatreducesthewealthof workers. Thetransitionaldynamicsassumethesteadystateisreachedafter60periods. Thedash-dottedblue line represents the response of the economy where capital requirements are 12% and bankers are subject to a liquiditystandard,andthesestandardsdonotchangeinresponsetothewealthshock. Thedashedblackline represents the response of the economy when capital requirements are relaxed temporarily. The pink dashed line represents the response of the economy when liquidity standards are eased temporarily (less stringent) and the red line represents the case where liquidity requirements are more stringent (see text for details). of output, the effects are fairly small for such a very large reduction in capital requirements. On the other hand, a relaxation of the liquidity requirement helps to mitigate the decline in aggregate output a bit more. As shown in the red line, output declines roughly 30 basis points less by period 3 relative to the baseline case in which liquidity requirements are quite stringent before the shock occurs (LCR of 125). 7 Conclusion Bank liquidity regulations have the highly desirable goals of both reducing the likelihood of bank runsandincreasingtheoddsthatbankswillsurviveruns,shouldtheyoccur. However,byincreasing banks’incentivestoholdlower-risk, moreliquidassets, suchregulationsmayalsoreducethesupply of loans and increase their cost to bank dependent borrowers. They may also interact with other 29

current regulations, such as capital regulations, in ways not completely intended. In this paper, we calibrate a nonlinear dynamic general equilibrium model in which banks are subject to both capital and liquidity requirements that bind only occasionally. We find that imposing liquidity regulations of the kinds currently envisioned under Basel III would, in the long run, reduce loans outstanding on banks’ books by nearly 3 percent, and aggregate output and consumption by about 0.3 percent and 0.1 percent, respectively. However, we also find that an economy with liquidity requirements that could be relaxed during a crisis period could dampen the effect of wealth shocks on aggregate output relative to an economy in which liquidity requirements are absent. Thus, introducing liquidity requirements creates an important macroprudential tool available to policymakers. We also report that the effects on lending and other banking variables are substantially larger in partial equilibrium analysis which takes prices as given. This result suggests that attempting to apply partial equilibrium results—i.e. results just on the banking sector–to derive the macroeconomic impact of changes in liquidity or capital regulations are likely to be misleading. But it also indicates that the macroeconomic impacts of changes in liquidity and capital regulation are sensitive to the effects of changes in bank behavior on prices. That said, our baseline calibration suggestsasmallimpactofbanksecuritiespurchasesonthereturnsonsuchsecurities–whichdecline a few basis points after the introduction of a liquidity requirement. The macroeconomic effects of imposing the liquidity requirement are also smaller the larger the supply of safe assets, suggesting that it would be desirable to have a large amount of such assets during the proposed transition period. Finally, we do not explicitly attempt to model the reduction in bank runs owing to the new regulations. Thus, our analysis should not be taken as a full evaluation of the costs and benefits associated with liquidity regulation; nor does it suggest what the optimal level of regulation should be. We leave that for future research. 30

Appendix Inthisappendixwederivethebanker’scapitalconstraints,thefirst-orderconditionsofthebanker’s problem, and provide an outline of the solution method. Banker’s capital constraint. The balance sheet constraint of the banker is given by b′+s′ = x −c −Φ(b′,δ¯b)−d′ b b where the left-hand side of this expression is the banker’s assets, b′+s′, and the right-hand side is the banker’s equity, e ≡ x −c −Φ(b′,δ¯b), and debt, −d′. The capital constraint can be written b b b as e > χb′ b b′+s′+d′ > χb′ d′ > (χ−1)b′−s′. Banker’s first-order conditions. The first-order conditions for b′ and s′ are as follows: ∂Φ(b′,b) ∂v ∂x ∂v 1+ u (c) = β E b b + b θ,d′ +(1−χ)λ+δ¯µ (cid:20) ∂b′ (cid:21) c b (cid:20)∂x ∂b′ ∂b′(cid:12) (cid:21) b (cid:12) ∂v ∂x (cid:12) u (c) = β E b b θ,d′ + (cid:12) λ+µR c b (cid:20)∂x ∂s′(cid:12) (cid:21) S b (cid:12) (cid:12) (cid:12) where λ is the Lagrange multiplier associated with the capital constraint and µ is the Lagrange multiplier associated with the liquidity constraint. Note that the envelope conditions are ∂v b = u (c) c ∂x b ∂v ∂Φ b = −u (c) . c ∂b ∂b Using the envelope condition on the set of first-order conditions one obtains: ∂Φ(b′,b) ∂Φ(b′′,b′) 1+ u (c) = β E θ′g (b′)+R −φ − u (c′) θ,d′ +(1−χ)λ+δ¯µ (cid:20) ∂b′ (cid:21) c b (cid:20)(cid:18) b L b ∂b′ (cid:19) c (cid:12) (cid:21) (cid:12) (cid:12) u (c) = β E R u (c′) θ,d′ +λ+µR (cid:12) c b S c S (cid:20) (cid:12) (cid:21) (cid:12) (cid:12) (cid:12) Numerical solution. Thenumericalalgorithmsolvesthebanker’sproblembysolvingforafixed point in the consumption function by time iteration as in Coleman [1990]. The policy function c (θ,x ,b,d′) is approximated using piecewise bilinear interpolation of the state variables x and b. b b b 31

The variables x and b are discretized in a non-uniformly spaced grid points with 100 nodes each. b More grid points are allocated to lower levels of each state variable. The two stochastic processes, θ and d′, are discretized into five and four states, respectively, using the method proposed by Tauchen [1986]. The policy functions of consumption for workers and entrepreneurs are also solved by time iteration. Because the state space is smaller the variables x and x are discretized in w e a non-uniformly spaced grid with 900 nodes. The invariant distributions of bankers, workers and entrepreneurs are derived by computing the inverse decision rules on a finer grid than the one used to compute the optimal decision rules. Finally, the equilibrium prices are determined using a standard quasi-newton method. Transitional dynamics. Thetransitiontothenewstationaryequilibriumiscalculatedassuming the new steady state is reached after 60 periods (T = 60). We take as inputs the steady state distribution of agents in period t = 1 (prior to the change in policy), guesses for the path of RL, RS, and K/L between t = 1 and t = T, and the optimal decision functions at the new steady state. Usingthoseguesseswesolvetheproblemofeachagentbackwardsintime,fort = T−1,...,1. With thetime-seriessequenceofdecisionrulesforeachagentwesimulatethedynamicsofthedistribution for workers, entrepreneurs and bankers and check if the loan market, the deposit market and goods market clear. If the these markets are not in equilibrium we update the path of RL, RS and K/L using a simple linear updating rule. Finally, after convergence of the algorithm, we compare the simulated distribution at T = 60, with the steady state distribution of each agent type obtained after the change in the policy parameters. Markov chains. Both the revenue and deposit shocks of the banker follow a first-order Markov process with 5 and 4 states, respectively. The Markov chain process for the revenue process is as follows. θ¯= [0.69;0.83;1.0;1.21;1.46] 0.42 0.55 0.03 0.00 0.00 0.05 0.62 0.33 0.00 0.00 Π(θ′,θ) = 0.00 0.15 0.70 0.15 0.00     0.00 0.00 0.33 0.62 0.05     0.00 0.00 0.03 0.55 0.42   32

As for the deposit shock process we assume: d¯= [0.47;0.78;1.28;2.12] 0.75 0.25 0.00 0.00   0.02 0.89 0.09 0.00 Π(d′|d) = 0.00 0.09 0.89 0.02     0.00 0.00 0.25 0.75   33

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