The Federal Reserve's Balance Sheet and Overnight Interest Rates

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. The Federal Reserve’s Balance Sheet and Overnight Interest Rates Jaime Marquez, Ari Morse, and Bernd Schlusche 2012-66 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.

The Federal Reserve’s Balance Sheet and Overnight Interest Rates Jaime Marquez∗ Ari Morse‡ Bernd Schlusche¶ September 10, 2012 ABSTRACT This paper provides a comprehensive study of the interplay between the Federal Reserve’s balance sheet and overnight interest rates. We model both the supply of and the demand for excess reserves, treating assets of the Federal Reserve as policy tools, and estimate the effects of conventional and unconventional monetary policy on overnight funding rates. We find that, in the current environment with quite elevated levels of reserves, the effect of further monetary policy accommodation on overnight interest rates is limited. Further, assuming a path for removing monetary policy accommodation that is consistent with the FOMC’s exit principles, weprojectthatthefederalfundsrateincreasesto70basispoints,settlinginacorridorbracketed by the discount rate and the interest rate on excess reserves, as excess reserves of depository institutions decline to near zero. JEL classification: E43, E47, E52, E65, G01, G17 Keywords: Reserve Balances, Federal Funds Rate, Balance Sheet, Large-Scale Asset Purchases, Interest Rate on Excess Reserves, Exit Strategy ∗Board of Governors of the Federal Reserve System. E-mail: jaime.marquez@frb.gov. ‡Tepper School of Business, Carnegie Mellon University. E-mail: amorse@tepper.cmu.edu. ¶Correspondingauthor: BoardofGovernorsoftheFederalReserveSystem,20thStreetandConstitutionAvenue NW, Mailstop 85, Washington, DC 20551. E-mail: bernd.schlusche@frb.gov. Phone: +1 (202) 452-2591. Fax: +1 (202) 452-2301. WehavegreatlybenefitedfromvaluablesuggestionsprovidedbySethCarpenter,JaneIhrig,RuthJudson,Elizabeth Klee,StephenMeyer,andViktorsStebunovs. TheauthorsalsothankMichaelBauer,FrankDiebold,DavidHendry, Spence Hilton, Todd Keister, David Skeie, Heather Wiggins, and Jonathan Wright; as well as seminar participants at the Federal Reserve Board, the Federal Reserve Bank of Cleveland System Conference, the 11th OxMetrics User Conference, the 4th International Finance and Banking Society Conference, and the Rimini Centre for Economic Analysis for many useful comments on the paper. We are grateful to Ruth Judson for providing Figures 2-4. Most partsofthepaperwerecompletedwhenAriMorsewaswiththeFederalReserveBoard. Theviewsexpressedinthis paperarethoseoftheauthorsandnotnecessarilythoseoftheBoardofGovernors,othermembersofitsstaff,orthe Federal Reserve System. Oxmetrics 6.1. was used for the empirical analysis. 1

1. Introduction In response to the financial crisis of 2008, the Federal Reserve adopted a variety of unconventional monetary policy measures.1 The use of these measures led to an unprecedented change in the size and composition of the Federal Reserve’s balance sheet that affected short-term interest rates.2 Initially, the Federal Reserve implemented various liquidity facilities to promote the functioning of financial markets. The associated increase on the asset side of the Federal Reserve’s balance sheet was matched by a comparable increase in reserve balances on the liability side of the balance sheet.3 As the crisis went on and various liquidity facilities wound down, the Federal Reserve beganitslarge-scaleassetpurchases. Reducingtheamountofprivately-heldsecuritieswasintended to reduce longer-term interest rates. Besides putting downward pressure on longer-term interest rates, theunconventionalpolicyactionsresultedinanunprecedentedincreaseinreservebalancesof depository institutions (DIs). Over this period, as reserve balances increased, short-term interest rates experienced an unprecedented deline (Figure 1). Indeed, the federal funds rate and other short-term interest rates reached their zero lower bound and have remained there since.4 The purpose of this paper is to model the interplay between the Federal Reserve’s balance sheet and overnight interest rates, while allowing for interdependencies among these rates. This framework is used to assess the effect of both conventional and unconventional monetary policy changes on overnight interest rates. In particular, we study both the impact of further policy accommodation by the Federal Reserve and the removal of the monetary policy accommodation currently in place. Our exit strategy simulation is based on the exit principles specified in the June 2011 minutes of the Federal Open Market Committee (FOMC), FOMC (2011b). Our results suggest that, in the current environment, where the level of excess reserve bal- 1For a summary of unconventional policy approaches at the zero lower bound, see Clouse et al. (2003), Bernanke and Reinhart (2004), and Bernanke et al. (2004). 2See Carpenter et al. (2012) for a discussion of the effect of unconventional monetary policies on the Federal Reserve’s balance sheet. 3Note that the Supplemental Financing Account (SFA), established by the U.S. Treasury in September 2008, somewhat offset the increase in reserve balances. 4See, e.g., Afonso et al. (2011), Bech et al. (2012), and Gorton and Metrick (2012) for details on the functioning of overnight funding markets during the financial crisis. 2

ances is quite elevated by historical standards, the demand curve for these balances is extremely flat: Further monetary policy accommodation therefore puts only limited downward pressure on overnight interest rates. Furthermore, under certain assumptions about the path for the removal of monetary policy accommodation that is consistent with the June 2011 FOMC exit principles, our projections suggest that the accommodative stance of monetary policy in place since 2008 is effectively reversed and excess reserves return to a normal level by historical standards. Under our assumptions, excess reserves of DIs decline to a level close to that observed prior to the crisis, which results in an increase in the federal funds rate to 70 basis points by 2016, a level that is in the middle of the corridor bracketed by the discount rate and the interest rate on excess reserves (IOER rate). Our framework differentiates the demand for reserves from the supply of reserves. To model the supply of reserve balances, we treat the assets of the Federal Reserve as policy variables and endogenize its liabilities. Specifically, we model required reserve balances held by DIs as a function of reservable deposits held at banks.5 Excess reserves respond to ensure that total assets of the Federal Reserve equal total liabilities plus capital. The demand for reserve balances is modeled as a non-linear, simultaneous system of equations determining the federal funds rate, the Treasury general collateral (GC) repo rate, and the Eurodollar rate. Our work contributes to the literature in several ways. First, this paper extends previous workonthe“liquidityeffect”—theresponseofshort-terminterestratestoachangeintheamountof reserve balances—as documented by Hamilton (1996) and Hamilton (1997).6 Specifically, previous empiricalworkontheliquidityeffect,exceptforBechetal.(2012),quantifiestheeffectofmonetary policychangeswithnoallowanceforinterdependenciesamongshort-terminterestrates. Incontrast, we accommodate linkages among banks’ various short-term funding options with the associated implications for overnight rates. Specifically, in our framework, a change in the federal funds rate simultaneously affects the repo rate and the Eurodollar rate; these changes then feed back to the 5Throughout the paper, we use the generic term bank and depository institution interchangeably when referring toinstitutionsholdingaccountsattheFederalReserve,i.e.,commercialbanks,creditunions,andthriftinstitutions. 6See,forinstance,CarpenterandDemiralp(2006),CarpenterandDemiralp(2008),JudsonandKlee(2010),Bech et al. (2012), and Kopchak (2011) for more work on the liquidity effect. 3

federal funds rate. Second, we use the full-information maximum likelihood method for parameter estimation in order to account for the simultaneous determination of reserves and the federal funds rate. Previous work uses limited information estimation methods to avoid simultaneity biases. Nevertheless, this approach is not suited for our work because it treats reserves as endogenous for parameter estimation but exogenous for policy analysis. Third, previous studies generally focus on the short-term dynamics of interest rates to temporary changes in reserve balances.7 Information on short-run dynamics, however, is not sufficient to study the effects of unconventional monetary policy and the removal of such policy. Our framework encompasses both short-run dynamics and steady states as well as their responses to temporary and permanent changes in policy actions. Fourth, the prior literature is mostly concerned with interest rate responses to changes in reserve balances. In contrast, we examine the relation between the levels of overnight interest rates and reserve balances, which allows us to answer important policy questions, such as the determination of the amount of reserve balances consistent with a certain level for the federal funds rate. Finally, all of these extensions can be used to assess the effects of monetary policy actions at the zero lower bound. In particular, we investigate the implications of further monetary policy accommodation and of an exit strategy, that is consistent with the June 2011 FOMC exit principles, on short-term interest rates. Theremainderofthepaperproceedsasfollows: Section2describesourempiricalframework, designed to capture the interplay between the evolution of the Federal Reserve’s balance sheet and overnight interest rates. Section 3 presents the estimation results. Section 4 shows projections of the effects of conventional and unconventional monetary policy on overnight interest rates. Section 5 concludes. 7See,forexample,Hamilton(1997),CarpenterandDemiralp(2006),CarpenterandDemiralp(2008),Judsonand Klee (2010), and Bech et al. (2012). 4

2. Framework 2.1. Supply of Reserve Balances Prior to the financial crisis, temporary open market operations (e.g., repurchase agreements) were the primary means of monetary policy by which aggregate reserve balances were altered in order to attain the target federal funds rate set by the FOMC.8 These operations were so finely tuned that reserve balances of DIs rarely exceeded $25 billion (Figure 2), of which balances held in excess of balance requirements represented only a tiny fraction.9 Federal Reserve notes (currency) in circulation constituted the largest liability and were collateralized by holdings of U.S. Treasury securities, the largest asset of the Federal Reserve (Figure 3).10 The initial response of the Federal Reserve to the financial crisis involved implementing various liquidity facilities to support the functioning of funding markets. As shown in Figure 4, the expansion of these facilities was initially sterilized through sales and redemptions of U.S. Treasury securities in an attempt to be “reserve-neutral” (see Open Market Operations Report (2008)). As the crisis continued, however, the Federal Reserve abandoned its sterilization efforts, while continuing to inject ample liquidity into the market. Repurchase agreements were brought to zero and replaced with outright acquisitions of substantial amounts of U.S. Treasury securities, Agency debt securities, and Agency mortgage-backed securities (MBS). These purchases increased deposits of DIs, which became the largest liability; most of these deposits constitute excess reserves. In the end, the size of the balance sheet (total assets) increased from $877 billion by the end of August 2007 to about $2.9 trillion by the end of April 2012. Formodelingpurposes,wetreatallsecuritiesholdingsoftheFederalReserveasasingleasset. This treatment assumes that U.S. Treasury securities, Agency MBS, and Agency debt securities are perfect substitutes and thus can be combined into a single aggregate that we denote by S. We retain explicitly repurchase agreements (RP), even though they are currently zero, because a resumption of normal market functioning may renew the interest in temporary open market 8The discussion of the supply of reserve balances follows closely the material in Judson and Klee (2010). 9The data for required and excess reserves are published in the Federal Reserve’s statistical release H.3. 10All balance sheet items are described in the Federal Reserve’s statistical release H.4.1. 5

operations. Foreign exchange swaps and loans extended through either the discount window or the liquidity facilities are combined into other assets (OA). In terms of liabilities, we disaggregate reserves into excess reserves (Re) and required reserves (Rr); we account for currency in circulation (C)separatelybecauseofitslargemagnitude. Allotherliabilities(e.g.,theU.S.Treasury’sGeneral Account, reverse repurchase agreements, and term deposits) as well as capital are combined into other liabilities (OL). The simplified balance-sheet identity is S +RP +OA = (Rr +Re)+C +OL. (1) We assume that S, RP, and OA are determined by monetary policy and are, therefore, exogenous. We also treat as exogenous C and OL but endogenize required reserves (Rr) and excess reserves (Re). We model Rr as a fraction λ of “reservable” deposits D held at DIs:11 Rr = λ·D, λ > 0, (2) where λ is the average required-reserve ratio.12 To explain these deposits, we postulate that D = fD(ifed, Y ), (3) (−) (+) where ifed is the federal funds rate, Y is personal income, and the signs underneath each variable representoura-prioriexpectationoftheeffectofthatvariable. Weexpectthatincreasesinifed raise short-term interest rates faster than interest rates on checkable deposits; hence, the opportunity costofholdingreservabledepositsincreases, andD decreases(seeCarpenterandDemiralp(2008)). To determine the supply of excess reserves, we substitute equation (3) into equation (2) and solve for Re in equation (1) to obtain 11Deposit data are published in the Federal Reserve’s statistical release H.6. 12Reserve ratios can be found on the Federal Reserve’s web page (http://www.federalreserve.gov/ monetarypolicy/reservereq.htm#table1). For more details on reserve ratio specifications, see the Federal Reserve Board’s Regulation D. 6

Re = S +RP +OA−(C +OL)−λ·fD(ifed,Y), (4) (cid:124) (cid:123)(cid:122) (cid:125) Rr which ensures that the Federal Reserve’s total assets equal total liabilities plus capital. Note that ∂Re ∂fD = −λ· > 0. (5) ∂ifed ∂ifed In other words, an increase in the federal funds rate raises the supply of excess reserves, all else constant. Intuitively, holding constant the size of the Federal Reserve’s balance sheet and total reserves, a higher federal funds rate reduces transaction deposits, which lowers required reserves. Lower required reserves, with constant total reserves, means more excess reserves. 2.2. Demand for Reserve Balances We assume that the (inverse) demand for excess reserve balances can be expressed as: ifed = ffed(Re, irepo, ieurdol, idisc, ier), (6) − + + + + where irepo is the overnight Treasury general collateral (GC) repo rate, ieurdol is the Eurodollar rate, idisc is the discount rate, and ier is the interest rate on excess reserves.13 A reduction in the federal funds rate lowers DIs’ opportunity cost of holding excess reserves and hence creates an incentive to demand additional reserves above required reserves. As a result, we expect an inverse relationship between Re and ifed, all else unchanged. However, all else need not be unchanged, and thus we include additional funding rates that affect the demand for excess reserves. Specifically, if other funding rates increase, the demand for funding in the federal funds market will increase, which, in turn, will raise the federal funds rate for a given supply of excess reserve balances. As shown in Figure 5, the federal funds, the repo, and the Eurodollar rates co-move around the intended target rate set by the FOMC.14 These co-movements stem from the overlap of par- 13On October 9, 2008, the Federal Reserve began to pay interest on banks’ required and excess reserve balances. 14The effective federal funds rate, which is published in the Federal Reserve’s H.15 release, is calculated as the weightedaveragerateonbrokeredovernightfederalfundstransactions,whichareaformofuncollateralizedborrowingbyDIs,typicallyovernight. AnexemptioninRegulationDallowsborrowingfromaspecificsetoflenders—other depository institutions, broker dealers, and the GSEs—to be classified as federal funds instead of deposits. Uncollateralized borrowing by DIs may also be booked through offshore affiliates. These borrowings are classified as 7

ticipants in various funding markets that generally leads to active arbitrage across these markets. Indeed, as noted in the top row of Table 1, DIs borrow in all three markets. DIs generally rely on federal funds and Eurodollars as sources of borrowing to meet general short-term funding needs. In addition, since the advent of payment of interest on reserves, DIs have also borrowed in these markets to arbitrage the market rates against the higher IOER rate. Institutions borrowing in the repo market—which include DIs, broker dealers, and others—typically finance the specific assets pledgedascollateralinthetrade. Onthelendingsideofthemarkets,asshowninthebottomrowof the table, there is more segmentation in participation across the markets. Depository institutions, broker dealers, and government-sponsored enterprises (GSEs) are the lenders in the federal funds market. Even though GSEs could lend Eurodollars as well, they tend, in practice, to be less active in this market. They are, however, active participants in the repo market. Money market mutual funds are active lenders in the Eurodollar market and in the repo market. Given these interdependencies, we endogenize both irepo and ieurdol as irepo = frepo(ifed, ieurdol), (7) + + ieurdol = feurdol(ifed, irepo). (8) + + Taken together, equations (6)-(8) extend the literature on the liquidity effect by recognizing interdependencies among wholesale funding markets and by including the IOER rate as an additional tool of monetary policy. 2.3. Transmission Channels Changes in S affect the federal funds rate through several channels. First, a reduction in S reduces reserve balances, as DIs’ deposits at the Federal Reserve are debited when DIs purchase the Eurodollar deposits and are brokered through the same brokers that serve the federal funds market. The series for theEurodollarrateisobtainedfromBloomberg. SeeStigumandCrescenzi(2007)foranoverviewoftheEurodollar market. The Treasury GC repo rate is calculated as a weighted average rate paid by dealers and their customers onovernightrepurchaseagreementscollateralizedwithU.S.Treasurysecurities. Thereporatedataarecollectedby theFederalReserveBankofNewYork(FRBNY)aspartofadailysurveyoftheprimarydealers. See, forinstance, Stigum and Crescenzi (2007) and Bech et al. (2012) for more institutional details on the repo market. 8

securities.15 These sales reduce excess reserves, which increases the federal funds rate: S ↓→ Re ↓→ ifed ↑ . Second,thisincreaseinthefederalfundsrateraisestheborrowingcostinallotherfundingmarkets, which then feeds back to the federal funds rate:    irepo ↑→ ifed ↑, S ↓→ ifed ↑→   ieurdol ↑→ ifed ↑ . Finally, these increases in ifed raise the opportunity cost of holding reservable deposits and reduce D. This reduction lowers reserve requirements, raises excess reserves, and lowers the federal funds rate: S ↓→ ifed ↑→ D ↓→ Rr ↓→ Re ↑→ ifed ↓ . Thus, the direction of the response of ifed to a change in S is not known in advance. We resolve this ambiguity empirically by specifying and estimating an econometric model. 15The opposite effects would be triggered by an increase in S. 9

2.4. Model Specification We postulate the following econometric model: lnifed = α + α lnirepo+ α lnieurdol + α lnidisc+ α Re t 0 1 t 2 t 3 t 4 t (±) (+) (+) (+) (−) +α ier + α lnifed +ufed, (9) 5 t 6 t−1 t (+) (+) lnirepo = β + β lnifed+ β lnieurdol + β lnirepo+urepo, (10) t 0 1 t 2 t 3 t−1 t (±) (+) (+) (+) lnieurdol = δ + δ lnifed+ δ lnirepo+ δ lnieurdol +ueurdol, (11) t 0 1 t 2 t 3 t−1 t (±) (+) (+) (+) Re = S +RP −(Rr +C −OA +OL ), (12) t t t t t t t Rr = λ + λ D + λ Rr +ur, (13) t 0 1 t 2 t−1 t (±) (+) (+) D = φ + φ Y + φ lnifed+ φ D +uD, (14) t 0 1 t 2 3 t−1 t (±) (+) (−) (+) u = (ufed,urepo,ueurdol,ur,uD)(cid:48) ∼ N(0,Ω). t t t t t t This model has three interesting properties. First, it allows for delayed responses to changes in market conditions. Second, modeling the logarithm of interest rates allows to capture nonlinearities. Finally, it includes the interest rate on excess reserves. This inclusion raises estimation challenges because this rate was “zero” prior to October 2008 and exhibited wide swings right after its introduction, before stabilizing at 25 basis points. To control for the “novelty” of this rate during its initial phase, we include a dummy variable in equation (9), not shown, with a value of 1 from October 2008 to December 2008 and zero otherwise.16 16Also,theequationforthelogarithmofthefederalfundsrate,equation(9),includesadummyvariabletocapture quarter-end effects (not shown). 10

Given the model, the response of the federal funds rate to a change in S is      channel1    ∂ifed = ifed·    (cid:122) α (cid:101) (cid:125)(cid:124) 4 (cid:123)    (cid:83) 0, (15) ∂S    1− α (cid:101) (cid:16) 1 ·(β(cid:101)1 +β(cid:101)2 δ(cid:101) (cid:17) 1 ) − α (cid:101)2 (cid:16) ·(δ(cid:101)1 +δ(cid:101)2 · (cid:17) β(cid:101)1 ) + λ(cid:101)1 φ(cid:101)2 α (cid:101)4      1−δ(cid:101)2 ·β(cid:101)2 1−δ(cid:101)2 ·β(cid:101)2 c (cid:124) han (cid:123) n (cid:122) el (cid:125) 3   (cid:124) (cid:123)(cid:122) (cid:125) channel2 where tildes denote long-run coefficients (e.g., φ(cid:101)2 = 1− φ2 φ3 ). For example, a decline in S reduces excess reserves directly, which then raises the federal funds rate (channel 1). This increase in the federal funds rate is transmitted to all other interest rates, which then feeds back as an additional impulse to the federal funds rate (channel 2). The increase in the federal funds rate also reduces reservabledepositswhich,inturn,decreasesreserverequirements,raisesexcessreserves,anddampens the increase in the federal funds rate (channel 3). Thus, whether securities holdings and the federal funds rate are negatively correlated, that is, ∂ifed < 0, is an empirical question which we ∂S now address. 3. Empirical Analysis 3.1. Sample Selection The data consist of daily observations (business days) from January 10, 2003 to March 30, 2012. We use this period for estimation because alternative periods, as discussed below, are not helpful in assessing the exit strategy principles: • Alternative 1: Use exclusively the pre-crisis period because subsequent observations are from a distorted sample. This alternative, however, cannot possibly recognize the role of the interest rate on excess reserves, which is problematic because the principles rely on this tool. • Alternative 2: Use exclusively the post-crisis sample because the crisis represents a break with the past. This alternative is problematic because the variability of interest rates in this 11

period is virtually absent, and, hence, the rates are not statistically reliable for assessing the principles. • Alternative 3: Use the pre-crisis sample to estimate a set of parameters and the post-crisis sample to estimate another set of parameters.17 This approach assumes that, as excess reserves are drained to their pre-crisis level, the economy switches automatically from the post-crisis parameter values to the pre-crisis parameter values. But, because the pre-crisis parameters are estimated before the introduction of interest payments on excess reserves and the Term Deposit Facility, these estimates are not applicable to the exit period. 3.2. Estimation Results We use the full-information maximum likelihood (FIML) method to estimate the parameters of equations (9)-(14).18 In terms of coefficient estimates, the results in Table 2 confirm the inverse, andstatisticallysignificant, relationbetweenexcessreservesandthefederalfundsrate. Theresults also confirm the interdependencies among overnight interest rates: the coefficients are positive and highly significant. As shown in Figure 6, the model has a good fit with a large degree of explanatory power (first column) and uncorrelated residuals (second column). In terms of out-ofsample predictive accuracy, the RMSE for the federal funds rate is 3 basis points (bottom row in Table 2). ThesensitivityoftheestimatestodifferentsampleperiodsisdocumentedinTable3,showing estimation results for three samples: pre-crisis, post-crisis, and full sample. We find that the parameters in the equations for the repo and Eurodollar rates are somewhat sensitive to the choice of the sample period. The parameters in the equation for the federal funds rate are fairly robust to different estimation samples. 17Bech et al. (2012) pursue this approach. 18OnepracticaldifficultyinimplementingtheequationforD isthedailyfrequencyofoursample. Specifically,we do not have a published measure of daily personal income, Y. Thus, we interpolate the monthly data for personal income from the Bureau of Economic Analysis. 12

The reduced-form coefficients are reported in Table 4.19 Row headings in the table correspond to endogenous variables and column headings correspond to exogenous variables. The estimates are statistically significant and their signs are consistent with our a-priori views. In terms of magnitudes, a change in S implies a nearly one-for-one change in excess reserves.20 The response of ifed to a change in S is difed = −ifed·0.933·dS. (18) Thus, the empirical analysis removes the ambiguity in the theoretical analysis: SOMA holdings, S, and the federal funds rate, ifed, are negatively correlated. Note that, due to the non-linearity of the model, the response of ifed to changes in S depends on the value of ifed.21 The long-run responses of ifed to changes in the discount rate and the interest rate on excess reserves are ifed difed = ·1.204·didisc, and (19) idisc difed = ifed·0.482·dier. (20) Using June 2012 values of the rates, we get 0.10 difed = ·1.204·didisc = 0.161·didisc, 0.75 which means that the federal funds rate reacts to policy rate changes less than one-for-one at the current level of rates. 19We express equations (9)-(14) as y (cid:98)t =A(cid:98)y t−1 +B(cid:98)x t , (16) wherey (cid:98)t isthevectorofpredictionsfortheendogenousvariables,x t isthevectorofexogenousvariables,andA(cid:98) and B(cid:98) are matrices of estimated parameters. The associated deterministic long-run solution is (cid:104) (cid:105)−1 y (cid:98)t = I−A(cid:98) ·B(cid:98)x t =Π(cid:98)·x, (17) where Π(cid:98) is the matrix of reduced-form coefficients reported in Table 4. 20The remaining exogenous variables on the balance sheet have the same coefficient (in absolute value). 21For example, if ifed = 10 basis points, then a contraction in S of $1 trillion (dS = −1) raises ifed to 19 basis points(=10−10·0.933·(−1))inthelong-run. If, however,ifed =20,thenthesamecontractioninS raisesifed to 39 basis points. 13

3.3. Impulse Responses and Steady States Reduced-formestimatescannotanswerthefollowingkeyquestions: Istheequilibriuminthefederal fundsmarketstable? Ifso,istheadjustmenttoequilibriumsmoothoroscillatory? Finally,howlong does it take for the federal funds rate to reach a new steady state? To address these questions, we rely on the model’s estimated impulse responses. Specifically, Figure 7 plots the impulse responses toaninnovationinthefederalfundsrate. Aftertheshock,theresponseofthefederalfundsratefalls quickly,withtheratereachingitsnewequilibriumin60dayswiththebulkoftheadjustmenttaking place within the first week. The other overnight rates also increase and reach their equilibrium in about 60 days.22 The innovation in the federal funds rate also lowers reservable deposits and requiredreserves, whichraisesexcessreservesandtendstodampentheincreaseinthefederalfunds rate. Figure8plotstheimpulseresponsestoaninnovationinreservabledeposits. Aftertheshock, the response of these deposits falls as the federal funds rate increases. These deposits reach their new equilibrium in about a year but half of the adjustment is reached after 100 days. The increase inrequiredreserveslowersexcessreservesaboutone-for-one, which, inturn, raisesthefederalfunds rate. This increase is transmitted to the other interest rates, pushing them in the same direction; their responses die out after one year. Theseimpulseresponsessuggestthatthemodelisstable,andsowenowexaminewhetherthe steadystateimpliedbytheseresponsesismeaningfulfromaneconomicstandpoint. Tothisend, we conduct dynamic simulations through December 2015 under the assumption that residuals are zero andthatallexogenousvariablesremainconstantattheirlasthistoricalvalueforestimation(March 30, 2012).23 As Figure 9 shows, the model reaches a meaningful steady state by the beginning of 2013 with reasonable values for the endogenous variables: the federal funds rate is about 11 basis 22Note that the full responses will take considerably longer because we assume a distribution of adjustments with exponentially declining weights. 23Formally, the simulations are generated as y (cid:98)T+h =A(cid:98)y (cid:98)T+h−1 +B(cid:98)x+0, where T is the last date of the estimation sample (March 30, 2012) and h is the simulation horizon, which is set to 1100 days. 14

points and the historical spreads among funding rates are preserved. That is, the rate on secured funding (repo rate) is below the rates on unsecured funding (the federal funds and Eurodollar rates). 4. Monetary Policy Simulations Based on our estimation results, we conduct dynamic simulations to assess the effects of monetary policy changes on overnight interest rates. In the following, we first describe the impact of changes in the supply of reserve balances on short-term interest rates in normal times—that is, the effect of changes in conventional monetary policy, with reserve balances at their pre-crisis level.24 Second, we analyze the effects of further monetary policy accommodation on short-term interest rates, either through another round of large-scale asset purchases or a cut in the IOER rate. Third, assuming a path for the removal of monetary policy accommodation by the Federal Reserve that is consistent with the June 2011 FOMC exit principles (FOMC (2011b)), we provide the first empirical assessment of the response of short-term interest to this exit strategy. 4.1. Effects of Conventional Monetary Policy Priortothefinancialcrisis,temporaryopenmarketoperations—primarilyrepurchaseagreements— were the Federal Reserve’s primary means for day-to-day monetary policy implementation. The FederalReserveconductedtheseoperationstoalignthesupplyofreservebalanceswiththedemand for these balances to attain the target federal funds rate set by the FOMC.25 Changes in the supply of reserve balances affect the federal funds rate, all else equal. This effect can be quantified by determining the slope of the demand curve for reserves. The estimation result in Table 4 (row 6, column 5) suggests that reserve balances adjust nearly one-for-one to changes in repurchase agreements (RP). The effect of a change in the Federal Reserve’s repurchase agreements on the federal funds rate is difed = −ifed ·0.933·dRP (row 6, column 5 in Table 4), which takes into account the effect of a change in reserve balances on the the federal funds rate. 24See,forexample,CarpenterandDemiralp(2006),CarpenterandDemiralp(2008),JudsonandKlee(2010),Bech et al. (2012), and Kopchak (2011) for further analysis on the “liquidity effect.” 25See Judson and Klee (2010) for a description of the demand and supply framework for reserve balances. 15

As discussed previously, the magnitude of the effect depends on the level of the federal funds rate. Assuming a federal funds rate of 4%, a $10 billion increase in RP, which raises reserve balances by nearly the same amount, lowers the federal funds rate by approximately 4 basis points. Clearly, in an environment with lower overnight interest rates, an equally-sized increase in RP has a much smaller effect on the federal funds rate. 4.2. Effects of Additional Unconventional Monetary Policy We now use the model to examine the effects of further policy accommodation by the Federal Reserve. When asked at the semi-annual testimony to Congress on July 17, 2012 about options for further monetary policy easing, Federal Reserve Chairman Bernanke mentioned various actions the Federal Reserve has at its disposal. In this study, we are assessing two of these options: (1) another round of large-scale asset purchases and (2) lowering the interest rate on excess reserves.26 First, we simulate a hypothetical increase in S. In our model, the federal funds rate declines as the supply of reserves increases with the expansion in S (the paths of SOMA and excess reserves under the different scenarios are shown in the bottom panel of Figure 10). In our simulation, for simplicity, we assume that S increases by $900 billion over a period of one year, starting in January 2013, the date when the Maturity Extension Program (MEP) will be completed.27 The simulations reveal that the gradual expansion in S lowers the federal funds rate gradually from 11 basis points to 5 basis points after one year, as indicated by the dashed line in Figure 10. The seemingly small response owes to the non-linearity of the model, as reflected in the low starting value of the federal funds rate. Indeed, as shown in equation (18), the response of the federal funds rate to a small change in S is difed = −ifed·0.933·dS. Second, we simulate a hypothetical reduction in the IOER rate of 10 basis points, from the current level of 25 basis points, on January 1, 2013. The downward pressure of a cut in the IOER 26Salesofshorter-datedTreasurysecuritiesandsimultaneouspurchasesofanequalamountoflonger-datedTreasury securities in the ongoing Maturity Extension Program are roughly reserve-neutral. Hence, potential effects of that program on short-term interest rates are beyond the scope of this paper. 27ThishypotheticalvalueisclosetothecombinedvalueofAgencyMBSandAgencydebtholdingsinSOMA($933 billionasofApril11,2012). TheincreaseinsecuritiesholdingsoftheFederalReserveperbusinessdayisabout$3.4 billion. 16

rate of 10 basis point on the federal funds rates is very small, leaving the federal funds rate nearly unchanged (see the short-dashed line in Figure 10). Again, the insignificance of this effect is not surprising in the context of the non-linearity of the model. Specifically, equation (20) indicates that difed = ifed·0.482·dier, that is, if the initial value of the federal funds rate is low, so will be its response to a change in the IOER rate. Finally, we combine these hypothetical policy actions. As indicated by the long-dashed line in Figure 10, the combined action—expanding S and cutting the IOER rate—lowers the federal funds rate by a marginal amount relative to the baseline. 4.3. Effects of the Removal of Unconventional Monetary Policy IntheJune2011FOMCminutes, theCommitteestateditsexit principles (FOMC(2011b)). These principles are listed, verbatim, in column 1 of Table 5. Greatly simplified, the stated principles envision an exit strategy implemented in four phases: 1. Stop reinvestments of securities. 2. Implement temporary reserve-drainage operations (e.g., expand the Term Deposit Facility (TDF) or conduct reverse repurchase agreements (RRP)). 3. Increase policy rates. 4. Sell SOMA securities. When removing the monetary accommodation, the FOMC has stated a preference for the federal funds rate to evolve in a corridor between the discount rate and the IOER rate: “[...] Mostoftheseparticipantsindicatedthattheypreferredthatmonetarypolicyeventually operate through a corridor-type system in which the federal funds rate trades in the middle of a range, with the IOER rate as the floor and the discount rate as the ceiling of the range, as opposed to a floor-type system in which a relatively high level of reserve balances keeps the federal funds rate near the IOER rate. [...]” (FOMC (2011a)) However, the principles do not include detailed information about the magnitude of the actions,theirpace,ortheirtiming. Thisabsenceofdetailedinformationraisestworelevantquestions. 17

First, does the sequence specified by the principles affect the dynamic path of the federal funds rate? Second, does the federal funds rate settle in a corridor as possibly preferred by the FOMC? We address these questions through model simulations, carried out under several assumptions.28 These hypothetical assumptions, which are one of many possible ways the FOMC can carry out these principles, are shown in column 2 of Table 5.29 We begin with changes in one policy at a time to assess the importance of non-linearities. We find that there are important non-linearities, which leads us to examine their implications for the principles’ sequencing. Finally, we change several policy variables at once to assess the feasibility of a corridor system. 4.3.1. Non-Linearities The first scenario is a hypothetical, instantaneous reduction in S of $900 billion. As indicated by the short-dashed line in Figure 11, the federal funds rate reaches a steady state of 25 basis points over a short period of time. This result suggests that, all other policy variables unchanged, a substantial reduction in S is needed to raise the federal funds rate to the level of the IOER rate, which so far has provided only an imperfect floor for the federal funds rate.30 This results is consistent with Bech and Klee (2011) who suggest that a large amount of reserve balances needs to be drained before DIs begin to enter the federal funds market to meet their financing needs, and the the IOER rate may be used as a monetary policy tool to help guide the federal funds rate. The second scenario is a hypothetical increase of 25 basis points in the discount rate (idisc). As indicated by the dashed line in Figure 11, this action raises the federal funds rate by about 5 basis points implying a less than proportional response because of the non-linearities. Recall, however, that this response is sensitive to the initial values of the two interest rates. To assess how important non-linearities are in the model, we include a third policy action, in which the above decline in S and the increase in the discount rate are implemented simultaneously. The dotted line in Figure 11 plots the response of the federal funds rate to that combination of 28Note that these scenarios are hypothetical and do not reflect any policy considerations by the Federal Reserve. 29See Carpenter et al. (2012) for an alternative modeling of the FOMC’s exit principles. 30SeeBechandKlee(2011)foradiscussionofreasonsfortheIOERrateprovidingonlyanimperfectfloorforthe federal funds rate. Foremost, GSEs ineligibility toreceive interest payments ontheir reservebalances at the Federal Reserve may explain their willingness to lend at a rate below the IOER rate. 18

policy actions. If the model were linear, then the response from the combination of actions should be approximately equal to the sum of the responses of the separate actions. As shown in Figure 11, the sum of the interest-rate responses to the two shocks is 20 basis points whereas the response associated with an implementation of both shocks at once is 25 basis points. In other words, the responsiveness of the federal funds rate to shocks is non-linear. This finding suggests that the sequencing of policy actions might affect the profile of the adjustment process. 4.3.2. Sequencing To study the implications of the principles’ stated sequencing for the federal funds rate, we use the two policy actions already considered but change the timing of their implementation: • Schedule A: – An instantaneous reduction in SOMA by $0.9 trillion on January 1, 2014. – An increase in the discount rate of 25 basis points on January 1, 2014. • Schedule B: – An instantaneous reduction in SOMA by $0.9 trillion on January 1, 2015. – An increase in the discount rate of 25 basis points on January 1, 2014. • Schedule C: – An instantaneous reduction in SOMA by $0.9 trillion on January 1, 2014. – An increase in the discount rate of 25 basis points on January 1, 2015. The simulations reveal that, although the steady state of the federal funds rate is invariant to changing the sequencing of the shocks, the adjustment profile of the federal funds rate is not (Figure 12). The sequencing from Schedule C (a reduction in S followed by an increase in the discount rate) raises the federal funds rate in two steps of roughly equal size (the dashed line) whereas the reverse sequencing results in a muted initial response of the federal funds rate but a sharp increase in the federal funds rate later (the short-dashed line). The optimal choice depends on policy makers’ preferences. 19

4.3.3. Feasibility of a Corridor The process of reversing the accommodative stance of monetary policy begins with the implementation of principles 2 and 3 in Table 5. Starting in June 2014, we assume that the FOMC stops reinvestments, which translates into a reduction in S of $20 billion per month until March 2015. Further, we assume that the FOMC expands the Term Deposit Facility (TDF): Deposits in this facility increase by $10 billion in bi-weekly auctions, which end in June 2015; the bottom panel of Figure 13 shows the profile of these two variables. Note that the combined reserve drainage amounts through the TDF and SOMA reductions that we chose is below the pace of the increase in reserves during the second large-scale asset purchase program.31 The implementation of the next principle is assumed to involve an increase in both the discount rate and the IOER rate. We assume this increase to be 25 basis points (see the top panel of Figure 13) and to take place in December 2014. The implementation of the last principle involves an active reduction of S. We assume a gradual reduction of $5 billion per day starting in March 2015 and ending in December 2015. Based on these assumptions, S declines from $2.6 trillion in 2012 to $1.4 trillion by the beginningof2016andexcessreservesdeclinefrom$1.5trilliontoalmostzerooverthesameperiod, while term deposits increase to $300 billion (bottom panel of Figure 13). Under these assumptions, our model projects that the federal funds rate rises gradually, reaching 70 basis points by the end of 2015, with the historical spreads between overnight interest rates preserved (top panel of Figure 13). These results suggest that, without drastic policy actions, the federal funds rate can move into a corridor between the IOER rate and the discount rate, consistent with most FOMC members’ preference, as stated in the April 2011 FOMC minutes (FOMC (2011a)). 31We do not experiment with large-scale reverse repurchase agreements. The effect of these operations on reserve balances would be similar to those of term deposits but the impact on repo rates would most likely be different. 20

5. Conclusion In this study, we model the interplay between the Federal Reserve’s balances sheet and overnight interest rates, while allowing for interdependencies among overnight funding rates. In particular, we formulate a system of equations modeling the federal funds rate, the repo rate, the Eurodollar rate, reserve balances held by depository institutions, and demand deposit holdings. We rely on full-information methods for parameter estimation, recognizing the interdependencies among overnight funding rates and accounting for possible simultaneity biases. We use this framework to assess the effects of both conventional and unconventional monetary policy changes on shortterm interest rates. As for unconventional policy actions, we estimate the impact of further policy accommodation by the Federal Reserve and the removal of the policy accommodation currently in place. According to our results, in the current environment with quite elevated levels of excess reserve balances by historical standards, the effect of further monetary policy accommodation, in the form of large-scale asset purchases or a cut in the IOER rate, on short-term interest rates is limited because these rates are already close to zero. Moreover, assuming a path for the removal of monetary policy accommodation that is consistent with the June 2011 FOMC exit principles, we project that the accommodative stance of monetary policy is effectively removed and short-term funding markets return to a more normal functioning. Under our assumptions, the federal funds rate is projected to increase to 70 basis points by 2016, while excess reserves of DIs decline to a level close to that observed prior to the crisis. Finally, we document that, while the steady state is invariant to the order of policy changes, the sequencing of different policy measures in an exit strategy matters for the profile of the response of the federal funds rate. 21

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FOMC (2011b). Minutes of the Federal Open Market Committee, June 21-22, 2011. http://www. federalreserve.gov/monetarypolicy/fomcminutes20110622.htm. Gorton, G. and A. Metrick (2012). Securitized banking and the run on repo. Journal of Financial Economics 104(3), 425–451. Hamilton, J. D. (1996). The daily market for federal funds. Journal of Political Economy 104(1), 26–56. Hamilton, J. D. (1997). Measuring the liquidity effect. American Economic Review 87(1), 80–97. Judson, R. A. and E. Klee (2010). Whither the liquidity effect: The impact of Federal Reserve open market operations in recent years. Journal of Macroeconomics 32(3), 713–731. Kopchak, S. J. (2011). The liquidity effect for open market operations. Journal of Banking & Finance 35(12), 3292–3299. Open Market Operations Report (2008). Domestic open market operations during 2008. Annual Report by the Markets Group of the Federal Reserve Bank of New York. Stigum, M. and A. Crescenzi (2007). Stigum’s Money Market (4 ed.). New York: McGraw-Hill. 23

Billions of Dollars Percent 3000 6 2500 SOMA 5 Reserve Balances Federal Funds Rate 2000 4 1500 3 1000 2 500 1 0 0 2003 2004 2005 2006 2007 2008 2009 2010 2011 Figure 1: Federal Funds Rate, Reserve Balances of Depository Institutions, and Securities Held by the Federal Reserve 24

Billions of dollars J 30 Excess reserve balances Required clearing balances Required reserve balances 25 20 15 10 5 0 Jan 1, 2003 Jul 1, 2003 Jan 1, 2004 Jul 1, 2004 Jan 1, 2005 Jul 1, 2005 Jan 1, 2006 Jul 1, 2006 Jan 1, 2007 Jul 1, 2007 Jan 1, 2008 Jul 1, 2008 Figure 2: Components of Deposits of Depository Institutions from 2003 to 2008 25

1,000 Assets Term auction credit fl 800 Repurchase agreements and all other assets 600 Primary, secondary, and seasonal credit › 400 Treasury securities held outright 200 0 200 400 Federal Reserve notes in circulation 600 fl U.S. Treasury accounts 800 Reverse RPs, capital, and all other liabilities Liabilities and Capital › Deposits of depository institutions and other deposits 1,000 snoilliB $ Jan 1, 2003 Jan 1, 2004 Dec 31, 2004 Dec 31, 2005 Dec 31, 2006 Dec 31, 2007 Wednesdays Figure 3: Composition of the Federal Reserve’s Balance Sheet from 2003 to 2008 Source: H.4.1 Statistical Release (http://www.federalreserve.gov/releases/h41/). Last updated April 5, 2012. 26

3,000 2,500 Support for specific institutions (ML LLCs, Bear, AIG) fl 2,000 Other credit facilities (PDCF, AMLF, CPFF, TALF) fi 1,500 Assets Central bank liquidity swaps 1,000 Agency debt and mortgage−backed securities holdings Term auction credit Primary, secondary, and seasonal credit 500 Repurchase agreements and all other assets Treasury securities held outright 0 Federal Reserve notes in circulation 500 1,000 Reverse RPs, capital, and all other liabilities U.S. Treasury accounts Liabilities 1,500 and Capital Deposits of depository institutions and other deposits 2,000 2,500 3,000 snoilliB $ Jan 2, 2008 Jul 2, 2008 Dec 31, 2008 Jul 1, 2009 Dec 30, 2009 Jun 30, 2010 Dec 29, 2010 Jun 29, 2011 Dec 28, 2011 Jun 27, 2012 Wednesdays Figure 4: Composition of the Federal Reserve’s Balance Sheet from 2008 to 2012 Source: H.4.1 Statistical Release (http://www.federalreserve.gov/releases/h41/). Last updated April 5, 2012. 27

Percent 7 Fed. Funds Rate Repo Rate Eurodollar Rate Target Fed. Funds Rate 6 5 4 3 2 1 0 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Figure 5: Overnight Interest Rates and the Federal Funds Target Rate 28

Autocorrelation Functions Federal Funds Rate 2 AAccttuuaall FFiitttteedd 1 Federal Funds Rate 0 -2 2004 2006 2008 2010 2012 0 5 10 Repo Rate 2.5 1 Repo Rate 0 -2.5 2004 2006 2008 2010 2012 0 5 10 2 Eurodollar Rate 1 Eurodollar Rate 0 -2 2004 2006 2008 2010 2012 0 5 10 1.25Reservable Deposits 1 Reservable Deposits 0 0.75 2004 2006 2008 2010 2012 0 5 10 0.06 Required Reserves 1 Required Reserves 0.04 0 0.02 2004 2006 2008 2010 2012 0 5 10 Figure 6: Fitted Values and Autocorrelation Functions 29

1.0 Federal Funds Rate Repo Rate 0.4 0.5 0.2 0.0 0.0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Eurodollar Rate Reservable Deposits (trill) 0.50 -0.002 0.25 -0.004 0.00 0 50 100 150 200 250 300 0 50 100 150 200 250 300 0.0000 Required Reserves (trill) 0.0002 -0.0001 0.0001 Excess Reserves (trill) -0.0002 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Figure 7: Impulse Response Functions to Federal Funds Rate Shock 30

0.03 0.03 Repo Rate Federal Funds Rate 0.02 0.02 0.01 0.01 0 50 100 150 200 250 300 0 50 100 150 200 250 300 1.00 0.03 0.75 Reservable Deposits (trill) 0.02 Eurodollar Rate 0.50 0.01 0.25 0 50 100 150 200 250 300 0 50 100 150 200 250 300 0.04 0.00 0.03 -0.01 Required Reserves (trill) Excess Reserves (trill) 0.02 -0.02 0.01 -0.03 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Figure 8: Impulse Response Functions to Required Reserves Shock 31

Basis Points Basis Points 16 25 Repo Rate - Steady State 14 20 12 15 Fed. Funds Rate - Steady State 10 10 8 5 2012 2013 2014 2015 2012 2013 2014 2015 Basis Points Trillions of Dollars 14 1.65 12 1.60 Eurodollar Rate - Steady State 10 1.55 Excess Reserves - Steady State 8 1.50 6 1.45 4 1.40 2012 2013 2014 2015 2012 2013 2014 2015 Trillions of Dollars Trillions of Dollars 0.060 1.30 Reservable Deposits - Steady State 1.25 0.055 Required Reserves - Steady State 1.20 0.050 1.15 0.045 1.10 0.040 1.05 2012 2013 2014 2015 2012 2013 2014 2015 Figure 9: Steady States 32

Basis Points 20 15 Fed. Funds Rate (Baseline) Fed. Funds Rate (IOER) Fed. Funds Rate (SOMA) Fed. Funds Rate (SOMA + IOER) 10 5 2012 2013 2014 2015 Trillions of Dollars 4 3 2 1 Excess Reserves (Baseline) Excess Reserves (IOER) Excess Reserves (SOMA) Excess Reserves (SOMA + IOER) SOMA (Expansion) SOMA (No Expansion) 2012 2013 2014 2015 Figure 10: Effects of Additional Unconventional Monetary Policy 33

Basis Points 40 SOMA + Rates SOMA 35 Rates Baseline 30 25 20 15 10 5 2012 2013 2014 2015 Figure 11: ImplicationsofExitStrategiesfortheFederalFundsRate: SOMAReductionsvs. InterestRate Deviations From Baseline Increase Basis Points 40 SOMA + Rates SOMA 35 Rates Summed 30 25 20 15 10 5 0 2012 2013 2014 2015 34

Basis Points 45 40 Fed. Funds Rate (SOMA Now + Rates Now) Fed. Funds Rate (SOMA Later + Rates Now) Fed. Funds Rate (SOMA Now + Rates Later) 35 Fed. Funds Rate (Baseline) 30 25 20 15 10 5 2012 2013 2014 2015 Figure 12: Steady States for the Federal Funds Rate: Schedules A-C 35

Basis Points 105 95 85 75 65 Federal Funds Rate 55 Repo Rate Eurodollar Rate 45 I D O is E c R o u R n a t t R e ate 35 25 15 5 2012 2013 2014 2015 Trillions of Dollars 3.0 2.5 2.0 Excess Reserve Balances Total TDF Currency SOMA 1.5 1.0 0.5 0.0 2012 2013 2014 2015 Figure 13: Effects of the Removal of Unconventional Monetary Policy 36

Table 1: Major Market Participants in Overnight Funding Markets (1) (2) (3) Federal Funds Market Eurodollar Market Repo Market Borrowers Depository Institutions Depository Institutions Depository Institutions Broker Dealers Lenders Depository Institutions Money Market Funds Money Market Funds Broker Dealers Financial and Nonfinancial Lenders Securities Lenders GSEs GSEs The table lists the major participants in the federal funds market (column (1)), the Eurodollar market (column (2)), and thetripartyrepomarket(column(3)). Government-sponsoredenterprisesaredenotedbyGSEs. 37

2102 ,03 hcraM ot 3002 ,01 yraunaJ morf LMIF :stluseR noitamitsE :2 elbaT sevreseR .qR stisopeD .seR etaR .lodruE etaRopeR etaRsdnuF .deF 559.0 )1-(sevreseR .qR 299.0 )1-(stisopeD .seR 436.0 )1-(etaR .lodruE 377.0 )1-(etaRopeR 897.0 )1-(etaRsdnuF .deF ]700.0[ ]300.0[ ]810.0[ ]410.0[ ]610.0[ 100.0tnatsnoC 050.0tnatsnoC 420.0 tnatsnoC 430.0tnatsnoC 160.0tnatsnoC ]000.0[ ]620.0[ ]300.0[ ]600.0[ ]600.0[ 200.0 stisopeD .seR 100.0etaRsdnuF .deF 803.0 etaRsdnuF .deF 401.0 etaRsdnuF .deF 610.0 etaRopeR ]000.0[ ]000.0[ ]910.0[ ]540.0[ ]500.0[ 600.0 emocnI 530.0 etaRopeR 341.0 etaR .lodruE 190.0 etaR .lodruE ]300.0[ ]010.0[ ]740.0[ ]410.0[ 021.0 etaR .csiD ]900.0[ 840.0 REOI ]520.0[ 390.0sevreseRssecxE ]010.0[ nb85.0$ nb32$ pb83.2 pb04.7 pb88.3 ESMR :omeM .stekcarbderauqsnidetropererasrorredradnatS .smhtiragolnieraemocnilanosrepdnasetartseretnillA .)41(-)9(snoitauqefosetamitseretemarapLMIFehtstroperelbatsihT 38

Table 3: Estimation Results for Alternative Samples AlternativeSamples 1/9/2003-7/31/2008 7/31/2008-3/30/2012 1/9/2003-3/30/2012 Coefficient Std.Error Coefficient Std.Error Coefficient Std.Error Fed. FundsRate Fed. FundsRate(-1) 0.764 0.067 0.712 0.025 0.798 0.016 RepoRate 0.012 0.009 0.022 0.008 0.016 0.005 Eurdol. Rate 0.180 0.064 0.071 0.022 0.091 0.014 ExcessReserves -0.206 0.187 -0.244 0.024 -0.093 0.010 DiscountRate 0.055 0.009 0.222 0.019 0.120 0.009 IOER — — 0.041 0.036 0.048 0.025 Constant -0.029 0.006 -0.035 0.011 -0.061 0.006 SER 0.031 0.100 0.072 RepoRate RepoRate(-1) 0.792 0.018 0.760 0.023 0.773 0.014 Fed. FundsRate 0.604 0.189 0.084 0.073 0.104 0.045 Eurdol. Rate -0.389 0.177 0.159 0.079 0.143 0.047 Constant -0.015 0.005 -0.078 0.034 -0.034 0.006 SER 0.077 0.388 0.249 Eurdol. Rate Eurdol. Rate(-1) 0.338 0.024 0.600 0.028 0.634 0.018 RepoRate -0.035 0.008 0.043 0.017 0.035 0.010 Fed. FundsRate 0.710 0.027 0.306 0.031 0.308 0.019 Constant -0.013 0.002 -0.018 0.020 0.024 0.003 SER 0.030 0.219 0.144 Res. Deposits Res. Deposits(-1) 0.959 0.007 0.975 0.008 0.992 0.003 FederalFundsRate 0.000 0.001 -0.003 0.001 -0.001 0.000 Income -0.001 0.004 0.079 0.026 0.006 0.003 Constant 0.038 0.038 -0.728 0.239 -0.050 0.026 SER 0.010 0.015 0.012 Rq. Reserves Rq. Reserves(-1) 0.976 0.006 0.933 0.013 0.955 0.007 Res. Deposits -0.001 0.001 0.004 0.001 0.002 0.000 Constant 0.001 0.000 -0.001 0.000 -0.001 0.000 SER 0.001 0.002 0.001 This table reports the FIML parameter estimates of equations (9)-(14) for alternative samples. All interest rates and personalincomeareinlogarithms. Standarderrorsarereportedinsquaredbrackets. 39

Table 4: Long-Run, Reduced-Form Estimation Results: FIML from January 10, 2003 to March 30, 2012 SOMA Disc. Rate IOER Constant Repos NetOther Currency Income Fed. FundsRate -0.933 1.204 0.482 -0.887 -0.993 0.993 0.993 0.035 [0.058] [0.033] [0.241] [0.156] [0.058] [0.058] [0.058] [0.016] RepoRate -0.981 1.265 0.507 -1.045 -0.981 0.981 0.981 0.037 [0.064] [0.044] [0.254] [0.168] [0.064] [0.064] [0.064] [0.017] Eurdol. Rate -0.881 1.136 0.455 -0.783 -0.881 0.881 0.881 0.033 [0.056] [0.034] [0.228] [0.148] [0.056] [0.056] [0.056] [0.015] Res. Deposits 0.078 -0.100 -0.040 -5.841 0.078 -0.078 -0.078 0.711 [0.021] [0.027] [0.023] [2.977] [0.021] [0.021] [0.021] [0.319] Rq. Reserves 0.004 -0.005 -0.002 -0.325 0.004 -0.004 -0.004 0.038 [0.001] [0.001] [0.001] [0.160] [0.001] [0.001] [0.001] [0.017] ExcessReserves 0.996 0.005 0.002 0.325 0.996 -0.996 -0.996 -0.038 [0.001] [0.001] [0.001] [0.160] [0.001] [0.001] [0.001] [0.017] Thistablereportsthelong-run,reduced-formparameterestimatesofequation(17). Allinterestratesandpersonalincomearein logarithms. Standarderrorsarereportedinsquaredbrackets. 40

Table 5: Outline of the Exit Strategy (1)Principle (2)Implementation (3)Timeline 1 TheCommitteewilldeterminethetimingandpaceof Nochangeneeded — policynormalizationtopromoteitsstatutorymandate ofmaximumemploymentandpricestability. 2 Tobegintheprocessofpolicynormalization,theCom- ReductioninSOMAof$20bil- June2014-March2015 mittee will likely first cease reinvesting some or all lionpermonth paymentsofprincipalonthesecuritiesholdingsinthe SOMA. 3 At the same time or sometime thereafter, the Com- Initiation of TDF: Increase in June2014-June2015 mittee will modify its forward guidance on the path Other Liabilities (OL) by $10 of the federal funds rate and will initiate temporary billionperbiweeklyauction reserve-draining operations aimed at supporting the implementation of increases in the federal funds rate whenappropriate. 4 When economic conditions warrant, the Committee’s Increase in IOER rate by 25 December2014 nextstepintheprocessofpolicynormalizationwillbe basispointsandincreaseinthe to begin raising its target for the federal funds rate, target federal funds rate to 50 andfromthatpointon,changingthelevelorrangeof basispoints thefederalfundsratetargetwillbetheprimarymeans ofadjustingthestanceofmonetarypolicy. Duringthe normalizationprocess,adjustmentstotheinterestrate on excess reserves and to the level of reserves in the banking system will be used to bring the funds rate towarditstarget. 5 Sales of agency securities from the SOMA will likely Gradual Reduction of SOMA March2015-December2015 commencesometimeafterthefirstincreaseinthetar- by$5billion/day getforthefederalfundsrate. Thetimingandpaceof sales will be communicated to the public in advance; that pace is anticipated to be relatively gradual and steady, but it could be adjusted up or down in responsetomaterialchangesintheeconomicoutlookor financialconditions. 6 Once sales begin, the pace of sales is expected to be Nochangeneeded — aimed at eliminating the SOMA’s holdings of agency securitiesoveraperiodofthreetofiveyears,thereby minimizing the extent to which the SOMA portfolio might affect the allocation of credit across sectors of the economy. Sales at this pace would be expected tonormalizethesizeoftheSOMAsecuritiesportfolio over a period of two to three years. In particular, the size of the securities portfolio and the associated quantity of bank reserves are expected to be reduced to the smallest levels that would be consistent with theefficientimplementationofmonetarypolicy. 7 The Committee is prepared to make adjustments to Nochangeneeded — its exit strategy if necessary in light of economic and financialdevelopments. Column(1)ofthetableoutlinestheprinciplesoftheexitstrategyasdescribedinthehistoricalminutesoftheJune2011FOMC meeting. Column(2)liststheimplementationofthesesprinciplesinoursimulations. Column(3)containsthetimelineforvarious stepsoftheexitstrategy. 41