Rewiring repo

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Rewiring repo Jin-Wook Chang, Elizabeth Klee, Vladimir Yankov 2025-013 Please cite this paper as: Chang, Jin-Wook, Elizabeth Klee, and Vladimir Yankov (2025). “Rewiring repo,” Finance and Economics Discussion Series 2025-013. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2025.013. 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.

∗ Rewiring repo † ‡ § Jin-Wook Chang Elizabeth Klee Vladimir Yankov February 13, 2025 Abstract We develop a model of the repo market with strategic interactions among dealers who compete for funding in a decentralized over-the-counter market and have access to a centrally cleared interdealer market. We show that such “wiring” of the repo market combined with imperfect competition in dealer funding results in market inefficiencies and instability. The model allows us to disentangle supply and demand factors, and we use these factors to estimate supply and demand elasticities. Our estimates suggest that the instability of the market in September 2019 was driven by a large supply shock facing inelastic dealer funding demand, amplified by strategic interactions among dealers. We evaluate different interventions for market functioning and efficiency, including the Standing Repo Facility. JEL Classification: D53, G23, G14, L14, L16 Keywords: Networked markets, repo market, Standing Repo Facility, over-the-counter markets, market efficiency, centrally cleared markets ∗We thank Darrell Duffie, Huberto Ennis, Joe Haubrich, Sebastian Infante, Annette Vissing- Jorgensen, Borghan Narajabad, Ned Prescott, Lubomir Petrasek, David Lopez-Salido, Bruno Sultanum, and Jan-Peter Siedlarek for helpful discussions. This work benefited from interactions with participantsinseminarsandconferencesattheFederalReserveBoard,theFRBCleveland,theFRB Richmond,andthe2024NSFNetworkScienceandEconomicsConference,UniversityofMinnesota. We are also grateful to Erik Larsson for technical data expertise in the initial phases of this project. All remaining errors are our own and this article represents the views of the authors and not the views of the Board of Governors of the Federal Reserve System. First draft: August 8, 2023. Latest draft: February 13, 2025 †Federal Reserve Board, E-mail: jin-wook.chang@frb.gov ‡Federal Reserve Board, E-mail: elizabeth.c.klee@frb.gov §Federal Reserve Board, E-mail: vladimir.l.yankov@frb.gov.

1 Introduction Financial markets are often assumed to be efficient, but evidence suggests otherwise. Imperfect competition, market segmentation, and associated frictions could result in deviations from market efficiency. Inefficient financial markets are less resilient to shocks and could affect the stability of the financial system. One large financial market that has exhibited instability is the tri-party repo market for government securities. The market is a general collateral repo market for Treasury and agency mortgage-backed securities (MBS) with about $4 trillion in daily transactions at the end of 2022.1 The tri-party repo market provides funding for dealers, is a conduit of U.S. monetary policy implementation, and its market rates form the basis of the Secured Overnight Financing Rate (SOFR),the reference rate for trillions of dollars of loan and derivative contracts. The tri-party repo market has experienced recent episodes of instability. In September 2019, repo spreads spiked, absent credit risk events or a financial crisis. In March 2020, repo spreads also climbed, reverberating the financial market shock associated with the onset of the COVID-19 pandemic. The Federal Reserve intervened by conducting temporary repo operations in 2019 and 2020 to provide additional cash to dealers. Later, the Federal Reserve established the Standing Repo Facility (SRF) as a liquidity backstop aimed at supporting monetary policy implementation and market functioning. Following the episodes of market stress, regulators have started to examine Treasury cash and repo market structure. Many recent proposals introduce central clearing of contracts to support market efficiency and stability. Our paper examines factors that affect tri-party repo market efficiency and stability. We argue that the structure of the repo market, or the wiring of the market, when combined with imperfect competition among market participants, affects the potential for the repo market to amplify shocks. The structure of the tri-party repo market integrates four components. The first component is a decentralized over-the-counter (OTC) funding market, characterized by stable relationships between borrowing dealers and cash lenders. The second component is a centrally cleared anonymous interdealer segment, where no additional aggregate cash is provided to dealers, but some dealers borrowand other dealers lend. Thethird component is a bilateral segment be- 1Agency mortgage-backed securities are issued by a government-sponsored enterprise (GSE). Information on the size of the tri-party repo market and its different segments can be found at Federal Reserve Bank of New York Tri-Party and GCF Repo website. 2

tween lending dealers and other borrowing counterparties in which specific collateral is pledged. The final component incorporates the repo and reverse repo operations of the the Federal Reserve, which borrows cash through the Overnight Reverse Repurchase Agreement Program (ON RRP) and lends cash through the Standing Repo Facility (SRF). Our main hypothesis is that imperfect competition and strategic interactions of dealers in the decentralized market, in which dealers compete for quantities, alongside an anonymous centrally cleared market, in which dealers face a common borrowing rate, amplify shocks and result in market instability. Large shifts in cash demand arising from the bilateral segment or large supply shocks in the OTC segment can also be destabilizing. Federal Reserve operations on both the lending side and the borrowing side can dampen supply and demand shocks and decrease volatility in rates. However, such interventions, if not parameterized properly, could introduce inefficiencies related to crowding-out of private borrowing and lending relationships. Our analysis has three main components. First, we introduce a model of a decentralized networked market with established trading relationships among dealers and cash lenders. We assume that dealers compete in quantities in the decentralized market in the spirit of Cournot. However, unlike the standard Cournot competition in a single market, competition occurs in a networked market in which strategic substitutability or complementarity of actions depends on the nature of connectedness or “wiring” of the market. We show that when interacting with common lenders, dealers’ funding decisions are strategic substitutes, but depending on the wiring of the market, dealers’ funding decisions across non-common lenders could be strategic complements, which results in amplification of supply shocks. We prove the existence and uniqueness of the equilibrium both without and with a centrally cleared market, and illustrate differences in strategic interactions depending on the existence of a centrally cleared market. Without a centrally cleared market, both individual supply and demand shocks affect all equilibrium quantities. Individual dealer demand shocks have larger effects on dealers that compete directly relative to those that compete indirectly. With a centrally cleared market, dealers’ interactions are coordinated by the equilibrium rate in the centrally cleared market. The equilibrium rate aggregates individual demand conditions, which implies that all dealer-specific demand shocks affect the equilibrium rate equally, and so idiosyncratic demand shocks have less price impact than they do in market wirings without cen- 3

tral clearing. In contrast, the centrally cleared market introduces higher sensitivity to supply, particularly from lenders with certain characteristics, including a form of higher supply elasticities in the decentralized market, a concept closely related to Katz-Bonacich centrality. This asymmetry between the effects of demand shocks and supply shocks is due to the existence of a centrally cleared market in which only dealers but not lenders can participate. Second, we empirically estimate and test the predictions of the model. To resolve the endogeneity of quantities and prices, we decompose observed movements in quantities into dealer demand and lender supply factors following Amiti and Weinstein [2018]. With these factors in hand, first, we test for strategic substitutability in actions in the decentralized market. We establish that if a dealer’s competitors increase borrowing from a common lender by a percentage point, the dealer responds by reducing its borrowing from the common lender by 30 basis points. Second, we use the supply and demand factors as instruments to estimate micro-level and aggregate supplyanddemandelasticities. Ourestimatesindicatedealerdemandissubstantially less elastic than lender supply. The estimates of the demand elasticity for dealers, which takes into account the endogenous participation of dealers in the interdealer market as either a borrower or a lender, indicates that net borrowers in the GCF market reduce borrowing by $0.028 billion for every 1 basis point increase in repo spreads, whereas dealers are willing to supply an additional $0.042 billion in funding for every 1 basis point widening in spreads. The estimated aggregate lender supply elasticity is substantially larger than the dealer demand elasticities. While small cash lenders may face capacity constraints, in the aggregate, unconstrained lenders are willing to supply an additional $4 billion to $6.5 billion of funding for every 1 basis point increase in spreads depending on the empirical specifications. Third, we create indices that track the build-up of imbalances in the repo market by aggregating the demand and supply factors identified in the previous step. These indices reveal that the disruptions in the repo markets on September 17, 2019, were due to a large supply shock facing inelastic dealer demand and our elasticity estimates can match the magnitudes of the repo spikes. Furthermore, as predicted by the model, the large supply shocks propagated through more central dealer-lender trading relationships. Finally, we examine how the SRF could affect equilibrium quantities and prices. We show that the SRF introduces a trade-off between providing a liquidity buffer to the repo market and potentially crowding out relationships in the decentralized 4

market. An optimal SRF design involves the calibration of quantity caps and the minimum bid rate to achieve a desirable balance between the use of SRF as a liquidity backstop and the incentives of dealers to maintain relationships with lenders. Our paper contributes to the empirical and theoretical literature on repo markets. The empirical literature often focuses on measuring repo market characteristics and describing key parts of its structure. For example, [Krishnamurthy, Nagel, and Orlov, 2014; Hu, Pan, and Wang, 2020] describe the market size and pricing of repo trades, [Anderson and Kandrac, 2017; Munyan, 2015] discuss monetary policy implementation and regulatory factors, and [Cocco, Gomes, and Martins, 2009; Han and Nikolaou, 2016; Anbil, Anderson, and Senyuz, 2020] explore the role of long-term trading relationships. Similar to our work, Huber [2023] applies a structural industrial organization model to the repo market, but focuses on the role of money market mutual funds. Copeland, Duffie, and Yang [2025] attribute the September 2019 spikes in repo rates to declines in reserves at large bank holding companies. We build on these results and examine lower-frequency strategic mechanisms that amplify supply and demand shocks and result in rate spikes. Beyond the literature on measurement and market structure, other literature explores repo market instability. Brunnermeier and Pedersen [2009] characterizes mechanisms that generate market instability and feedback loops between borrowing capacityandliquidityincollateralizedmarkets, andGortonandMetrick[2012]andGorton, Laarits, and Metrick [2020] provide empirical evidence for these feedback loops during the Global Financial Crisis. Martin, Skeie, and Von Thadden [2014] present a model of repo runs akin to bank runs, while Infante and Vardoulakis [2020] discuss repo runs that occur on the collateral assets rather than liabilities. Ennis [2011] emphasises the fragility of the tri-party repo market in the presence of strategic cash lenders and the provision of intraday credit by the custodian bank. Chang [2019] and Chang and Chuan [2024] show how contagion through both debt and collateral channels can lead to collapse in the repo market. Our analysis emphasizes a novel mechanism through which the repo market can become unstable; that is, imbalances in supply and demand that are amplified by strategic interactions in the decentralized market and market clearing conditions in the centralized market. We also contribute to a growing literature on networked markets. Kranton and Minehart [2001] were first to illustrate that network structure determines market efficiency, and Elliott [2015] shows how differences in bargaining power and incentives 5

to form relationships can lead to market inefficiency. Manea [2011] studies how bargaining is affected by network structure, while Nava [2015] and Wittwer [2021] show that networked markets approach efficiency with greater numbers of counterparties. Other literature has introduced imperfect competition in networked markets, including Bulow, Geanakoplos, and Klemperer [1985], Vives [2002], Vives [2011], Nava [2015], Malamud and Rostek [2017], and Bimpikis, Ehsani, and I ˙ lkılı¸c [2019].2 The Nash equilibrium incorporates the role of the market wiring for the equilibrium quantities and prices and has similar structure to equilibria defined in Ballester, Calv´o- ˙ Armengol, and Zenou [2006] and Bimpikis, Ehsani, and Ilkılı¸c [2019], where the Nash equilibrium action of each player is proportional to their Bonacich centrality. Similar to Malamud and Rostek [2017], we show that the existence of a centrally cleared market may not always be improving market efficiency. However, unlike Malamud and Rostek [2017], which emphasize differences in risk allocations, we emphasize the effects of different market structures on strategic interactions, clearing of supply and demand imbalances, and their price impacts. The remainder of the paper is as follows. Section 2 provides stylized facts on the wiring of the repo market. Then section 3 brings those key features into a model of a networked market that features a decentralized market and a centrally cleared market. Section 4 applies the model to the data, develops a decomposition of changes in quantities traded into supply and demand factors, estimates the main model parameters, and tests the main model assumptions and mechanisms. Section 5 explores different counterfactuals based on the estimated model to understand the role of the centrally cleared market for the propagation of supply and demand shocks, their price impacts, and policy interventions in the market including through the introduction of the Standing Repo Facility. Section 6 concludes. 2 The wiring of the tri-party repo market Figure 1 illustrates the wiring of the government collateral tri-party repo market. In the middle is the decentralized OTC repo market. The decentralized market is a bi-partite graph with dealers (purple squares) on one side that borrow cash from lenders(bluecircles)ontheotherside.3 Eachlinethatconnectsadealerwithalender 2Rostek and Yoon [2023] reviews the importance of imperfect competition in financial markets. 3Government collateral includes U.S. Treasury securities, agency debt, and agency mortgage backed securities (MBS). Private collateral such as asset backed securities (ABS), corporate bonds, 6

represents a long-term trading relationship between the dealer and the lender. Figure 1: The wiring of the tri-party repo market Decentralized (OTC) laretalloC hsaC Centrally-cleared (FICC GCF) Dealers Lenders Note: The decentralized dealer-lender OTC market is represented by the set of dealers in purple squares and the set of lenders as blue circles at the bottom along with the trading relationships indicated as gray lines among the two. Dealers that borrow from the GCF market are connectedwith a redline to theGCF, whereas the dealersthat lend to the GCF marketare connected with a gray line. Lenders with cash held at the Fed’s ON RRP are indicated with a lineconnectiontotheONRRP.Source: FRBNYTri-partyrepoandtheauthors’construction. The market also includes FICC-GCF, which is an anonymous centrally cleared market. It is represented as the node labeled GCF (General Collateral Finance) in the figure. A link between a dealer and the GCF indicates that the dealer on net borrows (red links) or lends (gray links) from the interdealer market. The centrallyclearedmarketonlyreallocatescashandcollateralamongdealersanddoesnotprovide additional funding; that is, aggregate borrowing equals aggregate lending. Finally, the Federal Reserve’s overnight reverse repo (ON RRP) facility is illustrated as a node at the bottom of the decentralized market. Not all lenders have equities, and private-label MBS are used in a smaller segment of the tri-party repo market, with different structure and pricing. 7

access to the ON RRP facility. However, all lenders that access the ON RRP have a trading relationship with a dealer in the OTC market. There are several stylized facts that emerge from the repo market wiring. First, the decentralized market is not fully connected. Each dealer borrows from a subset of lenders and no dealer has access to all lenders. Second, some dealers do not borrow from lenders in the decentralized market and instead obtain funding through the centrally-cleared GCF market only. Third, not all dealers participate in the GCF market and only transact in the decentralized market. Fourth, some dealers are net lenders in the GCF market, whereas others are net borrowers. Finally, not all lenders have access to the ON RRP facility. The model in the next section incorporates most of those features of the wiring. The incomplete wiring is also important for the ability to decompose movements in quantities in supply and demand and identify the supply and demand elasticities. Figure 2: Duration of trading relationships as fraction of the sample period )tnecrep( emulov oper CTO latot fo erahS )%01−0[ )%02−01[ )%03−02[ )%04−03[ )%05−04[ )%06−05[ )%07−06[ )%08−07[ )%09−08[ ]%001−09[ 50 40 30 20 10 0 Note: The x-axis is the duration of dealer-lender relationships as a fraction of the sample period from July 2014 to October 2022 or 2005 trading days. Source: FRBNY Tri-party repo and authors’ calculations. There are also important stylized facts regarding the duration of dealer-lender relationships in the OTC market. Most dealer-lender relationships and especially 8

thosethatinvolvethelargestcounterpartiesarelong-term. Figure2revealsthatmore than 50 percent of aggregate repo trade volume is among dealer-lender trading pairs thattransact continuouslyfor mostof oursampleperiod. More than78 percent ofthe aggregate repo trade volume are among dealers and lenders that trade continuously for at least 50 percent of the sample period or for at least 4 years. Figure 3: Trading volume at new, dissolved, and short-term trading relationships 2016 2018 2020 2022 emulov oper CTO latot fo tnecreP 8 6 4 2 0 New dealer−lender relationships Dissolved dealer−lender relationships Short−term relationships, (0−20% of sample) Note: The graph plots the volume of repo trades at newly established, dissolved, and shortterm dealer-lender trading relationships. Short-term trading relationships are defined as those that lastnomorethanafifthofthesampleperiodortwoyearsorless. Source: FRBNYTri-partyrepo and authors’ calculations. Our sample is an unbalanced panel, reflecting both entry and exit of repo counterparties as well as the creation and dissolution of trading relationships. Even so, the market wiring is stable and most trading occurs within long-term dealer-lender relationships. Figure 3 shows that new dealer-lender relationships represent a small share of aggregate trading volume in our sample period, with the largest new dealer-lender relationships contributing no more than 6 percent of aggregate volume. New relationships often reflect the entry of new counterparties in the sample, and 9

both borrower and lender entrants tend to be smaller than established ones. The dissolution of dealer-lender relationships is infrequent and contributes to a relatively small percent of the aggregate OTC repo trade volume.4 Finally, the share of OTC repo trades at short-term trading relationships, which last for less than 20 percent our sample or less than two years, comprise less than 2 percent of aggregate OTC repo volumeinthemiddleofoursample. Duetoleftandrightcensoring, relationshipsthat are dissolved within 2 years of the start or that are established within 2 years of the end of our sample, are classified as short-term even though their actual duration could exceed two years. The censoring results in higher shares of short-term relationships at the two ends of our sample. Nonetheless, more than 90 percent of trades on any given trading day in our sample are over established long-term relationships. The stability of the dealer-lender relationships allows us to treat the network of the OTC market as fixed in our theoretical and empirical analysis. In what follows, we use this assumption to characterize the wiring, demand, supply, and stability of the repo market. 3 A model of the repo market Define the set of dealers as D = {d ,...,d }, where n = |D| is the number of 1 n dealers. Dealers lend cash in reverse repo transactions to a range of counterparties in the bilateral segment of the repo market, B. The volume of bilateral reverse repo trades for dealer i is denoted by q . The aggregate cash lent by all dealers Bi in bilateral repo is q¯ = (cid:80)n q . Reverse repo transactions in the bilateral repo B i=1 Bi market determine dealers’ cash demand in the tri-party repo market. We treat the dealers’ lending commitments {q } as pre-determined. This assumption reflects Bi i∈D obligations to satisfy demand for funding by hedge funds or other asset managers as well as obligations by primary dealers to participate in Treasury auctions.5 Dealers borrow cash from the two segments of the tri-party repo market to satisfy commitmentsinB. ReflectingtherepowiringdescribedinSection2, thefirstsegment is a decentralized over-the-counter (OTC) market denoted by T , which corresponds 4There are limited counterparty credit risks in the repo market we are focusing on, as counterparty credit exposures are covered by government collateral and all trades are cleared by the tri-party (Bank of New York Mellon). In times of stress, trading relationships can fluctuate wildly if counterparty risks are of concern Beltran, Bolotnyy, and Klee [2019]. 5Whiletechnicallynotpartofthebilateralrepomarket,primarydealerparticipationinTreasury auctions is a determinant of dealers’ demand for cash and is assumed to be pre-determined. 10

to the bipartite dealer-lender component in Figure 1, and the second segment is a centrally cleared interdealer market denoted by C, which corresponds to the GCF market in Figure 1. The set of cash lenders in T is denoted by L = {ℓ ,...,ℓ }, where m = |L| is the 1 m number of lenders in T . With this structure, the decentralized market is described by a bipartite graph T = (D∪L,E), where E is the set of trading relationships (edges) from the set of lenders (L) to the set of dealers (D), with a slight abuse of notation of T , denoting both the market and the graph. For each lender ℓ ∈ L, we define the set of counterparties D = {d ∈ D|ik ∈ E}, k k i which is the set of dealers that borrow from lender ℓ and the number of dealers k borrowing from k are n = |D |. Similarly, for each dealer d ∈ D, define the set of k k i counterparties as L = {ℓ ∈ L|ik ∈ E}, which is the set of lenders that lend to dealer i k d and m = |L | is the number of lender counterparties of d .6 i i i i Dealers can either borrow or lend in C depending on whether they need or have additional cash at the market clearing rate ρ . Dealers are price-takers, because the C C market is blind-brokered. It is important to note that the C is a net zero supply funding market thatonly reallocates cash and collateral among dealers. We refer to thestructurethatcombinesthedecentralizedmarketandthecentrallyclearedmarket W = (T ,C) as the “wiring” of the repo market. We denote W = (T ,∅), if there is no C market. We denote the ON RRP as O and the SRF facility as S. 3.1 Cash lenders and funding supply A lender k in T requires a spread s over the rate earned from depositing at the k Fed’s overnight reverse repo facility (ON RRP). This spread linearly increases in the quantity supplied to dealers according to the following inverse supply curve (cid:88) (cid:88) s = c˜ −γ q +γ q = c +γ q , ∀k ∈ L. (1) k k k k jk k k jk k j∈D j∈D k k We assume that each lender k has an exogenously given capacity to invest in repo markets q .7 All else equal, lenders with greater capacity charge lower spreads. Varik 6Notethatweuseiord asagenericlabelforadealerandk orℓ asagenericlabelforalender. i k A generic trading relationship between d and ℓ is denoted as ik ∈E. i k 7The supply capacity of a lender can be determined by a portfolio optimization problem or 11

ations in c = c˜ −γ q are parallel shifts in the supply curve from the perspective of k k k k dealers borrowing from k. Lenders have some degree of market power encoded in a lender-specific supply elasticity γ > 0 for all k ∈ L.8 For the rest of the analysis, we k work with the spreads over the benchmark ON RRP rate and we assume that effects of the level of interest rates is encoded in variation in {c } . k k∈L 3.2 Cournot competition for funds Dealers compete in quantities a` la Cournot for funding in the T market.9 Dealer i competes with other dealers for funding from common lenders and obtains total (cid:80) funding q = q from its lending counterparties. Dealers can also borrow iT k∈Li ik from or lend to each other in the interdealer C market at the market clearing rate ρ . Taken together, the total net cash borrowed by dealer i is q¯ = q +q , where C i iC iT q is the net amount borrower or lent to the C market. Given a size of funding iC commitments q , each dealer i minimizes the total cost of funding defined as Bi (cid:32) (cid:33) (cid:88) (cid:88) β (cid:16) (cid:17)2 i V ≡ c +γ q ×q +ρ q + q¯ −q . (2) i k k jk ik C iC i Bi 2 k∈Li j∈D k The first term is the cost of borrowing from counterparties in the T market. The second term is the cost of funds or income from lending in the C market. The last term is quadratic cost of not meeting the exogeneously given dealer demand q . If Bi the dealer is unable to fund its pre-committed q , the dealer faces a quadratic cost Bi proportional to the shortfall, with β > 0, ∀i ∈ D is a dealer-specific shift of the i cost of funding shortfalls. The cost can be interpreted either as the costs of failing to deliver promised reverse repo funding or the marginal cost of raising additional funds from internal or external unsecured funding sources to make up for the shortfall.10 stochastic variation ina lender’s inflows ofcash due toinvestordeposits or withdrawals offunds. In the empirical section, we proxy this capacity with the lenders’ cash deposited at the ON RRP. 8Althoughwedonotexplicitlymodeltheoptimizationoflendersorthebargaininggamebetween lendersanddealers,shiftsinfundssupplycouldresultfromchangesintherelativebargainingpower of lenders. Huber [2023] and Beltran [2023] incorporate lender optimization frameworks. 9AnalternativewayofmodelingdealercompetitionisBertrand. However,Bertrandcompetition can be ruled out from the observed wiring of the tri-party repo markets and the observed rate dispersion. 10For example, the dealer affiliated with a bank holding company can obtain funding from its affiliated commercial bank or, alternatively, a dealer can issue commercial paper or other unsecured 12

The cost-minimization problem of dealer i is as follows V (q ) ≡ min V (3) i Bi i qiC,{q ik } k∈Li subject to: q ≥0, ∀k ∈ L ik i q¯ ≥0, i where the first constraint is the non-negativity constraint for the individual amount of borrowing from T lenders, and the second constraint implies that dealers cannot borrow from the bilateral market to be net lenders in the C plus T market. We focus on interior solutions first, and later provide conditions under which interior solutions consist of equilibrium by Lemma 1. The first-order condition for any dealer i ∈ D borrowing from lender k ∈ L with a trading relationship in the T market (i.e. ik ∈ E) is β q −β q −c β (cid:88) γ (cid:88) i Bi i iC k i k q = − q − q . (4) ik il jk 2γ +β 2γ +β 2γ +β k i k i k i l∈Li j∈D k l̸=k j̸=i Dealer i’s amount of borrowing from lender k not only depends on dealer i’s own demand conditions (q and β ) and the lender k’s supply conditions (γ and c ), but Bi i k k also depends on how the competing dealers j ∈ D are borrowing from lender k and k how much dealer i borrows from other lenders l ∈ L . Moreover, dealer i will reduce i its borrowing amount from the T market when i borrows more from C market and vice versa. In other words, dealer i’s decision on how much to borrow from lender k depends on Cournot competition with other connected dealers as well as dealer i’s own optimization across other sources of funding. The first-order condition for the net borrowing from the interdealer C market is (cid:88) 1 q = q − q − ρ , (5) iC Bi ik C β i k∈Li for any i ∈ D. A dealer lends in the C market, i.e. q < 0, when the dealer can iC fund the excess amount of cash from the T market at a rate lower than ρ . A dealer C borrows cash in the C market, i.e. q > 0, when the dealer’s marginal cost of funds iC wholesale funding to cover the shortfall. 13

in the T market is higher than the rate ρ . The dealer net borrowing from the C C market has an interest rate sensitivity determined by the inverse of the dealer’s funding shortfall cost β , so that dealers with higher funding shortfall costs will be i less price elastic. Thus, the inverse of β is a measure of the interest rate elasticity of i dealers’ repo demand. Plugging (5) into (4) gives us the following expression for the optimal amount borrowed of dealer i from cash lender k for interior solutions  βiqBi−c k − βi (cid:80) q − γ k (cid:80) q if W = (T ,∅) q = 2γ k +βi 2γ k +βi l∈Li,l̸=k il 2γ k +βi j∈D k ,j̸=i jk (6) ik ρC−c k − 1 (cid:80) q , if W = (T ,C). 2γ k 2 j∈D k ,j̸=i jk The dealers’ decisions to borrow from common lenders in the T market are strategic substitutes and the degree of substitution increases if dealers have access to the centrally cleared market, because γ k < 1 for all positive γ and β . We should 2γ k +βi 2 k i note that the best response functions (6) reflect only the direct strategic interactions among dealers connected through common lenders. The equilibrium strategic interactions among dealers are more complex once higher-order interactions along the bipartite network are taken into account as we discuss in the next sections. 3.3 Market equilibrium without a C market Suppose the wiring of the repo market does not include a C market. The market equilibrium can be defined as the solution to the system of equations (6) for the wiring W = (T ,∅), which we formalize as follows. Definition 1 A market equilibrium without a C market is a vector {q∗ } of transik ik∈E acted quantities that solves the system of first-order conditions (6) for all ik ∈ E. Define the |E|×1 vector of weights (cid:26) (cid:27) 1 ξ = . (7) 2γ +β k i ik∈E Then define the marginal surpluses of trade for any dealer-lender trading relationship ik ∈ E as the |E|×1 vector ϕ(q ) = {β q −c } , (8) B i Bi k ik∈E 14

where β q is the marginal benefit of an additional dollar of funding and c is the i Bi k marginal cost. In matrix notation, the system of first-order conditions can be written as q = ξ ◦ϕ(q )−ξ ◦Wq, B where q = {q } is a |E| × 1 vector of transacted quantities for each dealerik ik∈E lender relationship, q = {q }n is the vector of dealer repo demand, the operator B Bi i=1 ◦ signifies the Hadamard (element-wise) product, and the matrix W is a |E| × |E| matrix with elements  β if i = j,k ̸= ℓ   i  W = γ if i ̸= j,k = ℓ (9) ik,jℓ k    0 otherwise. The W matrix is the weighted adjacency matrix of the line graph of the connections between the dealer-lender pairs, where the line graph consists of every dealer-lender relationship ik ∈ E as a node and an edge between two nodes exists, if the trading pairs share a counterparty.11 For example, if two dealer-lender pairs are connected with a common dealer i, they are weighted by that dealer’s marginal funding cost parameter β . If two dealer-lender pairs are connected with a common lender k, then i the weight of their connection is the lender supply elasticity γ . k Under fairly general conditions discussed in the proof of Proposition 1 in the appendix, we show that there exists an inverse of the matrix I + ξ ◦ W, which we denote as the |E|×|E| matrix Ψ ≡ (I +ξ ◦W)−1. The equilibrium quantities are (cid:104) (cid:105)−1 q∗ = I +ξ ◦W (ξ ◦ϕ(q )) = Ψ(ξ ◦ϕ(q )). (10) B B 3.4 Market equilibrium with a C market Now consider a wiring W = (T ,C) that includes a C market. Introducing the C market results in a system of first-order conditions (4) and (5), that has |E| + n equations with |E| + n unknowns. The market equilibrium is the solution of this system of equations along with an equilibrium rate ρ∗ that satisfies the C market C 11Wecanformallydefinethelinegraphasthetransformationfromtheoriginalbi-partitenetwork T tothegraphL(T)=(E,EL). ThatiseveryedgeinT isanodeinL(T)andedgesareconnected if they share a common counterparty EL ={(ik,jℓ):i=j,k ̸=l or i̸=j,k =ℓ} . See Figure ik,iℓ∈E 5 for an example of a line graph transformation of the networks in Figure 4. 15

clearing condition, (cid:88) q (ρ∗) = 0. (11) iC C i∈D To solve for the market equilibrium, first note that (11) pins down the market clearing price ρ∗, while n unknowns (q , ∀ i ∈ D) are determined by n equations (first-order C iC conditions with respect to q , ∀ i ∈ D). Then, we examine the first-order conditions iC (6) in matrix form 1 ˜ ˜ q = ϕ(ρ )− Wq, (12) C 2 ˜ where ϕ(ρ ) is a |E|×1 vector such that C ρ −c ˜ C k ϕ (ρ ) = ,∀ik ∈ E, (13) ik C 2γ k ˜ and the |E|×|E| adjacency matrix W is  1 if i ̸= j,k = l ˜ W = (14) ik,jℓ 0 otherwise. Note that unlike the adjacency matrix (9) of the line-graph for a wiring without C market, theadjacencymatrixoftheline-graphofawiringwithaC marketconsiders connections between two dealer-lender pairs only if they share a common lender. This is because all dealers compare marginal cost of borrowing from available lenders with ρ , which dealers take as given. Hence, dealers only care about the borrowing C quantities of their directly competing dealers that affect the marginal cost of funds from their direct lenders. The increase in the sparsity of the adjacency matrix results in a change in the propagation of supply and demand shocks, which we come back in more detail in the next sections. (cid:18) (cid:19) 1 ˜ Similar to the case without a C market, the matrix I + W is full rank and 2 its inverse matrix, denoted as Ψ ˜ , exists.12 Therefore, the equilibrium quantities for 12By construction, the diagonal elements of W˜ are zero and W˜ is symmetric, as W˜ =W˜ . ik,jℓ jℓ,ik 1 Hence, I + W˜ will have full rank with diagonal entries being 1 and other entries being either 1/2 2 or 0. This structure of W˜ guarantees that it is invertible. 16

the |E|×1 dealer-lender pairs can be solved as (cid:18) 1 (cid:19)−1 ˜ ˜ ˜ ˜ q(ρ ) = I + W ϕ(ρ ) = Ψϕ(ρ ). (15) C C C 2 The equilibrium quantity borrowed by dealer i from lender k is ˜ (cid:88) ψ ik,jℓ q (ρ ) = (ρ −c ), ∀ik ∈ E. (16) ik C C ℓ 2γ ℓ jℓ∈E Finally, the equilibrium rate ρ∗ is determined by the market clearing condition C (cid:32) (cid:33) (cid:88) (cid:88) (cid:88) (cid:88) 1 q (ρ∗) = q − q (ρ∗)− ρ∗ = 0. (17) iC C Bi iT C β C i i∈D i∈D i∈D i∈D With the equilibrium conditions, we can formally define the market equilibrium with a C market. Definition 2 A market equilibrium with a C market is a vector ({q∗ } ,{q∗ } ) ik ik∈E iC i∈D of traded quantities and a rate for the centrally cleared market ρ∗ that satisfy the C system of equations (5) and (15) along with the market clearing condition (17). 3.5 Properties of market equilibria We have examined interior solutions of the dealers’ problems, where all edges are active in equilibrium (i.e. q∗ > 0 ∀ ik ∈ E). The following lemma provides the ik necessary and sufficient condition for all edges to be active. Lemma 1 The quantity borrowed q at any trading relationship ik ∈ E is positive, ik if and only if the following condition holds (cid:80) ψ ˜ ik,jℓ c q¯ + (cid:80) (cid:80) ψ ˜ ab,i′k′ c 2γ ℓ B 2γ k′ jℓ∈E ℓ ab∈Ei′k′∈E k′ < . (18) ˜ ˜ ψ ψ (cid:80) ik,jℓ (cid:80) 1 + (cid:80) (cid:80) ab,i′k′ jℓ∈E 2γ ℓ j∈D βj ab∈Ei′k′∈E 2γ k′ All proofs are summarized in Appendix A. As we derive in Proposition 1, the righthand side of (18) is the equilibrium rate in the C market. The left-hand side defines 17

the relative cost of borrowing of dealer i from lender k that takes into account the strategic reaction of other dealers, which depends on the connectedness of dealer i to all other dealers through its trading relationship with lender k. The equilibrium rate defines an upper bound on the acceptable relative cost of borrowing from lender k. If this bound is breached, dealer i is better off borrowing from the centrally cleared market.13 Although condition (18) appears restrictive, we can assume all edges to be active without loss of generality. In particular, we can solve for the equilibrium in which some trading relationships are inactive by removing those edges from the set of active edges E, focusing on a subset of active edges and solving the equilibrium for the trading relationships for which (18) holds.14 We assume that (18) holds from now on, and we can prove the existence and uniqueness of the market equilibrium in the following proposition. Proposition 1 There exists a unique market equilibrium both with and without a centrally cleared market C. 1. With a C market, the equilibrium quantities are ˜ (cid:88) ψ q∗ = ik,jℓ (ρ∗ −c ), ∀ik ∈ E ik 2γ C ℓ ℓ jℓ∈E (19) (cid:88) (cid:88) ψ ˜ (cid:16)(cid:88) (cid:88) ψ ˜ 1 (cid:17) q∗ = q + ik,jℓ c − ik,jℓ + ρ∗, ∀i ∈ D, iC Bi 2γ ℓ 2γ β C ℓ ℓ i k∈Lijℓ∈E k∈Lijℓ∈E where ρ∗ is the equilibrium rate in the C market equal to C (cid:80) (cid:80) ψ˜ q¯ + ik,jℓc B 2γ ℓ ℓ ρ∗ = ik∈Ejℓ∈E . (20) C (cid:80) 1 + (cid:80) (cid:80) ψ˜ ik,jℓ βi 2γ ℓ i∈D ik∈Ejℓ∈E 13A similar condition can be derived for the wiring without C market, discussed in the appendix. 14ThisresultissimilartothecasewithouttheC marketexaminedinBimpikis,Ehsani,andI˙lkılıc¸ [2019]. Inoursetting,itiseasytoshowthatremovinginactiveedgesresultsinthesameequilibrium quantities and market clearing rate ρ . In general, solving for the equilibrium requires a finite C number of steps to check that all the non-negativity constraints are satisfied. 18

2. Without a C market, the equilibrium quantities transacted in the T market are (cid:88) ψ q∗ = ik,jℓ (β q −c ), ∀ik ∈ E. ik 2γ +β j Bj ℓ (21) ℓ j jℓ∈E To understand the properties of the equilibrium with the C market, examine the ˜ ψ ik,jℓ term . We refer to this term as the strategic weight of ik to jℓ for any ik,jℓ ∈ E. 2γ ℓ The strategic weight captures how much q is affected by q , including its own ik jℓ ˜ ψ (cid:80) ik,jℓ supply elasticity for the case of ik = jℓ. We refer the term as the effective 2γ jℓ∈E ℓ supply elasticity of lender k to dealer i for any ik ∈ E and the sum across all lender ˜ ψ (cid:80) (cid:80) ik,jℓ counterparties is dealer i specific effective supply elasticity. 2γ k∈Lijℓ∈E ℓ The effective supply elasticity depends not only on the own supply elasticity 1 γ k but also on all the other lenders’ supply elasticities weighted by the strategic weights ˜ of other dealers to dealer i borrowing from k encoded in the ψ . The equilibrium ik,jℓ quantityq∗ dependsonthespreadbetweentheC marketrateandthemarginalcostc ik ℓ weighted by the strategic weights. If the strategic weight is positive on a dealer-lender pair jℓ, dealer i borrows more from lender k as c declines. ℓ Next examine the equilibrium without C market. In this wiring, the strategic ψ weight of ik to jℓ is ik,jℓ , and the effective supply elasticity of lender k to dealer 2γ ℓ +βj (cid:80) ψ i is ik,jℓ . Note that the strategic weights and effective supply elasticities jℓ∈E 2γ ℓ +βj involve also the dealers’ demand elasticities. Without a centrally cleared market, which equalizes the marginal costs of funds across dealers, the strategic responses of dealers vary with each dealer’s own demand elasticity. The equilibrium quantities are functions of the marginal surpluses β q − c along all dealer-lender pairs with j Bj ℓ weights equal to the strategic weight. To illustrate how the wiring of the market affects the effective supply elasticities and equilibrium quantities, examine the case of homogeneity in lender and dealer elasticities. We can express the equilibrium quantities as the following decomposition (cid:18) ∞ 12z ∞ 12z+1 (cid:19)   (cid:80) W ˜ 2z − (cid:80) W ˜ 2z+1 ϕ ˜ (ρ ) if W = (T ,C)  2 2 C q∗ = (cid:18) z=0 z=0 (cid:19) (22) ∞ ∞   (cid:80) ( 1 )2zW2z − (cid:80) ( 1 )2z+1W2z+1 1 ϕ(q ) if W = (T ,∅)  2γ+β 2γ+β 2γ+β B z=0 z=0 The decomposition reveals that changes in demand and supply conditions at any 19

dealer-lender trading relationship affect all the other dealer-lender relationships along the edges of the line graph with a rate of decay 1/2 for the wiring with C market, and a decay rate 1 for the wiring without C market.15 The powers of the adjacency 2γ+β matrices Wp and W ˜ p encode paths between any two edges of length p. The adjacency matrices are non-negative and the strategic quantity response of dealer j to changes in demand of dealer i would be a strategic complement, if the two edges (ik,jℓ) are linked by a path of even length, and a strategic substitute, if the two edges are linked by a path of odd length. The decomposition (22) allows us to express the equilibrium quantities as the Katz-Bonacich (KB) centrality of the dealer-lender trading relationship in the case without a C market (cid:32) (cid:33) (cid:34) (cid:35) ∞ (cid:88) (cid:88) KB(−ξ,W) ≡ (−ξW)z 1 = Ψ1 = ψ , (23) |E| |E| ik,jℓ z=0 jℓ∈E ik∈E where the first equality is the definition of the KB centrality measure and 1 is a |E| vector of ones of length |E|. The effective supply elasticity becomes the KB centrality measure in the homogeneous elasticities case. More central dealer-lender trading relationships have high effective supply elasticity, if they are part of more paths in the line graph network with ξ discounting the influence of longer paths. The equilibrium with a C market has a similar structure with the centrality KB(−1,W ˜ ) defining the 2 effective supply elasticity. We next examine the properties of the aggregate equilibrium quantities in the case of wirings with a C market in the following two corollaries of Proposition 1. Corollary 1 For a fixed aggregate demand q¯ , the gross volume of trades in the B C market, (cid:80) |q∗ |, is increasing in the heterogeneity of individual dealer-specific deiC i∈D mand and dealer-specific supply scaled by the dealer-specific supply and demand elasticities (cid:12) ˜ ˜ (cid:12) (cid:12) (cid:80) (cid:80) ψ ik,jℓ (cid:80) (cid:80) (cid:80) (cid:80) ψ ab,jℓ (cid:12) (cid:12)q + c q + c (cid:12) Bi ℓ Ba ℓ (cid:88)(cid:12) (cid:12) k∈Lijℓ∈E γ ℓ − a∈D a∈Db∈Dajℓ∈E γ ℓ (cid:12) (cid:12). (24) (cid:12) ˜ ˜ (cid:12) i∈D (cid:12) (cid:12) 1 + (cid:80) (cid:80) ψ ik,jℓ (cid:80) 1 + (cid:80) (cid:80) ψ ab,jℓ (cid:12) (cid:12) (cid:12) β γ β γ (cid:12) i k∈Lijℓ∈E ℓ a∈D a ab∈Ejℓ∈E ℓ 15The decomposition exists if the infinite sums are convergent, which is satisfied if the largest eigenvalue of ξW is less than 1 in absolute value. 20

Corollary 1 implies when there are no differences across dealers in their dealer-specific demand, demand elasticities, and in the effective supply elasticities, there will be no trades in the C market at the equilibrium rate ρ∗. The effect of dealer-specific demand C q on gross trades in the C market is scaled by a factor that sums the dealer-specific Bi ˜ ψ demand elasticity 1 and the dealer-specific effective supply elasticity (cid:80) (cid:80) ik,jℓ . βi 2γ k∈Lijℓ∈E ℓ The second term in (24) is the average of those dealer characteristics. All else equal, a dealer with a lower demand elasticity or a lower effective supply elasticity in the T market than the average dealer would be a net borrower in the C market, whereasadealerwithahigherdemandelasticityorahighereffectivesupply elasticity in the T market would be a net lender in the C market. Corollary 2 The interest rate sensitivity with respect to ρ∗ of the aggregate borrowing C from the T market is smaller than the sensitivity of the aggregate borrowing from the C market. (cid:12) (cid:18) (cid:19)(cid:12) (cid:12) (cid:18) (cid:19)(cid:12) (cid:12) (cid:12)∂ (cid:80) q∗ (cid:12) (cid:12) (cid:12)∂ (cid:80) q∗ (cid:12) (cid:12) ik (cid:12) (cid:12) iC (cid:12) (cid:12) ik∈E (cid:12) < (cid:12) (cid:12) i∈D (cid:12) (cid:12) (cid:12) ∂ρ∗ (cid:12) (cid:12) ∂ρ∗ (cid:12) (cid:12) C (cid:12) (cid:12) C (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) Corollary 2 highlights the difference in interest rate sensitivity between the aggregate borrowing from T market and the net borrowing in the C market. In response to an increase in ρ∗, dealers reduce their net borrowing in the C market. Simultaneously, C dealers also increase their borrowing from the T market. Therefore, the aggregate demand elasticity of the T market is less than the aggregate net demand elasticity of the C market. 3.6 Propagation of demand and supply shocks As we have discussed in the previous section, the existence of a centrally cleared market affects the propagation of supply and demand shocks in a fundamental way. We further characterize the properties of the propagation of demand and supply shocks in the following proposition. Proposition 2 The existence of a centrally cleared market affects the propagation of demand and supply shocks. 21

1. With a C market, dealer demand shocks affect the equilibrium quantities only indirectly through their effect on the equilibrium rate ρ∗, whereas supply shocks C affect the equilibrium quantities both directly and indirectly as follows ∂q ∂ρ∗ (cid:88) ψ ˜ jℓ = C jℓ,ab ∂q ∂q 2γ Bi Bi b ab∈E (25) ∂q ∂ρ∗ (cid:88) ψ ˜ (cid:88) ψ ˜ jℓ = C jℓ,hz − jℓ,ak ∂c ∂c 2γ 2γ k k z k hz∈E a∈D k for any jℓ ∈ E and i ∈ D,k ∈ L. Finally, the derivatives of the equilibrium rate ρ∗ is C ∂ρ∗ 1 C = ∂q Bi (cid:80) (cid:80) ψ˜ hz,ab + (cid:80) 1 2γ b βa hz∈Eab∈E a∈D (cid:80) (cid:80) ψ˜ (26) ab,hk ∂ρ 2γ k C = ab∈Eh∈D k . ∂c k (cid:80) (cid:80) ψ˜ hz,ab + (cid:80) 1 2γ b βa hz∈Eab∈E a∈D 2. Without a C market, demand shocks at any dealer i ∈ D and supply shocks at any lender k ∈ L influence the trades in all dealer-lender relationship jℓ ∈ E according to ∂q (cid:88) β jℓ i = ψ , jℓ,iz ∂q 2γ +β Bi z i z∈Li (27) ∂q (cid:88) 1 jℓ = − ψ . jℓ,dk ∂c 2γ +β k k d d∈D k For the wiring with a C market, idiosyncratic dealer demand shocks affect all dealers only through the change in equilibrium rate ρ∗. All else equal, all dealers C borrow more in response to a dealer-specific demand shock. However, supply shocks havebothglobaleffectsthroughtheequilibriumrateandlocaleffectsonanindividual dealer’s funding decisions. Therefore, with a C market, idiosyncratic lender supply shocksgenerateheterogeneouseffectsacrossdealers. Furthermore, localsupplyeffects ˜ propagate to all dealer-lender pairs through all possible paths encoded in Ψ. In the absence of a C market, the spillover effects of demand or supply shocks could affect the equilibrium trades of all dealer-lender pairs through all possible paths along the network encoded in the Ψ matrix. The sign of those coefficients determines 22

whether the action of a dealer in a trading relationship is a strategic substitute or complement to the actions of other dealers in other relationships. 3.7 Dispersion in marginal borrowing costs and spreads Define the marginal cost of dealer i of a dollar of additional funding from lender k evaluated at the equilibrium quantities as follows ∂q (c +γ (cid:80) q )(cid:12) ρ∗ ≡ ik k k j∈D k jk (cid:12) (cid:12) = s∗ +γ q∗ , (28) ik ∂q (cid:12) k k ik ik q∗ where the second equality indicates that the marginal cost always exceeds the repo rate or the average cost of funds. Proposition 3 The equilibrium dispersion in marginal costs of funding and in lender repo spreads depend on the market wiring. 1. Marginal costs: (a) With a C market, the marginal borrowing cost for all dealers across all lenders equals the equilibrium rate in the centrally cleared market ρ∗ = i ρ∗, ∀i ∈ D, where ρ∗ = ρ∗ , ∀k ∈ L . C i ik i (b) Without a C market, the marginal borrowing cost can differ across dealers. Even if the dealer and lender parameters are homogeneous as β = β,q = i Bi q , ∀i ∈ D, and γ = γ,c = c, ∀ℓ ∈ L, the marginal borrowing costs B ℓ ℓ across dealers are the same ρ∗ = ρ∗ for all i ∈ D, if and only if i (cid:88) (cid:88) ¯ ψ = ψ (29) ik,jℓ k∈Lijℓ∈E for all i ∈ D. 2. Lender spreads: (a) With a C market, the equilibrium spreads depend on the number of lenders (n ) , where n = |D |, and the distribution of lender marginal costs k k∈L k k 23

{c } as k k∈L n 1 s∗ = k ρ∗ + c , k ∈ L. (30) k n +1 C n +1 k k k (b) Without a C market, the equilibrium spreads are a function of the lender supply conditions and elasticities (c ,γ ) , the dealer demand conditions k k k∈L and elasticities (q ,β ) , as well as the wiring of the T market captured Bi i i∈D by the Ψ matrix as (cid:88) (cid:88) β q −c s∗ = c +γ ψ j Bj ℓ , k ∈ L. (31) k k k ik,jℓ 2γ +β ℓ j i∈D kjℓ∈E The first part of the proposition states that in the presence of a centrally cleared market dealers equalize marginal costs not only across their lender counterparties but also among themselves, thus eliminating dispersion in marginal costs. This result is intuitive, because ρ∗ is the common marginal borrowing cost for all dealers, and each C dealer equalizes the marginal costs across all possible funding sources. Without a centrally cleared market (1b), marginal costs are equalized only if the dealer specific ¯ effective supply elasticities are equalized to a constant proportional to ψ. The second part of the proposition is somewhat unexpected. There is equilibrium dispersion in rates even when all cost parameters are homogeneous (2a), and the dispersion in rates is a function of the wiring of the market. Even if dealers equalize marginal costs, the existence of a centrally cleared market does not necessarily eliminate rate heterogeneity. It is only in situations when the market wiring is symmetric across counterparties that the “law of one price” holds. According to (30), when cost parameters are homogeneous, lenders with larger number of counterparties would charge higher rates than lenders with fewer counterparties, and their rates would be more sensitive to the equilibrium rate in the centrally cleared market. Finally, without C market, (2b) reveals that equilibrium rate dispersion depends on both the heterogeneity of supply and demand parameters but also on the wiring of the market. Similar to (1b), when such heterogeneity is removed, there is still rate dispersion if the there are differences in connectedness of lenders captured by (cid:80) (cid:80) differences in ψ for any k ∈ L. ik,jℓ i∈D kjℓ∈E 24

3.8 Solving a simple closed-form example Figure 4: Alternative wirings of a market with 2 dealers and 3 lenders A. Symmetric but incomplete wiring (T sym) C d d 1 2 l l l 1 2 3 B. Asymmetric wiring (T asym) C. Fully wired (T full) C C d d d d 1 2 1 2 l l l l l l 1 2 3 1 2 3 Note: Linesbetweenadealerandalenderrepresentanestablishedrelationship. Linesbetween dealers and the C market represent access to the centrally-cleared market, which could be either borrowingorlending. Inthisexample,weassumethatq >q andthatdealerd needsadditional B1 B2 1 cash and borrows from dealer d through the C market. 2 We can gain intuition about the properties of the general model from solving a simple closed-form example. As shown in Figure 4, suppose there are two dealers D = {d ,d } and three lenders L = {ℓ ,ℓ ,ℓ } that interact in different T market wirings. 1 2 1 2 3 There are three different configurations of the T market, and each configuration may 25

include a C market. In panel A, the two dealers share a common lender ℓ , and 2 each dealer has an exclusive lender, lender ℓ for dealer d and lender ℓ for dealer 1 1 3 d . Because dealers have the same number of counterparties, but not all dealers and 2 lenders interact, the wiring is symmetric but incomplete. Suppose that lenders share common cost parameters, (c,γ) = (c ,γ ) for all k = k k 1,2,3, and dealers have the same balance sheet costs β = β = β . To examine 1 2 how demand imbalances are resolved, suppose that dealer d has higher demand for 1 borrowing than dealer d , that is, q > q . The equilibrium interdealer rate ρ∗ in 2 B1 B2 C the C-market is determined by the market clearing condition q (ρ∗) + q (ρ∗) = 0, 1C C 2C C which we can solve in closed form 3βγ 5β ρ∗ = q¯ + c, C 5β +6γ B 5β +6γ where q¯ = q +q is total dealer demand. The equilibrium rate is the sum of dealer B B1 B2 funding demand and the cost of funds in the T market, weighted by the supply and demand elasticities. The total quantity borrowed from the T market is increasing in the demand for and decreasing in the cost of funding:16 3βq¯ −2c q∗ = q∗ = B 11 23 2 5β +6γ βq¯ −2c q∗ = q∗ = B 12 22 5β +6γ q¯ q∗ = q − B 1C B1 2 q¯ q∗ = q − B . 2C B2 2 Firstnotethatinthepresenceofacentrallyclearedmarket, individualdealerdemand conditions affect the quantities traded only through their effect on aggregate dealer demand q¯ . Second, note that because ℓ is more central than ℓ and ℓ , demand and B 2 1 3 supply shocks have higher impact on quantities traded with l . This also translates 2 16Note that the existence of an interior equilibrium requires q¯ > 2c. In other words, there is B β sufficientdemandforfundsfromdealersrelativetolenders’costofsupplyingfunds. Thisisaspecial case of the more general condition (18). 26

in higher sensitivity of equilibrium repo rates 3βγ 5β +3γ s∗ = s∗ = q¯ + c 1 3 2(5β +6γ) B 5β +6γ 2βγ 5β +2γ s∗ = q¯ + c. 2 5β +6γ B 5β +6γ Finally, the quantity borrowed by each dealer in the centrally-cleared market is half the differential in dealer demands q −q q∗ = Bi Bj , i ̸= j, i,j ∈ {1,2}. iC 2 In this example, dealer 1 has higher demand than dealer 2 and will borrow q = 1C qB1−qB2 > 0, whereas dealer 2 will lend that same amount q = qB2−qB1 < 0. The 2 2C 2 transacted amounts in the C market reflect the heterogeneity in dealers’ demand conditions, andifdemandconditionsarethesame, therearenoequilibriumquantities traded at the equilibrium clearing rate. Note that this result is a special case to the derivations in Corollary 1. The simple example also illustrates the findings in Proposition 3. In the presence of the C market, the optimal borrowing decisions of dealers is to equalize the marginal (cid:12) ∂q (c+γ(cid:80) q )(cid:12) cost of funds across all sources of funds i.e. ρ∗ ≡ ik j∈Dk jk (cid:12) = ρ∗ at both ik ∂q ik (cid:12) C q∗ dealers i = d ,d and across all lenders. However, because of differences in the 1 2 quantities borrowed across lenders, the spread charged by the common lender ℓ is 2 higher than the spread charged by the exclusive lenders s > s = s . As a result, 2 1 3 there is dispersion in rates s − s = γ βq¯B−2c , which is positive because q¯ > 2c. 2 1 2(6γ+5β) B β This condition is equivalent to the general condition (18) and holds under any interior equilibrium. The dispersion in rates increases with the increase in overall dealer demand. Toillustratethepropagationofshocks, Figure5showsthelinegraphsforthethree market wirings in Figure 4. A dashed line between two dealer-lender pairs indicates a common dealer; a solid line between pairs indicates a common lender. Panel A displays the symmetric case. Suppose that a supply shock hits ℓ , the exclusive 1 lender for dealer d . Dealer d would decrease its borrowing from ℓ and increase its 1 1 1 borrowing from the common lender ℓ . Dealer d would then strategically respond 2 2 by increasing its borrowing from lender ℓ . Because (d ,ℓ ) is connected to (d ,ℓ ) 3 1 1 2 3 27

by an odd length path, the decisions of dealers d and d are strategic complements. 1 2 In contrast, dealer d reacts by reducing borrowing from ℓ as the actions of dealers 2 2 along the two edges (d ,ℓ ) and (d ,ℓ ) are strategic substitutes. 1 1 1 2 Figure 5: Line graph of 3× 2 market wiring A. Symmetric but incomplete wiring (d ,ℓ ) (d ,ℓ ) (d ,ℓ ) (d ,ℓ ) 1 1 1 2 2 2 2 3 B. Asymmetric and incomplete wiring (d ,ℓ ) (d ,ℓ ) (d ,ℓ ) (d ,ℓ ) 1 1 1 2 2 2 2 3 (d ,ℓ ) 1 3 C. Fully wired (d ,ℓ ) (d ,ℓ ) (d ,ℓ ) (d ,ℓ ) 1 1 1 2 2 2 2 3 (d ,ℓ ) (d ,ℓ ) 1 3 2 1 Note: The line graph of the bipartite networks in Figure 4. Dashed lines connect edges with common dealers and thick lines connect edges with common lenders. As the wiring of the decentralized market changes, so do the strategic interactions of dealers. For example, in the asymmetric and incomplete wiring in panel B, (d ,ℓ ) 1 1 and (d ,ℓ ) are connected both by an odd and an even length path. The strategic 2 3 28

interactions between the two dealers depends on the length of the paths, the supply and demand elasticities, and the decay factor as illustrated in equation (22). In this case, because the even length path (d ,ℓ )−(d ,ℓ )−(d ,ℓ ) is of length 2, whereas 1 1 1 3 2 3 the odd-length path is of length 3, discounting places a higher weight on the evenlength path. Finally, in the fully wired case in panel C, the two edges (d ,ℓ ) and 1 1 (d ,ℓ ) are connected by additional odd and even length paths. 2 3 4 Empirical analysis In this section, we apply the model to the data. We first provide a few important details on aggregate repo quantities and pricing, and summary statistics at the counterparty level.17 We then present a decomposition of changes in quantities traded into supply and demand factors. Using this decomposition and other controls, we estimate the key model parameters and formally test the assumptions and mechanisms of the model. The estimation of the model takes three steps. First, we characterize the marginal cost of lenders by estimating the parameters of the inverse supply function. Second, we evaluate dealers’ strategic substitutability of funding. This evaluation includes fundingfromthedecentralizedmarketaswellasnetborrowinginthecentrallycleared market. Third, we estimate the interest rate elasticity of dealer demand, controlling for the endogenous selection of dealers to be net borrowers or lenders in the centrally cleared market. 4.1 Aggregate quantities As illustrated in the top panel of Figure 6, OTC repo volume hovered around $400 billion at the beginning of our sample before it began to grow in 2016, peaked around $1 trillion in 2019, and then declined to $700 billion by end of our sample in October 2022. Centrally cleared GCF volume reached $400 billion in 2019 before falling to $200 billion in 2022. The GCF volume increased during the period from mid 2018 until the end of 2021. The volume of cash deposited by lenders with the Federal Reserve’s ON RRP facility is plotted in the lower panel of Figure 6. ON RRP takeup averaged about $200 billion in the period from 2014 through 2018 and was close 17AppendixCcontainsadetaileddescriptionofthedataconstructionandadditionalinstitutional details. 29

to zero between 2019 and 2021. By the end of our sample, take-up reached levels in excess of $2 trillion. Figure 6: Repo volumes by market segment 2016 2018 2020 2022 noillib$ 0001 008 006 004 002 0 Decentralized trades (OTC) Centrally−cleared market (GCF) 2016 2018 2020 2022 0052 0002 0051 0001 005 0 ON RRP noillib$ Note: The black line is trading volume in the decentralized OTC segment of the tri-party repo market. The light blue line is trading volume in the centrally cleared GCF market. The full list of ON RRP counterparties can be found at the FRB NY website. Vertical dashed lines indicate quarter-ends. Source: FRBNY Tri-party repo. The repo market turmoil of September 17, 2019 was unusual as it did not involve a major financial crisis or default of a systemic player in the market. The episodes 30

of market instability on September 17, 2019 prompted interventions by the Federal Reserve by executing a series of temporary repo operations that allowed dealers to access cash from the Federal Reserve at a pre-specified haircut and spread over the ON RRP rate. Figure 7: Borrowing from FRB repo operations and the GCF 2015 2016 2017 2018 noillib$ 005 004 003 002 001 0 81−20−10 81−11−70 91−52−10 91−42−70 02−82−10 02−13−80 12−40−50 2019−09−16 fi ON RRP GCF 2020−03−17 fi FRB Note: The temporary FRB repo operations we considered started on September 18, 2019 and were completed in June 2020. Borrowing from the repo operations in purple is indicated as FRB in the chart’s legend. The temporary repo operations were followed by the establishment of the permanent Standing Repo Facility (SRF) in July 2021. The SRF has not been actively used since its establishment. Source: FRBNY Tri-party repo. Figure7plotstheborrowingfromtheFed’srepooperations. Uponthecommencement of the operations on September 18, 2019, dealers borrowed around $70 billion and the amount quickly increased in subsequent months to above $100 billion, which is close to the drop in supply, which we document in section 4.8. As the COVID-19 pandemic created pressure in Treasury markets, dealers tapped the operations again and the borrowing peaked at about $200 billion before declining to zero by June 2020. 31

4.2 Summary statistics on repo counterparties There are 159 lenders and 49 dealers in our sample with some entry and exits. As discussed in Figure 3, the entry and exit of counterparties are mostly smaller entities and the bulk of trades are over established long-term relationships. In addition, we drop very small lenders that provide less than $1 million in cash. Table 1 provides summary statistics of the lenders in our sample. The average lender supplies around $4.5 billion of cash to dealer counterparties and there is significant heterogeneity in lender sizes. The 5th percentile lender provides about $6 million, the median lender provides more than $300 million, and the 95th percentile lender provides close to $30 billion.18 Table 1: Lenders’ provision of cash mean sd 5 25 50 75 95 Lending ($mln) 4,510 12,983 6 77 333 1,875 29,936 Number of dealers 5 6 1 1 3 7 20 Within-lender HHI 54 37 6 20 50 100 100 C1 concentration 60 34 12 29 55 100 100 C3 concentration 82 27 29 67 100 100 100 ON RRP ($mln) 2,528 18,143 0 0 0 0 6,500 Note: The sample period covers trading days from August 22, 2014 through October 31, 2022. C1 and C3 measure the shares of the top one and three dealer counterparty for each lender, respectively. HHI is the within-lender Herfindahl-Hirschman Index of concentration of dealer borrowing that is scaled to vary between 0 and 100. Source: FRBNY Tri-party repo, SEC Form N-MFP, iMoneyNet, and authors’ calculations. Lenders also differ in the number and concentration of lending to dealer counterparties. The average lender has about 5 dealer counterparties and the median lender has 3 dealer counterparties. Finally, not all lenders have access to the ON RRP facility, or, iftheyhaveaccess, overcertainperiodsofoursamplelenderschoosenottodeposit cash at the ON RRP as shown in Figure 6. Movingtodealers,thereissignificantheterogeneityindealers’borrowinginthetriparty market reflecting heterogeneity in dealers’ types, asset sizes, and connectedness 18We use information from the SEC’s Form N-MFP and iMoneyNet to identify money market mutualfunds(MMFs). AroundathirdofthevolumeoftradesingovernmentrepocomefromMMFs and the remainder are a diverse group of entities such as asset managers, insurance companies, pension funds, federal home loan banks, government sponsored enterprises, municipal treasurers, small commercial banks, credit unions, as well as nonfinancial corporations. 32

to the different market segments as summarized in Table 2. The average dealer is much larger and has a higher number of counterparties than an average lender. The average dealer borrows $13 billion from lenders and transacts with 13 lenders. Note that at least a quarter of mostly smaller dealers have one lender or do not maintain borrowing relationships with a lender in the decentralized market but instead mostly transact in the GCF market consistent with the market wiring in Figure 1. The within-dealer HHI of borrowing is about 23 percent. The average share of the largest lender is 29 percent of the borrowed amount and that share is 46 percent for the largest three lenders. Table 2: Dealers balance sheet characteristics and repo borrowing mean sd 5 25 50 75 95 Decentralizeddealer-lenderOTCmarket Borrowing($mln) 13,338 18,813 0 7 3,235 21,937 54,374 Numberoflenders 13 16 0 1 6 26 44 Within-dealerHHI 31 33 4 6 14 49 100 C1concentration 39 31 9 14 25 59 100 C3concentration 61 30 24 33 53 100 100 Dealerdemandgrowthδ,% 1.0 27.6 -22.6 -6.4 0 6.4 23.6 Averagedealersupplygrowth,% 0.3 15.3 -8.2 -2.5 0.1 2.9 9.2 CentrallyclearedinterdealerGCFmarket GCFborrowing($mln) 7,480 9,524 0 600 4,100 11,450 24,350 GCFlending($mln) 6,518 8,905 0 950 3,765 8,650 22,450 GCFnetborrowing($mln) 962 11,326 -14,904 -2,650 400 4,750 17,700 Dealerbalancesheetandcreditriskinformation Consolidatedassets($bn) 1,267.9 780 305.9 643.8 1,134.9 1,775.2 2,680.1 Consolidatedbookleverage 6.4 2.4 3.7 4.6 5.8 7.9 11.2 EDF1-year,bps 36.2 24.9 10.3 20.5 29.9 43.9 88.1 Market-to-bookratio 0.89 0.07 0.78 0.84 0.89 0.95 1.00 Note: The sample period covers data from August 22, 2014 through October 31, 2022. There are 49 unique dealers for which we observe information on tri-party repo trades over this period and 31 dealers for which we also have consolidated balance sheet and credit risk measures. C1 and C3 measure the shares of the top one and three lenders, respectively. The within-dealer HHI is the Herfindahl-Hirschman Index of concentration of dealer borrowing from lenders in the OTC market. GCF is the FICC centrally cleared market. Source: FRB NY, Moody’s CreditEdge (KMV), and and authors’ calculations. In the middle panel of Table 2, we examine dealers’ transactions in the interdealer market. On average, larger dealers are net borrowers and the average amount borrowed is about $7.5 billion, which is smaller than the average amount lent $6.5 billion. As a result, the average dealer is a net lender in the GCF market, even though the aggregate net cash provided by the GCF market is exactly zero. For a subset of the largest 31 dealers in our sample, we obtain information on their 33

parent holding companies’ consolidated balance sheets and credit risk from Moody’s CreditEdge (KMV) database. The summary statistics of this information is summarized in the lower section of Table 2. The average dealer parent holding company has total consolidated assets exceeding $1.3 trillion and those include the assets not only of the dealer subsidiary but also affiliated entities including commercial banks, insurance companies, and other financial entities. The ratio of dealers’ book equity to total assets is 6.4 percent for the average dealer and 5.8 for the median dealer. The average empirical default frequency over one year horizon (EDF1) is 36 basis points and the average market-to-book ratio is 0.89. Figure 8: Foreign dealer trades at quarter-ends and ON RRP take-up A. Foreign dealer repo trades (OTC) B. ON RRP deposits −4 −2 0 2 4 002 051 001 05 0 05− 001− 051− Days to quarter end noillib$ 2014−2017 2018−2020 2020−2022 −4 −2 0 2 4 051 001 05 0 05− 001− 051− Days to quarter end noillib$ 2014−2017 2018−2020 2020−2022 Note: The figures compute the average amounts over a 5-day window around the last trading date of the quarter. Source: FRBNY Tri-party repo and authors’ calculations. Dealers can be categorized into three broad groups: bank-affiliated domestic dealers, which are typically part of a large domestic bank holding company subject to bank regulation in the U.S.; non-bank affiliated dealers, which are typically not affiliated with a regulated bank; and foreign dealers, which are typically part of large foreign banking organizations subject to bank regulation in the respective foreign country. Figure 8 illustrates an important feature of the repo market at quarter-ends. 34

Foreign dealers pull back from the repo market at quarter-ends to improve the regulatory leverage ratios of their parent bank holding company, which are calculated on quarter-end values. At the same time, domestic dealers affiliated with regulated banks do not exhibit such behavior, because U.S. bank holding companies’ leverage ratios are based on quarterly average values.19 As foreign dealers pull from the repo market at quarter-ends, lenders with access to the ON RRP increase their deposits with the ON RRP with roughly the same magnitude. At the same time, foreign dealers borrow more from the GCF market inducing a spike in rates. Within a day following the end of the quarter, foreign dealers’ repo trades revert back to their typical levels. Similarly, lenders withdraw cash from the ON RRP to fund the renewed trading activity of foreign dealers. The periodic inflows and outflows of cash in the repo market create demand and supply imbalances that can potentially result in rises in repo rates at quarter-ends.20 4.3 Pricing of repo trades and repo rate spikes ThetimeseriesvariationofgovernmentreporatesisplottedinFigure9andsummary statistics are provided in panel A of Table 3.21 For most trading days, the dispersion of rates is very tight around the ON RRP rate with an average spread over the ON RRP rate of about 6 basis points and a standard deviation of 10 basis points. At quarter-ends, as foreign dealers exit the market, there are notable spikes in repo rates and significant increases in the levels and dispersion of rates. The average spread doubles to 12 basis points and the range of rates exceeds 60 basis points. Panel B of Table 3 shows that a large fraction of the variation in tri-party repo rates is due to dealers facing different rates across lenders. Close to 70 percent of the variation in rates are within-dealer across lenders, and during the large spike in rates on September 17, 2019, 82 percent of the variation in rates could be attributed to within-dealer variation. This stylized fact allow us to significantly simplify the modeling of the price formation as coming from differences in market power and marginal costs of lenders as we discuss in section 3.1 and we verify this assumption in the empirical analysis of section 4.5. 19See Munyan [2015] for more detailed analysis on the regulatory arbitrage. 20Note that a similar plot for domestic dealers does not show seasonal patterns in their repo borrowing around quarter-ends. 21Government repo includes repo trades in Treasuries, agency debt, and agency MBS, which collateral that is eligible for pledging at the ON RRP and the FICC’s GCF. 35

Figure 9: Distribution of government repo rates 2016 2018 2020 2022 stniop egatnecrep 6 5 4 3 2 1 0 OTC rates: 5/95th percentile OTC rates: Median ON RRP rate GCF rate 2019−09−17 fi Note: Spreads are expressed in percentage points. Government repo includes repo trades inTreasurysecurities,agencydebt,andagencyMBS.Thesampleperiodforratesonrepotrades in the GCF market begins in 2016. Source: FRBNY Tri-party repo and authors’ calculations. Panel C of Table 3 provides summary statistics of the borrowing rate in the GCF market. At 53 basis points, the average GCF spread is higher than the spread dealers face in the OTC market by about 15 basis points on within quarter trading days. At quarter-ends,thedifferenceincreasesby41basispointsindicatingthatthedisbalances in supply and demand from the pullback of foreign dealers are cleared through higher rates at the GCF market. Finally, there is also notable spike in the GCF spreads on September 17, 2019. Even though the GCF spread was lower for the average and median dealer as compared to the OTC market, the upper percentiles the GCF rates were significantly higher. These differences likely reflect the timing of the execution of the trades within the trading day. Our data do not provide a timestamp of a within day execution and we abstract from this high frequency information both in our empirical and theoretical analysis.22 There is a substantial increase in the level of spreads observed on September 17, 2019 from the typical 6 basis points to around 315 basis points and this spike in rates 22See Paddrik, Young, Kahn, McCormick, and Nguyen [2023] for analysis using high-frequency intra-day repo data collected by the Office of Financial Research (OFR). 36

Table 3: Summary statistics on government repo pricing mean sd 5 25 50 75 95 A. OTC market spreads over ON RRP (basis points) Within quarter 6 10 -3 1 4 10 20 Quarter-end 12 19 -5 0 6 19 62 Sept. 17, 2019 315 62 230 3 325 350 357 B. Variance decomposition of OTC spreads Within-dealer (within quarter) 0.68 0.12 0.48 0.60 0.69 0.76 0.86 Within-dealer (quarter-end) 0.61 0.13 0.41 0.50 0.63 0.71 0.80 Within-lender (within quarter) 0.42 0.14 0.15 0.35 0.45 0.52 0.59 Within-lender (quarter-end) 0.37 0.12 0.17 0.29 0.37 0.44 0.56 C. GCF market spreads over ON RRP (basis points) Within quarter 21 13 6 14 21 27 35 Quarter-end 53 45 8 24 43 66 135 Sept. 17, 2019 293 172 73 194 282 350 634 Note: The variance decomposition of rates is computed as a decomposition of the share in total variation in rates from within-dealer and across-dealer variation as well as an equivalent decomposition into within-lender and across-lender variation. The identity can be expressed as (cid:80) (cid:80) (r −r¯)2 = (cid:80) (cid:80) (r −r¯ )2+m (cid:80) (r¯ −r¯)2 = (cid:80) (cid:80) (r −r¯ )2+n (cid:80) (r¯ −r¯)2, i k ikt t i k ikt it t i it t i k ikt kt t i kt t wherer¯ istheaveragerateacrossalldealersandlenders,r¯ istheaveragerateofdealeri,r¯ is t it kt the average rate of lender k, and n and m are the number of dealers and lenders, respectively. t t was also associated with a significant increase in the dispersion of spreads across dealer-lender trading relationships as illustrated in Figure 10. In normal times, the cross-sectional dispersion in spreads is within 10 basis points, and at quarter-ends, the dispersion almost doubles to 19 basis points. However, on September 17, 2019, the standard deviation of the cross-sectional distribution of spreads increased to more than 60 basis points with the 5th percentile lender charging 230 basis points and the 95th percentile lender charging over 350 basis points. 4.4 Decomposition of supply and demand factors Proposition 2 illustrates the complex relationship of supply and demand conditions in a networked market. However, to a first-order approximation and under a set of assumptions, the incomplete connectedness of the T market allows us to decompose movements in quantities into changes in the relative supply and demand conditions of lenders and dealers. Such decomposition allows us to estimate demand and supply elasticities by controlling for endogeneity or simultaneity biases. We begin with a decomposition of movements in quantities in the T market into 37

Figure 10: Dispersion in spreads over the ON RRP rate OTC spreads over ON RRP (percentage points) ytisneD −2 0 2 4 6 8 6 4 2 0 September 17, 2019 Quarter−ends Other Note: Quarter-ends are the last trading day for the quarter. Other includes all trading days outside quarter-ends and the September 2019 spikes. Source: FRBNY Tri-party repo and authors’ calculations. dealer-specific demand and lender-specific supply factors, which we use as a set of instruments to estimate the supply and demand elasticities. First, we assume that the first-order effects of changes in dealer demand (lender supply) result in changes in quantities borrowed (lent) across lender (dealer) counterparties proportional to the laggedlender(dealer)shares. Thisassumptioniscommoninthenetworkpropagation literature [Greenwood, Landier, and Thesmar, 2015; Duarte and Eisenbach, 2021; Cetorelli, Landoni, and Lu, 2023] and resembles the concept of a Bartik instrument (e.g. Goldsmith-Pinkham, Sorkin, and Swift [2020]). Second, we assume that higher-order effects of demand shocks are mean zero in expectation. Under these assumptions, we can decompose the effects of demand and supply as in the following proposition. Proposition 4 For any dealer-lender pair ik ∈ E the growth rate in the quantity traded ∆q , can be decomposed into the change due to dealer i specific shock δ and ikt it the change due to a lender k specific supply shock λ kt ∆q = δ +λ +ϵ , ∀ik ∈ E, (32) ikt it kt ikt where δ ∝ dq and λ ∝ 1 dc . The error term ϵ contains remaining variation it Bit kt γ kt ikt k 38

related to higher-order interactions that is dealer-lender specific. The decomposition is similar to that proposed by Amiti and Weinstein [2018], hence we refer to it as the AW decomposition. The AW decomposition works for most trading relationships except for the cases in which a lender has an exclusive relationship with a single dealer. In those cases, similar to the fixed-effects methodology of Khwaja and Mian [2008], the supply factor is not identified. Therefore, we drop lenders with only one dealer, and such lenders form a small fraction of the overall trading volume. In addition, the decomposition takes into account the entry and exit of counterparties, as well as the establishment and dissolution of trading relationships. While these changes are not large in our data and provide the support in our theoretical model to assume the network is static, we control for the small changes in participation and relationships, as neglecting these transitions could bias our estimates. Figure 11: Decomposition of supply and demand factors 2016 2018 2020 2022 stniop egatnecrep ,htworg 03 02 01 0 01− 02− Demand Supply Note: The figure shows the monthly weighted averages of the daily supply and demand factors based on the solution of the system of equations. See appendix for details on the construction. Source: FRBNY Tri-party repo and authors’ calculations. Figure 11 plots the time series of the decomposition of supply and demand factors aggregated and averaged at a monthly frequency. The figure reveals significant 39

variation in supply and demand conditions over our sample period. Of note, supply and demand exhibit seasonal patterns. For example, from the start of our sample period through 2018, demand at quarter-ends declines, reflecting the pull back from repo markets by foreign dealers. Lenders deposit the freed up cash at the ON RRP. Foreign dealer demand usually bounces back following the end of the quarter with lenders increasing supply by reducing balances held at the ON RRP. However, this pattern is disrupted in 2018. Beginning in 2018, the magnitude of demand shocks declines, while the magnitude of supply shocks increases. This pattern is consistent with the dry up of excess cash deposited with the Federal Reserve’s ON RRP. The dry-upofexcesslendingcapacityincreasedtheparticipationofdealersinthecentrally cleared GCF market as we illustrated in Figure 7. 4.5 Lender marginal costs Weestimatethelendermarginalcostcurve(1)usingthefollowingregressionequation s =γ(q −q ) kt k,t O,k,t (33) c˜ +cQI{Quarter-end}+cOI{q = 0}+c2019I{Sept.16-18,2019}+ϵ , k O,k,t kt where s = r −r is the spread over the ON RRP rate, q is lender k total repo kt kt O,t k,t lendingtodealersinthedecentralizedmarket. Weassumeacommonsupplyelasticity γ across lenders and proxy for the lender available excess cash with the balance held at the ON RRP q . The time-invariant lender opportunity costs, c˜ parameters, O,k,t k are estimated as lender fixed effects. We also control for the last trading day of the quarter and we add a dummy for the days surrounding September 17, 2019. Table 4 reports the results from this estimation with repo spreads expressed in basispointsandquantitiesexpressedin$billions. Column(1)showsthesimplepooled OLS regression. Turning first to quantities supplied, the results reveal that greater lending in excess of cash deposited at the ON RRP leads to a higher spread over the ON RRP rate. The estimate of γ implies that, on average, an increase in lending of about $100 billion leads to an average increase in the spread of the repo rate over the ON RRP rate of about 5.2 basis points. Lenders that do not have deposits with the ON RRP (q = 0), which is a proxy for lack of excess cash, charge on average O,k,t about 5 basis points higher spreads. Turning next to calendar effects, there is an average 6.1 basis point increase in the 40

Table 4: Estimates of lender supply coefficients Dependent variable: Spread over ON RRP s =r −r kt k,t O,t (1) (2) (3) (4) (5) q −q , (γˆ1) 0.054∗∗∗ 0.039∗∗∗ k,t O,k,t (0.017) (0.013) qδ −qδ , (γˆ2) 0.154∗∗∗ k,t O,k,t (0.045) qδ , (γˆ3) 0.220∗∗∗ k,t (0.064) qδ , (γˆ4) −0.139∗∗∗ O,k,t (0.044) qλ −qλ , (1) −0.021 k,t O,k,t βˆ (0.019) I{q =0} 4.072∗∗∗ 6.516∗∗∗ O,k,t (0.904) (0.347) I{qδ ==0} 7.600∗∗∗ 7.600∗∗∗ O,k,t (0.304) (0.304) I{qλ ==0} 7.607∗∗∗ O,k,t (0.305) I{Quarter-end} 6.091∗∗∗ 6.175∗∗∗ 5.930∗∗∗ 5.945∗∗∗ 5.917∗∗∗ (0.201) (0.187) (0.171) (0.170) (0.170) I{2019-09-16} 34.092∗∗∗ 33.867∗∗∗ 33.988∗∗∗ 33.988∗∗∗ 33.995∗∗∗ (0.858) (0.756) (0.750) (0.750) (0.750) I{2019-09-17} 291.146∗∗∗ 290.860∗∗∗ 290.992∗∗∗ 290.993∗∗∗ 290.938∗∗∗ (5.457) (5.392) (5.394) (5.394) (5.395) I{2019-09-18} 41.660∗∗∗ 41.407∗∗∗ 41.432∗∗∗ 41.414∗∗∗ 41.471∗∗∗ (1.253) (1.155) (1.116) (1.117) (1.114) Constant 3.187∗∗∗ (0.310) Observations 167,546 167,546 167,546 167,546 167,546 R2 0.305 0.628 0.624 0.624 0.624 Adjusted R2 0.305 0.627 0.624 0.624 0.624 Note: The data consist of an unbalanced panel of 159 lenders and 1925 trading dates over the period 2014-08-27 to 2022-10-31. Spreads are measured in basis points. The quantity variables q and qO are the lender-level repo transaction volumes expressed in $billion in the decentralized k,t k,t tri-party repo market and the ON RRP facility, respectively. The predicted values from the supply and demand decomposition are computed as qλ ≡ λ ×q and qδ ≡ δ¯ ×q , where δ¯ is kt kt kt−1 k,t kt kt−1 kt the weighted average of lender k dealers’ demand factors. A Wald test on the null hypothesis of different signs but equality of the magnitudes of the coefficient estimates in specification (4) for qδ k,t and qδ (i.e. H :γˆ3+γˆ4 =0) has a Chi-squared value of 1.26 and a p-value of 26 percent, thus O,k,t 0 failing to reject the null hypothesis. Heteroscedasticity consistent standard errors are clustered at the lender level. Significant at ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01. 41

costoffundsatquarter-ends. Inaddition,duringthemarketturmoilonSeptember17, 2019, the average funding cost increased by about 291 basis points. Those estimates indicate that lender supply experiences large time series variation. The constant term provides an estimate of the lender-specific cost parameter c˜. The estimate for the average lender of c˜is about 3 basis points, which accounts for roughly 60 percent of the average repo spread variation outside the quarter-end periods. In columns (2) through (5), we add lender fixed effects {c˜ } to identify the unobserved lenderk k∈L specific variation in the marginal cost curves. With this addition, other parameter estimates are quantitatively similar to those in column (1). Of note, there is a slight attenuation in our estimate estimate of γ at 0.04, implying an increase in spread of about 4 bps for every $100 billion increase in aggregate lending. Our estimated rate elasticities in columns (1) and (2) have a positive sign indicative of an upward sloping supply curve with the quantities traded. However, the standard endogeneity problem of this regression holds as the spread charged is co-determined with the quantities transacted. The parameter estimates are biased downward, because we are not controlling for changes in dealer demand. Therefore, in columns (3) and (4), we report results from empirical specifications that use the AW decomposition to predict the changes in the quantities transacted for each lender k as coming from the average change in dealer demand conditions qδ ≡ δ ¯ q , k,t k,t k,t−1 ¯ (cid:80) q where δ = jk,t−1δ is the weighted change in dealer demand faced by k,t j∈D k,t−1 q k,t−1 j,t lender k, weighted by the lagged shares of lender k dealer counterparties. Similarly, in column (5), we use the change in quantities due to the changes in the lender supply conditions, which are constructed as qλ ≡ λ q . The change in quantities qλ k,t k,t k,t−1 k,t and qδ are parallel shifts in the quantities supplied and demanded that allow us to k,t condition on movements along demand and supply curves and identify supply and demand elasticities. Incolumn(3),theestimateofγ ishigherthantheestimatesincolumns(1)and(2), which is consistent with correcting for the downward bias of estimates in columns (1) and (2) by conditioning on changes in dealer demand. It implies that in the aggregate the funding costs for dealers increase by about 15 basis points for every additional $100 billion in funding. All else equal, lenders without excess cash deposited with the Fed’s ON RRP charge on average around 7.6 basis points higher spreads. Note that the rest of the parameter estimates are roughly unchanged indicating that the quarter-end effects and the effects around September 17, 2019 are likely driven by 42

supply factors not related to changes in supply elasticities. In column (4), we test our two assumptions embedded in equation (1) that excess cash deposited at the ON RRP reduces the opportunity cost of supplying funds to dealers and that the inverse supply elasticity is the same as the inverse elasticity of the cash provided to dealers. First, the coefficient estimate for the ON RRP balance γˆ4 is statistically significant and negative at −0.139 validating the first assumption. Second, the coefficient estimate γˆ3 is 0.220, which is higher than the estimate in specification (3). However, a Wald test for the equality of the magnitudes of the two coefficients fails to reject the null hypothesis of equality with a p-value exceeding 26 percent.23 The estimates in columns (3) and (4) give us some range of estimates of the supply elasticity. Based on estimates from column (3), the implied lender supply elasticity is $6.5 billion for every 1 basis point increase in interest rates. The estimate in column (4) is lower and implies that funds with excess cash are willing to supply an additional $4.5 billion for every 1 basis point increase in interest rates.24 Finally, the analysis in column (5) examines a test for the validity of the supply and demand decomposition. The previous three specifications were conditioning on movements in dealer repo demand tracing an upward sloping lender marginal cost curves. Inspecification(5),weexaminemovementsinreposupplytracingadownward sloping demand curve. Therefore, the coefficient estimate on the term (qλ −qλ ) is k,t O,k,t expectedtobenegativeconsistentwithmovementsalongadownward-slopingdemand curve and its magnitude inversely proportional to dealers’ inverse elasticity parameter β. The coefficient estimate is indeed negative and its magnitude is both economically small and statistically not significant. This estimate indicates that dealer repo demandisrelativelyinelastic. Wereturntoamorein-depthestimationofdealerdemand in the next section. We have assumed a common interest rate elasticity of lender supply and, thus, the estimate for the supply elasticities should be interpreted as an aggregate supply elasticity. At the individual lender level, there are capacity constraints that would make the supply elasticity much lower especially for smaller lenders in our sample. It 23Note that if we estimate the regression in specification (4) without the AW decomposition, we obtain qualitatively similar results to specification (1) with the Wald test also failing to reject the null hypothesis. 24In unreported estimation, we also run a weighted regression to underscore that larger funds are more likely to be unconstrained and have impact on the aggregate supply of funds. The estimates are in line with the unweighted regressions. 43

should be noted that while we assumed supply elasticities to be fixed, we let lender marginal cost intercepts {c˜ } to differ across lenders and in part capture variation k k∈L in capacity constraints and excess cash as discussed in Section 3.1. Table 5 shows the cross-sectional distribution of those estimates, which reveals that there is significant heterogeneityintheaveragemarginalcostsacrosslenderswitharighttailofhighcost lenders with marginal costs exceeding 20 basis points and a notable mass of low cost lenders, which are, all else equal, willing to supply funds to dealers at low rates with more than 10 basis point discount relative to the ON RRP rate. On average lenders with access to the Fed’s ON RRP have higher marginal costs than those lenders that do not have access. The median lender with access to the ON RRP charges 1.1 basis points spread over the ON RRP rate, whereas the median lender without access to the ON RRP charges 2.4 basis points lower spread over the ON RRP rate. Table 5: Estimates of the average lender marginal cost parameters c˜ mean w.mean sd 5 25 50 75 95 All lenders 0.2 3.15 9.6 -10.5 -4.3 -1.5 2.5 20.0 No access to ON RRP -1.2 2.12 8.9 -11.9 -5.4 -2.3 -0.2 20.7 Access to ON RRP 3.3 3.89 10.4 -2.5 -0.6 1.1 3.8 7.1 Note: The estimates of the lender fixed effects from regression Table 4 column (3). The units are basis points. w.mean is the volume-weighted mean. There are 159 lenders in our sample. Of those, 43 have access to the ON RRP with the Fed and 116 do not have access. 4.6 Dealers’ strategic substitutability of funding Before we estimate the repo demand elasticities, we first test whether dealers’ borrowing actions are strategic substitutes in the decentralized market. The system of first-order conditions (6) implies that dealer i reduces its own borrowing in response to higher borrowing by other dealers with whom dealer i shares a set of common lenders. The degree of substitution depends on on the relative supply and demand elasticities. To quantify the degree of substitution of dealer actions, we examine the following reduced-form empirical specification 44

(cid:88) (cid:88) ∆q = α ∆q +α ∆q +α ρ (34) ik,t 1 jk,t 2 il,t 3 C,t j∈D k ,j̸=i l∈Li,ℓ̸=k +δ +λ +u , i,t k,t ik,t where ∆q is the growth rate in repo volume between dealer i and lender k between ik,t (cid:80) trading days t − 1 and t. The term ∆q captures the growth rate in j∈D ,j̸=i jk,t k repo volume by lender k from all of its dealer counterparties excluding dealer i. (cid:80) Similarly, the term ∆q captures the growth rate in repo volume of all l∈Li,ℓ̸=k il,t lender counterparties of dealer i excluding lender k. The sign and magnitude of the coefficient estimates of α and α are of importance. 1 2 Both coefficients should be negative reflecting substitutions of dealers across different lenders in the OTC market as a response to other dealers’ funding decisions. Finally, all else equal, higher cost of borrowing from the GCF market should increase the borrowing from the decentralized market, implying that α should be positive. 3 This coefficient captures the degree of substitution between the decentralized and the centrally cleared GCF market. To control for the endogeneity of the equilibrium quantities, we condition on changes in dealer demand captured by δ and changes in lender supply captured i,t by λ . We also control for unobservable dealer and lender characteristics with a k,t set of dealer and lender fixed effects. The indicator function I{q = 0} takes the iCt value of 1 for the case when a dealer does not transact in the interdealer market, and I{q ̸= 0} takes the value of 1 for the case when a dealer borrows or lends in the iCt decentralized market. Estimates of (34) are reported in Table 6. In the first column, we present the regression without the demand and supply controls but with a full set of dealer and lender fixed effects. The terms that capture the strategic interactions among dealers andthesubstitutionsacrosslendersincolumn(1)arebothpositive, whichcontradicts the predictions of the model. However, this is expected, because the growth in repo trades are determined by common variation in demand and supply conditions among dealers and lenders. 45

Table 6: An estimate of dealers’ substitutability of funding Dependent variable: Growthindealer-lenderrepotrades∆q ik,t (1) (2) (3) GCFspreadρC 1.510∗∗ (0.610) (cid:80) ∆q −0.305∗∗∗ l∈Li,ℓ̸=k iℓ (0.056) (cid:80) ∆q −0.306∗∗∗ j∈Dk,j̸=i jk (0.038) GCFspreadρC|I{qiC ̸=0} 2.225∗∗∗ 1.646∗∗ (0.733) (0.675) GCFspreadρC|I{qiC =0} 0.879 0.907 (0.718) (0.696) (cid:80) l∈Li,ℓ̸=k ∆q iℓ |I{qiC =0} 0.230∗∗∗ −0.291∗∗∗ (0.058) (0.060) (cid:80) l∈Li,ℓ̸=k ∆q iℓ |I{qiC ̸=0} 0.075∗∗∗ −0.363∗∗∗ (0.024) (0.057) (cid:80) j∈Dk,j̸=i ∆q jk |I{qiC =0} 0.088∗∗∗ −0.306∗∗∗ (0.015) (0.039) (cid:80) j∈Dk,j̸=i ∆q jk |I{qiC ̸=0} 0.105∗∗∗ −0.304∗∗∗ (0.029) (0.045) λ 0.966∗∗∗ 0.966∗∗∗ k,t (0.074) (0.074) δi,t 0.891∗∗∗ 0.895∗∗∗ (0.064) (0.064) Observations 1,049,713 1,049,713 1,049,713 R2 0.016 0.135 0.135 AdjustedR2 0.015 0.135 0.134 ResidualStd. Error 35.8 33.6 33.6 Degreesoffreedom 1,049,506 1,049,504 1,049,507 Note: The data consist of an unbalanced panel of 159 lenders, 49 dealers, 1261 trading relationships, and 1926 trading dates over the period 2014-08-27 to 2022-10-31. The growth rates and the GCF repo spread are expressed in percentage points. Therefore, a percentage point increase in the GCF spread over the ON RRP spread leads to a 1.5 percentage points increase in the growth of repo trades in the OTC market. All regressions include a full set of dealer and lender fixed effects. Heteroscedasticityconsistentstandarderrorsareclusteredatthelenderlevel. Significantat∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01. In columns (2) and (3), we control for demand and supply conditions of dealer i and lender k. With these controls, the two terms switch signs to being negative as 46

predicted by the model. The estimates imply that for every percentage point increase in the borrowing of competing dealers, a dealer reduces its own borrowing by about 30 basis points. Similarly, a percentage point increase in the borrowing from lenders other than k in dealer i’s counterparties, results in about 30 basis points decline in the borrowing from lender k. The degree of substitution among lenders is smaller for dealers that access the interdealer market as revealed in column (2) that conditions on whether the dealer participates in the interdealer market. Finally, the signon theGCF spreadρ is positive, indicating thatdealers aremore C likely to borrow more from their counterparties in the decentralized market, when the cost of borrowing from the centrally-cleared market is higher. The dealers, that do not participate in the interdealer market, do not respond to changes in the GCF spread. The coefficient estimate for dealers that do not transact in the interdealer market is both smaller and statistically not significant. This substitution between the decentralized and the centrally cleared market is predicted by the model and the magnitude of the interest rate sensitivity is inversely related to the dealers’ balance sheet cost parameter. We can extract an estimate of dealers’ demand elasticities from the estimate of α , which is related to the dealer demand elasticity 1. The estimate implies that for 3 β every100basispointsincreaseintheGCFspread, dealersincreaseborrowingfromthe decentralized market by about 1.5 percent. This estimate implies a very low demand elasticity relative to the estimated lender supply elasticity in the previous section. However, this estimate is likely to be biased as it ignores the endogeneity in the choice of participating in the GCF market. We examine empirically the endogenous selection of dealers into net borrowers and net lenders in the centrally cleared market along the extensive and intensive margins in more detail in the next section and provide additional estimates of dealers’ demand elasticity. 4.7 Dealers’ participation in the interdealer market We next examine the extensive and intensive margins of dealers’ participation in the centrally-cleared interdealer market (FICC GCF). Equation (19) predicts that dealers with more costly access to the decentralized market would be net borrowers, whereas dealers with lower cost of accessing the decentralized market would be net lenders. In addition, dealers with low β or low funding shortfall costs are more elastic to interest rates. All else equal, those dealers are more likely to switch roles between being net 47

borrowers in the GCF market to being net lenders. To estimate β, we design the following empirical specification (cid:88) (cid:88) q = α qδ +α ψ ˜ qλ +α ( ψ ˜ )×ρ +α ρ +ϵ . iC,t 1 i,t 2 ik,jℓ,t l,t 3 ik,jℓ,t C,t 4 C,t it (35) k∈Li k∈Li jℓ∈E jℓ∈E We estimate equation (35) as a selection model with the main object of interest the estimate of α = 1. The model implies that conditional on demand dealers with 4 β higher funding cost and balance sheet costs β are more likely to select to be net borrowers. Table 7: Probit regression for the participation in the GCF market Dependent variable: ParticipationintheGCFmarket NetborrowerI{qiC,t>0} NetlenderI{qiC,t<0} (1) (2) EDF1-year,it −0.716∗∗∗ 1.092∗∗∗ (0.041) (0.041) Bookleverage,it 13.822∗∗∗ −5.821∗∗∗ (0.334) (0.325) Market-to-book,it −4.512∗∗∗ 3.715∗∗∗ (0.152) (0.147) log(Assets),it 0.131∗∗∗ 0.715∗∗∗ (0.010) (0.011) Constant 1.085∗∗∗ −13.282∗∗∗ (0.207) (0.219) Observations 43,811 43,811 Obs. I{qiC >0} 13,108 13,108 Obs. I{qiC <0} 21,047 21,047 LogLikelihood −25,704.680 −27,643.660 AkaikeInf. Crit. 51,419.370 55,297.320 Note: Thedataconsistofanunbalancedpanelof31dealersforwhichweobserveEDF 1-year, book leverage, market-to-book ratios, and total assets over the period 2014-08-27 to 2022-10-31. Significant at ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01. The first stage of the estimation is a probit model that examines the determinants 48

of the dealer’s choice to participate in the GCF market as either a net borrower I{q > 0} or as a net lender I{q < 0}. We introduce dealer-specific variables that iC iC are determined outside the tri-party repo market and relate to the dealers’ cost of access to unsecured credit markets as well as regulatory balance sheet constraints. In particular, we proxy for the cost of funds from external unsecured markets with measures of the default risk, leverage, asset size, and market valuation of the dealers’ parent holding company. For leverage constraints on bank affiliated dealers, we use measures of book leverage again measured at the parent holding company. We use the one-year empirical default frequency (EDF 1-year) constructed by the Moody’s KMV Merton-style default model as well as the book leverage of the dealer’s parent holding company. To condition on the parent’s alternative use of funds, we also include the parent holding company market-to-book ratio. Finally, we also control for the size of the parent holding company with the log of the market value of total assets. Results of the probit regression are reported in Table 7. Column (1) examines the choice to be a net borrower in the GCF market relative to being a net lender or not participating,andcolumn(2)examinesthechoicetobeanetlenderrelativetobeinga net borrower or not participating. Higher EDF 1-year predicts lower probability to be anetborrowerandhigherprobabilitytobeanetlender, whereashigherbookleverage predictshigherparticipationasanetborrowerandlowerparticipationasanetlender. A lower market-to-book ratio, which could be an indicator for market distress or the lack of good investment opportunities, is associated with higher participation as a net lender and a lower participation as a net borrower. The estimates of second stage of the selection model are presented in Table 8. In columns (1) and (2), we estimate the interest sensitivity of the amount borrowed or the amount lent, conditioning on the dealer selection to be net borrower or net lender, respectively. The quantities are expressed in billions of dollars and the GCF spread is expressed in basis points. Therefore, the amount borrowed decreases by about $28 million following a 1 basis point increase in spreads, whereas a similar increase in the spreads results in a $42 million increase in lending. This implies that dealers that select to provide funding in the GCF market have lower β as compared to those that demand funding. The estimate of the inverse demand elasticity β for dealers, that are net borrowers in the GCF market, implies that those dealers are willing to pay 36 basis points for every additional billion of dollars of funding, whereas the estimated β for dealers, that are net lenders in the GCF market, implies that those dealers are 49

willingtosupplyadditional$1billioninfundingifcompensatedbyadditional24basis points in spreads. Compared with estimates for the inverse loan supply elasticities in Table 4, dealer demand is significantly less interest rate elastic. Table 8: Net borrowing and lending in the GCF market Dependent variable: Netamount,$billions BorrowedqiC|qiC >0 LentqiC|qiC <0 (1) (2) GCFspreadρC,t −0.028∗∗∗ −0.042∗∗∗ (0.010) (0.007) ((cid:80) k∈Li (cid:80) jℓ∈E ψ˜ ik,jℓ )×ρC,t −0.007∗∗∗ 0.011∗∗∗ (0.002) (0.001) Lendersupply(cid:80) (cid:80) ψ˜ qλ −4.934∗∗∗ 3.087∗∗∗ k∈Li jℓ∈E ik,jℓ ℓ,t (0.282) (0.159) Dealerdemandqδ 0.046∗∗∗ −0.199∗∗∗ i,t (0.008) (0.004) Constant 18.426∗∗∗ −5.783∗∗∗ (0.412) (0.171) Observations 43,566 43,486 LogLikelihood −76,611.180 −102,358.700 ρ −0.428∗∗∗ (0.019) 0.295∗∗∗ (0.015) Note: The data consist of an unbalanced panel of 31 dealers for which we observe EDF 1-year, market value of assets, equity, and book leverage. The GCF spread over the ON RRP rate is expressed in basis points. The supply and demand factors are computed as qλ ≡ (1+λ )×q and qδ ≡ (1+δ )×q . The weights ψ˜ are elements of ℓt ℓt ℓt−1 k,t it it−1 ik,jℓ (cid:16) (cid:17)−1 the matrix Ψ˜ = I + 1W˜ , where W˜ is defined in (14). All quantities are expressed 2 in billions of dollars. Column 1 and 2 estimate regression equation (35) using maximum likelihoodconditioningonadealerbeinganetborroweroranetlenderaccordingtoselection model in Table 7. Significant at ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01. Finally, the empirical specification controls for the effects of dealer demand and the weighted cost of borrowing from the decentralized market and the strategic interactions of dealers in that market. As predicted by the model higher dealer demand increases the amount borrowed in the centrally cleared market, whereas higher supply of funds or lower cost of funds in the decentralized OTC market decreases the amount borrowed. The last row in Table 8 gives the estimate of the correlation ρ between 50

the unobserved determinants of the choice to borrow or lend in the GCF market with the unobserved components of the determinants of the amount borrowed or lent. The statistical significance of the ρ coefficient indicates that the selection into borrowing or lending in the GCF market is non-random. 4.8 Supply shocks and rate spikes in September 2019 The previous sections established that the repo market is characterized by significantly lower dealer demand elasticity as compared to the lender supply elasticity. This implies that the repo market would experience significant increases in spreads over the ON RRP rate, when there are significant reductions in lender supply of cash. Indeed, when we examine the daily decomposition of supply and demand around September 17, 2019 in Figure 12, we can see that the market experienced a large negative supply shock. The supply shock resulted in a 30 percent decline in supply at the median lender and some lenders experienced even larger declines in supplied quantities. At the same time, there was no notable change in aggregate demand with the change in demand at the median dealer hovering around zero. The volume-weighted supply declined by about 22 percent, which represents a reduction of about $160 billion, whereas the volume-weighted demand increased slightly by about 1 percent. Therefore, because of the large supply decline and the steady and inelastic demand, the repo spreads spiked as shown in Figure 10. Based on our estimates of the demand elasticities, we can do a simple back-ofthe-envelope calculation that such a large supply shock could result in a spike in repo spreads far exceeding the actual observed average spike of 315 basis points on September 17, 2019 documented in Table 3. Based on the estimates of the demand elasticity from Table 6, we can project that that repo rates would have increased by more than 14 percentage points, whereas the estimates in Table 8, which account for the selection into borrowing from the GCF market, imply an even larger spike in rates that exceeds 25 percentage points. Those back-of-the-envelope estimates are several orders of magnitude higher than those observed during this period, mainly because they ignore the substitutions dealers do across lenders and the centrally-cleared market as well as other factors that determine the equilibrium repo spread not captured by the model. However, the extrapolation is indicative that the model estimates of the elasticities and movements in supply and demand could match the volatility in repo spreads. Furthermore, as we 51

document next, the magnitudes of declines in supply are consistent with the observed borrowing of dealers from the temporary repo operations by the Federal Reserve. Figure 12: Supply and demand factors around September 19, 2019 egnahc tnecreP 02 0 02− 04− 2019−09−13 2019−09−16 2019−09−17 2019−09−18 2019−09−19 2019−09−20 02 0 02− 04− Demand Supply Note: Theboxplotsrepresenttheinterquartilerangesofthepercentchangesinsupplyand demand across lender and dealers, respectively. The solid black lines are the medians and the interquartile ranges are represented in the colored boxes. The whiskers represent the 5th and 95thpercentilesofthedistribution. Source: FRBNYTri-partyrepoandauthors’calculations. 5 Counterfactual and policy analysis We examine two counterfactuals related to potential and actual policy changes. First, wequantifytheimportanceofthecentrally-clearedmarketfortheavailabilityandcost of dealer funding, holding fixed the connectedness in the decentralized market. This exercise illustrates how the introduction of central clearing in decentralized financial markets could affect those markets. Second, we evaluate the role of the Standing Repo Facility (SRF) for market efficiency. 52

5.1 Welfare and market wiring To be able to conduct policy evaluations, we need to first define welfare. Define market welfare as the sum of the dealer and lender surpluses. The total funding cost of dealers is the sum of individual dealer funding costs (cid:88) V(W) = V (q |W). (36) i Bi i∈D All else equal, a market wiring with lower dealer funding costs is more efficient. Lender surplus is defined as the area under the lenders’ marginal cost curves Z = (r k −c k )2 = γ kq2, where q = (cid:80) q . The sum of all lenders’ surpluses is k 2γ 2 k k ik k i∈D k (cid:88) γ Z(W) = k q2. (37) 2 k k∈L Lender surplus increases with the quantities traded at lenders with higher monopoly power as captured by the interest rate elasticity parameter γ. The total welfare in the market is the sum of the dealer and lender surpluses U(W) = −V(W)+Z(W), (38) where the negative of the total dealer funding costs ensures that lower funding costs increases overall welfare. 5.2 Introduction of a centrally-cleared market We illustrate the main intuition of the analysis through our simple example, introduced in Section 3.8, which we can solve in closed form. The changes in the total dealer funding costs, the lender surplus, and the total market welfare can also be computed in closed form for the case of symmetric wiring as follows 53

βγ(β +2γ) V(C,T sym)−V(∅,T sym) = − (q −q )2 2(3β +2γ)2 B1 B2 β2γ L(C,T sym)−L(∅,T sym) = − (q −q )2 (39) 4(3β +2γ)2 B1 B2 βγ(β +4γ) W(C,T sym)−W(∅,T sym) = (q −q )2 4(3β +2γ)2 B1 B2 The total funding cost differential is always lower when a centrally-cleared market exists. Furthermore,theimprovementsinfundingcostsincreasewiththesquareofthe demand differentials between the two dealers q −q . This is not a very surprising B1 B2 result, becausethecentrallyclearedmarketallowsfortheexcessdemandconditionsof dealerstoberesolvedatamarginalcostthatisequalizedacrossallfundingsourcesfor both dealers. This allows for dealers to better coordinate on their borrowing decisions to achieve lower funding costs. Such improvements in funding costs of dealers are in part at the expense of lender surplus, which decreases in proportion to the square of the demand differentials. The existence of a centrally cleared market effectively reduces the overall market power of lenders. The equalization of marginal cost of funds with the centrally cleared market results in higher strategic substitutability of borrowing of dealers from their common lender. However, the reduction in lender surplus is dominated by the increases in dealer welfare and, as a result, the total market welfare increases. Now examine the situation in which the decentralized market is fully wired as in panel C of Figure 4. Following the steps outlined above, one can similarly solve for the differentials in equilibrium welfare in closed form as follows25 βγ2 V(C,T full)−V(∅,T full) =− (q −q )2 4(3β +γ)2 B1 B2 L(C,T full)−L(∅,T full) =0 (40) βγ2 W(C,T full)−W(∅,T full) = (q −q )2. 4(3β +γ)2 B1 B2 Dealers’ funding costs are lower in the presence of a centrally cleared market. This result is somewhat counter intuitive. To understand how the reduction in funding costs occurs, examine the dealer marginal costs in the fully wired T market. Without the centrally cleared market dealer’s funding costs are equalized across lenders but 25See the appendix for all the derivations. 54

not across dealers. In contrast, with a centrally cleared market, all dealers’ marginal costs are equalized to the equilibrium rate in the centrally cleared market. We can calculate how marginal costs differ between a wiring with and a wiring without a centrally cleared market βγ q −q ρ (C,T full)−ρ (∅,T full) = Bj Bi . C ik 3β +γ 2 Differences in dealer demand q > q result in lower marginal costs for the dealer B1 B2 with higher demand and higher marginal costs for the dealer with the low demand in the presence of a centrally cleared market as compared to a wiring without. This difference is needed to induce dealer d with low demand to borrow an additional 2 amount qB1−qB2 from cash lenders and lend it to the centrally cleared market to meet 2 dealer d with high demand. In equilibrium, lenders provide exactly the same amount 1 of cash, charge the same rates, and receive the same surplus. However, because of the higher substitutability of dealer actions, the overall market welfare is increased by the reduction in dealer funding costs for the dealer with high repo demand. 5.3 Introduction of the Standing Repo Facility In July 2021, the Federal Reserve established the Standing Repo Facility (SRF) as a liquidity backstop in the repo market to support monetary policy implementation. In the context of our model, the SRF introduces an alternative source of funding for the set of dealers, D , who are authorized SRF counterparties. The SRF would S charge a minimum bid spread of ρ over the ON RRP rate rO. Furthermore, the S SRF imposes an individual participant cap q¯S and an aggregate cap q¯¯S. Denote the (cid:8) (cid:9) effective aggregate cap as q˜S ≡ min |D |q¯S,q¯¯S , which is the effectively binding S constraint between the sum of individual caps and the aggregate cap.26 To characterize the usage of the facility, we assume that the equilibrium bid rate of a participating dealer is determined by the equilibrium market clearing rate of the 26There are 37 SRF counterparties as of December 2024 (see FRB NY website). The minimum bid spread is set by the FOMC and is currently set at 25 basis points over the ON RRP rate. The caps are $20 billion and $550 billion for the individual dealer and the aggregate, respectively. The settlement of SRF is integrated with the tri-party repo platform with pre-specified haircuts for Treasuries and Agency MBS. See Ennis and Huther [2021] and FRB NY website for additional institutional details of the Standing Repo Facility. 55

C market, and every participating dealer takes the equilibrium bid rate as given. We follow the convention in the general equilibrium literature (Walrasian taˆtonnement) and how we model the C market.27 Because of the centrally cleared market, dealers faceacommonmarginalfundingcostandtheirequilibriumbiddingratesshouldequal that marginal funding cost ρ . C First, consider the case in which the minimum bid rate exceeds the equilibrium C market funding rate ρ > ρ∗. Then, dealers find it optimal not to borrow from the S C SRF, because it is cheaper to borrow from the C market. Second, consider the case in which ρ∗ exceeds the minimum bid rate, i.e., ρ∗ > ρ . Then, every dealer with access C C S to the SRF will borrow from the SRF as dealers in D make profit from the arbitrage S between the SRF rate and the market rate by borrowing from the SRF and lending in the C market. All dealers in D submit the auction bid ρ . The new equilibrium S S C market rate must equal the equilibrium bid rate, i.e., ρ∗ = ρ . C,S S Denote the SRF borrowing amount of dealer i ∈ D as q . If the total SRF S iS borrowing amount (cid:80) q does not reach its effective cap q˜S with the equilibrium i∈DS iS market rate at the minimum bid rate, then the market rate will stay at the minimum bid rate, i.e. ρ∗ = ρ = ρ . The last equality is again coming from the same mech- C,S S S anism as in Proposition 3, as dealers would equalize their marginal cost of funding from all possible sources. The last case is when the effective cap is binding at the minimum bid rate ρ . In this case, dealers will bid at a new equilibrium C market S rate ρ∗ > ρ . The new market rate ρ∗ is determined by the following market C,S S C,S clearing condition (cid:88) (cid:88) qS(ρ∗ ) = q (ρ∗ )−q˜S = 0, (41) iC C,S iC C,S i∈D i∈D where qS(ρ∗ ) is the net C market demand of dealer i when there is SRF facility. iC C,S The first equality relates the equilibrium with SRF to the equilibrium without SRF. To derive the new equilibrium, one can use the individual net cash demand functions q as the ones in the equilibrium without the SRF and subtract the aggregate iC cash obtained from the SRF. However, under conditions described below high-cost dealer-lender trading relationships become inactive after the introduction of the SRF. 27Wecanprovideaformalmicrofoundationtothisassumptionwithastrategicinteractionthrough a discriminatory ascending auction. 56

Define the set of trading relationships that remain active after the introduction of the SRF as ES ⊆ E. The corresponding matrix Ψ ˜S is then derived for the new set of active trading relationships ES in the same way as in the previous sections. We can derive the aggregate demand for SRF funding as   (cid:88) (cid:88) (cid:88) ψ ˜S (cid:88) (cid:88) ψ ˜S (cid:88) 1 ik,jℓ ik,jℓ q iS (ρ S ) = q¯ B + c ℓ − + ρ S (42) 2γ 2γ β ℓ ℓ i i∈DS ik∈ESjℓ∈ES ik∈ESjℓ∈ES i∈D The next proposition summarizes the equilibrium of the market in the presence of an SRF facility. Proposition 5 Let ρ∗ and ρ∗ be the equilibrium C market rate without and with the C C,S SRF, respectively. When the SRF is introduced, the following statements are true. 1. If ρ∗ ≤ ρ , then no dealer borrows from the SRF, q = 0, for all i ∈ D . C S iS S 2. If ρ∗ > ρ , a trading relationship ik ∈ E becomes inactive in the equilibrium C S with the SRF if and only if ˜ ψ (cid:80) ik,jℓ c jℓ∈E 2γ ℓ ℓ > ρ∗ . (43) ˜ C,S ψ (cid:80) ik,jℓ jℓ∈E 2γ ℓ 3. If ρ∗ > ρ and (cid:80) q (ρ ) ≤ q˜S hold, then ρ∗ = ρ∗ = ρ and dealers borrow C S iS S S C,S S i∈DS (cid:80) from the SRF in the aggregate amount of q (ρ ). iS S i∈DS 4. If ρ∗ > ρ and (cid:80) q (ρ ) > q˜S hold, then the borrowed amount from the SRF C S iS S i∈DS is the cap amount and the new equilibrium rate is ψ ˜S q¯ + (cid:80) (cid:80) ik,jℓ c −q˜S B ik∈ES jℓ∈ES 2γ ℓ ρ∗ = ℓ , (44) C,S ψ ˜S 1 (cid:80) (cid:80) ik,jℓ (cid:80) + ik∈ES jℓ∈ES 2γ i∈D β ℓ i and the equilibrium SRF bid rate is ρ∗ = ρ∗ > ρ . S C,S S 57

The first statement of Proposition 5 implies that the SRF is not used when the C market rate is below the minimum bid rate. The second statement examines which trading relationships in the T market become inactive when dealers borrow from the SRF, which is condition similar to (18) of Lemma 1. The third statement proves that the C market rate stays at the SRF minimum bid rate when the SRF cap is not binding. The fourth statement examines the C market rate when borrowing from the SRF reaches the cap. In this situation, the equilibrium rate exceeds the minimum bid rate. Proposition 5 implies that the SRF lowers the marginal cost of funds in the repo market, as it can be easily shown that (44) in Proposition 5 is lower than (20) in Proposition 1. Therefore, the SRF provides a conditional funding buffer, which mitigates fluctuations of the C market rate due to supply and demand shocks. It is easy to see that the effect of the SRF on the repo market is equivalent to reducing the aggregate dealer demand up to the aggregate cap i.e. we can redefine dealer demand as q¯S = q¯ −q˜S. B B The market clearing condition pins down a unique aggregate demand for the SRF funding. However, individual dealer demand schedules q (ρ ) are not well defined iS S and there is multiplicity of equilibria with respect to the individual dealer borrowing from the SRF. This is because each dealer is indifferent between borrowing from the SRF and borrowing from the centrally-cleared market. Proposition 5 also illustrates a trade-off between the size of the cap on available SRF funding and the level of the minimum bid rate ρ and their impact on the S market. Lower SRF caps or a higher minimum bid rate provide smaller liquidity buffer against supply and demand shocks, limiting the effectiveness of the facility as a liquidity backstop. However, higher SRF caps or lower minimum bid rate reduce the incentives of dealers to maintain relationships with lenders. Moreover, expanded participation in the SRF through higher caps, larger set of counterparties |D | or S lower minimum bid rates could also result in no equilibrium trades in the C market. While this section illustrates how the market equilibrium is affected by the introduction of the SRF, deriving an optimal design of the SRF facility is beyond the scope of this paper. Such analysis requires a substantial extension of our model including examining issues of moral hazard and the cost of funding the SRF facility. We leave such extensions for future research. 58

6 Conclusion We have provided a novel framework to examine the efficiency with which the triparty repo market allocates cash and collateral between lenders and dealers in the decentralized OTC market, and among dealers in the anonymous centrally-cleared GCFmarket. Unlikeexistingliteratureonrepomarkets,weemphasizedtheroleofthe wiring of the two segments of the market and the strategic interaction among dealers resulting from competition in quantities. This allowed us to decompose movements in quantities into supply and demand factors and estimate the supply and demand elasticities. The model allows us to evaluate policy interventions in repo markets and the effects of different wirings for market efficiency. We have evaluated the role of the centrally cleared market for market efficiency as well as the density of connections in the decentralized market. The introduction of a standing repo facility was shown to be equivalent to absorbing some of the dealer demand and we have characterized its impact on the pricing of the centrally cleared market. The model also allows us to examine the necessary conditions for disbalances in supply and demand to result in the use of the standing repo facility. These conditions give policy makers tools to evaluate the capacity of the market to absorb supply and demand shocks before the need for market participants to use the government supplied liquidity backstops. Finally, even though we have assumed the market wiring to be exogenously given, we view our work as a first step in understanding the market in a structural way that opens the possibility to model and characterize the endogenous responses of the market wiring to policy interventions. Incorporating endogenous changes to the wiring of the market would allow for the evaluation of optimal design of liquidity backstops. We leave these extensions of our framework for future research. References Acharya, V. V., V. R. Anshuman, and S. V. Viswanathan (2024): “Bankruptcy Exemption of Repo Markets: Too Much Today for Too Little Tomorrow?,” Working Paper 32027, National Bureau of Economic Research. Afonso, G., M. Cipriani, A. M. Copeland, A. Kovner, G. La Spada, and 59

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“Rewiring repo” Jin-Wook Chang Elizabeth Klee Vladimir Yankov February 13, 2025 Online appendix not intended for publication A Proofs Proof of Proposition 1. The proof of the second case without the C market is based on a variation of ˙ arguments in Rosen [1965] and Bimpikis, Ehsani, and Ilkılı¸c [2019]. The proof of the first case with the C market utilizes the fact that equation (17) is monotonically decreasing in ρ . C Step 1. (Existence of a unique equilibrium for a fixed ρ ) C First, we show that there exists a unique equilibrium quantities for a fixed ρ . The C ˙ proof is based on derivations in Rosen [1965] and Bimpikis, Ehsani, and Ilkılı¸c [2019] applied to a convex n-person game with cost minimization by changing the conditions for concavity to convexity. Therefore, the sufficient condition for the existence of uniqueequilibriumistoshowthateachdealer’sstrategyspaceisconvexandcompact, and each dealer’s objective function (cid:32) (cid:33) (cid:88) (cid:88) β (cid:16) (cid:17)2 i V = ρ q + q × c +γ q + q¯ −q (A.1) i C iC ik k k jk i Bi 2 k∈Li j∈D k isconvexinthedealer’sownstrategy(q ,q )givenotherdealers’strategies(q ,q ) . i iC j jC j̸=i Step 1.1. (Existence of an equilibrium for a fixed ρ ) To prove existence, C we need to show that the Hessian matrix of any dealer i ∈ D is positive semi-definite. The Hessian is defined as the matrix of second-order derivatives of V i   ∂2V ∂2V ∂2V ∂2V i i i i ···  ∂q ∂q ∂q ∂q ∂q ∂q ∂q ∂q   i1 . i1 i1 . i2 . i1 . imi i1 . iC   . . . . .  . . . . .   H i =   ∂2V i ∂2V i ∂2V i ∂2V i   , (A.2)  ···   ∂q ∂q ∂q ∂q ∂q ∂q ∂q ∂q   imi i1 imi i2 imi imi imi iC  ∂2V ∂2V ∂2V ∂2V  i i i i  ··· ∂q ∂q ∂q ∂q ∂q ∂q ∂q ∂q iC i1 iC i2 iC imi iC iC 65

which is a (m +1)×(m +1) matrix, where m ≡ |L | is the number of lenders dealer i i i i i is connected to. Note that the second-order derivatives of V are i  2γ +β if i = j,k = l ̸= C   k i    β if i = j,k = l = C   i ∂2V  i = β if i = j,k ̸= l . (A.3) ∂q ∂q i ik jl    γ if i ̸= j,k = l ̸= C   k    0 otherwise Define a (m +1)×(m +2) full-rank matrix R as i i √  2γ if l = k ̸= C   k √ R = β if l = m +2 , (A.4) ik,l i i    0 otherwise which is  √ √  2γ 0 0 ··· 0 β k i √ √    0 2γ k 0 ··· 0 β i   . . . . . .  R =  . . . . . . . . . . . . , (A.5)    √ √   0 0 ··· 2γ 0 β   k √ i  0 0 ··· 0 0 β i Then, H = RRT, implying H is positive semi-definite. Therefore, according to i i Rosen [1965], there exists an equilibrium. Step 1.2. (Uniqueness of equilibrium for a fixed ρ ) Next, we prove unique- C ness of equilibrium for a fixed ρ . Denote the vector of all quantities by dealers as C q = (cid:0) qT,q ,qT,q ,...,qT,q (cid:1)T , where q = (q ,q ,...,q ) for any i ∈ D and 1 1C 2 2C n nC i ili1 ili2 ilimi l ∈ L for any k = 1,...,m . Theorems 2 and 6 in Rosen [1965] imply that the ik i i (cid:2) (cid:3) equilibrium is unique if the (|E|+n)×(|E|+n) matrix G(q)+G(q)T is positive 66

definite for any q with   ∂2V ∂2V ∂2V ∂2V 1 1 1 1 ···  ∂q ∂q ∂q ∂q ∂q ∂q ∂q ∂q   11 . 11 11 . 12 . 11 . nmn 11 . nC   . . . . .  . . . . .   G(q) =   ∂2V n ∂2V n ∂2V n ∂2V n   . (A.6)  ···   ∂q ∂q ∂q ∂q ∂q ∂q ∂q ∂q   n ∂ m 2 n V 11 n ∂ m 2 n V 12 nm ∂ n 2V nmn n ∂ m 2 n V nC   n n n n  ··· ∂q ∂q ∂q ∂q ∂q ∂q ∂q ∂q nC 11 nC 12 nC nmn nC nC Again, we are applying the theorems in Rosen [1965] to the cost minimization problem, so the signs are reversed.28 We take the fixed vector r to be a vector of 1s for the G(x,r) in the original theorems of Rosen [1965]. (cid:2) (cid:3) The matrix can be represented as 2Γ ≡ G(q)+G(q)T , where  2γ +β if i = j,k = l ̸= C   k i    β if i = j,k = l = C   i  Γ = β if i = j,k ̸= l . (A.7) ik,jl i    γ if i ̸= j,k = l ̸= C   k    0 otherwise Then, it is sufficient to show that there exists R with full rank of |E|+n such that Γ = RRT. We find the matrix R as a (|E|+n)×(|E|+2n+m) matrix, which can be arranged as a block matrix of R = [A, B], (A.8) where A is a (|E|+n)×(|E|+n) diagonal matrix such that √  γ if i = j,k = l ̸= C   k √ A = β if i = j,k = l = C , (A.9) ik,jl i    0 otherwise 28Instead of the sufficient condition for uniqueness of payoff maximization games, diagonal strict concavity, we use diagonal strict convexity to show uniqueness of equilibrium for the cost minimization game. 67

and B is a (|E|+n)×(n+m) matrix such that √  γ if t = n+k,k ̸= C   k √ B = β if t = i,k ̸= C . (A.10) ik,t i    0 otherwise Because A is a diagonal matrix with non-zero entries, R is full rank, and Γ is positive (cid:2) (cid:3) definite, implying G(q)+G(q)T is positive definite. Therefore, the equilibrium is unique for a fixed ρ . C Step 2. (Uniqueness of the market clearing price ρ ) Finally, we show C that the market clearing price ρ with resulting equilibrium quantities q that satisfies C the market clearing condition (17) is unique. The first-order condition (6) can be represented in a matrix equation 1 q˜ = ϕ ˜ (ρ )− Wq˜, (A.11) C 2 where q˜ = (q ,...q ,q ,...,q )T, ϕ ˜ is a |E|×1 vector such that 11 1m1 21 nmn ρ −c ˜ C k ϕ (ρ ) = , (A.12) ik C 2γ k and W is a |E|×|E| matrix such that  1 if i ̸= j,k = l W = (A.13) ik,jl 0 otherwise. Thus, the equilibrium quantities in T market in (A.11) can be rearranged as (cid:18) (cid:19) 1 I + W q˜ = ϕ ˜ (ρ ). (A.14) C 2 The left-hand side of (A.14) is a linear function of q˜, which is strictly increasing in q˜. Also, the right-hand side of (A.14) is a linear function of ρ , which is also strictly C increasing in ρ for γ > 0,∀k ∈ L. Hence, in equilibrium, the quantities funded C k in the T market are strictly and continuously increasing in ρ . From (5), we can C (cid:80) also easily see that for β > 0,∀i ∈ D, the excess net demand q (ρ ) in the i i∈D iC C interdealer market is a strictly decreasing continuous function in ρ . Therefore, the C 68

aggregate market clearing condition has a unique solution ρ∗ such that C (cid:88) (cid:88) (cid:88)(cid:88) (cid:88) 1 q (ρ∗) = q − q (ρ∗)− ρ∗ = 0. (A.15) iC C Bi ik C β C i i∈D i∈D i∈D k∈Li i∈D Step 3. (Closed-form representations of the equilibrium) The market clearing condition is linear in ρ and we can solve for the equilibrium ρ∗ in a closed- C C form as follows (cid:80) (cid:80) (cid:80) ψ˜ q + ik,jℓc Bi 2γ ℓ ℓ ρ∗ = i∈D ik∈Ejℓ∈E (A.16) C (cid:80) (cid:80) ψ˜ ik,jℓ + (cid:80) 1 2γ ℓ βi ik∈Ejℓ∈E i∈D ˜ (cid:88) ψ q∗ = ik,jℓ (ρ∗ −c ), ∀ik ∈ E. (A.17) ik 2γ C ℓ ℓ jℓ∈E Plugging the expression for ρ∗, in (5), we obtain C (cid:32) (cid:33) ˜ ˜ (cid:88) (cid:88) ψ (cid:88) (cid:88) ψ 1 q∗ = q + ak,jℓ c − ak,jℓ + ρ∗, ∀a ∈ D, (A.18) aC Ba 2γ ℓ 2γ β C ℓ ℓ a k∈Lajℓ∈E k∈Lajℓ∈E Finally, it is easy to verify that under the condition for Lemma 1, all equilibrium quantities q∗ are positive ∀ik ∈ E. ik Proof of Lemma 1. From (A.17), we can derive the following condition for 69

positivity of equilibrium quantities along any dealer-lender pair ab ∈ E   (cid:80) q + (cid:80) (cid:80) ψ˜ ik,i′k′c (cid:88) i∈D Bi ik∈Ei′k′∈E 2γ k′ k′  ψ ˜ ab,jℓ  −c  > 0  (cid:80) 1 + (cid:80) (cid:80) ψ˜ ik,i′k′ ℓ  2γ ℓ jℓ∈E i∈D βi ik∈Ei′k′∈E 2γ k′   (cid:80) q + (cid:80) (cid:80) ψ˜ ik,i′k′c (cid:88) i∈D Bi ik∈Ei′k′∈E 2γ k′ k′  ψ ˜ ab,jℓ (cid:88) ψ ˜ ab,jℓ   > c  (cid:80) 1 + (cid:80) (cid:80) ψ˜ ik,i′k′  2γ ℓ 2γ ℓ ℓ jℓ∈E jℓ∈E i∈D βi ik∈Ei′k′∈E 2γ k′ (cid:80) q + (cid:80) (cid:80) ψ˜ ik,i′k′c i∈D Bi ik∈Ei′k′∈E 2γ k′ k′ (cid:88) ψ ˜ ab,jℓ (cid:88) ψ ˜ ab,jℓ > c (cid:80) 1 + (cid:80) (cid:80) ψ˜ ik,i′k′ 2γ ℓ 2γ ℓ ℓ jℓ∈E jℓ∈E i∈D βi ik∈Ei′k′∈E 2γ k′ (cid:124) (cid:123)(cid:122) (cid:125) ρ∗ C Finally, rearranging the term on the left-hand side to equal the equilibrium C market rate ρ∗, we arrive at the following condition C (cid:80) ψ˜ ab,jℓc 2γ ℓ ℓ ρ∗ > jℓ∈E , (A.19) C (cid:80) ψ˜ ab,jℓ 2γ ℓ jℓ∈E The inequality (A.19) is the sufficient and necessary condition for q∗ > 0 for all ab dealer-lender pairs ab ∈ E. Proof of Corollary 1. Plugging in (20) into (19) results in ˜ ψ 1 (cid:80) (cid:80) ik,jℓ + (cid:32) (cid:33) q∗ =q + (cid:88) (cid:88) ψ ˜ ik,jℓ c − k∈Lijℓ∈E γ ℓ β i (cid:88) q + (cid:88) (cid:88) (cid:88) ψ ˜ ab,jℓ c . iC Bi γ ℓ ψ ˜ 1 Ba γ ℓ k∈Lijℓ∈E ℓ (cid:80) (cid:80) ab,jℓ + (cid:80) a∈D a∈Db∈Dajℓ∈E ℓ γ β ab∈Ejℓ∈E ℓ a∈D a 70

The absolute value of the equilibrium quantities for dealer i ∈ D can be written as (cid:12) ˜ ˜  (cid:12) (cid:12) (cid:80) (cid:80) ψ ik,jℓ (cid:80) (cid:80) (cid:80) (cid:80) ψ ab,jℓ (cid:12) |q∗ | = (cid:12) (cid:12) (cid:12)   q Bi + k∈Lijℓ∈E γ ℓ c ℓ − a∈D q Ba + a∈Db∈Dajℓ∈E γ ℓ c ℓ   (cid:32) (cid:88) (cid:88) ψ ˜ ik,jℓ + 1 (cid:33)(cid:12) (cid:12) (cid:12). iC (cid:12) (cid:12) (cid:12)   (cid:80) (cid:80) ψ ˜ ik,jℓ + 1 (cid:80) (cid:80) ψ ˜ ab,jℓ + (cid:80) 1   k∈Lijℓ∈E γ ℓ β i (cid:12) (cid:12) (cid:12) (cid:12) γ β γ β (cid:12) k∈Lijℓ∈E ℓ i ab∈Ejℓ∈E ℓ a∈D a Hence, the gross volume of trades in the C market, (cid:80) |q∗ |, is increasing in (24). iC i∈D Proof of Corollary 2. From (19), the coefficient of ρ∗ for (cid:80) q∗ is (cid:80) (cid:80) ψ˜ ik,jℓ C ik 2γ ℓ ik∈E ik∈Ejℓ∈E , while the coefficient of ρ∗ for − (cid:80) q∗ is (cid:80) (cid:80) ψ˜ ik,jℓ + (cid:80) 1 . Because (cid:80) 1 is C iC 2γ ℓ βi βi i∈D ik∈Ejℓ∈E i∈D i∈D always positive, (cid:18) (cid:19) ∂ (cid:80) q∗ ik (cid:88) (cid:88) ψ ˜ ik∈E ik,jℓ = ∂ρ∗ 2γ C ik∈Ejℓ∈E ℓ (cid:18) (cid:19) ∂ (cid:80) q∗ iC (cid:88) (cid:88) ψ ˜ (cid:88) 1 i∈D ik,jℓ < − = + . ∂ρ∗ 2γ β C ik∈Ejℓ∈E ℓ i∈D i Hence, the interest rate sensitivity of the aggregate borrowing from T market is lower than the interest rate sensitivity of the aggregate borrowing from C market. Proof of Proposition 2. 1. With a C market, individual dealer demand shocks affect the equilibrium quantities through their indirect effects on the equilibrium rate ρ∗, and lender supply C shocks affect equilibrium quantities both through their direct effects and their indirect effects on the equilibrium rate ρ∗. The partial derivatives of the equi- C 71

librium rate with respect to demand shocks and supply shocks are ∂ρ∗ 1 C = , ∀h ∈ D (A.20) ∂q Bh (cid:80) (cid:80) ψ˜ ik,jℓ + (cid:80) 1 2γ ℓ βi ik∈Ejℓ∈E i∈D (cid:80) (cid:80) ψ˜ ik,hz ∂ρ∗ 2γz C = ik∈Eh∈Dz , ∀z ∈ L. (A.21) ∂c z (cid:80) (cid:80) ψ˜ ik,jℓ + (cid:80) 1 2γ ℓ βi ik∈Ejℓ∈E i∈D (A.22) From (19), the partial derivative with respect to q for any h ∈ D is Bh ˜ ψ (cid:80) ik,jℓ ∂q∗ (cid:88) ψ ˜ ∂ρ∗ jℓ∈E 2γ ik = ik,jℓ C = ℓ , ∀ik ∈ E. (A.23) ∂q Bh 2γ ℓ ∂q Bh (cid:80) (cid:80) ψ˜ ik,jℓ + (cid:80) 1 jℓ∈E 2γ ℓ βi ik∈Ejℓ∈E i∈D Finally, the partial derivative with respect to a shock to any lender z ∈ L and plugging in the partial derivative of ρ∗ is C ∂q∗ ∂ρ∗ (cid:88) ψ ˜ (cid:88) ψ ˜ ik = C ik,jℓ − ik,jz (A.24) ∂c ∂c 2γ 2γ z z ℓ z jℓ∈E j∈Dz (cid:80) (cid:80) ψ˜ ab,jz = j∈Dzab∈E 2γz (cid:88) ψ ˜ ik,jℓ − (cid:88) ψ ˜ ik,jz , ∀ik ∈ E. (A.25) (cid:80) (cid:80) ψ˜ ab,jℓ + (cid:80) 1 2γ ℓ 2γ z 2γ ℓ βj jℓ∈E j∈Dz ab∈Ejℓ∈E j∈D 2. The partial derivatives of the equilibrium quantities (21), result in the following sensitivity of quantities along any dealer-lender trading relationship jl and shocks to any dealer i or lender k ∂q∗ (cid:88) β jℓ i = ψ ∀i ∈ D, jℓ,iz ∂q 2γ +β Bi z i z∈Li (A.26) ∂q∗ (cid:88) 1 jℓ = − ψ ∀k ∈ L, jℓ,dk ∂c 2γ +β k k d d∈D k 72

Proof of Proposition 3. 1. Marginal costs: We defined marginal costs of funds of borrowing of any dealerlender trading pair ik as ∂q (c +γ (cid:80) q )(cid:12) ρ∗ ≡ ik k k j∈D k jk (cid:12) (cid:12) = s∗ +γ q∗ , (A.27) ik ∂q (cid:12) k k ik ik q∗ (a) With a C market, equation (5) results in (cid:32) (cid:33) (cid:88) 1 (cid:88) ρ∗ = −β q − q∗ − ρ∗ + q∗ −q = ρ∗ ik i Bi il β C il Bi C i l∈Li l∈Li foranyi ∈ D andk ∈ L . Therefore,alldealersborrowfromcounterparties i in the decentralized market so that to equalize their marginal costs to ρ∗. C (b) Without a C market, the marginal cost (A.27) becomes (cid:32) (cid:33) (cid:88) ρ∗ = β q − q∗ , i i Bi il l∈Li where ρ∗ = ρ∗ for all k ∈ L comes directly from the optimality condition i ik i across all q∗ . Plugging (21) into the above equation implies ik (cid:32) (cid:33) (cid:88) (cid:88) β q −c ρ∗ = β q − ψ j Bj ℓ . i i Bi ik,jℓ 2γ +β ℓ j k∈Lijℓ∈E Thus, the marginal cost of funding for dealer i depends on the interconnectedness of dealer i through Ψ and may differ from ρ∗ for j ̸= i even if j all the parameters are homogeneous as β = β and q = q , ∀i ∈ D, and i Bi B γ = γ,c = c, ∀ℓ ∈ L. The only case that ρ∗ = ρ∗ for all i ∈ D is when ℓ ℓ i (cid:88) (cid:88) ¯ ψ = ψ ik,jℓ k∈Lijℓ∈E for all i ∈ D. 2. Lender spreads: (a) If there is a C market, dealers have homogeneous marginal cost of funding 73

as shown in the first part of the proposition. Recall that the equilibrium rate (spread) of borrowing from lender k is (cid:88) s∗ = c +γ q∗ , (A.28) k k k ik i∈D k and the equilibrium marginal cost of funding of dealer i for borrowing from lender k is ρ∗ = ρ∗ = s∗ +γ q∗ (A.29) C ik k k ik for any i ∈ D . Thus, in equilibrium, q∗ = q∗ for any i,j ∈ D . Thus, k ik jk k using this property and (A.28), (A.29) can be expressed as ρ∗ = c +γ (n +1)q∗ , (A.30) C k k k ik where n = |D | and i ∈ D . Rearranging (A.30) yields k k k ρ∗ −c q∗ = C k , (A.31) ik γ (n +1) k k and plugging this expression in (A.28) results in 1 n s∗ = c + k ρ∗. (A.32) k n +1 k n +1 C k k Thus, differences in rates across lenders do not depend on individual dealer demand conditions or interest rate sensitivity (β ,q ) . Furthermore, i Bi i∈D the wiring of the T market affects equilibrium rates only through the number of trading counterparties of lender k ∈ L i.e. n = |D |. k k Now consider the case without a C market. Plugging (21) into (A.28) results in (cid:88) (cid:88) β q −c s∗ = c +γ ψ j Bj ℓ , k k k ik,jℓ 2γ +β ℓ j i∈D kjℓ∈E for any k ∈ L. Hence, all dealer parameters (β ,q ) and lender pai Bi i∈D rameters (c ,γ ) as well as individual entries in the Ψ matrix affect the k k k∈L equilibrium rates and rate dispersion. 74

Proof of Proposition 4. Using the derivations of Proposition 2, we can write the change in equilibrium quantities following changes in demand and supply as follows ∂q∗ ∂q∗ (cid:88) ∂q∗ (cid:88) ∂q∗ dq∗ = ikdq + ikdc + ikdq + ikdc , ik ∂q Bi ∂c k ∂q Bj ∂c k′ Bi k Bj k′ j∈D k′∈L j̸=i k′̸=k wheredxdenotesaninfinitesimalchangeinthevariablexbetweentwoperiods. Next, ˜ define the percent changes in quantity demanded by dealer i as δ ≡ dq and the it Bi changes in quantity supplied by lender k as λ ˜ ≡ 1 dc , where 1 converts the change kt γ k γ k k in the lender spreads to changes in quantities supplied. We can approximate the total change in the quantity traded between period t and t−1 as follows ∆q = ϕδ(γ,β)δ ˜ +ϕλ(γ,β)λ ˜ +ϵ˜ , (A.33) ikt i it k kt ikt where ϕδ(γ,β) and ϕλ(γ,β) are dealer and lender specific constants that are functions i k of the supply and demand elasticities as shown in Proposition 2. To disentangle the dealer specific variation from the lender specific variation, we need additive separability of the marginal demand effects, which comes from (25) in Proposition 2. In other words, the constants can be written as ϕδ(γ,β) = ϕδ +ϕδ and ϕλ(γ,β) = ϕλ +ϕλ . i i ik k k ik We can redefine the dealer specific variation in quantities as δ = ϕδδ ˜ and the i,t i i,t lender specific variation in quantities as λ = ϕλλ ˜ . The error term ϵ contains k,t k k,t ikt remaining variation that is dealer-lender specific . Next, notethatEϵ = 0shouldhold, astheseareanyerrorsthatarenotcaptured ikt by the fundamental changes in the parameters. This allows us to express the changes in quantities at the dealer and lender level as follows (cid:88) ∆q =δ + ϕ λ , ∀i ∈ D, i,t i,t il,t−1 ℓ,t ℓ∈Li,t−1 (A.34) (cid:88) ∆q =λ + θ δ ∀k ∈ L, k,t k,t kj,t−1 j,t j∈D k,t−1 q where we define ϕ = ik,t−1 , the share of dealer i borrowing from lender ik,t−1 (cid:80) q l∈Li il,t−1 k across all lender counterparties L at time t − 1. Similarly, we define θ = i ki,t−1 q ik,t−1 as the share of lender k lending to dealer i across all dealer counterparties (cid:80) q j∈Dk jk,t−1 75

D at time t−1. The system of equations contains n+m unknowns and the rank k of the system is n+m−2. Therefore, the supply and demand factors are identified up to a scalar. We follow Amiti and Weinstein [2018] and normalize all the equations with a randomly selected reference entity and then re-normalize the factors with the median entity to eliminate the influence of the reference entity. Proof of Proposition 5. (cid:8) (cid:9) Recall that the effective SRF cap is q˜S ≡ min |D |q¯S,q¯¯S . S Step 1. (Dealer’s optimization problem) Dealers will take the equilibrium C market rate and SRF bid rate as given, i.e. ρ and ρ are macro variables. C S For each dealer i ∈ D , the dealers’ cost minimization problem in the presence of S the SRF facility is (cid:32) (cid:33) (cid:32) (cid:33)2 (cid:88) (cid:88) β (cid:88) i min ρ q +ρ q + q c +γ q + q +q + q −q C iC S iS ik k k jk iC iS ik Bi qiC,qiS, 2 {q ik } k∈Li k∈Li j∈D k k∈Li s.t. q ≤ q¯S iS q ≥ 0 iS q ≥ 0, ∀k ∈ L , ik i (A.35) where the first constraint is the individual SRF cap, the second constraint is the non-negativity for the SRF borrowing amount, and the third constraint is the nonnegativity for T market borrowing amounts. The first-order conditions are (cid:32) (cid:33) (cid:88) ρ +β q +q + q −q = 0 (A.36) C i iC iS ik Bi k∈Li (cid:32) (cid:33) (cid:88) ¯ ρ +β q +q + q −q +ξ −ξ = 0 (A.37) S i iC iS ik Bi k∈Li (cid:32) (cid:33) (cid:88) (cid:88) c +γ q +q +β q +q + q −q = 0 ∀k ∈ L , (A.38) k k jk ik i iC iS ik Bi i j∈D k k∈Li ¯ where ξ and ξ denote the Lagrangian multipliers for the individual cap constraint and the non-negativity constraint for q , respectively. iS Step 2. (Equilibrium quantities for given rates) 76

Case 1. Suppose that ρ < ρ . Then, the individual cap constraint (upper C S ¯ bound) cannot be binding, because otherwise ξ > 0 due to the complementarity slackness condition of ξ ¯ (q¯S − q ) = 0 (and automatically ξ = 0, as q > 0), and iS iS it would make the left-hand side of (A.37) strictly greater than the left-hand side of (A.36). If q > 0, then (A.36) and (A.37) imply iS ρ = ρ , C S which contradicts the initial assumption ρ < ρ . Therefore, the optimal decision C S should be q = 0 with ξ > 0 to make both (A.36) and (A.37) hold. Then, with iS q = 0 for all i ∈ D , the equilibrium quantities will be the same as the equilibrium iS S quantities without the SRF. Therefore, the equilibrium rate will be ρ∗ in this case. C The initial assumption of ρ < ρ is satisfied only if the C market rate is lower than C S the lowest possible bid rate, which is the minimum bid rate. Hence, if ρ∗ < ρ , then C S q = 0 for all i ∈ D . iS S Case 2. Suppose that ρ > ρ . Then, (A.36) and (A.37) imply that the upper C S bound for the SRF borrowing amount is binding with q = q¯S and ξ ¯ > 0. This iS implies that the SRF participating dealers have incentives to bid a higher rate and still willing to reach the upper bound, i.e. excess demand. Therefore, competition for funds with the given C market rate will increase the market clearing bid rate ρ S until it reaches indifference between borrowing from the SRF and the C market at ρ = ρ . Hence, there is no equilibrium in this case of ρ < ρ . S C S C Case 3. Suppose that ρ = ρ . Then, (A.36) and (A.37) imply that dealer i is C S indifferent between any combination of q and q with a fixed q +q that satisfies iC iS iC iS the first-order condition subject to quantity constraints. Rearranging (A.36) and (A.37) implies (cid:88) ρ C q = q − q −q − (A.39) iC Bi ik iS β i k∈Li (cid:88) ρ C q = q − q −q − , (A.40) iS Bi ik iC β i k∈Li and combining (A.39) with (A.38) results in ρ −c 1 (cid:88) q∗ = C k − q , (A.41) ik 2γ 2 jk k j∈D ,j̸=i k 77

which is exactly the same as the second case of (6). Also, for each dealer i ∈/ D , S the optimal quantities {q } and q are the same as in the case. Therefore, the ik k∈Li iC equilibrium T market quantities for fixed ρ = ρ are the same as in Proposition 1: C S ˜ (cid:88) ψ q∗ = ik,jℓ (ρ −c ) (A.42) ik 2γ C ℓ ℓ jℓ∈E  (cid:32) (cid:33) ˜ ˜   q + (cid:80) (cid:80) ψ ik,jℓ c − (cid:80) (cid:80) ψ ik,jℓ + 1 ρ if i ∈/ D   Bi k∈Li jℓ∈E 2γ ℓ k∈Li jℓ∈E 2γ β C S qS∗ = ℓ (cid:32) ℓ i (cid:33) iC ˜ ˜   q + (cid:80) (cid:80) ψ ik,jℓ c − (cid:80) (cid:80) ψ ik,jℓ + 1 ρ −q if i ∈ D .   Bi k∈Li jℓ∈E 2γ ℓ k∈Li jℓ∈E 2γ β C iS S ℓ ℓ i (A.43) The C market clearing condition is (cid:32) (cid:33) ˜ ˜ (cid:88) qS∗ = q¯ + (cid:88) (cid:88) ψ ik,jℓ c − (cid:88) (cid:88) ψ ik,jℓ + (cid:88) 1 ρ − (cid:88) q = 0. iC B 2γ ℓ 2γ β C iS ℓ ℓ i i∈D ik∈Ejℓ∈E ik∈Ejℓ∈E i∈D i∈DS (A.44) Hence, the market clearing rate with the SRF, ρ∗ is C,S ˜ ψ (cid:80) (cid:80) ik,jℓ (cid:80) q¯ + c − q B ik∈E jℓ∈E 2γ ℓ i∈DS iS ρ∗ = ℓ , (A.45) C,S ˜ ψ 1 (cid:80) (cid:80) ik,jℓ (cid:80) + ik∈E jℓ∈E 2γ i∈D β ℓ i and ρ∗ = ρ∗ by the initial assumption of this case. Then, for the fixed ρ∗, the S C,S S (cid:80) aggregate amount of the SRF borrowing, q is uniquely determined by (A.45) i∈DS iS as (cid:32) (cid:33) ˜ ˜ (cid:88) (cid:88) (cid:88) ψ (cid:88) (cid:88) ψ (cid:88) 1 q = q¯ + ik,jℓ c − ik,jℓ + ρ∗. (A.46) iS B 2γ ℓ 2γ β S ℓ ℓ i i∈DS ik∈Ejℓ∈E ik∈Ejℓ∈E i∈D Step 3. (Determination of the market clearing rates) The final step is to pin down the market clearing rates for C market and the SRF auction. Case 1. Suppose that ρ∗ ≤ ρ . Then, the equilibrium bid rate is bounded below C S by the minimum bid rate spread, ρ∗ ≥ ρ , and the equilibrium is in the situation of S S Case 1 in Step 2. Therefore, the equilibrium SRF amount is q = 0 for any i ∈ D , iS S 78

and the equilibrium rate is the same as in the equilibrium without the SRF ρ∗ = ρ∗ C,S C and the equilibrium quantities are the same as in the equilibrium without the SRF as well. Case 2. Suppose that ρ∗ > ρ . Then, the C market rate without the SRF C S exceeds the minimum SRF bid rate spread, so there will be positive demand for the SRF borrowing—i.e. q > 0 for some i ∈ D . Since Case 2 of Step 2 is not possible, iS S it should be Case 3 in Step 2 with ρ∗ = ρ∗. Then, the equilibrium aggregate SRF C,S S borrowing amount is determined by (A.46). Case 2.1. Suppose that for all the active links without the SRF, ∀ab ∈ E, the following condition holds ˜ ˜ ψ ψ (cid:80) ab,jℓ c q¯ + (cid:80) (cid:80) ik,jℓ c −min (cid:8) |D |q¯S,q¯¯S (cid:9) jℓ∈E 2γ ℓ B ik∈E jℓ∈E 2γ ℓ S ℓ < ℓ . (A.47) ˜ ˜ ψ ψ 1 (cid:80) ab,jℓ (cid:80) (cid:80) ik,jℓ (cid:80) + jℓ∈E 2γ ik∈E jℓ∈E 2γ i∈D β ℓ ℓ i The condition (A.47) implies that all the equilibrium quantities are positive—i.e., q∗ > 0 for all ab ∈ E—even when dealers borrow from the SRF as much as possible.29 ab Case 2.1.1. Suppose that (cid:32) (cid:33) ˜ ˜ (cid:88) (cid:88) (cid:88) ψ (cid:88) (cid:88) ψ (cid:88) 1 ik,jℓ ik,jℓ q =q¯ + c − + ρ (A.48) iS B ℓ S 2γ 2γ β ℓ ℓ i i∈DS ik∈Ejℓ∈E ik∈Ejℓ∈E i∈D (cid:8) (cid:9) ≤min |D |q¯S,q¯¯S , (A.49) S which implies the equilibrium aggregate SRF amount is below the minimum between the sum of individual caps or the aggregate cap even when the dealers bid the minimum bid rate spread. Then, by (A.44) and (A.45), the equilibrium C market rate is ρ∗ = ρ = ρ∗, and the equilibrium aggregate SRF amount is (A.48). C,S S S Case 2.1.2. Suppose that (cid:32) (cid:33) ˜ ˜ (cid:88) (cid:88) (cid:88) ψ (cid:88) (cid:88) ψ (cid:88) 1 ik,jℓ ik,jℓ q =q¯ + c − + ρ iS B ℓ S 2γ 2γ β ℓ ℓ i i∈DS ik∈Ejℓ∈E ik∈Ejℓ∈E i∈D (cid:8) (cid:9) >min |D |q¯S,q¯¯S , (A.50) S 29This condition corresponds to the condition for Lemma 1 that makes all links to be active for the market equilibrium without the SRF. 79

which implies that the equilibrium aggregate SRF amount will reach its upper bound if the SRF participants bid the minimum bid rate spread. In other words, dealers’ marginal cost of borrowing from other sources are greater than the minimum bid rate ρ . Then, by the same logic as in Case 2 of Step 2, the equilibrium SRF bid rate S should increase to match the C market rate, i.e. ρ = ρ , and the SRF participants S C,S will borrow from the SRF up to the aggregate upper bound—the minimum between the sum of individual caps or the aggregate cap. Then, the equilibrium C market rate is determined by (A.45) as ˜ ψ q¯ + (cid:80) (cid:80) ik,jℓ c −min (cid:8) |D |q¯S,q¯¯S (cid:9) B ik∈E jℓ∈E 2γ ℓ S ρ∗ = ℓ , (A.51) C,S ˜ ψ 1 (cid:80) (cid:80) ik,jℓ (cid:80) + ik∈E jℓ∈E 2γ i∈D β ℓ i the equilibrium SRF bid rate is ρ∗ = ρ∗ , and the equilibrium aggregate SRF bor- S C,S rowing amount is (cid:80) q∗ = min (cid:8) |D |q¯S,q¯¯S (cid:9) . i∈DS iS S Case 2.2. Finally, suppose that for there exists a link ab ∈ E, which is active without the SRF but inactive in the equilibrium with the SRF as ˜ ˜ ψ ψ (cid:80) ab,jℓ c q¯ + (cid:80) (cid:80) ik,jℓ c − (cid:80) q∗ jℓ∈E 2γ ℓ B ik∈E jℓ∈E 2γ ℓ i∈DS iS ℓ > ℓ , (A.52) ˜ ˜ ψ ψ 1 (cid:80) ab,jℓ (cid:80) (cid:80) ik,jℓ (cid:80) + jℓ∈E 2γ ik∈E jℓ∈E 2γ i∈D β ℓ ℓ i where the equilibrium SRF quantities are determined below. Under this case, we can redefine the set of active edges with the SRF as ES ⊂ E, and the corresponding ψ ˜S, (cid:18) (cid:19) 1 which is the inverse of I + W ˜ S , where W ˜ S is defined by 14 for ES instead of E. 2 Case 2.2.1.   (cid:88) (cid:88) (cid:88) ψ ˜S (cid:88) (cid:88) ψ ˜S (cid:88) 1 ik,jℓ ik,jℓ q iS =q¯ B + c ℓ − + ρ S (A.53) 2γ 2γ β ℓ ℓ i i∈DS ik∈ESjℓ∈ES ik∈ESjℓ∈ES i∈D (cid:8) (cid:9) ≤min |D |q¯S,q¯¯S , (A.54) S then, this case is similar to Case 2.1.1. Therefore, the equilibrium C market rate is ρ∗ = ρ = ρ∗, and the equilibrium aggregate SRF amount is (A.53). C,S S S This will be an equilibrium, only if, for any ab ∈ E such that ab ∈/ ES, the 80

following condition holds ψ ˜ ψ ˜  ψ ˜S  ψ ˜S 1   j (cid:80) ℓ∈E 2 a γ b, ℓ jℓ c ℓ q¯B+ ik (cid:80) ∈Ejℓ (cid:80) ∈E 2 ik γ , ℓ jℓ c ℓ −  q¯B+ ik∈ (cid:80) ESjℓ∈ (cid:80) ES 2 ik γ , ℓ jℓ c ℓ −  ik∈ (cid:80) ESjℓ∈ (cid:80) ES 2 ik γ , ℓ jℓ +(cid:80) i∈D β i   ρS   > , ˜ ˜ ψ ψ 1 (cid:80) ab,jℓ (cid:80) (cid:80) ik,jℓ (cid:80) + 2γ ik∈E jℓ∈E 2γ i∈D β jℓ∈E ℓ ℓ i ψ ˜  ψ ˜S  ψ ˜S 1   ik,jℓ ik,jℓ ik,jℓ (cid:80) (cid:80) 2γ c ℓ −  (cid:80) (cid:80) 2γ c ℓ −  (cid:80) (cid:80) 2γ +(cid:80) i∈D β   ρS   ik∈Ejℓ∈E ℓ ik∈ESjℓ∈ES ℓ ik∈ESjℓ∈ES ℓ i = , ˜ ψ 1 (cid:80) (cid:80) ik,jℓ (cid:80) + ik∈E jℓ∈E 2γ i∈D β ℓ i (A.55) whichimpliesthelinkbecominginactiveaftertheequilibriumSRFborrowingamount lowers the equilibrium marginal cost of funds. Case 2.2.2. Suppose that   (cid:88) (cid:88) (cid:88) ψ ˜S (cid:88) (cid:88) ψ ˜S (cid:88) 1 ik,jℓ ik,jℓ q iS =q¯ B + c ℓ − + ρ S 2γ 2γ β ℓ ℓ i i∈DS ik∈ESjℓ∈ES ik∈ESjℓ∈ES i∈D (cid:8) (cid:9) >min |D |q¯S,q¯¯S , (A.56) S which implies that the equilibrium aggregate SRF amount will reach its upper bound if the SRF participants bid the minimum bid rate spread. As in Case 2.1.2, the equilibrium C market rate is ψ ˜S q¯ + (cid:80) (cid:80) ik,jℓ c −min (cid:8) |D |q¯S,q¯¯S (cid:9) B ik∈ES jℓ∈ES 2γ ℓ S ρ∗ = ℓ , (A.57) C,S ψ ˜S 1 (cid:80) (cid:80) ik,jℓ (cid:80) + ik∈ES jℓ∈ES 2γ i∈D β ℓ i the equilibrium SRF bid rate is ρ∗ = ρ∗ , and the equilibrium aggregate SRF bor- S C,S rowing amount is (cid:80) q∗ = min (cid:8) |D |q¯S,q¯¯S (cid:9) . i∈DS iS S This will be an equilibrium, only if, for any ik ∈ E such that ik ∈/ ES, the 81

following condition holds ˜ ˜ ψ ψ (cid:80) ik,jℓ c q¯ + (cid:80) (cid:80) i′k′,jℓ c −min (cid:8) |D |q¯S,q¯¯S (cid:9) jℓ∈E 2γ ℓ B i′k′∈E jℓ∈E 2γ ℓ S ℓ > ℓ . (A.58) ˜ ˜ ψ ψ 1 (cid:80) ik,jℓ (cid:80) (cid:80) i′k′,jℓ (cid:80) + jℓ∈E 2γ i′k′∈E jℓ∈E 2γ i∈D β ℓ ℓ i B Derivations of the simple example Here we detail the algebra needed to to solve the simple example in section 3.8 for different wirings of the repo market illustrated in Figures 4 and 5. B.1 Symmetric but incomplete wiring StartingwiththewiringinpanelAofFigure4,thefirst-orderconditionsforquantities borrowed in the decentralized market are: 1 q (ρ ) = (ρ −c) 11 C C 2γ 1 1 q (ρ ) = (ρ −c)− q 12 C C 22 2γ 2 1 1 q (ρ ) = (ρ −c)− q 22 C C 12 2γ 2 1 q (ρ ) = (ρ −c). 23 C C 2γ Given these first order conditions, the equilibrium quantities borrowed from the decentralized market along each dealer-lender pair are q = q = 1 (ρ − c) and 11 23 2γ C q = q = 1 (ρ −c). It is easy to verify that for any ρ > c each dealer borrows less 12 22 3γ C C from their common lender ℓ than their exclusive lenders ℓ and ℓ ; that is, q > q 2 1 3 11 12 and q > q . We briefly provide intuition behind the quantities. Recall that the 23 22 borrowing spread is determined by (cid:88) s = c+γ q ,for each k ∈ L. k jk j∈D k Ifadealerisborrowingfromalenderexclusively,thenthedealerexertsmonopsony 82

power and the sensitivity to lender supply is 1/2γ. However, if a dealer is competing with another dealer for funding from the same lender, then the Cournot competition decreases the sensitivity to lender supply to 1/3γ. This is because dealers do not internalize the increase in marginal cost of funding for their competitors. Therefore, Cournot competition results in a rate higher than the rate at each dealer’s exclusive lender, becausethetotalamountborrowedfromthecommonlender 2 (ρ −c)exceeds 3γ C the total amount borrowed from an exclusive lender 1 (ρ −c). 2γ C The total amount borrowed by each dealer is q = 5 (ρ −c) for i = 1,2. The iT 6γ C total amount borrowed from the decentralized market is a function of the borrowing rate in the interdealer market: (cid:88) 5 q (ρ ) ≡ q (ρ ) = (ρ −c). T C jT C C 3γ j∈{1,2} The demand for net funding from the interdealer market is ρ C q (ρ ) = q −q (ρ )− , i ∈ {d ,d }. iC C Bi iT C 1 2 β The market clearing condition for C market is q (ρ )+q (ρ ) = 0, 1C C 2C C and plugging in the T market quantities allows us to solve for the equilibrium rate 5 2ρ C q¯ − (ρ −c)− = 0 B C 3γ β 3βγ 3βγ 5 ⇒ ρ = q¯ + c. C B 6γ +5β 6γ +5β 3γ To summarize, the equilibrium with C market in closed form is 3βγ 5β ρ∗ = q¯ + c C 6γ +5β B 6γ +5β 5β 10 q = q¯ − c T B 6γ +5β 6γ +5β q −q Bi Bj q = . iC 2 Examine now how the equilibrium changes without a C market. The equilibrium 83

quantities in the decentralized market satisfy the following optimality conditions β 1 β q = q − c− q 11 B1 12 2γ +β 2γ +β 2γ +β β 1 β γ q = q − c− q − q 12 B1 11 22 2γ +β 2γ +β 2γ +β 2γ +β (B.1) β 1 β γ q = q − c− q − q 22 B2 23 12 2γ +β 2γ +β 2γ +β 2γ +β β 1 β q = q − c− q . 23 B2 22 2γ +β 2γ +β 2γ +β To solve the system of equations, we first plug in q and q into the second and 11 23 third equations, respectively. This leaves us with a system of two equations in two unknowns that define the best response functions of the two dealers when borrowing from their common lender l 2 β 1 2γ +β q = q − c− q 12 B1 22 2(γ +β) 2(γ +β) 4(γ +β) (B.2) β 1 2γ +β q = q − c− q . 22 B2 12 2(γ +β) 2(γ +β) 4(γ +β) Note that it is easy to show that the best-response function has a slope less than one-half 2γ+β < 1 for all positive values of the underlying coefficients. The strategic 4(γ+β) 2 substitutability of the dealers’ borrowing from their common lender are dampened when there is no C market. The resulting equilibrium quantities are the following functions of the underlying parameters 7β2 +6γβ 2β2 9β +6βγ q∗ = q + q − c 11 A(β,γ) B1 A(β,γ) B2 A(β,γ) 8β(β +γ) 2β(β +2γ) 6β +4γ q∗ = q − q − c 12 A(β,γ) B1 A(β,γ) B2 A(β,γ) (B.3) 8β(β +γ) 2β(β +2γ) 6β +4γ q∗ = q − q − c 22 A(β,γ) B2 A(β,γ) B1 A(β,γ) 7β2 +6γβ 2β2 9β +6βγ q∗ = q + q − c 23 A(β,γ) B2 A(β,γ) B1 A(β,γ) The term A(β,γ) = 15β2 + 28γβ + 12γ2 is a polynomial function of the two cost parameters. There are two properties of the equilibrium quantities that can be easily inferred. First, increases in the lender marginal costs c reduce equilibrium quantities 84

for all trading relationships. Second, increases in demand to a competing dealer result in a reduction of borrowing from the common lender ℓ consistent with strategic 2 substitutability of actions. In contrast, an increase in the demand of a competitor increases the borrowing from the exclusive lenders ℓ and ℓ for dealers 1 and 2, 1 3 respectively, which indicates strategic complementarity of dealer actions. The simple example illustrates that in a networked market with Cournot competition actions of agents could be strategic substitutes or complements depending on the nature of the connectedness of the market. B.2 Fully connected T market Finally, we examine how the equilibrium changes, if all dealers can borrow from all lenders or the T is fully connected. In particular, we are interested in comparing the equilibrium of a fully-connected T and the role of the centrally cleared C market. When the T market is not fully connected, the C market allows for the equalization of the marginal cost of funds across all lenders. We can solve the system of equation formed by the first-order conditions as a function of the underlying parameters and the equilibrium rate ρ∗ as follows C ρ∗ −c q = C , ∀ik ∈ E ik 3γ (B.4) 1 β +γ q =q + c− ρ∗, for i = {1,2} iC B,i γ βγ C The market clearing condition q +q = 0 can be easily solved to obtain the equi- 1C 2C librium rate ρ∗ C βγ β ρ∗ = q¯ + c, C 2(β +γ) B β +γ The equilibrium quantities borrowed from lenders in the decentralized market are β 1 q∗ = q¯ − c, ∀ik ∈ E ik 6(β +γ) B 3(β +γ) β 2 q∗ = q¯ − c T β +γ B β +γ 85

The quantities transacted between the two dealers in the C market are q −q 1B 2B q = 1C 2 q −q 2B 1B q = . 2C 2 ThesametradesasthecasewithsymmetricbutincompleteT -market. Thequantities traded along any dealer-lender relationship depend on the total dealer demand rather thantheindividualdealerdemandconditions. Movingtothecaseofafullyconnected T market without an interdealer C market, the equilibrium quantities are β(2γ +3β) βγ 1 q∗ = q − q − c, where i,j ∈ {d ,d }. ik 3(γ +β)(γ +3β) Bi 3(γ +β)(γ +3β) Bj 3(γ +β) 1 2 The symmetric wiring introduces also symmetry in the sensitivity of quantities to demand and supply shocks across all trading relationships. The total quantity traded in the T market is β 2 q∗ = q¯ − c, (B.5) T β +γ B β +γ The total amount borrowed is the same as in the equilibrium with a centrally cleared market. The difference is that with a centrally cleared market, the dealer with low demand borrows extra and lends the extra cash to the dealer with high demand through the centrally cleared market.30 B.3 Asymmetric wiring of the T market Examine a wiring in which dealer d borrows from all lenders, whereas dealer d only 1 2 borrows from l and l . In this case, dealers share l and l , and dealer d has an 2 3 2 3 1 exclusive lender l as illustrated in Panel B of Figure 4. 1 Beginning with an asymmetric wiring that involves a C market and following the same steps as before we can easily solve for the equilibrium quantities as follows. 1 First, the optimal quantities borrowed across the three lenders are q = (ρ∗ −c) 11 2γ C 30Note that condition (18) becomes q¯ > 2c and is required to guarantee that equilibrium quan- B β tities are positive. 86

1 and q = q = q = q = (ρ∗ − c) and the total quantities borrowed by each 12 22 13 23 3γ C dealer are 7 q∗ (ρ∗) = (ρ∗ −c) 1T C 6γ C 2 q∗ (ρ∗) = (ρ∗ −c). 2T C 3γ C For any spread between the lender marginal cost c and the centrally cleared rate, dealer d has a higher borrowing than the less connected dealer d . The market 1 2 clearing condition 6βγ 11β ρ∗ = q¯ + c, C 12γ +11β B 12γ +11β gives us a solution for the centrally cleared market rate. The quantities borrowed in the decentralized market are 7β 14 q∗ = q¯ − c 1T 12γ +11β B 12γ +11β 4β 8 q∗ = q¯ − c 2T 12γ +11β B 12γ +11β 11β 22 q∗ = q¯ − c. T 12γ +11β B 12γ +11β The quantities for the C market are 7β +6γ 3 q = q − q¯ + c 1C B1 B 12γ +11β 12γ +11β 4β +6γ 3 q = q − q¯ − c. 2C B2 B 12γ +11β 12γ +11β Note that unlike the symmetric cases, the asymmetric case introduces dependence ofthequantitiestransactedintheinterdealermarketonthelenders’themarginalcost parameter c. Furthermore, the net borrowing of dealer d in the interdealer market 1 increases with higher c, whereas the net borrowing of dealer d decreases. If there 2 is no centrally cleared market and following the steps from before, the equilibrium quantities borrowed in the decentralized market can be solved as follows 87

4β2 +3βγ 2β2 6β +3γ q∗ = q + q − c 11 A(γ,β) B1 A(γ,β) B2 A(γ,β) 4β2 +4βγ β2 +2βγ 3β +2γ q∗ =q∗ = q − q − c (B.6) 12 13 A(γ,β) B1 A(γ,β) B2 A(γ,β) 6β2 +4βγ 2βγ 6β +2γ q∗ =q∗ = q − q − c, 22 23 A(γ,β) B2 A(γ,β) B1 A(γ,β) where A(γ,β) = 12β2 + 19βγ + 6γ2. Similar to the symmetric case, the effects of dealer changes in demand result in strategic substitutability of actions across shared lenders and strategic complementarity of actions at exclusive lenders. C Data and institutional details C.1 Data construction We use confidential tri-party OTC repo data collected by the Federal Reserve Bank of New York from the two clearing banks—Bank of New York Mellon (BNYM) and JP- Morgan Chase (JPM). The data contain information on the borrower, lender, amount borrowed, maturity, interest rate and collateral. We focus on government collateral which includes U.S. Treasury securities, agency debt, and agency MBS. Note that we do not observe haircuts in this dataset. However, as discussed below, we add information on haircuts from the money market mutual funds (MMFs) data collected with the SEC’s N-MFP reporting form. We first identify all counterparties in the data and assign unique identifiers. We then identify subsidiaries of large conglomerates and create a unique identifier to track the parent company over time and across different datasets. We then aggregate all trades of subsidiaries under the same parent holding company. For example, all the trades of individual mutual funds under the same fund complex are aggregated under the parent fund complex or under the parent holding company. Similarly, trades of dealers and commercial banks affiliated with a financial holding company are consolidated under the top-holder parent holding company. We also identify internal transactions as trades that involve a borrower and a lender belonging to the same financial conglomerate.31 In most cases, the data do not 31Alargeshareoflendinginthedecentralizedmarketisdonebyassetmanagementfundsaffiliated withbankholdingcompanies. Thosefundsdonotlendtoaffiliateddealers. Thisabsenceisexpected and reflects SEC restrictions on dealings between the affiliated funds and their parents. 88

allow us to identify the subsidiaries that execute internal transactions. However, in a few cases we are able to identify the type of subsidiaries. For example, we observe trades between two affiliated broker-dealers, one domestic and the other located in a foreign country, or between a commercial bank and a broker-dealer. Because internal transactions are netted for the purposes of the supplementary leverage requirement, those transactions are likely used by financial conglomerates to optimize their regulatory requirements, while taking advantage of regulatory arbitrage opportunities.32 We exclude all internal transactions from our analysis. Once we construct consistent entities identifiers across the different datasets, we merge the information on centrally-cleared general collateral repurchase agreements provided by the Fixed-Income Clearing Corporate (FICC). Those data include both the general collateral anonymous GCF segment and the centrally-cleared delivery versus payment (DvP) segment. We follow the same process to normalize the counterparty names to their parent holding company, assign a unique identifier to match the dealers to the tri-party OTC repo dataset. We supplement the repo data with information on the dealers’ and lenders’ balance sheets. On the dealer side, we use Moody’s KMV data to obtain information on dealers’ credit risk, market valuations, and balance sheet information. On the lender side, we classify lenders into two categories—money market mutual funds (MMFs) and other lenders. We focus on money fund complexes, as detailed balance sheet information is usually only available at this level. We use two data sources for MMF data. For information on money fund liabilities, we use iMoneyNet, which contains comprehensive information on expense ratios, minimum investment, investor flows by share class, and investor types. We supplement information from iMoneyNet with the monthly N-MFP form SEC filings. These data contain detailed CUSIP-level information on the composition of securities holdings of money market funds including repurchase agreements and the corresponding counterparties. For repurchase agreements, we are able to verify the counterparties, collateral type, haircuts, and the interest rates for individual repo transactions with the tri-party repo data. 32Correa, Du, and Liao [2020] use confidential supervisory data and provide evidence for internal repo transactions that allow large conglomerates to take advantage of arbitrage opportunities in foreign exchange markets and minimize impact on their leverage ratios. 89

C.2 Tri-party repo and other repo markets The tri-party repo market is a large, systemically-important funding market with close to $4 trillion of cash and collateral exchanged daily. The tri-party repo market provides cash to dealers for their repo trades with clients in the bilateral repo market. As such, the tri-party repo market is the first leg of an intermediation chain that funnels cash from cash lenders such as money funds to dealer counterparties in bilateral markets, such as as hedge funds and REITs.33 The tri-party market involves repurchase agreements or repo contracts between dealers as cash borrowers and money funds and others as cash lenders. A repo is a secured loan that combines a temporary sale of securities with an agreement to repurchase those securities at a later date.34 A repo agreement specifies the loan amount, the collateral type, the maturity date, the interest rate and the haircut. The institutional details of how repo contracts are executed differ across the triparty and the bilateral repo markets. The first difference is that the tri-party market uses the clearing, collateral allocation, and settlement services of a custodian or clearing bank, which is the third party in the repo contract and the reason this market is called “tri-party”.35 The services of the custodian bank are also used for the anonymous FICC interdealer market as well as the Federal Reserve’s ON RRP facility. In contrast, in the bilateral segment, cash and collateral are directly exchanged between the lender and the borrower in delivery versus payment (DvP) settlement. The second difference is the nature of collateral pledged. Tri-party repo are governed by a master repo agreement, which specifies a broad class of generic securities such as Treasury securities, agency debt, and agency MBS, private label collateralized mortgage obligations (CMOs), corporate bonds, equities, asset backed securities, municipal bonds, and other. In contrast, the bilateral repo contracts involve pledging of specific securities and the settlement is done by the counterparties themselves 33See Banegas and Monin [2023] for a review of recent developments in bilateral repo markets, including a discussion of hedge funds that engage in Treasury futures basis trading. 34The repo contract receives different treatment under bankruptcy laws than other types of lending. In the event of bankruptcy, repo lenders can sell the collateral, rather than be subject to an automatic stay, as would be the norm for other collateralized loans. Refer to Acharya, Anshuman, and Viswanathan [2024] for a discussion. 35At the beginning of our sample, clearing in the tri-party segment was facilitated by one of two custodianbanks—BankofNewYorkMellonandJPMorganChase. In2016,JPMorganChaseexited the market leaving Bank of New York Mellon as the single clearing bank. The role of the clearing bank is to provide settlement of trades, book keeping, collateral management, and also ensures that the collateral is available to lenders in case of dealer default. 90

through a delivery versus payment (DvP). Both features of the tri-party repo market, the settlement via a clearing bank and the pledging of general collateral, makes it easier for money market funds and other cash lenders to participate in the market without the need to establish their own collateral management systems and instead rely on the infrastructure provided by the clearing bank.36 36See Copeland, Martin, and Walker [2010], Ennis [2011], Copeland, Martin, and Walker [2014], and Copeland, Davis, and Martin [2014], and for a more detailed exposition of the institutional details of the tri-party repo market and how those institutional features have evolved since the Global Financial Crisis. 91