Private money creation with safe assets and term premia

Private Money Creation with Safe Assets and Term Premia

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Private Money Creation with Safe Assets and Term Premia Sebastian Infante PII: DOI: Reference:

S0304-405X(19)30286-7 https://doi.org/10.1016/j.jfineco.2019.11.007 FINEC 3142

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Journal of Financial Economics

Received date: Revised date: Accepted date:

27 November 2018 26 February 2019 10 April 2019

Please cite this article as: Sebastian Infante, Private Money Creation with Safe Assets and Term Premia, Journal of Financial Economics (2019), doi: https://doi.org/10.1016/j.jfineco.2019.11.007

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Private Money Creation with Safe Assets and Term Premia

✩

Sebastian Infante Federal Reserve Board, Division of Monetary Affairs, 20th Street and Constitution Avenue N.W., Washington, DC 20551, United States

Abstract The existing literature has shown that an increase in the demand for safe assets induces the private sector to create more of them. Focusing on repos backed by US Treasuries, I theoretically and empirically show that an increase in the demand for safe assets leads to a decrease in repos outstanding. Because Treasuries are safe assets, an increase in the demand for safe assets compresses their term premia, reducing incentives to issue repos. Thus, the sensitivity of private safe asset creation depends on whether the collateral backing them are safe assets themselves. The sensitivity of the Federal Reserve’s reverse repurchase agreement (RRP) operations has the same sign as existing studies. Keywords: safe assets, private money, repo, monetary policy, Federal Reserve JEL classification: G24, G12, E41, E51

✩ I would like to thank Gary Gorton (the referee), Bill Schwert (the editor), Mark Carlson, Giovanni Favara, Yesol Huh, Michael Schwert, Francisco Vazquez-Grande, Jason Wu, Egon Zakrajsek, and seminar participants at the Federal Reserve Bank of New York, System Committee Meeting on Financial Institutions, Regulation, and Markets (FRB Cleveland), the University of Chile, and the MA lunch for very insightful comments and discussions. I would also like to thank Jessica Goldenring and Joseph Shadel for excellent research assistance. The views of this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. Email address: [email protected] (Sebastian Infante)

Preprint submitted to Elsevier

November 26, 2019

1. Introduction The growth of the shadow banking system has been cited as one of the important precursors of the 2007–2009 financial crisis. In particular, some researchers have argued that the shortage of publicly produced safe assets induced the private sector to create more of them in the form of shortterm debt. The newly created short-term debt helped satisfy the demand for safe assets because it provided additional money services that agents could consume.1 For example, Sunderam (2014) provides empirical evidence that, prior to the crisis, private issuance of asset-backed commercial paper (ABCP) responded positively to increases in the demand for safe assets. More broadly, Krishnamurthy and Vissing-Jorgensen (2015) show that safe and liquid government debt crowds out the financial sector’s short-term debt. Both of these findings indirectly imply that the growth of the shadow banking system was driven, in part, by the need to satisfy the demand for safe assets. In this paper I provide evidence that the issuance of private repurchase agreements (repos) backed by US Treasuries decreases as the demand for safe assets increases. The empirical results stem from studying the US Treasury tri-party repo market between 2009 and 2017. I find that aggregate and individual firm repos outstanding decreases as measures of the demand for safe assets increase. Following the previous literature, the empirical analysis measures the demand for safe assets with the spread between the four-week Treasury bill (T-bill) and the one-month overnight index swap (OIS), a spread known as the convenience yield. Given that T-bills are publicly produced short-term safe assets and the OIS is merely a contractual agreement promising a risk-free payoff, the spread measures the convenience of holding safe assets. Interestingly, I find that the Federal Reserve’s reverse repo operations (henceforth labeled RRP program) has the opposite sensitivity: take-up in the program increases as the demand for safe assets increases.2 This opposite sensitivity suggests that the Federal Reserve can, in fact, increase the supply of safe assets as demand for them increases. The above result complements the existing literature and can easily be understood by noting that US Treasuries already satisfy the demand for safe assets. That is, in terms of providing money services, US Treasuries and repos backed by US Treasuries serve a similar purpose. The mechanism proposed in this paper operates through the spread between long-term safe assets and short-term safe assets. The return on both assets is lower because of their safe asset status. But long-term safe assets are risky in the short run; therefore, they trade at a discount relative to short-term safe assets. That is, long-term safe assets have term premia.3 As the demand for safe assets increases, the difference in risk between long- and short-term safe assets becomes less important. That is, at the margin, investors care less about interest rate risk and more about consuming money services. Therefore, long-term safe assets’ term premia compress, prompting private issuers to reduce the amount of repos outstanding. This reduction results in cash investors holding more public safe assets directly rather than private safe assets backed by public ones. The above substitution is markedly different from the increase in private safe assets already 1 Money services are broadly defined as nonpecuniary benefits from holding safe/liquid assets. See Gorton (2017) for a detailed description of the literature’s history and terminology. 2 The Federal Reserve’s RRP program allows the Federal Reserve to accept cash from qualified nonbank financial institutions in the form of repos. The program is intended to support interest rate control. 3 It may seem contradictory to assume safe assets can have a risky payoff. As in Gorton (2017), this paper defines a safe asset as one that pays par with a very high probability. US Treasury bonds have this property. But in the short run, the value of these assets can change because of interest rate risk. Section 2.6 gives a detailed discussion of the main modeling assumptions.

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documented in the literature. In those settings, as the demand for safe assets increases, the private sector creates more of them using assets that do not have a safe asset status (for example, ABCP). That is, the aggregate amount of safe assets increases. The sensitivity of the RRP program is similar to this channel. In effect, as the demand for safe assets increases, nonbank cash investors increase their participation with the central bank’s facility, increasing their holdings of safe assets that they could not access otherwise.4 In the main result of this paper, rather than a change in the total amount of safe assets, there is a substitution from private safe assets to public ones. The paper’s mechanism gives rise to a natural question: if US Treasuries already satisfy the demand for safe assets, why are US Treasury repos issued in the first place? The reason is that repos allow for a more risk-tolerant financial sector to hold interest rate risk while supplying money services to the rest of the economy. More specifically, because long-term safe assets are risky in the short run, they are better held by more risk-tolerant investors. And because risk-averse investors consume money services, there are benefits from creating private safe assets. The financial sector can fill both of these roles by buying US Treasuries and issuing repos to finance them. Thus, in equilibrium both public and private forms of safe assets coexist. To highlight this intuition, the paper provides a simple theoretical model in the spirit of Krishnamurthy and Vissing-Jorgensen (2015). The model considers an economy with two sectors, households and banks, that can purchase two types of government securities: short-term bonds (Tbills) and long-term bonds (Treasury bonds). Both securities provide money services, but T-bills are risk free, while Treasury bonds have a stochastic payoff in the short run. Households are risk averse and consume money services that safe assets provide. Banks are risk neutral and do not consume money services but have a costly technology to produce safe assets backed by securities (i.e., repos). The resulting equilibrium involves both banks and households holding Treasury bonds, with banks issuing repos to households. When households’ preference for money services increases, the relative importance of risk diminishes, compressing term premia. This compression makes banks’ maturity transformation less profitable and, because repo is costly to produce, induces banks to reduce their repos outstanding. An extension of the model introduces a central bank that can issue repos directly to households and shows conditions under which the central bank’s repo issuance has the opposite sensitivity to that of private banks. The intuition is that take-up at the central bank’s repo facility is not sensitive to term premia, and thus, the central bank will provide safe assets just to meet households’ demand. The main theoretical contribution of the paper is to consider long-term safe assets with term premia. The previous literature has highlighted the difference between long- and short-term safe assets. Krishnamurthy and Vissing-Jorgensen (2012) and Krishnamurthy and Vissing-Jorgensen (2015) highlight this difference by assuming that each asset provides different types of money services. Greenwood, Hanson and Stein (2015) note that some safe assets provide “short-term safety,” which refers to immediate and certain repayment, and others provide “long-term safety,” which refers to absolute certainty of ultimate repayment. These differences arise because investors value these types of safety differently. Although money services may differ across maturities, the model in this paper places long- and short-term safe assets on the same “safe asset footing.” That is, this paper assumes both types of safe assets are perfect substitutes in providing money services but recognizes that long-term safe assets have term premia. Although this is an extreme case, it 4 In theory, there are individual and aggregate caps to the size of the RRP program, but in practice, they do not bind.

3

captures that risk-averse agents have to balance the benefits from holding long-term safe assets to consume money services with their inherent riskiness. An extension of the model considers a case where the asset used as repo collateral does not provide money services. This extension gives the traditional sensitivity of private safe asset creation already documented in the literature. The coexistence of this result with the main one in the paper is due to the safe asset status of the collateral backing the private safe asset. In the model extension, an increase in the demand for safe assets increases the spread between long-term assets that do not provide money services and short-term assets that do, increasing banks’ incentives to issue more repos. Because banks can issue repos that provide money services with collateral that does not, they increase the amount of safe assets in the economy. The model also gives predictions on the sensitivity of private repo issuance to changes in the supply of public safe assets. Specifically, an increase in short-term T-bills satiates households’ demand for safe assets, resulting in a decrease in private repo issuance. However, an increase in long-term Treasury bonds has an ambiguous effect. On the one hand, it reduces households’ marginal demand for safe assets, decreasing the amount of private repo issuance (as with T-bills). On the other hand, it increases both households’ and banks’ holdings of long-term Treasury bonds, which increases term premia and the amount of repo needed to finance the bonds, increasing the amount of private repo issuance. The tri-party repo market provides an ideal setting to test the main theoretical predictions. In this market, broker-dealers raise short-term funding from cash-rich investors. The main economic motive to participate in this market is to borrow and lend funds rather than securities.5 Borrowers are highly rated dealers, many of which are primary dealers associated with bank holdings companies, implying that counterparty credit concerns are relatively small. Investors are cash-rich asset managers and include money market funds, securities lenders, insurance companies, and corporate cash managers. Importantly, the main theoretical result depends on investors substituting shortterm safe assets with long-term safe assets. This sensitivity may be limited for money market funds, given their preference for short maturity portfolios, but is very relevant for other types of investors in this market. For example, securities lenders manage both short- and long-duration portfolios, and they participate in the tri-party market, in part, to reinvest the proceeds of their securities lending activity. This activity makes them the ideal type of investor who would directly exhibit the substitution in the model.6 The data confirm the main prediction of the model: as the demand for safe assets—measured through the convenience yield—increases, there is a decrease in the issuance of private repo. The data also confirm that changes in short-term T-bills outstanding decreases private repo issuance and changes in Treasury bonds outstanding increase private repo issuance. This sensitivity suggests that changes in short-term T-bills outstanding can be interpreted as demand shocks because they alter investors’ demand to consume money services. In practice, these changes are unlikely to affect dealers’ supply of repo because short-term T-bill yields are low relative to repo rates, implying a negative carry trade for that position. These observations motivate the use of short-term T-bill issuance as an instrument to test this paper’s main mechanism, which is confirmed empirically. This paper provides additional evidence that the results are not driven by changes in the direct or indirect costs of issuance and studies the sensitivity of repo issuance backed by riskier collateral classes. This 5 The tri-party repo market is a general collateral market implying that, within an asset class, cash borrowers have the flexibility to choose any security to post as collateral. 6 For more details on the institutional arrangement of repo markets, see Copeland, Martin and Walker (2014).

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paper also examines different sensitivities across regulatory jurisdictions and repo maturities.7 The empirical results rule out alternative supply-driven explanations for the sensitivity of private US Treasury repo issuance to the convenience yield. The results of this paper suggest that measuring the private sector’s provision of safe assets is more subtle than merely summing all private short-term liabilities. Financial firms engage in true safe asset creation when the collateral backing their liabilities is not a safe asset to begin with. In addition, these results suggest that the safe asset status of US Treasuries is not the consequence of a deep and liquid repo market. Rather, long-term US Treasuries provide money services directly, in line with the empirical findings of Krishnamurthy and Vissing-Jorgensen (2012). The paper is structured as follows. The end of this section gives a brief overview of the literature. Section 2 characterizes the model, showing under what conditions repo issuance is negatively related to households’ demand for safe assets, as well as extensions that consider repo issuance backed by riskier collateral classes and repo issuance by a central bank. Section 3 provides empirical evidence from the US tri-party market, ruling out supply-driven explanations, and highlights how the sensitivity of the Federal Reserve’s RRP program differs from the rest of the private market. Finally, Section 4 gives some concluding remarks. The aforementioned story hinges on a number of components. The first is that the financial sector has incentives to create short-term debt, which is in the spirit of traditional banking models such as Diamond and Dybvig (1983), Holmstrom and Tirole (1998), and Gorton and Pennacchi (1990). Although these papers differ in their rationale behind the creation of private short-term debt—be it for liquidity risk sharing or to alleviate asymmetric information frictions—the main theme is the private creation of liquid assets. Another necessary ingredient is the existence of a convenience yield for safe assets, a characteristic that T-bills and US Treasuries have. Typically modeled in reduced form, a growing literature argues that safe, money-like assets provide benefits above and beyond their risk/return trade-off. For example, Greenwood, Hanson and Stein (2015) study the monetary premium associated with short-term government debt, and Krishnamurthy and Vissing-Jorgensen (2012) show that the US Treasury has benefited from issuing long-term bonds at reduced yields because of their safe asset status. Using options data to estimate longer-term risk-free rates, van Binsbergen, Diamond and Grotteria (2018) also find a significant convenience yield for long-term US Treasuries. In addition, this paper’s mechanism relies on the ability of privately produced short-term debt to satisfy the economy’s demand for safe assets. In effect, Gorton, Lewellen and Metrick (2012) show that in the United States the share of safe assets relative to GDP has been constant over the past 60 years, but the share of safe assets provided by the shadow banking sector has grown over the past 30 years. Relatedly, Carlson et al. (2016) study whether the central bank can reduce systemic risks by providing short-term safe assets, effectively crowding out excessive private safe asset creation. Conceptually, this paper is similar to the analysis in Xie (2012), Krishnamurthy and VissingJorgensen (2015), Sunderam (2014), and Diamond (2018), who show the positive sensitivity between privately produced safe assets and the demand for safe assets in the United States. Kacperczyk, Perignon and Vuillemey (2017) find a similar sensitivity for the European commercial paper market. These papers have focused on cases where the explicit or implicit collateral backing private safe 7 The bulk of the analysis is at a daily frequency. Because repos tend to have short maturities (less than one week), the most meaningful sensitivities are likely to be over short horizons. The main empirical results still hold at a weekly frequency.

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asset creation are not safe assets themselves, giving rise to true safe asset creation. This paper extends these results by noting that the sensitivity of private safe asset creation depends on its characteristics, namely, the safe asset status of the assets backing the private safe asset. Lenel (2017) provides a quantitative model with long- and short-term safe assets, focusing on the supply channel through intermediaries’ holdings of long-term public safe assets to produce short-term private ones. As in the model herein, that paper predicts that short-term public safe assets will only be held by households, suggesting that changes in the supply of short-term public safe assets can identify the demand channel in this paper. Finally, this paper builds and expands on several insights documented in Nagel (2016). Nagel shows that the safe asset premium depends on the opportunity cost of holding money.8 That is, the convenience yield is largely determined by the level of rates. This paper takes convenience yield dynamics as exogenous and studies changes in the relative value and holdings of safe assets. But the model outcome of this paper also suggests that the level of rates is important in determining the safe asset premium. Nagel also provides evidence that the elasticity of substitution between money-like claims is equal to ones. That is, money and money-like claims behave like perfect substitutes in terms of the money services they provide. The setup of this paper assumes that money-like assets are perfect substitutes when satisfying the demand for safe assets, placing them all on the same “safe asset footing,” but recognizes that they may have different risks.9 Finally, Nagel studies central banks’ implementation of interest on reserves and shows that the relation between the convenience yield and the level of rates remains unchanged. This result suggests that market segmentation created by the banking sector’s unique ability to hold reserves has a strong effect. I show that the Federal Reserve’s RRP program expands to satisfy the demand for safe assets, alluding to the program’s ability to circumvent the banking sector and provide safe assets directly to the economy. 2. Model The theoretical model in the paper is in the spirit of Krishnamurthy and Vissing-Jorgensen (2015) with an important difference: long- and short-term safe assets are perfect substitutes in terms of the money services they provide, but long-term safe assets have a stochastic payoff in the short run.10 That is, long-term safe assets have term premia. The difference in risk between maturities generates a nontrivial portfolio problem for risk-averse agents that also consume money services. 2.1. Setup The model consists of two periods, t ∈ {0, 1}. In the initial period, agents choose their optimal portfolio, how many contracts to trade between each other, and how much to consume. In the final period, asset payoffs are realized, contracts are settled, and agents consume their final wealth. The model consists of two types of agents: households and financial firms. Households should be interpreted as a broad set of cash investors such as money market mutual funds, securities lenders, and corporate cash managers. These investors can invest in any security and consume 8 What

this current paper calls safe assets, Nagel calls “near-money assets.” assumption is discussed in detail in Section 2.6. 10 See the detailed discussion of important modeling assumptions in Section 2.6. 9 This

6

money services from their portfolio (details below).11 Financial firms should be interpreted as large broker-dealers that in the model are called “banks.” Banks have a costly technology to create collateralized debt contracts (i.e., repos) that can be purchased by households. Both households and banks start with an initial endowment to purchase an exogenous supply of securities and any privately created contracts. 2.1.1. Assets and contracts There are two exogenously supplied securities in the economy. One security is called a T-bill, which pays off 1 in period t = 1 and trades at an endogenously determined price pT in t = 0. The ˜ in period t = 1 and trades at an second security is called a Treasury, which has a random payoff U ˜ follows an exogenously specified endogenously determined price pU in period t = 0. I assume that U distribution F (·) with mean U and positive variance, which is the only risk in the economy. This setup captures the idea that long-term Treasuries are risky in the short run—that is, they expose investors to interest rate risk. In t = 0, there is a fixed aggregate amount of QT T-bills and QU Treasury securities in the economy. Banks have the technology to issue repos, which are collateralized debt contracts backed by either T-bills or Treasuries. For simplicity, I assume there is no limited liability and banks can always repay their debts, making repos risk free. That is, repos pay off 1 in period t = 1 and trade at an endogenously determined price pRP in t = 0.12 In addition to providing a profitable store of value and a risky payoff, assets can provide additional money services for holding them. Specifically, a portfolio of T-bills, Treasuries, and repos H , qRP ) can provide money services (qTH , qU H M = qTH + αU U qU + αRP qRP

(1)

in t = 1. Only households value the consumption of money services, which affects their demand and, ultimately, their trading price (see Section 2.1.2). In this characterization, an asset’s contribution to the portfolio’s money services is represented by its expected market value in period 1.13 In the general setup, T-bills’ contribution to the portfolio’s money services is normalized to one, and Treasuries’ and repos’ contributions are scaled by αU and αRP , respectively. Importantly, Eq. (1) assumes that assets are perfect substitutes in providing money services. Asset prices and thus expected returns are determined endogenously in equilibrium. 2.1.2. Households Households have a fixed initial endowment e that they use to purchase assets and consume. They are risk averse and have time separable utility, discounting consumption in the future period 11 In practice, money market funds are restricted from investing in long-term securities, but other types of cash investors do not have such restrictions. For example, securities lenders manage both long- and short-term portfolios when managing their securities lending business. Duchin et al. (2017) show that corporate cash managers hold diverse portfolios, which include long-term government and corporate debt. 12 Following the previous literature on private safe asset creation, this assumptions implies that the model abstracts away from counterparty risk. The idea is to focus on the trade-off between a portfolio’s risk and its ability to satisfy the demand for safe assets in “good times.” In the context of repos, this assumption can be micro-founded with a bounded positive support for dF , allowing for zero value-at-risk contracts for a large enough haircut, which is discussed when describing the banking sector. 13 This assumption implies that money services are consumed when assets pay off, as in Krishnamurthy and VissingJorgensen (2015).

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by β. Given a pair of consumption plans (c0 , c˜1 ), households’ utility function takes the following form, U H = u(c0 ) + βE(u(˜ c1 + v(M ; η))),

(2)

where v(M ; η) captures households’ added utility for consuming money services M . I assume that both u and v satisfy u0 , v 0 > 0 and u00 , v 00 < 0. The exogenous parameter η serves to increase and decrease households’ preferences for money services. This parameter will be useful in studying how the equilibrium changes when the relative preference for money services increases. I assume vη , vη0 > 0—that is, the level and marginal utility for money services increases with η. Given H households’ holdings of T-bills, Treasuries, and repos (qTH , qU , qRP ), their consumption in both periods is c0 c˜1

H = e − pT qTH − pU qU − pRP qRP H H ˜ = qT + U qU + qRP .

(3) (4) (5)

For the subsequent analysis, it is useful to rewrite the model returns. Consider RT :=

1 , pT

˜ ˜ := U , R pU

˜ = U , µ := E(R) pU

RRP :=

1 pRP

,

(6)

˜ is the gross stochastic return of US Treasuries, µ is the where RT is the gross return of T-bills, R ˜ gross expected return of US Treasuries, and RRP is the gross return of repos. The variance of R ˜ In this case, given a households’ holdings of T-bills, Treasuries, and repos is denoted by V(R). H (qTH , qU , qRP ), we can rewrite the money services of households’ portfolio, and their consumption plans, as M

H = RT θTH + αU µθU + αRP RRP RP

(7)

c0

= e − θTH − θTU − RP H ˜ U = RT θTH + Rθ + RRP RP,

(8)

c˜1

(9)

H , and RP := pRP qRP is the total amount of cash households invest where θTH := pT qTH , θTU := pU qU in T-bills, Treasuries, and repos, respectively. For the notation change, it is also useful to rewrite the total supply of T-bills and Treasuries as ΘT := pT QT and ΘU := pU QU , respectively. Under this transformation, households optimally choose the amount of cash invested in each H , RP ) to maximize Eq. (2), resulting in the following Euler equations, security (θTH , θU

˜ E(S)(1 + v 0 (M ; η))RT = 1 ˜R ˜ + αU v 0 (M ; η)µ)) = 1 E(S( ˜ E(S)(1 + αRP v 0 (M ; η))RRP

=

(10) (11)

1,

(12)

0

)) where S˜ = β u (c˜u10+v(M is the household’s stochastic discount factor. (c0 ) Note that if αRP < 1, then RT < RRP , and if αRP = 1, then RT = RRP . To simplify the characterization of the equilibrium, I assume that T-bills and repos have the same contribution to the portfolio’s money services. That is, in Eq. (1) αRP = 1; thus, RT = RRP . Note that assuming different contributions to money services will mechanically create a wedge between T-bill and repo returns. I also assume that αU ∈ {0, 1} to consider two starkly different cases: one where Treasuries

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are just as useful as T-bills in providing money services, αU = 1, and another where the collateral used to create repos does not provide money services at all, αU = 0. This difference will give distinct predictions on the sensitivity of repo issuance, which depends on the collateral’s ability to provide money services.14 2.1.3. Banks The model considers one representative risk-neutral bank with the technology to issue repos at a cost C(·), which is paid in t = 1, with C(0) = 0, C 0 , C 00 > 0.15 Given the banking sector’s risk preference, they provide a service to the economy by holding risky long-term Treasuries and issuing repos. That is, households are able to shift risk to the bank that is more willing to take it, yet still enjoy the money services from the repos the bank issues. The representative bank starts with an initial endowment w and wants to maximize dividends in t = 0, 1, which take the following form Dvd0 Dvd1

B = w + RP − θTB − θU

= −RRP RP +

RT θTB

(13) B ˜ U + Rθ − C(RP ),

(14)

B are the bank’s holdings in Treasuries, and RP is the where θTB are the bank’s holdings in T-bills, θU amount of repos issued. For simplicity, I assume that the bank is not subject to limited liability, but it must satisfy its initial budget constraint, B w + RP ≥ θTB + θU .

(15)

In the general version of the model, repo haircuts can be incorporated. That is, the amount of repos issued must be lower than a fraction of the bank’s portfolio value,16 B RP ≤ (1 − hcT )θTB + (1 − hcU )θU .

(16)

For the baseline model, I will consider that the bank has a large enough endowment so that restriction (16) does not bind. The bank is risk neutral, and, given households’ pricing of securities, it will always want to purchase more risky assets. With a high enough initial endowment, the marginal decision to issue repos depends on the costs and benefits of issuing them, not on the bank’s ability to pay for haircuts. Formally, the representative bank solves the following problem, max

B ,θ B ,RP } {θT U

Dvd0 + βE(Dvd1 )

subject to w + RP (1 −

hcT )θTB

+

B (1 − hcU )θU B θTB , θU , RP

B ≥ θTB + θU

≥ RP ≥ 0.

14 Details

for these assumption are given in Section 2.6. assumption captures the idea that repos are very balance sheet intensive and new regulatory initiatives, such as the leverage ratio, restrict the size of banks balance sheets (see Duffie, 2017). This assumption implies that the marginal cost of an additional dollar of repo issuance is higher for larger balance sheets. See the detailed discussion in Section 2.6. 16 With finite support for dF , a high enough haircut, and a large enough endowment, repos can be made risk free without limited liability. 15 This

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Denoting λ and ξ the Lagrange multiplier associated with the budget and haircut constraint, respectively, the bank’s problem gives rise to the following first-order conditions −1 + βRT − λ + (1 − hcT )ξ −1 + βµ − λ + (1 − hcU )ξ 0

1 − βRRP − βC (RP ) + λ − ξ

≤ 0

(17)

≤ 0.

(19)

≤ 0

(18)

By focusing on equilibria where the bank holds either Treasuries or T-bills—that is, max{βRT , βµ} > 1—from Eq. (17) or (18), it is clear that a slack budget constraint (λ = 0) and a binding haircut constraint (ξ > 0) cannot be an equilibrium: the bank would always prefer to increase its holdings of Treasuries or T-bills, making the haircut constraint slack. An interesting case is when the budget constraint binds and the haircut restriction is slack (λ > 0, ξ = 0). In this case, if RT ≥ µ, then the bank holds as many T-bills as its budget constraint allows and does not issue repos. In effect, in this case λ = βRT − 1, and as RRP = RT from Eq. (19), RP ∗ = 0.17 Alternatively, if µ > RT , then the bank holds as many Treasuries as it can and issues repos—i.e., inequality in Eq. (19) binds. In this case λ = βµ − 1, using Eq. (18), gives C 0 (RP ) = µ − RRP .

(20)

That is, the marginal cost to issue repos is equal to the expected return of holding Treasuries minus the cost of financing them. Under these conditions, the bank never holds T-bills—i.e., inequality in Eq. (17) is slack. Therefore, when µ ≤ RT , the bank’s optimal strategy is to not issue repos and to hold the following portfolio, θTB∗ = w,

B∗ θU = 0.

(21)

Alternatively, if µ > RT , the bank’s optimal strategy is to issue repos, according to Eq. (20), and hold the following portfolio, θTB∗ = 0,

B∗ θU = w + RP.

(22)

Note that in both optimal strategies, a higher endowment w only translates into purchasing more T-bills or Treasuries and does not affect the marginal decision to issue repos.18 The above optimal strategies are still feasible when w = 0 and there are no repo haircuts, hcU = 0. 2.2. Equilibrium Because T-bills and repos are both risk free and contribute equally to the portfolio’s money services, households treat both assets identically. In addition, Eq. (11) can be rewritten as µ ˜ R) ˜ + E(S)(1 ˜ − 1 = −cov(S, − αU )v 0 µ. RT

(23)

17 Recall that α 0 RP = 1 implies RRP = RT , and because C(0) = 0 and C > 0, it would be too costly to issue repos backed by T-bills. 18 Because banks are more risk tolerant, they are the natural holders of risky Treasuries. If they did not have a limited endowment, in equilibrium they would purchase the entire supply of Treasuries, making Eq. (11) slack and the model uninteresting.

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The optimal strategies characterized in Section 2.1 and market clearing conditions θTH∗ + θTB∗ = ΘT ,

H∗ B∗ θU + θU = ΘU ,

(24)

H∗ where θTH∗ and θU are households’ optimal choices of T-bills and Treasures, leads to the following equilibrium.

˜ is sufficiently high enough, equilibrium returns are given Proposition 1. If ΘU − w > 0 and V(R) by Eq. (10) and (23), with RT = RRP . The amount of repos issued by the bank is given by C 0 (RP ∗ ) = µ − RT , and households hold ΘT T-bills and ΘU − (w + RP ∗ ) Treasuries. Proof. From the previous section, the strategies characterized in Proposition 1 are optimal if µ − ˜ R) ˜ is RT > 0 and βµ > 1. Because of Eq. (23), the first condition holds for all αU ∈ [0, 1] if cov(S, ˜ negative. Given u’s concavity, this condition is true if c˜1 is correlated with R—that is, households’ holdings of Treasury securities are positive. Reasoning by contradiction, assume that µ − RT ≤ 0. In that case, the bank’s optimal strategies imply zero repo issuance and zero Treasury holdings. Thus, households hold all Treasury securities because of market clearing, leading to a contradiction. In the case when µ−RT > 0, then households’ holdings of Treasury securities is ΘU −(w+RP ∗ ), which is positive because ΘU − w > 0 and C 0 (RP ∗ ) = µ − RT with C 0 > 0 and C(0) = 0. ˜ βµ > 1. Finally, from Eq. (23) it is easy to see that for a high enough V(R), Proposition 1 characterizes the equilibrium where households hold all T-bills, the bank and households split the total supply of Treasuries, and the bank issues repos to households. This equilibrium captures the model’s main economic intuition: in spite of the exogenous cost of issuing repos, there are welfare gains in doing so because the bank is better at bearing interest rate risk. The equilibrium allows for a case in which the Treasury is just as useful as a T-bill to satisfy safe asset demand, αU = 1, and when it doesn’t contribute at all, αU = 0. In addition, denoting Rf := E(1S) ˜ as the canonical one-period risk-free rate, Eq. (10) can be rewritten as RT − Rf = −v 0 (M ; η)RT .

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That is, the difference between the return of the tradable risk-free rate, relative to the theoretical risk-free rate, is negatively related to the marginal benefit of holding safe assets scaled by the level of short-term rates, as in Nagel (2016). This spread is commonly known as the convenience yield and motivates the empirical measurement of the marginal demand for safe assets in Section 3. The equilibrium characterized in Proposition 1 can shed light on how prices and repo issuance respond to changes in the convenience yield, modeled through changes in η. In addition, the model can show how the supply of public safe assets can affect the equilibrium outcome. To simplify the comparative statics of the model, I assume agents have constant absolute risk aversion (CARA) utility and the issuance cost function takes a simple quadratic form: C(RP ) = 12 c × (RP )2 with c > 0. 2.3. Repos backed by collateral satisfying safe asset demand The first result is for the case in which Treasuries are just as useful as T-bills to satisfy safe asset demand: αU = 1. For this analysis, it is useful to define the total amount of short- and long-term Treasuries outstanding net of the bank’s endowment: κ = (ΘU + ΘT − w). Under this specific setup, the model gives the following comparative statics. 11

Proposition 2. If households have CARA utility with risk aversion γ, αU = 1 in Eq. (1), C(RP ) = 1 2 2 c × (RP ) , and the parameter conditions of Proposition 1 hold with γ(ΘT + ΘU − w) := γκ > 1, then repo issuance has the following comparative statics:      −1 1 µ ∂RP ∗ ˜ T γκvη v 00 + vη0 −γκ(1 + v 0 ) + 1 = − 1 E(S)R <0 ∂η |D| c RT RT   ∂RP ∗ −1 1 µ ˜ T v 00 (1 + γκ) < 0 = − 1 E(S)R ∂ΘT |D| c RT    ∂RP ∗ −1 1 1 ˆ = − −γκ(1 + v 0 ) + γ V RP ∂ΘU |D| c RT     µ µ 00 ˜ ˆ +E(S)RT v −γ V κ + −1 + γκ RT RT    ∂RP ∗ 1 1 (µ − RT ) 1 0 ˆ 1− = − −γκ(1 + v ) + γ V RP ∂c c2 |D| c RT !)! 2   µ 1 00 0 ˆ ˜ Tv − 1 RT − γκV RP < 0, −E(S)R −γκ(1 + v ) + RT RT ˜R ˜ − µ)2 ), V RP ˆ := Vˆ − where Vˆ := E(S(



µ RT

2 − 1 (1 + v 0 )RT , and |D| < 0 is the determinant of

the Jacobian matrix of partial derivatives of Eq. (10) and (23) with respect to µ, RT when αU = 1. Proof. See the Appendix. Proposition 2 provides the model’s main results: if Treasuries’ contribution to the portfolios money services is equal to that of T-bills (i.e., αU = 1), then an increase in the convenience yield, measured through η, reduces the amount of repo issuance. Intuitively, as households’ preference for safe assets increases, their marginal utility for consuming money services becomes more important relative to their risk aversion. That is, to consume more money services, households are willing to take on more interest rate risk. This preference shock reduces the spread between a safe asset with a random payoff and a safe asset with a fixed payoff if both assets provide the same amount of money services. Thus, because in equilibrium the bank’s marginal cost to issue repo equals the marginal benefit of doing so (i.e., term premia), the amount of repo issuance decreases with η. In addition, the proposition shows how public safe asset issuance affects repo issuance. Specifically, an increase in T-bills outstanding decreases repos outstanding. As the amount of T-bills increase, households become satiated with safe assets, effectively reducing term premia and thus repo issuance. Interestingly, an increase in Treasuries outstanding has an ambiguous sign, highlighting an important trade-off between money services and risk. On the one hand, more Treasuries in the hands of households satiate their demand for safe assets and decreases repo outstanding, much like the effect of T-bill issuance. On the other hand, more Treasuries in the hands of households increase their risk exposure, increasing term premia, and thus the bank’s incentive to issue repos. In addition, an increase in Treasury issuance implies more repos are needed to finance them. The empirical analysis shows that the latter effects are stronger. Finally, unsurprisingly, an increase in the bank’s direct cost to create repos decreases repo issuance, a result that will be useful in the empirical section. Note that the partial derivative with respect to η has two components: one is related to a level increase in the demand for safe assets, and the other is related to a marginal increase in the 12

demand for safe assets. Eq. (25) shows that changes in the convenience yield capture changes in the marginal demand for safe assets. Thus, to relate theoretical results to the empirical analysis, the focus will be on the sensitivity of RP ∗ to movements in v 0 —that is, vη0 . 2.4. Repos backed by collateral not satisfying safe asset demand This section considers the case in which the risky asset used as repo collateral does not satisfy households’ demand for money services: αU = 0. This analysis should be interpreted as a world where either Treasuries do not provide any money services at all, or banks decide to issue repos backed by collateral classes that do not provide money services, such as equities. Under this specific setup, the model gives the following comparative statics. Proposition 3. If households have CARA utility with risk aversion γ, αU = 0 in Eq. (1), C(RP ) = 1 2 00 2 c × (RP ) , and the parameter conditions of Proposition 1 hold with v < 0 sufficiently small and γΘT > 1, then repo issuance has the following comparative statics:   ˜  1 E(S) 1 ∂RP ∗ 0 00 0 0 ˇ 2 ) − RT vη −γˇ = − −γvη (v + v RT κ κ1 − γˇ κ2 v + ˇ ∂η c |D| RT (1 + v 0 )     ∗ ∂RP (µ − RT ) 1 1 1 ˇ = − γ V RP −γˇ κ1 − γˇ κ2 v 0 + 1− + ˇ ∂c c2 c R |D| T     1 00 0 ˇ ˜ + γ V RP κ ˇ2 E(S)v RT RT γˇ < 0, κ1 + γˇ κ2 v − RT (1 + v 0 )  2 µ T) ˇ := Vˆ − , V RP (1 + v 0 )RT , and where κ ˇ 1 := ΘT + ΘU − w, κ ˇ 2 := ΘT + (µ−R c (1+v 0 )RT − 1 ˇ < 0 is the determinant of the Jacobian matrix of partial derivatives of Eq. (10) and (23) with |D| respect to µ, RT when αU = 0. Proposition 3 shows that the sensitivity of repo issuance depends on the underlying collateral’s ability to provide money services. Specifically, if the underlying collateral does not provide money services, an increase in households’ marginal demand for safe assets, vη0 , increases the wedge between assets that provide money services and those that do not. In the model, this increase in η increases term premia and prompts the banking sector to issue more repos. Proposition 3 captures the main intuition behind the existing literature: an increase in the demand for safe assets increases the private sector’s incentive to provide them and thus increases private safe asset creation. Unsurprisingly, Proposition 3 also shows that an increase in the cost of issuance prompts banks to reduce their repo issuance. The results in Proposition 3 will help empirically identify the model’s main mechanism. 2.5. Introduction of central bank repos The original model considered three assets in the economy: two publicly produced assets and one privately produced asset. In this section, the model introduces a fourth: repos issued by a central bank that households can hold directly. The new asset is intended to model the Federal Reserve’s RRP introduced in 2013.19 19 This policy tool allows the Federal Reserve to interact directly with cash investors, giving them an option to deposit funds with the central bank at a predetermined policy rate, effectively circumventing the traditional banking sector.

13

In this extension, households and the bank must also choose what fraction of their portfolio to invest in the central bank’s repo facility, θCB , which earns the policy rate RCB and contributes to the portfolio’s money services in the following way, M = RT θT + µαU θU + RRP αRP RP + RCB αCB θCB .

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Solving for household optimal portfolio choice gives the same pricing equations as the previous section Eq. (10) – (12), plus an additional one: ˜ E(S)(1 + αCB v 0 (M ; η))RCB = 1.

(27)

As before, if αCB > 1, then RCB < RT , and if αCB = 1, then RCB = RT . Turning to the bank’s portfolio problem, if µ > RCB , it is unattractive for the bank to invest in repos issued by the central bank. Therefore, as before, the bank and households split the total amount of Treasuries, the bank issues repos to households, and households hold the remaining assets in the economy. To simplify the analysis, I consider a case in which only long-term bonds exist (i.e., ΘT = 0) and αU = αRP = αCB = 1. In this case, the private market repo rate is equal to the central bank’s repo rate, and the characterization of the equilibrium collapses into two equations, ˜ E(S)(1 + v 0 (M ; η))RCB µ −1 RCB

=

1

(28)

˜ R). ˜ = −cov(S,

(29)

Although the equilibrium characterization looks identical to the one in the previous section, there is an important difference: the central bank interest rate is exogenous, and the amount invested in the central bank’s repo program is an equilibrium outcome. That is, in this model, the central bank sets the policy rate RCB , and the total amount of take-up at the central bank’s facility is determined in equilibrium, denoted by ΘCB . The other equilibrium variable is the risky asset’s expected return µ.20 Focusing on symmetric equilibrium so that the individual household’s portfolio choice coincides with aggregate take-up at the central bank’s repo facility, the following proposition characterizes the equilibrium. ˜ is sufficiently high enough, the equilibrium expected return Proposition 4. If ΘU − w > 0 and V(R) for the risky asset and the total amount of takeup in the central bank’s repo facility is given by Eq. (28) and (29), with RCB = RRP . The amount of repos issued by the private bank is given by C 0 (RP ∗ ) = µ−RCB , and households hold all of the central bank’s repo issuance and ΘU −(w+RP ∗ ) Treasuries. Proof. The proof is identical to the proof of Proposition 1 by relabeling ΘT as ΘCB and RT as RCB and using Eq. (28) and (29). Proposition 4 characterizes the equilibrium where the central bank sets the interest rate on its repo facility and households choose how much to invest in it. Both households and banks share the supply of Treasuries, and banks issue a positive amount of repos. This equilibrium shows that both the central bank and the private bank can issue repos to satisfy households’ demand for safe assets. From this equilibrium we can characterize how take-up in the facility and private repo 20 To simplify notation, I will use the same variable to denote the risky asset’s expected return and the amount of private repo issuance.

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issuance responds to changes in the demand for safe assets. As in the previous section, I consider the simplifying case when households have CARA utility and C(RP ) = 12 c × (RP )2 with c > 0. Proposition 5. If households have CARA utility with risk aversion γ, C(RP ) = 21 c × (RP )2 , and the parameter conditions of Proposition 4 hold with v 00 < 0 sufficiently small, then central bank repo issuance and private repo issuance have the following comparative statics:    −1 1 µ ∂RP ∗ ˜ CB vη v 00 RCB − v 0 ((1 + v 0 )RCB + 1) < 0 = − 1 γE(S)R η ∂η |D| c RCB   2    −1 γ ∂M γ ∂ΘCB µ ˆ − v 00 γRCB E(S) ˜ = vη − V RP −1 − + ∂η c RCB ∂µ RCB |D| !)   µ 1 γ Vˆ 0 ∂M 0 ˜ +γ − 1 (1 + v ) + , E(S)RCB vη c RCB ∂µ RCB ˜R ˜ − µ)2 ), V RP ˆ := Vˆ − where Vˆ := E(S(



µ RT

2 − 1 (1 + v 0 )RT , and |D| < 0 is the determinant of

the Jacobian matrix of partial derivatives of Eq. (28) and (29) with respect to µ, ΘCB . Proof. See the Appendix.

Proposition 5 shows how both private and public repo issuance respond to changes in households’ demand for safe assets. The effect over private repo issuance is similar to the one in Proposition 2: an increase in households’ preference to consume money services increases their willingness to hold risky assets with money services, thus decreasing the spread between µ and RCB and, consequently, private repo issuance. Keeping the focus on the change in households’ marginal demand for safe assets, the term accompanying vη0 in ∂ΘCB / ∂η is positive, implying that an increase in v 0 will increase take-up in the central bank’s facility. This result suggests that as households’ demand for safe assets increases, the central bank can help satisfy said demand. The results in Proposition 5 are consistent with the empirical results in Anderson and Kandrac (2017), which show that the Fed’s RRP facility crowds out private repo issuance. The following section gives more details on the model’s main assumptions and predictions. 2.6. Discussion of modeling assumptions and equilibrium outcome An important difference between the model in this paper and those in the existing literature is how long-term safe assets contribute to the economy’s total supply of safe assets. Specifically, Eq. (1) assumes that long- and short-term safe assets are perfect substitutes in providing money services. The model focuses on the case where the contribution of each asset is assumed to be equal: αU = αRP = 1. The alternative assumptions used in the literature can be summarized by inspecting u(˜ c + v(M )),

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where differences arise in the characterization of the stock of money services (M ) and how agents consume those money services (v). Greenwood, Hanson and Stein (2015) assume that M only consists of short-term safe assets. In their framework, short maturity is a necessary condition to satisfy the demand for money services. But some types of cash investors may not have such strong maturity preferences. For example, securities lenders are active lenders in money markets and hold long-term illiquid portfolios, and corporate cash managers are said to have a preference for 15

highly liquid portfolios, yet have diverse portfolio allocations, which include long-term Treasuries (see Duchin et al., 2017).21 Importantly, Krishnamurthy and Vissing-Jorgensen (2012) provide strong evidence that longterm US Treasuries have a significant premium because of their safe asset status. In their theoretical setup, they assume that investors’ demand for safe assets can be expressed by a short-term component vST (·) and a long-term component vLT (·).22 This view is consistent with the idea that the demand for safe assets stems from different types of safety/liquidity needs. For example, shortterm safety is a useful means to store value, allowing investors to access funds at a moment’s notice. Overnight repos are more likely to provide short-term safety. Long-term Treasuries may not be as useful, not only because of term premia but also because of the market’s liquidity. In effect, buying a Treasury and then selling it the following day could result in significant round trip costs when bid/ask spreads are large. Instead, long-term Treasuries provide long-term safety by giving absolute certainty of ultimate repayment in the future. Naturally, US Treasuries are more useful than repos to fill that role. The exact way in which money services are consumed is still an open empirical question. The starting point of this paper is that long- and short-term safe assets are equally useful in providing money services, but there are inherent differences in the short-run risks they pose. The response of repo issuance to changes in households’ preference to consume money services depends on the bank’s incentive to supply safe assets. Importantly, the model assumes that the marginal cost to issue an additional dollar of repo is increasing in the amount of total repos outstanding. This assumption is motivated, in part, by new regulatory initiatives that have made repo issuance more costly. Specifically, keeping bank equity fixed, regulatory initiatives, such as the leverage ratio, act like a limit on the size of a bank’s balance sheet. This restriction has caused banks to cut back on low-yielding, balance sheet-intensive activities, such as repo backed by Treasuries (see Duffie, 2017).23 The effect of regulation can also be appreciated on quarter-end dates, where the regulatory reporting frequency of some jurisdictions prompts banks to significantly reduce their repo activity on those dates. This effect has a meaningful impact on volumes and rates (see Munyan, 2017) and suggests that regulation increases the marginal cost of repo issuance. Differences in regulatory jurisdictions also suggest a differential response to changes in the demand for safe assets, which will motivate part of the empirical analysis in the following section. Turning to the model’s main insights, Proposition 2 provides the intuition behind the mechanisms at play. The model’s main result is the sensitivity of repo issuance to changes in households’ preference to consume money services, captured through η. Specifically, an increase in η increases households’ preference to consume money services relative to their risk exposure. Thus, at the margin, they are less concerned about the risk of a long-term safe asset, which compresses its term premia. With a smaller term premia, the bank has less incentive to issue repo, and thus total repos outstanding decreases. The model extension in Section 2.3 directly shows how the results in Proposition 2 can coexist with the existing literature. If the collateral backing the private safe asset does not satisfy agents’ 21 Other examples of active cash investors with diverse portfolios are sovereign wealth funds and insurance companies. 22 In their paper, v LT (·) is written as µ(·). I adopt a different notation to avoid confusion with the model in this paper. 23 Although outside the scope of the model, absent regulatory restrictions, the marginal cost to issue repo may be increasing because lenders internalize banks’ additional risk-taking. That is, an increase in repo would increase counterparty credit risk, increasing the cost of all other activities the bank may be pursuing.

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demand for money services, an increase in the demand for safe assets increases the spread between assets that do and do not satisfy the demand for safe assets. Thus, banks have more incentive to engage in safe asset “creation.” The key insight is that true private safe asset creation occurs only when the firm creating them holds assets that are not safe assets in the first place. In the model, an increase in the total amount of T-bills reduces households’ need to satisfy their demand for safe assets, reducing the bank’s incentive to issue private ones. That is, changes in the total stock of short-term public safe assets operates through a demand channel by satiating the demand for safe assets. The response to an increase in Treasury bonds outstanding has two opposing effects: as with T-bills, they fill the demand for safe assets, but they also increase households’ allocation to them, increasing their risk exposure and thus term premia. Krishnamurthy and Vissing-Jorgensen (2015) characterize similar effects of changes in US Treasuries outstanding. They call these effects bank portfolio substitution effect and household debt substitution effect and note that the response of private safe asset creation depends on whichever dominates. In the empirical section I show that the correlation between Treasury note issuance and aggregate repo issuance is positive, suggesting that the bank portfolio substitution effect dominates. Finally, Section 2.5 studies the effect of a central bank’s initiative to issue repos directly to cash investors, such as the Federal Reserve’s RRP. Proposition 5 shows that the amount of central bank repos increases as the demand for money services increases. The intuition is that households cannot directly access the Treasuries backing the central bank’s repos (unmodeled). Because the central bank can issue short-term safe assets, an increase in the demand for safe assets increases participation in its facility. 3. Empirical analysis The theoretical model motivates a number of empirical exercises. Following an analysis similar to Sunderam (2014), the strategy is to empirically test how the convenience yield—which in the model measures households’ marginal demand for safe assets [see Eq. (25)]—affects repo issuance. The baseline model, and its extensions, give the following empirical predictions. * Prediction 1: From Proposition 2, an increase in the demand for money services compresses term premia for long-term safe assets, reducing private repo issuance backed by those assets. That is, an increase in the convenience yield reduces the amount of Treasury repo. * Prediction 2: From Proposition 2, the supply of short-term public safe assets reduces households’ marginal demand for more, decreasing the supply of private repo backed by long-term safe assets. That is, an increase in short-term T-bills reduces the amount of Treasury repo. * Prediction 3: From Proposition 2 and Proposition 3, an increase in banks’ costs of issuing repos reduces the amount of repo, irrespective of whether the underlying collateral can satisfy households’ demand for money services. That is, an increase in the cost of issuance should decrease the total amount of repo, independent of the underlying collateral. * Prediction 4: From Proposition 3, an increase in the demand for money services widens term premia for assets that do not provide money services, increasing private repo issuance backed by those assets. That is, an increase in the convenience yield increases the amount of repo backed by riskier collateral classes.

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* Prediction 5: From Proposition 5, an increase in the demand for safe assets increases the central bank’s issuance of safe assets to the nonbanking sector. That is, an increase in the convenience yield increases take-up in the Federal Reserve’s RRP program. The main result of the paper comes from Prediction 1. Contrary to previous results, the model predicts that a higher convenience yield (i.e., an increase in η) decreases the amount of US Treasury repo outstanding. Prediction 2 posits a substitution effect between private and public short-term safe assets. Prediction 3 states that, irrespective of the underlying collateral, an increase in the cost of issuance decreases the amount of repo issuance, and Prediction 4 predicts that the typical sensitivity of private safe asset creation arises when the underlying collateral is not a safe asset to begin with. These last two results are useful to dispute possible alternative explanations detailed in the following section. Finally, Prediction 5 shows that cash lenders will “lend” to the central bank when their demand for safe assets increases. 3.1. Alternative explanations The main mechanism of the paper operates though changes in investors’ demand for safe assets. An alternative explanation could posit that changes in the convenience yield capture changes in dealers’ willingness to supply safe assets (i.e., bank supply shock). This could operate through changes in direct or indirect costs of issuing repos—potentially driven by changes in dealers’ own liquidity needs or solvency risk or mechanically through changes in the total amount of collateral needed to be financed. If the convenience yield were measuring changes in repos financing costs, then short-term rates related to repo should be a better determinant of repo issuance. Also, if the convenience yield were measuring changes in dealers’ liquidity or solvency risk, then measures of dealer default should have an effect on the convenience yield’s sensitivity. In addition, if the convenience yield were measuring changes in the direct cost of repo issuance, it would affect all types of repos, irrespective of the underlying collateral’s ability to provide money services. Changes in the stock of short-term public safe assets has a direct effect on investors’ safe asset holdings and hence their demand for alternative safe assets. It is unlikely that these changes would affect the supply of repos because investing in short-term T-bills financed though repos would entail a loss (i.e., short-term T-bill rates are lower than repo rates). In effect, Fig. 1 shows that the fourweek T-bill rates trade lower than the overnight Treasury repo rate in the GCF Repo and non-GCF Repo tri-party market, even without adjusting for the difference in maturity. This difference in rates suggests that changes in the total amount of short-term T-bills does not affect the supply of repo: the exclusion restriction is the unprofitability of issuing repo backed by short-term T-bills.24 [Insert Fig. 1 Here] Finally, if the convenience yield were measuring changes in the direct or indirect costs of supplying repo, it would be hard to find the statistical result at the individual dealer level. Controlling for individual measures of lagged issuance and default probability, changes in costs would have to occur across dealers through some other unspecified mechanism. In the empirical section I control for these effects and provide additional evidence to dismiss supply-driven explanations for the main result. 24 It is also important to note that investing in T-bills financed through repo does not increase the amount of high quality liquid assets in order to comply with new liquidity regulation because those assets would be considered encumbered, discarding any potential regulatory benefits.

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3.2. Data I use the tri-party allocation data collected by the Federal Reserve Bank of New York (FRBNY) and used internally at the Federal Reserve Board (Board). The data are collected from the two tri-party clearing banks and contain the total amount borrowed by each dealer in the tri-party system, per collateral class, at a daily frequency. From these data, I can calculate changes in the amount of repos outstanding at the borrower level, a proxy for repo issuance. The analysis focuses on primary dealers and the Federal Reserve’s RRP program.25 The period of analysis is between January 2, 2009 and March 25, 2017 at a daily frequency.26 This data source is the same one used in Copeland, Martin and Walker (2014) and Munyan (2017). Those papers provide a detailed description of the data. Fig. 2 highlights a peculiar pattern of repo volumes at quarter-end (also see Fig. 3). Munyan (2017) shows that some dealers choose to reduce the total amount of their repos outstanding to “window dress” the size of their balance sheet. Because the incentive to window dress is outside the scope of this paper, I exclude quarter-end observations. Specifically, for any given quarter-end date t, I exclude {t, t + 1}. In case lagged repo issuance is used as a control variable, I also exclude dates {t + 2, t + 3, · · · , Nlag }, where Nlag is the number of lags. Table 1 presents summary statistics of the data, excluding quarter-end observations.27 [Insert Fig. 2 Here] [Insert Fig. 3 Here] [Insert Table 1 Here] Following a specification similar to Sunderam (2014) and the insight from Eq. (25), the convenience yield for holding safe assets is measured by the return difference between holding a risk-free safe asset (T-bills) and a contract with a risk-free payoff that does not imply physical ownership of an asset. In the data, I use the four-week T-bill rate for the safe asset rate, downloaded from the Federal Reserve H.15 Statistical Release, and the one-month OIS rate for the risk-free rate, downloaded from Bloomberg. Fig. 4 shows the time series of the convenience yield. [Insert Fig. 4 Here] Using Treasury auction results published by TreasuryDirect, I construct a time series of the total amount of marketable T-bills and Treasury notes and bonds outstanding. Given that the model has predictions on short-term T-bill issuance, I consider the total amount of T-bills outstanding with one month left to mature. Focusing on short-term T-bill issuance ensures that the exclusion restriction holds to capture investor demand shocks. 3.3. Empirical results The empirical results in Sections 3.3.1 through 3.3.8 support the model’s main predictions, discard alternative supply driven explanations, and provide a number of robustness checks for the sensitivity of private repo to the demand for safe assets. Section 3.3.9 shows the empirical results for the the Federal Reserve’s RRP program. 25 The set of primary dealers considered in this paper are all dealers that were official counterparties of the New York Fed at one point during the sample period. 26 The repo data available to the Board start in January 2009. 27 All results are robust to excluding more days around quarter-end dates.

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3.3.1. Baseline sensitivity of convenience yield and US Treasury repo Prediction 1 motivates the empirical specification that measures the sensitivity of private repo issuance to the convenience yield. This preduction leads to the following regression, ∆log(RepoOutt ) = α + β(T Bill − OIS)t−1 + t ,

(31)

where RepoOutt is the total US Treasury repos outstanding at time t for all primary dealers, (T Bill − OIS)t−1 is the convenience yield measured in t − 1, and ∆ is the first-difference operator. That is, changes in repos outstanding—a proxy for repo issuance—are regressed against lagged measures of the safe asset convenience yield. For robustness, the remaining specifications control for lagged repo issuance. The lags serve to control for spurious relation that may stem from any possible autocorrelation in the data.28 Regressions use Newey-West errors with 21-day lags (approximately one calendar month) to control for possible autocorrelation in the error terms. X ∆log(RepoOutt ) = α + β(T Bill − OIS)t−1 + γj ∆log(RepoOutt−j ) + t . (32) j

Some specifications include week-of-year fixed effects to capture any possible seasonality in the time series (for example, tax paydowns or the Fannie float period). These specifications use clustered errors around the week-of-year fixed effect.29 Table 2 shows results for specifications with and without week-of-year fixed effects. The sensitivity of primary dealers’ repo issuance to the convenience yield is positive and statistically significant at a significance level of 1% for regressions without week-of-year fixed effects.30 Because the convenience yield is negative, a positive loading implies that a lower convenience yield (that is, a higher marginal demand for safe assets) reduces the total amount of repo outstanding, consistent with Prediction 1. [Insert Table 2 Here] 3.3.2. Inclusion of financial data controls Tables 3 shows the sensitivity of private repo issuance to the convenience yield, controlling for a number of financial variables that can account for other possible mechanisms at play. For example, if the response of private repo issuance to the convenience yield is due to changes in repo pricing, then lagged short-term rates relevant to repo markets should have an effect on the convenience yield’s sensitivity. Including the overnight Treasury repo rate of the GCF Repo market does not alter the magnitude or significance of the convenience yield.31 28 As shown in Table 2, the baseline results are robust to using zero to four lags. Other results are also robust to using a smaller number of lags. 29 Following the existing literature, previous versions of this paper contained month-year fixed effects. Although the results are statistically and economically similar to those without them, it is unclear how meaningful month-year fixed effects are at a daily frequency. The current version of the paper does not report these results but are available upon request. 30 Results with week-of-year fixed effects become statistically significant when including financial data controls. See section 3.3.2. 31 The GCF Repo rate is the overnight Treasury DTCC GCF Repo Index rate. Curiously, the sensitivity of repo issuance to the GCF Repo rate is positive, which can be understood by noting that primary dealers are typically lenders to the GCF Repo market, not borrowers. A better proxy for the cost of repo issuance in the non-GCF Repo tri-party repo rate (BNY Tri-Party Repo Index), which has a shorter time series. Using the non-GCF Repo tri-party repo rate does not alter the statistical significance of the convenience yield on repo issuance.

20

[Insert Table 3 Here] If the response of private repo issuance to the convenience yield is due to liquidity or solvency shocks faced by dealers, then lagged default probability measures should have an effect on the convenience yield’s sensitivity. Including the lagged investment-grade credit default swap (CDS) index does not alter the magnitude or significance of the convenience yield.32 If the convenience yield is capturing changes in the riskiness of repo itself, then measures of nonprice contracting terms, such as the haircut, would have an effect on the convenience yield’s sensitivity. Including the lagged weighted average margin of tri-party Treasury repo does not alter the magnitude or significance of the convenience yield.33 The convenience yield may be capturing general risk appetite in equity or bond markets. Controlling for both lagged implied and realized volatility of both the stock market and the ten-year Treasury does not affect the main results. Finally, including a measure of long-term US Treasury term premia, the ten-year minus two-year yield on off-the-run Treasuries, only sharpens the effect of the convenience yield. It is important to note that in the model the response of private repo issuance operates through changes in term premia. Empirically, one might expect that including term premia would, at least, attenuate the sensitivity to the convenience yield. This is not the case empirically because the model term premia is over short horizons—that is, the expected excess return of a long-term safe asset over a short period. The ten-year minus two-year yield captures additional long-term considerations that are not modeled. In addition, term premia in the US Treasury market responds to multiple factors, making the convenience yield a more precise measure to capture investors’ demand for safe assets. 3.3.3. Changes in US Treasury supply In the model, changes in the supply of public safe assets has an effect on repo issuance. Taking into account changes in the amount of US Treasuries outstanding leads to the following regression: ∆log(RepoOutt )

= α + β(T Bill − OIS)t−1 +

X

γj ∆log(RepoOutt−j ) +

j

η∆log(ShT BillsOutt ) + η 0 ∆log(U ST N otesOutt ) + θXt−1 + t , (33) where ∆log(U ST N otesOutt ) and ∆log(ShT BillsOutt ) are log changes in the total outstanding of marketable US Treasury bonds and short-term T-bills outstanding (i.e., T-bills with less than onemonth maturity), respectively. The reason behind focusing on only short-term T-bills, rather than all T-bills outstanding, is to capture changes in the most money-like public safe assets. In addition, this focus sharpens the exclusion restriction, as the yield on short-term T-bills is smaller than that on repo rates. Lagged private repo issuance and financial variable controls are also included. Table 4 shows the results for the specification in Eq. (33). The positive correlation between primary dealer repo issuance and US Treasury bond issuance shows that the bank portfolio substi32 The

investment-grade CDS index is the Markit CDX North America Investment Grade Index. margin is the value of the collateral over the amount of money lent minus one. It is economically equivalent to the haircut, which is one minus the money lend over the amount of collateral. These data come from the tri-party allocation data. 33 The

21

tution effect described in Krishnamurthy and Vissing-Jorgensen (2015) is stronger.34 In the model, this substitution occurs, in part, because term premia widens as households bear more interest rate risk. But there is also a mechanical effect at play: long-term Treasury issuance is typically financed through repos. Thus, changes in US Treasury notes may be affecting dealers’ willingness to supply repos as they need to finance more Treasuries outstanding. For these reasons, long-term Treasury issuance would be an unsuitable instrument to isolate demand shocks. [Insert Table 4 Here] In contrast, the loading on short-term T-bill issuance is in line with Prediction 2: an increase in the supply of short-term public safe assets induces the private sector to produce less of them. This result means that changes in short-term US T-bills outstanding isolate demand shocks, which suggests its validity as an instrument in the instrumental variable (IV) specification. 3.3.4. Instrumenting with changes in short-term T-bill supply As mentioned in the previous section, changes in the total supply of short-term T-bills should only affect demand because the yield on short-term T-bills is lower than the repo rate. Fig. 1 shows that the four-week T-bill rate is lower than both the overnight Treasury repo rate in the GCF Repo and non-GCF Repo market, meaning that dealers would have negative carry if they purchased short-term T-bills and financed them with repos. Thus, it is improbable that changes in short-term T-bills outstanding would capture supply effects. In addition, T-bill auction dates are known days in advance; thus, the variation of the amount of T-bills outstanding is exogenous to daily changes in the convenience yield or repo issuance. This implies that the variation in the short-term T-bill supply is a good instrument to capture changes in demand. These observations prompt the following two-stage regression, CYt−1 ∆log(RepoOutt )

= α1 + η1 ∆log(ShT BillsOutt−1 ) + ˆ t−1 + = α2 + β CY

X

X

γ1j ∆log(RepoOutt−j ) + θ1 Xt−1 + t−1

j

γ2j ∆log(RepoOutt−j ) + θ2 Xt−1 + t ,

j

ˆ t−1 is the fitted values of the first-stage regression. That is, in the first stage, the lagged where CY convenience yield is regressed onto lagged short-term T-bill issuance and lagged financial controls. In the second stage, private repo issuance is regressed onto the fitted values of the lagged convenience yield and financial variable controls. Table 5 shows the results of the two-stage regression, with and without week-of-year fixed effects. The first stage shows that an increase in short-term T-bill issuance increases the convenience yield (that is, makes the spread between T-bills and OIS less negative) and thus decreases the demand for safe assets. The second-stage regression captures the main sensitivity of the model: as the portion of the convenience yield attributed to demand increases (that is, the demand for safe assets decreases), private repo issuance increases. These results confirm the main mechanism described in the model. 34 Nagel (2016) also suggests that in the short run, changes in public safe asset supply would be absorbed by intermediaries, resulting in an increase in privately produced safe assets.

22

(34)

[Insert Table 5 Here] 3.3.5. Different collateral classes The model also gives insights into different sensitivities for repos backed by collateral that does not provide money services. Prediction 3 says that if issuance costs increase, repo issuance backed by all types of collateral classes should decrease. Table 6 shows the different collateral class loadings for the specification in Eq. (33), with and without week-of-year fixed effects (Panels A and B, respectively), and the IV specification in Eq. (34) (Panel C). The results can also be visualized in Fig. 5, which shows the the loadings, and associated confidence intervals at 95%, for the three types of regression estimates in Table 6. US Treasuries are the only collateral class with a statistically significant response across all three specifications. The remaining collateral classes do not have statistically significant responses to the convenience yield, making it unlikely that the convenience yield is capturing changes in the costs of repo issuance. [Insert Fig. 5 Here] [Insert Table 6 Here] Although the remaining assets do not provide any robust insights, interesting patterns do emerge. The first observation is that the only other collateral class with a sensitivity similar to Treasury repos is agency mortgage-backed security (MBS) repos. Given agency MBS’s government guarantee and its eligibility for open market operations by the Federal Reserve, it is not surprising that the sensitivity of its repo issuance is similar to that of US Treasuries. That is, the safe asset status of agency MBS makes it comparable to long-term US Treasuries. The second observation is that from Prediction 4, one might expect that the sensitivity of repo backed by riskier collateral classes should be in line with the existing literature on private safe asset creation. That is, repo issuance should increase whenever the demand for safe assets is high. The point estimates for riskier collateral classes are insignificant, but some collateral classes, such as corporate bonds, exhibit negative loadings and have relatively small confidence intervals, suggestive of the mechanism behind Prediction 4. More generally, this result raises the question as to whether repos backed by riskier collateral classes can in fact provide money services, as they may have important collateral and counterparty risk components that the model in this paper is not designed to capture. One important exception is the IV specification of repo backed by agency debentures. This asset class may include both short- and long-term unsecured debt issued by government-sponsored entities (GSEs). Short-term agency debentures are issued weekly and can have maturities ranging from overnight to one year. One hypothesis behind the IV result is that as the demand for safe assets increases, GSEs issue more agency debentures, in line with the typical sensitivity of private issuance to the demand for safe assets.35 The increase in issuance prompts dealers to purchase more of these securities and to finance them with repos. From this perspective, repo issuance backed by agency debentures would increase with the demand for safe assets. Incorporating the incentives of the original issuers, along with those of dealers intermediating funding, is an area of future research. 35 Given that the main purpose of the model is to understand repo issuance backed by US Treasury collateral, the model does not capture the incentives of the original security issuer.

23

3.3.6. Different regulatory jurisdictions Primary dealers associated with foreign bank holding companies are subject to different regulatory requirements. Specifically, in many jurisdictions, capital and liquidity regulations are measured at a month- or quarter-end frequency.36 These differences effectively mean that, outside of quarterend, domestic dealers have a higher cost of repo issuance than foreign dealers. The model suggests that banks with higher issuance costs should exhibit lower repo issuance. Empirically, this result implies that repo issuance by foreign dealers should have a higher sensitivity to the convenience yield. Table 7 shows the jurisdictional results for the specification in Eq. (33), with and without week-of-year fixed effects (Panels A and B, respectively), and the IV specification in Eq. (34) (Panel C). Primary dealer repo issuance is separated into dealers from the United States, the United Kingdom (UK), and the rest of the world as well as combinations between these partitions. Note that dealers in the UK are treated separately because in January 2017 the Bank of England changed banks’ reporting requirements from month-end averages to daily averaging, implying that their regulatory costs increased toward the end of the sample period. [Insert Table 7 Here] Panels A and B indicate that the sensitivity is larger for non-US dealers, confirming that dealers with lower issuance costs will have a larger response to the convenience yield. Focusing on Panel C, all jurisdictional partitions give statistically significant results, and the difference between the two most extreme cases of regulatory costs (US versus rest of the world ex-UK) is in line with the model’s prediction. 3.3.7. Different repo maturities The maturity of the underlying repo is likely to affect its ability to provide money services. In effect, it is reasonable to expect that shorter-term repos would have more money-like properties, making them more sensitive to changes in the demand for safe assets. Table 8 shows the repo maturity results for the specification in Eq. (33), with and without week-of-year fixed effects (Panels A and B, respectively), and the IV specification in Eq. (34) (Panel C). The table shows results for repos with maturity less than one week, open contracts, maturity less than one week plus open contracts, and maturity greater than one week.37 [Insert Table 8 Here] Panels A and B confirm that regressions with short-term repos have a stronger sensitivity than the aggregate. This is because short-term repos provide more money services (investors get their funds back sooner) and thus have greater sensitivity to changes in the convenience yield. Curiously, in Panels A and B, repos with maturities greater than one week increase with a higher convenience yield, which suggests a portfolio rebalancing effect between long- and short-term repos, which is not captured by the model. Panel C, which instruments for changes in the demand for safe assets, does not show significant sensitivity between longer-term repo issuance and the convenience yield. The null result in the IV specification suggests that the sensitivity captured in Panels A and B may be driven by something unrelated to changes in investor demand for safe assets. 36 Quarter-end

disruptions are driven, in part, by foreign firms’ regulatory reporting frequencies. repos are automatically rolled over every day, with both counterparties having the option to terminate the contact on any given date. It is unclear whether these contracts should be considered to have short or long maturity. 37 Open

24

3.3.8. Weekly repo issuance All of the empirical results so far have focused on daily repo issuance. Analyzing high-frequency sensitivities is important to understand private safe asset creation using public safe assets as collateral. Moreover, daily changes in repos outstanding are likely to be more relevant, as a large fraction of the tri-party repo market is overnight (see the discussion in Section 3.4).38 But the results also hold at lower frequencies. Table 9 shows the weekly results for the specification in Eq. (33), with and without week-of-year fixed effects (Panels A and B, respectively), and the IV specification in Eq. (34) (Panel C). In this specification, five-day changes in repo outstanding are a proxy for weekly repo issuance. Each panel reports results with two, three, and four lags of weekly repo issuance as controls. [Insert Table 9 Here] In spite of the predominance of short-term repos, these results show that the main sensitivity of the paper still holds at lower frequencies. 3.3.9. Federal Reserve’s RRP program Prediction 5 suggests that the sensitivity of the Federal Reserve’s RRP program to the convenience yield should be the opposite of that of the private sector. The analysis of the Federal Reserve’s RRP program starts on the December 23, 2013, when the cap on individual investor participation was raised from $1 billion to $3 billion, increasing the program’s usage and significance. Table 10 presents the results of the RRP program for the specification in Eq. (33), with and without week-of-year fixed effects (Panels A and B, respectively), and the IV specification in Eq. (34) (Panel C). For comparison, the table reports the sensitivity of primary dealer issuance over the same period. [Insert Table 10 Here] The regression results in Panel A and Panel B are consistent with the model. Whenever the demand for safe assets increases, take-up at the Federal Reserve’s repo facility increases, suggesting that the Federal Reserve does in fact provide safe assets to the economy when needed, in line with Carlson et al. (2016). Interestingly the IV specification for the RRP program does not give a statistically significant result, which may be due, in part, to the incentives investors have to participate in the RRP program. Anderson and Kandrac (2017) show that cash investors’ participation in the RRP program increases their bargaining power relative to borrowers, allowing them to increase the repo rate on private issuance. Therefore, participation in the program may be driven by investors’ incentive to improve terms of trade with private issuers. 3.3.10. Simultaneous equations Finally, the previous analysis can be repeated by taking advantage of individual borrower activity and characteristics. Focusing on primary dealers that have Treasury repo activity thought the entire sample and dealers that have individual CDS quotes, individual dealer data can be used to isolate the effect of the convenience yield. Specifically, I estimate the following system of equations jointly, 0 ∆log(RepoOutit ) = αi + β(T Bill − OIS)t−1 + θXt−1 + θi Zit−1 + it ,

(35)

38 Copeland, Martin and Walker (2014) and Krishnamurthy, Nagel and Orlov (2014) report that the vast majority of tri-party repos overnight or have a maturity of a few days. The data used in this paper confirm that observation.

25

0 0 using Xt−1 , Zit−1 , and ∆log(ShT BillsOutt−1 ) as instruments. In this specification, Xt−1 are aggregate financial controls used in previous sections: lagged overnight Treasury GCF Repo rate, lagged implied and realized volatility of both the stock market and the ten-year Treasury bond, and the ten-year to two-year slope of the Treasury yield curve. Zit−1 are controls relevant to each individual dealer: four lags of repo issuance, lagged CDS quotes, and lagged Treasury repo margins. The estimation considers a weighting matrix using Newey-West errors with 21 lags and the errors are also estimated using Newey-West with 21 lags. The estimate for the sensitivity of the lagged convenience yield on private Treasury repos (i.e., β) is 1.467, at a 1% significance level (error estimate of 0.217).39 This result provides robust evidence that the sensitivity of repo issuance to the convenience yield captures changes in demand rather than supply-driven explanations such as an increase in issuance costs or changes in risk profile. That is, when controlling for individual risk and liquidity, and instrumenting demand shocks using changes in short-term T-bill outstanding, there is a highly statistically significant effect of the convenience yield on private Treasury repo issuance, which operates through investors’ demand for safe assets.

3.4. Discussion of empirical results The empirical results support the model’s main prediction: as the demand for safe assets increases (that is, the convenience yield decreases), issuance of private repo backed by public safe assets decreases. The sensitivity is present in standalone regressions and when controlling for variables that capture alternative mechanisms at play such as changes in dealers’ counterparty risk or changes in dealers’ costs of issuing repos. The controls do not alter the main sensitivity, and the results are robust to different specifications, seasonal effects, and time periods.40 In addition, the statistically insignificant finding using riskier collateral classes supports the hypothesis that the convenience yield is not capturing changes in the cost of issuing repo. Importantly, changes in the total stock of public short-term safe assets can isolate the demand effect. That is, changes in short-term T-bills outstanding does not affect repo supply because repo financing costs are larger than short-term T-bill yields. Dealers would lose money if they expanded their repo book using T-bills as collateral.41 Also, given that T-bill auction schedules are known in advance and the high frequency of the analysis, changes in the total supply of short-term safe assets are exogenous to the variables of interest. Thus, changes in short-term T-bills satisfy the exclusion restriction and have exogenous variation. The use of this variable as an instrument in aggregate and simultaneous equation estimations—which have the ability to control for individual dealer characteristics—provides very strong evidence for a demand-driven sensitivity. Additional empirical specifications show that the sensitivity of repo issuance is higher for firms that have lower costs of repo issuance (i.e., foreign firms) and for repos with shorter maturity (i.e., repos that provide more money services). Although the paper’s main results also hold at a weekly frequency, it is important to note that the daily frequency is likely to be more informative. In effect, the vast majority of tri-party Treasury repos are overnight or less than one week; thus, it is reasonable to expect that any meaningful sensitivity of repo issuance would be at a daily frequency. Because of their short maturity, repos are among the most flexible liabilities in dealers’ balance sheets, allowing them to expand and contract 39 These

results are statistically similar to a panel specification. results are also robust to the inclusion of month-year fixed effects. 41 This finding is consistent with Lenel (2017) and the model in this paper: financial intermediaries do not hold levered positions in short-term public safe assets. 40 The

26

their repo activity at a moment’s notice. This flexibility can be clearly seen in the dramatic swings of repos outstanding on quarter-end dates, which stem from dealers’ desire to window dress and thus have to be excluded from the analysis. Dealers’ flexibility of their repo activity suggests that the elasticity of repo supply is high, and any significant change in repos outstanding will be at a daily frequency. The results in the paper give a nuanced view on private safe asset creation. As the demand for safe assets increases, there is substitution from private safe assets backed by public ones to public safe assets. From this perspective, the overall stock of money assets has not changed, but its composition has. To gauge the economic magnitude of these effects, consider the weekly estimates reported in Panel A of Table 9. A back of the envelope calculation suggests that a one standard deviation increase in the convenience yield (i.e., decrease in demand for safe assets) leads to a weekly increase of approximately $ 4 billion US Treasury repos.42 For comparison, the standard deviation of weekly changes in US Treasury repo is approximately $24 billion. The mechanism of this paper is markedly different than the existing literature on safe asset creation, where financial firms in fact create new safe assets to satisfy the increase in demand. Putting these results together suggests that an increase in the demand for safe assets will decrease the amount of private safe assets in the form of Treasury repos and increase the amount of private safe assets backed by riskier collateral. The net effect on the overall stock of private safe assets is unclear and hard to quantify. First, directly comparing with estimates from the existing literature may be misleading given the different sample periods and methodologies.43 Second, to understand the overall effect of investors’ demand for safe assets on private safe asset creation, it would be necessary to measure all private safe asset creation. Finally, the results from the RRP program suggest that by directly issuing repos to a broader class of investors, central banks can supply public safe assets to the economy when their demand is high. 4. Concluding remarks This paper provides evidence that the private sector’s ability to satisfy the demand for safe assets depends on the type of liabilities it creates. Contrary to standard results, the actual creation of private safe assets is limited if the underlying collateral is a public safe asset. This paper argues that the creation of private safe assets with long-term public safe assets is beneficial because it shifts risk to agents that have a higher tolerance for it. As the demand for safe assets increases, differences in risk tolerance are less meaningful. Thus, long-term safe asset term premia are compressed, reducing the incentive to produce private safe assets. This insight has implications on liquidity regulation and wholesale funding in general. The model shows that the banking sector can provide an important service by assuming the risk of government debt and issuing short-term claims to satisfy the demand for safe assets. But this operation does not 42 Specifically, multiplying the point estimate by the weekly standard deviation of the convenience yield, and taking into account the average weekly repo outstanding, one can back out a rough approximation of the weekly change in repo in response to changes in the convenience yield. 43 The paper most directly comparable to this paper is the study of the ABCP market in Sunderam (2014). Employing the same back of the envelope calculation of the previous paragraph, and using the average total outstanding between 2009 and 2017, suggests that a one standard deviation increase in the convenience yield (i.e., decrease in demand for safe assets) leads to a weekly decrease of approximately $0.8 billion in ABCP.

27

create safe assets; it merely transforms them from private safe assets to public ones. The paper’s analysis implies that the safety premium of US Treasuries is not the consequence of a deep and liquid wholesale funding market that allows agents to monetize assets seamlessly. Rather, the results suggest that US Treasuries’ safety premium comes from the securities themselves, highlighting the importance of money services that long-term safe assets can provide. In addition, the results show that the Federal Reserve can expand the public supply of safe assets with its RRP program. By circumventing the banking sector and issuing liabilities directly to the nonbanking sector, the Federal Reserve can satisfy the demand for safe assets without relying on the traditional banking sector or altering its portfolio holdings. This effect can have important macroprudential implications. Appendix Proof of Proposition 2. equilibrium equations, T1

=

T2

=

The result is derived from invoking the implicit function theorem.

˜ E(S)(1 + v 0 (M ; η))RT − 1 = 0 ˜ ˜ ˜ E(S(R − µ)) + E(S)(1 + v 0 (M ; η))µ − 1 = 0,

Consider the two (36) (37)

where T1 and T2 stems from rewriting Eq. (10) and (23) for the case αU = 0. Recall that the equilibrium variables are RT and µ, and the Proposition’s cost function is RP = 1c (µ − RT ). Thus the result depends on studying the sensitivities of µ − RT with respect to model parameters ∂RT ∂x ∂µ ∂x

!

=−

" |

∂T1 ∂RT ∂T2 ∂RT

∂T1 ∂µ ∂T2 ∂µ

{z

:=D −1

#−1

}

∂T1 ∂x ∂T2 ∂x

!

,

(38)

˜ S˜ − µ)); therefore, ˜ + v 0 (M ; η)) and h := E(R( where x ∈ {η, ΘT , ΘU , c}. To simplify the derivation, define g := E(S)(1 ∂T1 ∂RT ∂T1 ∂µ ∂T2 ∂RT ∂T2 ∂µ

= = = =

g+

∂g RT ∂RT

(39)

∂g RT ∂µ ∂h ∂g + µ ∂RT ∂RT ∂h ∂g + µ + g. ∂µ ∂µ

(40) (41) (42)

First, I calculate the inverse of D, which has the following determinant,

|D|

= =

∂T1 ∂T2 ∂T1 ∂T2 − ∂RT ∂µ ∂µ ∂RT     ∂g ∂h ∂g ∂g ∂h ∂g ∂h − RT + µ+ RT g + g + g2 . ∂RT ∂µ ∂µ ∂RT ∂µ ∂RT ∂µ

28

(43)

In this case, the equilibrium in Proposition 1 results in the following household consumption and money holdings: c0 M

e0 − ΘT − (ΘU − w)

=

RT ΘT + µ(ΘU − w) − (µ − RT )

=

c˜1

(44) 21

(45)

c

˜ U − w) − (R ˜ − RT )(µ − RT ) 1 RT ΘT + R(Θ c   1 ˜ − µ) (ΘU − w) − (µ − RT ) . M + (R c

= =

Defining S˜c1 :=

(46)

˜ ∂S , ∂c1

we can have simple expressions for changes in the stochastic discount factor (SDF) due to ˜ Using the Euler CARA utility’s defining property: u00 (c) = −γu0 (c). This implies that S˜c1 = −γ S˜ and S˜c0 = γ S. equations gives the following partial derivatives of g and h, ∂g ∂RT

= =

∂g ∂µ

= =

∂h ∂RT

= =

∂h ∂µ

= =

  ∂M 1 ˜ ˜ − µ))(1 + v 0 ) + E(S˜c1 )(1 + v 0 )2 + v 00 E(S) ˜ E(Sc1 (R c ∂RT     (1 + v 0 ) ∂M µ 1 0 00 ˜ − 1 (1 + v ) − γ − v E(S) γ c RT RT ∂RT   1 ˜ ˜ ∂M ˜ − µ))(1 + v 0 ) + E(S˜c1 )(1 + v 0 )2 + v 00 E(S) − E(Sc1 (R c ∂µ     1 (1 + v 0 ) µ ∂M 0 00 ˜ −γ − 1 (1 + v ) − γ − v E(S) c RT RT ∂µ   ∂M 1 ˜ ˜ − µ)2 ) + E(S˜c1 (R ˜ − µ))(1 + v 0 ) E(Sc1 (R c ∂RT   1ˆ µ 0 ∂M −γ V + γ − 1 (1 + v ) c RT ∂RT   1 ˜ ˜ − µ)2 ) + E(S˜c1 (R ˜ − µ))(1 + v 0 ) ∂M − E(Sc1 (R c ∂µ   µ 1ˆ 0 ∂M − 1 (1 + v ) , γ V +γ c RT ∂µ

(47)

(48)

(49)

(50)

˜ R ˜ − µ)2 ). where Vˆ = E(S( Household’s optimal portfolio implies ∂M 1 = ΘT + 2(µ − RT ) , ∂RT c

∂M 1 = ΘU − w − 2(µ − RT ) . ∂µ c

(51)

Therefore, ∂g ∂h ∂g ∂h − ∂RT ∂µ ∂µ ∂RT

=

  γ(1 + v 0 ) ∂M ∂M ˜ + v 00 E(S) + + RT ∂RT ∂µ  2   µ ∂M ∂M 1 2 γ − 1 (1 + v 0 )2 + , c RT ∂RT ∂µ

1 γ Vˆ c



−

(52)

and ∂g ∂g RT µ+ RT = −γ ∂µ ∂RT c



 2   µ γ(1 + v 0 ) ∂M ∂M ˜ − 1 (1 + v 0 ) − − v 00 E(S) µ+ RT . RT RT ∂µ ∂RT

Returning to Eq. (43),

29

(53)

|D|

Note that

=

∂M ∂µ

|D|

!    2 γ(1 + v 0 ) µ ∂M 1 2 ∂M 00 0 2 ˜ − RT + v E(S) + γ − 1 (1 + v ) + RT c RT ∂RT ∂µ  2  !  µ ∂M 1 ∂M 1 γ(1 + v 0 ) ˜ µ+ −γRT − 1 (1 + v 0 ) + − + v 00 E(S) RT c RT RT ∂µ ∂RT RT     1 µ 1 ∂M 1 γ Vˆ + γ − 1 (1 + v 0 ) + 2 . c RT ∂µ RT RT 1 γ Vˆ c

µ+

=

∂M ∂RT



RT =



(µ − RT ) + ( ∂M + ∂µ

∂M ∂RT

)RT , and denoting ( ∂M + ∂µ

∂M ∂RT

) = ΘT + ΘU − w := κ gives

!  2 µ 1 + − 1 (1 + v 0 )RT −γκ(1 + v 0 ) + RT RT       1 1 µ ˜ γκ 1 Vˆ RT + ∂M −γκ(1 + v 0 ) + + v 00 E(S) −1 +κ . RT RT c ∂µ RT

γ

1 c

Vˆ −

Note that −γκ(1 + v 0 ) + Vˆ −

∂M ∂µ

(54)



1 RT

(55)

˜ < 1. Note that expression < 0 since γκ > 1 and E(S)

2 µ − 1 (1 + v 0 )RT RT

(56)

is positive. In effect, Vˆ = E

˜ S˜ E(S) ˜ − µ)2 (R ˜ E(S)

!

   2 ˆ (R ˆ R ˜ E ˜ − µ)2 > E(S) ˜ E( ˜ − µ) = = E(S)

2 2  µ 1  ˜ ˜ E(S(R − µ)) = − 1 (1+v 0 )RT ,(57) ˜ RT E(S)

ˆ is the risk-neutral measure. That is, deflating by the risk-free rate, changing measure, and applying Jensen’s where E   µ ∂M inequality gives the desired bound. Therefore, since v 00 < 0 and ∂M − 1 + κ = Rµ ∂M + ∂R > κ > 0, ∂µ R ∂µ T

|D| < 0. Given that the interest of the proposition is the repo issuance sensitivity,   1 ∂µ ∂RT ∂RP = − . ∂x c ∂x ∂x Using the expression for the implicit function theorem above gives      ∂µ ∂RT −1 ∂T1 ∂T2 ∂T2 ∂T1 ∂T1 ∂T2 − = + − + . ∂x ∂x |D| ∂RT ∂µ ∂x ∂RT ∂µ ∂x

T

T

(58)

(59)

Note that from the above characterizations, we have ∂T1 ∂T1 + ∂RT ∂µ

= =

∂T2 ∂T2 + ∂RT ∂µ

= =

∂g ∂g RT + RT + g ∂RT ∂µ   (1 + v 0 ) ˜ + 1 RT κ −γ + v 00 E(S) RT RT ∂h ∂h ∂g ∂g + + µ+ µ+g ∂RT ∂µ ∂RT ∂µ     µ (1 + v 0 ) ˜ + 1 . γκ − 1 (1 + v 0 ) + µκ −γ + v 00 E(S) RT RT RT

(60)

(61)

Therefore, ∂µ ∂RT −1 − = ∂x ∂x |D|

        (1 + v 0 ) ∂T2 ∂T1 µ ∂T1 1 ∂T2 ∂T1 ˜ κ −γ + v 00 E(S) RT − µ − γκ − 1 (1 + v 0 ) + − .(62) RT ∂x ∂x RT ∂x RT ∂x ∂x

30

In addition,

∂T1 ∂x

=

∂µ ∂RT − ∂x ∂x

∂g R ∂x T

=

and

∂T2 ∂x

∂h ∂η

∂h ∂x

+

therefore,

       (1 + v 0 ) µ 1 ∂g ∂h ∂h ∂g ˜ κ −γ RT − γκ RT + (µ − RT ) + + v 00 E(S) − 1 (1 + v 0 ) RT ∂x RT ∂x RT ∂x ∂x        1 −1 1 ∂h ∂h µ ∂g 0 00 0 ˜ T −κγ(1 + v ) + + κv E(S)R + . (63) − 1 RT −γκ(1 + v ) + |D| RT ∂x ∂x RT RT ∂x 1 RT

< 0 and calculating

=

˜ 0 E(S˜c1 vη )(1 + v 0 ) + E(S)v η

=

−

=

˜ − µ))vη E(S˜c1 (R   µ γ − 1 vη > 0, RT

=

∂g µ; ∂x

−1 |D|

By noting that −γκ(1 + v 0 ) + example, the case for η gives ∂g ∂η

=

∂g ∂h , ∂x ∂x

for x ∈ {η, ΘT , ΘU } gives the desired result. For

γvη ˜ 0 + E(S)v η RT

(64)

(65)

resulting in ∂RP ∗ 1 ∂(µ − RT ) −1 1 = = ∂η c ∂η |D| c



    µ ˜ T γκvη v 00 + v 0 −γκ(1 + v 0 ) + 1 − 1 E(S)R < 0. η RT RT

(66)

The case for ΘT stems from ∂g ∂ΘT

∂h ∂ΘT

=

˜ T E(S˜c1 )(1 + v 0 )2 RT − E(S˜c0 )(1 + v 0 ) + v 00 E(S)R

=

−

=

˜ − µ))(1 + v 0 )RT − E(S˜c0 (R ˜ − µ)) E(S˜c1 (R  
µ − 1 (1 + v 0 )RT + 1 , γ RT

=


γ ˜ T (1 + v 0 )RT + 1 + v 00 E(S)R RT

(67)

(68)

where S˜c0 = γ S˜ since u00 (c) = −γu0 (c) resulting in, ∂RP ∗ 1 ∂(µ − RT ) −1 1 = = ∂ΘT c ∂ΘT |D| c



 µ ˜ T v 00 (1 + γκ) < 0. − 1 E(S)R RT

(69)

The case for ΘU stems from ∂g ∂ΘU

= =

∂h ∂ΘU

= =

˜ − µ))(1 + v 0 ) + E(S˜c1 )(1 + v 0 )2 µ − E(S˜c0 )(1 + v 0 ) + v 00 E(S)µ ˜ E(S˜c1 (R  
γ µ ˜ γ − 1 (1 + v 0 ) − (1 + v 0 )µ + 1 + v 00 E(S)µ RT RT ˜ − µ)2 ) + E(S˜c1 (R ˜ − µ))(1 + v 0 )µ − E(S˜c0 (R ˜ − µ)) E(S˜c1 (R  
µ −γ Vˆ + γ − 1 (1 + v 0 )µ + 1 , RT

resulting in

31

(70)

(71)

∂RP ∗ ∂ΘU

= =

1 ∂(µ − RT ) c ∂ΘU ( # "   2 µ −1 1 1 Vˆ − −γ −γκ(1 + v 0 ) + − 1 (1 + v 0 )RT |D| c RT RT     µ µ 00 ˜ Tv −1 + γκ . +E(S)R −γ Vˆ κ + RT RT

(72)

And finally, the case for c stems from (µ − RT ) 1 ∂(µ − RT ) ∂RP =− + , ∂c c2 c ∂c

(73)

with ∂g ∂c

= =

∂h ∂c

= =

˜ − µ))(1 + v 0 )RT E(S˜c1 (R

2 (µ − RT ) (µ − RT )2 ˜ T (µ − RT ) + E(S˜c1 )(1 + v 0 )2 RT + v 00 E(S)R 2 2 2 c c c

2 ˜ T (µ − RT ) v 00 E(S)R c2 2 ˜ − µ)2 ) (µ − RT ) + E(S˜c1 (R ˜ − µ))(1 + v 0 ) (µ − RT ) E(S˜c1 (R 2 2 c c " #  2 (µ − RT ) ˆ µ 0 V − − 1 (1 + v )RT , −γ c2 RT

(74)

(75)

resulting in ∂RP ∗ ∂c

=

−

(µ − RT ) c2

˜ T v 00 −E(S)R

#  "  2 µ γ Vˆ − − 1 (1 + v 0 )RT RT " #!)! 2 2    1 µ µ 0 0 ˆ −γκ(1 + v ) + − 1 RT − γκ V − − 1 (1 + v )RT (76), RT RT RT

1−

1 1 |D| c

(

−γκ(1 + v 0 ) +

1 RT

which is negative. 

Proof of Proposition 3. equilibrium equations, Tˇ1 Tˇ2

= =

The result is derived from invoking the implicit function theorem.

˜ E(S)(1 + v 0 (M ; η))RT − 1 = 0 ˜ R ˜ − µ)) + E(S)µ ˜ − 1 = 0, E(S(

Consider the two (77) (78)

where Tˇ1 and Tˇ2 stems from rewriting Eq. (10) and (23) for the case αU = 0. As before, repo issuance sensitivity ˜ depends on the sensitivity of µ − RT with respect to model parameters. To simplify the derivation, define gˇ := E(S)

32

ˇ := E(R( ˜ S˜ − µ)); therefore, and h ∂ Tˇ1 ∂RT ∂ Tˇ1

= =

∂µ ∂ Tˇ2

=

∂RT ∂ Tˇ2

=

∂µ

∂ˇ g ∂M (1 + v 0 )RT + gˇ(1 + v 0 ) + gˇv 00 RT ∂RT ∂RT ∂ˇ g ∂M (1 + v 0 )RT + gˇv 00 RT ∂µ ∂µ ˇ ∂h ∂ˇ g + µ ∂RT ∂RT ˇ ∂h ∂ˇ g + µ + gˇ. ∂µ ∂µ

(79) (80) (81) (82)

First, I calculate the corresponding determinant of the Jacobian: ˇ = |D|

∂ Tˇ1 ∂ Tˇ2 ∂ Tˇ1 ∂ Tˇ2 − . ∂RT ∂µ ∂µ ∂RT

(83)

In this case, the equilibrium in Proposition 1 results in the following household consumption and money holdings: c0

=

M

=

c˜1

= =

e0 − ΘT − (ΘU − w)

(84)

1 RT ΘT + RT (µ − RT ) c

(85)

˜ U − w) − (R ˜ − RT )(µ − RT ) 1 RT ΘT + R(Θ c   1 ˜ M + R (ΘU − w) − (µ − RT ) . c

(86)

ˇ Using the Euler equations gives the following partial derivatives of gˇ and h: ∂ˇ g ∂RT

= =

∂ˇ g ∂µ

= =

ˇ ∂h ∂RT

= =

ˇ ∂h ∂µ

= =

1 ˜ ˜ − µ)) + 1 E(S˜c1 )µ + E(S˜c1 )(1 + v 0 ) ∂M E(Sc1 (R c c ∂RT γ γ ∂M − − c RT ∂RT   1 ˜ ˜ − µ)) + E(S˜c1 ) (ΘU − w) − (µ − RT ) 1 − µ + E(S˜c1 )(1 + v 0 ) ∂M − E(Sc1 (R c c c ∂µ   1 γ ∂M γ − γˇ g (ΘU − w) − (µ − RT ) − c c RT ∂µ   1 ˜ ∂M µ ˜ − µ)2 ) + E(S˜c1 (R ˜ − µ)) E(Sc1 (R + (1 + v 0 ) c c ∂RT   γˇ ∂M µ 0 ˇ − V − γh + (1 + v ) c c ∂RT   1 ˜ 2 ˜ ˜ ˜ − µ)) (ΘU − w) − (µ − RT ) 1 − µ + (1 + v 0 ) ∂M − E(Sc1 (R − µ) ) + E(Sc1 (R c c c ∂µ   1 γˇ µ ∂M ˇ (ΘU − w) − (µ − RT ) − + (1 + v 0 ) V − γh , c c c ∂µ

(87)

(88)

(89)

(90)

˜ R ˜ − µ)2 ). where Vˇ = E(S( Household’s optimal portfolio implies ∂M (µ − RT ) RT = ΘT + − , ∂RT c c

∂M RT = . ∂µ c

(91)

33

Therefore, ∂ˇ g ∂RT ∂ˇ g ∂µ ˇ ∂h ∂RT ˇ ∂h ∂µ

= = = =

  (µ − RT ) γ ΘT + RT c   (µ − RT ) −γˇ g (ΘU − w) − c    (µ − R (1 + v 0 )) (µ − RT ) γˇ T ˇ + (1 + v 0 ) ΘT + − V − γh c c c   0 )) γˇ (µ − R (1 + v (µ − R ) T T ˇ − V − γh + (ΘU − w) − . c c c −

(92) (93) (94) (95)

Note that 0 ˇ (µ − RT (1 + v )) = 1 (1 − gµ) h c c



  2 µ 1 µ − 1 RT (1 + v 0 ) = − − 1 RT (1 + v 0 ), 0 0 RT (1 + v ) c RT (1 + v )

(96)

and similar to the proof of Proposition 2, changing measure and using Jensen’s inequality gives    2 ˆ (R ˆ R ˜ E ˜ − µ)2 > E(S) ˜ E( ˜ − µ) = Vˇ = E(S) Therefore, ˇ ∂h ∂RT

ˇ ∂h ∂RT

= =

ˇ ∂h ∂µ

= =

,

ˇ ∂h ∂µ

"

2 2  1  ˜ ˜ µ − 1 (1 + v 0 )RT . (97) E(S(R − µ)) = 0 ˜ RT (1 + v ) E(S)

can be written as

# 2   µ 0 ˇ + v 0 ) ΘT + (µ − RT ) − 1 (1 + v )R − γ h(1 T RT (1 + v 0 ) c   γ ˇ ˇ + v 0 ) ΘT + (µ − RT ) − V RP − γ h(1 c c " #  2   γ ˇ (µ − RT ) µ 0 ˇ V − − 1 (1 + v )R − γ h (Θ − w) − T U c RT (1 + v 0 ) c   γ ˇ (µ − R ) T ˇ (ΘU − w) − V RP − γ h . c c γ − c

Vˇ −



(98)

(99)

Returning to the partial derivatives of Tˇ1 and Tˇ2 gives ∂ Tˇ1 ∂RT ∂ Tˇ1 ∂µ ∂ Tˇ2 ∂RT ∂ Tˇ2 ∂µ

= = = =

  (µ − RT ) ∂M 1 −γ ΘT + + gˇv 00 RT (1 + v 0 ) + c RT ∂RT   (µ − RT ) ∂M −γ (ΘU − w) − + gˇv 00 RT c ∂µ   γ ˇ (µ − RT ) − V RP − γ ΘT + (1 + v 0 ) c c   γ ˇ (µ − RT ) V RP − γ (ΘU − w) − + gˇ. c c

Denoting κ ˇ := (ΘT + ΘU − w), the Jacobian can be expressed as

34

(100) (101) (102) (103)

ˇ |D|

=

     ˇ  (µ − RT ) 1 1 V RP −γˇ κ − γ ΘT + v0 + + gˇ −γˇ κ(1 + v 0 ) + + c c RT RT        ˇ RT (µ − RT ) 1 V RP (µ − RT ) gv 00 RT γˇ κ + γ ΘT + v0 − − + γ Θ + T c c RT (1 + v 0 ) c c      (µ − RT ) µ − RT (µ − RT ) +γˇ g ΘT + − γ ΘT + ΘU − w − . c c c

γ

˜ < 1. With v 00 sufficiently small, |D| ˇ < 0. Note that −γˇ κ + R1 < 0 since γΘT > 1 and E(S) T Given that the interest of the proposition is the repo issuance sensitivity,   ∂RP ∗ 1 ∂µ ∂RT = − . ∂x c ∂x ∂x

(104)

(105)

As before, using the the implicit function theorem above gives  ˇ   ˇ   ∂µ ∂RT −1 ∂ T1 ∂ Tˇ1 ∂ Tˇ2 ∂ T2 ∂ Tˇ2 ∂ Tˇ1 − = + − + . ˇ ∂x ∂x ∂RT ∂µ ∂x ∂RT ∂µ ∂x |D|

(106)

and from the above characterization we have ∂ Tˇ1 ∂ Tˇ1 + ∂RT ∂µ ∂ Tˇ2 ∂ Tˇ2 + ∂RT ∂µ

= =

−γˇ κ−γ −γˇ κ−γ

 

ΘT + ΘT +

(µ − RT ) c (µ − RT ) c

 

v0 +

1 + gv 00 RT RT

v0 +

1 . RT (1 + v 0 )



ΘT +

(µ − RT ) c



(107) (108)

Calculating equations sensitivities to η gives ∂ Tˇ1 ∂η ∂ Tˇ2 ∂η

∂ˇ g (1 + v 0 )RT + gˇRT vη0 = −γvη + gˇRT vη0 ∂η ˇ ∂h ∂ˇ g + µ = −γvη , ∂η ∂η

= =

(109) (110)

resulting in ∂RP ∗ 1 −1 = ˇ ∂η c |D|

  −γvη

v0 + gv 00 RT RT (1 + v 0 )



ΘT +

(µ − RT ) c



− gˇRT vη0



−γˇ κ−γ



ΘT +

(µ − RT ) c



v0 +

The case for c stems from ∂ Tˇ1 ∂c ∂ Tˇ2 ∂c

∂ˇ g ∂M 2 (µ − RT ) (1 + v 0 )RT + gˇv 00 RT = −ˇ g v 00 RT ∂c ∂c c2 ˇ ∂h ∂ˇ g (µ − R ) T ˇ + µ = −γ V RP ∂c ∂c c2

= =

(112) (113)

resulting in ∂RP ∗ ∂c

=

      (µ − RT ) 1 1 (µ − RT ) 1 ˇ 1− γ V RP −γˇ κ − γ ΘT + v0 + + 2 ˇ c c RT |D| c         (µ − RT ) 1 (µ − RT ) ˇ gˇv 00 RT RT γˇ κ + γ ΘT + v0 − + γ V RP Θ + (114) , T c RT (1 + v 0 ) c

−

35

1 RT (1 + v 0 )



.(111)

which is negative for v 00 sufficiently small enough. 

Proof of Proposition 5. Given that the equilibrium characterization of Proposition 1 is identical to that of Proposition 4, the partial derivatives of the new equilibrium equations are the same as before with a mere change in notation. Specifically, RT = RCB and ΘT = ΘCB . Defining

T1

=

T2

=

˜ E(S)(1 + v 0 (M ; η))RCB − 1 = 0 ˜ ˜ ˜ E(S(R − µ)) + E(S)(1 + v 0 (M ; η))µ − 1 = 0,

(115) (116)

˜ ˜ S˜ − µ)), the above observation implies that the expressions of and labeling g := E(S)(1 + v 0 (M ; η)) and h := E(R( ∂g ∂h , are the same as for Proposition 1 for all variables x in the model. Therefore, ∂x ∂x

|D|

= = =

∂T 1 ∂T 2 ∂T 1 ∂T 2 − ∂ΘCB ∂µ ∂µ ∂ΘCB   ∂g ∂h ∂g ∂g ∂h − RCB + gRCB ∂ΘCB ∂µ ∂µ ∂ΘCB ∂ΘCB !  2   1 1 RCB µ −γ 2 ((1 + v 0 ) + ) Vˆ − − 1 (1 + v 0 )RCB − γ (1 + v 0 ) + + c RCB RCB RCB " #   ˆ µ ∂M ˜ 00 RCB γ V RCB − γ E(S)v −1 +1 . c RCB ∂µ

(117)

As before, the final equality stems from using u00 (c) = −γu0 (c) to express derivatives of the SDF and use the equilibrium equations T 1 , T 2 . The term accompanying v 00 may have an ambiguous sign, but for v 00 sufficiently small, ∗ = 1c ∂µ ; therefore, we have it can be directly seen that |D| is negative. In this equilibrium we have ∂RP ∂η ∂η ∂µ ∂η

= =

   1 ∂g ∂h ∂g ∂h − − RCB ∂ΘCB ∂η ∂η ∂ΘCB D      µ ˜ CB v 00 vη − v 0 (1 + v 0 ) + 1 γ − 1 E(S)R , η RCB RCB

(118)

which is clearly positive. Turning to changes in central bank repo take-up gives ∂ΘCB ∂η

= =

  ∂g ∂h ∂g ∂h ∂g − RCB + gRCB ∂η ∂µ ∂µ ∂η ∂η D ( " # !  2   γ −1 γ2 ˆ µ µ ∂M ˜ V − − 1 (1 + v 0 )RCB − v 00 γRCB E(S) −1 − + vη − c RCB RCB ∂µ RCB |D| !)   ˆ µ 1 0 ∂M ˜ CB v 0 γ V + γ E(S)R − 1 (1 + v ) + . η c RCB ∂µ RCB

−

1



To sign the term accompanying vη0 , note that Treasuries are given by ΘU − w − (µ −

RCB ) 1c ,

∂M ∂µ

= ΘU − w − 2(µ − RCB ) 1c and households’ holdings of

which is positive. Separating 2(µ − RCB ) so that half creates  2 households allocations in Treasuries and the other half is grouped with Vˆ to create Vˆ − R µ − 1 (1 + v 0 )RCB CB implies that the overall expression is positive. 

36

References References Anderson, A.G., Kandrac, J., 2017. Monetary policy implementation and financial vulnerability: evidence from the overnight reverse repurchase facility. Review of Financial Studies 31, 3643–3686. van Binsbergen, J.H., Diamond, W., Grotteria, M., 2018. Risk free interest rates. Unpublished working paper. Wharton School, University of Pennsylvania. Carlson, M., Duygan-Bump, B., Natalucci, F., Nelson, B., Ochoa, M., Stein, J., Van den Heuvela, S., 2016. The demand for short-term, safe assets and financial stability: some evidence and implications for central bank policies. International Journal of Central Banking 12, 307–333. Copeland, A., Martin, A., Walker, M., 2014. Repo runs: evidence from the tri-party repo market. Journal of Finance 69, 2343–2380. Diamond, D.W., Dybvig, P.H., 1983. Bank runs, deposit insurance, and liquidity. Journal of Political Economy 91, 401–419. Diamond, W., 2018. Safety transformation and the structure of the financial system. Unpublished working paper. Harvard University. Duchin, R., Gilbert, T., Harford, J., Hrdlicka, C., 2017. Precautionary savings with risky assets: when cash is not cash. Journal of Finance 72, 793–852. Duffie, D., 2017. Financial regulatory reform after the crisis: an assessment. Management Science 64, 4471–4965. Gorton, G., 2017. The history and economics of safe assets. Annual Review of Economics 9, 547–586. Gorton, G., Lewellen, S., Metrick, A., 2012. The safe-asset share. American Economic Review 102, 101–106. Gorton, G., Pennacchi, G., 1990. Financial intermediaries and liquidity creation. Journal of Finance 45, 49–71. Greenwood, R., Hanson, S.G., Stein, J.C., 2015. A comparative-advantage approach to government debt maturity. Journal of Finance 70, 1683–1722. Holmstrom, B., Tirole, J., 1998. Private and public supply of liquidity. Journal of Political Economy 106, 1–40. Kacperczyk, M.T., Perignon, C., Vuillemey, G., 2017. The private production of safe assets. Unpublished working paper. CEPR. Krishnamurthy, A., Nagel, S., Orlov, D., 2014. Sizing up repo. Journal of Finance 69, 2381–2417. Krishnamurthy, A., Vissing-Jorgensen, A., 2012. The aggregate demand for Treasury debt. Journal of Political Economy 120, 233–267. Krishnamurthy, A., Vissing-Jorgensen, A., 2015. The impact of Treasury supply on financial sector lending and stability. Journal of Financial Economics 118, 571–600. Lenel, M., 2017. Safe assets, collateralized lending, and monetary policy. Unpublished working paper. SIEPR. Munyan, B., 2017. Regulatory arbitrage in repo markets. Unpublished working paper. Vanderbilt University. Nagel, S., 2016. The liquidity premium of near-money assets. Quarterly Journal of Economics 131, 1927–1971. Sunderam, A., 2014. Money creation and the shadow banking system. Review of Financial Studies 28, 939–977. Xie, L., 2012. The seasons of money: ABS/MBS issuance and the convenience yield. Unpublished working paper. Yale University.

37

Fig. 1. Short-term money market rates The top panel depicts the time series for the the four-week T-bill rate and the overnight Treasury repo rate in the GCF market. The bottom panel depicts the series for the the four-week T-bill rate and the Treasury repo rate in the non-GCF market. Rates and spreads are measured in basis points. Data are daily and runs from January 2011 to March 2017.

Basis points Daily GCF Repo rate 4−week T−bill

140

120

100

80

60

40

20

0

−20 Jan. Jun. Nov. Apr. Oct. Mar. Aug. Jan. Jun. Nov. Apr. Oct. Mar. Aug. Jan. Jun. Nov. Apr. Oct. Mar. 2009 2010 2011 2012 2013 2014 2015 2016 2017

Basis points Daily BNY TPR rate 4−week T−bill

140

120

100

80

60

40

20

0

38 −20 Jan. Jun. Nov. Apr. Oct. Mar. Aug. Jan. Jun. Nov. Apr. Oct. Mar. Aug. Jan. Jun. Nov. Apr. Oct. Mar. 2009 2010 2011 2012 2013 2014 2015 2016 2017

Fig. 2. Total tri-party repo outstanding backed by US Treasury collateral The series depict the total amount of US Treasury repo outstanding in the tri-party market. Amounts outstanding of primary dealers, non primary dealers, and the Federal Reserves’ RRP program are shown separately and measured in billions of dollars. Data are daily and runs from January 2011 to March 2017.

Billions Primary dealers Non primary dealers FRBNY

800

700

600

500

400

300

200

100

0 2009

2010

2011

2012

2013

39

2014

2015

2016

2017

Fig. 3. Total private repo issuance The series depicts daily log changes in the total amount of primary dealer US Treasury repo outstanding. Changes around quarter-end are highlighted by circular markers. These observations are excluded from the empirical analysis. Data are daily and runs from January 2011 to March 2017.

0.3

0.25

0.2

∆ log(RepoOut t)

0.15

0.1

0.05

0

-0.05

-0.1

-0.15 Jan09 Apr09

Jul09

Oct09 Jan10 Apr10

Jul10

Oct10 Jan11 Apr11

Jul11

Oct11 Jan12 Apr12

Jul12

Oct12 Jan13 Apr13

40

Jul13

Oct13 Jan14 Apr14

Jul14

Oct14 Jan15 Apr15

Jul15

Oct15 Jan16 Apr16

Jul16

Oct16 Jan17 Apr17

Fig. 4. Convenience yield The series depicts the daily convenience yield, measured as the difference between the four-week T-bill rate and the one-month OIS rate. Rates are measured in basis points. Data are daily and runs from January 2011 to March 2017.

Basis points

30

(T−bill − OIS) 20

10

0

−10

−20

−30

−40

−50 2009

2010

2011

2012

2013

41

2014

2015

2016

2017

−.1

−.05

0

.05

.1

Fig. 5. Confidence intervals for CY loading for different asset classes The plot depicts the loading on the lagged CY for different asset classes. Bands represent the 95% confidence interval. The regression specification is as in Eq. (33) where ∆log(RepoOutt ) considers primary dealer issuance of repos using different collateral classes. Newey-West with 21-lag confidence intervals is shown in exhibit 5a, clustered errors with week-of-year fixed effects confidence intervals are shown in exhibit 5b, and IV regression using short-term T-bill issuance as an instrument and Newey-West errors with 21-lag confidence intervals are shown in exhibit 5c. Confidence intervals are at 95%. The collateral classes, ordered from left to right, are US Treasuries (UST), agency CMO (AgCMO), agency debentures (AgDeb), agency MBS (AgMBS), asset-backed securities (ABS), corporate bonds (Corp), equities (Eq), municipal bonds (Muni), private-label CMO (PLCMO), and whole loans (WL). The first four asset classes are government securities, backed by the full faith and credit of the federal government. Table 6 contains the numerical results of the regression.

| | | | UST AgCMO AgDeb AgMBS

| ABS

| Corp

| Eq

| | Muni PLCMO

| WL

−.05

0

.05

.1

(a) Newey-West (21)

| | | | UST AgCMO AgDeb AgMBS

| ABS

| Corp

| Eq

| | Muni PLCMO

| WL

−6

−4

−2

0

2

(b) Week-of-year clustering

| | | | UST AgCMO AgDeb AgMBS

| ABS

| Corp

| Eq

| | Muni PLCMO

(c) IV short-term T-bill

42

| WL

Table 1 Summary statistics of daily data This table presents summary statistics for the variables used in the paper. ∆log(RepoOutt ) is the log change of total US Treaury repo outstanding by primary dealers. (T Bill − OIS)t is the spread of the four-week Tbills over the one-month overnight index swap (OIS) rate. ∆log(T BillsOutt ) is the log change in T-bills outstanding, ∆log(ShT BillsOutt ) is the log change in T-bills outstanding with maturity less than one month, and ∆log(U ST N otesOutt ) is the log change in US Treasury notes outstanding. T Billt is the T-bill rate, and GCFt is the overnight Treasury GCF repo rate. The sample runs daily from January 2009 to March 2017. Quarter-end dates are excluded.

PD ∆log(RepoOutt ) FRB ∆log(RepoOutt ) (T bill − OIS)t T Billt GCFt ∆log(T billsOutt ) ∆log(ShT billsOutt ) ∆log(U ST N otesOutt )

Count 2,001 789 2,059 2,059 2,059 2,020 2,020 2,020

Mean –.0006 .0035 –.0904 .0966 .2026 –.0001 .0001 .0006

43

Sdev .0235 .2049 .0524 .1106 .1485 .0066 .0990 .0024

Min –.1124 –.8871 –.3820 –.0300 –.1930 –.0805 –.3480 –.0022

Max .1293 1.060 .2430 .7600 1.266 .0805 .4875 .0219

Table 2 Daily primary dealer repo issuance P This table shows regressions of the following form: ∆log(RepoOutt ) = α + βCYt−1 + j γj ∆log(RepoOutt−j ) + t , where ∆log(RepoOutt ) is the log change of total repo outstanding by primary dealers. CYt−1 is (T Bill − OIS)t−1 , the spread of the four-week T-bills over the one-month overnight index swap (OIS) rate. ∆log(RepoOutt−j ) is the j-th lagged log change of repo outstanding. The sample runs daily from January 2009 to March 2017. Quarter-end dates are excluded. Regressions run with and without week-of-year fixed effects. Newey-West errors with 21 lags are reported in regressions without fixed effects (NW), and clustered errors are reported in regressions with week-of-year fixed effects (SC). Intercept of regression not reported. *, **, ***, denote significance at the 10%, 5%, and 1% levels, respectively. LHS: ∆log(RepoOutt ) of primary dealer repo outstanding (T Bill − OIS)t−1

0.028*** (0.008)

0.033*** (0.009) –0.197*** (0.021)

0.036*** (0.009) –0.216*** (0.023) –0.061*** (0.022)

0.038*** (0.010) –0.219*** (0.023) –0.065*** (0.022) –0.005 (0.028)

N NW 0.004 1,992

N NW 0.042 1,959

N NW 0.048 1,925

N NW 0.050 1,893

∆log(RepoOutt−1 ) ∆log(RepoOutt−2 ) ∆log(RepoOutt−3 ) ∆log(RepoOutt−4 ) WOY FE Error type R2 N obs

44

0.040*** (0.010) –0.222*** (0.023) –0.072*** (0.023) –0.026 (0.029) –0.059** (0.024) N NW 0.054 1,859

0.012 (0.009) –0.345*** (0.025) –0.205*** (0.020) –0.145*** (0.034) –0.136*** (0.031) Y SC 0.181 1,859

Table 3 Daily primary dealer repo issuance with financial data controls P This table shows regressions of the following form: ∆log(RepoOutt ) = α + βCYt−1 + j γj ∆log(RepoOutt−j ) + θXt−1 + t , where ∆log(RepoOutt ) is the log change of total repo outstanding by primary dealers. CYt−1 is (T Bill − OIS)t−1 , the spread of the four-week T-bills over the one-month OIS. Xt−1 are financial data controls, which include GCFt−1 , the overnight Treasury repo rate in the GCF market; IG CDXt−1 , the standardized CDX IG index; V IXt−1 , the standardized VIX index; S&P V olt−1 , the standardized realized volatility of the S&P Index; 10yImpV ol, the standardized implied volatility of the 10-year US Treasury; 10yrV olt−1 , the standardized realized volatility of the 10-year US Treasury; M argint−1 , the aggregate tri-party Treasury repo margin; and (10yr−2yr)t−1 , the standardized yield difference between the 10- and 2-year US Treasury yield curve. Four lags of ∆log(RepoOutt ) are included as controls (not shown), reporting the p-value of lags equal to zero. The sample runs daily from January 2009 to March 2017. Quarter-end dates are excluded. Newey-West errors with 21 lags are reported in regressions without fixed effects (NW), and clustered errors are reported in regressions with week-of-year fixed effects (SC). Intercept of regression not reported. *, **, ***, denote significance at the 10%, 5%, and 1% levels, respectively. LHS: ∆log(RepoOutt ) of primary dealer repo outstanding (T Bill − OIS)t−1 GCFt−1

0.055*** (0.011) 0.010** (0.004)

0.055*** (0.012) 0.010** (0.004) 0.000 (0.001)

0.058*** (0.012) 0.012*** (0.004) –0.002* (0.001) 0.003** (0.001)

0.059*** (0.012) 0.012*** (0.004) –0.002* (0.001) 0.002 (0.002) 0.001 (0.001)

0.060*** (0.012) 0.012*** (0.004) –0.002* (0.001) 0.003 (0.002) 0.001 (0.001) –0.001 (0.001)

0.058*** (0.012) 0.012*** (0.005) –0.002 (0.001) 0.003 (0.002) 0.000 (0.001) –0.002 (0.001) 0.001 (0.001)

0.058*** (0.012) 0.012*** (0.005) –0.002 (0.001) 0.003 (0.002) 0.000 (0.001) –0.002 (0.001) 0.001 (0.001) 0.102 (0.773)

N NW 0.000 0.057 1,859

N NW 0.000 0.057 1,846

N NW 0.000 0.059 1,844

N NW 0.000 0.060 1,844

N NW 0.000 0.061 1,844

N NW 0.000 0.061 1,840

N NW 0.000 0.061 1,840

IG CDXt−1 index V IXt−1 S&P V olt−1 10yImpV olt−1 10yrV olt−1 M argint−1 (10yr − 2yr)t−1 WOY FE Error type p-value lag R2 N obs

45

0.067*** (0.013) 0.003 (0.005) –0.002* (0.001) 0.003* (0.002) -0.000 (0.001) –0.000 (0.001) 0.000 (0.001) –0.958 (0.874) –0.003*** (0.001) N NW 0.000 0.065 1,840

0.032*** (0.011) 0.005 (0.005) –0.002 (0.001) 0.003** (0.002) 0.000 (0.001) –0.002 (0.001) 0.001 (0.001) –0.829 (0.830) –0.001* (0.001) Y SC 0.000 0.189 1,840

Table 4 Daily primary dealer repo issuance with Treasury issuance and financial data controls This table shows regressions P of the following form: ∆log(RepoOutt ) = α + βCYt−1 + η1 ∆log(ShT BillsOutt ) + η2 ∆log(U ST N otesOutt ) + j γ1j ∆log(RepoOutt−j ) + θXt−1 + t , where ∆log(RepoOutt ) is the log change of total repo outstanding by primary dealers. CYt−1 is (T Bill − OIS)t−1 , the spread of the four-week T-bills over the one-month OIS. ∆log(ShT BillsOutt ) is the log change in T-bills outstanding with maturity less than one month, and ∆log(U ST N otesOutt ) is the log change in US Treasury notes outstanding. Four lags of ∆log(RepoOutt ) are included as controls (not shown). Xt−1 are financial data controls used in Table 3 (not shown). The sample runs daily from January 2009 to March 2017. Quarter-end dates are excluded. Regressions are run with and without week-of-year fixed effects. Newey-West errors with 21 lags are reported in regressions without fixed effects (NW), and clustered errors are reported in regressions with week-of-year fixed effects (SC). *, **, ***, denote significance at the 10%, 5%, and 1% levels, respectively. LHS: ∆log(RepoOutt ) of primary dealer repo outstanding (T Bill − OIS)t−1 ∆log(ShT BillsOutt ) ∆log(U ST N otesOutt ) WOY FE Error type R2 N obs

0.072*** (0.013) –0.051*** (0.005) 3.217*** (0.281) N NW 0.192 1,807

0.040*** (0.010) –0.049*** (0.005) 2.816*** (0.327) Y SC 0.288 1,807

Table 5 Daily primary dealer repo issuance instrumenting with short-term T-bill issuance This table shows instrumental variable estimations of the following specification: CYt−1 = α1 + P η∆log(ShT BillsOutt−1 ) + j γ1j ∆log(RepoOutt−j ) + θ1 Xt−1 + t−1 in the first stage and ∆log(RepoOutt ) = ˆ t−1 + P γ2j ∆log(RepoOutt−j )+θ2 Xt−1 +t in the second stage, where ∆log(RepoOutt ) is the log change α2 +β CY j

of total repo outstanding by primary dealers. CYt−1 is (T Bill − OIS)t−1 , the spread of the four-week T-bills over ˆ t−1 is the fitted value of the convenience yield from the first stage. ∆log(ShT BillsOutt−1 ) the one-month OIS. CY is the lagged log change in T-bills outstanding with maturity less than one month. Four lags of ∆log(RepoOutt ) are included as controls (not shown). Xt−1 are the financial variable controls used in Table 3 (not shown). The sample runs daily from January 2009 to March 2017. Quarter-end dates are excluded. Regressions are run with and without week-of-year fixed effects. Newey-West errors with 21 lags are reported in regressions without fixed effects (NW), and clustered errors are reported in regressions with week-of-year fixed effects (SC). *, **, ***, denote significance at the 10%, 5%, and 1% levels, respectively. LHS: ∆log(RepoOutt ) of primary dealer repo outstanding IV with ShTBill IV with ShTBill & WOY FE 1st stage 2st stage 1st stage 2st stage (T Bill − OIS)t−1 ∆log(ShT BillsOutt−1 ) WOY FE Error type R2 N obs

1.430*** (0.243) 0.043*** (0.006) N NW 0.388 1,839

N NW . 1,806

46

1.796*** (0.443) 0.028*** (0.007) Y SC 0.491 1,839

Y SC . 1,806

Table 6 Daily primary dealer repo issuance separated by different asset classes Panel A and B shows regressions P of the following form: ∆log(RepoOutct ) = α + βCYt−1 + η1 ∆log(ShT BillsOutt ) + η2 ∆log(U ST N otesOutt ) + j γ1j ∆log(RepoOutct−j ) + θXt−1 + t , and Panel C shows instrumental variable estiP mations of the following form: CYt−1 = α1 + η∆log(ShT BillsOutt−1 ) + j γ1j ∆log(RepoOutct−j ) + θ1 Xt−1 + t−1 P ˆ t−1 + in the first stage and ∆log(RepoOutct ) = α2 + β CY γ2j ∆log(RepoOutct−j ) + θ2 Xt−1 + t in the second j

stage. ∆log(RepoOutct ) is the log change of total repo outstanding by primary dealers using different collateral ˆ t−1 is the fitted classes. CYt−1 is (T Bill − OIS)t−1 , the spread of the four-week T-bills over the one-month OIS. CY value of the convenience yield from the first stage (not shown). ∆log(ShT BillsOutt−1 ) is the lagged log change in T-bills outstanding with maturity less than one month, and ∆log(U ST N otesOutt ) is the log change in US Treasury notes outstanding (not shown). Four lags of ∆log(RepoOutct ) are included as controls (not shown). Xt−1 are the financial variable controls used in Table 3 (not shown). The collateral classes, ordered from left to right, are US Treasuries (UST), agency CMO (AgCMO), agency debentures (AgDeb), agency MBS (AgMBS), asset-backed securities (ABS), corporate bonds (Corp), equities (Eq), municipal bonds (Muni), private-label CMO (PLCMO), and whole loans (WL). Newey-West errors with 21 lags are shown in Panel A, clustered errors with week-of-year fixed effects are shown in Panel B, and IV regression using short-term T-bill issuance as an instrument and Newey-West errors with 21 lags are shown in Panel C. The sample runs daily from January 2009 to March 2017. Quarter-end dates are excluded. *, **, ***, denote significance at the 10%, 5%, and 1% levels, respectively.

Panel A (T Bill − OIS)t−1 R2 N obs Panel B (T Bill − OIS)t−1 R2 N obs Panel C (T Bill − OIS)t−1 R2 N obs

LHS: ∆log(RepoOutct ) MBS ABS Corp

UST

AgCMO

AgDeb

0.072*** (0.013) 0.192 1,807

0.007 (0.014) 0.080 1,807

0.033* (0.019) 0.163 1,807

0.019** (0.009) 0.075 1,807

0.011 (0.015) 0.096 1,807

0.040*** (0.010) 0.288 1,807

0.003 (0.014) 0.187 1,807

–0.005 (0.020) 0.234 1,807

0.007 (0.012) 0.159 1,807

1.430*** (0.243) . 1,806

–0.085 (0.212) . 1,806

–3.226*** (1.044) . 1,806

0.353 (0.218) . 1,806

47

Eq

Munis

PLCMO

WL

–0.003 (0.008) 0.067 1,807

0.002 (0.012) 0.041 1,807

0.008 (0.026) 0.082 1,807

0.006 (0.013) 0.082 1,801

–0.014 (0.033) 0.017 1,807

0.011 (0.016) 0.122 1,807

–0.008 (0.010) 0.114 1,807

–0.006 (0.019) 0.084 1,807

0.017 (0.030) 0.118 1,807

0.003 (0.015) 0.112 1,801

0.012 (0.033) 0.062 1,807

0.200 (0.188) . 1,806

0.153 (0.128) . 1,806

0.270 (0.211) . 1,806

0.502 (0.489) . 1,806

0.101 (0.179) . 1,800

0.479 (0.407) . 1,806

Table 7 Daily primary dealer repo issuance separated by firms’ regulatory jurisdictions Panel A and B shows regressions of the following form: ∆log(RepoOutlt ) = α + βCYt−1 + η1 ∆log(ShT BillsOutt ) + P η2 ∆log(U ST N otesOutt )+ j γ1j ∆log(RepoOutlt−j )+θXt−1 +t , and Panel C shows instrumental variable estimaP tions of the following form: CYt−1 = α1 + η∆log(ShT BillsOutt−1 ) + j γ1j ∆log(RepoOutlt−j ) + θ1 Xt−1 + t−1 in P ˆ t−1 + the first stage and ∆log(RepoOutlt ) = α2 + β CY γ2j ∆log(RepoOutlt−j ) + θ2 Xt−1 + t in the second stage. j

∆log(RepoOutlt ) is the log change of total repo outstanding by primary dealers, separated by different regulatory jurisdictions l. The regulatory jurisdictions considered are: the United States (US PD), the United Kingdom (UK PD), the United States and the United Kingdom (US+UK PD), the United Kingdom and the rest of the world (UK+Rest PD), and the rest of the world (Rest PD). CYt−1 is (T Bill − OIS)t−1 , the spread of the four-week T-bills over the one-month OIS. ∆log(ShT BillsOutt ) is the log change in T-bills outstanding with maturity less than one month, and ∆log(U ST N otesOutt ) is the log change in US Treasury notes outstanding. Four lags of ∆log(RepoOutlt ) are included as controls (not shown). Xt−1 are financial data controls used in Table 3 (not shown). Newey-West errors with 21 lags are shown in Panel A, clustered errors with week-of-year fixed effects are shown in Panel B, and IV regression using short-term T-bill issuance as an instrument and Newey-West errors with 21 lags are shown in Panel C. The sample runs daily from January 2011 to March 2017. Quarter-end dates are excluded. *, **, ***, denote significance at the 10%, 5%, and 1% levels, respectively.

Panel A (T Bill − OIS)t−1 R2 N obs Panel B (T Bill − OIS)t−1 R2 N obs Panel C (T Bill − OIS)t−1 R2 N obs

LHS: ∆log(RepoOutlt ) US+UK PD UK+Rest PD

US PD

UK PD

0.040* (0.022) 0.166 1,807

0.086*** (0.028) 0.125 1,807

0.066*** (0.019) 0.182 1,807

0.082*** (0.016) 0.146 1,807

0.087*** (0.019) 0.129 1,807

0.022 (0.020) 0.200 1,807

0.061** (0.029) 0.177 1,807

0.046** (0.018) 0.228 1,807

0.043*** (0.014) 0.263 1,807

0.031* (0.017) 0.234 1,807

1.762*** (0.546) . 1,806

1.258*** (0.347) . 1,806

1.329*** (0.323) . 1,806

1.509*** (0.255) . 1,806

1.880*** (0.346) . 1,806

48

Rest PD

Table 8 Daily primary dealer repo issuance separated by different repo maturities Panel A and B shows regressions P of the following form: ∆log(RepoOutmt ) = α + βCYt−1 + η1 ∆log(ShT BillsOutt ) + η2 ∆log(U ST N otesOutt ) + j γ1j ∆log(RepoOutmt−j ) + θXt−1 + t and Panel C shows instrumental variable estiP mations of the following form: CYt−1 = α1 +η∆log(ShT BillsOutt−1 )+ j γ1j ∆log(RepoOutmt−j )+θ1 Xt−1 +t−1 P ˆ t−1 + in the first stage and ∆log(RepoOutmt ) = α2 + β CY γ2j ∆log(RepoOutmt−j ) + θ2 Xt−1 + t in the second j

stage. ∆log(RepoOutmt ) is the log change of total repo outstanding by primary dealers, separated by different repo maturities m. The maturities considered are: all maturities (All), less than 1 week (LT1W), open (Open), less than 1 week and Open (LT1W+Open), and greater than 1 week (GT1W). CYt−1 is (T Bill − OIS)t−1 , the spread of the ˆ t−1 is the fitted value of the convenience yield from the first stage four-week T-bills over the one-month OIS. CY (not shown). ∆log(ShT BillsOutt−1 ) is the lagged log change in T-bills outstanding with maturity less than one month, and ∆log(U ST N otesOutt ) is the log change in US Treasury notes outstanding (not shown). Four lags of ∆log(RepoOutmt ) are included as controls (not shown). Xt−1 are the financial variable controls used in Table 3 (not shown). Newey-West errors with 21 lags are shown in Panel A, clustered errors with week-of-year fixed effects are shown in Panel B, and IV regression using short-term T-bill issuance as an instrument and Newey-West errors with 21 lags are shown in Panel C. The sample runs daily from January 2011 to March 2017. Quarter-end dates are excluded. *, **, ***, denote significance at the 10%, 5%, and 1% levels, respectively.

All Panel A (T Bill − OIS)t−1 R2 N obs Panel B (T Bill − OIS)t−1 R2 N obs Panel C (T Bill − OIS)t−1 R2 N obs

LHS: ∆log(RepoOutmt ) LT1W Open LT1W+Open

GT1W

0.066*** (0.014) 0.180 1,365

0.135*** (0.025) 0.378 1,365

0.075 (0.066) 0.150 1,365

0.121*** (0.025) 0.374 1,365

–0.129* (0.069) 0.601 1,365

0.046*** (0.012) 0.284 1,365

0.102*** (0.024) 0.468 1,365

0.073 (0.095) 0.180 1,365

0.089*** (0.023) 0.464 1,365

–0.164** (0.070) 0.633 1,365

1.706*** (0.289) . 1,364

2.811*** (0.627) . 1,364

3.371** (1.589) . 1,364

2.779*** (0.650) . 1,364

–2.142 (1.557) . 1,364

49

Table 9 Weekly primary dealer repo issuance 5 5 Panel A and B shows regressions P of the following form ∆ log(RepoOutt ) = α + βCYt−5 + η1 ∆ log(ShT BillsOutt ) + η2 ∆5 log(U ST N otesOutt )+ j γ1j ∆5 log(RepoOutt−j∗5 )+θXt−5 +t and Panel C shows instrumental variable estiP mations of the following form: CYt−5 = α1 + η∆log(ShT BillsOutt−5 ) + j γ1j ∆5 log(RepoOutt−j∗5 ) + θ1 Xt − 5 + P ˆ t−5 + t−5 in the first stage and ∆5 log(RepoOutt ) = α2 + β CY γ2j ∆5 log(RepoOutt−j∗5 ) + θ2 Xt−5 + t in the j

second stage. ∆5 log(RepoOutt ) is the five-day log change of total repo outstanding by primary dealers. CYt−5 is ˆ t−5 is the fitted value of the (T Bill − OIS)t−5 , the spread of the four-week T-bills over the one-month OIS. CY convenience yield from the first stage (not shown). ∆5 log(ShT BillsOutt ) is the five-day log change in T-bills outstanding with maturity less than one month, and ∆5 log(U ST N otesOutt ) is the five-day log change in US Treasury notes outstanding. ∆5 log(RepoOutt−j∗5 ) is the j ∗ 5th lagged five-day log change of repo outstanding. The first column shows regressions with two lags, second column shows regressions with three lags, and third column shows regressions with four lags; reporting P -values of lags equal to zero. Xt−5 are financial data controls used in Table 3 (not shown). Newey-West errors with 21 lags are shown in Panel A, clustered errors with week-of-year fixed effects are shown in Panel B, and IV regression using short-term T-bill issuance as an instrument and Newey-West errors with 21 lags are shown in Panel C. The sample runs daily from January 2009 to March 2017. Quarter-end dates, with two days before and after, are excluded. *, **, ***, denote significance at the 10%, 5%, and 1% levels, respectively. LHS: ∆5 log(RepoOutt ) 2 lags 3 lags 4 lags Panel A (T Bill − OIS)t−5 P -value lag R2 N obs Panel B (T Bill − OIS)t−5 P -value lag R2 N obs Panel C (T Bill − OIS)t−5 P -value lag R2 N obs

0.136*** (0.045) 0.019 0.186 1,361

0.143*** (0.047) 0.045 0.176 1,205

0.143*** (0.051) 0.116 0.152 1,047

0.079** (0.036) 0.000 0.394 1,361

0.077* (0.040) 0.000 0.395 1,205

0.058 (0.043) 0.000 0.380 1,047

0.229 (0.167) 0.000 . 1,359

0.376** (0.181) 0.000 . 1,200

0.561*** (0.206) 0.002 . 1,045

50

Table 10 Daily primary dealer and federal reserve repo issuance Panel A and B shows regressions of the following form: ∆log(RepoOutt ) = α + βCYt−1 + η∆log(ShT BillsOutt ) + P η∆log(U ST N otesOutt ) + j γ1j ∆log(RepoOutt−j ) + θXt−1 + t and Panel C shows instrtumental variable estimaP tions of the following form: CYt−1 = α1 + η∆log(ShT BillsOutt−1 ) + j γ1j ∆log(RepoOutt−j ) + θ1 Xt−1 + t−1 P ˆ t−1 + in the first stage and ∆log(RepoOutt ) = α2 + β CY γ2j ∆log(RepoOutt−j ) + θ2 Xt−1 + t in the second j

stage. ∆log(RepoOutt ) is the log change of total repo outstanding by primary dealers (PD) or the Federal Reserve’s RRP program (FRB). CYt−1 is (T Bill − OIS)t−1 , is the spread of the four-week T-bills over the one-month OIS. ˆ t−1 is the fitted value of the convenience yield from the first stage (not shown). ∆log(ShT BillsOutt ) is the CY log change in T- bills outstanding with maturity less than one month, and ∆log(U ST N otesOutt ) is the log change in US Treasury notes outstanding. Four lags of ∆log(RepoOutt ) are included as controls (not shown). Xt−1 are financial data controls used in Table 3 (not shown). Newey-West errors with 21 lags are shown in Panel A, clustered errors with week-of-year fixed effects are shown in Panel B, and IV regression using short-term T-bill issuance as an instrument and Newey-West errors with 21 lags are shown in Panel C. The sample runs daily from December 23, 2013 to March 2017. Quarter-end dates are excluded. *, **, ***, denote significance at the 10%, 5%, and 1% levels, respectively. LHS: ∆log(RepoOutt ) PD FRB Panel A (T Bill − OIS)t−1 R2 N obs Panel B (T Bill − OIS)t−1 R2 N obs Panel C (T Bill − OIS)t−1 R2 N obs

0.053*** (0.017) 0.119 700

–0.587*** (0.197) 0.056 700

0.039* (0.020) 0.260 700

–0.608*** (0.201) 0.227 700

1.220*** (0.314) . 700

–2.630 (1.759) . 700

51