Elsevier

Journal of Monetary Economics

Volume 106, October 2019, Pages 59-77
Journal of Monetary Economics

The short rate disconnect in a monetary economy

https://doi.org/10.1016/j.jmoneco.2019.07.008Get rights and content

Highlights

  • The nominal short market interest rate is below the short rate of a stochastic discount factor that prices longer term assets.

  • The spread between the two rates is procyclical.

  • The short rate disconnect arises because banks value short safe nominal bonds to back inside money.

  • Our model predicts, and we confirm in the data, that at a higher spread, banks choose more risky asset portfolios and lower leverage.

  • The results imply that the transmission of interest rate policy runs through bank balance sheets.

Abstract

In modern monetary economies, most payments are made with inside money provided by payment intermediaries. This paper studies interest rate dynamics when payment intermediaries value short bonds as collateral to back inside money. We estimate intermediary Euler equations that relate the short safe rate to other interest rates as well as intermediary leverage and portfolio risk. Towards the end of economic booms, the short rate set by the central bank disconnects from other interest rates: as collateral becomes scarce and spreads widen, payment intermediaries reduce leverage, and increase portfolio risk. We document stable business cycle relationships between spreads, leverage, and the safe portfolio share of payment intermediaries that are consistent with the model. Structural changes, especially in regulation, induce low frequency shifts, such as after the financial crisis.

Introduction

Current research on monetary policy relies heavily on standard asset-pricing theory. Indeed, it assumes the existence of real and nominal pricing kernels that can be used to value all assets. Moreover, the central bank’s policy rate is typically identified with the short rate in the nominal pricing kernel. With nominal rigidities as in the New Keynesian framework, the central bank then has a powerful lever to affect valuation of all assets – nominal and real – and hence intertemporal decisions in the economy. Focus on this lever makes the pricing kernel a central element of policy transmission.

In spite of its policy relevance, empirical support for monetary asset pricing models has been mixed at best. Models that fit the dynamics of long duration assets, such as equity and long term bonds, often struggle to also fit the policy rate. This is true not only for consumption based asset-pricing models that attempt to relate asset prices to the risk properties of growth and inflation, but also for more reduced-form approaches to describe the yield curve. The finding is typically attributed informally to a convenience yield on short term debt. We refer to it as the “short rate disconnect”.1

This paper proposes and quantitatively assesses a theory of the short rate disconnect that is based on the role of banks in the payment system. We start from the fact that short safe instruments that earn the policy rate are predominantly held by payment intermediaries, in particular commercial banks and money-market mutual funds. We argue that these intermediaries, which we call “banks” throughout this paper, are on the margin between short safe debt and other fixed income claims. We derive new asset-pricing equations that relate the short rate to bank balance-sheet ratios. We show that those equations account quite well for the short rate disconnect, especially at business cycle frequencies.

Our asset-pricing equations follow from the fact that banks issue short nominal debt used for payments. In our model, leverage requires collateral, and the ideal collateral to back short nominal debt is in turn short nominal debt. When such debt becomes more scarce, its equilibrium price rises and the short interest rate falls. In particular, the market short rate disconnects from the short rate of the nominal pricing kernel used to value other assets, such as long term bonds or equity.

Empirically, our approach places restrictions on the joint dynamics of the yield curve and bank-balance sheets that we evaluate with US data since the 1970s. Our measure of the short rate disconnect is the spread between a “shadow” short rate – measured as the short end of a yield-curve model estimated with only medium and long maturity Treasury rates – and the three month T-bill rate. This “shadow spread” captures a cost of safety for banks and rises consistently at the end of booms. As safe collateral becomes scarce and its cost increases, banks increase their share of risky collateral and thereby have a riskier portfolio overall. At the same time, banks lower risk by reducing their leverage in booms, as our theory predicts.

An important feature of the model is that banks choose both their leverage ratios and the share of short safe bonds in their asset portfolio. Optimal leverage trades off low funding costs (due to the liquidity benefit of inside money) against an increasing marginal cost of leverage, as in models with bankruptcy costs. The optimal safe portfolio share trades off the higher return on risky instruments against the cost of backing inside money with worse collateral. Leverage and portfolio safety optimally go together: a safe bank faces a lower cost of leverage and can more cheaply produce inside money.

Adjustment along both margins is crucial for our model to account for the comovement of the safe share, leverage, and the shadow spread in the data. Indeed, a higher shadow spread makes safe bonds more costly to hold, and banks shift their asset portfolio towards risky instruments. As a result, leverage becomes more costly and is optimally reduced. In contrast, a lower shadow spread pushes banks towards safer collateral and higher leverage. Through this mechanism, the model successfully captures the dynamics of bank-balance sheets at business cycle frequencies: a procyclical shadow spread goes along with countercyclical leverage and procyclical portfolio risk taking.

We also study lower frequency movements in balance-sheet ratios and spreads, with an emphasize on the role of macro-prudential regulation. The model predicts low bank leverage in the 1980s when the shadow spread was particularly high. It does so even assuming that bank balance-sheet costs remained unchanged for the last four decades. At the same time, our results suggests that the 2008 financial crisis triggered a structural break: after 2008, higher balance-sheet costs induced banks to hold more safe assets – including a much larger share of reserves – and as a result produce more inside money relative to assets. More generally, once we allow for slow moving shifts in balance-sheet cost parameters over the whole sample, the model captures the low frequency trends in bank leverage while maintaining the fit at business cycle frequencies.

Our results call into question the traditional account of how monetary policy is transmitted to the real economy. The existence of a volatile shadow spread implies that the central bank does not control the short rate of the nominal pricing kernel. Interest rate policy thus relies on pass-through from the policy rate to the shadow rate and hence to intertemporal decisions in the economy. Our bank-based asset-pricing equations suggest that the transmission of monetary policy works at least to some extent through bank-balance sheets. As a result, monetary policy and macroprudential policy are likely to both matter for the course of interest rates.2

Formally, our model describes the behavior of a banking sector that maximizes shareholder value subject to financial frictions. We capture the rest of the economy by two standard elements: a pricing kernel used by investors to value assets – in particular bank equity – and a broad money demand equation that relates the quantity of deposits to their opportunity cost. Our approach is thus in the spirit of consumption-based asset pricing pioneered by Breeden (1979) and Hansen and Singleton (1983): we test valuation equations that must hold in general equilibrium, without taking a stand on many other features of the economy, in particular the structure of the household sector, and the technology and pricing policy of firms.3

In our model, the key friction faced by banks is that delegated asset management is costly, and more so if it is financed by debt. We assume that a bank financed by equity requires a proportional balance-sheet cost per unit of assets. If the bank also issues deposits, the resource cost per unit of assets is increasing in bank leverage, so banks’ marginal cost of debt is upward sloping. One interpretation is that debt generates the possibility of bankruptcy, which entails deadweight costs proportional to assets. An upward sloping marginal cost of debt implies that the portfolio choice of levered banks looks as if the banks are more risk averse than their shareholders.4 In particular, since banks issue short nominal debt, they value safe short nominal debt as collateral. It is this collateral benefit of short debt that generates the short rate disconnect in our model.

We solve banks’ optimization problem and evaluate their first order conditions, given an incomplete asset market structure: banks can invest in reserves, short safe bonds that earn the policy rate, as well as risky assets that stand in for other fixed income claims available to banks such as loans. We show that there is no short rate disconnect when bank assets are safe, that is, banks only hold reserves and short nominal bonds. More generally, however, the collateral benefit of short bonds generates a wedge between the market short rate and the short rate in the nominal pricing kernel. The resulting shadow spread is higher when banks have a larger share of their portfolio invested in risky assets: risky banks place a particularly high value on short nominal bonds relative to other investors, such as bank shareholders. The banks’ optimization problem also implies that when the shadow spread is high, banks counteract the increase in risk on their asset side by reducing risk on their liability side. During these times, banks thus reduce their leverage.

Quantitative assessment of our theory requires data on balance sheets. To measure the positions of payment intermediaries, we consolidate banks and money market funds: both institutions offer payment services to households and corporations. We further define safe assets as assets with short maturity that are nominally safe (such as reserves, vault cash, and government bonds). Finally, we define leverage as the ratio of inside money to total fixed income assets net of other debt that can be viewed as senior to inside money. To measure inside money, we use a broad concept of money that includes money market accounts. The raw fact that provides evidence for our mechanism is that payment intermediaries have a portfolio share of safe assets as well as a leverage ratio that are strongly negatively correlated with the shadow spread, both at business cycle frequencies and over longer periods.5

Our approach builds on the idea that bonds earn a convenience yield, pioneered by Patinkin (1956) and Tobin (1963). Recent examples include Bansal and Coleman (1996), Krishnamurthy and Vissing-Jorgensen (2012), Venkateswaran and Wright (2014), Andolfatto and Williamson (2015), Nagel (2016), and Woodford (2016). In these models, the convenience yield reflects a nonpecuniary benefit to investors who hold the bonds, analogously to a convenience yield on money: for example, bonds enter the utility function or relax cash-in-advance constraints. In our model, in contrast, investors receive a nonpecuniary benefit from inside money, but do not hold short bonds directly. Indeed, they perceive short bonds as too expensive because the short rate reflects a convenience yield earned by banks that supply inside money. Investors receive the convenience yield on short bonds – and the nonpecuniary benefit of lower balance-sheet cost – only indirectly as bank shareholders.

Our model thus contributes to the growing literature on intermediary-based asset pricing that studies equilibrium relationships between asset prices and balance-sheet ratios.6 However, while the literature has focused on assets that are held by intermediaries because of their complexity – for example, mortgage-backed securities or credit-default swaps – our intermediaries price what is arguably one of the simplest assets: short nominal bonds. At the same time, our approach is not inconsistent with the presence of convenience yields in assets other than short bonds. For example, the model in Lenel (2018) incorporates a convenience yield on long bonds earned by hedge funds that use such bonds as collateral. Through the lens of the current model, this convenience yield is incorporated into the pricing kernel of investors.

Our theory is based on the scarcity of safe short assets available to banks, measured by the shadow spread. A related, but distinct, concept is the scarcity or reserves, measured by the spread between a market short rate (such as the three month T-bill rate) and the interest rate on reserves. The distinction has come into sharp focus recently as central bank operating procedures have changed. Indeed, after quantitative easing increased the quantity of reserves in 2008, the spread between T-bill and reserve rates turned negative. In contrast, the short rate disconnect we document is present both before and after 2008. Our paper is thus only tangentially related to work on bank liquidity management that relates bank behavior to the level of the short rate (for example, Bhattacharya, Gale, 1987, Bianchi, Bigio, 2014, Cúrdia, Woodford, 2011, De Fiore, Hoerova, Uhlig, 2018, Drechsler, Savov, Schnabl, 2018, Reis, 2016, Whitesell, 2006.) In general, we would expect bank Euler equations for both safe and liquid assets to hold jointly. For example, Piazzesi and Schneider (2018) consider a model that incorporates both bank liquidity management and a scarcity of bank collateral as in the present paper and derive its implications for monetary policy.

In the wake of the recent financial crisis, a growing literature studies monetary policy when banks face financial frictions. One strand assumes that banks have a special ability to lend, and hence add value via positions on the asset side of their balance sheets (for example, Brunnermeier, Sannikov, 2016, Christiano, Motto, Rostagno, 2012, Christiano, Motto, Rostagno, 2014, Cúrdia, Woodford, 2010, Del Negro, Eggertsson, Ferrero, Kiyotaki, 2017, Gertler, Karadi, 2011, Gertler, Kiyotaki, Queralto, 2012, and Brunnermeier and Koby, 2018. These papers also distinguish assets priced by banks – for example bank loans – from assets priced by households, which include the policy instrument. Policy transmission depends on pass-through from the policy rate (which aligns with households’ expected marginal rate of substitution) to the loan rate and hence to bank-dependent borrowers.

Our paper assumes that banks have a special ability to provide inside money as a medium of exchange. We share this “liability centric” view of banking with e.g. Williamson (2012), Hanson et al. (2015), Williamson (2016), Begenau (2019), and Diamond (2019). As in these papers, banks’ portfolio choice in our model is shaped by banks’ ability to fund themselves with deposits. In our case, banks value short safe debt as particularly good collateral for inside money, which serves as the only medium of exchange.

Section snippets

The short rate disconnect in the data

Our theory implies that the interest rate on nominal safe short bonds reflects valuation by payment intermediaries, whereas other bonds – including longer Treasuries – may be priced directly by investors. The shadow rate – the short rate in investors’ pricing kernel – is thus not directly observable in the market since investors do not hold short bonds.

However, we can derive an estimate of the shadow rate from the prices of longer safe bonds. Indeed, interest rates of different maturities are

A model of the short rate disconnect

We study an economy with a single consumption good and an infinite horizon. There is a group of agents, whom we will call “investors”, who hold bank equity as well as other risky assets directly. Investors use inside money as a payment instrument. The inside money is provided by competitive banks. We do not model in detail what the investor sector does: Section 3.1 simply summarizes how that sector values assets, including inside money. With this approach, we can focus on a model mechanism that

Quantitative evaluation

In this section we connect the model to the data. Section 4.1 provides evidence on a key assumption of the model, that short safe bonds are not held directly by households, but are held through intermediaries, in particular payment intermediaries. Section 4.2 provides measures of bank balance-sheet ratios and uses them to test the bank Euler equations under the assumption that the regulatory environment remains constant. Finally, Section 4.3 extends the model to allow for changes in regulation

Conclusion

The results presented in this paper support the idea that financial intermediaries value short bonds as safe collateral to back the issuance of payment instruments. The emerging collateral premium drives a wedge between the policy rate and the short rate associated with the pricing kernel of non-bank investors. In our model, this short-rate disconnect has implications for banks’ balance-sheet decisions, which are consistent with data. Our findings question the standard assumption in current

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      We also provide strong empirical support for the theoretical predictions. Our paper is also related to studies of the collateral market of safe assets, including Duffie (1996), Duffie et al. (2002), Gorton and Metrick (2012), Krishnamurthy et al. (2014), Bartolini et al. (2011), Hu et al. (2019), Song and Zhu (2019), and Lenel et al. (2019). Our paper contributes to the literature on intermediary-based asset pricing à la He and Krishnamurthy (2013), especially studies that highlight constraints on dealers such as He et al. (2017), Klingler and Sundaresan (2019), Jermann (2019), Fleckenstein and Longstaff (2020), Boyarchenko et al. (2018), and He et al. (2019a).

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    We thank Hengjie Ai, Alan Moreira, Tyler Muir, Ricardo Reis, Oreste Tristani, Michael Woodford as well as an anonymous referee for helpful comments. We also thank the NSF (Grant number: 1559446) for a research grant that supported this project.

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