Does the cost of private debt respond to monetary policy? Heteroskedasticity-based identification in a model with regimes

Abstract

We investigate the effects of the Federal Reserve's quantitative easing and maturity extension programs on the yields of US dollar-denominated corporate bonds using a multiple-regime heteroskedasticity-based VAR identification approach. Impulse response functions suggest that a traditional, rate-based expansionary policy may lead to an increase in yields while quantitative easing is linked to a general and persistent decrease in yields, particularly for long-term bonds. The responses generated by the maturity extension program are significant and of larger magnitude. A decomposition shows that the unconventional programs reduce the cost of private debt primarily through a reduction in risk premia that cannot be entirely accounted for by a reduction in corporate default risk.

KEYWORDS:

• Unconventional monetary policy
• transmission channels
• heteroskedasticity
• vector autoregressions
• identification
• corporate bond yields

JEL code::

• G12
• C32
• G14

Acknowledgements

We thank Chris Adcock (the editor of the Journal), one anonymous associate editor, and two anonymous referees for insightful comments and encouragement.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Krishnamurthy and Vissing-Jorgensen (2012) and Gagnon et al. (2011) found that LSAP1 induced a decline in the 10-year Treasury yield of 100 bps and 91 bps, respectively. LSAP2 was studied, among others, by Greenwood and Vayanos (2014), Krishnamurthy and Vissing-Jorgensen (2012), Meaning and Zhu (2011), and Swanson (2011) who reported a reduction in Treasury yields in the range 15–55 bps. Hamilton and Wu (2012) have documented that MEP reduced Treasury yields with a maturity in excess of 2 years by about 17 bps, while short-term yields increased by a similar amount.

2 The performance of the identification via IH depends on the relative size of the volatility shifts (that should be large for accurate identification) and the length of the sample (to exceed 200 observations). Our application fulfills the requirements in Herwartz and Plodt to support an IH identification scheme.

3 The existence of regimes in the (long-run) relationships between interest rates (official, credit and government debt), monetary aggregates (money stock and monetary base) and real income has been recently exploited by Olmo and Sanso-Navarro (2015) to test the existence of a shift in the transmission mechanism through which the unconventional policies affected the economy. However, their focus is not explicitly on the effectiveness of different types of unconventional monetary policies on yields.

4 We consider U.S. Corporate Debentures, Corporate Medium Term Notes, and U.S. Corporate MTN Zeros.

5 For some trades, the yield is missing in the TRACE repository: in that case we use the coupon rate, payment frequency, issue date, and remaining time to maturity to calculate the yield using standard formulas. We have also tried to build portfolios weighted by their outstanding amounts and found qualitatively similar results in terms of their means and standard deviations of the portfolio yields.

6 Results are insensitive to replacing 1mT_t with the effective Federal funds rate.

7 As it is customary, a VAR(p) with p > 1 can also be represented in companion form as a VAR(1) by simply expanding the vector of endogenous variables to include lags of ${\mathit{y}}_t$ up to p -1. In the following, we work with a VAR(1) representation while being aware that a higher-order VAR may be easily accommodated. Although a 8-variable system is by no means small, higher-dimensional systems have been considered, e.g. in Bernanke, Boivin, and Eliasz (2005), that contain more variables than just the interest rates that we entertain in this paper. Resorting to a ninth common factor variable in Section 5.1 takes steps in this direction. There is also a literature that has extended such large systems to study the effects of the sacrifice ratio between growth and inflation. For instance, Gross and Semmler (2019) use regime switching SVARs to contrast the effects of conventional and unconventional monetary policies.

8 As shown in Rigobon (2003), the estimates of the conditional mean coefficients are consistent, regardless of how the heteroskedasticity is modelled, provided the number of regimes has been correctly specified.

9 When the data exhibit S heteroscedasticity regimes, the system that has S[N + (N²−N)/2] equations (one covariance matrix per regime) and N² − N + SN unknowns (N structural variances for each regime, plus the parameters of A). A solution is guaranteed for S[N + (N²−N)/2] ≥ N² − N + SN, which is satisfied for S ≥ 2. In particular, the system is exactly identified in presence of two regimes. Otherwise, the system has more equations than unknowns and the additional equations provide testable over-identifying restrictions.

10 A rotation is the multiplication of the matrix A by another matrix that is full rank and has determinant equal to one. Since both the matrix A and its rotation solve the system, the problem of how to differentiate the two is solved in practice by imposing additional exclusion or sign restrictions to force upon the methodology the selection of a unique rotation.

11 The sign of the restrictions are negative but this is not inconsistent with standard economic meaning because the matrix A pre-multiplies the endogenous variables on the left-hand side of (1).

12 The sign restrictions limit the space in which parameters have to be searched to minimize the moment restrictions. This influences the speed of convergence but does not affect precision unless the estimates are on the boundaries. As we will see later, very few of the coefficients are on the boundaries.

13 Bacchiocchi and Fanelli (2015) show that identification may be achieved even allowing the VAR matrices to change across regimes as well. However, this requires imposing additional exclusion restrictions on A, which may be undesirable in our application, or—which is our case—that the number of regimes exceed the strict minimum to achieve identification, here S = 2.

14 The ADS index is based on a number of observable economic indicators: weekly initial jobless claims, monthly payroll employment, industrial production, personal income less transfer payments, manufacturing and trade sales, and quarterly real GDP, see Aruoba, Diebold, and Scotti (2009).

15 Additional details concerning the bootstrapping exercise can be found in a working paper version of the manuscript at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3458310.

16 The IRFs are not altered by adding (simultaneous and lagged) common shocks, as the latter are not perturbed by the policy impulse(s) and thus they cancel out.

17 Such shock sizes compare to an estimated one-standard deviation of errors equal to 15 bps in the case of 10-year Treasuries and of 4 bps in the case of 1-month T-bills in the crisis regime. The estimated error standard deviations are substantially lower in regimes 1 and 2. This means that the baseline results in Section 4 may grossly under-estimate the potential quantitative effects of QE. Separate calculations that asymmetrically increase 1-month T-bills by one standard deviation but decrease 10-year Treasury rates by twice their standard deviation to represent a MEP-style shock also confirm that Section 4 provides a substantial under-estimation of the potential effects derived in our exercise, especially in the crisis regime.

18 To select the proper order of the VAR model, we use the Bayesian Information Criterion (BIC). When p ranges between 0 and 10, we select a VAR(1) model. The VAR(1) turns is stable and hence covariance stationary. The OLS estimates of the model are reported in an Appendix available upon request.

19 We formally test the occurrence of the regimes in the reduced-form variances through a standard LR Chow-type test. We focus on the null hypothesis that the VAR reduced-form residual variances are constant across the three regimes, ${\mathbf{\Sigma }}_{ϵ}^1={\mathbf{\Sigma }}_{ϵ}^2={\mathbf{\Sigma }}_{ϵ}^3$ for a total of 72 restrictions. The null hypothesis of constant covariance parameters is starkly rejected.

20 The preferred-habitat theory has been recently formalized by Vayanos and Vila (2009). While the expectation hypothesis states that the presence of risk-neutral agents implies that the term structure is determined only by current and expected short rates, the preferred-habitat theory states that markets are segmented and the relative supply of assets influences their yields for each specific maturity. In this framework, preferred-habitat investors have a strong preference for a specific maturity segment and demand only bonds that correspond to their maturity habitat.

21 Even in normal times, the Fed might be using non-borrowed reserves in addition to short rate impulses to implement conventional policies. Moreover, in spite of their high correlations, 1-month rates are an imperfect proxy for shocks to the Fed funds rate. We abstract from these aspects in our analysis.

22 The finding that the undesirable effects of rate cuts would be weaker and imprecisely estimated in correspondence to regime 1 (that characterizes the sub-period 2011–2016) is fully consistent with the finding in Brunnermeier and Koby (2018) that over time, after the end of the GFC and the normalization of the functioning of the US credit markets, the reversal interest rate would slowly increase as asset revaluation fades out and fixed-income holdings mature: most of regime 1 may be characterized by rates close to zero but yet large enough to fall close to this endogenous lower bound without causing contractionary effects, also because the net interest margins and the overall profitability of US banks did improve starting in 2012–2013 (see Tran, Lin, and Nguyen 2016). Ampudia and van den Heuvel (2018) show that banks’ profitability response to interest rate cuts is non-monotonic – in normal times, interest rate cuts increase banks’ valuations, although this does not hold in low-rate environments.

23 Guidolin, Orlov, and Pedio (2017) perform robustness checks on the Cholesky ordering and report generalized IRFs, but the tendency of the response of high-grade to exceed that of low-grade rates turns out to be pervasive.

24 Guidolin et al.'s triangular factorization follows two criteria: variables to be shocked, i.e. long, medium and short Treasury rates, are placed on top of the ordering; the rest of the variables are ordered on the basis of their residual maturity, with Treasuries preceding corporate bonds. Figure 6 concerns the effects of a one standard deviation shock to 10-year Treasury yields that want to mimic the effects of QE, but a similar figure has been produced in the case of the MEP and is available upon request from the authors.

25 A set of plots available upon request shows that especially in the crisis regime 3 and with reference to short-term bonds, expansionary conventional rate-based policies keep leading to undesirable effects on the cost of debt of corporations, even though most of the response functions fail to be precisely estimated. We thank one anonymous referee for suggesting this robustness check.

26 We discretize the time-to-maturity of each corporate bond in the following categories, by selecting the closest from the list: 1 month, 3 months, 6 months, 1 year, 2 years, 3 years, 5 years, 7 years, and 10 years. Then, we match such imputed maturity with Treasuries of similar maturity traded in the market.

27 The model contains eight endogenous variables, i.e. the 1-month T-bill rate along with seven corporate and government bond yield spreads. Therefore 4 of the spreads concern corporate bonds and are obtained in the way described in the main text and the remaining three are term spread inferred from the term structure of riskless interest rates, computed as a difference between long-term and 1-month yields.

28 This is consistent with the empirical findings in Guo, Kontonikas, and Maio (2020) for the GFC period and with the result in Figure 6 that the negative relationship between changes in short rates and spreads is most pronounced for lower-rated corporate credits, a segment of the market that was especially vulnerable to adverse macroeconomic shocks during the early stages of the GFC.

29 During a crisis, IGST bonds may become illiquid and this may increase their yields above the level justified by a decline of the riskless rate as well as of the default risk premia induced by QE.

30 This is more realistic than the results in Figure 7 on the total, weekly credit spreads on corporate bonds, in which credit spread would be shooting up in a significant matter for several weeks after the initial shock. The wide confidence bands attached to the regime 1 IRF in the plots derive from the fact that in this monthly analysis, regime 1 just characterizes 20 observations out of 150 (a fraction of the sample similar to what is reported in Figure 2, but for weekly data) which leads to imprecise estimates.