Credit Risk and the Macroeconomy
Simon Gilchrist∗
Egon Zakrajšek†
May 6, 2010
Abstract
We construct a new credit spread index, employing an extensive micro-level data
set of secondary market prices of outstanding senior unsecured bonds over the 1973–
2009 period. Compared with the standard default-risk indicators such as the Baa-Aaa
corporate bond spread and the paper-bill spread, our credit spread index is a robust
predictor of future economic activity across a variety of economic indicators, sample
periods, and forecast horizons. Using a flexible empirical bond-pricing framework, we
decompose our credit spread index into a predictable component that captures the available firm-specific information on default risk and a residual component—the so-called
excess bond premium. The results indicate that a substantial portion of the predictive
content of our credit spread index for economic activity is attributable to the excess
bond premium. Indeed, in the post-1985 period, the excess bond premium accounts
for all of the predictive content of our credit spread index. Shocks to the excess bond
premium that are orthogonal to current economic activity, the information contained
in the term structure of interest rates, and news embedded in the stock market returns
are shown to cause economically and statistically significant declines in consumption,
investment, and output. Overall, our findings are consistent with the notion that an
increase in the excess bond premium reflects a reduction in the risk appetite of the
financial sector and, as a result, a contraction in the supply of credit, which has significant adverse consequences for economic outcomes.
JEL Classification: E32, E44, G28
Keywords: corporate bond credit spreads, economic fluctuations, financial frictions
Robert Kurtzman and Michael Levere provided outstanding research assistance. The views expressed in
this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of
the Board of Governors of the Federal Reserve System or of anyone else associated with the Federal Reserve
System.
∗
Department of Economics Boston University and NBER. E-mail: sgilchri@bu.edu
†
Division of Monetary Affairs, Federal Reserve Board. E-mail: egon.zakrajsek@frb.gov
1
Introduction
The United States is in the process of emerging from the throes of an acute liquidity and
credit crunch, by all accounts, the most severe financial crisis since the Great Depression.
At the height of the crisis in the autumn of 2008, the government, in an attempt to prevent
the financial meltdown from engulfing the real economy, effectively assumed control of a
number of systemically important financial institution; the Congress, faced with investors’
rapidly deteriorating confidence in the financial sector, approved the plan to inject a massive
amount of capital into the banking system; and the Federal Reserve dramatically expanded
the number of emergency credit and liquidity facilities in an attempt to support the functioning of private debt markets. Throughout this period of extreme financial turmoil, credit
spreads—the difference in yields between various private debt instruments and government
securities of comparable maturity—served as a crucial gauge of the degree of strains in
the financial system. In addition, movements in credit spreads were thought to contain
important signals regarding the evolution of the real economy and risks to the economic
outlook.1
This focus on credit spreads is motivated, in part, by financial theories that depart
from the Modigliani and Miller [1958] paradigm of frictionless financial markets, theories
that emphasize linkages between the quality of borrowers’ balance sheets and their access
to external finance. Movements in credit spreads may also reflect shifts in the effective
supply of funds offered by financial intermediaries, which, in the presence of financial market
frictions, have important implication for the usefulness of credit spreads as predictors of
future economic activity. In this interpretation, a deterioration in the balance sheets of
financial intermediaries leads to a reduction in the supply of credit, causing an increase
in the effective cost of external funds—the widening of credit spreads—and a subsequent
reduction in spending and production. In either case, credit spreads play a crucial role in
the dynamic interaction of financial conditions with the real economy.
In this paper, we re-examine and reconsider the evidence on the relationship between
credit spreads on corporate bonds and economic activity. We extend the standard empirical
analysis by attempting to separate the predictive content of such default-risk indicators for
economic activity into two components: a component capturing the usual countercyclical
movements in expected defaults; and a component representing the cyclical changes in the
relationship between expected default risk and credit spreads. Our approach builds on the
recent work of Gilchrist, Yankov, and Zakrajšek [2009] (GYZ hereafter), in that we use prices
1
The predictive content of various credit spreads for future economic activity has been analyzed by
Bernanke [1990]; Friedman and Kuttner [1992, 1998]; Emery [1999]; Gertler and Lown [1999]; Mody and
Taylor [2004]; King, Levin, and Perli [2007]; Mueller [2007]; Gilchrist, Yankov, and Zakrajšek [2009]; and
Faust, Wright, Gilchrist, and Zakrajšek [2010].
1
of individual corporate securities traded in the secondary market to construct a credit spread
index with a high information content for future economic activity. Our forecasting results
indicate that the predictive content of this credit spread for various measures of economic
activity significantly exceeds that of widely-used financial indicators such as the standard
Baa-Aaa corporate credit spread and indicators of the stance of monetary policy such as
the shape of the yield curve or the real federal funds rate. However, as shown recently
by Philippon [2009], the predictive content of credit spreads for economic activity could
reflect—absent any financial market frictions—the ability of the corporate bond market to
signal more accurately than the stock market a decline in economic fundamentals resulting
from a reduction in the expected present-value of corporate cash flows prior to a cyclical
downturn.2
To address this thorny identification issue, we decompose our high-information content
credit spread index into a component that captures expected default risk and other observable pricing factors and a residual component that reflects a premium in the bond market.
We then examine the extent to which the forecasting power of credit spreads is due to the
measurable default component or the excess bond premium. According to our analysis, a
substantial portion of the information content of default-risk indicators can be attributed
to the deviations in the pricing of corporate debt instruments relative to the expected default risk of the underlying issuer. This finding indicates that information about impending
financial disruptions embedded in prices of corporate bonds may account for a significant
portion of the forecasting power of credit spreads for economic activity. Using an identified
vector autoregression (VAR) framework, we also analyze the dynamic interaction between
the real economy, the stock market, and the excess bond premium.
The remainder of the paper is organized as follows. Section 2 describes the construction
of our high-information content credit spread index. In Section 3, we compare the forecasting power of the GZ index to that of some standard financial indicators. In Section 4,
we describe the methodology for decomposing credit spreads into a predicted component
due to expected defaults and a residual component—the so-called excess bond premium.
In Section 5, we evaluate the relative predictive ability of the default component and the
excess bond premium for various measures of economic activity; we also analyze the effect of
financial shocks—identified by orthogonalized movements in the excess bond premium—on
the macroeconomy. Section 6 concludes.
2
The information content of the stock market for future economic activity has been analyzed by Fama
[1981] and Harvey [1989].
2
2
Data Sources and Methods
Yield spreads on corporate debt instruments have long been used to gauge the degree of
strains in the financial system. Moreover, because financial asset prices are forward looking,
movements in corporate credit spreads have been shown to be particularly useful for forecasting economic activity. Despite considerable empirical success, results from this strand
of research are often sensitive to the choice of a credit spread index under consideration,
as credit spreads that contained useful information about macroeconomic outcomes in the
past often lose their predictive power for the subsequent cyclical downturn.3 These mixed
results are partly attributable to the rapid pace of financial innovation that likely alters the
forecasting power of financial asset prices over time or results in one-off developments that
may account for most of the forecasting power of a given credit spread index.
In part to address these problems, GYZ utilized secondary market prices of individual
senior unsecured corporate debt issues to construct a broad array of corporate bond spread
indexes that vary across maturity and default risk. Compared with other corporate financial
instruments, senior unsecured bonds represent a class of securities with a long history
containing a number of business cycles, and the rapid pace of financial innovation over
the past two decades has done little to alter the basic structure of these securities. Thus,
the information content of spreads constructed from yields on senior unsecured corporate
bonds is likely to provide more consistent signals regarding economic outcomes relative
to spreads based on securities with a shorter history or securities whose structure or the
relevant market has undergone a significant structural change. The results of GYZ confirm
this: At forecast horizons associated with business cycle fluctuations, the predictive ability
of their credit spreads significantly exceeds—both in-sample and out-of-sample—that of
the commonly-used default-risk indicators, such as the paper-bill spread or the Baa and the
high-yield corporate credit spread indexes.
In this paper, we employ the same “bottom-up” approach. In particular, for a sample of
U.S. nonfinancial firms, month-end secondary market prices of their outstanding securities
were obtained from the Lehman/Warga (LW) and Merrill Lynch (ML) databases.4 To
3
For example, the spread of yields between nonfinancial commercial paper and comparable-maturity
Treasury bills—the so-called paper-bill spread—has lost much of its forecasting power since the early 1990s.
Indeed, according to Thoma and Gray [1998] and Emery [1999], the predictive content of the paper-bill
spread may have reflected a one-time event. Similarly, yield spreads based on indexes of high-yield corporate
bonds, which contain information from markets that were not in existence prior to the mid-1980s, have done
particularly well at forecasting output growth during the previous decade, according to Gertler and Lown
[1999] and Mody and Taylor [2004]. Stock and Watson [2003], however, find mixed evidence for the high-yield
spread as a leading indicator during this period, largely because it falsely predicted an economic downturn
in the autumn of 1998.
4
These two data sources include secondary market prices for a majority of dollar-denominated bonds
publicly issued in the U.S. corporate cash market. The ML database is a proprietary data source of daily
bond prices that starts in 1997. Focused on the most liquid securities in the secondary market, bonds in the
3
ensure that we are measuring long-term borrowing costs of different firms at the same point
in their capital structure, we limited our sample to senior unsecured issues only. For the
securities carrying the senior unsecured label and with market prices in both the LW and
LM databases, we spliced their month-end prices across the two data sources.
To calculate credit spreads, we constructed for each individual corporate issue a corresponding risk-free security that mimics exactly the cash-flows of the corresponding corporate
debt instrument. In particular, consider a corporate bond k issued by firm i that at time
t is promising a sequence of cash-flows {C(s) : s = 1, 2, . . . , S}, consisting of the regular
coupon payments and the repayment of the principle at maturity. The price of this bond
is given by
Pit [k] =
S
X
C(s)D(ts ),
s=1
where D(t) = e−rt t is the discount function in period t. To calculate the price of a corresponding risk-free security—denoted by Ptf [k]—we discounted the cash-flow sequence
{C(s) : s = 1, 2, . . . , S} using continuously-compounded zero-coupon Treasury yields in
period t, obtained from the daily estimates of the U.S. Treasury yield curve reported by
Gürkaynak, Sack, and Wright [2007]. The resulting price Ptf [k] can then be used to calculate the yield—denoted by ytf [k]—of a hypothetical Treasury security with exactly the same
cash-flows as the underlying corporate bond. The credit spread sit [k] = yit [k] − ytf [k], where
yit [k] denotes the yield of the corporate bond k, is thus free of the “duration mismatch”
that would occur were the spreads computed simply by matching the corporate yield to the
estimated yield of a zero-coupon Treasury security of the same maturity.5
Table 1 contains summary statistics for the key characteristics of bonds in our sample.
Note that a typical firm has only a few senior unsecured issues outstanding at any point
in time—the median firm, for example, has two such issues trading at any given month.
This distribution, however, exhibits a significant positive skew, as some firms can have
as many as 74 different senior unsecured bond issues trading in the market at a point in
time. The distribution of the real market values of these issues is similarly skewed, with the
range running from $1.2 million to more than $5.6 billion. Not surprisingly, the maturity of
these debt instruments is fairly long, with the average maturity at issue of about 13 years.
ML database must have a remaining term-to-maturity of at least two years, a fixed coupon schedule, and a
minimum amount outstanding of $100 million for below investment-grade and $150 million for investmentgrade issuers. By contrast, the LW database of month-end bond prices has a somewhat broader coverage
and is available from 1973 through mid-1998 (see Warga [1991] for details).
5
To mitigate the effect of outliers on our analysis, we eliminated all observations with credit spreads below
5 basis points and with spreads greater than 3,500 basis points. We also eliminated a small number of putable
bonds from our sample. These selection criteria yielded a sample of 5,269 individual securities between
January 1973 and December 2009. We matched these corporate securities with their issuer’s quarterly and
annual income and balance sheet data from Compustat and daily data on equity valuations from CRSP,
yielding a matched sample of 944 firms.
4
Because corporate bonds typically generate significant cash flow in the form of regular
coupon payments, the effective duration is considerably shorter, with both the average and
the median duration of about 6 years.
According to the S&P credit ratings, our sample spans the entire spectrum of credit
quality, from “single D” to “triple A.” At “BBB1,” however, the median bond/month observation is still solidly in the investment-grade category. Turning to returns, the (nominal)
coupon rate on these bonds averaged 7.31 percent during our sample period, while the average total nominal return, as measured by the nominal effective yield, was 7.82 percent
per annum. Reflecting the wide range of credit quality, the distribution of nominal yields is
quite wide, with the minimum of 0.66 percent and the maximum of more than 44 percent.
Relative to Treasuries, an average bond in our sample generated a return of about 202 basis
points above the comparable risk-free rate, with the standard deviation of 284 basis points.
Figure 1 shows the average credit spread (GZ spread) for our sample of bonds at each
point in time; it also displays two widely used default-risk indicators: the yield spread
between 1-month A1/P1-rated nonfinancial commercial paper and the 1-month Treasury
yield (i.e., the paper-bill spread); and the spread between yields on indexes of Baa- and
Aaa-rated seasoned industrial corporate bonds (i.e., Baa-Aaa spread).6 All three credit
spreads exhibit pronounced countercyclical movements, rising prior to and during economic
downturns. Nonetheless, the pair-wise correlations between the three series are fairly small:
The correlation between the paper-bill and the Baa-Aaa spread is 0.22, whereas the correlation between the paper-bill spread and the GZ credit spread is only 0.09. Perhaps not too
surprising, the highest correlation, 0.36, is between the two corporate bond credit spread
indexes. With regards to variability, the Baa-Aaa spread is the least volatile with a standard deviation of about 50 basis points. In contrast, the volatility of the paper-bill and the
GZ spread, at about 67 basis points, is somewhat higher.7
6
Other than than the GZ spread, all yields are taken from the “Selected Interest Rates” (H.15) statistical
release published by the Federal Reserve Board. Note that the GZ credit spread is measured relative
to Treasury yields, whereas the Baa-Aaa spread is defined as the difference between yields on long-term
corporate debt instruments of varying credit quality. As emphasized by Duffee [1998], for example, the
corporate-Treasury yield spreads can be influenced significantly by time-varying prepayment risk premiums,
reflecting the call provisions on corporate issues. According to Duca [1999], corporate bond spread indexes
measured relative to the yield on Aaa-rated bonds are more reflective of default risk than those measured
relative to comparable-maturity Treasuries.
7
A significant portion of the volatility in the paper-bill spread reflects year-end funding pressures. These
pressures can arise as the maturity of the paper crosses over year-end, and investors demand a premium to
hold paper—especially lower-rated paper—over the turn of the year. Trends in business sector credit quality
and the amount of outstanding commercial paper are important determinants of year-end pressures.
5
3
Credit Spreads and Economic Activity
This section examines the predictive power of the GZ credit spread for various measures of
economic activity and compares its forecasting performance with that of several commonly
used financial indicators. Letting Yt denote a measure of economic activity—in logarithms
if necessary—in period t, we define
h
∇ Yt+h
c
≡
h
Yt+h
Yt
,
where h denotes the forecast horizon and c is a scaling constant, with c = 1, 200 in the
case of monthly data and c = 400 in the case of quarterly data. We estimate the following
univariate forecasting specification:
h
∇ Yt+h = α +
p
X
i=0
βi ∇Yt−i + γ1 TSt3M −10Y + γ2 RFFt + γ3 CSt + ǫt+h ,
(1)
where TSt3M −10Y denotes the “term spread”—that is, the slope of the Treasury yield curve,
defined as the difference between the three-month constant-maturity Treasury yield and the
10-year constant-maturity yield;8 RFFt denotes the real federal funds rate;9 CSt denotes a
credit spread; and ǫt+h is the forecast error. The forecasting regression given by equation 1
is estimated using OLS, and the MA(h − 1) structure of the error term induced by overlap-
ping observations is taken into account by computing the covariance matrix of regression
coefficients according to Hodrick [1992].10
Within this forecasting framework, we analyze the predictive content of financial asset
8
The role of the term spread in forecasting economic growth or for assessing the near-term risk of recession
has been analyzed by Dotsey [1998], Estrella and Hardouvelis [1991], Estrella and Mishkin [1998], and
Hamilton and Kim [2002]. More recent work on this topic includes Ang, Piazzesi, and Wei [2006] and
Wright [2006].
9
In calculating the real federal funds rate, we employed a simplifying assumption that the expected
inflation is equal to lagged core PCE inflation. Specifically, real funds rate in period t is defined as the
average effective federal funds rate during period t less realized inflation, where realized inflation is given by
the log-difference between the core PCE price index in period t − 1 and its lagged value a year earlier. Of
course, under the expectations hypothesis—and neglecting term premiums—the term spread is an indicator
of the stance of monetary policy—the higher the term spread, the more restrictive is the current stance of
monetary policy and, hence, the more likely is economy to decelerate in subsequent quarters. In general,
however, the shape of the yield curve contains information about term premiums and the average of expected
future short-term interest rates over a relatively long horizon. As emphasized by Hamilton and Kim [2002]
and Ang et al. [2006], the term premium and expectations hypothesis components of the term spread have
very different correlations with future economic growth. The federal funds rate, in contrast, is a measure of
the stance of monetary policy that is relatively unadulterated by the effects of time-varying term premiums.
10
In a recent paper, Ang and Bekaert [2007] undertook a systematic comparison of various HAC estimators
of standard errors in the context of overlapping observations. According to their findings, the use of Newey
and West [1987] standard errors leads to severe over-rejections of the null hypothesis of no predictability,
whereas the standard errors developed by Hodrick [1992] retain the correct size even in relatively small
samples. That said, all of our results were robust to the choice of Newey-West or Hodrick standard errors.
6
prices for several categories of economic activity indicators. First, we examine the forecasting ability of financial indicators for changes in monthly economic indicators related to labor
market conditions: the growth of private (nonfarm) payroll employment and the change in
the (civilian) unemployment rate. Given the lagging nature of labor market indicators,
we also consider a coincident economic indicator, the growth in manufacturing industrial
production. Using quarterly data, we also consider the broadest measures of economic
activity, namely the growth rate of real GDP. Our first set of forecasting results utilizes
data over the entire sample period (1973–2009). In light of the well-documented decline in
macroeconomic volatility since the mid-1980s, we also examine the predictive power of these
financial indicators for economic activity over the post-1984 period, the so-called “Great
Moderation.”
3.1
Forecasting Results: 1973–2009
The results in Table 2 detail the predictive power of various financial indicators for the
growth rate of the three monthly economic indicators over the full sample period. The top
panel of the table reports baseline results, which include as predictors the lagged growth
rates of the variable to be forecasted, along with the term spread and the real federal funds
rate. Consistent with previous findings, the term spread provides significant predictive
content for all three monthly indicators at both the 3- and 12-month horizons. The real
funds rate provides additional predictive content for employment growth and the change in
the unemployment rate at both forecast horizons but does not add significant explanatory
power to the regression for growth in industrial production.
The next panels of Table 2 report results from adding the various credit indexes to this
baseline regression. Relative to the baseline, the paper-bill spread adds explanatory power
for all three economic indicators at the 3-month horizon and to the unemployment and IP
growth regressions at the year-ahead horizon. The improvement in in-sample goodness of fit
as measured by the adjusted R2 is relatively modest however. At the 3-month horizon, the
Baa-Aaa spread adds significant explanatory power only in the regression for the changes
in the unemployment rate. At the 12-month horizon, the Baa-Aaa spread adds significant
explanatory power for the growth in employment but not the other two monthly indicators.
Moreover, conditional on the term-spread, a rise in the Baa-Aaa spread predicts an increase
in employment growth over the subsequent year, a finding that highlights the the capricious
nature of signals obtained from the Baa-Aaa credit spread regarding the course of future
economic activity.
In contrast to the forecast results obtained for standard credit spread indexes, the GZ
credit spread is highly statistically significant at both the 3-month and 12-month horizons
for all three monthly economic indicators. Moreover, the coefficients estimates imply a
7
robust economically significant negative relationship between credit spreads and real economic activity. For example, a one standard deviation increase in the GZ credit spread
predicts a 0.25 percentage point reduction in employment, a 0.32 percentage point increase
in unemployment and a 0.36 percentage point drop in the growth of industrial production
at the 1-month horizon. In addition, the gains in the goodness-of-fit obtained by adding the
GZ credit spread to the baseline regression are substantial. This is especially true at the
12-month horizon, where the addition of the GZ credit spread results in an increase in the
adjusted R2 from 0.43 to 0.59 for employment growth and from 0.23 to 0.38 for the growth
in industrial production.
Table 3 examines the predictive content of these financial indicators for the growth of
real GDP. Here we report results for the 1-, 2-, and 4-quarter forecast horizons. According
to the baseline specification, the shape of the yield curve contains substantial predictive
power for the growth in real output at the 2- and 4-quarter horizons, whereas the current
stance of monetary policy—as measured by the real federal funds rate—has no marginal
predictive content. The standard Baa-Aaa credit spread index and the paper-bill spread
also have no marginal predictive power for real GDP growth at any horizon. Similar to
the findings reported for the monthly indicators of economic activity, the GZ credit spread
is, economically and statistically, a highly significant predictor of real GDP growth at all
three forecasting horizons. For example, a one standard deviation widening in the GZ credit
spread implies a 0.36 percentage point drop in economic growth over the subsequent four
quarters.
3.2
Forecasting Results: 1985–2009
As a robustness check, this section repeats the in-sample forecasting exercise for the Great
Moderation period, namely from 1985:Q1 onward. Although no clear consensus has emerged
regarding the dominant cause(s) of the decline in macroeconomic volatility since the mid1980s, changes in the conduct of monetary policy appear to be at least partly responsible
for the significantly diminished variability of both output and inflation over the past two
decades; see, for example, Clarida, Galı́, and Gertler [2000] and Stock and Watson [2002].
Because monetary policy affects the real economy by influencing financial asset prices, the
change in the monetary policy regime may have also altered the predictive content of various
financial indicators for economic activity. Moreover, as emphasized by Dynan, Elmendorf,
and Sichel [2006], the rapid pace of financial innovation since the mid-1980s—namely, the
deepening and emergence of lending practices and credit markets that have enhanced the
ability of households and firms to borrow and changes in government policy such as the
demise of Regulation Q—may have also changed the information content of financial asset
8
prices for macroeconomic outcomes.11
Table 4 contains forecasting results for the growth in real GDP over the 1985–2009
period. As evidenced by the entries in these tables, the GZ credit spread continues to
provide significant information for real GDP growth at the 1-, 2-, and 4-quarter horizons.
Indeed, the estimated coefficients on the credit spread are very similar in magnitude to
those reported in Table 3. As to be expected given the smaller sample size, the associated
confidence intervals are somewhat larger compared with those estimated over the full sample
period. All told, forecasting results using the GZ credit spread appear to be highly robust
across sample periods.
Using data for the 1985–2009 subsample, the paper-bill spread and the Baa-Aaa spread
now provide significant predictive content for GDP growth. This contrasts with the full
sample results where neither index provided additional explanatory power. The explanatory
power of the paper-bill spread is strongest at the 1-quarter horizon, while the explanatory
power of the Baa-Aaa credit spread is strongest at the year-ahead horizon. In all cases,
the coefficients on these credit spread indexes have increased relative to the full sample
results. This finding is mainly attributable to the rise in all credit spreads during the
current economic crisis, however. Although not reported, estimates over the 1985–2007
period imply similar results to the full sample estimates—that is, neither the paper-bill nor
the Baa-Aaa spread provide predictive content for GDP growth unless one uses a relatively
short sample that includes the most recent financial crisis.
All told, these results are consistent with those reported by GYZ for the 1990–2008 period: Credit market conditions as measured by the GZ credit spread index hold substantial
information content for leading, coincident, and lagging economic indicators. Moreover,
in contrast to forecasting results using either the paper-bill spread or the Baa-Aaa spread,
forecasting results using the GZ index appear to be remarkably stable across the full sample
versus the post-1985 period.
4
The Excess Bond Premium
The above results imply that the GZ credit spread index constructed as a series of the crosssectional average of properly constructed credit spreads of individual bond issues provides
substantial predictive content for economic activity. As emphasized by Philippon [2009],
11
Although a full formal investigation of potential parameter instability is beyond the scope of this paper,
we tested for time variation in the coefficients associated with financial indicators in the forecasting equation 1, using the methodology proposed by Elliott and Müller [2006]. These tests do not reject—even at
the 10 percent level—the null hypothesis of fixed regression coefficients on financial indicators for all specifications reported in Tables 2 and 3. This limited evidence suggests a stable relationship between our set
of financial indicators and changes in labor market conditions, the growth in industrial output, inventories,
and the growth in real GDP.
9
corporate bond spreads may predict future economic activity if such spreads reflect changes
in expected default risk owing to lower expected future cash flows. This result would be
true even in environments where there is no significant frictions in the financial markets.
In addition, in an environment where financial frictions have real economic consequences,
disruptions in financial markets may cause corporate bond spreads to widen relative to the
change implied by movements in expected default risk. To the extent that these disruptions
in financial markets have a causal influence on economic activity, movements in corporate
bond spreads that are unrelated to expected default risk may also predict future economic
outcomes.
In this section, we exploit the panel aspect of our underlying data set to decompose
the GZ credit spread index into a component that is related to systematic movements in
expected default risk and a residual component that we label the excess bond premium. We
then examine the extent to which the ability of the GZ credit spread to forecast economic
activity can be accounted for by the default component versus the excess bond premium.
More concretely, our methodology considers a standard bond pricing framework, where
the log of the credit spread on bond k at time t, ln Sit [k], is related to a firm-specific
measure of expected default (DFit ), additional bond-specific controls Xit [k], and a residual
component εit [k]:
ln Sit [k] = α + βDFit + γXit [k] + ǫit [k].
This regression is estimated using a standard OLS procedure. Given the estimated parameter vector (α̂, β̂, γ̂, σ̂ǫ ), we then obtain the predicted component for the level of the spread
of bond k of firm i at time t using:
Sitp [k] = exp α̂ + β̂DFit + γ̂Xit [k] + 0.5σ̂ǫ2 .
Aggregating across bonds at time t, we can define the realized average spread and its
predicted component as:
St =
X
Sit [k]
X
Sitp [k].
i,k
Stp =
i,k
The excess bond premium is then defined by the linear decomposition:
St = Stp + EBPt
Within this framework we are interested in determining the extent to which the forecasting
power of St documented in the previous section is due to variation in the default component,
10
Stp , versus the excess bond premium, EBPt . We now discuss in more detail the variables
that serve as proxies for the default risk and other controls. We then turn to the estimation
results.
4.1
Distance to Default:
To measure a firm’s probability of default at each point in time, we employ the “distanceto-default” (DD) framework developed in the seminal work of Merton [1973, 1974]. The
key insight of this contingent claims approach to corporate credit risk is that the equity of
the firm can be viewed as a call option on the underlying value of the firm with a strike
price equal to the face value of the firm’s debt. Although neither the underlying value of
the firm nor its volatility can be directly observed, they can, under the assumptions of the
model, be inferred from the value of the firm’s equity, the volatility of its equity, and the
firm’s observed capital structure.
The first critical assumption underlying the DD-framework is that the total value of the
a firm—denoted by V —follows a geometric Brownian motion:
dV = µV V dt + σV V dW,
(2)
where µV denotes the expected continuously compounded return on V ; σV is the volatility
of firm value; and dW is an increment of the standard Weiner process. The second critical
assumption pertains to the firm’s capital structure. In particular, it is assumed that the
firm has just issued a single discount bond in the amount D that will mature in T periods.12
Together, these two assumption imply that the value of the firm’s equity E can be viewed as
a call option on the underlying value of the firm V with a strike price equal to the face value
of the firm’s debt D and a time-to-maturity of T . According to the Black-Scholes-Merton
option-pricing framework, the value of the firm’s equity then satisfies:
E = V Φ(δ1 ) − e−rT DΦ(δ2 ),
(3)
where r denotes the instantaneous risk-free interest rate, Φ(·) is the cumulative standard
normal distribution function, and
δ1 =
ln(V /D) + (r + 0.5σV2 )T
√
σV2 T
12
and
δ2 = δ1 − σV
√
T.
Recent structural default models relax this assumption and allow for endogenous capital structure as
well as for strategic default. In these models, both the default time and default boundary are determined
endogenously and depend on firm-specific as well as aggregate factors; the voluminous literature on structural
default models is summarized by Duffie and Singleton [2003]; Lando [2004] contains an excellent practical
exposition of the contingent claims approach to corporate credit risk.
11
According to equation 3, the value of the firm’s equity depends on the total value of the
firm and time, a relationship that also underpins the link between volatility of the firm’s
value σV and the volatility of its equity σE . In particular, it follows from Ito’s lemma that
V ∂E
σV .
σE =
E ∂V
Because under the Black-Scholes-Merton option-pricing framework
(4)
∂E
∂V
= Φ(δ1 ), the rela-
tionship between the volatility of the firm’s value and the volatility of its equity is given
by
V
Φ(δ1 )σV .
σE =
E
(5)
From an operational standpoint, the most critical inputs to the Merton DD-model are
clearly the market value of the equity E, the face value of the debt D, and the volatility of
equity σE . Assuming a forecasting horizon of one year (T = 1), we implement the model
in two steps: First, we estimate σE from historical daily stock returns. Second, we assume
that the face value of the firm’s debt D is equal to the sum of the firm’s current liabilities
and one-half of its long-term liabilities.13 Using the observed values of E, D, σE , and r
(i.e., the 1-year constant-maturity Treasury yield), equations 3 and 5 can be solved for V
and σV using standard numerical techniques. However, as pointed out by Crosbie and Bohn
[2003] and Vassalou and Xing [2004], the excessive volatility of market leverage (V /E) in
equation 5 causes large swings in the estimated volatility of the firm’s value σV , which are
difficult to reconcile with the observed frequency of defaults and movements in financial
asset prices.
To resolve this problem, we implement an iterative procedure recently proposed by
Bharath and Shumway [2008]. The procedure involves the following steps: First, we initialize the procedure by letting σV = σE [D/(E + D)]. We then use this value of σV in
equation 3 to infer the market value of the firm’s assets V for every day of the previous
year. In the second step, we calculate the implied daily log-return on assets (i.e., ∆ ln V )
and use the resulting series to generate new estimates of σV and µV . We then iterate on σV
until convergence. The resulting solutions of the Merton DD-model can be used to calculate
the firm-specific distance-to-default over the one-year horizon as
DD =
ln(V /D) + (µV − 0.5σV2 )
.
σV
13
(6)
This assumption for the “default point” is also used MKMV in the construction of their Expected
Default Frequencies (EDFs) based on the Merton DD-model, and it captures the notion that short-term
debt requires a repayment of the principal relatively soon, whereas long-term debt requires the firm to meet
only the coupon payments. Both current and long-term liabilities are taken from quarterly Compustat files
and interpolated to daily frequency using a step function.
12
The corresponding implied probability of default—the so-called EDF—is given by
ln(V /D) + (µV − 0.5σV2 )
= Φ(−DD),
EDF = Φ −
σV
(7)
which, under the assumptions of the Merton model, should be a sufficient statistic for
predicting defaults.14
To assess the relevance of the Merton model for the pricing of corporate bonds, Figure 2
plots the median distance to default along with the inter-quartile range for the firms in our
sample over the 1973–2009 time period. The firms in our sample all have senior unsecured
debt outstanding that can be matched to the Lehman-Warga/Merill-Lynch bond pricing
data. As a point of comparison, this figure also plots the median distance to default for
the entire set of nonfinancial firms for which distance to default is available (i.e., firms that
are reported on CRSP and can be matched to Compustat to obtain information on their
liability structure). For both our sample and the full sample of nonfinancial firms, distance
to default is strongly pro-cyclical, implying that expected default rises in recessions. On
average, the firms in our sample have a higher distance to default than the full sample. This
reflects the fact that firms with senior unsecured debt are on average higher-quality firms.
In the current financial crisis, distance to default reached its lowest point in the sample
period. Thus, according to this measure, default risk rose substantially during the crisis.
The insights of the Merton model are regularly used by industry practitioners to provide
information on expected default. Notably, MKMV provides explicit estimates of expected
default using a semi-parametric mapping between a modified distance to default measure
and realized defaults. The MKMV year-ahead expected default frequency (EDFit ) for firm
i at time t is available for our sample of firms over the 1990–2009 period. Figure 3 plots
the log of the EDF against the distance to default measure that we have constructed.
Although there is a clear systematic relationship, there is substantial variation between the
two measures. Thus, when decomposing credit spread movements into a default component
versus a residual component, it is natural to start with a direct comparison of MKMV’s
EDFit and the distance-to-default measure, DDit described above.
Table 5 reports the results of this comparison. As discussed above, the dependent
variable is the log of the credit spread for issue k of firm i at time t which is regressed on
the default measure (either EDFit or DDit ), along with control variables that capture bondspecific characteristics that could influence bond yields through either liquidity or term
premiums, including the bond’s duration (DURt [k]); the amount outstanding (PARt [k]);
the bond’s (fixed) coupon rate (COUP[k]); and an indicator variable that equals one if the
14
Note that, even if the EDF is not a sufficient statistic for predicting defaults, DD may still be a good indicator for ranking firms into different categories of risk. Indeed, that is essentially the operational philosophy
used by MKMV when constructing their EDFs; see Crosbie and Bohn [2003] for a complete discussion.
13
bond is callable and zero otherwise (CALL[k]). The equation is estimated over the sample
period from February 1990 to December 2009 by OLS.
The first two columns of table report baseline results. In both cases, the default measure
is a highly statistically significant predictor of the logarithm of the credit spread. According
to the entries in the first rows of columns 1a and 1b, a 10 percent increase in the expected
default frequency implies about a 1 percent increase in the credit spread. The estimate
is slightly higher when using distance to default rather than MKMV’s expected default
frequency as a measure of default risk. In the baseline equation, the distance to default
measure provides a substantially higher R2 however—0.524 when estimated using DDit
relative to 0.420 when estimated using EDFit as the proxy for default risk. The next two
columns add bond rating dummy variables to this regression. The bond rating dummy
variables are highly statistically significant and the R2 improves substantially. Nonetheless,
both default measures still provide important explanatory power, although not surprisingly,
the coefficients fall with the introduction of the bond-rating dummy variables. Finally,
the last two columns allow for a nonlinear effect of the default measure by including a
quadratic term. Consistent with the nonlinear relationship between credit spreads and
leverage documented by Levin, Natalucci, and Zakrajšek [2004], the quadratic terms are
highly statistically significant. Again, the regression results imply that using distance to
default rather than expected default frequency provides a better overall fit to the bond
pricing equation.
The above set of results imply that the distance-to-default measure provides as good if
not a better proxy of default risk for bond pricing equations than the widely used expected
default frequency constructed by MKMV. We now turn to estimation results over the full
sample period when only the distance to default measure is available as a proxy for default
risk.
The Merton model implies that distance to default is a sufficient statistic for the credit
spread. In particular, movements in risk free rates only influence the credit spread to the
extent that they changes expected future cash flows and hence distance to default. To the
extent that corporate bonds are callable, interest rate movements have a direct effect on
credit spreads however. In particular, as interest rates rise, the call option becomes more
valuable and the price response of callable bonds is muted relative to the price response
of non-callable bonds. As a result, a rise in interest rates reduces the credit spread for
callable bonds relative to non-callable bonds. In addition, callable bonds are more sensitive
to interest rate volatility owing to their embedded options. Similarly, to the extent that
callable bonds have an effectively lower duration, they may be less sensitive to default risk.
One way to deal with this issue would be to confine the analysis to a sub-sample of noncallable bonds. As shown in Figure 4, the fraction of callable bonds in our sample varies over
14
time, with nearly 100 percent of bonds having call options prior to 1982 and the fraction
falling to less than 30 percent by 1994 before returning to roughly 90 percent by then end
of the sample period. Thus, confining the analysis to non-callable bonds would result in a
substantially reduced sample especially during the current crisis period. As an alternative,
we follow Duffee [1998] and control for the effects of interest rates and interest rate volatility
directly by including a call option dummy variable interacted with three standard interest
rate factors that capture the level, slope, and curvature of the Treasury yield curve. We also
interact the call option dummy with the realized volatility of the 10-year Treasury yield,
and the firm-specific measure of the distance to default.
The results of this regression exercise are reported in Table 6. The first two columns of
the table report estimation results for the full-sample period (1973–2009) that are comparable to those reported in column 3b of Table 5 for the 1990–2009 subsample. The coefficient
values on the distance to default variables are virtually identical and the overall fit of the
regression is highly comparable across the two estimation periods. The second two columns
of Table 6 report results from the regression that allows for the call-option dummy interacted with the interest rate factors and distance to default. Consistent with theoretical
predictions, the call option attenuates the effect of interest rate movements on bond prices.
As a result, the credit spreads of callable bonds fall as interest rates rise. The effect of
distance to default is similarly mitigated by the call-option mechanism. Also consistent
with theory, increased interest rate volatility raises the callable bond spreads relative to the
non-callable bond spreads.
Table 7 translates the implications of the coefficients obtained from this log specification
into economic impact of variation in the interest rate factors and default risk for the level
of the credit spread. Both the level of interest rates and the interest rate volatility have a
quantitatively important effect on credit spreads for callable bonds. A 1 standard deviation
increase in the level of interest rates implies a 60 basis point reduction in the credit spread
for callable bonds. A 1 standard deviation increase in the realized volatility of the 10-year
Treasury yield implies a 29 basis point rise in the credit spread of callable bonds. The
attenuation effect also applies to default risk—a 1 standard deviation increase in distance
to default implies a 35 basis point rise in the default probability. For non-callable bonds
this increase in default risk implies a 20 basis point increase in credit spreads whereas for
callable bonds, credit spreads rise by only 15 basis points in response.
The distance to default measure is composed of several components: the log of leverage,
the return on assets, and the volatility of asset returns. In the previous regression, these
terms are constrained to enter the credit spread regression through their effect on distance
to default. To the extent that distance to default is not a sufficient statistic for firm-specific
default risk, these terms may have independent influences that should be accounted for when
15
fitting the bond pricing equation. Thus, our final and most general specification allows for
these individual components of the distance to default to influence credit spreads separately
in both linear and quadratic terms. These individual components are also interacted with
the call-option dummy variable to allow for the attenuation discussed above. The estimation
results for this specification are reported in Table 8. The log of leverage, the return on assets
and the log-volatility all have coefficients that are statistically and economically significant
and of the right sign relative to the theoretical predictions.
Again we translate these coefficients into more easily understandable economic quantities
by reporting the marginal effects for the level of the credit spreads in Table 9. For example,
a 1 standard deviation increase in firm value relative to debt (V /D) implies a 9 basis point
reduction in credit spreads when evaluated at the mean leverage. The estimation results
again imply attenuation of the marginal impact of each component of distance to default
for the credit spreads of callable bonds. The effect of the interest rate factors and realized
interest rate volatility on the credit spreads for callable bonds is economically very similar to
the results reported in Table 7 that were obtained using distance to default as the proxy for
default risk. In addition, this more general specification provides a similar goodness of fit as
measured by adjusted R2 (0.692) to the specification that uses distance to default directly.
Thus, most of the variation in credit spreads that is related to firm-specific measures of
default risk appears to be well captured by the distance to default measure without further
need for generalization.
Nonetheless for robustness, we use the more general specification defined in column 3 of
Table 8 to construct the fitted values for the log of the credit spread at the individual bond
issue level. We then aggregate these spreads in the manner described at the beginning of
this section. This produces the fitted value for the aggregate spread, Stp . For comparison
purposes, we also construct the fitted value obtained from the specification that does not
allow for the callable bond interaction terms which is obtained using the regression reported
in column 1 of Table 8.
Figure 5 plots the GZ credit spread along with the fitted values from the two specifications for the bond equation—the specification that adjusts for callable bonds (optionadjusted) and the specification that assumes callable and non-callable bonds are priced in
the same manner. Overall, the fitted values capture a substantial fraction of the movement
in the GZ credit spread. Nonetheless, there is a clear divergence between the GZ credit
spread and the fitted values, especially during the periods of financial and economic turmoil.
Over most of the sample period the option adjustment has relatively little effect. The
1979–1982 period of non-borrowed reserves targeting resulted in increased interest rate
volatility which implies a higher fitted value for the spread when adjusting for the option
component relative to the fitted value that does not adjust for this volatility. In addition,
16
the volatility of the credit spread implies a more volatile fitted value over this time period.
The option adjustment has a clearly noticeable effect during the current economic downturn,
owing to the fact that interest rates are at an all time low during the economic crisis. Low
interest rates implies a higher predicted value for the credit spreads on callable bonds. This
adjustment accounts for a full 2 percentage points of the total increase in the GZ index
during the financial crisis.15
Figure 6 plots the excess bond premium—that is the difference between the GZ credit
spread index and the fitted value from the option-adjusted specification. The excess bond
premium increases noticeably during all economic downturns except the 1990 recession. It
also reaches an all time low during the easy-credit period in 2003 and remains low during the
ensuing boom in house prices. The excess bond premium rises sharply in the first quarter
of 2007 as housing prices growth turned negative and continues to rise throughout the onset
of the financial crisis. The excess bond premium reaches an all time high of 2.5 percentage
points in October 2008, following the collapse of Lehman Brothers. Since then, the excess
bond premium has fallen considerably as financial market turmoil has subsided.
5
The Excess Bond Premium and Economic Activity
The decomposition of the GZ index discussed above implies that an important component
of the variation in corporate credit spreads is due to an excess bond premium that arguably
reflects variation in the pricing of default risk rather than variation in the risk of default. We
now examine the extent to which variation in the excess bond premium provides independent
information about future economic activity. We do this in two stages. First, we consider the
extent to which the forecasting power of the GZ credit spread documented in Section 3 is
attributable to the predicted component, Stp versus the residual component, EBPt . We then
add the excess bond premium to an otherwise standard macroeconomic VAR and examine
whether orthogonalized shocks to the excess bond premium cause movements in economic
activity and other asset prices in the economy.
Table 10 reports the results from re-estimating our forecasting equation for monthly
economic activity variables, this time allowing for the two individual components of the GZ
credit spread—StP and EBPt to enter the regression separately. The top panel of this table
reports estimation results based on the 1973–2009 period, while the bottom panel reports
estimation results based on the 1985–2009 subsample. The estimates reported in table
highlight the fact that the excess bond premium provides predictive content for all three
15
Because there is such a strong negative comovement of credit spreads and economic activity during this
episode, the option adjustment attributes more explanatory power to the predicted component of credit
spreads rather than the excess bond component relative to the predicted series that does not adjust for the
option on callable bonds.
17
economic activity measures at both the short (3-month) and long (12-month) horizons. For
the full sample period, both the predicted component and the excess bond premium provide
independent explanatory power. The coefficient estimates and the t-statistics are roughly
equivalent in magnitude. In the later sample period, the predictive content of the excess
bond premium increases, as evidence by a substantial increase in the t-statistic. In contrast,
the predictive component, Stp , is no longer significant for either employment or industrial
production at the 3-month horizon, and the t-statistics of the coefficient estimate decline in
value across all variables and forecast horizons.
Table 11 reports estimation results for GDP growth at the 1-, 2-, and 4-quarter horizons.
Estimation results based on the full sample period imply that the excess bond premium
provides economically and statistically significant explanatory power for GDP growth at all
three horizons. The coefficient estimates imply that a 1 percentage point increase in the
excess bond premium predicts a 25 basis point drop in economic growth at all horizons.
Consistent with the results reported in the upper panel of Table 10, both the predicted
component, Stp and the EBPt provide independent explanatory power over the full sample
period. In contrast, the estimation results for the 1985–2009 subsample imply that only
the excess bond premium provides predictive power for real GDP growth. The coefficient
estimate on Stp is both economically small and statistically insignificant across all horizons.
The coefficient estimate on the excess bond premium is substantially higher in the later
sample period—a 1 percentage point increase in the excess bond premium predicts a 50
basis point decline in the real GDP growth at all horizons.
In summary, the excess bond premium is a robust predictor of economic activity. This
finding is true across economic indicators, forecast horizons, and sample periods. Furthermore, these forecasting results imply that, in the latter sample period, all of the predictive
content of the GZ credit spread for output growth can be attributed to variation in the
excess bond premium rather than variation in default risk as measured by Stp .
We now consider the economic consequences of shocks to the excess bond premium for
future economic activity. To do so, we add the excess bond premium to an otherwise standard VAR framework and consider the effect of a shock to the excess bond premium that is
orthogonal to standard measures of macroeconomic activity, namely the stance of monetary
policy and returns on other financial assets. The VAR includes the following variables: real
GDP growth, real consumption growth, real growth in business fixed investment, inflation
as measured by the change in the GDP price deflator, the effective federal funds rate, the
10-year Treasury yield, and the excess return on the value-weighted CRSP stock market
portfolio. By including short and long-term interest rates along with stock market returns,
we are therefore considering shocks to the excess bond premium that are orthogonal to
the information embedded in the level and slope of the yield curve and news in the stock
18
market.
Figure 7 presents the impulse responses to an orthogonalized shock to the excess bond
premium for the VAR estimated over the full sample period. A one standard deviation rise
in the excess bond premium causes a statistically significant reduction in all three economic
activity variables—consumption, investment, and output—with the peak output response
occurring about five quarters after the shock. The rise in the excess bond premium also
causes a decline in the price level and a significant easing of monetary policy, evidenced by
the decline in the effective federal funds rate. The magnitude of the decline in output is
large—a 20 basis point shock to the excess bond premium implies a 25 basis point decline in
the level of output. Despite falling interest rates, the stock market experiences a significant
decline—on the order of 4 percentage points relative to trend growth.
Figure 8 presents the amount of variation that can be explained by orthogonalized
shocks to the excess bond premium for the variables in the VAR. The excess bond premium
accounts for roughly 10 percent of the variation in output and 20 percent of the variation
in investment at business cycle frequencies. This exceeds the amount of variation typically
explained by monetary policy shocks.
Figure 9 presents the impulse responses for the VAR estimated over the 1985–2009
period. Orthogonalized shocks to the excess bond premium are the same order of magnitude
as in the full-sample case—a 1 standard deviation implies a 20 basis point rise in the
excess bond premium upon impact. Again, these shocks have statistically and economically
important effects on consumption, output, and investment. The overall decline in output
is nearly 60 basis points, more than double the size of the effect obtained from the full
sample estimates. It is also much more persistent. The decline in the cumulative market
return is also larger. The larger impact of shocks to the excess bond premium for the
later period may be attributable to the fact that the federal funds rate no longer exhibit
a sharp decline in response to the rising excess bond premium. Shocks to the excess bond
premium also account for a larger fraction of the variation in output as measured by the
variance decomposition. According to Figure 10, the amount of variation in output that
can be explained by this shock has roughly doubled. Because the fraction of variance for
investment that can be explained by this shock remains unchanged across the different
estimation periods, most of this increase is attributable to an increase in the explanatory
power of shocks to the excess bond premium for consumption rather than investment during
the later sample period.
The VAR findings are consistent with the notion that the excess bond premium measures
credit supply conditions and that a deterioration in those conditions causes a contraction
in both asset prices and economic activity through the financial accelerator mechanisms
emphasized by Kiyotaki and Moore [1997] and Bernanke, Gertler, and Gilchrist [1999]. More
19
recently, Gertler and Karadi [2009] and Gertler and Kiyotaki [2009] have emphasized models
in which shocks to the value of assets held by financial intermediaries have independent
effects on economic activity through the reduction in credit supply. Because the banking
sector is a relatively small source of funding for the corporate sector, it is difficult to argue
that the direct effects of contractions in bank lending have large economic effect via the
corporate bond market unless these contractions also influence the supply of credit more
broadly.
To the extent that “financial shocks” cause variation in the risk attitudes of the agents
pricing corporate bonds, such variation may also influence the supply of credit available via
the corporate bond market. By and large, the corporate bond market is dominated by large
institutional players such as banks, insurance companies, pensions funds, and other financial
entities. These institutional players have specialized knowledge and thus may be considered
“natural buyers” in this market. These institutional players also face either explicit or
implicit capital requirements. As financial capital becomes impaired, such agents act in a
more risk-averse manner, causing a rise in the excess bond premium and a reduction in the
supply of credit available to potential borrowers, both within the banking system and those
who rely on external forms of credit such as corporate bonds.
Figure 11 provides one piece of evidence in favor of this interpretation. It plots the
change in lending standards on C&I loans at commercial banks obtained from the Federal
Reserve’s Senior Loan Officer Opinion Survey on Bank Lending Practices along with the
excess bond premium. The C&I lending standard series is available from 1973 to 1982
and again during the 1990–2009 period. The correlation between these two series—one
obtained from survey information and the other obtained from bond market prices—is
strikingly high. Effectively, the willingness of banks to make loans comoves strongly with
the supply conditions in corporate credit markets as measured by the excess bond premium.
These findings are also consistent with recent work by Adrian, Moench, and Shin [2010],
who emphasize variation in the risk attitudes of financial intermediaries as a source of
macroeconomic risk premiums.
6
Conclusion
In this paper, we construct a new corporate credit spread index—the GZ credit spread
index—employing an extensive micro-level data set of secondary market prices of outstanding senior unsecured bonds. In contrast to the widely-used credit spread indexes, the GZ
index uses all information embedded in the Treasury yield curve, along with the bond’s
coupon payments and the remaining time-to-maturity, to correctly compute the risk-free
interest rate necessary to construct the credit spread for each underlying bond issue. Com-
20
pared with standard credit spread indexes such as the Baa-Aaa corporate bond spread
and the paper-bill spread, the GZ credit spread is shown to be a robust predictor of future economic activity across a variety of economic indicators, sample periods, and forecast
horizons.
Using a flexible empirical bond-pricing framework, we also decompose the GZ credit
spread index into a predictable component that reflects all available firm-specific information
on default risk and a residual component that we label the excess bond premium. According
to our results, a substantial fraction of the predictive content of the GZ credit spread index
for economic activity is attributable to the excess bond premium. Indeed, in the post 1985
period, the excess bond premium can account for all of the predictive content of credit
spreads for economic activity. Shocks to the excess bond premium that are orthogonal to
current economic activity, the information contained in the term structure of interest rates,
and news embedded in the stock market returns are shown to cause economically significant
contractions in economic activity. These findings are consistent with the notion that a rise in
the excess bond premium reflects a reduction in the risk appetite of the financial sector and,
as a result, a reduction in the supply of credit, which has significant adverse consequences
for macroeconomic outcomes.
21
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24
Tables & Figure
Table 1: Summary Statistics of Corporate Bond Characteristics
Bond Characteristic
Mean
SD
Min
P50
Max
# of bonds per firm/month
Mkt. value of issuea ($mil.)
Maturity at issue (years)
Term to maturity (years)
Duration (years)
Credit rating (S&P)
Coupon rate (pct.)
Nominal effective yield (pct.)
Credit spread (bps.)
2.83
310.1
13.3
11.4
6.50
7.31
7.82
202
3.46
315.6
9.5
8.6
3.20
1.95
3.24
284
1.00
1.22
1.0
1.0
0.91
D
1.95
0.66
5
2.00
231.0
10.0
8.2
6.10
BBB1
7.00
7.25
116
74.0
5,628
50.0
30.0
15.6
AAA
17.5
44.3
3,499
Panel Dimensions
Obs. = 322, 371 N = 5, 539 bonds
Min. Tenure = 1 Median Tenure = 48 Max. Tenure = 302
Note: Sample period: Jan1973–Dec2009; No. of firms = 1,086. Sample statistics are based
on trimmed data (see text for details).
a
Market value of the outstanding issue deflated by the CPI (1982–84 = 100).
25
Table 2: Financial Indicators and Economic Activity
(Sample Period: Jan1973–Dec2009)
Forecast Horizon (h months)
h=3
h = 12
Financial Indicator
EMP
UER
IPM
EMP
UER
IPM
Term spread
-0.080
[1.919]
-0.079
[1.753]
0.661
-0.085
[2.028]
-0.009
[0.143]
-0.108
[2.410]
0.668
-0.084
[2.037]
-0.075
[1.624]
-0.019
[0.494]
0.661
-0.097
[2.373]
-0.125
[2.737]
-0.274
[6.660]
0.706
0.131
[4.815]
0.071
[2.431]
0.344
0.148
[5.754]
-0.089
[2.555]
0.239
[9.924]
0.378
0.155
[5.707]
0.048
[1.667]
0.088
[3.443]
0.348
0.166
[6.132]
0.134
[4.517]
0.316
[14.08]
0.415
-0.144
[2.152]
-0.070
[0.973]
0.276
-0.166
[2.476]
-0.117
[1.277]
-0.285
[4.225]
0.325
-0.174
[2.716]
-0.048
[0.667]
-0.108
[1.632]
0.283
-0.189
[2.875]
-0.142
[2.046]
-0.359
[4.941]
0.365
-0.240
[4.814]
-0.122
[2.340]
0.432
-0.241
[4.783]
-0.108
[1.706]
-0.023
[0.683]
0.431
-0.220
[4.719]
-0.156
[3.154]
0.108
[2.197]
0.441
-0.264
[5.447]
-0.204
[4.011]
-0.474
[14.64]
0.590
0.356
[42.22]
0.063
[7.569]
0.287
0.369
[45.51]
-0.037
[4.083]
0.154
[29.09]
0.300
0.353
[42.50]
0.066
[8.283]
-0.014
[1.792]
0.286
0.391
[46.88]
0.148
[17.99]
0.418
[81.91]
0.431
-0.332
[3.953]
-0.099
[1.075]
0.225
-0.346
[4.115]
0.016
[0.151]
-0.179
[3.020]
0.243
-0.323
[3.882]
-0.107
[1.201]
0.032
[0.393]
0.224
-0.371
[4.478]
-0.187
[2.122]
-0.434
[6.099]
0.375
Real FFR
Adj. R2
Term spread
Real FFR
CP-Bill spread
Adj. R2
Term spread
Real FFR
Baa-Aaa spread
Adj. R2
Term spread
Real FFR
GZ spread
Adj. R2
Note: Dependent variable is ∇h Yt+h , where Yt denotes an indicator of economic activity in
month t and h is the forecast horizon: EMP = log of private nonfarm payroll employment; UER =
civilian unemployment rate; and IPM = log of the index of manufacturing industrial production. In
addition to the specified financial indicator in month t, each specification also includes a constant,
current, and p lags of ∇Yt (not reported), where p is determined by the AIC. Entries in the
table denote standardized estimates of the OLS coefficients associated with each financial indicator;
absolute t-statistics reported in brackets are based on the asymptotic covariance matrix computed
according to Hodrick [1992].
26
Table 3: Financial Indicators and Output Growth
(Sample Period: 1973:Q1–2009:Q4)
Forecast Horizon (h quarters)
Financial Indicator
h=1
h=2
h=4
Term spread
-0.148
[1.429]
-0.112
[1.055]
0.171
-0.179
[1.675]
0.104
[0.717]
-0.264
[2.402]
0.192
-0.185
[1.646]
-0.074
[0.681]
-0.112
[1.002]
0.165
-0.202
[1.991]
-0.171
[1.694]
-0.337
[3.624]
0.240
-0.245
[2.127]
-0.132
[1.130]
0.229
-0.258
[2.193]
-0.005
[0.035]
-0.178
[1.521]
0.241
-0.251
[2.067]
-0.129
[1.101]
-0.030
[0.268]
0.224
-0.289
[2.679]
-0.226
[1.997]
-0.378
[3.967]
0.333
-0.380
[2.849]
-0.072
[0.537]
0.235
-0.384
[2.843]
-0.033
[0.199]
-0.056
[0.486]
0.232
-0.369
[2.602]
-0.081
[0.599]
0.054
[0.428]
0.232
-0.418
[3.332]
-0.152
[1.158]
-0.364
[3.747]
0.341
Real FFR
Adj. R2
Term spread
Real FFR
CP-Bill spread
Adj. R2
Term spread
Real FFR
Baa-Aaa spread
Adj. R2
Term spread
Real FFR
GZ spread
Adj. R2
Note: Dependent variable is ∇h Yt+h , where Yt denotes the log of real GDP in
quarter t and h is the forecast horizon. In addition to the specified financial indicator
in quarter t, each specification also includes a constant, current, and p lags of ∇Yt (not
reported), where p is determined by the AIC. Entries in the table denote standardized
estimates of the OLS coefficients associated with each financial indicator; absolute tstatistics reported in brackets are based on the asymptotic covariance matrix computed
according to Hodrick [1992].
27
Table 4: Financial Indicators and Output Growth
(Sample Period: 1985:Q1–2009:Q4)
Forecast Horizon (h quarters)
Financial Indicator
h=1
h=2
h=4
Term spread
-0.112
[1.026]
0.120
[0.907]
0.235
-0.218
[1.788]
0.356
[1.768]
-0.254
[2.070]
0.265
-0.222
[1.832]
0.172
[1.213]
-0.280
[1.846]
0.267
-0.065
[0.623]
-0.007
[0.060]
-0.321
[2.109]
0.283
-0.186
[1.472]
0.175
[1.171]
0.231
-0.293
[2.294]
0.411
[2.056]
-0.266
[1.986]
0.265
-0.257
[1.988]
0.179
[1.205]
-0.205
[1.761]
0.249
-0.125
[0.125]
0.014
[0.097]
-0.343
[2.590]
0.291
-0.255
[1.999]
0.157
[1.064]
0.182
-0.387
[2.853]
0.436
[2.188]
-0.262
[1.822]
0.203
-0.400
[2.958]
0.244
[1.704]
-0.288
[2.921]
0.223
-0.201
[1.707]
0.036
[0.260]
-0.382
[3.029]
0.263
Real FFR
Adj. R2
Term spread
Real FFR
CP-Bill spread
Adj. R2
Term spread
Real FFR
Baa-Aaa spread
Adj. R2
Term spread
Real FFR
GZ spread
Adj. R2
Note: Dependent variable is ∇h Yt+h , where Yt denotes the log of real GDP in
quarter t and h is the forecast horizon. In addition to the specified financial indicator
in quarter t, each specification also includes a constant, current, and p lags of ∇Yt (not
reported), where p is determined by the AIC. Entries in the table denote standardized
estimates of the OLS coefficients associated with each financial indicator; absolute tstatistics reported in brackets are based on the asymptotic covariance matrix computed
according to Hodrick [1992].
28
Table 5: Credit Spreads and Expected Default Risk
(Sample Period: Feb1990–Dec2009)
Model Specification
Explanatory Variable
a = EDFit / b = −DDit
a = EDF2it / b = (−DDit )2
CALL[k]
ln(DUR[k])
ln(PAR[k])
ln(COUP[k])
Adj. R2
Industry Effectsa
Credit Rating Effectsb
(1a)
(1b)
(2a)
(2b)
(3a)
(3b)
0.104
(0.005)
-
0.112
(0.004)
-
0.065
(0.003)
-
0.075
(0.003)
-
0.482
(0.033)
-0.011
(0.017)
0.162
(0.032)
1.293
(0.070)
0.420
0.000
-
0.497
(0.027)
0.003
(0.016)
0.140
(0.028)
1.015
(0.069)
0.524
0.000
-
0.264
(0.020)
0.136
(0.012)
0.106
(0.016)
0.380
(0.052)
0.621
0.000
0.000
0.292
(0.018)
0.137
(0.011)
0.101
(0.017)
0.259
(0.055)
0.669
0.000
0.000
0.164
(0.009)
-0.004
(0.000)
0.262
(0.019)
0.142
(0.012)
0.106
(0.016)
0.348
(0.052)
0.636
0.000
0.000
0.173
(0.007)
0.006
(0.000)
0.291
(0.017)
0.146
(0.011)
0.080
(0.016)
0.278
(0.054)
0.694
0.000
0.000
Note: Obs. = 265,936; No. of bonds/firms = 5,222/1,021. Dependent variable is ln(S[k]it ), the log of the
credit spread on bond k—issued by firm i—in period t. In columns 1a, 2a, and 3a, the default-risk indicator
is the year-ahead expected default frequency (EDF) as calculated by the MKMV; in columns 1b, 2b, and 3b,
the default-risk indicator is the negative of the distance-to-default (DD) based on the Merton [1974] model
(see text for details). All specifications include a constant term (not reported) and are estimated by OLS.
Robust asymptotic standard errors are clustered at the firm level and are reported in parentheses.
a
p-value for the robust Wald statistics of the exclusion test of industry fixed effects.
b
p-value for the robust Wald statistics of the exclusion test of credit rating fixed effects.
29
Table 6: Credit Spreads and the Distance-to-Default
(Sample Period: Jan1973–Dec2009)
Model Specification
Explanatory Variable
Est.
−DDit
(−DDit )2
−DDit × CALL[k]
(−DDit )2 × CALL[k]
LEVELt × CALL[k]
SLOPEt × CALL[k]
CURVEt × CALL[k]
VOLt × CALL[k]
CALL[k]
ln(DUR[k])
ln(PAR[k])
ln(COUP[k])
Adj. R2
Industry Effectsa
Credit Rating Effectsb
0.170 0.007
0.006 0.000
0.263 0.017
0.100 0.012
0.138 0.014
0.472 0.059
0.649
0.000
0.000
S.E.
Est.
S.E.
0.193 0.012
0.006 0.001
-0.046 0.012
-0.001 0.001
-0.320 0.013
-0.073 0.008
-0.035 0.005
0.120 0.004
-0.351 0.047
0.107 0.011
0.025 0.013
0.770 0.055
0.685
0.000
0.000
Note: Obs. = 322,371; No. of bonds/firms = 5,539/1,086. Dependent variable is
ln(S[k]it ), the log of the credit spread on bond k—issued by firm i—in period t. The
term structure is represented by the following three factors: LEVEL = level; SLOPE =
slope; and CURVE = curvature; see Litterman and Scheinkman [1991] for details; VOL
= annualized realized monthly volatility of the daily 10-year Treasury yield (see text for
details). All specifications include a constant term (not reported) and are estimated by
OLS. Robust asymptotic standard errors are clustered at the firm level.
a
p-value for the robust Wald statistics of the exclusion test of industry fixed effects.
b
p-value for the robust Wald statistics of the exclusion test of credit rating fixed effects.
30
Table 7: Selected Marginal Effects by Type of Bond
Non-Callable Bonds
Callable Bonds
Variable
Est.
S.E.
Est.
S.E.
Mean
STD
Distance-to-default: −DDit
Term structure: LEVELt
Term structure: SLOPEt
Term structure: CURVEt
Term structure: VOLt (%)
0.205
-
0.008
-
0.153
-0.608
-0.138
-0.067
0.289
0.005
0.025
0.015
0.010
0.008
6.754
0.000
0.000
0.000
1.866
4.055
1.000
1.000
1.000
1.249
Note: The table contains the estimates of the marginal effect of a one unit change in the specified
variable on the level of credit spreads (in percentage points) for non-callable and callable bonds based on
the parameter estimates reported in Table 6; see text for for details. All marginal effects are evaluated at
sample means; by construction, the level, slope, and curvature factors are standardized to have the mean
equal to zero and the standard deviation equal to one. Robust asymptotic standard errors are computed
according to the delta method.
31
Table 8: Credit Spreads and Components of the Distance-to-Default
(Sample Period: Jan1973–Dec2009)
Model Specification
Explanatory Variable
Est.
ln[V /D]it
µit
ln σit
(ln[V /D]it )2
µ2it
(ln σit )2
ln[V /D]it × CALL[k]
µit × CALL[k]
ln σit × CALL[k]
(ln[V /D]it )2 × CALL[k]
µ2it × CALL[k]
(ln σit )2 × CALL[k]
LEVELt × CALL[k]
SLOPEt × CALL[k]
CURVEt × CALL[k]
VOLt × CALL[k]
CALL[k]
ln(DUR[k])
ln(PAR[k])
ln(COUP[k])
Adj. R2
Industry Effectsa
Credit Rating Effectsb
S.E.
-0.566 0.066
-0.649 0.021
0.530 0.130
0.114 0.011
0.148 0.042
0.012 0.051
0.242 0.017
0.112 0.012
0.026 0.013
0.535 0.054
0.660
0.000
0.000
Est.
S.E.
-0.771 0.061
-0.669 0.039
1.248 0.183
0.145 0.015
0.061 0.077
0.221 0.070
0.241 0.066
0.147 0.042
-1.063 0.175
-0.045 0.016
0.088 0.081
-0.302 0.065
-0.293 0.012
-0.068 0.009
-0.033 0.005
0.114 0.004
-1.222 0.114
0.117 0.010
0.028 0.012
0.792 0.051
0.692
0.000
0.000
Note: Obs. = 322,371; No. of bonds/firms = 5,539/1,086. Dependent variable is
ln(S[k]it ), the log of the credit spread on bond k—issued by firm i—in period t. The
term structure is represented by the following three factors: LEVEL = level; SLOPE =
slope; and CURVE = curvature; see Litterman and Scheinkman [1991] for details; VOL
= annualized realized monthly volatility of the daily 10-year Treasury yield (see text for
details). All specifications include a constant term (not reported) and are estimated by
OLS. Robust asymptotic standard errors are clustered at the firm level.
a
p-value for the robust Wald statistics of the exclusion test of industry fixed effects.
b
p-value for the robust Wald statistics of the exclusion test of credit rating fixed effects.
32
Table 9: Selected Marginal Effects by Type of Bond
Non-Callable Bonds
Variable
Leverage: [V /D]it
Return on assets: µit (%)
Volatility of assets: σit (%)
Term structure: LEVELt
Term structure: SLOPEt
Term structure: CURVEt
Term structure: VOLt (%)
Callable Bonds
Est.
S.E.
Est.
S.E.
Mean
STD
-0.087
-1.259
4.416
-
0.006
0.072
0.230
-
-0.060
-0.962
2.851
-0.558
-0.128
-0.063
0.217
0.005
0.042
0.144
0.024
0.017
0.010
0.008
6.730
5.292
27.33
0.000
0.000
0.000
1.866
7.514
27.33
12.56
1.000
1.000
1.000
1.249
Note: The table contains the estimates of the marginal effect of a one unit change in the specified
variable on the level of credit spreads (in percentage points) for non-callable and callable bonds based on
the parameter estimates reported in Table 8; see text for for details. All marginal effects are evaluated at
sample means; by construction, the level, slope, and curvature factors are standardized to have the mean
equal to zero and the standard deviation equal to one. Robust asymptotic standard errors are computed
according to the delta method.
33
Table 10: Excess Bond Premium and Economic Activity
Sample Period: Jan1973–Dec2009
Forecast Horizon (h months)
h=3
h = 12
Financial Indicator
EMP
UER
IPM
EMP
UER
IPM
Term spread
-0.098
[2.403]
-0.112
[2.342]
-0.179
[4.250]
-0.173
[2.999]
0.708
0.170
[6.321]
0.110
[3.539]
0.185
[7.777]
0.229
[11.18]
0.422
-0.198
[3.016]
-0.107
[1.470]
-0.195
[2.848]
-0.292
[4.604]
0.382
-0.266
[5.487]
-0.195
[3.771]
-0.344
[8.814]
-0.262
[9.958]
0.591
0.403
[47.81]
0.112
[13.49]
0.243
[41.16]
0.325
[65.73]
0.444
-0.382
[4.442]
-0.161
[1.796]
-0.284
[4.015
-0.297
[4.208]
0.381
Real FFR
Predicted GZ spread
Excess bond premium
Adj. R2
Sample Period: Jan1985–Dec2009
Forecast Horizon (h months)
h=3
h = 12
Financial Indicator
EMP
UER
IPM
EMP
UER
IPM
Term spread
-0.101
[2.891]
0.053
[1.267]
-0.064
[1.424]
-0.181
[5.523]
0.824
0.126
[3.832]
-0.030
[0.763]
0.157
[4.192]
0.290
[10.76]
0.495
-0.155
[1.871]
0.089
[0.852]
-0.163
[1.478]
-0.395
[4.409]
0.451
-0.264
[7.579]
0.067
[1.722]
-0.096
[2.691]
-0.295
[10.00]
0.718
0.320
[34.34]
-0.092
[9.851]
0.112
[14.18]
0.395
[64.72]
0.548
-0.294
[3.448]
0.134
[1.372]
-0.218
[2.672]
-0.455
[4.927]
0.402
Real FFR
Predicted GZ spread
Excess bond premium
Adj. R2
Note: Dependent variable is ∇h Yt+h , where Yt denotes an indicator of economic activity in
month t and h is the forecast horizon: EMP = log of private nonfarm payroll employment; UER =
civilian unemployment rate; and IPM = log of the index of manufacturing industrial production. In
addition to the specified financial indicators in month t, each specification also includes a constant,
current, and p lags of ∇Yt (not reported), where p is determined by the AIC. Entries in the table denote
standardized estimates of the OLS coefficients associated with each financial indicator; absolute tstatistics reported in brackets are based on the asymptotic covariance matrix computed according to
Hodrick [1992].
34
Table 11: Excess Bond Premium and Output Growth
Sample Period: 1973:Q1–2009:Q4
Forecast Horizon (h quarters)
Financial Indicator
h=1
h=2
h=4
Term spread
-0.210
[2.936]
-0.138
[1.305]
-0.161
[1.831]
-0.279
[3.619]
0.254
-0.298
[2.702]
-0.198
[1.681]
-0.200
[2.183]
-0.279
[3.263]
0.343
-0.421
[3.298]
-0.142
[1.038]
-0.250
[2.454]
-0.205
[2.448]
0.338
Real FFR
Predicted GZ spread
Excess bond premium
Adj. R2
Sample Period: 1985:Q1–2009:Q4
Forecast Horizon (h quarters)
Financial Indicator
h=1
h=2
h=4
Term spread
-0.293
[2.115]
0.321
[1.675]
0.061
[0.332]
-0.505
[3.737]
0.320
-0.353
[2.598]
0.365
[2.056]
0.130
[0.915]
-0.524
[4.056]
0.381
-0.401
[3.089]
0.322
[2.093]
0.023
[0.162]
-0.475
[3.773]
0.322
Real FFR
Predicted GZ spread
Excess bond premium
Adj. R2
Note: Dependent variable is ∇h Yt+h , where Yt denotes the log of real GDP in
quarter t and h is the forecast horizon. In addition to the specified financial indicators
in quarter t, each specification also includes a constant, current, and p lags of ∇Yt (not
reported), where p is determined by the AIC. Entries in the table denote standardized
estimates of the OLS coefficients associated with each financial indicator; absolute tstatistics reported in brackets are based on the asymptotic covariance matrix computed
according to Hodrick [1992].
35
Figure 1: Selected Corporate Credit Spreads
Percentage points
8
NBER
Peak
Monthly
GZ spread
Baa-Aaa spread
CP-Bill spread
6
4
2
0
-2
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
2009
Note: Sample period: Jan1973–Dec2009. The figure depicts the following default-risk indicators: GZ spread = average credit spread on senior unsecured bonds issued by nonfinancial firms in
our sample (the black line); Baa-Aaa = the spread between yields on Baa- and Aaa-rated long-term
industrial corporate bonds (the blue line); and CP-Bill = the spread between the yield on 1-month
A1/P1 nonfinancial commercial paper and the 1-month Treasury yield (the red line). The shaded
vertical bars represent the NBER-dated recessions.
36
Figure 2: Distance-to-Default
Std. deviations
20
NBER
Peak
Monthly
Nonfinancial corporate sector (median)
Median
Interquartile range
15
10
5
0
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
2009
Note: Sample period: Jan1973–Dec2009. The figure depicts the distance-to-default (DD) calculated using the Merton [1974] model (see text for details). The black line depicts the (weighted)
median DD of the firms in our sample, and the shaded yellow band depicts the corresponding
(weighted) inter-quartile range. The red line depicts the (weighted) median DD in the U.S. nonfinancial corporate sector; all percentiles are weighted by the firm’s outstanding liabilities. The
shaded vertical bars represent the NBER-dated recessions.
37
Figure 3: Expected Default Frequency and Distance-to-Default
40.00
Expected default frequency (percent, log scale)
20.00
10.00
5.00
1.00
0.25
0.05
0.01
-5
0
5
10
15
20
Distance-to-default (std. deviations)
Note: Sample period: Feb1900–Dec2009 (Obs. = 265,936; No. of firms = 1,021) The figure
depict the scatter plot of the year-ahead expected default frequency (EDF) for firm i in month t
calculated by MKMV and the corresponding year-ahead distance-to-default (DD) calculated using
the Merton [1974] model (see text for details).
38
Figure 4: Callable Senior Unsecured Corporate Bonds
Percent
NBER
Peak
Monthly
100
Proportion of total bonds
Proportion of total par value
80
60
40
20
0
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
2009
Note: Sample period: Jan1973–Dec2009. The figure depicts the proportion of bonds in our
sample that are callable. The shaded vertical bars represent the NBER-dated recessions.
39
Figure 5: Actual and Predicted Credit Spreads
Percentage points
8
NBER
Peak
Monthly
Actual GZ spread
Predicted GZ spread
Predicted GZ spread with option adjustments
7
6
5
4
3
2
1
0
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
2009
Note: Sample period: Jan1973–Dec2009. The black line depicts the average credit spread for
our sample of bonds. The blue line depicts the predicted credit spread based on the regression
specification that includes linear and quadratic components of the distance-to-default but excludes
the option-adjustment terms; the red line depicts the predicted credit spread based on the same
regression specification but that includes the option-adjustment terms (see text for details). The
shaded vertical bars represent the NBER-dated recessions.
40
Figure 6: Option-Adjusted Excess Bond Premium
Percentage points
2.5
NBER
Peak
Monthly
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
2009
Note: Sample period: Jan1973–Dec2009. The figure depicts the estimated excess bond premium based on the regression specification that includes linear and quadratic components of the
distance-to-default and the option-adjustment terms (see text for details). The shaded vertical bars
represent the NBER-dated recessions.
41
Figure 7: Implications of a Shock to the Excess Bond Premium
(Sample Period: 1973:Q1–2009:Q4)
Consumption
Investment
Percentage points
Percentage points
0.6
1
0.4
0
0.2
-1
0.0
-2
-0.2
-3
-0.4
-4
-0.6
0
2
4
6
8
10
12
14
16
18
-5
20
0
2
4
6
Quarters after shock
8
10
12
14
16
18
20
Quarters after shock
Output
Prices
Percentage points
Percentage points
0.6
0.5
0.4
0.0
0.2
0.0
-0.5
-0.2
-1.0
-0.4
-1.5
-0.6
-0.8
0
2
4
6
8
10
12
14
16
18
-2.0
20
0
2
4
6
Quarters after shock
8
10
12
14
16
18
20
Quarters after shock
Cumulative excess market return
10-year Treasury yield
Percentage points
Percentage points
2
0.1
0.0
0
-0.1
-2
-0.2
-4
-0.3
-6
-0.4
-8
0
2
4
6
8
10
12
14
16
18
-0.5
20
0
2
4
6
Quarters after shock
8
10
12
14
16
18
20
Quarters after shock
Federal funds rate
Excess bond premium
Percentage points
Percentage points
0.2
0.25
0.0
0.20
0.15
-0.2
0.10
-0.4
0
2
4
6
8
10
12
14
16
18
0.05
-0.6
0.00
-0.8
-0.05
20
0
Quarters after shock
2
4
6
8
10
12
14
16
18
20
Quarters after shock
Note: The figure depicts the impulse response functions from an 8-variable VAR(2) model to
a 1 standard deviation orthogonalized shock to the excess bond premium. The VAR is ordered as
follows: (1) log-difference of real PCE; (2) log-difference of real BFI; (3) log-difference of real GDP;
(4) log-difference of the GDP price deflator; (5) 1-quarter value-weighted excess (total) log-return
from CRSP; (6) nominal 10-year Treasury yield; (7) effective federal funds rate; and (8) (optionadjusted) excess bond premium. The responses of consumption, investment, and output growth and
that of the excess market return have been cumulated. Shaded bands denote 95-percent confidence
intervals based on 2,000 bootstrap replications.
42
Figure 8: Forecast Error Variance Decomposition
(Sample Period: 1973:Q1–2009:Q4)
Consumption
Investment
Percent
0
2
4
6
8
10
12
14
16
18
Percent
40
40
30
30
20
20
10
10
0
0
20
0
2
4
Forecast horizon (quarters)
6
8
10
12
14
16
18
20
Forecast horizon (quarters)
Output
Prices
Percent
Percent
40
40
30
30
20
20
10
10
0
0
2
4
6
8
10
12
14
16
18
0
20
0
2
4
Forecast horizon (quarters)
6
8
10
12
14
16
18
20
Forecast horizon (quarters)
Cumulative excess market return
10-year Treasury yield
Percent
Percent
40
40
30
30
20
20
10
10
0
0
2
4
6
8
10
12
14
16
18
0
20
0
2
4
Forecast horizon (quarters)
6
8
10
12
14
16
18
20
Forecast horizon (quarters)
Federal funds rate
Excess bond premium
Percent
Percent
40
100
30
80
60
20
40
10
20
0
0
2
4
6
8
10
12
14
16
18
0
20
0
Forecast horizon (quarters)
2
4
6
8
10
12
14
16
18
20
Forecast horizon (quarters)
Note: The figure depicts the forecast error variance decomposition from an 8-variable VAR(2)
model to a 1 standard deviation orthogonalized shock to the excess bond premium. The VAR is
ordered as follows: (1) log-difference of real PCE; (2) log-difference of real BFI; (3) log-difference
of real GDP; (4) log-difference of the GDP price deflator; (5) 1-quarter value-weighted excess
(total) log-return from CRSP; (6) nominal 10-year Treasury yield; (7) effective federal funds rate;
and (8) (option-adjusted) excess bond premium. The responses of consumption, investment, and
output growth and that of the excess market return have been cumulated. Shaded bands denote
95-percent confidence intervals based on 2,000 bootstrap replications.
43
Figure 9: Implications of a Shock to the Excess Bond Premium
(Sample Period: 1985:Q1–2009:Q4)
Consumption
Investment
Percentage points
Percentage points
1
0.2
0
0.0
-1
-0.2
-2
-0.4
-3
-0.6
-4
-0.8
-5
-1.0
0
2
4
6
8
10
12
14
16
18
-6
20
0
2
4
6
Quarters after shock
8
10
12
14
16
18
20
Quarters after shock
Output
Prices
Percentage points
Percentage points
0.2
0.3
0.0
0.2
-0.2
0.1
-0.4
0.0
-0.6
-0.1
-0.8
-0.2
-1.0
-0.3
-1.2
0
2
4
6
8
10
12
14
16
18
-0.4
20
0
2
4
6
Quarters after shock
8
10
12
14
16
18
20
Quarters after shock
Cumulative excess market return
10-year Treasury yield
Percentage points
Percentage points
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
2
0
-2
-4
-6
-8
-10
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
Quarters after shock
8
10
12
14
16
18
20
Quarters after shock
Federal funds rate
Excess bond premium
Percentage points
Percentage points
0.2
0.25
0.1
0.20
0.0
0.15
-0.1
0.10
-0.2
0.05
-0.3
0
2
4
6
8
10
12
14
16
18
-0.4
0.00
-0.5
-0.05
20
0
Quarters after shock
2
4
6
8
10
12
14
16
18
20
Quarters after shock
Note: The figure depicts the impulse response functions of an 8-variable VAR(2) model to
a 1-standard-deviation orthogonalized shock to the excess corporate bond premium. The VAR is
ordered as follows: (1) log-difference of real PCE; (2) log-difference of real BFI; (3) log-difference
of real GDP; (4) log-difference of the GDP price deflator; (5) 1-quarter value-weighted excess
(total) log-return from CRSP; (6) nominal 10-year Treasury yield; (7) effective federal funds rate;
and (8) (option-adjusted) excess bond premium. The responses of consumption, investment, and
output growth and that of the excess market return have been cumulated. Shaded bands denote
95-percent confidence intervals based on 2,000 bootstrap replications.
44
Figure 10: Forecast Error Variance Decomposition
(Sample Period: 1985:Q1–2009:Q4)
Consumption
Investment
Percent
0
2
4
6
8
10
12
14
16
18
Percent
40
40
30
30
20
20
10
10
0
0
20
0
2
4
Forecast horizon (quarters)
6
8
10
12
14
16
18
20
Forecast horizon (quarters)
Output
Prices
Percent
Percent
40
40
30
30
20
20
10
10
0
0
2
4
6
8
10
12
14
16
18
0
20
0
2
4
Forecast horizon (quarters)
6
8
10
12
14
16
18
20
Forecast horizon (quarters)
Cumulative excess market return
10-year Treasury yield
Percent
Percent
40
40
30
30
20
20
10
10
0
0
2
4
6
8
10
12
14
16
18
0
20
0
2
4
Forecast horizon (quarters)
6
8
10
12
14
16
18
20
Forecast horizon (quarters)
Federal funds rate
Excess bond premium
Percent
Percent
40
100
30
80
60
20
40
10
20
0
0
2
4
6
8
10
12
14
16
18
0
20
0
Forecast horizon (quarters)
2
4
6
8
10
12
14
16
18
20
Forecast horizon (quarters)
Note: The figure depicts the forecast error variance decomposition of an 8-variable VAR(2)
model to a 1-standard-deviation orthogonalized shock to the excess corporate bond premium. The
VAR is ordered as follows: (1) log-difference of real PCE; (2) log-difference of real BFI; (3) logdifference of real GDP; (4) log-difference of the GDP price deflator; (5) 1-quarter value-weighted
excess (total) log-return from CRSP; (6) nominal 10-year Treasury yield; (7) effective federal funds
rate; and (8) (option-adjusted) excess bond premium. The responses of consumption, investment,
and output growth and that of the excess market return have been cumulated. Shaded bands
denote 95-percent confidence intervals based on 2,000 bootstrap replications.
45
Figure 11: Excess Bond Premium and Changes in Bank Lending Standards
Percentage points
2.0
Net percent
100
NBER
Peak
Quarterly
Excess bond premium (left scale)
Change in C&I lending standards (right scale)
1.5
75
1.0
50
0.5
25
0.0
0
-0.5
-25
-1.0
-50
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
2009
Note: The black line depicts the quarterly average of the estimated (option-adjusted)
excess bond premium (see text for details). The red line depicts the net percent of respondents
to the Federal Reserve’s Senior Loan Officer Opinion Survey on Bank Lending Practices that
indicated that they had tightening their credit standards on C&I loans to large and middlemarket firms over the quarter. Reported net percent equals the percent of banks that reported
tightening their standards minus the percent that reported easing their standards. (There was
no survey conducted during the 1984-89 period.) The shaded vertical bars denote NBER-dated
recessions.
46