Inﬂation Risk in Corporate Bonds · berger (1973)). Tax and other debt beneﬁts create an...

Inflation Risk in Corporate Bonds

JOHNNY KANG and CAROLIN E. PFLUEGER*

ABSTRACT

We argue that corporate bond yields reflect fears of debt deflation. When debt is nominal, un-

expectedly low inflation increases real liabilities and default risk. In a real business cycle model

with optimal but infrequent capital structure choice, more uncertain or pro-cyclical inflation leads

to quantitatively important increases in corporate log yields in excess of default-free log yields.

A panel of credit spread indexes from six developed countries shows that credit spreads rise by

14 basis points if inflation volatility or the inflation-stock correlation increases by one standard

deviation.

*Kang: AQR Capital Management, Greenwich CT 06830. [email protected]. Pflueger: University of BritishColumbia, Vancouver BC V6T 1Z2, Canada. [email protected]. We are grateful to an anonymous AE,an anonymous referee, Shai Bernstein, Harjoat Bhamra, Murray Carlson, Anna Cieslak, Josh Coval, Adlai Fisher, BenFriedman, Josh Gottlieb, Francois Gourio, Robin Greenwood, Cam Harvey, Robert Hall, Sam Hanson, Peter Hordahl,Stephanie Hurder, Jakub Jurek, Jacob Leshno, Robert Merton, Nick Roussanov, Alp Simsek, Jeremy Stein, Jim Stock,Adi Sunderam, Yaniv Yedid-Levi, seminar participants at the University of British Columbia, Brown University, theFederal Reserve Board, the Federal Reserve Bank of Chicago, Harvard University, the University of Illinois at Urbana-Champaign, London Business School, the University of Michigan, the University of Rochester, Washington Universityin St. Louis, the University of Wisconsin-Madison, and the Yale School of Management for helpful comments andsuggestions. We thank Ari Achiaz and Roni Michaely for help with Israeli corporate bond data. We thank StephenZhang for able research assistance. We are especially grateful to John Campbell, Erik Stafford, and Luis Viceira forinvaluable advice and guidance.

Corporate and sovereign bonds in developed countries are overwhelmingly nominal. Firms are

therefore exposed to the possibility of “debt deflation”, when a surprise drop in inflation leads to

increases in real liabilities and corporate default risk (Fisher (1933)). The literature has argued that

corporate bonds price the volatility of real firm values as proxied by equity volatility (Campbell

and Taksler (2003), Collin-Dufresne, Goldstein, and Martin (2001)). We find that inflation risk can

explain at least as much variation in credit spreads as can equity volatility and the dividend-price

ratio. In a panel of credit spread indexes from six developed countries, a one standard deviation

move in either inflation volatility or the inflation-stock correlation increases credit spreads by 14

basis points (bps), relative to average credit spreads around 100 bps.

This paper identifies a new link between inflation risk and the credit component in corpo-

rate bond yields. This channel is on top of and separate from any inflation risk premia in nomi-

nal default-free bonds.1 In contrast to corporate bonds, nominal government bonds are plausibly

default-free if governments can inflate away their own debt. We argue theoretically and confirm

empirically that inflation risk is priced into corporate bond log yields above and beyond its im-

pact on nominal default-free log yields. Indeed, we find that inflation risk affects empirical credit

spreads even after controlling for the term structure of nominal government log yields.

Corporate bond spreads price two types of inflation risk: inflation volatility and inflation cycli-

cality. First, more volatile inflation increases the ex-ante probability that firms will default due to

high real liabilities. Second, when inflation and real cash flows are highly correlated, there is a risk

of low inflation recessions. In this case, low real cash flows and high real liabilities tend to hit firms

at the same time, and this interaction increases default rates and real investor losses. Moreover,

inflation cyclicality may also increase the default risk premium in credit spreads if investors are

risk averse.

[FIGURE 1 ABOUT HERE]

1

Figure 1A illustrates the close historical relation between time-varying inflation uncertainty

and firms’ cost of debt finance in the United States.2 Figure 1B shows that the relation between the

lower tail of inflation uncertainty and credit spreads is even stronger, consistent with our intuition

that lower than expected inflation raises credit risk. In Section III of this paper, we confirm the

relation between credit spreads and inflation uncertainty in a panel of six developed countries,

controlling for proxies for business conditions, real uncertainty, and time-varying risk aversion.

It might at first seem surprising that the risk of debt deflation should have been salient during

the high inflation 1970s and 1980s. However, debt deflation can occur whenever inflation is lower

than expected, even if the level of inflation remains high. In 1982, the New York Times argued:

“Among those most distressed by slowing inflation are individuals and businesses that took out

large loans in the past few years based on the assumption that inflation would remain at very high

levels. . . . The farmer’s new, expensively financed machinery is harvesting crops fetching lower

market prices.”3

Not only inflation volatility but also inflation cyclicality have varied over time in the U.S.

Moreover, high inflation cyclicality can rationalize investors’ recent relative reluctance to hold

corporate bonds. When inflation dropped to extremely low levels during the financial crisis, our

measure of inflation pro-cyclicality—the inflation-stock correlation—reached a peak and captured

significant public concerns about debt deflation. In contrast, investors in the 1970s feared high

inflation recessions—or “stagflations”—implying countercyclical inflation.

While concerns about a deflationary drop in U.S. aggregate demand have been especially strong

over the past three years, our measure suggests that they have been present since at least the early

2000s. They have also been salient, as evidenced by a widely noted 2002 speech by then-Federal

Reserve Governor Ben Bernanke.4 Concerns about debt deflation are also evident in recent news

reporting. For instance, ProQuest reports 230 news mentions of the key word “debt deflation”

2

versus only 132 for the keyword “stagflation” over 2000 to 2009. Internationally, the Japanese

experience during the 1990s provides one of the more salient examples of recent debt deflation

(Kuttner and Posen (2001)).

As of December 2010, the U.S. Baa-Aaa Moody’s log yield spread was close to its historical

average over the period 1969.Q4 to 2010.Q4.5 On the other hand, equity valuations were high,

with the S&P 500 index dividend-price ratio a full standard deviation below its sample average.

Based on our estimates, 34 bps of the 104 bps U.S. Baa-Aaa log yield spread in December 2010

were due to above average inflation pro-cyclicality.

We develop a model with stochastic productivity and optimal but infrequent capital structure

choice. This model provides new, testable, and quantitative predictions. Regressions of model

credit spreads onto inflation volatility and the inflation-stock correlation predict that the impact

of inflation volatility and the inflation-stock correlation on credit spreads should be substantial,

while controlling for equity volatility, the dividend yield, inflation surprises, and equity returns.

Simulated credit spreads increase by 27 bps if the annualized standard deviation of inflation shocks

increases by 1 percentage point and by 20 bps if the inflation-stock correlation increases by 100

percentage points.

Three key features in our model generate large, dynamic responses of credit spreads to inflation

risk. First, we model both the size of inflation shocks and their correlation with real outcomes as

varying over time independently of real activity.

Second, we assume that firms issue nominal long-term bonds and that expected inflation is

persistent, consistent with U.S. and international evidence (Ball and Cecchetti (1990), Stock and

Watson (2007)). The assumption that debt is nominal is plausible for developed countries, where

bonds are denoted in nominal terms by historical convention, and where inflation-indexed cor-

porate debt plausibly carries a substantial liquidity premium. In our calibrated model, a liquidity

3

premium comparable to that documented for U.S. inflation-indexed government bonds during their

first few years of issuance (D’Amico, Kim, and Wei (2009), Pflueger and Viceira (2011)) deters

firms from switching to inflation-indexed bonds.

The combination of long-term nominal bonds and persistent inflation implies that small per-

manent shocks to inflation can have large effects on real liabilities. For instance, a permanent

decrease in log inflation from three to one percent per annum increases the expected real principal

repayment on a ten-year nominal bond by 22%. Surprise inflation matters for credit spreads above

and beyond shocks to the real economy. In contrast, a decrease in the real interest rate also affects

credit risk, but it does so because it reflects expected real growth and real risk premia.

Third, firms in our model choose leverage optimally but infrequently, according to a textbook

tradeoff theory (Modigliani and Miller (1958), Modigliani and Miller (1963), Kraus and Litzen-

berger (1973)). Tax and other debt benefits create an incentive for taking on debt, while bankruptcy

costs discourage taking on debt. When the ex-ante risk-adjusted cost of bankruptcy increases due

to inflation risk, young firms in our overlapping generations model respond by reducing leverage.

However, old firms’ inability to respond magnifies the increase in credit spreads. The empirically

well-founded assumption of infrequent capital structure adjustment helps generate a realistic level

of credit spreads.

We provide new empirical evidence that corporate bond investors price the risk of debt deflation

in a panel of corporate bond spread indexes from Australia, Canada, Germany, Japan, the United

Kingdom, and the United States over four decades. Following authors such as Chen, Collin-

Dufresne, and Goldstein (2009), we compute U.S. corporate bond spreads in excess of the Moody’s

Aaa log yield. Due to their worldwide benchmark status, U.S. Treasuries may enjoy extreme

liquidity and therefore the Moody’s Aaa yield may provide a better proxy of the long-term default-

free bond yield.6 We calculate spreads in excess of duration-matched government bond log yields

4

for all non-U.S. countries.

In a pooled regression, one standard deviation increases in inflation volatility or the inflation-

stock correlation are associated with spread increases of 14 bps. Our proxies for inflation risk

explain as much variation in credit spreads as do equity volatility and the dividend-price ratio, our

proxies for real uncertainty and risk aversion. Consistent with model predictions, the empirical

impact of inflation risk is especially large when real stock returns are low or when inflation shocks

are low.

Our empirical evidence from corporate bond spreads is both consistent with predicted model

magnitudes and with ex-post realized corporate bond credit losses and risk premia. We test whether

inflation risk raises physical expected credit losses, default risk premia, or both, using U.S. data

on Baa-rated corporate defaults, loss given default, and long-term corporate log returns in excess

of government log returns. We find that a one standard deviation move in U.S. inflation volatility

(58 bps) predicts a 10 bps increase in the annual credit loss rate over the next five years, while

controlling for the equity volatility, the dividend-price ratio, and business cycle controls. A one

standard deviation move in the U.S. inflation-stock correlation (34 percentage points) predicts a 6

bps increase in the annual credit loss rate over the next five years. We find that the inflation-stock

correlation, but not the inflation volatility, forecasts excess log returns on long-term corporate

bonds over long-term government bonds.

Our results suggest that the inflation-stock correlation raises both expected physical loss rates

and default risk premia, and that both channels are quantitatively important. On the other hand,

inflation volatility appears to raise expected physical credit loss rates, but not default risk premia.

These findings are consistent with our proposed mechanism, where an increase in the inflation-

stock correlation should make corporate defaults more likely to occur in the worst economic states

when marginal utility is high.

5

Evidence from the Israeli inflation-indexed corporate bond market provides additional direct

evidence that the nominal nature of U.S. and international corporate bonds generates time-varying

risk of debt deflation. In contrast to the other financial markets in our sample, Israeli govern-

ment and corporate bonds have been conventionally inflation-indexed since the 1950s (Koninsky

(1997)). Consistent with our proposed theory, we find no evidence that Israeli inflation-indexed

corporate bond spreads are driven by time-varying risk of debt deflation. On the contrary, invest-

ment grade Israeli inflation-indexed corporate bond spreads increased from 54 bps in 2000.Q1 to

146 bps in 2010.Q4 while inflation volatility decreased from 283 bps to 155 bps.

The findings in this paper have broad implications not only for asset pricing, but also for pol-

icy, macroeconomic research, and corporate finance. For instance, firms might optimally want to

decrease their share of long-term nominal debt when inflation risk is high.

The remainder of the paper is organized as follows. After a brief literature review, Section I

introduces the model. Section II argues that inflation risk should be quantitatively important for

credit spreads in a calibrated version of the model. Section III tests the model predictions in an

international panel of credit spread indexes, and Section IV concludes.

A. Literature Review

Time variation in inflation volatility was first modeled by Engle (1982). There is also sub-

stantial bond market evidence of time-varying inflation cyclicality (Li (2002), Baele, Bekaert, and

Inghelbrecht (2010), David and Veronesi (2013), Viceira (2012), Wright (2011), Campbell, Sun-

deram, and Viceira (2013)).

We add to previous structural models of credit risk such as Merton (1974), and Longstaff and

Schwartz (1995) by allowing the risk of inflation to vary over time. We also contribute to the

literature on asset pricing models with optimal leverage and default by arguing that firms should

6

adjust their capital structure in response to time-varying inflation risk (Leland and Toft (1996),

Goldstein, Ju, and Leland (2001), Hackbarth, Miao, and Morellec (2006), Chen, Collin-Dufresne,

and Goldstein (2009), Bhamra, Kuehn, and Strebulaev (2010a), Bhamra, Kuehn, and Strebulaev

(2010b), Gomes and Schmid (2010), Gourio (2013)). Our model of optimal firm capital structure

has analogies to optimal household mortgage choice under inflation risk (Campbell and Cocco

(2003), Koijen, van Hemert, and van Nieuwerburgh (2009)), but it differs in that all assets are

priced by the same representative investor.

This paper is closely related to recent models of monetary policy when firms’ liabilities are

nominal (Bhamra, Fisher, and Kuehn (2011), De Fiore and Tristani (2011)). Our model highlights

inflation volatility and inflation cyclicality as driving credit risk, and has directly testable predic-

tions. Transition dynamics in our model increase the quantitative impact of inflation risk on credit

spreads.

Ferson and Harvey (1991) estimate the risk premium for exposure to inflation surprises using

government bond, corporate bond, and stock portfolio returns for the period 1964 to 1986. We add

to their analysis by arguing that the time-varying second moments of inflation surprises are priced

into corporate bonds.

I. A Dynamic Model of Inflation Risk in Corporate Bonds

We model production and the optimal choice of capital structure in a standard manner, similarly

to Gourio (2013). We depart from standard practice by assuming that corporate debt is nominal

and long-term, and by assuming that the second moments of inflation are time-varying. We model

7

overlapping generations of firms to tractably capture infrequent debt refinancing.

A. Intuition: Contingent Claim Payoff Profiles

We illustrate the main model intuition using contingent claim payoff profiles. Black and Sc-

holes (1973) and Merton (1974) model a corporate bond as a default-free bond minus a put option

on the underlying firm’s assets. In such a framework, credit spreads decrease in the underlying

firm’s asset value and increase in the volatility of the firm’s assets. In our proposed mechanism,

an unexpected drop in inflation increases the default probability. Inflation volatility and inflation

cyclicality should therefore increase the corporate bond spread. This effect is similar to but sepa-

rate from the effect of real asset volatility on the credit spread.7


Figure 2 shows conditional expected real payoffs on nominal corporate and default-free bonds

for different inflation risk scenarios. In Figure 2B, inflation is uncertain and uncorrelated with real

asset values. The default probability is nonzero for any underlying real asset value, and the payoff

gap increases relative to Figure 2A.

Comparing Figures 2C and 2D shows that when inflation is pro-cyclical, credit spreads should

be higher. In Figure 2C, firms get hit twice during recessions because they experience low real

asset values and high real liabilities at the same time. The gap between default-free and corporate

bonds is especially large when real asset values are low and risk-averse investors’ marginal utility is

likely to be high, so credit spreads should increase further to include a larger default risk premium.

B. Timing of Cohort t


8

Figure 3 illustrates the timing for a firm that enters at the end of period t and produces for

two periods. At the end of period t, the firm chooses its face value of nominal two-period debt B$t

and purchases capital Kyt+1, which will be available for production at time t +1. The firm’s newly

issued corporate bonds have two periods remaining to maturity.

In period t +1, aggregate productivity and inflation shocks are realized. The firm experiences

an idiosyncratic shock to its capital stock and produces. The firm cannot modify its capital struc-

ture, so leverage is sticky. The firm’s seasoned corporate bonds have one period remaining to

maturity.

In period t +2, the firm again receives shocks and produces. At the end of period t +2, equity

holders decide whether to default. Equity and debt holders then receive payments.

C. Production

Firms have a standard Cobb-Douglas production function with capital and labor inputs. At

time t, firm i with capital Kit and labor Ni

t produces output Y it :

Y it =

(ztNi

t)1−α (

Kit)α

. (1)

Total factor productivity (TFP) zt is independently and identically distributed with a trend:

zt+1 = exp(µt)exp(

εT FPt+1 −

12

σ2)

with εT FPt+1

iid∼ N(0,σ2) . (2)

We calibrate one time period to equal five years, which is close to business cycle frequency, so

independent TFP shocks are a reasonable approximation. TFP trend µ is also the equilibrium trend

growth rate for output and consumption in the economy.

Firm i chooses labor optimally to maximize single period operating revenue, while taking the

9

aggregate wage as given. We assume that the aggregate supply of labor is fixed at 1, abstracting

from unemployment. The equilibrium wage adjusts to clear the labor market.

We define aggregate output, capital, and investment at time t by integrating over all firms:

Yt =∫

iY i

t di, Kt =∫

iKi

t di, Nt =∫

iNi

t di, It =∫

iIit di. (3)

Capital depreciates at a constant rate δ and we impose the resource constraint that total output

equals aggregate consumption plus investment:

Kt+1 = It +(1−δ)Kt , (4)

Yt = Ct + It . (5)

Solving for the equilibrium hiring policy, total output at time t is given by Yt = z1−αt Kα

t . Young

and old firms are heterogeneous in their capital stock, but constant returns to scale imply that for

any firm the return on capital from time t to time t +1 equals:

RKt+1 =

[α

(zt+1

Kt+1

)1−α

+(1−δ)

]. (6)

From (6) the expected level and the volatility of real returns on capital are endogenously higher

when the capital stock Kt+1 is low relative to trend.

D. Inflation

Let Pt denote the price level at time t and πt log inflation from time t−1 to time t:

πt = log(Pt/Pt−1) . (7)

10

Consistent with U.S. and international empirical evidence (e.g., Stock and Watson (2007), Ball

and Cecchetti (1990)), we model expected log inflation as following a random walk. The dynamics

of expected inflation resemble a backward-looking Phillips curve, consistent with empirical evi-

dence (Fuhrer (1997)). Inflation persistence implies that uncertainty about the price level increases

with the time horizon, so inflation risk should be larger for longer maturity bonds:8

πt+1 = πt + επt+1, (8)

επt+1∣∣σπ

t+1 ∼ N(

0,(σ

πt+1)2), (9)

Corr(

επt+1,ε

T FPt+1∣∣ρπ

t+1)

= ρπt+1. (10)

Higher σπt implies more uncertainty about the price level. When ρπ

t is positive, the relation

between inflation and real activity slopes upward, similarly to an upward-sloping Phillips curve.

When ρπt is negative, the Phillips curve is unstable—potentially due to supply shocks or to shifting

inflation expectations.

The magnitude of inflation surprises and their relation with productivity shocks can vary over

time. We model time variation in σπt and ρπ

t in the simplest possible manner by assuming that they

follow two-state Markov switching processes, independent of each other and of all other shocks in

the economy. Inflation uncertainty σπt and inflation cyclicality ρπ

t each take a low or a high value:

σπt ∈

σπ,L,σπ,H , ρ

πt ∈

ρπ,L,ρπ,H . (11)

The probabilities of going from state σπ,X to σπ,Y and of going from state ρπ,X to ρπ,Y are:

p(σ

π,X → σπ,Y) , p

(ρ

π,X → ρπ,Y) . (12)

11

E. Default Decision

A firm’s default decision depends on the initial level of debt, aggregate real shocks, aggregate

nominal shocks, and idiosyncratic real shocks.

Corporate debt promises a fixed nominal payment after two periods, when the firm pays a

liquidating dividend. We denote logs by small letters throughout. All firms in cohort t are identical

ex-ante. Denote the initial log nominal face value of debt by b$t and initial log leverage adjusted

for expected inflation by lt . Then firms choose:

lt = b$t −2πt− ky

t+1. (13)

Inflation persistence implies that the inflation shock in period t + 1 enters twice into the log

real liabilities of an old firm:

breal,oldt+2 = lt + ky

t+1−2επt+1− ε

πt+2. (14)

Firm i in cohort t experiences identical and independent idiosyncratic shocks to log capital at

times t +1 and t +2, ai,1t+1 and ai,2

t+2. We assume:

ai,idt+2 = ai,1

t+1 +ai,2t+2, (15)

ai,1t+1,a

i,2t+2

ind∼ N(−1

4

(σ

id)2

,12

(σ

id)2). (16)

Using (6) the log real value of an old firm at the end of period t +2 equals:

vi,oldt+2 = ky

t+1 + rKt+1 + rK

t+2 +ai,idt+2. (17)

12

Equity holders have the option to default on debt payments and to receive a zero liquidating

dividend. They optimally decide to default if and only if the real value of the firm (17) is less than

its real liabilities (14).9 Conditional on aggregate shocks, firms with the most adverse idiosyncratic

shocks default:

ai,idt+2 < lt−2ε

πt+1− ε

πt+2− rK

t+1− rKt+2︸︷︷︸

Survival Threshold a∗t+2

. (18)

Equation (18) formalizes the intuition that low inflation shocks επt+1 and επ

t+2 increase the survival

threshold a∗t+2 and defaults. Low productivity shocks at times t +1 and t +2 lower real returns on

capital and also increase defaults. The real interest rate does not enter into the default threshold

directly. However, a drop in real interest rates either reflects a fall in expected real growth rates or

a change in real risk premia, which can affect default risk.

F. Stochastic Discount Factor

We model a representative consumer with expected power utility over consumption, risk aver-

sion γ, and discount rate β:

Ut = Et

∞

∑s=t

exp(−β(s− t))C1−γ

s

1− γ. (19)

The two-period stochastic discount factors for pricing two-period real and nominal payoffs are:

Mt,t+2 = exp(−2β)(Ct+2/Ct)−γ , (20)

M$t,t+2 = Mt,t+2/exp

(2πt +2ε

πt+1 + ε

πt+2). (21)

13

G. Corporate Bond Prices

Let the functions H(a∗t+2), Ω(a∗t+2) denote the time t + 2 default probability and average de-

faulted firm value conditional on the survival threshold a∗t+2. Let G(a∗t+1,ai,1t ) and W (a∗t+1,a

i,1t )

denote the time t + 1 default probability and average defaulted firm value of a cohort t − 1 firm

conditional on the survival threshold a∗t+1 and on the firm’s first-period idiosyncratic shock ai,1t :

H(a∗t+2

)= P

(ai,id

t+2 < a∗t+2

), (22)

Ω(a∗t+2

)= E

(exp(

ai,idt+2

)I(

ai,idt+2 < a∗t+2

)), (23)

G(

a∗t+1,ai,1t

)= P

(ai,id

t+1 < a∗t+1

∣∣∣ai,1t

), (24)

W(

a∗t+1,ai,1t

)= E

(exp(

ai,idt+1

)I(

ai,idt+1 < a∗t+1

)∣∣∣ai,1t

). (25)

Here, I denotes the indicator function. The prices of a new corporate bond at time t and a

duration-matched two-period government bond then equal:

qcorp,newt = Et

M$t,t+2

1− H(a∗t+2

)︸︷︷︸Default Rate

+θΩ(a∗t+2

)exp(a∗t+2

)︸︷︷︸Recovery Rate

, (26)

qgov,2t = Et

[M$

t,t+2

]. (27)

Similarly, firm i’s seasoned corporate bond and a duration-matched one-period government bond

14

are then priced according to:

qi,seast = Et

M$t,t+1

1−G(a∗t+1,ai,1t )︸︷︷︸

Cond. Def. Rate

+θW (a∗t+1,a

i,1t )

exp(a∗t+1

)︸︷︷︸Cond. Recovery

, (28)

qgov,1t = Et

[M$

t,t+1

]. (29)

Let logqi,seast denote the log seasoned corporate bond price averaged across firms. We define credit

spreads as the average log yield spread:

spreadnewt = −1

2logqcorp,new

t +12

logqgov,2t , (30)

spreadseast = −logqi,seas

t + logqgov,1t (31)

Note that these measures are not mechanically linked to the level of inflation expectations in the

nominal stochastic discount factor.

H. Capital Structure Choice

Firms choose leverage according to a standard tradeoff view of capital structure. We follow

Gourio (2013) in assuming that firms receive benefits χ > 1 for each dollar of debt issued. Eq-

uity holders of cohort t firms choose capital Kyt+1 and nominal liabilities B$

t subject to the budget

constraint:

Kyt+1 = St︸︷︷︸

Value of New Equity

+ χ × qcorp,newt︸︷︷︸

New Nominal Bond Price

× B$t . (32)

Higher χ increases the incentive to raise leverage. There is a debate whether tax benefits are suf-

ficiently large to explain observed leverage ratios (Graham (2000), Almeida and Philippon (2007)).

15

We interpret χ broadly to include more general benefits and costs of debt, such as constraining

managers from empire-building and reducing informational asymmetries (Jensen and Meckling

(1976), Myers (1977), Myers and Majluf (1984), Jensen (1986)).

Equity holders trade off the benefits of debt with expected bankruptcy costs. We assume that

debt investors only recover a constant fraction θ < 1 of firm value in bankruptcy, see also Leland

(1994). A lower recovery rate θ reduces the incentive to lever up. There exists an interior opti-

mal leverage ratio if bankruptcy costs are sufficiently large relative to debt benefits. We formally

assume that θχ < 1 (Gourio (2013)).

By imposing the resource constraint (5), we follow Gourio (2013) in assuming that bankruptcy

costs and debt benefits are redistributive and do not have a direct effect on output. This simplifying

assumption should not substantially affect the model results, as long as time variation in default

rates is small relative to aggregate output fluctuations.

We define the marginal default probability:

h(a∗t+2

)= H ′

(a∗t+2

). (33)

Equity holders equate the marginal benefit of raising another dollar of debt with the increase in

bankruptcy costs according to the first-order condition:

0 =−χ(1−θ)Et

(M$

t,t+2h(a∗t+2

))︸︷︷︸

Marginal Bankruptcy Cost

+(χ−1)Et

(M$

t,t+2(1−H

(a∗t+2

)))︸︷︷︸

Marginal Benefit of Debt

. (34)

16

Firms choose the optimal level of capital, yielding the first-order condition:

1 = Et[Mt,t+2RK

t+1RKt+2Ft+2

], (35)

Ft+2 = 1− (1−θχ)Ω(a∗t+2

)︸︷︷︸Bankruptcy Cost

+(χ−1)exp(a∗t+2

)(1−H

(a∗t+2

))︸︷︷︸Benefit of Debt

. (36)

The Euler equation (35) says that the expected discounted return on capital, adjusted for

bankruptcy costs and benefits of debt by the factor Ft+2, equals 1. Inflation affects the first-order

conditions (34) and (35) through the survival threshold a∗t+2. When inflation is more volatile or

more pro-cyclical, the default threshold becomes more volatile and marginal bankruptcy costs in-

crease. While equity holders do not incur any bankruptcy costs upon default, debt investors require

compensation for bankruptcy costs ex-ante, incentivizing firms to reduce leverage ratios.

II. Calibrated Model

A. Parameter Values and Model Moments

We show two model calibrations, which separately capture time-varying inflation volatility

and time-varying inflation cyclicality. Model 1 focuses on stochastic inflation volatility and holds

the correlation between inflation shocks and TFP shocks constant at 0. Model 2 holds inflation

volatility constant, but allows the inflation-TFP correlation to vary.

We focus on moderate inflation volatility to highlight the relevance of inflation risk for credit

spreads even in a stable inflation environment. In Model 1, the standard deviation of annual in-

flation expectation shocks switches between 0% and 2%. The higher volatility of 2% corresponds

approximately to the U.S. experience in the early 1980s, and is half as large as our estimate of

U.K. inflation volatility during the late 1970s. To focus on the impact of inflation volatility, we

17

set the inflation-TFP correlation to zero. Volatility states are persistent, consistent with a five-year

autoregressive coefficient for U.S. inflation volatility of 0.5. The volatility process spends about

two-thirds of its time in the low state.

In Model 2, we assume that the inflation-TFP correlation follows a symmetric process, switch-

ing between−0.6 and 0.6, within the range of our empirical estimates for the inflation-stock return

correlation in developed countries.10 We study the impact of inflation cyclicality with moderate

inflation uncertainty of 1% per annum (p.a). The average duration for each state is 15 years, con-

sistent with three different regimes over a forty-year period.

[TABLE I ABOUT HERE]

Parameter values are summarized in Table I. We face a tradeoff in choosing the length of the

time period. Five-year time periods imply that seasoned corporate bond durations are slightly

shorter than their empirical counterparts, and that firm leverage and investment are constant for

ten-year periods.11 We choose standard values for the capital share, depreciation, and the discount

rate (Cooley and Prescott (1995)). We choose a risk aversion of 10, the upper bound of plau-

sible coefficients of risk aversion considered by Mehra and Prescott (1985). We constrain trend

growth to be equal to average U.S. real GDP growth between 1970 and 2009. The recovery rate

in bankruptcy equals 40%, consistent with the empirical evidence in Altman (2006).12 The debt

benefit parameter is a free parameter, and we choose χ = 1.4 to generate empirically plausible

default rates. Almeida and Philippon (2007) calculate that tax benefits account for approximately

16% of the debt value, so our high benefits incorporate significant agency benefits of debt.

[TABLE II ABOUT HERE]

Table II reports calibrated asset price moments together with empirical U.S. moments from

1970 to 2009.13 The high volatility of TFP shocks and idiosyncratic shocks generate plausi-

18

ble levels of aggregate and idiosyncratic equity market volatility. We do not attempt to explain

the equity volatility puzzle (Shiller (1981), LeRoy and Porter (1981)), which can be resolved if

consumption and dividend growth contain a time-varying long-run component (e.g., Bansal and

Yaron (2004)), or if preferences induce persistent fluctuations in risk premia (e.g., Campbell and

Cochrane (1999)).

Unexpectedly low inflation also increases real off-balance sheet liabilities, such as defined ben-

efit pension plans, health care obligations, and operating leverage. Pension obligations were espe-

cially salient during the United Airlines bankruptcy negotiations in the 2000s (Maynard (2005)).

Jin, Merton, and Bodie (2006) argue that a firm’s equity risk reflects the risk of its pension plan.

Shivdasani and Stefanescu (2010) and Bartram (2012) calculate that consolidating post-retirement

benefits can increase leverage by about a third. We interpret model leverage of 41% broadly to

include off-balance sheet liabilities.

We compare the seasoned model credit spread to the average Moody’s Baa over Aaa log yield,

which is based on secondary market prices rather than prices at issuance. Recent papers have

argued that structural models of credit risk can only explain a small portion of empirical credit

spreads while matching historically low default rates (Huang and Huang (2012)). We obtain high

credit spreads with plausible default rates due to volatile TFP shocks and to high risk aversion.

Leverage ratios of model seasoned firms are heterogeneous across firms, and credit spreads are con-

vex in leverage ratios, so the cross-section of firms further raises average credit spreads (Bhamra,

Kuehn, and Strebulaev (2010a), Bhamra, Kuehn, and Strebulaev (2010b)).

Our model raises the question of why firms do not issue inflation-indexed debt. If bond issuance

in our sample countries is nominal by historical convention, it is plausible that inflation-indexed

corporate bond yields would contain a liquidity premium. Such a liquidity premium could capture

investors’ and issuers’ increased accounting and training expenses from holding both nominal and

19

indexed bonds at the same time. U.S. government inflation-indexed bond yields, first issued in

1997, initially contained a substantial liquidity premium of over 50-100 bps (Pflueger and Viceira

(2011)).

Our model is consistent with a nominal-only corporate bond market for plausible liquidity

premia. Consider the problem of an infinitely small firm, which can deviate from the nominal-only

equilibrium by issuing inflation-indexed bonds. In our calibrated model, such a firm finds it optimal

to continue issuing nominal debt as long as the liquidity premium in corporate inflation-indexed

bond yields is at least 29 bps. For the derivation of the optimality condition, see Supplementary

Appendix C.

B. Model Implications for Credit Spreads

[TABLE III ABOUT HERE]

Table III shows that calibrated credit spreads are highly sensitive to both inflation volatility

and the inflation-stock correlation, even for moderate levels of inflation volatility. We focus on

seasoned credit spreads, which take into account non-optimal and heterogeneous firm leverage

ratios and correspond most closely to empirical secondary market prices of corporate debt. We

estimate the following model regressions:

Model 1: spreadseast = λ

01 +λ

σπ

1 σπt +λ

σeq

1 σeqt +λ

DP1 DPseas

t +λeq1 req

t +λπ

1επt +η1,t ,

Model 2: spreadseast = λ

02 +λ

ρπ

2 ρπt +λ

σeq

2 σeqt +λ

DP2 DPseas

t +λeq2 req

t +λπ

2επt +η2,t .

(37)

We report means and standard deviations of regression coefficients from 500 simulated time se-

ries of length 100. The simulation length corresponds to approximately forty years of independent

bi-annual data from five countries. Since our empirical quarterly observations are likely correlated

20

over time and across countries, we have to exercise caution in relating the model standard errors to

empirical standard errors.14

A one percentage point increase in the standard deviation of annual inflation shocks leads to an

economically significant increase in credit spreads of 27 bps (Panel A). Credit spreads increase by

20 to 27 bps as the inflation-stock return correlation increases by 100 percentage points. As we go

from column (1) to column (2) in Panel A, we add inflation volatility as an explanatory variable,

and the regression R2 increases by four percentage points. Adding the inflation-stock correlation

in Panel B similarly increases the regression R2 by two percentage points.

Equity returns, inflation shocks, equity volatility, and the dividend-price ratio enter with the

expected signs in Table III. Capital structure adjustments are slow and therefore high equity returns

and high inflation shocks decrease seasoned firms’ leverage and credit risk. Model real interest

rates reflect time-varying expected consumption growth and time-varying precautionary savings,

and are highly correlated with the dividend-price ratio and equity volatility, so controlling for real

interest rates would not explain any additional variation in model credit spreads.

Our right-hand side variables can jointly account for over 80% of the variation in credit spreads,

which is unsurprising because the simulated model credit spreads are a function of real shocks,

nominal shocks, and the inflation risk regime. We would not expect an equally high R2 in our

empirical results, especially if empirical nominal and real shocks were imperfectly measured.


Intuitively, inflation risk matters most when stock returns are low or when inflation is unexpect-

edly low. Figure 4 shows that inflation volatility and the inflation-TFP correlation increase credit

spreads especially strongly when stock returns and inflation surprises are low.15 The asymmetry in

Figure 4 is large relative to the average effect of inflation risk on credit spreads. For instance, the

21

difference between high inflation volatility credit spreads and low inflation volatility credit spreads

is 133 bps larger in the lowest stock return quintile than in the middle stock return quintile.

III. Empirical Inflation Risk and Corporate Bonds

A. Data Description

We compute credit spreads as the continuously compounded (or log) corporate bond index yield

over the log default-free yield, analogously to model corporate bond spreads. This credit spread

also equals the log of (one plus) the proportional credit spread, and is therefore not mechanically

linked to inflation expectations.

U.S. Treasury yields may not equal the risk-free rate due to their benchmark status in worldwide

financial markets. Following authors such as Chen, Collin-Dufresne, and Goldstein (2009), we use

the Moody’s Baa over Aaa log yield spread as a measure of credit risk in long-term U.S corporate

bonds. Subtracting the Aaa log yield should also help adjust for tax and callability effects on

corporate bond yields, if those are similar for corporate bonds with different ratings. Historical

defaults of Aaa rated bonds have been extremely rare, but any default component in Aaa bond

yields should bias us against finding an empirical result. Our results become even stronger using

the Baa-Treasury spread, as shown in Table B.IV in the Supplementary Appendix. Non-U.S. credit

spreads are computed in excess of a duration-matched government bond yield.

We obtain corporate bond yield indexes, government bond yields, GDP growth, stock returns,

and CPI inflation from Global Financial Data (GFD).16

We obtain empirical proxies for each country’s standard deviation of equity returns, standard

deviation of inflation surprises, and inflation-stock correlation from a rolling three-year backward-

looking window of quarterly log real stock return surprises and log inflation surprises. Unexpected

22

log inflation is the residual from a regression of quarterly log inflation onto its own four lags, the

lagged log T-bill, and seasonal dummies. The quarterly log real stock return shock is the residual

from regressing the quarterly log real stock return onto its own first lag. Real GDP growth surprises

are estimated analogously to inflation surprises by regressing log real GDP growth onto its own

four lags, the lagged log T-bill, and seasonal dummies.

Our baseline inflation forecasting regression follows Campbell, Sunderam, and Viceira (2013)

and Campbell and Shiller (1996). A number of different inflation forecasting relations have been

proposed in the literature. Atkeson and Ohanian (2001) argue that inflation over the past year

outperforms Phillips curve-based inflation forecasts, which also include a measure of real activity,

in the U.S. after 1984. We verify in the Supplementary Appendix Table B.V that our empirical

results are robust to including lagged log real stock returns and to excluding the nominal T-bill;

the results are also robust to rolling forecasts, the Atkeson and Ohanian (2001) model, and a wide

range of reasonable inflation forecasting models considered in Stock and Watson (2007). We use

consumer prices to measure inflation risk, but our results are robust to using a producer price index.

We control for lagged stock returns, real GDP growth, unemployment, and lagged inflation sur-

prises. We explicitly control for equal-weighted market leverage ratios of non-financial Compustat

firms over a shorter time period.17

We control for the volatility of real quarterly stock returns and the volatility of real quarterly

GDP growth. We also control for idiosyncratic stock return volatility, when available. We follow

Campbell, Lettau, Malkiel, and Xu (2001) in decomposing individual daily stock returns into a

market component, an industry component, and a firm component. Idiosyncratic volatility is cal-

culated as the volatility of the firm component over the past quarter, averaged over all individual

stocks.18

In our model the dividend-price ratio helps capture the time-varying risk of equity returns,

23

while in a model of time-varying risk aversion, such as in Campbell and Cochrane (1999), it serves

as a proxy for aggregate risk aversion. We therefore control for the dividend-price ratio from

Datastream.19

Campbell, Sunderam, and Viceira (2013) have argued that the comovement between nomi-

nal government bond returns and stock returns reflects time-varying inflation risk. If nominal

long-term bond yields reflect long-term inflation expectations, the correlation between changes in

nominal government log yields and log real stock returns should reflect investors’ perception of

inflation cyclicality. Similarly, the volatility of changes in nominal government log yields should

reflect inflation volatility. However, bond volatility and the bond-stock correlation may also reflect

real interest rate risk, and it is therefore important to control for them. We construct the bond-stock

correlation and bond volatility using daily or weekly government bond and stock returns over the

past quarter, using the highest frequency available.20

The difference between nominal and inflation-indexed bond yields, or breakeven inflation, is

the inflation rate that would equalize ex-post returns on nominal and inflation-indexed bonds. If

inflation risk and liquidity components in breakeven change only slowly over time, the correlation

between changes in breakeven and stock returns should give a high-frequency, financial markets-

based measure of the inflation-stock correlation. Indeed, Figure B.3 in the Supplementary Ap-

pendix shows that the nominal bond-stock correlation tracks the breakeven-stock correlation very

closely over the available samples 1999 to 2010 in the U.S. and 1985 to 2010 in the U.K, sug-

gesting that much of the time-variation in the nominal bond-stock correlation reflects time-varying

inflation risk.

B. Summary Statistics

[TABLE IV ABOUT HERE]

24

Summary statistics in Table IV reveal that both the volatility and the cyclicality of inflation

have varied substantially over time in each country. Average annualized inflation volatility ranges

from 101 bps for Germany to 161 bps for the U.K., consistent with the average inflation volatility

in our calibrated model. Inflation volatility displays significant time variation within each country

with standard deviations around the U.S. value of 58 bps. Inflation volatility in our sample reached

a peak of 412 bps in the U.K. during the 1970s, which exceeds the largest inflation volatility in our

calibrated model by a factor of two.

The inflation-stock correlation, our measure of the slope of the Phillips curve, is negative or

zero on average in every country. Its time variation within each country is substantial, with standard

deviations close to the U.S. value of 0.34.

Credit spreads average around 100 bps and have within country standard deviations between 32

bps and 98 bps. Rare negative values are most likely due to measurement error. The correlations

of international credit spreads with U.S. credit spreads, shown in Table B.2 in the Supplementary

Appendix, range from -0.17 for Japan to 0.71 for Australia, so international credit spreads are not

perfectly correlated.


Figure 5 shows the clear time-series comovement between international credit spreads and

inflation volatility in each country. Figure 5 indicates that when a country has higher inflation

volatility, it also has higher credit spreads. U.S. inflation volatility and credit spreads were both

high in the 1970s and 1980s. Both inflation volatility and credit spreads were even more elevated

in the U.K. during the same period.


25

Figure 6 visually illustrates the positive relation between international credit spreads and the

inflation-stock correlation. The U.S. inflation stock correlation was at an all-time high at the end of

2010, indicating procylical inflation. At the same time, credit spreads peaked during the financial

crisis. In contrast, the U.S. inflation-stock return correlation was mostly negative during the 1970s

and 1980s, indicating that supply shocks and shifting inflation expectations moved inflation and

real outcomes in opposite directions.21

C. Benchmark Results

Our main empirical tests in Table V proceed as follows. We first report a pooled regression of

credit spreads against business cycle controls.22 We then add inflation risk proxies, equity volatil-

ity, and the dividend-price ratio. Finally, we add time fixed effects and investigate the robustness

of our results to additional controls and sub-periods.

We estimate a pooled regression of the country i quarter t credit spread, spreadi,t , on country

fixed effects, λ0i , measures of inflation volatility, σπ

i,t , the inflation-stock correlation, ρπi,t , equity

volatility, σeqi,t , the dividend yield, DPi,t , and a vector of control variables, Xi,t :

spreadi,t = λ0i +λ

σπ

σπi,t +λ

ρπ

ρπi,t +λ

σeqσ

eqi,t +λ

DPDPi,t +Λ×Xi,t +ηi,t . (38)

The standard errors take into account potential cross-country correlation, heteroskedasticity, and

serial autocorrelation. We use Driscoll and Kraay (1998)’s extension of Newey and West (1987)

standard errors with 16 lags, as implemented by Hoechle (2007). Corporate bond markets vary

significantly across countries. Our regressions therefore contain country fixed effects.23

[TABLE V ABOUT HERE]

Table V shows that inflation volatility and the inflation-stock correlation are important in

26

explaining the time- and cross-country variation in credit spreads. Inflation volatility and the

inflation-stock correlation both enter with positive, large, and significant coefficients, which are

close to the model coefficients in Table III.

We note the following results in Table V. First, inflation volatility and the inflation-stock cor-

relation jointly increase the residual R2 by nine percentage points relative to a regression of credit

spreads onto business cycle controls. In comparison, equity volatility and the dividend-price ratio

raise the residual R2 only by three percentage points. Including inflation volatility and the inflation-

stock correlation in addition to equity volatility and the dividend-price ratio raises the residual R2

by eight percentage points. Taken together, the regressions in columns (1) through (5) show that

inflation risk can explain at least as much variation in credit spreads as equity volatility and the

dividend-price ratio.

Second, our benchmark estimation in column (5) shows that a 58 bps move in inflation volatil-

ity, or one standard deviation in U.S. inflation volatility, is associated with a 14 bps increase in

empirical credit spreads. A one standard deviation move in the inflation-stock correlation (34

percentage points) is associated with a 14 bps increase in credit spreads. The magnitudes are eco-

nomically meaningful relative to average credit spreads of around 100 bps. The empirical effect

of inflation volatility on credit spreads is extremely close to the theoretical magnitude in Table III.

The empirical slope coefficient of the inflation-stock correlation is somewhat larger, but within two

standard deviations of the theoretical slopes in Table III.

The sensitivities of credit risk with respect to real growth shocks and inflation shocks play

crucial roles in our proposed mechanism. We include inflation surprises to disentangle the effect

of news about the level of inflation and inflation risk, which is especially important if inflation

surprises and the second moments of inflation are correlated. Quarterly and three-year inflation

shocks enter negatively, and in some specifications significantly, with magnitudes comparable to

27

model slopes in Table III. Our measures of inflation surprises could plausibly contain larger mea-

surement error than the second moments of inflation if the timing of inflation surprises is impre-

cisely measured. Quarterly real GDP growth enters with a large and negative coefficient, but the

coefficients on real growth variables need to be interpreted with caution because of collinearity

between different real activity controls.

The coefficients on inflation volatility and the inflation-stock correlation are remarkably stable

across different specifications. Including time fixed effects in column (6) shows that the results are

not driven by any global omitted variable, such as global real interest rate risk, global growth risk,

or global time-varying liquidity. From our theoretical analysis, we would expect that inflation risk

should have especially large effects on credit spreads during crises. Excluding the financial crisis in

column (7), we find that the inflation volatility and inflation-stock correlation coefficients decrease

by about 35% relative to their full-sample values, but that they remain positive and statistically

significant. In column (8) we find that GDP volatility does not enter significantly in addition to our

main control for uncertainty about long-term real asset values, equity volatility, and other control

variables.

We include the slope of the yield curve and the nominal T-bill in column (8), and find that

our benchmark results are unchanged. Empirical credit spread indexes contain both callable and

non-callable bonds. Duffee (1998) shows that callability features can substantially affect credit

spreads, and that the T-bill and the slope of the nominal yield curve can help capture the value

of the call option. To the extent that controlling for the slope of the yield curve and the nominal

T-bill captures the value of the corporate bond call features, column (8) indicates that our empirical

results are not driven by the value of corporate bond call options.

Nominal government bond yields should reflect inflation expectations, inflation risk premia,

and real interest rates. The results in column (8) therefore indicate that corporate bond yields price

28

inflation risk above and beyond the effect of inflation risk on nominal government bond yields.

Interestingly, the slope coefficients for the log T-bill and log yield curve slope are within two stan-

dard deviations of the theoretical inflation shock coefficient in Table III, which is what we would

expect if inflation expectations are an important determinant of long-term nominal government

bond yields.

In column (9) we include as additional control variables idiosyncratic equity volatility, market

leverage, the nominal government bond volatility, and the bond-stock correlation over a shorter

sample period starting in 1989. The bond-stock correlation and the bond volatility enter positively

and significantly with large regression coefficients, while inflation volatility and the inflation-stock

correlation remain statistically significant. The bond-stock correlation and the bond volatility con-

trol for real interest rate risk. However, to the extent that these variables reflect inflation risk, we

interpret the results in column (9) as additional evidence that inflation risk is priced into credit

spreads.

Having estimated the pooled regression (38) in an international panel of forty years of quarterly

data, we now estimate the same relation for the U.S. time series of credit spreads. This time series

is likely to be especially familiar to readers, and we can include additional liquidity controls for

the U.S. Campbell and Taksler (2003) have argued forcefully that idiosyncratic equity volatility is

an important determinant of credit spreads and we control for it in our U.S. time series regressions

throughout.

[TABLE VI ABOUT HERE]

Table VI shows that U.S. credit spreads are clearly related to inflation risk, although the smaller

sample size reduces the statistical power relative to Table V. Inflation volatility enters with a posi-

tive and significant coefficient, which is slightly larger than the comparable coefficient in the pooled

29

international regression. The inflation-stock correlation coefficient is positive, but not significant

for the full time series. However, for the pre-crisis sub-sample it is positive and indistinguishable

from the model coefficient in Table III. The different result for the full sample could potentially

reflect a small number of observations during the financial crisis when measurement error was ar-

guably substantial. Going from column (4) to column (5) shows that inflation risk increases the

regression R2 from 61% to 73%.

Given that our time series includes the financial crisis of 2008 to 2009, it is important to control

for time-varying corporate bond liquidity using several liquidity proxies. We follow Garleanu and

Pedersen (2011) by including the three-month Eurodollar over T-bill spread as a liquidity control.

Garleanu and Pedersen (2011) argue that funding constraints and margin requirements can create a

price wedge between assets with identical cash flows but different margin requirements. Garleanu

and Pedersen (2011) predict that the Eurodollar over T-bill spread and the price gap between credit

default swaps and corporate bonds should be tightly linked and provide empirical evidence in the

time series and in the cross-section. Intuitively, larger corporate bond mispricings can persist when

hedge funds and other arbitrageurs face tight funding constraints, as proxied by the Eurodollar

over T-bill spread. Using the Eurodollar over T-bill spread as a corporate bond liquidity proxy is

also consistent with previous work on the determinants of corporate bond spreads (Campbell and

Taksler (2003)).24

We also include the off-the-run on-the-run U.S. nominal Treasury yield spread, which reflects

liquidity in the U.S. Treasury market (Krishnamurthy (2002)). We think of the off-the-run spread as

capturing a liquidity component that is common across U.S. Treasury and corporate bond markets,

consistent with the evidence in Ericsson and Renault (2006).25 Both the Eurodollar over T-bill

spread and the off-the-run spread enter with positive coefficients, as we would expect, but they

leave the inflation volatility coefficient unchanged.

30


We next explore the asymmetric model implications: the impact of inflation risk on credit

spreads should be especially strong when either real stock returns or inflation surprises are low.

Figure 7 shows empirical analogues to the theoretical relations in Figure 4, using a non-parametric

approach.

We construct the top left panel in Figure 7 by splitting observations in each country into quin-

tiles of real stock returns and into equal-sized subsamples for high and low inflation volatility. We

sort by three-year real stock returns for consistency with the construction of the inflation risk vari-

ables. The panel averages credit spreads across all countries within each inflation risk regime and

quintile and shows credit spreads relative to the middle quintile credit spread. The other panels are

constructed similarly.

The empirical relationships between credit spreads, stock returns, and inflation shocks in Figure

7 bear striking resemblance to the theoretical relationships in Figure 4. The top left panel in Figure

7 shows that the gap between credit spreads in the high and low inflation volatility regimes widens

by 30 bps in the lowest stock return quintile, indicating a larger put option in defaultable bonds

when inflation uncertainty is greater. This number is smaller, but a substantial fraction of the

theoretical analogue in Figure 4 of 133 bps.

The top right panel of Figure 7 similarly suggests that the impact of inflation volatility on credit

spreads is larger when inflation is surprisingly low, even if the largest difference in credit spreads

obtains in the second-lowest quintile of inflation shocks rather than the lowest.

In our benchmark empirical results, a one standard deviation move in either inflation volatility

or the inflation-stock correlation is associated with a credit spread increase of 14 bps. In com-

parison, the empirical magnitudes in Figure 7 are large. However, the magnitudes in Figure 7 are

smaller than the theoretical magnitudes in Figure 4. Besides measurement error, one reason is that

31

in Figure 7 we average the above median and below median inflation risk regimes, while in Figure

4 we compare credit spreads at the largest and the smallest values of inflation risk.

Further robustness checks, including individual country regressions, different inflation indexes,

inflation forecasting models, and HP filtered explanatory variables are reported in the Supplemen-

tary Appendix. Table B.IV in the Supplementary Appendix in particular shows that our bench-

mark results in Table V become stronger when we compute the U.S. credit spread with respect to

a duration-matched government bond log yield instead of the Moody’s long-term Aaa log yield.

D. Expected Credit Losses and Default Risk Premia

The mechanism we propose predicts that both inflation volatility and the inflation-stock corre-

lation raise expected losses from bond defaults. An increase in the inflation-stock correlation also

increases the likelihood that credit losses will occur in stock-market downturns, when marginal

utility of risk-averse investors is likely to be high. An increase in the inflation-stock correlation

should therefore raise the required excess return on corporate bonds over default-free bonds and

the default risk premium in corporate bond yields. In contrast, an increase in inflation uncertainty

may raise defaults and credit losses in both high and low marginal utility states, such as in the

contingent claim payoff profile depicted in Figure 2B. Therefore, an increase in inflation volatility

does not need to give rise to a default risk premium.

We estimate the effect of inflation volatility and the inflation-stock correlation on the n-year

credit loss rate lossUS,t→t+n, defined as the product of default rates and loss given default.26 Table

VII regresses annual credit loss rates on inflation volatility, the inflation-stock correlation, and

32

control variables:

lossUS,t→t+n︸︷︷︸Loss rate

= λ0US +λ

σπ

σπUS,t +λ

ρπ

ρπUS,t +λ

σeqσ

eqUS,t +λ

DPDPUS,t +ΛXUS,t +ηUS,t . (39)

[TABLE VII ABOUT HERE]

Columns (1) through (5) of Table VII show that both inflation volatility and the inflation-stock

correlation predict credit losses positively and significantly over the next two through five years

while controlling for idiosyncratic equity volatility, the dividend-price ratio, inflation surprises,

stock return surprises, GDP growth, and unemployment. The inflation volatility and inflation-

stock correlation coefficients are positive at all horizons and largest at the three-year forecasting

horizon. A one standard deviation move in U.S. inflation volatility (58 bps) predicts a 10 bps

increase in the annual credit loss rate over the next five years. This magnitude is statistically

indistinguishable from our baseline results on credit spreads, indicating that investors accurately

price expected credit losses due to increased inflation uncertainty. A one standard deviation move

in the U.S. inflation-stock correlation (34 percentage points) predicts a 6 bps increase in the annual

credit loss rate over the next five years. This magnitude is about half the empirical effect of the

inflation-stock correlation on credit spreads documented in Table V.

Columns (6) through (10) show that including a comprehensive set of control variables leaves

the inflation volatility and inflation-stock correlation coefficients unaffected. Inflation volatility

remains a strongly significant forecaster of credit losses at the three- and four-year horizons, while

the inflation-stock correlation remains significant at the three-year forecasting horizon. Column

(10) shows that at the five-year forecasting horizon, inflation volatility and the inflation-stock cor-

relation remain marginally significant while none of the additional control variables enters signif-

icantly. Supplementary Appendix Table B.VIII shows that the results are robust to using default

33

rates.

[TABLE VIII ABOUT HERE]

Table VIII predicts U.S. long-term corporate bond log returns in excess of long-term govern-

ment bond log returns using lagged inflation volatility, the lagged inflation-stock correlation, and

control variables.27 We estimate the regression:

retcorpUS,t→t+n− retgov

US,t→t+n = λ0US +λ

σπ

σπUS,t +λ

ρπ

ρπUS,t

+λσeq

σeqUS,t +λ

DPDPUS,t +Λ×XUS,t +ηUS,t . (40)

Table VIII shows that a one standard deviation move in the inflation-stock correlation (34 percent-

age points) predicts an increase in corporate bond excess returns of 51 bps over the next quarter

and of 126 bps over the next five years. On the other hand, Table VIII provides no evidence that

inflation volatility predicts corporate bond excess returns.

A rough calculation allows us to compare the magnitudes in Table VIII to those in Table

V. If the duration of the Ibbotson long-term corporate bond index is comparable to that of the

Moody’s long-term corporate bond index (10.7 years), then a one standard deviation move in

the U.S. inflation-stock correlation (34 percentage points) corresponds to an increase of (0.34×

370.6/10.7) bps = 12 bps in the five-year corporate default risk yield premium.

To summarize, the empirical results on credit losses and corporate bond risk premia indicate

that the effect of inflation volatility on corporate bond spreads acts largely through expected credit

losses. On the other hand, the inflation-stock correlation affects corporate bond spreads through

both the expected credit loss and the default risk channels and both channels are similarly quanti-

tatively important.

34

E. Inflation-Indexed Corporate Bonds in Israel

Theory predicts that corporate bond spreads and inflation risk should be unrelated in financial

markets with conventionally inflation-indexed liabilities. We study this prediction using Israeli data

for the period 2000 to 2010. Israeli government and corporate bonds have conventionally been

inflation-indexed since the 1950s (Koninsky (1997)) providing an ideal setting for this placebo

test.28 Moreover, Israeli inflation was low and comparable to the U.S. during 2000 to 2010, so

differing findings cannot be attributed to fundamentally different inflation environments.

We construct an index of Israeli corporate bond spreads over maturity-matched government

bonds for 2000.Q1 to 2010.Q4. Individual bond yields are from Bloomberg and a proprietary data

source. We include non-convertible bonds issued by non-financial firms with five to eleven years

remaining to maturity. All included corporate bonds are rated A- or higher by the rating agency

S&P Maalot or A3 or higher by the rating agency Midroog. Maturity-matched government bond

yields are from the Bank of Israel. For a detailed data description see Supplementary Appendix

C.4.

In contrast to the findings for nominal corporate bonds, we find no evidence that inflation-

indexed corporate bond spreads increase in either inflation volatility or the inflation-stock corre-

lation. On the contrary, Israeli inflation-indexed corporate bond spreads increased from 54 bps

to 146 bps over the sample while inflation volatility decreased from 283 bps to 155 bps. At the

same time, daily turnover in corporate bonds increased almost tenfold, so liquidity is not a likely

explanation for the increase in credit spreads.29

We test the relation between Israeli inflation-indexed corporate bond spreads and inflation

volatility and the inflation-stock correlation analogously to the baseline empirical results in Ta-

ble V. Table IX regresses Israeli inflation-indexed corporate log yield spreads onto inflation risk

variables and controls as in (38). Due to the limited sample size, we restrict the set of control

35

variables to those included in the model regressions in Table III, and we use Newey-West standard

errors with four lags. Including a reduced number of control variables is conservative in that it

might bias us against finding zero slope coefficients.

[TABLE IX ABOUT HERE]

Table IX column (5) shows that inflation volatility and the inflation-stock correlation do not

enter significantly while controlling for equity volatility, the dividend-price ratio, and inflation and

stock return surprises. Inflation volatility enters negatively both for the full sample and for a pre-

crisis sample shown in column (6). The inflation-stock correlation’s slope estimate is positive but

insignificant for the full sample, and it becomes negative for the pre-crisis sample.

While inflation risk does not appear to drive inflation-indexed corporate bond spreads, Israel

as a small open economy is especially exposed to international macroeconomic risks. The Euro-

pean debt crisis was likely an important determinant of Israeli corporate bond spreads during our

sample, as evidenced by the fact that the Israeli inflation-indexed corporate bond spread is 68%

correlated with the log yield spread of 10 year Italian government bonds over German government

bonds.30 Table IX column (7) shows that the regression R2 increases by 15 percentage points and

both the inflation volatility and the inflation-stock correlation enter with negative and insignificant

coefficients when we include the Italy-Germany sovereign log yield spread. The role of global risk

factors for Israeli corporate bonds underscores the importance of controlling for such factors in our

benchmark empirical results. Table V shows that results for nominal corporate bond spreads are

robust to flexibly controlling for time-varying global risks with time fixed effects.

Taken together, we find no evidence that Israeli inflation-indexed corporate bond spreads in-

crease in either inflation volatility or the inflation-stock correlation. The evidence from Israeli

inflation-indexed corporate bonds supports the view that time-varying risk of debt deflation, rather

36

than omitted variables, drives the positive empirical relation between inflation risk and nominal

corporate bond spreads in our benchmark results.

IV. Conclusion

While during the 1970s and 1980s investors and policy makers were concerned about stagfla-

tion, the two most recent U.S. recessions have been accompanied by low inflation. This paper

argues that uncertainty about the long-run price level and the changing relationship of inflation

with the business cycle are major macroeconomic determinants of corporate bond spreads. Recent

high inflation cyclicality can help understand the high level of corporate bond spreads.

In a real business cycle model with time-varying inflation risk, inflation persistence generates

large effects of inflation risk on credit spreads. Using data on international corporate bond spreads,

we provide new evidence that corporate bond investors price the time-varying risk of debt deflation.

Our results have broader implications for the macroeconomic determinants of optimal capital

structure of firms and households. While our model only allows for one dimension of capital

structure choice, in reality firms and households might adjust to changing inflation risk along

a rich number of dimensions. Firms could issue inflation-indexed corporate debt, floating-rate

debt, callable debt, or shorter term debt in response to inflation risk. However, each of these

adjustments is likely to come at a cost, such as rollover risk (He and Xiong (2012), Acharya, Gale,

and Yorulmazer (2011)), short-term variability in real payments (Campbell and Cocco (2003)), or

agency costs (Bodie and Taggart (1978)).

The results in this paper highlight the importance of better understanding the macroeconomic

and monetary policy determinants of bond and inflation risks. A decomposition of time-varying

inflation risk into macroeconomic shocks, such as cost push shocks and shocks to aggregate de-

37

mand, and time-varying monetary policy, could be of particular interest to central banks around

the world.

From a policy point of view, our results indicate that policy makers should take the possibil-

ity of debt deflation as seriously as investors appear to do so. Concerns about debt deflation are

especially relevant given the potentially important macroeconomic feedback effects of debt defla-

tion (Bernanke and Gertler (1989), Kiyotaki and Moore (1997)) and renewed concerns about a

deflationary drop in aggregate demand in the U.S.

38

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Notes

1A number of recent papers on inflation risk premia in government bonds include D’Amico,

Kim, and Wei (2009), Christensen, Lopez, and Rudebusch (2010), Haubrich, Pennacchi, and

Ritchken (2012), Campbell, Sunderam, and Viceira (2013), Pflueger and Viceira (2011), and Kung

(2013).

2The Survey of Professional Forecasters provides forecasters’ average survey probabilities that

annual-average over annual-average GDP index inflation will fall into a particular range. Panel

A shows the difference between the 90th and the 10th inflation distribution percentiles smoothed

over the past eight quarters. Panel B shows the smoothed difference between the 50th and the

10th percentiles. When the lowest probability range receives a weight of more than 10%, we fit

a unimodal beta distribution following Engelberg, Manski, and Williams (2009). Supplementary

Appendix C.1 provides a detailed variable description.

3Hershey, Robert D. Jr., 1982, Inflation hurts, but deflation could be worse, The New York

Times, April 18.

4Bernanke, Ben, 2002, Deflation: Making sure that ‘it’ doesn’t happen here, Remarks Before

the National Economists Club, Washington D.C., November 21.

5Throughout the paper we refer to the log of the gross yield as the log yield. That is, if we have

a bond that yields 3%, we obtain the log yield as log(1.03) ≈ 0.03. We measure the U.S. credit

spread as the difference between the log Moody’s Baa long-term yield over the log Aaa long-term

yield. Moody’s long-term corporate bond yields are based on seasoned bonds with 20 to 30 years

remaining to maturity.

49

6See e.g. Duffie and Singleton (1997), Grinblatt (2001), Krishnamurthy (2002), Krishnamurthy

and Vissing-Jorgensen (2012), Longstaff (2004), and Feldhutter and Lando (2008).

7For simplicity, in Figure 2 both the defaultable and default-free bonds are zero coupon with

fixed and equal nominal face values. The representative firm defaults when the real asset value

falls below the real face value of liabilities. In default bond holders become the residual claimants

on the firm’s assets.

8It is important for our quantitative results that expected inflation is persistent. The assumption

of an exact random walk is primarily for analytical tractability.

9The firm never finds it optimal to default in its intermediate period because no debt payments

come due during the intermediate period.

10See Table IV.

11Welch (2004) finds that the mechanistic effects of stock returns can explain about 40% of

movements in leverage ratios over a five-year horizon. Baker and Wurgler (2002) find that corpo-

rations are likely to raise more equity when their market valuations are relatively higher, and that

these effects can explain leverage ten years out. For empirical evidence on sticky leverage, also

see Leary and Roberts (2005).

12A recovery rate in the range of 40% to 50% is also consistent with the evidence in Cremers,

Driessen, and Maenhout (2008), Glover (2011) and Coval, Jurek, and Stafford (2009).

13We simulate 250 runs of length 100. Both model and empirical equity returns are defined as

ten-year log nominal equity returns in excess of the continuously compounded ten-year nominal

interest rate.

50

14To ensure that regressors are never perfectly collinear, we add small measurement errors to

the inflation shock and inflation risk variables. The standard deviations of the model measurement

errors are approximately 2% of the standard deviations of the underlying parameters.

15Figure 4 plots average seasoned credit spreads for different inflation risk regimes against

lagged stock returns and inflation surprises. We average credit spreads within stock return and

inflation shock quintiles and within inflation risk regimes. We simulate 500 runs of length 100. We

use quintile cutoffs from Model 2 for both Models 1 and 2, because inflation quintiles in Model 1

are not well defined.

16According to GFD, the original sources for government bond yields and T-bill rates are the Re-

serve Bank of Australia, Bank of Canada, Deutsche Bundesbank, Bank of Japan, Bank of England,

and Federal Reserve Bank. The original inflation sources are the Australian Bureau of Statistics,

Statistics Canada, German Statistisches Bundesamt, Japanese Statistics Bureau, UK Central Statis-

tical Office, and U.S. Bureau of Labor Statistics. Quarterly GDP in millions of national currency,

volume estimates, OECD reference year, annual levels, seasonally adjusted is from OECD Stat.

Stock returns correspond to the following equity indexes: Australia ASX Accumulation Index,

Canada S&P/TSX-300 Total Return Index, Germany CDAX Total Return Index, Japan Topix To-

tal Return Index, United Kingdom FTSE All-Share Return Index, and United States S&P 500 Total

Return Index. We are extremely grateful to Yoichi Matsubayashi for providing us with Japanese

corporate bond yield data. Durations are estimated from bond maturities, assuming that bonds

sell at par following Campbell, Lo, and MacKinlay (1997), p. 408. For a description of Moody’s

corporate bond indexes, see http://credittrends.moodys.com/chartroom.asp?r=3. Table B.1 in the

Supplementary Appendix lists further details on the corporate bond data sources and durations.

17Data for the U.S. and Canada is from Compustat North America and the Center for Research in

51

Security Prices (CRSP). Data for all other countries is from Compustat Global. We divide annual

book debt values from the previous year end by the sum of the same book debt and quarterly market

equity. Following Baker and Wurgler (2002), we define book debt as the sum of total liabilities

and preferred stock minus deferred taxes and convertible debt. When preferred stock is missing,

we use the redemption value of preferred stock. Corporate bond yield indexes, such as Moody’s

long-term yield indexes, weight observations equally, and therefore we control for equal-weighted

market leverage.

18We obtain U.S. stock returns from CRSP, Canadian stock returns from Datastream, and all

other country stock returns from Compustat Global. Industries are defined according to GIC clas-

sification codes.

19For a given MSCI index, the dividend yield is computed as the market-value weighted average

dividend yield of all constituents. The dividend yield for an individual stock is based on its most

recent annualized dividend rate (i.e., dividends per share) divided by the current share price.

20Bond volatility and the bond-stock correlation report the annualized standard deviation of

changes in long-term nominal government bond log yields and the correlation between changes in

nominal government bond log yields and log stock returns, respectively. These measures are also

equal to the volatility of government bond log returns scaled by the bond duration and the negative

of the correlation between government bond log returns and log stock returns, where bond returns

are approximated using changes in yields.

21Using bond-market derived measures, Wright (2011) argues that inflation cyclicality has in-

creased since 1990 in most developed countries.

22We use the sum of log inflation surprises and log real stock return surprises over the past three

52

years and over the past quarter, quarterly and three-year log real GDP growth, and the three-year

change in unemployment.

23For an analysis of the Japanese corporate bonds market, see Hattori, Koyama, and Yonetani

(2001), who argue that the default risk of the individual issuer is the most important determinant

of corporate bond spreads in Japan after 1997. Reserve Bank of Australia (2001) provides an

overview of the Australian corporate bond market. Galati and Tsatsaronis (2003) and De Bondt

and Lichtenberger (2003) study Euro corporate bonds during the Euro introduction.

24We obtain the three-month BBA LIBOR Rate from Bloomberg as ”US0003m Index” available

starting 1971.Q1.

25We obtain the off-the-run bond yield by pricing the on-the-run bond cash flows with the off-

the-run bond yield curve of Gurkaynak, Sack, and Wright (2007). On-the-run bond yields and

issue characteristics are from the monthly CRSP Treasury master file. The off-the-run spread is the

difference between the off-the-run and on-the-run bond yields, both continuously compounded.

The Supplementary Appendix provides a detailed variable description.

26We use the Moody’s Corporate Default Risk Service database to compute loss rates corre-

sponding as closely as possible to the Moody’s long-term Baa corporate bond yield. We compute

annualized issuer-weighted loss rates as the product of average default rates times average loss

given default. We consider U.S. domiciled firms in the industrial and public utilities sectors with a

senior long-term Baa rating. lossUS,t→t+n includes all defaults of firms that were rated Baa in year t

and defaulted in years t+1 through t+n. Because of the lag between credit loss rates and inflation

risk variables, the five year default forecasts effectively only use data on inflation volatility and the

inflation-stock correlation until 2005.

53

27We obtain long-term corporate and government bond return indexes from Ibbotson Associates.

28The proportion of non-linked corporate bond issuances has increased over time, but the ma-

jority of corporate debt raised on the Tel Aviv Stock Exchange in 2007, 2008, and 2009 was still

CPI-linked (Tel-Aviv Stock Exchange (2009)).

29Annual statistics from the Tel Aviv Stock Exchange

http://www.tase.co.il/Eng/Statistics/AnnualTables/Pages/Annual Tables.aspx.

30Italian and German benchmark yields from Datastream (TRBD10T, TRIT10T).

54

Figure 1: U.S. Credit Spreads and Survey Inflation Uncertainty

Panel A: Inflation Uncertainty

Panel B: Lower Tail Inflation Uncertainty

Average log yield spread on Moody's long-term Baa-rated corporate bonds over long-term Aaa-ratedcorporate bonds and survey inflation uncertainty. The Survey of Professional Forecasters providesforecasters' average survey probabilities that annual-average over annual-average GDP index inflationwill fall into a particular range. We interpolate the cumulative density function linearly and smoothquantiles over the past eight quarters. When the lowest inflation range receives a weight of more than10%, we infer quantiles from a fitted beta distribution following Engelberg, Manski, and Williams(2009). Supplementary Appendix C.1 provides a detailed variable description. Panel A shows thesmoothed difference between the 90th and the 10th inflation percentiles. Panel B shows the smootheddifference between the 50th and the 10th percentiles.

1.5

2

2.5

3

3.5

4

4.5

5

0

1

2

3

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010NBER Recession Baa-Aaa Log Yield Spread90-10 Infl. Quantile Spread (Right Axis)

Correlation=43%

End of Bretton Woods

Volcker DisinflationFinancial

Crisis

0.5

1.0

1.5

2.0

2.5

3.0

0

1

2

3

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010NBER Recession Baa-Aaa Log Yield Spread50-10 Infl. Quantile Spread (Right Axis)

Correlation=51%



Crisis

Percent (%)Percent (%)

Percent (%) Percent (%)

Figure 2: Contingent Claim Payoff Profiles

Panel B: Inflation Volatility > 0

Panel D: Countercyclical Inflation

Panel A: Inflation Volatility = 0

Panel C: Procyclical Inflation

Illustrative conditional expected real payoffs on nominal corporate and default-free bonds for different inflation risk scenarios. Both bondsare zero coupon with nominal face values of 1. We assume that the representative firm defaults when the real asset value is less than thereal face value of the bond, and that bond holders become residual claimants in default. Let P denote the price level, V the real asset value,and I() the indicator function. In Panel A, there is no uncertainty about the price level. In Panel B, inflation surprises are independent fromV. In Panels C and D, inflation surprises are perfectly positively or negatively correlated with V. The conditional expected payoff on thenominal default-free bond is E[1/P|V], and on the corporate bond is E[V I(VP<1)+(1/P) I(VP≥1)|V]. The detailed numericalimplementation is discussed in the Supplementary Appendix A.

Exp

ecte

d R

eal P

ayof

f

Recession Asset Value Boom

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t t + 1 t + 2

· Young firm · Seasoned firm · Old firm

· Choose nominal debt B$t · Real aggregate TFP shock εTFP

t+1 · Real aggregate TFP shock εTFPt+2

· Purchase capital Kyt+1 · Nominal aggregate shock επt+1 · Nominal aggregate shock επt+2

· New credit spreads · Real idiosyncratic shock ai,1t+1 · Real idiosyncratic shock ai,2

t+2

· Seasoned credit spreads · Default decision

· Liquidating dividend

Figure 3: Timeline of Firm i Cohort t

Figure 4: Asymmetric Model Predictions

Simulated average seasoned corporate log yield spreads versus stock returns and inflation shocks. Lowand high inflation volatility corresponds to 0% p.a. and 2% p.a., while inflation is uncorrelated withTFP shocks (Model 1). High and low inflation-TFP correlation corresponds to 0.6 and -0.6, whileinflation volatility is constant at 1% p.a. (Model 2). We average credit spreads within real stock returnquintiles and inflation shock quintiles over 500 simulations of length 100. Quintile cutoffs in all panelsare based on the simulated Model 2 stock return and inflation shock distributions. We normalize creditspreads to zero in the middle quintile of each panel and show a horizontal line at 0.

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Figure 5: International Credit Spreads and Inflation Volatility

This figure shows the comovement of quarterly credit spreads (solid) and inflation volatility (dashed) for Australia, Canada, Germany, Japan, the U.K., andthe U.S. Credit spreads are computed as investment grade corporate bond index log yields in excess of duration-matched nominal government bond logyields, except for the U.S. credit spread, which is the Moody's Baa minus Aaa log yield spread. Inflation volatility is computed using a three-year backward-looking window of quarterly inflation surprises.

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Corporate Log Yield Spread (% Ann.) Inflation Volatility (% Ann.)

Figure 6: International Credit Spreads and Inflation-Stock Correlation

This figure shows the comovement of quarterly credit spreads (solid) and the inflation-stock correlation (dashed) for Australia, Canada, Germany, Japan, theU.K., and the U.S. Credit spreads are computed as investment grade corporate bond index log yields in excess of duration-matched nominal governmentbond log yields, except for the U.S. credit spread, which is the Moody's Baa minus Aaa log yield spread. The inflation-stock correlation is computed using athree-year backward-looking window of quarterly surprises in inflation and stock returns, as described in Table IV.

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Figure 7: Empirical Credit Spreads, Stock Returns and Inflation Shocks

International empirical credit spreads versus stock returns and inflation shocks. The top left panelaverages credit spreads within quintiles of lagged three-year real stock returns and two inflationvolatility regimes. The other panels are constructed similarly by sorting credit spreads into quintiles oflagged three-year inflation shocks and two inflation-stock return correlation regimes, as indicated.Inflation risk regimes are defined relative to the country-specific median. We normalize credit spreadsto zero in the middle quintile of each panel and show a horizontal line at 0.

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General ParametersPeriod length 5 yearsDiscount rate β 3%*Risk aversion γ 10Capital share α 0.33Depreciation δ 8%*Trend growth μ 2.8%*Volatility of TFP shock σ 26%*Recovery rate θ 0.40Tax benefit of debt χ 1.40

Idiosyncratic volatility σid 17%*

Model 1: Time-Varying Inflation Volatility

Inflation-TFP correlation ρπ 0.00

High inflation volatility σπ,H 2%*

Low inflation volatility σπ,L 0%*

Persistence of σπ,H p (σπ,H→ σπ,H) 0.60

Persistence of σπ,L p (σπ,L→ σπ,L) 0.80

Model 2: Time-Varying Inflation TFP Correlation

Inflation volatility σπ 1%*

High inflation-TFP correlation ρπ,H 0.60

Low inflation-TFP correlation ρπ,L -0.60

Persistence of ρπ,H p (ρπ,H→ ρπ,H) 0.70

Persistence of ρπ,L p (ρπ,L→ ρπ,L) 0.70

Table I: Model Parameters

We show model parameters used in our calibrations. * denotes per annumunits. Annualized inflation volatility is the standard deviation of a one-year inflation shock. p(X→X) denotes the probability that the state at timet+1 will be X conditional on the time t state being X.

Empirical Model 1 Model 2

U.S. 1970-2009 Time-Varying σπ Time-Varying ρπ

Equity volatility (% Ann.) 18.4% 18.5% 18.0%Firm volatility (% Ann.) 47.2% 29.3% 29.0%Equity premium (% Ann.) 2.90% 7.82% 7.83%

ytgov,10 - πt 2.50% 2.80% 2.72%

ytgov,10 - yt

gov,5 0.25% 1.16% 1.08%

New corporate log yield spread 1.18% 1.23%Seasoned corporate log yield spread 1.01% 1.64% 1.53%Default probability 0.52% 0.45% 0.40%Leverage 25% 41% 40%

We compare simulated moments of calibrated Models 1 and 2 with empirical U.S. moments estimated between1970-2009. Equity volatility is the standard deviation of 10 year log nominal equity returns in excess of the 10 yearlog nominal government yield. Firm volatility is the standard deviation of idiosyncratic 10 year log nominal stockreturns for non-defaulted firms. The equity premium is the average 10 year log nominal equity return in excess ofthe 10 year log nominal government yield (adjusted for Jensen's inequality). The average seasoned credit spread iscomputed as the average Moody's Baa- Aaa corporate log yield spread. We use the historical U.S. 10-yearinvestment grade bond default probability 1970-2001 reported by Almeida and Philippon (2007). We report theaggregated book leverage ratio, computed as long-term debt plus short-term debt divided by total assets fromCompustat. For a detailed description of model moments see Supplementary Appendix E.

Table II: Empirical and Model Moments

Seas. corporate log yield spread (% Ann.) (1) (2) (3) (4)Inflation volatility (Ann.) 27.10 27.13

(9.37) (8.51)Equity volatility (Ann.) 8.69 2.27

(6.67) (6.96)Dividend-price ratio (Ann.) 17.51 30.16

(14.12) (14.63)Equity return -1.36 -1.36 -1.71 -1.45

(0.21) (0.21) (0.34) (0.34)Inflation shock -10.75 -10.76 -10.58 -10.70

(2.39) (2.16) (2.30) (2.11)Constant 2.27 2.09 1.03 1.29

(0.12) (0.09) (0.50) (0.50)

R2 0.75 0.79 0.81 0.85

Seas. corporate log yield spread (% Ann.) (1) (2) (3) (4)Inflation-stock correlation 26.62 19.70

(9.75) (11.94)Equity volatility (Ann.) 10.84 4.91

(4.19) (6.12)Dividend-price ratio (Ann.) 12.96 24.00

(10.53) (14.17)Equity return -1.41 -1.40 -1.85 -1.61

(0.21) (0.20) (0.26) (0.32)Inflation shock -9.29 -9.31 -9.11 -9.20

(1.14) (1.09) (0.97) (0.96)Constant 2.18 2.15 0.83 1.21

(0.11) (0.11) (0.31) (0.42)

R2 0.72 0.74 0.80 0.81

Panel A: Time-Varying Inflation Volatility (Model 1)

Table III: Model Credit Spread Regressions

Panel B: Time-Varying Inflation-TFP Correlation (Model 2)

We estimate the sensitivity of model seasoned corporate log yield spreads to inflationvolatility and the inflation-stock correlation in the calibrated models. In Panel A, inflationvolatility switches between 0% p.a. and 2% p.a., and the inflation-TFP correlation is zero.In Panel B, inflation volatility is constant at 1% p.a., and the inflation-TFP correlationswitches between -0.6 and 0.6. We use log seasoned equity returns and one-period changesin log inflation expectations as control variables. We also control for the dividend-priceratio, defined as the expected return on seasoned equity. The inflation-stock correlation isdefined as the correlation between log seasoned equity returns and shocks to log inflationexpectations. Equity volatility is defined as the standard deviation of log real returns onseasoned equity.

Australia Canada Germany Japan U.K. U.S.Start date 1983.Q3 1969.Q4 1969.Q4 1973.Q1 1969.Q4 1969.Q4End date 2010.Q2 2010.Q4 2010.Q4 2010.Q2 2010.Q4 2010.Q4Credit spread (%) mean 0.99 1.02 0.65 0.33 1.28 1.02

std 0.56 0.45 0.67 0.32 0.98 0.42min -0.10 0.28 -0.20 -0.38 -0.16 0.50max 3.02 3.76 3.83 1.28 6.25 3.17

Avg. corp. bond duration (years) 6.9 10.1 5.1 8.2 8.5 10.7Inflation vol. (%, Ann.) mean 1.26 1.19 1.01 1.33 1.61 1.23

std 0.40 0.43 0.36 0.77 0.88 0.58min 0.70 0.45 0.48 0.42 0.70 0.42max 2.09 1.97 2.11 3.72 4.12 2.93

Inflation-stock correl. mean -0.09 -0.03 -0.15 0.00 -0.12 -0.26std 0.31 0.34 0.32 0.27 0.31 0.34min -0.61 -0.77 -0.83 -0.56 -0.70 -0.90max 0.64 0.66 0.63 0.51 0.59 0.55

Equity Vol. (%, Ann.) mean 16.72 16.19 19.50 19.61 18.57 16.06std 8.35 5.55 7.62 6.32 8.09 5.34min 6.72 7.87 7.80 5.51 5.85 5.66max 37.57 27.40 40.20 36.04 44.41 27.99

Div.-price ratio (%, Ann.) mean 3.86 2.96 3.39 1.30 4.26 3.12std 0.80 1.00 1.12 0.66 1.24 1.32min 2.60 0.99 1.67 0.43 2.11 1.14max 6.95 5.67 6.20 2.86 10.46 6.14

Panel A: Long Sample Period Variables

We report summary statistics for the spread of investment grade corporate bond log yields in excess ofduration-matched nominal government bond log yields. For the U.S., we show the spread betweenMoody's Baa long-term log yields over Moody's Aaa long-term log yields. Corporate bond yields fromthe Economist (Australia), Bank of Canada and Datastream (Canada), Bundesbank (Germany), NikkeiCorporate Bond Index (Japan), Financial Times and the Economist (U.K.), and Moody's (U.S.).Average corporate bond durations are estimated assuming that bonds sell at par (Campbell, Lo, andMacKinlay (1997)). The annualized standard deviation of inflation surprises, the inflation-stockcorrelation, and the annualized standard deviation of real stock return surprises use a moving three-year window of quarterly inflation and stock return surprises. Inflation surprises are residuals fromregressing quarterly log inflation onto its own four lags, the lagged log T-bill, and seasonal dummies.Stock return surprises are residuals from regressing the quarterly log real stock return onto its own lag.Dividend-price ratios from MSCI. Panel B reports additional control variables only available for ashorter time period. Idiosyncratic volatility is the standard deviation of daily firm stock returns inexcess of market and sector returns using GIC sector classifications (Campbell et al. (2001)). Equal-weighted market leverage from Compustat. Bond volatility is the annualized standard deviation ofdaily or weekly changes in nominal government bond log yields over the past quarter. The bond-stockcorrelation reports the correlation between real log stock returns and changes in nominal governmentbond log yields over the past quarter.

Table IV: Summary Statistics

Australia Canada Germany Japan U.K. U.S.Start date 1989.Q1 1989.Q1 1990.Q1 1989.Q1 1989.Q1 1989.Q1End date 2010.Q2 2010.Q2 2010.Q2 2010.Q2 2010.Q2 2010.Q2Bond vol. (%, Ann.) mean 0.80 0.66 0.54 0.49 0.66 0.72

std 0.22 0.18 0.17 0.20 0.21 0.22min 0.42 0.28 0.28 0.19 0.30 0.40max 1.62 1.32 0.97 1.18 1.42 1.54

Bond-stock correl. mean -0.04 0.00 -0.09 0.11 -0.03 -0.04std 0.35 0.32 0.39 0.31 0.41 0.42min -0.65 -0.62 -0.84 -0.69 -0.80 -0.77max 0.78 0.68 0.72 0.64 0.72 0.77

Idiosync. vol. (%, Ann.) mean 22.23 26.80 26.24 31.28 18.28 25.95std 12.03 5.20 9.02 7.46 12.36 7.61min 5.02 19.69 15.91 19.08 4.04 16.26max 57.68 54.67 54.95 58.00 52.75 50.39mean 17.89 22.58 41.23 34.28 21.45 23.11std 6.25 6.11 13.51 6.69 3.94 3.91min 8.69 12.70 21.72 19.59 13.84 16.84max 40.76 35.53 63.12 47.40 31.67 33.67

Panel B: Shorter Sample Period Variables

Equal-Weighted Mkt. Leverage (%)

(1) (2) (3) (4) (5) (6) (7) (8) (9)Inflation risk

Inflation volatility (Ann.) 29.71** 28.04** 24.61** 12.49** 15.09** 22.94** 22.76**(8.36) (6.96) (6.97) (4.30) (4.50) (6.22) (5.66)

Inflation-stock correlation 40.42** 42.37** 39.99** 27.80** 44.88** 26.81**(9.10) (10.22) (8.62) (9.65) (7.66) (3.94)

Real uncertainty and other control variablesEquity volatility (Ann.) 1.26 0.86 1.52* 1.35* 1.62* -0.18

(0.86) (0.88) (0.59) (0.66) (0.62) (0.85)Dividend-price ratio (Ann.) 8.68* 8.41 14.65** 4.65 26.00** 28.77**

(4.32) (4.50) (5.28) (3.43) (7.42) (10.22)GDP vol. 6.77

(4.68)Log T-bill -11.78**

(3.46)Log yield curve slope -9.64*

(4.36)Idiosyncratic volatility (Ann.) 0.87

(0.58)Leverage -1.19**

(0.44)Bond volatility (Ann.) 56.21*

(23.28)Bond-stock correlation 71.35**

(19.66)Business cycle and inflation shock variables (Logs)

3-Year inflation shock 2.27 -0.98 -0.89 1.02 -1.69 -2.29* 0.79 -1.04 -3.54(1.90) (1.95) (1.72) (1.88) (1.88) (1.13) (1.23) (1.51) (1.80)

3-Year real stock return -0.36** -0.36** -0.32* -0.20 -0.19 0.04 -0.10 0.11 0.01(0.12) (0.12) (0.12) (0.11) (0.11) (0.14) (0.10) (0.12) (0.10)

3-Year GDP growth -2.58 -2.51* -1.32 -2.96* -1.66 -0.49 -0.41 0.68 0.34(1.31) (1.07) (0.85) (1.41) (0.91) (1.37) (0.74) (0.70) (1.14)

3-Year change unemployment -1.82 -5.51 -3.03 -3.04 -3.72 -1.24 1.08 0.07 0.48(3.39) (3.81) (3.40) (3.75) (3.72) (2.12) (2.02) (2.28) (2.43)

Quarterly inflation shock -5.67 -4.20 -5.01 -4.93 -4.51 0.91 -0.37 -6.26* -3.89(3.99) (3.62) (3.65) (3.74) (3.35) (2.11) (1.62) (2.91) (2.03)

Quarterly real stock return -0.47 -0.50 -0.51 -0.44 -0.48 0.52 -0.02 -0.52 -0.51(0.43) (0.43) (0.43) (0.43) (0.43) (0.28) (0.22) (0.36) (0.30)

Quarterly GDP growth -11.00* -10.87* -11.13* -10.50* -10.44* -2.81 -4.98** -10.08** -15.33**(5.54) (5.25) (5.00) (5.02) (4.40) (2.39) (1.63) (3.43) (3.42)

Residual R2 0.19 0.25 0.28 0.22 0.30 0.30 0.27 0.41 0.55Time fixed effects YesPeriod Full Full Full Full Full Full 69.Q4-07.Q4 Full 89.Q1-09.Q4

Table V: International Credit Spreads and Inflation Risk (1969.Q4-2010.Q4)Quarterly pooled regressions of Australia, Canada, Germany, Japan, U.K., and U.S. corporate log yield spreads (% Ann.) against inflation volatility, theinflation-stock correlation, and control variables. We report Driscoll and Kraay (1998) standard errors accounting for cross-country correlation and 16

lags. All regressions contain country fixed effects. The residual R2 reflects explanatory power in excess of fixed effects. Japan data starts in 1973.Q1.Australia data starts in 1983.Q3. Variables are constructed as described in Table IV. * and ** denote significance at the 5% and 1% levels,respectively.

(1) (2) (3) (4) (5) (6) (7) (8) (9)Inflation risk

Inflation volatility (Ann.) 40.02** 39.93** 35.28** 47.36** 38.38** 30.75** 33.48**(10.75) (10.39) (7.02) (6.35) (7.56) (6.25) (4.94)

Inflation-stock correlation 0.83 0.13 27.80** 0.47 -0.49 2.48(16.23) (12.35) (9.79) (12.57) (9.75) (10.32)

Real uncertainty and other control variablesIdiosyncratic volatility (Ann.) 1.96* 2.27** 1.56** 2.20** 1.47* 0.79*

(0.76) (0.75) (0.51) (0.81) (0.73) (0.38)Dividend-price ratio (Ann.) 16.28** 13.85** 10.58** 10.17 10.43** 7.89*

(2.59) (2.15) (1.64) (6.15) (1.86) (3.13)GDP vol. -3.91

(6.83)Log T-bill 2.91

(3.37)Log yield curve slope 2.35

(4.47)Equity volatility (Ann.) 0.02

(0.29)Leverage 0.96

(0.59)Bond volatility (Ann.) 50.00**

(7.74)Bond-stock correlation 9.48

(5.89)Liquidity variables

Treasury off-the-run spread 48.99(39.41)

Eurodollar over T-bill 12.51**(3.60)

Business cycle and inflation shock variables (Logs)3-Year inflation shock -0.08 -0.49 -0.45 -2.01 -1.87 -0.91 -1.97 -10.85** -2.72

(3.95) (2.95) (3.24) (2.41) (2.10) (1.81) (2.24) (3.23) (1.96)3-Year real stock return -0.26 -0.14 -0.13 -0.30 -0.21 -0.04 -0.28 -0.70** -0.31

(0.26) (0.21) (0.24) (0.17) (0.22) (0.17) (0.21) (0.14) (0.20)3-Year GDP growth -0.45 2.55 2.57 -3.13 -0.67 1.36 0.06 1.98 -0.54

(2.44) (1.93) (2.00) (3.17) (2.10) (1.83) (2.51) (1.11) (1.80)3-Year change unemployment 4.53 4.13 4.23 -0.34 -0.96 6.53* 0.31 -7.32* -0.29

(4.76) (4.23) (5.37) (5.49) (4.50) (2.51) (5.34) (3.53) (3.64)Quarterly inflation shock -16.72** -17.88** -17.89** -10.84** -11.64** -9.15* -11.71** -1.59 -10.97**

(4.18) (4.63) (4.56) (3.02) (3.93) (4.34) (3.93) (2.91) (3.89)Quarterly real stock return -0.18 -0.13 -0.13 0.29 0.40 0.69** 0.42 0.10 0.43

(0.48) (0.40) (0.39) (0.39) (0.27) (0.17) (0.29) (0.22) (0.24)Quarterly GDP growth -12.62 -12.22* -12.22* -7.22 -6.06 -5.71 -7.00 -15.24** -7.20

(6.51) (5.88) (5.88) (5.20) (4.38) (3.72) (4.37) (3.90) (4.03)R2 0.38 0.54 0.54 0.61 0.73 0.75 0.73 0.76 0.82

Period Full Full Full Full Full72.Q1-07.Q4 Full Full

72.Q1-09.Q4

We regress quarterly U.S. Baa-Aaa Moody's log yield spreads against inflation volatility, the inflation-stock correlation, and control variables.We obtain the off-the-run bond yield by pricing the on-the-run bond cash flows with the off-the-run bond yield curve of Gurkaynak, Sack, andWright (2007). On-the-run bond yields and issue characteristics are from the monthly CRSP Treasury master file. The off-the-run spread is thedifference between the off-the-run and on-the-run bond yields, both continuously compounded. The three-month BBA LIBOR Rate is fromBloomberg (US0003m Index). All other variables are as described in Table IV. We report Newey-West standard errors with 16 lags inparentheses. * and ** denote significance at the 5% and 1% levels, respectively.

Table VI: U.S. Credit Spreads and Inflation Risk (1972.Q1-2010.Q4)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Horizon n (Years) 1 2 3 4 5 1 2 3 4 3Inflation risk

Inflation volatility (Ann.) 2.66 13.89* 19.34** 16.97** 17.31** -0.61 6.24 16.53** 14.96* 16.97(4.89) (5.69) (2.71) (3.61) (5.58) (4.43) (5.32) (3.79) (6.09) (10.32)

Inflation-stock correlation 7.52 11.74** 21.83** 17.05** 18.47** 1.57 5.69 17.10* 11.32 13.06(6.84) (3.71) (7.85) (5.51) (6.52) (6.61) (3.25) (6.60) (7.00) (6.46)

Real uncertainty and other control variablesIdiosyncratic volatility (Ann.) 0.19 0.51* 0.62* 0.52* 0.20 -0.21 0.09 0.16 -0.16 -0.43

(0.36) (0.23) (0.24) (0.25) (0.34) (0.87) (0.38) (0.20) (0.31) (0.36)Dividend-price ratio (Ann.) -0.20 -1.45 -1.65 -0.53 -0.81 -9.04 -9.01 -8.82** -8.17 -8.49

(1.33) (1.78) (1.07) (1.04) (0.94) (12.95) (5.35) (2.57) (4.54) (5.33)GDP vol. 15.93 18.66* 7.21* 3.61 1.74

(8.58) (6.90) (2.94) (5.94) (8.36)Equity volatility (Ann.) 0.81 0.18 -0.16 -0.36 -0.38

(0.82) (0.50) (0.24) (0.35) (0.49)Leverage -0.24 0.26 0.59 1.10* 0.97

(1.76) (0.93) (0.36) (0.45) (0.62)Bond volatility (Ann.) 11.95 5.08 13.55* 20.16* 21.49

(20.14) (8.51) (5.25) (8.63) (12.15)Bond-stock correlation -14.79 -3.08 -7.60 -2.34 -5.91

(20.37) (9.68) (5.73) (12.60) (13.28)Business cycle and inflation shock variables (Logs)

3-Year inflation shock -0.83 -0.43 0.68 0.49 -0.14 -1.60 -1.21 -0.36 -1.02 -1.61(0.69) (0.51) (0.69) (0.69) (0.96) (1.78) (0.80) (0.63) (0.98) (1.23)

3-Year real stock return -0.03 0.13 0.26** 0.30** 0.31** -0.04 0.13 0.23** 0.28** 0.27*(0.11) (0.08) (0.08) (0.07) (0.10) (0.11) (0.07) (0.06) (0.10) (0.12)

3-Year GDP growth 3.66* 3.47** 3.97** 4.33** 3.44** 2.28 1.05 3.31** 3.71** 3.36(1.33) (0.99) (0.71) (0.43) (0.82) (1.70) (1.58) (0.96) (1.21) (1.87)

3-Year change unemployment 4.47 5.95** 7.23** 7.13** 4.61** -0.57 -0.76 4.74 4.72 3.38(3.21) (2.01) (1.75) (1.25) (1.35) (3.89) (3.87) (2.43) (3.23) (3.45)

Quarterly inflation shock -3.25 4.13 2.43 0.78 3.85 1.12 5.02 3.52 2.29 5.94(5.93) (6.28) (3.69) (3.12) (4.08) (5.07) (5.25) (2.93) (3.99) (6.59)

Quarterly real stock return 0.76* 0.52 0.39* 0.34* 0.32 0.37 0.29 0.17 0.14 0.09(0.30) (0.35) (0.16) (0.15) (0.16) (0.46) (0.30) (0.11) (0.19) (0.25)

Quarterly GDP growth -0.64 -0.08 -2.55 -2.72 -4.13 -5.28 -1.94 -3.73* -3.18 -5.02(2.32) (1.91) (1.52) (2.38) (2.50) (4.69) (3.12) (1.33) (2.44) (3.04)

R2 0.29 0.48 0.75 0.69 0.59 0.37 0.61 0.83 0.78 0.67

Table VII: Predicting U.S. Baa Credit Loss Rates (1969-2010)

We regress annual data on annualized issuer-weighted credit loss rates of Baa-rated U.S. issuers in the industrial and publicutility sectors onto lagged end-of-year inflation volatility, the inflation-stock correlation, and control variables. Loss rates arecalculated as the product of default rates and loss given default based on post default trading prices. The n-year loss rate in-yeart includes all defaults of firms with a senior long-term Baa rating in year t and at least one default during years t+1 through t+n.Our data source is the Moody's default risk database. We report Newey-West standard errors with 6 lags. Variables areconstructed as described in Table IV. * and ** denote significance at the 5% and 1% levels, respectively.

(1) (2) (3) (4) (5) (6) (7) (8)

Horizon (Quarters) 1 4 12 20 1 4 12 20Inflation risk

Inflation volatility (Ann.) 18.07 -42.65 -187.92 98.86 -25.26 -74.42 -123.08 227.28(35.24) (92.40) (196.22) (255.45) (59.21) (140.95) (165.92) (223.61)

Inflation-stock correlation 149.52** 349.56** 452.86* 370.62** 60.29 347.14** 466.53** 427.03**(53.11) (126.05) (206.14) (140.50) (66.92) (69.35) (123.23) (130.39)

Real uncertainty and other credit risk variablesIdiosyncratic vol. (Ann.) 3.70 14.98* 33.81** 36.10** 3.01 31.87** 19.24* 27.37**

(2.99) (5.86) (7.14) (9.89) (3.40) (7.84) (9.70) (5.91)Dividend-price ratio (Ann.) 20.05 68.49* 162.45** 185.62* 67.40* 356.86** -29.59 27.12

(18.14) (34.48) (49.01) (92.72) (33.50) (111.40) (119.21) (95.54)GDP vol. 4.16 -44.68 -57.03 269.69

(69.74) (158.23) (176.29) (191.81)Log T-bill 6.40 28.44* 17.24* -2.18

(6.02) (13.65) (8.69) (11.06)Log yield curve slope -57.44** -142.70** 25.86 -33.86

(11.69) (36.79) (60.10) (22.98)Equity volatility (Ann.) -115.98** -197.68** 55.38 -34.75

(27.74) (61.15) (56.69) (47.21)Leverage 6.68 -26.12 42.11** 43.69**

(6.26) (23.17) (14.27) (13.50)Bond volatility (Ann.) 331.33** -156.93 404.73** -92.13

(99.95) (252.25) (103.58) (205.00)Bond-stock correlation -141.93 -333.09 -19.63 29.27

(116.43) (238.45) (107.05) (188.17)Liquidity variables

Treasury off-the-run spread -295.37** -185.49 89.73 1,031.13(102.73) (325.84) (346.55) (711.30)

Eurodollar over T-bill -60.71** 24.22 16.75 16.35(17.66) (82.13) (47.72) (73.04)

Business cycle and inflation shock variables (Logs)3-Year inflation shock -15.11 -18.46 -1.47 28.17 -35.82* -22.30 -15.11 -18.46

(9.61) (15.08) (17.49) (22.26) (16.73) (28.31) (9.23) (15.10)3-Year real stock return -0.57 -2.54 -3.51 3.86 -0.16 -1.57 -0.57 -2.54

(0.68) (1.77) (2.30) (3.10) (1.07) (1.39) (1.05) (1.70)3-Year GDP growth 4.52 17.64 76.88* 154.60** -5.87 21.35 4.52 17.64

(6.92) (25.11) (29.75) (32.14) (11.31) (48.94) (12.73) (20.54)3-Year change unemploymen 38.24** 93.52 211.38** 305.93** 26.83 124.97 38.24 93.52*

(13.55) (50.36) (46.41) (75.15) (25.03) (98.10) (25.86) (42.41)Quarterly inflation shock 39.37 -119.96* -170.78** -176.81 61.54 -100.27** 39.37 -119.96*

(63.98) (53.07) (43.47) (102.45) (65.30) (26.75) (30.46) (53.37)Quarterly real stock return 1.72 -1.53 1.37 -4.67 1.22 -1.70 1.72 -1.53

(3.13) (2.74) (4.22) (6.35) (3.43) (2.54) (2.56) (4.25)Quarterly GDP growth -3.05 -20.94 -91.17 -77.22 12.50 -31.93 -3.05 -20.94

(22.69) (40.58) (62.58) (44.33) (23.30) (63.09) (26.96) (43.57)

R2 0.14 0.32 0.52 0.50 0.28 0.49 0.64 0.63

Period Full Full Full Full72.Q1-09.Q4

72.Q1-09.Q4

72.Q1-09.Q4

72.Q1-09.Q4

We regress quarterly U.S. long-term corporate bond log returns in excess of long-term government bond log returns against lagged inflationvolatility, the inflation-stock correlation, and control variables. Corporate and government bond return indices are from Ibbotson. For a laghorizon of n quarters, we report Newey-West standard errors with 16+n lags. * and ** denote significance at the 5% and 1% levels,respectively.

Table VIII: Predicting U.S. Corporate Bond Excess Returns (1969.Q1-2009.Q4)

(1) (2) (3) (4) (5) (6) (7)Inflation risk

Inflation volatility (Ann.) -127.00* -1.14 -53.74 -61.14** -110.86(52.09) (66.19) (56.89) (20.13) (56.86)

Inflation-stock correlation 267.43 178.27 -46.67 -171.35(147.59) (112.28) (55.41) (130.31)

Real uncertainty and other control variablesEquity volatility (Ann.) 4.48 5.83 -0.08 -3.00

(5.36) (4.95) (1.66) (4.50)Dividend-price ratio (Ann.) 0.88 0.19 -0.03 -0.35*

(0.73) (0.40) (0.07) (0.14)Italy-Germany 10 year gov. yield spread 3.80


Quarterly inflation shock -20.87 -31.13 -18.00 -29.58 -24.05 7.80 -25.28(28.45) (30.83) (24.71) (29.85) (26.95) (6.90) (21.97)

Quarterly real stock return -3.48 -3.69 -3.79 -2.44 -3.70 0.18 -3.45(3.20) (2.60) (2.90) (2.70) (2.53) (0.37) (1.97)

R2 0.08 0.32 0.42 0.19 0.45 0.53 0.60Period Full Full Full Full Full 00.Q1-07.Q4 Full

We regress the spread of Israeli inflation-indexed corporate bond log yields over government bond log yields against inflation volatility,the inflation-stock correlation, and control variables. Israeli corporate bond yields reflect corporate bonds issued by non-financial firmswith five to eleven years remaining to maturity. All corporate bonds are rated A- or higher by S&P Maalot or A3 or higher by Midroog.Maturity-matched inflation-indexed government bond yields are from the Bank of Israel. A detailed data description is available inSupplementary Appendix C.4. We report Newey-West standard errors with 4 lags in parentheses. * and ** denote significance at the 5%and 1% levels, respectively.

Table IX: Israeli Inflation-Indexed Credit Spreads and Inflation Risk (2000.Q1-2010.Q4)

Internet Appendix to Inflation Risk in Corporate Bonds

JOHNNY KANG and CAROLIN E. PFLUEGER*

*Citation format: Johnny Kang and Carolin E. Pflueger, 2013, Internet Appendix to “Inflation Risk in CorporateBonds”, Journal of Finance [DOI STRING]. Please note: Wiley-Blackwell is not responsible for the content or func-tionality of any supporting information supplied by the authors. Any queries (other than missing material) should bedirected to the authors of the article.

1

A. Generating Contingent Claim Payoff Profiles

Figure 2 shows real payoffs of nominal default-free and nominal corporate bonds. We generate

the figures as follows.

For i = gov,corp, let Ci(V ) denote the conditional expected bond payoff, where we condition

with respect to the asset value of the representative firm V . We consider bonds with nominal face

values normalized to one. We denote the price level by Π. The conditional expected payoffs on

government and corporate bonds are:

Pgov(V ) = E[Π−1 |V

], (1)

Pcorp(V ) = E[

1V Π>1Π−1 +1V Π<=1V

∣∣V ] . (2)

We plot conditional expected payoffs for V ∈ [0.2,5]. Panel A uses constant Π = 1, Panel C

uses Π =V 0.2, and Panel D uses Π =V−0.2.

Panel B assumes that log(Π) is normally distributed with standard deviation σ = 0.6 and

mean 0.5×σ2 so the expected payout of the government bond is 1 for any V . For this choice

of functional forms, the conditional expected corporate bond payoff can then be computed as

Ccorp(V ) = Φ

(log(V )−0.5σ2

σ

)+V

(1−Φ

(log(V )+0.5σ2

σ

)). We show real payoffs for realized price

levels Π = 1.5 and Π = 0.75 in dashed.

2

B. Model Solution

B.1. Optimal Choice of Labor

Firm i chooses labor optimally to maximize single period operating revenue, while taking the

aggregate wage Wt as given:

Nit = argmax

Nit

Y it −WtNi

t︸︷︷︸Operating Revenue

. (3)

From the firm’s single period optimization we obtain the first-order condition with respect to labor:

(1−α)z1−αt

(Ki

t

Nit

)α

=Wt . (4)

The capital to labor ratio is constant across firms and equal to Kt . Substituting back into operating

revenue gives firm i′s one-period equilibrium revenue as αKit

(ztKt

)1−α

. The expression for the

equilibrium return on capital follows as:

RKt+1 =

[α

(zt+1

Kt+1

)1−α

+(1−δ)

]. (5)

B.2. First-Order Conditions

The time t +2 real cash flow of a corporate bond issued by firm i at time t is:

(1− I

ai,id

t+2 < a∗t+2

)exp(2πt +2επ

t+1 + επt+2) +θ

Kyt+1

B$t

RKt+1RK

t+2 exp(

ai,idt+2

)I

ai,idt+2 < a∗t+2

. (6)

3

The time t price of the bond is given by the expected stochastic discounted value of real cash flows:

qcorp,newt = Et

[M$

t,t+2(1−H

(a∗t+2

))],

+θEt

[Mt,t+2

Kyt+1

B$t

RKt+1RK

t+2Ω(a∗t+2

)]. (7)

The expression for the survival threshold then implies:

qcorp,newt = Et

M$t,t+2

1− H(a∗t+2

)︸︷︷︸Default Rate

+θΩ(a∗t+2

)exp(a∗t+2

)︸︷︷︸Recovery

. (8)

Equity holders maximize:

Et

[Mt,t+2 max

(V i,old

t+2 −B$t exp

(−2πt−2ε

πt+1− ε

πt+2),0)]−St (9)

subject to:

vi,oldt+2 = ky

t+1 + rKt+1 + rK

t+2 +ai,idt+2, (10)

Kyt+1 = St +χqcorp,new

t B$t . (11)

Given constant returns to scale and no equity issuance costs, the net equity value (9) will equal

zero in equilibrium, reflecting free entry. Substituting (10), (11), and (8) into (9) we can rewrite

the firm’s problem as maximizing:

exp(2πt)Kyt+1LtEt

M$t,t+2

exp(−a∗t+2

)+(χ−1)

(1−H

(a∗t+2

)),

+(χθ−1)Ω(a∗t+2

)exp(−a∗t+2

)−Ky

t+1. (12)

4

Differentiating (12) with respect to Kyt+1 while holding constant the initial leverage ratio Lt

gives:

0 = exp(2πt)LtEt

M$t,t+2

exp(−a∗t+2

)+(χ−1)

(1−H

(a∗t+2

))+(χθ−1)Ω

(a∗t+2

)exp(−a∗t+2

)−1. (13)

Using a∗t+2 = lt−2επt+1−επ

t+2− rKt+1− rK

t+2 for the survival threshold gives the first-order con-

dition for capital with Ft+2 as in the main text:

1 = Et[Mt,t+2RK

t+1RKt+2Ft+2

]. (14)

Differentiating (12) with respect to Lt while holding constant the level of capital Kyt+1 gives:

0 =

(1+

∂

∂a∗t+2

)Et

M$

t,t+2

exp(−a∗t+2

)+(χ−1)

(1−H

(a∗t+2

))+(χθ−1)Ω

(a∗t+2

)exp(−a∗t+2

) . (15)

Using ∂

∂a∗t+2Ω(a∗t+2

)= exp

(a∗t+2

)h(a∗t+2

)gives the first-order condition with respect to lever-

age:

0 =−χ(1−θ)Et

(M$

t,t+2h(a∗t+2

))+(χ−1)Et

(M$

t,t+2(1−H

(a∗t+2

))). (16)

B.3. Numerical Solution Method

Define rescaled variables relative to trend productivity exp(µt):

Kt =Kt

exp(µt),Ct =

Ct

exp(µt),Yt =

Yt

exp(µt), zt =

zt

exp(µt).

We denote logs by lower case letters. Since zt is identically and independently distributed, our

5

only state variable is end of period total wealth W = Y +(1−δ) K. We use projection methods to

solve for the two policy functions for leverage and consumption (Aruoba, Fernandez-Villaverde,

and Rubio-Ramirez (2006)). A recursive equilibrium has to satisfy the two first-order conditions

(14) and (16) with the additional dynamics Kt+1 =(Wt−Ct

)exp(−µ). We define ER(w) as the

expected two-period return on capital in a model with zero inflation volatility. We then solve for

both log detrended consumption c and scaled leverage L/ER as polynomials of degree two in log

detrended wealth w by minimizing the errors of the first-order conditions along a grid of 19 nodes

for w. Intuitively, the survival threshold is related to the ratio of leverage over the two-period return

on capital and the scaling makes the survival threshold well-behaved.

C. Data Construction

C.1. Survey Inflation Uncertainty

This section describes in detail the construction of survey inflation uncertainty shown in Figure

1 in the main paper. Starting in 1968.Q4 the Survey of Professional Forecasters has provided

forecasters’ average probabilities that annual-average over annual-average GDP index inflation

will fall into a particular range. The probability ranges vary over time and the number of categories

has varied between six and 15. The highest probability category considered in any sub period is

16+ and the lowest probability category considered is <−3, both in annualized percentage units.

We use the mean probability inflation forecasts to construct points on the corresponding cu-

mulative density function (cdf) for annual-average over annual-average GDP price index inflation

πa. For instance, for 1982.Q1 the SPF reports that P(πa < 4) = 2.18%, P(4≤ πa < 6) = 11.85%,

P(6 ≤ πa < 8) = 57.73%, P(8 ≤ πa < 10) = 24.55%, P(10 ≤ πa < 12) = 3.39%, and P(12 ≤

πa) = 0.30%. Denoting the corresponding cdf by Fπ, we can then infer that Fπ(4) = 2.18%,

6

Fπ(6) = 14.03%, Fπ(8) = 71.76%, Fπ(10) = 96.30%, and Fπ(12) = 99.70%. The highest prob-

ability range always receives a weight of less than 10%. When the lowest probability range also

receives a weight of less than 10%, we interpolate the survey cdf linearly to obtain 10th, 50th, and

90th percentiles.

When the lowest probability range receives a weight of more than 10%, we fit a generalized

beta distribution with support [−5,18] to the known points on the Fπ following Engelberg, Manski,

and Williams (2009). Let Beta(t;a,b, l,r) denote the cdf of the generalized beta distribution with

shape parameters a and b and support [l,r]. We consider a support of [−5,18] covering the highest

and lowest survey probability ranges for all sub periods. Small variations in the choice of the

support do not affect the results displayed in Figure 1. We require that a > 1 and b > 1 to ensure

that the beta distribution is unimodal. If there are I known points ti on the cdf Fπ, we minimize:

mina>1,b>1

I

∑i=1

[Beta(ti;a,b,−5,18)−Fπ(ti)]2. (17)

Federal Reserve Bank of Philadephia (2013) lists 14 quarters when the survey should have asked

about GDP price index growth for the current year but instead asked about GDP price index growth

for the following year. Eleven of these quarters are fourth quarters. Due to this change in how the

survey was conducted, we drop all fourth quarter observations. We then use the 10th, 50th, and

90th percentiles of the fitted beta distribution. We report the difference between the 90th and

the 10th percentiles, the difference between the 50th and the 10th percentiles, and the difference

between the 90th and 50th percentiles, all smoothed over the past eight quarters.

Dropping all fourth quarter observations does not materially change our results, but it reduces

noise in our measure of survey inflation uncertainty. When we include all fourth quarter obser-

vations instead, the correlation between the Baa-Aaa log yield spread and the smoothed 90-10

7

inflation quantile spread is 38%, the correlation with the smoothed 50-10 inflation quantile spread

is 48%, and the correlation with the smoothed 90-50 inflation quantile spread is 22%.

C.2. Off-the-Run Spread

We use the Gurkaynak, Sack, and Wright (2007) off-the-run yield curves to price the cash flows

of the 10 year on-the-run Treasury bond. The corresponding yield serves as our off-the-run yield.

We use the monthly CRSP Treasury master file to obtain end-of-quarter yields and issue char-

acteristics for Treasury notes and bonds. We exclude all flower bonds and all bonds that are not

fully taxable. We use the most recently issued bond with an original maturity of 10 years as the

on-the-run bond. We obtain the on-the-run bond’s yield, issue date, maturity date, and coupon

from the CRSP Treasury master file.

We can replicate the on-the-run bond cash flows with a par bond and a zero coupon bond with

the same maturity. Consider an on-the-run bond at time t with face value 100, maturity date matt ,

and yield yon−the−runt . The yield yon−the−run

t is semi-annually compounded in percent per annum.

The on-the-run bond has semi-annual coupon payments of con−the−runt /2, where con−the−run

t is the

bond coupon rate in percent per annum. At maturity matt , the on-the-run bond provides a cash

flow of 100.

A zero-coupon bond with face value 100, maturity matt , and price Pzerot provides a cash flow

of 100 at matt and zero at all other times. A par-bond with the same maturity and face value and

semi-annually compounded percent per annum yield ypart provides semi-annual coupon payments

of ypart /2 and a cash flow of 100 at maturity. Hence, we can replicate the cash flows of the on-the-

run bond using a portfolio with weight con−the−runt

ypart

on the par bond and weight(

1− con−the−runt

ypart

)on

the zero coupon bond.

We obtain the price of the on-the-run cash flows discounted at the off-the-run yield curve by

8

pricing the replicating portfolio with the Gurkaynak, Sack, and Wright (2007) smoothed off-the-

run curves. Since Gurkaynak, Sack, and Wright (2007) provide par yields and zero coupon yields

with integer maturities, we interpolate linearly to obtain the off-the-run par yield ypart and the off-

the-run zero coupon bond price Pzerot with the same maturity as the on-the-run bond. The price of

the on-the-run cash flows discounted at the off-the-run yield curve is then given by:

Pcurvet =

con−the−runt

ypart

×100+

(1− con−the−run

t

ypart

)×Pzero

t . (18)

We use the YIELD function in Excel to compute the semi-annually compounded percent per

annum yield ycurvet for a bond with price Pcurve

t , coupon rate con−the−runt and maturity mt . The

off-the-run spread obtains as the difference between the curve yield and the on-the-run yield in

continuously compounded units:

off-the-runt = 200× log(1+ ycurvet /200)−200× log(1+ yon−the−run

t /200). (19)

C.3. Credit Loss Rates

The Moody’s Corporate Default Risk database provides default and recovery information for

Moody’s rated bond issuers. Bond recovery rates are based on the market value of defaulted debt

as a percentage of par one month after default. Defaulting issuers usually have multiple bonds

outstanding at default and we calculate each issuer’s recovery rate as the face-value weighted

average across bonds with recovery information. We only keep firms domiciled in the U.S. We

keep firms in the public utility and industrial categories, but we drop firms in the banking, finance,

insurance, other non-bank, real-estate finance, securities, sovereign, and thrift categories.

The default rate de fUS,t→t+n is the ratio of defaults during years t + 1 through t + n of firms

9

rated Baa in year t over the number of firms rated Baa in year t. To obtain the credit loss rate

lossUS,t→t+n, we multiply the number of defaults of firms that were rated Baa in year t and de-

faulted in year t + k with the issuer weighted loss given default. We then sum over years t + 1

through t +n and divide by the number of Baa rated firms in year t.

C.4. Israeli Corporate Bond Spreads

We construct an investment grade inflation-indexed Israeli corporate bond index from individ-

ual corporate bond issuances with five to eleven years to maturity. We download daily corporate

bond yields from Bloomberg for all available, non-convertible, inflation-indexed corporate bonds

issued by non-financial firms and with an initial maturity of at least 5 years. Bloomberg provides

yields on such bonds starting in June 2002.

We complement the Bloomberg data with proprietary data allowing us to extend our data series

back to March 2000. This additional data is consistent with Bloomberg data for overlapping time

periods and also provides spreads relative to matched government bond yields. While inflation-

indexed bond yields can take negative values, we exclude yields smaller than -2% and yields greater

than 90% because these are likely to be errors or outliers.

We focus on highly rated corporate bond issuances to ensure that the Israeli corporate bond

index is as comparable as possible to international investment grade corporate bond indexes. Most

Israeli companies are rated by national, rather than global, rating agencies. The major national

rating agencies are Midroog and S&P Maalot. The ratings scale comparison in Midroog (2009)

shows that a Midroog A3 rating corresponds approximately to B1 on the Moody’s global ratings

scale. S&P Maalot provides a similar comparison at

http://www.maalot.co.il/Content/Ratings/ratingScale.aspx showing that A on the S&P Maalot na-

tional ratings scale corresponds to BB to B on the global S&P ratings scale.

10

Bonds with a single A rating by one of the Israeli national rating agencies are generally re-

garded as easily tradable (Bank Hapoalim (2013)). Only very few Israeli corporate bonds achieve

a rating of AA/Aa or higher. We therefore consider bonds with a rating of at least A- by S&P

Maalot or at least A3 by Midroog.

We benchmark corporate bond yields against government bond yield indexes with the same

remaining time to maturity, rounded to integer values. If such a government bond yield index is

not available, we consider a yield index with a maturity differential of less than one year. The Bank

of Israel provides fixed maturity inflation-indexed government bond yield indexes for five through

eleven years to maturity at http://www.boi.org.il/en/DataAndStatistics/Pages/Series.aspx.

The corporate bond index includes corporate bonds with a remaining time to maturity between

five and eleven years. Our earliest corporate bond data is for a bond with eleven years, so including

bonds with eleven years to maturity maximizes our sample size. We drop bonds with less than five

years to maturity in order to maintain a stable average time to maturity throughout the sample. In

order to ensure that corporate bond spread movements are not driven by frequent entry and exit

of individual corporate bond issuances, we require that each corporate bond issuance has at least

eight quarterly consecutive observations. The index spread is an equally weighted average of the

constituent spreads.

Appendix Table B.XI shows details for the constituent bonds including entry and exit dates

from the index. We obtain a corporate bond index with an average maturity of 7.7 years. The

average bond index maturity varies between 6.2 and 10.9 years over our sample. The average

approximate duration is slightly at 6.5 years, where we approximate the duration assuming that the

bond sells at par.

11

D. Additional Empirical Results

Table B.I shows details of the corporate bond data.

Table B.II shows cross-country correlations of credit spreads, inflation volatility and the inflation-

stock correlation and the cross-correlation between inflation volatility and the inflation-stock cor-

relation.

Table B.III shows that the benchmark empirical results are remarkably consistent across coun-

tries.

Table B.IV shows that the benchmark empirical results hold up when controlling for market

leverage excluding cash, and when using smoothed inflation volatility and the smoothed inflation-

stock correlation. Table B.IV also shows that our benchmark results become even stronger when

we compute the U.S. credit spread as the difference in the Baa log yield and a duration-matched

log Treasury yield.

Table B.V shows that our benchmark results are robust to a variety of reasonable inflation

forecasting models. We construct measures of inflation volatility and the inflation-stock return

correlation using a rolling three year window of quarterly surprises. Our baseline inflation fore-

casting regression is similar to those employed by Campbell, Sunderam, and Viceira (2013) and by

Campbell and Shiller (1996). We regress quarterly inflation onto its own four lags and the lagged

three month T-bill rate.

A number of different models have been proposed in the literature. However, as noted by Stock

and Watson (2007), most popular inflation forecasting models cannot outperform consistently sim-

ple models that use only lagged inflation to forecast future inflation.

12

The forecasting relations are given by:

Baseline πt = a0 +a1πt−1 + ...+a4πt−4 +b1T billt−1 + εt

Baseline w/o T-bill πt = a0 +a1πt−1 + ...+a4πt−4 + εt

Baseline+Stock πt = a0 +a1πt−1 + ...+a4πt−4 +b1T billt−1 + c1ret−1 + εt

AR(AIC) ∆πt = a0 +a1∆πt−1 + ...+a4∆πt−4 + εt

AO πt =14 (πt−1 +πt−2 +πt−3 +πt−4)+ εt

PC−u ∆πt = a0 +a1∆πt−1 + ...+a4∆πt−4 +b1ut−1 + ...+b4ut−4 + εt

PC−∆u ∆πt = a0 +a1∆πt−1 + ...+a4∆πt−4 +b1∆ut−1 + ...+b4∆ut−4 + εt

PC−∆y ∆πt = a0 +a1∆πt−1 + ...+a4∆πt−4 +b1∆yt−1 + ...+b4∆yt−4 + εt .

We denote the quarterly change in inflation from time t−1 to t by ∆πt , unemployment by ut ,

the change in unemployment by ∆ut and real GDP growth by ∆yt . All our forecasting relations,

except for the AO forecast, also include seasonal dummies to account for seasonal variation in

inflation.

Column (2) removes the lagged T-bill from the set of forecasting variables and shows that re-

sults are unchanged. Column (3) adds lagged stock returns to the predictive variables as in Camp-

bell, Sunderam, and Viceira (2013), which leaves our results unchanged. Columns (4) through (8)

replace our baseline inflation forecasting relation with a range of standard forecasting models as de-

scribed in Stock and Watson (2007). These forecasts include an autoregression in inflation changes

(AR(AIC)), the Atkeson-Ohanian forecasting relation (AO), and backward looking Phillips curves

with the level of unemployment (PC-u), the change in unemployment (PC-∆u), and GDP growth

(PC-∆y).

Column (5) uses the extremely simple Atkeson and Ohanian (2001) model, which forecasts

inflation as the average inflation over the past four quarters. This model requires no estimation and

13

therefore it imposes minimal information requirements on agents. Atkeson and Ohanian (2001)

argued that since 1984 in the U.S. this extremely simple model outperformed Phillips curve-based

forecasts.

Columns (9) and (10) show that our benchmark results are robust to using Producer Price Index

(PPI) inflation instead of CPI inflation and to using a rolling estimate of our baseline inflation

forecasting model.

Table B.VI adds additional controls to the U.S. regression reported in Table VI in the main

text. We control for the percent of zero daily corporate bond returns from Datastream as in Chen,

Lesmond, and Wei (2007) and we use separate corporate bond log yield spreads for callable and

non-callable bonds.1 Figure B.6 shows the time series of the percent zero returns. Unfortunately,

these additional data series are only available starting in 1993.Q1. Due to the short sample period,

these regressions are subject to severe over-fitting, as illustrated by the R-squareds of over 90%,

and we regard these short sample results as less reliable than the results in Tables V and VI in the

main text. The percent of zero daily returns does not enter significantly into the regression.

A firm entirely financed with callable debt can call its debt at the nominal face value when

expected inflation and nominal interest rates fall, and it may therefore be less subject to the risk of

debt deflation. Inflation risk should therefore be more relevant for non-callable corporate bonds.

The last two columns of Table B.VI show that inflation volatility and the inflation-stock correlation

enter more positively for non-callable bonds than for callable bonds, consistent with this hypothe-

sis. If the relation between inflation risk and corporate bond spreads is weaker for callable bonds,

then using broad corporate bond indexes of both callable and non-callable bonds might only create

a bias against finding a relation between corporate bond spreads and inflation risk in Tables V and

VI in the main text.

Table B.VII runs our main regressions in Table V in changes. Denoting the change from quarter

14

t to t +n by ∆n(·)t→t+n, we show regressions:

∆nspreadi,t→t+n = λ0 +λ

σeq∆nσ

eqi,t→t+n +λ

σπ

∆nσπi,t→t+n +λ

ρπ

∆nρπi,t→t+n +Λ×Xi,t +ηi,t+n. (20)

The vector of control variables includes n-quarter real GDP growth, the sum of inflation shocks

over the past n quarters, the change in unemployment over the past n quarters, quarterly real GDP

growth, the contemporaneous quarterly inflation shock, and the contemporaneous quarterly real

stock return.

Inflation volatility and the inflation-stock correlation change slowly and short-term movements

may be measured with noise. It is therefore intuitive that the relation between changes in credit

spreads and changes in inflation volatility and changes in the inflation-stock correlation is strongest

and most statistically significant at three to five year horizons.

To better understand the contribution of the changing composition of the credit spread index,

we would ideally like to run similar regressions using credit returns. In Table B.XII Panel B we

find that U.S. nominal corporate bond excess returns are negatively related to changes in inflation

volatility and to changes in the inflation-stock correlation at a three year horizon. Table B.XII also

shows analogous regressions for inflation-indexed Israeli corporate bond returns, for which we do

not find a relation between corporate bond excess returns and changes in inflation risk, as expected.

Comparing empirical results for credit loss rates in Table VII and empirical results for default

rates in Supplementary Appendix Table B.VIII shows that the slope coefficients in Table VII are

about 45% smaller, positive, and strongly statistically significant. The relative magnitudes of re-

gression coefficients in Table VII and Supplementary Appendix Table B.VIII are broadly consistent

with a 40% recovery rate estimated by Altman (2006).

15

Tables B.IX and B.X show that the regressions in Table VII in the main text are robust to an

alternative measures of default rates and credit losses, extracted from Moody’s (2011). Our n-year

credit loss rate in Table VII counts all companies that were rated Baa at time t and that defaulted

at least once in years t +1 through t +n. The n-year credit loss rate in Table VII therefore includes

firms that were downgraded prior to defaulting. In contrast, the default rate in Table B.IX captures

the five year default rate of firms that were rated Baa immediately prior to defaulting and it also

includes non-U.S. companies rated by Moody’s.

Table B.X predicts global Baa credit losses from Moody’s (2011) instead of default rates again

using inflation volatility, the inflation-stock correlation and control variables. Global Baa credit

losses are constructed exactly analogously to the global Baa default rates in Table B.IX. Unfortu-

nately, global Baa credit losses are only available starting in 1981. Over this shorter sample period,

the inflation-stock correlation no longer predicts credit losses significantly, but inflation volatility

still does. Hence, these results again confirm our finding in Table VII in the main text that infla-

tion volatility affects credit spreads largely through its impact on expected defaults, whereas the

inflation-stock correlation also acts through the default premium in corporate bond spreads.

Supplementary Appendix Table B.XII shows additional evidence for the findings in Section

III.E in the main paper using price index data instead of yield data. When debt is nominal, such

as in the U.S., log corporate bond returns in excess of log government bond returns should be neg-

atively related to changes in inflation volatility and to changes in the inflation-stock correlation,

since bond prices are inversely related to yields. On the other hand, in a financial markets envi-

ronment where liabilities are conventionally inflation-indexed, such as in Israel, corporate bond

excess returns should not be related to changes in inflation risk.

Supplementary Appendix Table B.XII shows empirical evidence consistent with this hypothe-

sis, using Israeli inflation-indexed corporate bond log excess returns and U.S. nominal corporate

16

bond log excess returns over identical time periods 1989.Q3 to 2009.Q4. We find that three-

year U.S. nominal corporate bond excess returns are negatively related to both contemporaneous

changes in inflation volatility and to contemporaneous changes in the inflation-stock correlation.

In contrast, the relations between Israeli inflation-indexed corporate bond excess returns and

changes in either inflation risk variable are indistinguishable from zero. We interpret the empirical

results in Table B.XII as supportive of the hypothesis that the nominal as opposed to indexed nature

of corporate bonds in the U.S. is responsible for the main empirical finding. Since real risk should

be priced into both inflation and nominal corporate bonds in excess of government bonds, this

placebo test helps us alleviate concerns that inflation volatility or the inflation-stock correlation

might proxy for real risk rather than nominal risk.

Denoting the change from quarter t to t +n by ∆n(·)t→t+n, we estimate the following relation

for country i ∈ IL,US:

retcorpi,t→t+n− retgov

i,t→t+n = λ0i +λ

σπ

i ∆nσπi,t→t+n +λ

ρπ

i ∆nρπi,t→t+n

+λσeq

i ∆nσeqi,t→t+n +λ

govi retgov

i,t→t+n +λeqi reteq

i,t→t+n +ηi,t+n.

We estimate this relation using data on Israeli inflation-indexed corporate bond excess returns

and U.S. nominal corporate bond excess returns. We run two separate regressions for the two

countries. The slope coefficients with respect to contemporaneous government bond and equity

returns λgovi and λ

eqi can be interpreted as empirical estimates of the corporate bond hedge ratios

(Merton (1974), Schaefer and Strebulaev (2008)). Unfortunately, the short Israel sample does not

allow us to include a large number of controls without running the risk of overfitting.

For Israel, we would expect to find zero coefficients λσπ

IL = 0 and λρπ

IL = 0, so including only

a limited number of controls is conservative and biases us against finding zero coefficients. For

17

the U.S. we would expect to find negative coefficients λσπ

US < 0 and λρπ

US < 0. Moreover, the U.S.

coefficients should be approximately proportional to the slope coefficients estimated in Table V in

the main text. The proportionality factor should be approximately the bond duration.

Our equity volatility variables require a three-year lag, so our Israel regressions start in 1989.Q2.2

Unfortunately, Israel nominal T-bill data is only available for an even more limited sample size and

our baseline measure of inflation surprises requires a short-term nominal T-bill. For the purpose

of the analysis in Table B.XII Panels A and B, we therefore construct inflation surprises as the

residual of regressing quarterly inflation onto its own four lags and seasonal dummies in order to

preserve our sample size. The results in Table B.V column (2) show that our benchmark results in

the main text are unchanged if we use this “Baseline w/o T-bill” inflation forecasting model.

Table B.XII Panel A shows that the slope coefficients λσπ

IL and λρ

IL are indistinguishable from

zero either for the full sample period 1989.Q3 to 2009.Q4 or for the pre-crisis sub-sample 1989.Q3

to 2007.Q4. We cannot reject the null hypothesis that Israeli inflation-indexed corporate bond

excess returns are unrelated to changes in inflation risk at one, four, and twelve quarter horizons.

Columns (4) through (6) report results for the sub-period 1989.Q2 to 2007.Q4. This sub-sample

excludes the financial crisis, which was a period of especially sharp movements in financial markets

and might therefore disproportionately affect the empirical results. This shorter sub-period also

focuses on those years when inflation-indexing was most dominant in the Israel economy and

it therefore provides the most relevant laboratory for our placebo test. Indeed, we find that for

this earlier sub-period the estimates of λσπ

and λρ are even closer to zero and that they are more

precisely estimated.

In contrast, Panel B shows that both λσπ

US and λρ

US are negative and statistically significant at

the twelve quarter horizon. We would expect the twelve quarter horizon to be the most relevant, if

inflation risk moves slowly over time and if our measures of inflation risk contain short-term noise.

18

The first six columns in Panel B use the same sample periods as Panel A to facilitate comparison

between U.S. and Israel results. Columns (7) through (9) show results for the full U.S. sample

1969.Q4 to 2009.Q4, which are more precisely estimated.

Figure B.3 shows the close comovement between the bond-stock correlation and the breakeven-

stock correlation in the U.S. and in the U.K. Figure B.4 shows the inverse relationship between

quarterly inflation shocks and credit spreads in the U.S.

Figure B.7 shows the one- through five-year credit loss rates used in Table VII in the main text.

E. Computing Model Moments

Our simulations require the computation of asset prices along a three-dimensional grid for w,

the leverage ratio of seasoned firms, and the inflation risk regime. We compute asset prices along

a dense grid of size 70×35×2. This grid covers seasoned leverage ratios from 0.1 to 1.9 and the

full solution range for w. In our simulations, we compute asset prices by interpolating linearly over

this grid.

19

E.1. Book Leverage and Investment to Capital

We obtain new book leverage by discounting the nominal face value of debt by the long-term

nominal risk free rate:

Lbookt = Lt exp(2πt)qgov,10

t . (21)

E.2. Idiosyncratic Equity Volatility

In Table II in the main text we report the idiosyncratic volatility of ten year equity returns

conditional on not defaulting. The time t real cash flow to equity holders of firm i in cohort t−2

conditional on not defaulting is:

Kyt−1 RK

t−1RKt︸︷︷︸

Return on Capital

exp(

aid,it

)︸︷︷︸

Idiosyncratic Shock

− exp(a∗t )︸︷︷︸Debt Payment

. (22)

The idiosyncratic volatility of log real stock returns conditional on not defaulting is therefore given

by:

σFirmt =

1√10

Var[

log(

exp(

aid,it

)− exp(a∗t )

)∣∣∣aid,it ≥ a∗t ,a

∗t

]. (23)

E.3. Dividend-Price Ratio, Equity Volatility, and Inflation-Stock Correlation

In Table III in the main text we show regressions that include the model dividend-price ratio,

model equity volatility and the model inflation-stock correlation. Since the left-hand side of our

regression has seasoned credit spreads, we focus on the moments of seasoned equity returns on the

right-hand side. The real equity dividend at time t +1 averaged over all cohort t−1 firms is given

20

by:

Kyt RK

t RKt+1(1− exp

(a∗t+1

)(1−H

(a∗t+1

))−Ω

(a∗t+1

)). (24)

The time t price of seasoned equity is therefore equal to:

Sseast = exp(−(β+ γµ))×Ky

t RKt

×Et

[(Ct+1

Ct

)−γ

RKt+1(1− exp

(a∗t+1

)(1−H

(a∗t+1

))−Ω

(a∗t+1

))]. (25)

Log seasoned real equity returns from time t to time t +1 are then equal to:

req,seast+1 = rK

t+1 + log(1− exp

(a∗t+1

)(1−H

(a∗t+1

))−Ω

(a∗t+1

))−(sseast − ky

t). (26)

where sseast is the log seasoned equity price at time t. We compute the seasoned dividend-price ratio

as the expected log return on seasoned equity:

DPseast = Et

[req,seast+1

]. (27)

Seasoned equity volatility is the backward-looking annualized standard deviation of log real

seasoned stock returns conditional on the inflation risk regime:

σeq,seast =

√Var

[rseas,eqt

∣∣σπt ,ρ

πt , wt−1,Lold

t−1]

√5

. (28)

The inflation-stock correlation is the backward-looking correlation between shocks to log in-

flation expectations and log seasoned real stock returns conditional on the inflation risk regime:

ρeq,πt = Corr

[rseas,eqt ,επ

t∣∣σπ

t ,ρπt , wt−1,Lold

t−1

]. (29)

21

E.4. Decision to Issue Corporate Inflation-Indexed Bonds

Consider a nominal-only equilibrium and the problem of a firm that decides whether or not

to deviate by issuing corporate inflation-indexed bonds. We can use our calibrated model to un-

derstand whether an infinitely small firm would find it profitable to deviate from a nominal-only

equilibrium for a reasonable liquidity premium. A firm issuing corporate inflation protected secu-

rities (CIPS) faces an equilibrium liquidity premium. We model this liquidity by assuming that the

tax and other benefits on CIPS are less than those on nominal corporate bonds χCIPS < χ.

The survival threshold for a deviating firm that decides to issue CIPS instead of nominal bonds

does not depend on surprise inflation and it chooses optimal leverage according to a first-order

condition analogous to (16). The deviating firm takes the stochastic discount factor Mt,t+2 and the

aggregate return on capital rKt+1, rK

t+2 as given. Equity investors are unwilling to invest into the

deviating firm if and only if the expected discounted return on capital, adjusted for default costs

and benefits of debt, is less than that for the aggregate firm:

Et

[Mt+2RK

t+1RKt+2FCIPS

t+2

]< Et

[Mt+2RK

t+1RKt+2Ft+2

]. (30)

where FCIPSt+2 is defined analogously to Ft+2,. When (30) holds, no firm decides to issue

inflation-indexed debt in equilibrium as long as ten year CIPS have a log yield liquidity premium

of 29 bps.

[TABLES B.I THROUGH B.XII ABOUT HERE]

[FIGURES B.1 THROUGH B.8 ABOUT HERE]

22

References

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Economic Statistics 27, 30–41.

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1961 to the present, Journal of Monetary Economics 54, 2291–2304.

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24

Notes

1Callable corporate bond yields are an equal-weighted average of corporate bond issuances with

some callability feature, while non-callable bonds are an equal-weighted average of bond issuances

with no callability feature from Datastream. We obtain callable and non-callable corporate bond

spreads by subtracting the ten-year U.S. Treasury yield, which closely matches the time-varying

average duration of callable and non-callable corporate bond issuances.

2 We obtain price indexes of Israel government and corporate inflation-indexed bonds from the

Tel Aviv Stock Exchange. We use the Tel Aviv CPI Linked Corporate Bond index and Tel Aviv

CPI Linked Government Bond index available from Bloomberg to calculated log excess returns.

These are price indexes as opposed to total return indexes, so we can only capture bond returns

due to price appreciation but not due to interest payments. We measure stock returns by the TA

200 index. We measure Israeli inflation with the CPI price index.

25

Corp. Bond Corp. Corp. Govt. Govt.Country Data Source Maturity Duration Maturity Duration SampleAustralia Economist; Telstra 10 6.9 10 7.3 1983.Q3 - 2010.Q4Canada Bank of Canada; Datastream 20 10.1 15 9.6 1969.Q4 - 2010.Q4Germany Bundesbank 6 5.1 6 5.2 1969.Q4 - 2010.Q4Japan Nikkei Corp. Bond Index 10 8.2 10 8.3 1973.Q1 - 2010.Q4U.K. Financial Times; Economist 15 8.5 10 7.2 1969.Q4 - 2010.Q4U.S. Moody's Baa, Aaa 25 10.7 NA NA 1960.Q1 - 2010.Q4

Table B.I: Corporate Bond Spread Data Sources

Corporate bond maturities are based on data descriptions provided by the listed data sources. Governmentbond maturities are from Global Financial Data. Time-varying corporate and government bond durationsare estimated assuming that bonds sell at par following Campbell, Lo, and MacKinlay (1997). This tablereports durations averaged over the sample period.

Australia Canada Germany Japan U.K. U.S.Australia 1.00Canada 0.66 1.00Germany 0.56 0.70 1.00Japan -0.23 0.02 0.03 1.00U.K. 0.72 0.71 0.54 0.10 1.00U.S. 0.71 0.60 0.41 -0.17 0.54 1.00

Panel B: Inflation volatilityAustralia Canada Germany Japan U.K. U.S.

Australia 1.00Canada 0.29 1.00Germany 0.17 0.36 1.00Japan 0.11 0.10 0.32 1.00U.K. 0.54 0.25 0.25 0.52 1.00U.S. 0.25 0.50 0.08 -0.05 0.45 1.00

Panel C: Inflation-stock correlationAustralia Canada Germany Japan U.K. U.S.

Australia 1.00Canada 0.08 1.00Germany -0.29 0.37 1.00Japan -0.10 0.26 0.15 1.00U.K. -0.06 0.30 0.34 0.16 1.00U.S. 0.33 0.38 0.46 0.24 0.14 1.00

Panel D: Inflation volatility vs. Inflation-stock correlationInflation vol.\Infl.-stock corr. Australia Canada Germany Japan U.K. U.S.Australia -0.22 -0.23 0.06 -0.26 -0.11 -0.20Canada -0.31 -0.10 0.43 0.06 0.13 -0.12Germany -0.16 0.07 -0.07 -0.13 -0.18 -0.21Japan -0.27 -0.28 -0.13 -0.27 0.33 -0.25U.K. 0.03 -0.17 -0.12 -0.19 0.35 -0.17U.S. 0.20 0.18 0.15 0.05 0.30 0.17

Panel A: Corporate log yield spread

Table B.II: International Correlations (1969.Q4-2010.Q4)

This table reports correlations among credit spreads, inflation volatility, and inflation-stock correlation across countries. Panel Dreports correlations between inflation volatility (along the vertical axis) and inflation-stock correlation (along the horizontal axis).Japan credit spreads start in 1973.Q1. Australia data starts in 1983.Q3.

(1) (2) (3) (4) (5) (6)AUS CAN GER JPN UKI USA

Inflation riskInflation volatility (Ann.) 26.13 63.17** 1.88 10.93 -1.06 31.36**

(16.92) (14.94) (11.44) (11.39) (37.19) (7.16)Inflation-stock correlation -20.67 57.49** 48.93* 36.83** 141.62** 7.81

(37.25) (10.01) (22.72) (7.66) (45.48) (11.80)Real uncertainty and other control variables

Equity volatility (Ann.) -0.59 3.53** 0.21 0.54 1.33 0.10(0.77) (0.63) (1.26) (0.66) (3.08) (0.51)

Dividend-price ratio (Ann.) 45.20** 10.44* 9.67 -0.25 6.24 11.72**(15.81) (4.73) (5.91) (7.71) (9.83) (2.63)

Business cycle and inflation shock variables (Logs)3-Year inflation shock 13.40** -2.70 2.04 3.49 -7.03 -1.94

(3.83) (2.31) (3.77) (2.22) (6.19) (2.41)3-Year real stock return 0.50* -0.21 -0.13 0.05 -1.24* -0.10

(0.21) (0.18) (0.24) (0.07) (0.61) (0.21)3-Year GDP growth -0.60 0.79 -8.41** 0.39 7.04 1.72

(3.24) (1.06) (1.51) (0.86) (4.04) (1.81)3-Year change unemployment 9.40 -5.26 -19.18** 12.12 17.07** 4.18

(6.46) (3.05) (5.46) (6.60) (5.27) (4.02)Quarterly inflation shock 3.64 -4.18 -25.57** -0.85 -4.82 -15.69**

(7.30) (2.66) (8.03) (4.39) (9.16) (3.70)Quarterly real stock return -0.84 -0.25 -0.93* -0.11 -0.04 -0.00

(0.48) (0.30) (0.40) (0.21) (0.60) (0.39)Quarterly GDP growth -7.28 -13.31* -9.98* -2.87 -25.56 -12.18*

(4.49) (5.60) (3.90) (2.00) (14.43) (4.89)

R2 0.45 0.69 0.66 0.39 0.43 0.64Period 83.Q3-10.Q4 Full Full 73.Q1 - 10.Q4 Full Full

Table B.III: Individual Country Credit Spreads and Inflation Risk (1969.Q4-2010.Q4)

We report individual country regressions of corporate bond log yield spreads onto inflation volatility, the inflation-stockcorrelation, and control variables. The regression setup is identical to Table V, except for not being pooled. Newey-Weststandard errors with 16 lags in parentheses. Japan data starts in 1973.Q1. Australia data starts in 1983.Q3. Variables areconstructed as described in Table IV. * and ** denote significance at the 5% and 1% levels, respectively.

(1) (2) (3)

Additional Control Mkt. Leverage Excl. Cash Smoothed Infl. Risk Proxies U.S. Baa-Treasury Spread

Inflation riskInflation volatility (Ann.) 21.10** 21.32** 26.05**

(4.56) (7.99) (8.10)Inflation-stock correlation 26.87** 69.40** 49.08**

(5.86) (17.88) (10.78)Real uncertainty and other control variables

Equity volatility (Ann.) 0.18 0.78 0.94(0.80) (0.87) (0.92)

Dividend-price ratio (Ann.) 24.80** 9.30 4.52(7.08) (5.01) (4.66)

Idiosyncratic volatility (Ann.) 0.77(0.58)

Leverage excl. cash -0.44(0.40)

Bond volatility (Ann.) 46.39**(14.20)

Bond-stock correlation 75.93**(21.62)

Business cycle and inflation shock variables (Logs) 3-Year inflation shock -2.93 -2.86 -0.90

(1.51) (1.54) (1.84) 3-Year real stock return 0.15 0.01 -0.19

(0.09) (0.09) (0.11) 3-Year GDP growth 0.07 -0.57 -1.19

(1.76) (1.06) (0.69) 3-Year change unemployment 3.92 0.08 -2.34

(2.55) (2.42) (3.35)Quarterly inflation shock -6.01** -5.74* -6.62

(2.15) (2.45) (4.05)Quarterly real stock return -0.57 -0.34 -0.39

(0.31) (0.31) (0.39)Quarterly GDP growth -11.64** -12.39** -10.98*

(2.60) (3.63) (4.68)

Residual R2 0.54 0.32 0.41Period Full Full Full

Table B.IV: Additional Robustness Controls (1969.Q4-2010.Q4)

This table reports additional robustness checks for the benchmark results in Table V in the main text. We report pooled regressionsexactly as in Table V. Column (1) controls for equal-weighted market leverage, excluding cash. Column (2) reports regression resultsusing smoothed inflation volatility and the smoothed inflation-stock correlation instead of the non-smoothed proxies. We use an HPfilter with smoothing parameter 500. Column (3) illustrates that if we use the U.S. Baa over government log yield spread instead of theU.S. Baa over Aaa log yield spread, our benchmark results become stronger.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Inflation Surprise Measure Baseline Baseline w/o T-bill Baseline+Stock AR(AIC) AO PC-u PC-Δu PC-Δy PPI Infl. RollingInflation risk

Inflation volatility (Ann.) 24.61** 23.60** 23.90** 17.19** 12.30** 16.23* 17.38* 19.11** 15.70** 18.33**(6.97) (7.73) (6.71) (6.05) (4.13) (7.51) (7.13) (5.56) (2.52) (5.92)

Inflation-stock correlation 42.37** 42.68** 42.94** 43.98** 38.03** 40.47** 40.67** 40.87** 24.42* 37.26**(10.22) (10.22) (10.01) (11.05) (11.04) (10.11) (10.78) (11.02) (9.56) (9.40)

Real uncertainty and other control variablesEquity volatility (Ann.) 0.86 1.00 0.90 0.91 0.80 0.94 0.87 0.78 0.74 0.71

(0.88) (0.86) (0.87) (0.88) (0.86) (0.89) (0.89) (0.89) (0.84) (0.86)Dividend-price ratio (Ann. 8.41 9.73* 8.52 7.61 7.71 8.13* 7.52 7.65 11.07** 8.07

(4.50) (4.87) (4.49) (3.89) (4.12) (3.98) (3.93) (3.91) (3.99) (4.54)Business cycle and inflation shock variables (Logs)

3-Year inflation shock -1.69 -2.65 -1.50 -0.05 0.40 -1.13 0.22 0.09 -0.58 -0.63(1.88) (2.45) (1.80) (2.12) (2.27) (2.76) (2.18) (1.98) (0.68) (1.67)

3-Year real stock return -0.19 -0.18 -0.18 -0.19 -0.20 -0.20* -0.19 -0.18 -0.10 -0.20(0.11) (0.10) (0.11) (0.10) (0.10) (0.09) (0.10) (0.10) (0.08) (0.11)

3-Year GDP growth -1.66 -1.25 -1.68 -1.80* -1.98 -2.19* -2.24* -2.03* -0.93 -1.88(0.91) (0.76) (0.93) (0.88) (1.00) (1.01) (0.96) (0.92) (0.55) (1.09)

3-Year change unemploym -3.72 -3.31 -3.69 -2.99 -2.62 -3.39 -3.50 -3.31 -1.04 -3.42(3.72) (3.61) (3.76) (3.88) (4.06) (3.44) (3.25) (3.81) (2.34) (4.01)

Quarterly inflation shock -4.51 -5.77 -4.54 -5.57 -5.29 -4.19 -4.55 -4.72 -2.84** -4.01(3.35) (3.39) (3.43) (3.32) (3.20) (2.99) (3.13) (2.79) (0.93) (3.46)

Quarterly real stock return -0.48 -0.47 -0.48 -0.49 -0.48 -0.49 -0.49 -0.49 -0.44 -0.46(0.43) (0.41) (0.43) (0.42) (0.43) (0.43) (0.44) (0.42) (0.43) (0.44)

Quarterly GDP growth -10.44* -10.93* -10.36* -10.37* -10.15* -10.75* -10.53* -10.36* -10.08* -10.04*(4.40) (4.42) (4.38) (4.66) (4.74) (4.58) (4.71) (4.57) (4.00) (4.48)

Residual R2 0.30 0.30 0.30 0.30 0.29 0.29 0.29 0.29 0.34 0.28Period Full Full Full Full Full Full Full Full Full Full

Table B.V: Robustness to Inflation Model and Inflation Measure (1969.Q4-2010.Q4)

We check that benchmark results in Table V column (5) are robust to various standard inflation forecasting models and to using PPI inflation insteadof CPI inflation. Baseline denotes our baseline inflation forecasting model, which regresses quarterly log inflation onto its own four lags, the laggedlog T-bill, and seasonal dummies. Column (2) excludes the lagged T-bill. Column (3) includes the lagged real stock return as an additional predictorvariable similarly to the inflation forecasting model in Campbell, Sunderam, and Viceira (2012). Columns (4) through (8) use standard inflationforecasting models as listed in Stock and Watson (2007). AO refers to the Atkeson and Ohanian (2001) inflation forecasting model, which forecastsinflation with average inflation over the past four quarters. We describe the different inflation forecasting models in detail in the SupplementaryAppendix D. Column (9) uses PPI inflation instead of CPI inflation and our benchmark inflation forecasting model. Column (10) estimates CPIinflation surprises from a rolling regression of our benchmark inflation forecasting model. We report Driscoll and Kraay (1998) standard errors with

16 lags. The residual R2 reflects explanatory power in excess of fixed effects. * and ** denote significance at the 5% and 1% levels, respectively.

(10) (11) (12)Inflation risk

Inflation volatility (Ann.) 49.38** 70.89** 46.55**(5.76) (12.32) (14.26)

Inflation-stock correlation -25.01** -35.53* -47.51**(6.42) (15.03) (13.55)

Real uncertainty and other control variablesIdiosyncratic volatility (Ann.) 1.97** 4.93** 4.24**

(0.72) (1.35) (1.41)Dividend-price ratio (Ann.) 27.59* 0.25 -1.71

(12.59) (20.38) (19.03)Liquidity variables

Percent zero returns -2.17*(1.03)

Business cycle and inflation shock variables (Logs)3-Year inflation shock -11.97** -16.89* -18.93**

(3.82) (6.53) (6.76)3-Year real stock return -0.81** -1.59** -1.47**

(0.10) (0.19) (0.18)3-Year GDP growth 2.66 -0.54 4.68

(3.05) (6.57) (7.05)3-Year change unemployment -10.70** -8.92 0.36

(3.89) (9.80) (8.34)Quarterly inflation shock -0.31 9.15 4.09

(1.93) (5.28) (3.34)Quarterly real stock return -0.02 -0.18 -0.59

(0.25) (0.45) (0.40)Quarterly GDP growth -8.20* -25.01** -33.76**

(3.92) (6.28) (6.47)

Residual R2 0.90 0.94 0.91Period 93.Q1-10.Q4 93.Q1-10.Q4 93.Q1-10.Q4Callability All Non-call. Callable

Table B.VI: Additional U.S. Credit Spread Controls (1993.Q1-2010.Q4)This table adds additional controls to the regression reported in Table VI in the main text for amuch shorter time period. We use the percent of zero daily corporate bond returns fromDatastream following Chen, Lesmond, and Wei (2007) as a liquidity control. Callable corporatebond yields are an equal-weighted average of corporate bond issuances with some callabilityfeature, while non-callable bonds are an equal-weighted average of bond issuances with nocallability feature from Datastream. We obtain callable and non-callable corporate bond spreadsby subtracting the ten-year U.S. Treasury yield, which closely matches the time-varying averageduration of callable and non-callable corporate bond issuances. We report Newey-West standarderrors with 16 lags in parentheses. * and ** denote significance at the 5% and 1% levels,respectively.

(1) (2) (3) (4) (5) (6) (7) (8)Horizon n (in quarters) 1 4 12 20 20 20 20 20Change in Inflation Risk

Δn Inflation Volatility (% Ann.) 0.15 0.15 0.20* 0.22** 0.26** 0.29**

(0.09) (0.09) (0.09) (0.06) (0.07) (0.07)Δn Inflation-Stock Correlation 0.21** 0.21** 0.33** 0.39** 0.37*

(0.08) (0.08) (0.12) (0.08) (0.15)Change in real uncertainty and dividend price ratio

Δn Equity Volatility (% Ann.) 0.01 0.02* 0.02** 0.01* 0.02**

(0.01) (0.01) (0.01) (0.01) (0.01)Δn Dividend-price ratio (Ann.) 0.32** 0.45** 0.33* 0.34** 0.34*


n-Quarter inflation shock -0.04 -0.05 -0.39** -0.20** -0.25** -0.26** -0.34**(0.04) (0.03) (0.09) (0.07) (0.08) (0.09) (0.10)

n-Quarter real stock return 0.00 0.00 0.01 -0.02** -0.02 -0.01 0.01(0.00) (0.00) (0.01) (0.01) (0.01) (0.01) (0.01)

n-Quarter GDP growth 0.01 -0.01 0.00 -0.07 -0.03 0.01 -0.08(0.02) (0.01) (0.05) (0.06) (0.05) (0.04) (0.04)

n-Quarter change unemploymen 0.02 0.02 0.06** -0.01 -0.00 0.03 0.03(0.02) (0.02) (0.02) (0.03) (0.02) (0.02) (0.02)

Quarterly inflation shock -0.06 -0.09* -0.08* -0.06 -0.07 -0.05 -0.06 -0.06(0.04) (0.04) (0.03) (0.04) (0.04) (0.04) (0.05) (0.03)

Quarterly real stock return 0.00 -0.00 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01(0.00) (0.00) (0.00) (0.00) (0.01) (0.01) (0.01) (0.00)

Quarterly GDP growth -0.01 -0.07* -0.13** -0.11 -0.16 -0.17 -0.15 -0.13(0.02) (0.03) (0.04) (0.06) (0.10) (0.10) (0.08) (0.07)

Residual R2 0.12 0.30 0.36 0.36 0.15 0.20 0.24 0.29Period Full Full Full Full Full Full Full Full

Table B.VII: Changes in in Credit Spreads (1969.Q4-2010.Q4)This table checks that the benchmark regressions in Table V are robust to an estimation in changes. We report quarterly pooledregressions of changes in corporate log yield spreads against contemporaneous changes in inflation volatility, changes in the inflationstock correlation, and control variables. We report Driscoll and Kraay (1998) standard errors accounting for cross-country correlation

and 16 lags. All regressions contain country fixed effects. The residual R2 reflects explanatory power in excess of fixed effects. Japandata starts in 1973.Q1. Australia data starts in 1983.Q3. * and ** denote significance at the 5% and 1% levels, respectively.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Horizon n (Years) 1 2 3 4 5 1 2 3 4 5Inflation risk

Inflation volatility (Ann.) 4.33 15.98 27.36** 25.32** 31.08** 0.07 -1.23 15.92* 15.19* 23.76(9.16) (10.78) (4.31) (5.64) (7.40) (8.69) (9.86) (6.33) (6.13) (12.37)

Inflation-stock correlation 7.55 16.26 34.30** 31.21** 32.19** -5.69 2.17 21.44* 16.88* 18.91*(12.59) (8.24) (9.20) (6.65) (9.08) (10.14) (8.13) (8.68) (7.54) (8.45)

Real uncertainty and other control variablesIdiosyncratic volatility (Ann.) 0.29 0.97* 1.51** 1.65** 1.19* -0.60 0.34 0.86 0.43 0.06

(0.78) (0.42) (0.38) (0.37) (0.55) (1.96) (0.66) (0.42) (0.48) (0.56)Dividend-price ratio (Ann.) -0.78 -1.71 -1.00 2.98 0.87 -20.21 -12.18 -10.57 -11.03* -11.95

(2.50) (3.45) (1.91) (1.97) (1.87) (26.96) (12.89) (6.56) (4.11) (5.99)GDP vol. 29.21 38.48* 23.29* 17.46** 10.96

(18.09) (14.75) (9.11) (5.09) (9.64)Equity volatility (Ann.) 2.08 1.39 0.73 0.33 -0.04

(1.16) (0.89) (0.51) (0.60) (0.97)Leverage -0.60 -0.61 -0.22 1.18* 1.21

(3.20) (1.79) (0.93) (0.46) (1.12)Bond volatility (Ann.) 31.41 6.63 15.53* 32.06** 35.23*

(43.29) (16.88) (6.43) (10.01) (15.71)Bond-stock correlation -38.98 -2.33 -9.06 -7.22 -8.69


3-Year inflation shock -1.84 -1.04 0.78 0.29 -0.65 -3.58 -1.87 -0.27 -1.99* -2.99(1.26) (0.89) (1.01) (0.76) (1.28) (3.25) (1.67) (1.03) (0.95) (1.62)

3-Year real stock return -0.16 0.17 0.33* 0.40** 0.45** -0.19 0.20 0.30** 0.38* 0.40*(0.21) (0.13) (0.12) (0.12) (0.16) (0.20) (0.14) (0.09) (0.14) (0.18)

3-Year GDP growth 5.68* 5.52* 5.40** 5.35** 3.82* 3.55 1.10 3.30 3.16** 2.92(2.51) (2.31) (1.17) (0.98) (1.50) (3.11) (3.57) (2.96) (0.77) (2.25)

3-Year change unemployment 5.31 10.09* 10.25** 9.60** 5.65** -4.04 -3.37 2.71 1.67 0.96(5.61) (4.64) (2.45) (1.60) (2.03) (7.44) (8.21) (6.87) (2.18) (3.28)

Quarterly inflation shock -6.35 2.46 -0.82 -5.00 2.70 4.16 4.97 2.78 -1.57 6.20(11.73) (11.00) (6.66) (5.73) (6.69) (10.83) (9.73) (5.45) (5.18) (8.91)

Quarterly real stock return 1.63** 1.13 1.05* 1.03** 0.76* 0.70 0.62 0.62 0.56 0.31(0.50) (0.76) (0.47) (0.29) (0.33) (0.91) (0.83) (0.40) (0.33) (0.44)

Quarterly GDP growth -1.94 0.18 -2.34 -0.74 -3.18 -13.01 -5.47 -6.24 -3.44 -5.47(4.68) (4.18) (2.77) (3.85) (3.49) (10.21) (7.35) (3.68) (3.61) (4.59)

R2 0.26 0.38 0.70 0.74 0.63 0.37 0.51 0.80 0.83 0.72

Table B.VIII: Predicting U.S. Baa Default Rates (1969-2010)We regress annual data on annualized issuer-weighted corporate default rates of Baa-rated U.S. issuers in the industrial andpublic utility sectors onto lagged end-of-year inflation volatility, the inflation-stock correlation, and control variables. The k-year default rate in year t includes all defaults of firms with a senior long-term Baa rating in year t and at least one defaultduring years t+1 through t+k. Our data source is the Moody's default risk database. We report Newey-West standard errorswith 6 lags. Variables are constructed as described in Table IV. * and ** denote significance at the 5% and 1% levels,respectively.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)Horizon (Years) 1 2 3 4 5 5 5 5 5 5 5Inflation risk

Inflation volatility (Ann.) 10.32 25.50* 30.45** 25.29** 19.95** 8.99 10.47* 16.11** 16.71**(8.35) (11.42) (6.58) (4.52) (4.23) (4.95) (5.04) (3.47) (5.24)

Inflation-stock correlation 9.86 19.80** 15.45* 12.66** 8.09 6.42 4.98 4.21(11.77) (5.82) (6.65) (3.19) (4.39) (5.06) (3.76) (5.83)

Real uncertainty and other control variablesIdiosyncratic volatility (Ann.) 0.37 0.82* 0.89* 0.76** 0.43** 0.31 0.26* 0.66*

(0.79) (0.34) (0.32) (0.16) (0.13) (0.15) (0.12) (0.29)Dividend-price ratio (Ann.) -1.29 -4.71 -4.52** -2.90* -2.58 1.28 -6.29** 1.46

(2.13) (2.78) (1.26) (1.18) (1.61) (2.05) (1.92) (3.92)GDP vol. 11.68**


(0.37)Leverage -1.14

(0.65)Bond volatility (Ann.) 0.64

(5.68)Bond-stock correlation -1.30


3-Year inflation shock -2.20 -1.51 -1.49 -0.61 -0.23 0.27 -0.17 -0.02 0.10 -0.53 0.31(1.47) (0.90) (0.73) (0.62) (0.49) (0.61) (0.48) (0.49) (0.68) (0.54) (0.46)

3-Year real stock return -0.11 0.15 0.14 0.18* 0.19* 0.12 0.15 0.18* 0.11 0.19* 0.15(0.17) (0.10) (0.11) (0.08) (0.08) (0.08) (0.07) (0.07) (0.08) (0.07) (0.09)

3-Year GDP growth 3.67 1.14 0.98 1.67 1.37 2.12 2.06 2.14 1.92 -0.15 2.92**(2.36) (2.22) (1.44) (1.10) (0.97) (1.55) (1.36) (1.36) (1.53) (0.96) (0.93)

3-Year change unemployment 1.73 1.50 -0.05 1.05 0.63 2.20 1.50 2.09 1.76 -3.35 3.35*(6.11) (3.63) (2.42) (1.52) (1.30) (2.36) (2.02) (2.18) (2.25) (1.82) (1.58)

Quarterly inflation shock -5.87 10.44 6.37 0.98 -2.02 -11.07* -8.40 -7.79 -10.75* -1.26 -1.03(9.38) (11.34) (5.03) (4.39) (4.67) (4.23) (4.36) (4.15) (4.22) (3.97) (4.45)

Quarterly real stock return 0.71 0.22 0.41* 0.63** 0.45** 0.33** 0.40** 0.41** 0.44** 0.35 0.39**(0.63) (0.24) (0.19) (0.14) (0.10) (0.10) (0.13) (0.12) (0.13) (0.18) (0.13)

Quarterly GDP growth -7.93 -4.65 -5.18 -3.06 -3.76 0.01 -1.08 -1.58 0.33 -4.77* -4.83(5.28) (3.86) (3.23) (3.66) (2.47) (2.14) (2.15) (2.03) (2.67) (2.30) (2.52)

R2 0.25 0.39 0.55 0.70 0.64 0.48 0.55 0.56 0.51 0.72 0.70

Period Full Full Full Full Full Full Full Full Full1972-2010 Full

Table B.IX: Predicting global Default Rates with U.S. Inflation Risk (1969-2010)We check that the default prediction results in Table VII in the main text are robust to using a measure of global Baa default rates onthe left-hand side. Since defaults of Moody's rated firms predominantly have occurred in the U.S., the one-year global Baa-rated defaultrate is very similar to the one-year U.S. Baa-rated default rate. In this table, we use annual global default rates of Baa-rated firms fromMoody's (2011). The n-year default rate at time t is computed as the average default rate in years t+1 through t+n of firms that wererated Baa prior to defaulting. We report Newey-West standard errors with 6 lags. * and ** denote significance at the 5% and 1% levels,respectively.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)Horizon (Years) 1 2 3 4 5 5 5 5 5 5 5Inflation risk

Inflation volatility (Ann.) 10.77 20.54* 21.25** 16.40** 11.78** 4.22 4.43 7.00* 2.16(8.20) (7.95) (4.11) (2.60) (3.83) (3.69) (4.36) (3.16) (6.65)

Inflation-stock correlation -1.30 7.36 2.46 5.93 2.33 1.12 -1.70 -2.23(10.51) (8.46) (7.64) (3.16) (4.04) (4.08) (2.06) (4.99)

Real uncertainty and other control variablesIdiosyncratic volatility (Ann.) 1.01 0.95 1.08** 0.86** 0.45 0.24 -0.01 0.92**

(1.18) (0.46) (0.28) (0.21) (0.29) (0.21) (0.34) (0.25)Dividend-price ratio (Ann.) 1.11 -2.30 -2.79 -1.47 -1.83 0.50 -5.61** 5.49

(3.28) (2.71) (1.88) (1.10) (2.46) (2.08) (1.68) (3.71)GDP vol. 13.22**


(0.39)Leverage -1.88*

(0.81)Bond volatility (Ann.) 3.11

(8.03)Bond-stock correlation 3.86


3-Year inflation shock 0.01 0.81 -0.36 0.61 0.41 0.45 0.76 0.81 0.50 0.82 -0.32(2.32) (0.84) (1.33) (0.52) (1.13) (0.81) (0.85) (0.97) (1.23) (0.53) (0.95)

3-Year real stock return -0.24 0.02 0.04 0.11 0.12 0.10 0.11 0.12* 0.08 0.15* 0.12(0.22) (0.15) (0.08) (0.05) (0.09) (0.06) (0.06) (0.05) (0.08) (0.06) (0.08)

3-Year GDP growth 2.88 3.06 0.47 0.86 0.95 2.56** 2.82** 2.82** 1.87** 0.97 0.57(3.46) (2.39) (1.67) (0.80) (0.66) (0.44) (0.79) (0.81) (0.44) (0.69) (1.03)

3-Year change unemployment -0.33 3.38 -2.08 -0.36 0.22 3.62* 3.87 4.00 2.13 -0.87 -1.56(8.83) (5.45) (2.65) (1.70) (1.88) (1.28) (2.07) (2.11) (1.75) (1.89) (2.66)

Quarterly inflation shock -1.85 8.94 2.21 -2.83 -2.98 -8.60 -6.72 -6.62 -8.80 -1.11 -4.54(9.94) (8.83) (4.72) (2.18) (5.05) (4.89) (5.63) (5.87) (4.54) (3.61) (7.05)

Quarterly real stock return 0.68 0.12 0.39 0.63** 0.37 0.19* 0.20 0.21 0.31 0.03 0.47(0.62) (0.33) (0.22) (0.12) (0.23) (0.09) (0.10) (0.12) (0.21) (0.14) (0.25)

Quarterly GDP growth -4.38 -4.24 -1.15 2.30 0.06 1.38 1.29 1.29 2.10 -0.71 -2.82(8.21) (4.48) (3.24) (2.45) (3.64) (1.93) (2.06) (2.09) (3.64) (1.77) (5.84)

R2 0.37 0.55 0.66 0.92 0.71 0.60 0.63 0.63 0.62 0.86 0.82Period Full Full Full Full Full Full Full Full Full Full Full

Table B.X: Global Baa Credit Losses and U.S. Inflation Risk (1981-2010)We check that the default prediction results in Table VII in the main text are robust to using a measure of global Baa credit loss rates fora shorter time period. Global Baa credit loss rates are computed analogously to global Baa default rates in Table B.IX from credit lossrates reported in Moody's (2011). We report Newey-West standard errors with 6 lags. and ** denote significance at the 5% and 1%levels, respectively.

Issuer Name Issue Date Maturity Cpn S&P Maalot Midroog Enter Index Leave Index Bloomberg DataIsrael Electric Corp Ltd 30-May-93 31-Oct-10 2.8 AA 30-Mar-00 29-Sep-05 NoIsrael Electric Corp Ltd 2-Jun-02 20-Feb-15 6.5 AA- Aa3 30-Jun-04 31-Mar-10 NoU Dori Group Ltd 9-Mar-05 10-Aug-12 6.25 A3 31-Mar-05 28-Jun-07 YesAzorim-Investment Develop. & Construction

25-May-05 9-Mar-13 4.8 BBB+ A3 30-Jun-05 31-Mar-08 Yes

YH Dimri Construction & Develop. Ltd

2-Jun-05 30-Sep-12 4.15 A2 30-Jun-05 30-Sep-07 Yes

One Software Technologies Ltd 7-Jun-05 5-Jul-13 3.95 A2 30-Jun-05 30-Jun-08 YesAlliance Tire Co 1992 Ltd 5-Sep-05 31-Aug-12 6 A3 29-Sep-05 30-Sep-07 YesFox Wizel Ltd 12-Jun-06 7-Jul-13 4.8 A1 29-Jun-06 30-Jun-08 YesS Sholomo Holdings Ltd 4-Sep-06 30-Sep-13 5.5 A A2 28-Sep-06 28-Sep-08 YesPaz Oil Co Ltd 7-Dec-06 30-Nov-14 4.7 A+ 31-Dec-06 31-Dec-09 YesPaz Oil Co Ltd 7-Dec-06 29-Oct-14 5 A+ 31-Dec-06 30-Sep-09 YesAvgol Industries 1953 Ltd 22-Jan-07 31-Dec-14 5.2 A 29-Mar-07 30-Dec-09 YesAmir Marketing & Investments in Agriculture

12-Jun-07 31-May-15 4.6 A- 28-Jun-07 30-Jun-10 Yes

Ashot -Ashkelon Industries Ltd 10-Jun-07 1-Jun-14 6 A3 28-Jun-07 30-Jun-09 YesE Schnapp Co Works Ltd 7-May-07 1-May-14 5.35 A2 28-Jun-07 31-Mar-09 YesDelek Group Ltd 25-Oct-07 24-Oct-14 4.75 A A1 31-Dec-07 30-Sep-09 YesStrauss Group Ltd 21-May-07 1-Feb-18 4.1 AA+ Aa1 31-Mar-08 30-Dec-10 YesYH Dimri Construction & Development Ltd

5-Mar-08 31-Mar-15 6.1 A2 31-Mar-08 31-Mar-10 Yes

Hilan Ltd 6-Mar-08 31-May-15 4.5 A+ 31-Mar-08 30-May-10 YesKnafaim Holdings Ltd 11-Jun-08 30-Apr-15 6.9 A- NR 30-Jun-08 31-Mar-10 YesShikun & Binui Ltd 27-May-08 18-Apr-15 5.2 A2 30-Jun-08 31-Mar-10 YesAzorim-Investment Develop. & Construction

12-Aug-08 31-Dec-17 5.5 BBB+ A3 28-Sep-08 30-Dec-10 Yes

Hadera Paper Ltd 20-Jul-08 10-Jul-18 4.65 A 28-Sep-08 30-Dec-10 Yes

Yields from Bloomberg and a proprietary source. We consider non-convertible inflation-indexed corporate bonds with a rating of at least A- (S&P Maalot) or A3 (Midroog), five to eleven years to maturity, non-financial issuer, and at least eight quarterly consecutive spread observations.

Table B.XI: Israeli Corporate Bond Index Composition

rett→t+ncorp - rett→t+n

gov (%) (1) (2) (3) (4) (5) (6)Horizon n (in quarters) 1 4 12 1 4 12Change in Inflation Risk

Δn Inflation Volatility (% Ann.) -57.05 -47.76 43.35 -45.36 -15.07 -7.70(65.95) (51.58) (44.69) (5.48) (30.42) (31.19)

Δn Inflation-Stock Correlation -523.66 -315.83 -841.57 -45.36 259.82 92.01(334.82) (241.15) (444.21) (39.01) (202.79) (79.77)

Change in real uncertainty, stock and government bond returnsΔn Equity Volatility (% Ann.) -17.73 -2.07 -3.90 7.61 22.91* 18.82**

(15.69) (8.51) (12.57) (5.48) (8.89) (4.99)

rett,t+ngov (%) 10.35 28.18** 59.13** 5.05 14.27** 34.05**

(7.03) (9.81) (11.66) (2.95) (3.40) (2.59)

rett,t+neq (%) 6.80* 11.82** 9.15** 2.88** 6.49** 7.55**

(3.05) (4.03) (1.94) (0.66) (1.37) (0.53)Constant -0.14 -2.22 -14.42** -0.03 -0.70 -6.96**

(0.33) (1.12) (3.13) (0.16) (0.36) (0.65)

R2 0.30 0.48 0.69 0.13 0.50 0.82

Period89.Q3-09.Q4

89.Q3-09.Q4

89.Q3-09.Q4

89.Q3-07.Q4

89.Q3-07.Q4

89.Q3-07.Q4

rett→t+ncorp - rett→t+n

gov (%) (1) (2) (3) (4) (5) (6) (7) (8) (9)Horizon n (in quarters) 1 4 12 1 4 12 1 4 12Change in Inflation Risk

Δn Inflation Volatility (% Ann.) 629.62* 128.98 -749.85** 629.62* 128.98 -749.85** 170.02 -113.66 -540.03**(304.10) (286.04) (121.01) (304.10) (286.04) (121.01) (273.93) (171.96) (144.70)

Δn Inflation-Stock Correlation 124.92 -136.24 -757.25** 124.92 -136.24 -757.25** 162.78 -63.81 -377.25*(173.03) (184.27) (172.01) (173.03) (184.27) (172.01) (116.20) (126.10) (157.79)

Change in real uncertainty, stock and government bond returnsΔn Equity Volatility (% Ann.) 8.41 4.03 -5.35 8.41 4.03 -5.35 12.50 0.91 -4.06

(12.30) (14.44) (6.04) (12.30) (14.44) (6.04) (8.27) (10.19) (10.17)

rett,t+ngov (%) 629.62* 128.98 -749.85** -12.50 -23.79** -32.16** 170.02 -113.66 -540.03**

(304.10) (286.04) (121.01) (11.70) (8.11) (6.50) (273.93) (171.96) (144.70)

rett,t+neq (%) 124.92 -136.24 -757.25** 14.89 6.70 -9.78* 10.82* 8.36 -3.24

(173.03) (184.27) (172.01) (11.44) (11.56) (3.70) (5.21) (5.81) (3.70)Constant -12.50 -23.79** -32.16** 0.00 1.17 7.96** 0.13 0.54 2.55**

(11.70) (8.11) (6.50) (0.46) (1.38) (2.26) (0.22) (0.72) (0.61)

R2 0.37 0.30 0.40 0.57 0.42 0.63 0.24 0.22 0.22

Period89.Q3-09.Q4

89.Q3-09.Q4

89.Q3-09.Q4

89.Q3-07.Q4

89.Q3-07.Q4

89.Q3-07.Q4 Full Full Full

Panel B: U.S. (1969.Q4-2009.Q4)

Table B.XII: Placebo Test - Israel and U.S. Credit Return Regressions

Panel A: Israel (1989.Q3-2009.Q4)

We estimate a regression of corporate bond log returns in excess of government bond log returns onto changes in inflation volatility, changes in the inflation-stock correlation, and control variables:

Panel A reports the regression estimates for Israel inflation-indexed corporate log excess returns, while Panel B reports the regression estimates forU.S. nominal corporate log excess returns. U.S. corporate and government bond return indices are from Ibbotson. Israel corporate and governmentCPI-linked bond return indices are from the Tel-Aviv Stock Exchange. Quarterly equity returns are in excess of long-term bond returns. For a laghorizon of n quarters, we report Newey-West standard errors with 16+n lags in parentheses. Variables are constructed as described in Table IV. *and ** denote significance at the 5% and 1% levels, respectively. Inflation surprises are extracted as the residual from a regression of quarterlyinflation onto its own four lags and seasonal dummies, as in column (2) of Table B.V.

Figure B.1: International Credit Spreads and GDP Volatility

This figure shows the comovement of quarterly credit spreads (solid) and the three-year backward-looking standard deviation of real GDP growth surprises(dashed) for Australia, Canada, Germany, Japan, the U.K., and the U.S. Quarterly GDP growth surprises are computed analogously to inflation surprises as theresidual of log real GDP growth onto its own four lags, the log T-bill rate, and seasonal dummies. Credit spreads are computed as investment grade corporatebond index log yields in excess of duration-matched nominal government bond log yields, except for the U.S. credit spread, which is the Moody's Baa minus Aaalog yield spread. GDP volatility is computed using a three-year backward-looking window of quarterly GDP surprises.

0.0

1.0

2.0

3.0

4.0

5.0

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010

Per

cent

(%

)

Australia

Corporate Log Yield Spread (% Ann.) GDP Volatility (Right Axis)

-0.5

0.5

1.5

2.5

3.5

4.5

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010P

erce

nt (

%)

Canada

0.0

1.0

2.0

3.0

4.0

5.0

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010

Per

cent

(%

)

Germany

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010

Per

cent

(%

)

Japan

0.0

1.0

2.0

3.0

4.0

5.0

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010

Per

cent

(%

)

U.K.

-0.50.31.11.92.73.54.35.15.9

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010

Per

cent

(%

)

U.S.

Figure B.2: International Credit Spreads and Bond-Stock CorrelationThis figure shows the comovement of quarterly credit spreads (solid) and bond-stock correlation (dashed) for Australia, Canada, Germany, Japan, the U.K.,and the U.S. Credit spreads are computed as investment grade corporate bond index log yields in excess of duration-matched nominal government bond logyields, except for the U.S. credit spread, which is the Moody's Baa minus Aaa log yield spread. The bond-stock correlation is the correlation between dailyor weekly changes in long-term nominal government bond log yields and contemporaneous real stock log returns over the past quarter as described in TableIV.

-0.8

-0.4

0.0

0.4

0.8

1.2

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010

Per

cent

(%

)

Australia

Corporate Log Yield Spread (% Ann.) Bond-Stock Correlation (Right Axis)

-1.2

-0.6

0.0

0.6

1.2

1.8

2.4

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010P

erce

nt (

%)

Canada

-1.2

-0.6

0.0

0.6

1.2

1.8

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010

Per

cent

(%

)

Germany

-1.2

-0.6

0.0

0.6

1.2

1.8

2.4

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010

Per

cent

(%

)

Japan

-1.2

-0.6

0.0

0.6

1.2

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010

Per

cent

(%

)

U.K.

-1.2

-0.7

-0.2

0.3

0.8

1.3

1.8

-0.5

0.5

1.5

2.5

3.5

4.5

1970 1980 1990 2000 2010

Per

cent

(%

)

U.S.

Figure B.3: Breakeven-Stock Correlation

This figure illustrates the close correspondence between the nominal bond-stock correlation andbreakeven-stock correlation, when data is available. Breakeven is the difference between continuouslycompounded zero coupon nominal and inflation-indexed government yields. Ten-year yields are fromGurkaynak, Sack, and Wright (2010) and fifteen-year U.K. yields are from Anderson and Sleath (2001).The breakeven-stock correlation is the correlation between daily changes in breakeven and daily logstock returns over the past quarter.

-1.0

-0.5

0.0

0.5

1.0

1998 2000 2002 2004 2006 2008 2010

U.S.

Nominal Bond-Stock Corr. Breakeven-Stock Corr.

-1.0

-0.5

0.0

0.5

1.0

1985 1990 1995 2000 2005 2010

U.K.

Nominal Bond-Stock Corr. Breakeven-Stock Corr.

Figure B.4: U.S. Credit Spreads and Inflation Shocks

Moody's Baa over Aaa log yield spread and quarterly U.S. log inflation shocks as described inTable IV.

-5

-4

-3

-2

-1

0

1

2

0

0.5

1

1.5

2

2.5

3

3.5

1970 1975 1980 1985 1990 1995 2000 2005 2010

Per

cent

(%

)

Per

cent

(%

)

Baa - Aaa Log Yield Spread Quarterly Inflation Shock

Figure B.5: U.S. Credit Spreads and Upper Tail Survey Inflation Uncertainty

This figure shows the comovement between the U.S. Moody's long-term Baa-Aaa log yield spreads and the upper tail of inflation uncertainty for comparison with Figure 1 in the main text. Data is constructed as in Figure 1.

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

2.40

0

1

2

3

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Per

cent

(%

)

NBER Recession Baa-Aaa Log Yield Spread 90-50 Infl. Quantile Spread

Correlation=29%



Crisis



Crisis

Correlation=



Crisis



Crisis

Percent (%)Percent (%)

Figure B.6: U.S. Corporate Bond Percent Zero Daily Returns

This figure shows the additional liquidity control variable in Table B.VI. The percent of zero dailyreturns in U.S. corporate bonds 1993.Q1-2010.Q4 is from Datastream.

0

10

20

30

40

50

1993 1995 1997 1999 2001 2003 2005 2007 2009

Per

cent

(%

)

Percent Zero Returns

Mean=13.4%

We show one- through five-year annualized issuer-weighted default and credit loss rates of Baa-rated industrial and public utility U.S.firms. We compute default rates using the Moody's corporate default risk service database. Credit loss rates are calculated as default ratestimes issuer-weighted loss given default. This subset of firms and the weighting scheme correspond as closely as possible to the Baacorporate bond yield index used in our analysis of corporate long-term credit spreads. In computing the n-year default rate at time t, weinclude all firms that were rated Baa in year t and defaulted during years t+1 through t+n. For detailed variable descriptions seeSupplementary Appendix C.3.

Figure B.7: U.S. Annualized Baa Default Rates and Credit Loss Rates

0

0.5

1

1.5

1969 1979 1989 1999 2009

1‐Year Default

2‐Year Default

3‐Year Default

0

0.5

1

1.5

1969 1979 1989 1999 2009

3‐Year Default

4‐Year Default

5‐Year Default

0

0.5

1

1.5

1969 1979 1989 1999 2009

1‐Year Loss

2‐Year Loss

3‐Year Loss

0

0.5

1

1.5

1969 1979 1989 1999 2009

3‐Year Loss

4‐Year Loss

5‐Year Loss

Figure B.8: Israeli Inflation-Indexed Credit Spreads, Inflation Volatility, and Inflation-Stock Correlation

This figure shows the comovement of Israeli quarterly credit spreads (solid), inflation volatility (dashed), and inflation-stock correlation (dashed). Israelicorporate bond yields reflect corporate bonds issued by non-financial firms with five to eleven years remaining to maturity and rated A- or higher by S&PMaalot or A3 or higher by Midroog. Maturity-matched government bond yields are from the Bank of Israel. A detailed data description is available inSupplementary Appendix C.4.

1.25

1.75

2.25

2.75

3.25

3.75

4.25

4.75

-10123456789

2000 2002 2004 2006 2008 2010

Corporate Log Yield SpreadInflation Volatility (Right Axis)

-0.75-0.55-0.35-0.150.050.250.450.650.851.051.25

-10123456789

2000 2002 2004 2006 2008 2010

Corporate Log Yield SpreadInflation-Stock Correlation (Right Axis)

Inﬂation Risk in Corporate Bonds · berger (1973)). Tax and other debt beneﬁts create an...

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