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Discussion ofEquilibrium Credit Spreads and the

Macroeconomy

by J. Gomes and L. Schmid

Aubhik KhanOhio State University

November 2010

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A macroeconomists perspective

The authors focus their paper on recent business cycles.

The Great Recession of 2008-2009 oers a primaryexample of the important role that uctuations in credit

risk play in the aggregate economy. Unfortunately thesedevelopments also exposed the current need for new stateof the art models suitable to understand the jointbehaviour of credit risk, nancial prices, and the keymacroeconomic aggregates. (page 2, paragraph 1)

This is my license to oer a macroeconomists perspective.

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Production

y = zkz aggregate shock

idiosyncratic shock

k parameter

(z, , b, k) = (z b ) k.

k required investment

bk debt payment per period

aggregate state s = (z, )

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Homogeneity in capitaldefault

Q(, s; b) = maxn

0, (1 ) (1 )

z b

+Z

d

s, s0

Q0, s0; b

F

, d0

s, ds0o

,

= 0 when z b 0. Firms default by choice when 2 E (b, s),

E (b, s) = f 2 R+jQ(, s; b) = 0g

Let (b, s) = sup E(b, s). An important insight is that if d is constant, (b, s) is proportional to z. However, when d(s, s0) is a stochasticdiscount factor, it moves with z and, in this instance, (b, s) respondsdierently to positive and negative shocks. (See also Chen,Collin-Dufresne and Goldstein 2009).

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Loan size and credit spreadsdebt and equity

B(, s; b) =

b+Z

d

s, s0

B0, s0; b

F

, d0

s, ds0

1 E(b,s) ()

+ (1 ) (1 + z)E(b,s) ()

The yield on corporate debt is yb (, s) =b

B(,s;b) , and the creditspread is yb (, s) yfb (, s). Debt,

RB(, s; b) G(d), is

determined by b,

A (s) = maxb

ZhQ(, s; b) + B(, s; b)iG(d) .

Given random costs of entry, e, potential rms are introduced if

e A0 (s) .

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Abstraction from rm-level factor adjustment

1 Young rms tend to be smaller, higher failure rates.

2 Conditional on survival, they grow faster.1 Dunne, Roberts and Samuelson 19892 Jovanovic 1982, Hopenhayn 1992

3 On average it takes 10 years for an entrant to reach the size

of the typical entrant (collateral constraints). Do new rmsissue corporate bonds?

Age and size dynamics show ongoing rm-level investment

ik

( i0k ,i1

k )

rm 0.139 0.4

plant 0.337 0.058

Firm data (COMPUSTAT) from Bloom 2009, table 3, bottom panel. Plantdata (LRD) from Cooper and Haltiwanger 2006.

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Implication of rm-level investment and Calibration

The average annual investment rate across establishments is 0.122.

In GS model, there is no capital adjustment in rms. This makesrm value less sensitive to idiosyncratic shocks, and somewhat less

sensitive to aggregate shocks. It follows that any generalisationthat addresses the data on rm-level investment is likely to changeQ(, s; b), therefore E (s, b), and thus credit spreads.

Perhaps more important is that the model is not calibrated.(z,z)

is chosen to match GDP moments, and (,) is chosen to matchcredit spreads. The upper bound on the distribution of rmcreation costs, h, varies with the aggregate shock.

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Entry and exitasymmetric business cycles

1 The GS model predicts that default is strongly countercyclical. Thisraises credit spreads in recessions, lowering the value of entry.

2 Asymmetric business cycles are driven by countercyclical entry.

1 Model predictions for entry would be useful to evaluate thismechanism

2 Default in the model is associated with exit.

3 Aggregate investment, given a xed scale in rms, involvestime-varying movements in entry.

entry rate exit rate

0.22 0.351source: Campbell (1998)

Clementi and Palazzo (2010) reproduce entry and exit in a modelconsistent with age and size dynamics.

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Mechanics of credit spreads and default

Default rises with the marginal rate of substitution, in recessions.

This drives large credit spreads.

Model with z shocks has strongly countercyclical default: (GDP,default) = 0.81.

DATA has weakly countercyclical default: (GDP,default) = 0.33.

model inconsistent with data when TFP shocks are the solesource of aggregate uctuations.

Importantly, credit spreads remain high with two shocks: z and .

Default rates are no longer implausibly countercyclical: (GDP,default) = 0.59.

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Importance of credit shocks

GS assume credit shocks 2 f0.25, 0.75g

Pr f = 0.25 j = 0.25g = 0.98

Pr f = 0.75 j = 0.75g = 0.5

As credit shocks reconcile large credit spreads with weakly

countercyclical default, their measurement appears important.

Jermann and Quadrini (2009), Khan and Thomas (2010)

Credit shocks to collateral constraints can increase dispersion.

Dispersion of rm growth rates is countercyclical (Bloom 2009and Arellano, Bai and Kehoe 2010).

Dicult to implement in a model without variable inputs.

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Credit shocks and the recent recession

Unanticipated shock to , changing from 0.75 to 0.25. Essentially monotone response in GDP and investment (g. 5). Recovery in default is (1 ) (1 + z) .

The variability of investment relative to GDP appears large. Consumption must fall with the credit shock. Response is similar to a persistent shock to TFP.

Lack of employment hampers quantitative analysis. Authorsshow that economy with leverage propagates technologyshock relative to only equity model. Ordinarily, employmentpropagates technology shock.

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Total Factor Productivity in the recent recession

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Credit shocks in a model with production heterogeneityKhan and Thomas (2010)

competitive rms (k, b, ): y = zF (k, n) labor from households (real wage ) one-period debt with face value b0 2 R (relative price q1)

2 frictions inuencing choices of k0

, b0

, and D specicity of capital: k2 (0, 1) from each unit uninstalled collateralized debt limit: b0 b[kk]

An unanticipated shock to b shifts the distribution ofproduction towards larger, relatively unproductive rms.

Future TFP falls and GDP starts to gradually fall Consumption shows an initial rise

( )

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Credit crisis in Khan and Thomas (2010)An unanticipated reduction in the value of collateral

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