Inflation, Debt, and Default Sewon Hur (University of Pittsburgh) Illenin Kondo (Board of Governors) Fabrizio Perri (Minneapolis Fed) University of Pittsburgh

January 18, 2017

The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis, the Federal Reserve Board, or the Federal Reserve System.

0 / 29

How does inflation affect debt and default? I

The co-movement between inflation and consumption growth varies over time and across countries

I

The majority of sovereign debt in advanced economies is I I

I

Pro-cyclical inflation makes nominal debt I I

I

Held domestically data Nominal: subject to inflation risk

Less risky to lender: receives more in bad times More risky to borrower: pays out more bad times

Inflation cyclicality affects debt pricing and default dynamics

1 / 29

Motivation: U.S. inflation cyclicality and real rates (a) Inflation and Consumption growth

(b) Real Interest Rates 8

16

6 Inflation

12

2 Percent

Percent

4 8

4

0 -2 -4

0 Real rate Trend

-6

Consumption growth

-8

-4 50

55

60

65

70

75

80

85

90

95

00

05

10

50

15

55

60

65

70

75

80

85

90

95

00

05

10

15

(c) Co-movement and Real Interest Rates 1.8

1972-1993

1.6

Real Interest Rate

1.4 1.2 1.0

1950-1971

0.8 0.6 0.4

1994-2015

0.2 -.8

-.6

-.4

-.2

.0

.2

.4

Correlation of Inflation and Consumption Growth Note: Inflation is the log difference between CPI in quarter t and CPI in quarter t-4. Consumption growth is the log difference in real personal consumption expenditures over the same interval. Real interest rates are nominal interest rates on government securities (from the IMF IFS database) minus expected inflation computed using a linear univariate forecasting model estimated on actual inflation.

2 / 29

Inflation, debt, and default: empirics I

How does the co-movement between inflation and consumption growth affect real interest rates?

I

Use data on inflation, consumption, debt, interest rates for 21 OECD countries from 1985 to 2015

I

Procyclicality discount I I

Higher covariance associated with lower real rates But not so much in bad states

3 / 29

Inflation, debt, and default: model I

Construct a model of inflation, debt, and default

I

Using a simple 2-period model, demonstrate I I

Procylicality discount How inflation cylicality affects default dynamics

I

Calibrate quantitative model

I

Higher covariance economy I I I

Lower real rates But more likely to default in bad states Debt crises more likely

4 / 29

Related literature I

Sovereign default: Eaton and Gersovitz (1981), Arellano (2008), Aguiar and Gopinath (2007), Chatterjee and Eyigungor (2012), Hatchondo and Martinez (2009)

I

Domestic/Selective default: Reinhart and Rogoff (2011), D’Erasmo and Mendoza (2013), Mallucci (2015), Jeon and Kabukcuoglu (2017)

I

Default and inflation: Aguiar, Amador, Farhi and Gopinath (2012), Sunder-Plassman (2013)

I

Cyclicality of inflation: Boudoukh (1993), Ang, Bekaert, and Wei (2008), Campbell, Pflueger, and Viceira (2014), Song (2014)

I

Monetary unions: Neumeyer (1998), Aguiar et al. (2013), Corsetti and Dedola (2013) 5 / 29

Data

5 / 29

Evidence on real yields and inflation cyclicality I

Compute co-movement of innovations to inflation and to consumption growth

I

Sample: 21 OECD countries; quarterly data 1985-2015

I

Measure country-specific time-varying co-movement I

Follow Boudoukh (1993)’s country-by-country VAR "

I

I

πit gitc

#

"

= Ai

πi,t−1 c gi,t−1

#

"

+

επit εgit

#

Compute conditional co-movement between επit and εgit Graph using overlapping ten-year windows

Real yields adjust for expected future inflation 6 / 29

-4

-2

0

real yield* 2

4

6

Inflation consumption covariance and real interest rate

-1.5

-1

-.5 0 .5 inflation consumption covariance*

1

*: conditional residual from a linear model with country and time fixed effects

7 / 29

Real interest rates: the inflation cyclicality discount Real sovereign yield

Inflation consumption covariance Mean of π and gc residuals Variance of π and gc residuals Lagged Debt adj. R 2 N

(1)

(2)

(3)

-1.892*** (.386)

-1.527*** (.330)

-1.569*** (.452)

No No Yes

Yes No Yes

Yes Yes Yes

0.854 1841

0.884 1841

0.884 1841

Countries: AUS,AUT,BEL,CAN,CHE,DEU,DNK,ESP,FIN,FRA,GBR, GRC,ITA,JPN,KOR,MEX,NLD,NOR,PRT,SWE,USA. Standard errors clustered by country. ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 All regressions include country and time fixed effects I

One standard deviation increase (0.199) is associated with a 31 b.p. decrease in the real yield 8 / 29

Inflation cyclicality discount – more in good times Real sovereign yield Countries

Inflation consumption covariance Covariance*1goodtimes 1goodtimes other controls adj. R 2 N

(1) all countries

(2) ex. KOR/ MEX/GRC

(3) Adv. & Euro ex. GRC

-1.369** (.595) -.722 (1.094)

-1.163 (.801) -1.576* (.857)

-1.563 (1.868) -3.916** (1.385)

Yes Yes

Yes Yes

Yes Yes

0.887 1841

0.915 1644

0.921 1102

Good times: average cons. growth (conditional residual) > 0 Countries in (3): AUS,BEL,DEU,ESP,FIN,FRA,GBR,ITA,JPN,NLD,PRT,USA Standard errors clustered by country. ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 All regressions include country and time fixed effects 9 / 29

Model

9 / 29

Model I

We develop a model of sovereign debt I I

I

I

Builds on standard model (Arellano 2008) Inflation, exogenous (e.g. changes monetary independence, changes in nature of shocks supply/demand in the economy) Risk-averse, domestic lenders hold nominal bonds

Use calibrated model to investigate how inflation cylicality affects debt pricing and dynamics of debt and default

10 / 29

First, a simple model without default I

Two-period lived lender and borrower with endowments I I

First period: y` = 1 − τ and yb = τ Second period: y` = (1 − τ )x and yb = τ x

I

Debt b is nominal with price q

I

Cyclical inflation is (1 − γx )−1 where x is random I I

γ: cyclicality of inflation If γ > 0, high x ⇒ high inflation

11 / 29

First, a simple model without default I

Borrower solves Z

max bb

I

u (τ + qbb ) + βb

X

u (τ x − (1 − γx ) bb ) dF (x )

Lender solves max b`

u (1 − τ − qb` ) + β`

Z X

u ((1 − τ ) x + (1 − γx ) b` ) dF (x )

12 / 29

First, a simple model without default I

Borrower solves Z

max bb

I

X

u (τ x − (1 − γx ) bb ) dF (x )

Lender solves max b`

I

u (τ + qbb ) + βb

u (1 − τ − qb` ) + β`

Z

Let u(c) = Ac − φ2 c 2 , µx = R σx2 = X x 2 dF (x )

u ((1 − τ ) x + (1 − γx ) b` ) dF (x )

X

R X

x dF (x ) = 0, and

12 / 29

Simple model – the inflation hedging discount The lender’s Euler: qu 0 (1 − τ − qb) = β`

Z X

(1 − γx ) u 0 ((1 − τ ) x + (1 − γx ) b)dF (x ) | {z } | {z } deflation

output

⇔

q (A − φ (1 − τ − qb)) = β` A + φ(1 − τ )γσx2 − β` φ 1 + γ 2 σx2 b

Theorem Near γ = 0, there is an inflation hedging discount on the interest rate: ∂q > 0. ∂γ

13 / 29

Simple model with default I

Suppose now that the borrower can default I

I

During default: y` = (1 − τ )xd and yb = τ xd

Borrower chooses to default if x < xb ≡ I

τ xd +b τ +γb

Ceteris paribus and for xd low enough,




default probability F b x increases with debt (b) and inflation cyclicality (γ)

14 / 29

Simple model with default I

Suppose now that the borrower can default I

I

During default: y` = (1 − τ )xd and yb = τ xd

Borrower chooses to default if x < xb ≡ I

τ xd +b τ +γb

Ceteris paribus and for xd low enough,




default probability F b x increases with debt (b) and inflation cyclicality (γ) I

Borrower solves Z max bb

I

u (τ x − (1 − γx ) bb ) dF (x )+βb u (τ xd ) F (b x)

u (τ + qbb )+βb b X \X

Lender solves max u (1 − τ − qb` ) b` Z + β` u ((1 − τ )x + (1 − γx ) b` ) dF (x ) + β` u ((1 − τ )xd ) F (b x) b X \X 14 / 29

Simple model with default I

The lender’s Euler: Z u (1 − τ − qb) = β`

(1 − γx ) u 0 ((1 − τ )x + (1 − γx ) b) dF (x )

b X \X ⇔   q (A − φ (1 − τ − qb)) = (1 − F (b x )) β` A + φ(1 − τ )γσR2 + other terms ...

where (1 − F (xb ))σR2 = I

R b X \X

x 2 dF (x )

The interest rate now features a default premium and a conditional inflation hedging discount.

15 / 29

Model I

Closed economy, discrete time t = 0, 1, 2, ..., one good

I

Endowments y and inflation π follow a joint Markov Process

I

Agents I I

Representative household (lenders) Government issues nominal bonds

16 / 29

Lenders I

Household (lender) preferences are given by E0

∞ X

β`t u(ct )

t=0

where 0 < β` < 1 is the time discount factor I

Lenders receive (1 − τ )y

17 / 29

Government I

Government preferences are given by E0

∞ X

βgt u(gt )

t=0

where 0 < βg < β` < 1 and g is government consumption I

Government revenue: τ y

18 / 29

Government I

Government preferences are given by E0

∞ X

βgt u(gt )

t=0

where 0 < βg < β` < 1 and g is government consumption I

Government revenue: τ y

I

Given the option to default, the government chooses n

V o (B, s) = max V c (B, s), V d (B, s)

o

c,d

where B is incoming assets and s = (π, y ) 18 / 29

Value of default I

The value of default is given by  

V d (B, s) = u τ y − φd (y ) 

+βh Es|s 0 θV

o





λB , s 0 + (1 − θ)V d 1 + π0 



λB , s0 1 + π0



0 ≤ λ ≤ 1 : recovery rate,

18 / 29

Value of default I

The value of default is given by  

V d (B, s) = u τ y − φd (y ) 

+βh Es|s 0 θV

o





λB , s 0 + (1 − θ)V d 1 + π0 



λB , s0 1 + π0



0 ≤ λ ≤ 1 : recovery rate, 0 ≤ θ ≤ 1 : probability of regaining access to credit, and

19 / 29

Value of default I

The value of default is given by  

V d (B, s) = u τ y − φd (y ) 

+βh Es|s 0 θV

o





λB , s 0 + (1 − θ)V d 1 + π0 



λB , s0 1 + π0



0 ≤ λ ≤ 1 : recovery rate, 0 ≤ θ ≤ 1 : probability of regaining access to credit, and (

!

d1 d1 y2 φ (y ) = max 0, y + d1 − d0 d0

)

d

quadratic cost of default where I I

default cost at mean is φd (1) = d1 default costs matter when φd (y ) > 0, when y < 1 + d0 19 / 29

Value of repayment I

The value, conditional on not defaulting is given by  

V c (B, s) = max u (τ y − q(B, s, B 0 )B 0 + B) B0  "

+ βh Es 0 |s V o

B0 , s0 1 + π0

!#   

where q(B, s, B 0 ) is the bond price I

Real return on government debt is stochastic (even in absence of default)

20 / 29

Bond price In this environment, the bond price satisfies  q(B, s, B 0 ) = β` Es 0 |s 

1 − d∗



B0 0 1+π 0 , s



 u 0 (c 0 )  u 0 (c)

1 + π0    0

 B   0 0 d 0 d ∗ 1+π 0 0,s (1 − τ ) y − φ (y ) u B  + β` Es 0 |s  qd , s0 1 + π0 1 + π0 u 0 (c)

where q d is the price of a bond in default.

default price

21 / 29

Cyclicality of inflation and borrowing costs I

When λ = 0, the bond price can be written as q(B, s, B 0 )

I

     0 0  1 B0 u (c ) ∗ 0 0 0 E 1 − d , s E s |s s |s 1 + π0 1 + π0 u 0 (c)       1 B0 u 0 (c 0 ) ∗ 0 0 cov 1 − d , s , +β` Es 0 |s s |s 1 + π0 1 + π0 u 0 (c)      B0 1 u 0 (c 0 ) 0 0 +β` Es 0 |s 1 − d ∗ , s cov , s |s 1 + π0 1 + π 0 u 0 (c)  0 0     u (c ) B0 1 ∗ 0 0 +β` Es 0 |s cov , 1 − d , s s |s u 0 (c) 1 + π0 1 + π0 

=

β` Es 0 |s

Default and inflation increase borrowing costs

22 / 29

Cyclicality of inflation and borrowing costs I

When λ = 0, the bond price can be written as q(B, s, B 0 )

     0 0  1 B0 u (c ) ∗ 0 0 0 E 1 − d , s E s |s s |s 1 + π0 1 + π0 u 0 (c)       1 B0 u 0 (c 0 ) ∗ 0 0 cov 1 − d , s , +β` Es 0 |s s |s 1 + π0 1 + π0 u 0 (c)      B0 1 u 0 (c 0 ) 0 0 +β` Es 0 |s 1 − d ∗ , s cov , s |s 1 + π0 1 + π 0 u 0 (c)  0 0     u (c ) B0 1 ∗ 0 0 +β` Es 0 |s cov , 1 − d , s s |s u 0 (c) 1 + π0 1 + π0 

=

β` Es 0 |s

I

Default and inflation increase borrowing costs

I

Countercyclical default increases borrowing costs

22 / 29

Cyclicality of inflation and borrowing costs I

When λ = 0, the bond price can be written as q(B, s, B 0 )

     0 0  1 B0 u (c ) ∗ 0 0 0 E 1 − d , s E s |s s |s 1 + π0 1 + π0 u 0 (c)       1 B0 u 0 (c 0 ) ∗ 0 0 cov 1 − d , s , +β` Es 0 |s s |s 1 + π0 1 + π0 u 0 (c)      B0 1 u 0 (c 0 ) 0 0 +β` Es 0 |s 1 − d ∗ , s cov , s |s 1 + π0 1 + π 0 u 0 (c)  0 0     u (c ) B0 1 ∗ 0 0 +β` Es 0 |s cov , 1 − d , s s |s u 0 (c) 1 + π0 1 + π0 

=

β` Es 0 |s

I

Default and inflation increase borrowing costs

I

Countercyclical default increases borrowing costs

I

Pro-cyclical inflation reduces borrowing costs 22 / 29

Quantitative experiment I

Calibrate model with zero covariance to match spreads and conditional default probabilities in advanced economies

I

Assess impact of different inflation processes on interest rates, debt dynamics, and crises

23 / 29

Functional forms I

Preferences u(c) =

I

c 1−γ 1−γ

Stochastic Process 













log y 0   ρy ρπ,y  log y  εy   = + π0 ρy ,π ρπ π επ where





  



ε 0 σ 2 σπ,y   y  = N   ,  y 0 επ σπ,y σπ2

24 / 29

Calibration Parameters Gov’t discount factor βh Default cost cutoff d0 Default cost at mean d1

Values 0.80 -0.05 0.06

Persistence ρy , ρπ Spillovers ρπ,y , ρy ,π Volatility σy , σπ Covariance of innovations σπ,y Tax rate τ

0.80 0.00 0.01 0.00 0.20

Lender discount factor β` Risk aversion γ Probability of re-entry θ Recovery parameter λ

0.99 2 0.10 0.96

Joint targets default prob. in good times: 1.11%∗ average spread: 0.74%∗∗ default prob. in bad times: 2.71%∗ VAR estimates – OECD cross section

± 0.0000199 gov’t expenditure share of GDP 1985-2015 (US) risk-free rate: 1 percent average exclusion: 10 quarters† recovery rate: 50%‡

∗

: CDS-implied default probabilities 2001-2015 (threshold: 1 s.d. below trend output), ∗∗ : Eurozone (ex. Greece) nominal rates less German rates 1999-2015, † : Richmond and Dias (2008), ‡ : Benjamin and Wright (2009) 25 / 29

Results I

The pro-cyclical inflation regime has I I I

Lower borrowing costs More debt More default

Spreads (percent) definition Debt (percent of income) Default prob. (percent)

Positive co-movement 0.802 18.199 1.740

Negative co-movement 0.837 18.281 1.683

Difference -0.035 0.082 0.057

26 / 29

Decomposition of bond price I I

The pro-cyclical inflation economy has lower borrowing costs This is driven by procyclicality of inflation, despite higher default and the comovement of default with inflation

price

q

no default

E [1 − d]

E [no def.] cov (irms, defl.) E [irms] cov (no def., defl.) E [defl.] cov (no def., irms) I

Positive co-movement 98.86

Negative co-movement 98.85

difference (annual bp) 4

99.77

99.76

-4

0.02 -0.03 -0.42

-0.03 0.02 -0.44

20 -17 5

20 bp accounts for one third of the difference in the data 27 / 29

Procyclicality not always good I

The pro-cyclical inflation economy has I I

Lower borrowing costs during good times Higher borrowing costs during bad times, when output is more than 1 s.d. below mean

Spreads overall (percent) Spreads in good times (pct) Spreads in bad times (pct)

Positive co-movement 0.802 0.687 1.373

Negative co-movement 0.837 0.733 1.326

Difference -0.035 -0.046 0.047

28 / 29

Conclusion I

In good times, the procyclical economy enjoys lower real rates and accumulates more debt

I

In bad times, the risk of default increases more for the procylical economy which leads to higher real rates

I

For monetary unions, recessions increase the contrast over monetary policy

I

Provides an alternative explanation of the secular decline in real rates

29 / 29

Appendix

29 / 29

Domestic share of government debt is high Country Australia Belgium Canada Denmark Finland France Germany Greece Italy Japan Netherlands Norway Portugal Spain Sweden United Kingdom United States Mean

2004 83.3 50.7 77.6 74.5 23.1 57.9 68.6 40.8 59.9 95.7 44.4 43.5 24.0 55.7 64.4 81.9 80.8 63.3

Year 2008 85.6 41.0 83.8 75.2 38.1 57.8 53.5 41.2 60.9 91.9 45.2 50.6 27.3 62.6 75.5 78.1 78.0 63.9

2012 61.9 58.9 72.1 70.9 25.9 51.5 41.4 22.2 66.1 92.1 55.8 71.5 35.9 78.1 61.4 72.4 73.3 60.4

back

Mean 76.9 50.2 77.8 73.5 29.0 55.7 54.5 34.7 62.3 93.3 48.5 55.2 29.0 65.5 67.1 77.5 77.3 62.5

Sources: BIS, Haver

30 / 29

q1

q1 10

20

00

q1

90 20

19

q1

q1 10

20

00

q1

90 20

19

q1

q1

10

20

00

q1

90

20

19

q1

q1

10

20

00

q1

90

20

19

q1

q1

10

20

00

q1

90

20

19

q1

q1

10

20

00

q1

90

20

19

q1

q1

10

20

00

q1

90

20

19

-.5

0

.5

-.5

0

.5

-.5

0

correlation of inflation consumption growth .5

Conditional correlation between inflation and consumption growth AUS AUT BEL CAN CHE DEU DNK

ESP FIN FRA GBR GRC ITA JPN

KOR MEX NLD NOR PRT SWE USA

back

Graphs by Country code

31 / 29

Bond price in default

back

The price of a bond in default satisfies 

1 − d∗



λB 0 1+π 0 , s



0

0



u (c )  1 + π0 u 0 (cdef )  0    B   0 0 0 1 − θ + θd ∗ 1+π , s 0 λB u (c ) def  + β` λEs 0 |s  qd , s0 1 + π0 1 + π0 u 0 (cdef )

q d (B, s) = β` λθEs 0 |s 

32 / 29

Measuring spreads in the model

back

We measure spread as the real rate minus the risk-free rate: spreadt =

1 qt+1 Et [1 + πt+1 ]

where

" RF qt+1

= β` Et

!4

u 0 (ct+1 ) u 0 (ct )

−

1

!4

RF qt+1

#

33 / 29

Robust to alternative yield measures Real sovereign yield Yield source Inflation consumption covariance other controls adj. R 2 N

(1)

(2)

(3)

IFS

Fame 5-year

Fame 10-year

-1.569***

-2.211**

-2.582***

(.452)

(.982)

(.831)

Yes 0.884 1841

Yes 0.857 1216

Yes 0.896 1465

Countries: AUS,AUT,BEL,CAN,CHE,DEU,DNK,ESP,FIN,FRA,GBR, GRC,ITA,JPN,KOR,MEX,NLD,NOR,PRT,SWE,USA. Standard errors clustered by country. ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 All regressions include country and time fixed e 34 / 29

Robust to alternative debt measures Real sovereign yield Debt source

(1)

(2)

(3)

(4)

Oxford &

OECD

Oxford

OECD &

-1.569***

-1.321

-1.605***

-1.243**

(.452)

(1.581)

(0.430)

(0.467)

Yes 0.884 1841

Yes 0.818 933

Yes 0.892 1663

Yes 0.902 1785

OECD

Inflation consumption covariance other controls adj. R 2 N

Oxford

Countries: AUS,AUT,BEL,CAN,CHE,DEU,DNK,ESP,FIN,FRA,GBR, GRC,ITA,JPN,KOR,MEX,NLD,NOR,PRT,SWE,USA. Standard errors clustered by country.

∗

p < 0.10,

∗∗

p < 0.05,

∗∗∗

p < 0.01

All regressions include country and time fixed effects 35 / 29

Robust to alternative blocs Real sovereign yield Countries Inflation consumption covariance other controls adj. R 2 N

(1)

(2)

(3)

all

ex. KOR/

Adv. & Euro

countries

MEX/GRC

ex. GRC

-1.569***

-1.987**

-1.269

(.452)

(.751)

(1.152)

Yes 0.884 1841

Yes 0.914 1644

Yes 0.915 1102

Countries in (3): AUS,BEL,DEU,ESP,FIN,FRA,GBR,ITA,JPN,NLD,PRT,USA Standard errors clustered by country.

∗

p < 0.10,

∗∗

p < 0.05,

∗∗∗

p < 0.01

All regressions include country and time fixed effects

36 / 29