1. society
2. work
3. unemployment

A Model of the Twin Ds:
Optimal Default and Devaluation
by
S.Na S.Schmitt-Groh´
e M.Uribe V.Yue
November 18, 2014
1
Motivation
There is a strong empirical link between
sovereign default and large devaluations
• Reinhart (2002) examines data for 58 countries over the period
1970 to 1999 and finds that:
– The unconditional probability of a large devaluation in any
24-month period is 17%.
— The probability of a large devaluation conditional on the 24month period containing a default is 84%.
• Reinhart refers to this phenomenon as the Twin Ds.
2
Devaluation Around Default, 1975-2013
50
Excess devaluations
Default date
45
40
35
percent
30
25
20
15
10
5
0
−3
−2
−1
0
Years after default
1
2
3
Median of cumulative devaluations conditional on default in year 0 minus unconditional median. Sample contains 116 default episodes between 1975 and 2013 in 70 countries. Source:
Default dates, Uribe and Schmitt-Groh´
e (2014), chapter 11. Exchange rates, WDI.
3
Argentina 1996-2006
Nominal Exchange Rate (E )
4
Unemployment Rate + Underemployment Rate
40
3
35
Percent
Pesos per U.S. Dollar
t
2
1
0
1996
30
25
1998
2000
2002
Year
2004
20
1996
2006
1998
Nominal Wage (W )
2000
2002
Year
2004
2006
Real Wage (W /E )
t
t
t
1.4
Index 1996=1
Pesos per Hour
1.2
12
0.8
0.6
6
1996
1
1998
2000
2002
Year
2004
2006
0.4
1996
1998
2000
2002
Year
2004
2006
Vertical Line 1998, beginning of recession.
Vertical Line 2002, default and devaluation.
4
•
This Paper
– Develop a model that explains the Twin Ds phenomenon as
an optimal policy outcome.
•
Main Elements
– Imperfect enforcement of debt contracts
– Downward nominal wage rigidity.
• Intuition
– Under the optimal policy, default occurs during large recessions.
– A contracting demand for labor puts downward pressure on real
wages.
– A large devaluation reduces the real value of wages, thereby
preventing massive unemployment.
– The devaluation is necessary to bring real wages down because
nominal wages are downwardly rigid.
5
Analytical Findings
Two Decentralizations
of the Eaton-Gersovitz Model
• Decentralization I: Real models of sovereign default in the
tradition of Eaton and Gersovitz (1981) can be decentralized via
optimal capital controls.
• Decentralization II: Real models of sovereign default in the
tradition of Eaton and Gersovitz (1981) can be interpreted as
the centralized version of economies with default risk, downward
nominal wage rigidity, optimal capital controls, and optimal devaluation policy.
6
Quantitative Findings
• The optimal policy features large devaluations of 40% around
default events, which is in line with the data. That is, the Twin
Ds emerge endogenously as an optimal policy outcome.
• Under currency pegs, default episodes are accompanied by massive involuntary unemployment of around 20%.
• Due to larger default incentives, currency-peg economies can
support less external debt than optimally floating economies
(20% versus 60% of traded GDP).
7
The Model: The Household’s Problem
max
N
{cT
t ,ct ,dt+1 }
E0
∞
X
β t U (ct )
t=0
subject to
N)
ct = A(cT
,
c
t
t
N +d =y
T + w h + (1 − τ d)q d
cT
+
p
c
˜
t
t
t t
t
t
t
t t t+1
ht ≤ ¯
h
Households take ht as given. All debt is denominated in foreign
currency (original sin).
The Demand For Nontradables
N
A2(cT
t , ct ) = p
t
N)
A1(cT
,
c
t
t
8
The Demand For Nontradables
A 2 (c T0 , c N )
price, p
A 1 (c T0 ,c N )
A 2 (c T1 , c N )
A 1 (c T1 , c N )
quantity, cN
T
cT
1 < c0
A Contraction in Traded Absorption, cT
t ↓, Shifts the
Demand for Nontradables Down and to the Left
9
Firms
max {pt F (ht) − wt ht}
{ht}
wt ≡ WTt real wage in terms of tradables.
Pt
Wt nominal wage.
PtT nominal price of tradable goods.
∗
PtT = Et P T t , law of one price.
Et nominal exchange rate (pesos per dollar).
∗
PtT foreign-currency (dollar) price of tradables,
∗
normalized to unity, PtT = 1.
⇒ PtT = Et .
Profit Maximization Condition
pt =
Wt/Et
F 0(ht)
10
The Supply of Nontraded Goods
p
W0 /E0
F 0 (h)
W0 /E1
F 0 (h)
h
(E1 > E0)
11
Downward Nominal Wage Rigidity
Wt ≥ γWt−1
γ = degree of downward wage rigidity.
γ = 0 ⇒ fully flexible wages.
Think of γ as being around 1. Schmitt-Groh´
e and Uribe (2013)
estimate γ = 0.99 at quarterly frequency.
12
Optimal Exchange-Rate Policy
p
A2 (cT0 , F (h))
A1 (cT0 , F (h))
A2 (cT1 , F (h))
p0
pPEG
A1 (cT1 , F (h))
A
W0 /E0
F 0 (h)
C
W0 /E1
F 0 (h)
B
pOPT
hPEG
¯ = hOPT
h
h
T
cT
1 < c0
E1 > E0 (optimal devaluation)
13
The Government
• Each period t, the government can be either in good financial
standing or in bad financial standing.
• If the government is in good financial standing, it can choose
to either honor its debt (indicated by It = 1) or default. If it defaults, it immediately acquires bad financial standing (indicated
by It = 0).
• If the government is in bad financial standing in t, then it
regains good financial standing in t+1 with exogenous probability
θ, and maintains bad standing with probability 1 − θ.
14
Two Exogenous Cost of Default II
(1) Financial Exclusion: While the country is in bad financial
standing (It = 0), it cannot participate in international credit
markets,
(1 − It)dt+1 = 0.
(2) Output Loss: The endowment received by households, is
given by
(
ytT
if It = 1 (good standing)
ytT − L(ytT ) if It = 0 (bad standing)
where L(·) is a nondecreasing (loss) function and ytT is an exogenous stochastic process.
15
A Typical Default Episode Under Optimal Policy
Consumption of Tradables, cTt
1
1
0.95
ytT &
0.95
0.85
↑ ytT − L(ytT )
0.8
−12 −8 −4
0
4
8
12
Real Wage, wt
0.58
1.6
0.56
1.4
0
4
8
12
0.48
−12 −8 −4
2
2.6
5
1.8
2.4
1.6
2.2
0
4
8
12
2
−12 −8 −4
0
4
8
4
8
12
4
8
12
20
15
4
2
−12 −8 −4
0
Capital Control Tax, τtd
10
3
0
0.8
−12 −8 −4
12
Risk premium
%/yr
6
1.4
−12 −8 −4
1
0.5
Relative Price of Nontradables, pt
2.8
2.2
1.2
0.52
0.85
0.8
−12 −8 −4
Nominal Exchange Rate, Et
0.54
0.9
0.9
Debt, dt
%
Tradable Output
0
4
8
12
5
−12 −8 −4
16
0
4
8
12
A Typical Default Episode Under A Currency Peg
Tradable Endowment, yT
t
1.2
T
Debt, dt
Consumption of Tradables, ct
1
Unemployment Rate, 1− ht
0.8
20
1
%
0.6
0.9
10
0.4
4
8
12
Real Wage, w
0
4
8
0.2
−12 −8 −4
12
Relative Price of Nontradables, p
t
3
2
4
8
12
4
8
0
−12 −8 −4
12
2
−12 −8 −4
0
peg
4
8
12
0
4
8
12
Capital Control Tax, τd
t
10
2.5
0
0
Risk premium, r−r*
t
2.5
1.5
−12 −8 −4
0.8
−12 −8 −4
20
15
%
0
%/yr
0.8
−12 −8 −4
5
10
0
−12 −8 −4
0
4
8
12
5
−12 −8 −4
optimal devaluation
17
0
4
8
12
Peggers can support less external debt
2.5
Currency Peg
Optimal Devaluation Policy
2
density
1.5
1
0.5
0
−1
−0.5
0
0.5
external debt (dt)
1
1.5
Note. Debt distributions are conditional on being in good financial standing.
18
Conclusions
• This paper shows that real economies with default risk `
a la
Eaton-Gersovitz can be interpreted as the centralized version of
economies with default risk, downward nominal wage rigidity,
optimal capital controls, and optimal devaluation policy.
• The model developed in this paper predicts that under the
optimal policy defaults are accompanied by large devaluations.
Hence the Twin Ds phenomenon emerges as an optimal outcome.
• In the model, the central role of devaluations around default
episodes is to fend off unemployment.
• Under currency pegs, defaults are predicted to be accompanied
by massive unemployment.
• Fixed-exchange-rate economies are shown to support much less
debt in equilibrium than optimal float economies.
19
Extras
20
Functional Forms and Calibration
• Time unit: one quarter
• Probability of reentry: θ = 0.0385
1−σ −1
c
• U (c) = 1−σ ; σ = 2
• A(cT , cN ) =
1− 1ξ
T
a(c )
+ (1 −
11
1
1− 1− ξ
a)(cN ) ξ
;
ξ=1
2 ; a = 0.26
• ytN = hα
α = 0.75
t;
• Output loss function: L(ytT ) = max {0, δ1ytT + δ2(ytT )2}
• Set β = 0.85, δ1 = −0.35, and δ2 = 0.44 to ensure:
(a) E(dt/ytT ) = 60%,
(b) Prob of default equal to 2.6 per century, and
(c) Average output loss in autarky of 7%.
• Set γ = 0.99 ⇒ wages can fall by up to 4% per year.
T +0.037µ ; µ ∼ N (0, 1) (Argentina, 1983:1-2001:4)
•ytT = 0.93yt−1
t
21
The Twin Ds: Six Examples
Uruguay
Argentina
5
2.5
2
1.5
Exchange Rate
2.5
Exchange Rate
Exchange Rate
3
Ukraine
2
1.5
1
1
1998
2000
2002
Year
2004
2006
2002
2004
Year
2006
1996
Paraguay
6
4
2
1
2004
2000
Year
2002
2004
Ecuador
2
1.8
1.6
1.4
1.2
1
2002
1998
10
Exchange Rate
Exchange Rate
Exchange Rate
8
2000
Year
2
2008
2.2
1998
3
1
2000
Russia
1996
4
2000
2002
2004
Year
Nominal Exchange Rate
2006
2008
8
6
4
2
1
0
1996
1998
2000
Year
2002
Default Date
Note: Exchange rates are nominal dollar exchange rates, annual average, first observation
normalized to unity. Data sources: Default dates from Moody’s (2011) and Standard &
Poor’s (2006). Nominal exchange rates from World Development Indicators.
22
Average Debt And Default Probability Across Devaluation
Policies
Debt-to-traded-output ratio (qtr)
Number of Defaults per century
Optimal
Devaluation Currency
Policy
Peg
60%
20%
2.6
2.0
23
Data and Model Predictions: Optimal Devaluation Policy
Data
Model
E(r − r∗ )
7.4
3.5
σ(r − r∗ )
2.9
3.2
corr(r − r∗, y)
-0.64
-0.54
corr(r − r∗ , tb/y)
0.72
0.81
Note. Data moments are from Argentina over the inter-default period 1994:1 to 2001:3,
except for the default frequency, which is calculated over the period 1824 to 2013.
In
the theoretical model, all moments are conditional on the country being in good financial
standing.
24
Business-Cycle Statistics:
Data and Model Predictions Under Optimal Exchange Rate Policy
σ(c)/σ(y) σ(tb/y)/σ(y) corr(c, y) corr(tb/y, y)
Data
Emerging Countries
1.23
0.69
0.72
-0.51
Argentina
1.11
0.48
0.75
-0.87
Model
1.22
0.57
0.88
-0.14
25
Do Countries Default in Bad Times?
Output Around Default Episodes
5
4
3
Percent deviation from trend
2
1
0
−1
−2
−3
−4
−5
−3
−2
−1
0
Years after default
1
2
3
Source: Uribe and Schmitt-Groh´
e, Open Economy Macroeconomics, 2014. Output is measured as real per capita GDP, log quadratically detrended at annual frequency. Median across
105 default episodes over the period 1975-2014.
26
Consumption, Investment, The Trade Balance, and The
Real Exchange Rate Around Default Episodes
Consumption
Investment
20
Percent deviation from trend
Percent deviation from trend
6
4
2
0
−2
−4
−3
−2
−1
0
1
Years after default
2
3
10
Source: Uribe and Schmitt-Groh´
e, Open
0
Economy Macroeconomics, 2014. Con-
−10
−20
−3
sumption, investment, and the real ex−2
Trade−Balance−To−Output Ratio
3
1
0.5
0
−0.5
−2
−1
0
1
Years after default
2
3
change rate are log-quadratically detrended.
4
Percent deviation from trend
Percent deviation from trend
2
Real Exchange Rate
1.5
−1
−3
−1
0
1
Years after default
The trade-balance-to-output
ratio is linearly detrended.
2
0
An increase
in the real exchange rate indicates a real
−2
appreciation of the domestic currency.
−4
−6
−3
−2
−1
0
1
Years after default
2
3
27
Is there wage restraint during booms?
Example: Periphery of Europe during the 2000-2008 Boom
28
Boom-Bust Cycle in Peripherical Europe: 2000-2011
Current Account / GDP
Labor Cost Index, Nominal
−2
110
−4
100
Unemployment Rate
14
13
Percent
−6
−8
−10
90
11
Percent
Index, 2008 = 100
12
80
10
9
70
8
−12
−14
60
2002 2004 2006 2008 2010
Date
50
7
2002 2004 2006 2008 2010
Date
6
2002 2004 2006 2008 2010
Date
Data Source: Eurostat. Data represents arithmetic mean of Bulgaria, Cyprus,
Estonia, Greece, Ireland, Lithuania, Latvia, Portugal, Spain, Slovenia, and Slovakia
⇒ Wages grew by 70 percent between 2000 and 2008!
29
Let’s take a closer look at Spain and Ireland ...
30
Nominal hourly wages in Spain increase by 44 percent during the 2000-2008 boom
Nominal Hourly Wages: Spain
Index, 2008 = 100
110
100
90
80
70
60
2000 2002 2004 2006 2008 2010 2012
31
Nominal hourly wages in Ireland increase by 57 percent
during the 2000-2008 boom
Nominal Hourly Wages: Ireland
Index, 2008 = 100
110
100
90
80
70
60
2000 2002 2004 2006 2008 2010 2012
32
... Despite No Growth in Total Factor
Productivity
115
Spain
Ireland
TFP, Index 1995=100
110
105
100
95
90
1996
1998
2000
2002
2004
2006
33
Total Factor Productivity: 2000-2007
(value added based), Index (1995=100)
2000 2001 2002 2003 2004 2005 2006 2007
Spain
96.2
95.6
94.8
94.1
93.4
92.4
91.9
92.1
Ireland 109.0 111.2 112.6 110.5 110.9 108.6 106.4 107.8
Source: EU KLEMS Growth and Productivity Accounts. This database includes measures of output and input growth, and derived variables such as
multifactor productivity at the industry level. The input measures include
various categories of capital (K), labour (L), energy (E), material (M) and
service inputs (S). The measures are developed for 25 individual EU member
states, the US and Japan and cover the period from 1970 to 2007. The
variables are organised around the growth accounting methodology, a major
advantage of which is that it is rooted in neo-classical production theory. It
provides a clear conceptual framework within which the interaction between
variables can be analysed in an internally consistent way. The data series are
publicly available on http://www.euklems.net. November 2009 release.
34
Evidence On Downward Nominal Wage Rigidity
• Downward nominal wage rigidity is the central friction in the
present model ⇒ natural to ask if it is empirically relevant.
• Downward wage rigidity is a widespread phenomenon:
— Evident in micro and macro data.
— Rich, emerging, and poor countries.
— Developed and underdeveloped regions of the world.
• Byproduct: Will obtain an estimate of the parameter γ governing wage stickiness in the model (useful for quantitative analysis).
35
Downward Nominal Wage Rigidity:
Evidence From Micro Data
36
Probability of Decline, Increase, or No Change in Wages
U.S. data, SIPP panel 1986-1993, between interviews one year apart.
Decline
Constant
Increase
Interviews One Year apart
Males
Females
5.1%
4.3%
53.7%
49.2%
41.2%
46.5%
Source: Gottschalk (2005)
• Large mass at ‘Constant’ suggests nominal wage rigidity.
• Small mass at ’Decline’ suggests downward nominal wage rigidity.
37
Distribution of Non-Zero Nominal Wage Changes
United States 1996-1999
Source: Barattieri, Basu, and Gottschalk (2012)
38
Evidence From The Great Contraction Of 2007
Distribution of Nominal Wage Changes, U.S. 2011
Source: Daly, Hobijn, and Lucking (2012).
39
Micro Evidence On Downward Nominal Wage Rigidity From
Other Developed Countries
• Canada: Fortin (1996).
• Japan: Kuroda and Yamamoto (2003).
• Switzerland: Fehr and Goette (2005).
• Industry-Level Data: Holden and Wulfsberg (2008), 19 OECD
countries from 1973 to 1999.
40
Evidence From Informal Labor Markets
• Kaur (2012) examines the behavior of nominal wages, employment, and rainfall in casual daily agricultural labor markets in
rural India (500 districts from 1956 to 2008).
• Finds asymmetric nominal wage adjustment:
— Wt increases in response to positive rainfall shocks
— Wt fails to fall, labor rationing, and unemployment are observed in response to negative rain shocks.
• Inflation (uncorrelated with local rain shocks) tends to moderate rationing and unemployment during negative rain shocks,
suggesting downward rigidity in nominal rather than real wages.
41
Evidence From the Great Depression,1929-1933
• Enormous contraction in employment: 31% between 1929 and
1931.
• Nonetheless, during this period nominal wages fell by 0.6% per
year, while consumer prices fell by 6.6% per year. See the figure
on the next slide.
• A similar pattern is observed during the second half of the
Depression. By 1933, real wages were 26% higher than in 1929,
in spite of a highly distressed labor market.
42
Nominal Wage Rate and Consumer Prices, United States
1923:1-1935:7
0.05
0
1929:8=0
−0.05
−0.1
−0.15
−0.2
−0.25
−0.3
log(Nominal Wage Index)
log(CPI Index)
1924
1926
1928
1930
1932
1934
Year
Solid line: natural logarithm of an index of manufacturing money wage rates. Broken line:
logarithm of the consumer price index.
43
Evidence From the Great Depression In Europe
• Countries that left the gold standard earlier recovred faster
than countries that remained on gold.
— Left Gold Early (sterlingbloc): United Kingdom, Sweden,
Finland, Norway, and Denmark.
— Countries That Stuck To Gold (gold bloc): France, Belgium, the Netherlands, and Italy.
• Think of the gold standard as a currency peg (a peg not to a
currency, but to gold).
• When sterling-bloc left gold, they effectively devalued, as their
currencies lost value against gold.
• Look at the figure on the next slide. Between 1929 and 1935,
sterling-bloc countries experienced less real wage growth and
larger increases in industrial production than gold-bloc countries.
44
Changes In Real Wages and Industrial Production,
1929-1935
Source. Eichengreen and Sachs (1985).
45
Evidence From Emerging Countries
• Argentina: pegged the peso at a 1-to-1 rate to the dollar
between 1991 and 2001.
•Starting in 1998, the economy was buffeted by a number of
large negative shocks (weak commodity prices, large devaluation
in Brazil, large increase in country premium, etc.).
• Not surprisingly, between 1998 and 2001, unemployment rose
sharply.
• Nontheless, nominal wages remained remarkably flat.
• This evidence suggests that nominal wages are downwardly
rigid, and that γ is about 1.
• Why γ ≈ 1? The slackness condition (¯
h − ht)(Wt − γWt−1 )
(recall t = 1 during this period), implies that if unemployment
is growing, wages must grow at the gross rate γ.
46
Evidence From Peripheral Europe (2008-2011)
• Look at the table on the next slide.
• Between 2008 and 2011, all countries in the periphery of Europe experienced increases in unemployment. Some very large
increases.
• In spite of this context of extreme duress, nominal hourly wages
experienced significant increases in most countries and modest
declines in very few.
• The slide following the table explains how to use the information in the table to infer a range for γ.
47
Unemployment, Nominal Wages, and γ
Evidence from the Eurozone
Unemployment Rate
2008Q1
2011Q2
Country
Bulgaria
Cyprus
Estonia
Greece
Ireland
Italy
Lithuania
Latvia
Portugal
Spain
Slovenia
Slovakia
Wage Growth
W2011Q2
W2008Q1
(in percent)
(in percent)
(in percent)
6.1
3.8
4.1
7.8
4.9
6.4
4.1
6.1
8.3
9.2
4.7
10.2
11.3
6.9
12.8
16.7
14.3
8.2
15.6
16.2
12.5
20.8
7.9
13.3
43.3
10.7
2.5
-2.3
0.5
10.0
-5.1
-0.6
1.91
8.0
12.5
13.4
Implied
Value of
γ
1.028
1.008
1.002
0.9982
1.0004
1.007
0.996
0.9995
1.001
1.006
1.009
1.010
Source: EuroStat.
48
How To Infer γ
The model implies that if unemployment increaes form one period to the next, then nominal wages must be growing at the
rate γ.
How to calculate γ:
γ=
W2011:Q2
W2008:Q1
!
1
13
Subtract 0.6% per quarter to adjust for foreign inflation and
long-run growth (because they are not explicitly incorporated in
the model) to obtain the estimate:
γ ∈ [0.99, 1.022]
49