%slides_sovereign_debt.tex
%Slides for Chapter 13 of ``Open Economy Macroeconomics'' by Martín Uribe and Stephanie Schmitt-Grohé, Princeton University Press 2017. 
%© Martín Uribe and Stephanie Schmitt-Grohé.

\input{slides_preamble}

\begin{slide}
\begin{minipage}{5in}
\rightline{\includegraphics[width=4.5in]{USG_cover.eps}}

\centerline{\tiny  Princeton University Press,  2017}
\end{minipage}
\begin{minipage}{5in}
\centering 
{\small slides 

chapter 13   

  sovereign default}



\vspace{1in}
\end{minipage}
\end{slide}


\topleft{\textit{Open Economy Macroeconomics, Chapter 13} }
\topright{M.\ Uribe and S.\ Schmitt-Groh\'e}



 
\begin{slide}
{\bf \large Motivation}

$\bullet$ We do observe a significant amount of borrowing and lending across nations. 

$\bullet$ But why do countries pay their international debts?

$\bullet$ There is no  supranational authority capable of enforcing international debt  contracts. 

$\bullet$ Defaulting on international financial contracts appears to have no legal consequences.


\end{slide}

\begin{slide}

$\bullet$ Two reasons typically offered for why countries honor their  debts: \\
1. Economic sanctions\\
2. Reputation 

$\bullet$ In this chapter: 

-- Empirical regularities about international lending, default, and costs of default. 

-- Theoretical models of sovereign debt. 

-- Quantitative models of sovereign debt. 

\end{slide}

\begin{slide}
\begin{center}

{\bf Section 13.1}

{\bf \large  Sovereign Default:
 Empirical Regularities}

\end{center}
\end{slide}



\begin{slide}
{\bf \large Empirical Definition of Default}\\
Much of the data on sovereign default is produced by credit rating agencies, especially Standard and Poor's (S\&P). 


{\bf Entrance To Default Status:} S\&P defines default as the failure to meet a principal or interest payment on the due date. 
This includes  situations in which the sovereign 
forces an exchange  of old  debt for  new debt with less-favorable terms or  converts debt  into a different 
currency of less   value.

{\bf Exit From Default Status:}
S\&P considers a country to have   emerged from default when it resumes payments of interest and principal (including arrears), or 
after a debt settlement 
that leads the rating agency 
to conclude that no further near-term resolution of creditors' claims is likely. 


\end{slide}

\begin{slide}
\centerline{\bf Table 13.1 Frequency And  Length of Sovereign Defaults: 1824-2014% \label{table:sd_default_probability}
}
\centerline{\begin{tabular}{lcccc}
\hline\hline
&Number of        &\multicolumn{2}{c}{Probability of Default} & Years in State of\\
\cline{3-4}
&Defaults &  all  &years not &Default per\\
Country&1824-2014 & years &in default& Default Episode\\
\hline
Argentina&   5&  0.026&  0.035&  10\\
Brazil&   7&  0.037&  0.047&   6\\
Chile&   3&  0.016&  0.020&  14\\
Colombia&   7&  0.037&  0.058&  10\\
Egypt&   2&  0.010&  0.012&  11\\
Mexico&   8&  0.042&  0.056&   6\\
Philippines&   1&  0.005&  0.006&  32\\
Turkey&   6&  0.031&  0.037&   5\\
Venezuela&  10&  0.052&  0.079&   6\\
\hline
Mean&5.4&  0.029&  0.039&  11\\
\hline\hline
\end{tabular}}
%produced with: sd_default_probability.m in directory 
%z:\uribe\book\sovereign_debt
%%%%%%%%%%%%%%%%%

{\tiny Note. The sample includes only emerging countries with at least one external-debt default  or restructuring episode between 1824 and 1999.  The 2014 selective default of Argentina with 1 percent of the holdout investors that did not enter the debt restructurings of 2005 and 2010 is not counted as a default event. 
Source: Own calculations based on
 Reinhart, Rogoff, and Savastano (2003) table 1 for the period 1824-1999 and 
 USG (2017) table 13.19 for the period 2000-2014.\par}
\end{slide}

\begin{slide}
Observations

{
$\bullet$ 49 defaults in 9 countries over 191 years. $\Rightarrow$ average probability of default is 2.9\% per year (once per 33 years). 

$\bullet$ suppose we divide not by all years, but only by years not in default, then the average probability of default is 3.9\% per year. 

$\bullet$ When a country defaults it stays in default status on average for 11 years. 

}

\end{slide}

\begin{slide}

\centerline{\bf \large Has The Frequency and Length}
\centerline{\bf \large Of Default Changed Over Time?}

\vspace{0.5in}


\centerline{\bf Table 13.2 
 1824-1999 Versus 1975-2014}
\medskip

\centerline{\begin{tabular}{lcc}
\hline\hline
        &Probability & Years in State of\\
 &of Default & Default per\\
Period & per year & Default Episode\\
\hline
1824-1999&0.029&11\\
1975-2014&0.040&8\\
\hline\hline
\end{tabular}
}



{\bf Observation:} Defaults have become more frequent but shorter. Important for calibrating default models. 
\end{slide}

\begin{slide}

\begin{minipage}{5in}
{\large \bf Figure 13.1 Distribution Of The Length Of Default Episodes}

\rightline{\includegraphics[width=5in]{sd_length_of_default_slides.eps}}
%Produced with length_of_default.m
%in
%c:\data\uribe\book\sovereign_debt\data
1975-2014 sample of 147 defaults in 93 defaulting nations

\end{minipage}\hfill\begin{minipage}{4in}
\centerline{\bf Observations on figure} 

{(1) Distribution of length of default  is  skewed (mean 8 years, median 5). \par}

{(2) Distribution looks exponential $\Rightarrow$ not unreasonable to assume probability of reaccess to credit markets constant over time as in most Eaton-Gersovitz-style models of default. \par}

\end{minipage}

\end{slide}

\begin{slide}
\begin{center}
{\bf \large 13.1.2 Haircuts\\ The Size of Defaults}
\end{center}
$\bullet$ Most models of default assume that defaults are always on 100\% of the debt.  
In reality, this is not the case. 

$\bullet$ A haircut is the  loss inflicted to creditors upon  restructuring, measured as  the decrease in the present value of current and future expected payments. 

$\bullet$ A number of studies estimate  similar values of haircuts (Sturzenegger and Zettelmeyer, 2008; Cruces and Trebesch, 2013; Benjamin and Wright, 2008):

--  Average Haircut: 40\%\\
--  Standard deviation of haircut: 22\%.
\end{slide}


\begin{slide}
\centerline{\bf Debt to GNP Ratio is Higher Than Usual Prior to Default}

\medskip

\centering

{Table 13.3 Debt-to-GNP Ratios  Among Defaulters: 1970-2000 \label{table:sd_debt_default}}

\begin{tabular}{lcc}
\hline\hline
      &Average       &Debt-to-GNP \\    &Debt-to-GNP&Ratio in Year  \\
Country&Ratio &of Default \\
\hline
Argentina &37.1 & 54.4 \\
Brazil &30.7 & 50.1 \\
Chile &58.4 & 63.7 \\
Colombia &33.6 & \\
Egypt &70.6 & 112.0 \\
Mexico &38.2 & 46.7 \\
Philippines & 55.2 & 70.6  \\
Turkey &31.5 & 21.0\\
Venezuela&41.3 & 46.3 \\
\hline
Average &44.1 &58.1 \\
\hline\hline
\end{tabular}

{\tiny Source: Own calculations based on Reinhart, Rogoff, and Savastano (2003), tables 3 and 6. \par}
\end{slide}




\begin{slide}
\begin{center}
{\bf \large Table 13.4 Interest Rate Spreads Among Defaulters: 1999-2013 \label{table:sd_country_premium}}


{\begin{tabular}{lcc}
\hline\hline
&\multicolumn{2}{c}{Average Country Spread}\\
    \cline{2-3} &  All & Years Not  \\
Country&Years&In Default\\
\hline
Argentina  & 15.8&7.43 \\
Brazil  & 5.61&5.61 \\
Chile  & 1.44&1.44 \\
Colombia  & 3.70&3.70 \\
Egypt &2.46&2.46 \\
Mexico & 3.47&3.47 \\
Philippines & 3.49&3.49 \\
Turkey & 4.10&4.10 \\
Venezuela & 9.24&9.23\\
\hline
Average  & 5.5&4.5 \\
\hline\hline
\end{tabular}}
%Spread Data taken from Excel Spreadsheet: sd_default_debt_premium.xlsx in the directory U:\uribe\book\sovereign_debt ; October 2, 2014. 
%%%%%%%%%%%%%%%%%
\end{center}
{\tiny
Notes:  The sample includes only emerging countries with at least one external-debt default  or restructuring episode between 1824 and 1999.  
 Country spreads are measured using the EMBI Global index,  produced by 
J.P.\ Morgan, and expressed in percent, and are averages through 2013, with varying starting dates as follows: Argentina  1994; 
Brazil 1995;
Chile 2000; 
Colombia 1998;
Egypt 2002; 
Mexico 1994; 
Philippines 1998;
Turkey 1997; 
Venezuela 1994. 
Start and end dates of default episodes are taken from table 13.9 of USG (2017).\par}
\end{slide}
\begin{slide}
\begin{center}
{\bf The Spread-Default-Frequency Differential is Positive}
\\
{After Correcting for the Sample-Mismatch Bias}
\end{center}
\centerline{Table 13.5}
\centerline{\small \begin{tabular}{lcccc}
\hline\hline
&Sample&Country Spread 
&\multicolumn{2}{c}{Default Probability} \\
&for spread&(percent)&common& 1824-2014\\
\hline
Argentina & 1994-2013& 7.43&  6.7&3.5\\
Brazil &1995-2013 & 5.61&   0&4.7\\
Chile & 2000-2013 &1.44&   0&2.0\\
Colombia&1998-2013&3.70&0&5.8\\
Egypt&2002-2013&2.56&0&1.2\\
Mexico &1994-2013&  3.47&   0&5.6\\
Philippines&1998-2013&  3.49&   0&0.6\\
Turkey& 1997-2013& 4.10&   0&3.7\\
Venezuela&1994-2013&9.23&13.3&7.9\\
\hline
Mean& &  4.5&   2.2&3.9\\
\hline\hline
\end{tabular}}

\vfill 

{\small {\bf The sample-mismatch bias:}  Due to data limitations, spread samples are short,  starting in the mid 1990s or later for  most countries. By contrast, default data is much longer, starting at least in  1975 and going back almost two centuries for some countries.  Computing  spread default-frequency differentials using samples of different lengths yields quite different results than using samples spanning the same periods.}\\
{\small With risk neutral lenders,  spreads should equal default probability.
With partial default, and risk neutral lenders, spreads should be smaller than default probabilities. Evidence of spreads in excess of default probability suggests risk aversion on the part of  lenders. \par }

\end{slide}
\begin{slide}
\centerline{\bf\large Do Countries Default In Bad Time? Yes.}

\centerline{\bf Figure 13.2 Output Around Default Episodes}

\centerline{\includegraphics[width=4.5in]{sd_default_bad_times.eps}}

{\small Note: Annual log-quadratically detrended real GDP per capita.   The year of default is normalized to 0. Median over 105 default episodes between 1975 and 2014.  \par}
%Produced with default.m
%in
%c:\data\uribe\book\sovereign_debt\data
\end{slide}


\begin{slide}
{\bf Observations}\\
{\small $\bullet$ Detrended output falls by 6.5 percent in the 3 years leading up to default. 

$\bullet$ 75 percent of the default episodes are associated with a contraction in detrended output (i.e, a fall in detrended output between years -1 and 0). 

$\bullet$ Relation to Tomz and Wright (2007): Also find that countries default in bad times, but claim that the evidence is weak. Why? \\
-- In the period of default output is only 1.5 percent below trend.  Same true in current data set,  but what about the 5\% contraction  in output between years -3 and -1? 

-- Tomz and Wright find that  in only 60 percent of the default episodes output is below trend. Same true in current data set. But if one asks how many countries are contracting at the time of default (i.e., displaying a fall in output), the answer is 75\%. 

$\bullet$ {Default comes at the end of a large contraction and the beginning of a growth (but not level) recovery as stressed by Levy-Yeyati and Panizza (2011). \par}
}
\end{slide}

\begin{slide}
{ \bf Other Macro Indicators  Around Defaults}
support view that countries default in bad times

\centerline{\tiny Figure 13.3 Consumption, investment, the trade balance, }\centerline{\tiny and the real exchange rate around default episodes}
\centerline{\includegraphics[width=6.75in]{sd_default_other_variables.eps}}
%Produced by running default_other_variables.m
%in
%c:\data\uribe\book\sovereign_debt\data
\end{slide}

\begin{slide}
{\bf Observations}\\
$\bullet$ Consumption contracts by as much as output in the run up  to  default (about 6 percent). 

$\bullet$ The contraction of investment leading up  to default is 3 times as large as that of output. 

$\bullet$ The trade balance is below average up until the year of default. And in the year  of default it experiences a reversal of about 2\% of GDP. 

$\bullet$ The real exchange rate depreciates significantly in the default year
(by over  4\%), and then begins to gradually appreciate. 

\end{slide}

\begin{slide}



\centering

{\bf \large 

Section 13.2 

The Cost of Default: 

Empirical Evidence}

\end{slide}

\begin{slide}
What are possible costs of default?
\begin{enumerate}
  \item Use of force?
  \item Financial Exclusion? (Reputation)
  \item Output Losses?
  \item Reductions in trade?
  \end{enumerate}
\end{slide}


\begin{slide}

\begin{minipage}{4.5in}
\centerline{\bf The Drago Doctrine---No Use of Force}
\rightline{\includegraphics[width=4.5in]{sd_Drago_sculpture.eps}}
\centerline{\Tiny Photo Credit: Crist\'obal Uribe, Buenos Aires, December 2015.}
\end{minipage}
\begin{minipage}{4.5in}
{\small  The use of force by one country or a group of countries to
 collect debt from another country was not uncommon until the beginning of the twentieth century. In  1902,  an attempt by Great Britain,
 Germany, and Italy to collect the public debt of Venezuela by force prompted the Argentine  jurist {\bf Luis-Mar\'{\i}a Drago}, who at the time was serving as minister of foreign affairs of Argentina, to articulate a doctrine stating that  no public debt should be collected from a sovereign American state by armed force or through the occupation of American territory by a foreign power.
{\bf  The Drago doctrine } was  approved by the  Hague Conference of 1907.\par}
\end{minipage}
\end{slide}

\begin{slide}
\centering{\bf \large Exclusion Costs}{\bf  \\Are Defaulters Excluded From Financial Markets? \\And For How Long?}\\


\begin{tabular}{lcc}
\hline\hline
            &Partial&Full\\
           &Reaccess&Reaccess\\
Measure&{\small (flows$>0$)}&{\small(flows$>1\%$GDP)}\\
\hline
Length of Default*
&8&\\
Issuance of New Debt\\
-Gelos, et al. (2011)*&4.7&\\
-Richmond and Dias (2009)**&5.7&8.4\\
-Adjusted
Richmond and Dias*&13.7&16.4\\
-Cruces and Trebesch (2013)**&5.1&7.4
\\
-Adjusted Cruces and Trebesch*&13.1&15.4\\
\hline
Average&9.8&15.9\\
\hline\hline
\end{tabular}
\begin{quote}
{\small Note. Reaccess  is measured in years. after the beginning of default (*) or in years after the end of default (**).
Averages are taken over single-star lines.}
\end{quote}

\end{slide}

\begin{slide}
{\bf Observations}\\
$\bullet$ Estimates of the average length of the exclusion period is important for the calibration of default models. 

$\bullet$ The change in net external  debt is an  equilibrium outcome. 
Thus, if a country does not borrow, it could be due to lack of demand, and not necessarily to a supply restriction motivated by  punishment.  Thus, estimates of exclusion may carry an upward bias. 


\end{slide}

\begin{slide}
{\bf \large Determinants of the Exclusion Period}

$\bullet$ Frequency of default is not a significant determinant of the length of exclusion (Gelos et al., 2011)

$\bullet$ Defaults that resolve quickly  are associated with  short  exclusion periods (Gelos et al., 2011). 

$\bullet$ Excusable 
defaults (such as those following a natural disaster) are associated with reduced exclusion periods (Richmond and Dias, 2009). 

$\bullet$  Restructurings involving higher  hair cuts (i.e., higher losses to creditors)  are associated with significantly longer periods of capital market exclusion (Cruces and Trebesch, 2013).
 
$\bullet$ In most theoretical models of default, the  length of exclusion  is assumed to be random and  exogenous. 

\end{slide}

\begin{slide}

{\bf \large Output Cost of Default}

 Theoretical default literature relies on assumption that default leads to output loss. What does the data show?

Standard approach: Growth regressions   augmented with default variables (see, for example, Chuan and Sturzenegger, 2005; Borensztein and Panizza, 2009;  De Paoli, Hoggarth, and Saporta, 2006; and Levy Yeyati and Panizza, 2011).
\end{slide}

\begin{slide}
{\bf \large Default Dummies in Growth Regressions}

Borensztein and Panizza (2009) estimate the equation
\[
\mbox{Growth}_{it} = \alpha + \beta X_{it} +
\gamma \mbox{Default}_{it}
+\sum_{j=0}^3
\delta_j  \mbox{DefaultB}_{it-j} 
\]
where  $\mbox{Growth}_{it}$ is the growth rate of real per capital GDP in country $i$ between years $t-1$ and $t$, $X_{it}$ is a vector of standard controls in growth regressions (initial income, education, population, etc.), $\mbox{Default}_{it}$ is a dummy taking the value 1 if  country $i$ is in default in year $t$ and 0 otherwise, and $\mbox{DefaultB}_{it}$ is a dummy taking the value 1 if country $i$ enters default in year $t$. 
\end{slide}

\begin{slide}
{\bf Estimation Results}\\
Using annual data for 83 countries for the period 1972 to 2000,  Borensztein and Panizza estimate 
\begin{eqnarray*}
\mbox{Growth}_{it} &=& \alpha + \beta X_{it} -1.184 \mbox{Default}_{it}\\
&&
- 1.388  \mbox{DefaultB}_{it} 
+0.481 \mbox{DefaultB}_{it-1} 
\\&&
+0.337 \mbox{DefaultB}_{it-2}
+0.994 \mbox{DefaultB}_{it-3}
\end{eqnarray*}
with $\gamma$ and $\delta_0$ significant at confidence level of 5\% or less.

This estimate implies that the beginning of a default is associated with a fall in the growth rate of 2.5 percentage points ($=\gamma+\delta_0$). 

More importantly, default is associated with a permanent loss of output. This is shown in  the 
next figure, which displays a simulation of the log of output per capita implied by the regression equation (default occurs in period 0). 

\end{slide}

\begin{slide}
{\centering 
{\bf \large Simulated Path Of Output After A Default\\
Implied By the Borensztein-Panizza  Regression}


\centerline{\includegraphics[width=5in]{sd_borensztein_panizza.eps}}
%Produced with borensztein_panizza.m
%in
%c:\data\uribe\book\sovereign_debt\data
}

{\small  In producing the figure, long-run growth is set to  1.5\%, and  exclusion is set to 5 years (median from figure 13.1)}
\end{slide}

\begin{slide}
{\bf Observations on Default Dummies in Growth Regressions}

$\bullet$ After an initial fall,  growth gradually regains its long-run level. 

$\bullet$  However, the level of output never recovers.  It remains  5.5\% below the no-default trajectory.  Taken at  face value,  the cost of default is enormous. 

$\bullet$  Reasons why the output loss estimate can be upwardly biased:\\
-- The regression doesn't include lags in the variable $\mbox{Default}_{it}$ and may include insufficient lags in $\mbox{DefaultB}_{it}$. If they entered with positive signs, these extra lags could capture a catch-up effect. 
\\
-- {\bf More importantly,} output growth and default are both endogenous variables. Not clear who causes whom. If default occurs during recessions, estimated effect of default may be negative even if in reality they are zero. 
\end{slide}

\begin{slide}
{\bf Output Cost Of Default: A Growth Accounting Approach (Zarazaga, 2012)}\\
Take a look  at the behavior of  the  capital-output ratio around  the Argentine defaults of 1982 and 2001:

\centerline{\includegraphics[width=4.5in]{sd_zarazaga.eps}}
%this figure was cropped from chart 2 of 

Observation: Both defaults are associated with a fall in the capital-output ratio. What does this imply for output per worker? 
\end{slide}
\begin{slide}
{\bf \large Default and Growth Accounting (continued)}: Let the production function be\\ $y_t=k_t^{0.4}h_t^{0.6}\Rightarrow
y_t/h_t = (k_t/y_t)^{2/3}$\\
In the 2002 default, $k_t/y_t$ fell from 1.9 to 1.35 in 2007. Therefore, \\
$ \mbox{ Percent change in } y_t/h_t$  equals  
$\left[
\left(\frac{1.9}{1.35}\right)^{2/3}-1
\right]\times 100 = 26\%
$. 
This means that, on average, output was 13\% (=26\%/2) lower every year between 2002 and 2007. Large output cost of default!

{\bf Usual cautionary note:} This calculation assumes that all of the change in $k_t/y_t$ is due to default. 
But causality may go the other way as well. 
To the extent that this is the case, the 13\% output loss must be interpreted as an upper bound of the cost of default. 

\end{slide}


\begin{slide}
\centerline{\bf \large Trade Costs of Default}


{\bf Hypothesis: }
Countries honor their debts, among other things,  to avoid trade sanctions. 


 {\small Rose (2005) sets out to test this hypothesis by  estimating the following gravity model augmented with default variables:}

\centerline{$\ln T_{ijt} = \beta_0 +\beta X_{ijt}
+ \sum_{m=0}^M
\phi_{m} ACRED_{ijt-m} +\epsilon_{ijt}$}

{\bf Definitions:} $T_{ijt}=$ real value of trade between countries $i$ and $j$ in year $t$; $X_{ijt} =$ usual gravity variables; $ACRED_{ijt}=1$  if 
one country is a  
restructuring debtor and the other a negotiating creditor (the affected creditor), 0 otherwise. \\
{\bf Sample: }1948-1997 annual, 217 countries. 

{\bf Finding:}  $\sum_{m=0}^{15}
\phi_{m}  = -1.12$.  Thus, the   cumulative cost  of default is over one year of trade over 16 years.  It looks like the trade costs of default are enormous. 

 But is it sanctions or general economic stress around default episodes?  Keep reading...

\end{slide}

\begin{slide}
\centerline{\large \bf Does Default Disrupt Int'l Trade So Much?}

Mart\'{\i}nez and Sandleris (2011) estimate the following variant of Rose's gravity model:
\[
\ln T_{ijt} = \beta_0 +
\beta X_{ijt}
+ \sum_{m=0}^M
\phi_{m} ACRED_{ijt-m} 
+ \sum_{m=0}^M
\gamma_{m} DEBTOR_{ijt-m} +\epsilon_{ijt},
\]
{\bf Definition:} $DEBTOR_{ijt}=1$ if either country is a restructuring debtor, 0 otherwise. 

{\bf Finding:} $ \sum_{m=0}^{15}
\phi_{m} = 0.01$ and  
$ \sum_{m=0}^{15}
\gamma_{m} = -0.41$.

{\bf Implication:} It might not be trade sanctions to defaulters, but general economic stress around default episodes. 

But if default is punished with collective trade sanctions, not just sanctions by the affected creditors, the variable $DEBTOR_{ijt}$ may not pick up just economic distress, but also the effect of collective punishment. 

\end{slide}
\begin{slide}
{\bf Controlling for  Collective Sanctions}
To control for collective sanctions, Mart\'{\i}nez and Sandleris (2011) estimate the following equation
\[
\ln T_{ijt} = \beta_0 +
\beta X_{ijt}
+ \sum_{m=0}^M \phi_{m} CRED_{ijt-m} 
+ \sum_{m=0}^M \gamma_{m} DEBTOR_{ijt-m} +\epsilon_{ijt}
\]
{\bf Definition:} $CRED_{ijt} = 1$ if one country is a renegotiating debtor and the other is a (not necessarily renegotiating) creditor. 

{\bf Finding:}  $\sum_{m=0}^M \phi_{m}$ positive at horizons 0, 5, and 10, and negative at horizons 15 or  longer. 

{\bf Interpretation:} No sanction effect, unless creditors have very long memories (at least 15 years) and are willing or have reasons to delay punishment. 
\end{slide}

\begin{slide}
{\bf Mart\'{\i}nez and  Sandleris III:}
\begin{eqnarray*}
\ln T_{ijt}& &= \beta_0 
+\beta X_{ijt}
+ \sum_{m=0}^M \phi_{m} ACRED_{ijt-m} 
+ \sum_{m=0}^M \xi_{m} NACRED_{ijt-m} \\
&&
+ \sum_{m=0}^M \gamma_{m} NOTCRED_{ijt-m} +\epsilon_{ijt}. 
\end{eqnarray*}
{\bf Definitions: } $NACRED_{ijt} = 1$ if one country is a renegotiating debtor and the other a nonrenegotiating creditor, 0 otherwise. $NOTCRED_{ijt} = 1$ if one country is a renegotiating debtor  and the other is not a creditor. \\
{\bf Finding:} 
$ \sum_{m=0}^M \xi_{m}<0$, but 
$ \sum_{m=0}^M \phi_{m} >0$ at horizons 0, 5, 10, and negative only at horizon 15. \\
{\bf Interpretation:} Again, no sanction effect, unless creditors have very long memories (at least 15 years) and are willing or have reasons to delay punishment. 


\end{slide}


\begin{slide}

\centering{\bf Section 13.3}



{\bf \large  Default Incentives With 


State-Contingent Contracts}

[slides incomplete] 

\end{slide}

\begin{slide}

\centering{\bf Section 13.4}



{\bf \large  Default Incentives With 


Non-State-Contingent Contracts}

[slides for this section are not complete] 

\end{slide}

\begin{slide}
\centerline{\bf \Large The Eaton-Gersovitz  Model}

References: Eaton and Gersovitz (RES, 1981); Arellano (2008). 

Some analytical results: 
\begin{enumerate}
  \item Countries default in low income states. 
\item The more indebted the country is, the higher the default probability. 
\end{enumerate}
\end{slide}



\begin{slide}
Preferences: 
\[
E_0 \sum_{t=0}^{\infty}
\beta^t u(c_t)
\]
Endowment: 
\[
y_t \in Y \equiv [\underline{y},\bar{y}], \quad \quad \mbox{i.i.d.}
\]
One-period non-statecontingent debt, d. 

Value of bad financial standing: 
\[
v^b(y)  = u(y) + \beta E v^b({y'})
\]
Value of good financial standing: 
\[
v^g(d, y) = \max \left\{v^b(y), v^c(d,y)\right\}
\]
Value of continuing to honor debt: 
\[
v^c(d, y) = \max_{d'}\left[ u(y+q(d') d' -d) + \beta Ev^g(d',y')\right]
\]
\end{slide}

\begin{slide}
The Default Set: 
\[
D(d) = \{y\in Y: v^b(y)>v^c(d,y)\}
\]


\begin{proposition}[Must pay part of interest, trade surplus]
\label{prop:default-inflow}
If $D(d)\ne \emptyset$, then 
$tb =d-q(d')d'>0$ for all $d'\le \bar{d}$.
\end{proposition}
\begin{proposition}[Default in bad times] If $y_1\in D(d)$ and $\underline{y}\le y_2<y_1$, then $y_2\in D(d)$.
\end{proposition}

Compare to figure  13.2 in  USG (2017).

\begin{proposition}[Default when debt is high]
\label{proposition:y^*}
If $D(d)\ne \emptyset$, then $D(d)$ is an interval,  $[\underline{y},y^*(d)]$, where $y^*(d)$ is increasing in $d$ if $y^*(d)<\bar{y}$.
\end{proposition}

see table 13.3 of USG (2017)


\end{slide}
\begin{slide}
{\bf Default Risk and the Country Premium}

World interest rate, $r^*$. Risk neutral lenders. 

Participation constraint: 
\[
1+r^* = \frac{\mbox{Prob}\left\{
y'\ge y^*(d')\right\}
}
{q(d')}.
\]
Note the country spread is equal to the probability of default. 
[Yet, in the data, country spreads typically exceed the probability of default, see tables 13.1, 13.2, 13.4, and  13.5 of USG (2017).] 


\begin{proposition}[More debt, higher spread]
The country spread, given by $1/q(d')-(1+r^*)$ is nondecreasing in the stock of debt.
\end{proposition}


\end{slide}
\begin{slide}

\centerline{\bf Section 13.5}



\centerline{\bf \large  Saving and the Breakdown}


\centerline{\bf \large of Reputational Lending}



Bulow and Rogoff (1989) show that if defaulters cannot borrow but can save, then no lending can be supported on reputational grounds. 


[slides incomplete] 

\end{slide}

\begin{slide}

\centering{\bf Section 13.6}


{\bf \large  Quantitative Analysis of the 


The Eaton-Gersovitz  Model}


\end{slide}



\begin{slide}

Additional features of the default model relative to the analytical example discussed thus far:

$\bullet$ Serially correlated output.\\
$\bullet$ Nonzero probability of reentry.\\
$\bullet$ Asymmetric output cost of default. 

\end{slide}


\begin{slide}

\centerline{\bf  Section 13.6.1: Serially Correlated Output} 

$y_t = $ tradable output measured as sum of  GDP in agriculture,   forestry, fishing, mining, and manufacturing. 


Sample:   Argentina,  1983:Q1 to 2001:Q4.


\[
\ln y_t  = 0.9317
\ln y_{t-1} + 
0.037\, \epsilon_t
\]

with
$\epsilon_t \sim N(0,1)$

Now probability of default in $t+1$ depends on $y_t$. Thus $q_t=q(d_{t+1}, y_{t})$.


\end{slide}


\begin{slide}

\centerline{\bf  Section 13.6.2:  Nonzero Probability of Reentry} 



constant  probability of reentry,  $\theta$.

Prob. to be excluded exactly 1 quarter: $\theta$\\
Prob. to be excluded exactly 2 quarters: $\theta (1-\theta)$\\
$\vdots$\\
Prob. to be excluded exactly j quarters: $\theta (1-\theta)^{j-1}$\\



$\Rightarrow$ expected length of exclusion is $\frac{1}{\theta}$ quarters.


[table 13.6 of USG (2017), typical exclusion period is 4.7-13.7 years.]
\end{slide}



\begin{slide}
\centerline{\bf  Section 13.6.3: The Output Cost of Default}


The endowment received by households, $\tilde{y}^T_t$ is given by
\[
\tilde{y}_t = 
\left\{
\begin{array}{ll}
y_t & \mbox{if the country is in good standing}\\
y_t - L(y_t)& \mbox{if  the country is in bad standing}
\end{array}
\right.,
\]


where $L(y_t)$ is an output loss function assumed to be positive and nondecreasing. 

[Why? Because exclusion is not enough punishment to support empirically realistic amounts of debt, see section 13.6.11 of USG (2017).]
\end{slide}


\begin{slide}
\centerline{\bf  Section 13.6.4: The Model}

Value of continuing to participate in financial markets
\[
v^c(d,y) = \max_{d'}
\left\{
u(y+q(d',y)d' -d) + \beta E_yv^g(d',y')
\right\}
\]
Value of being in bad financial standing 
\[
v^b(y) = u(y-L(y)) + \beta \theta E_yv^g(0,y') + \beta (1-\theta)E_yv^b(y')
\]
Value of being in good financial standing
\[
v^g(d,y) = \max\{v^c(d,y),v^b(y)\} 
\]
Participation Constraint 
\[
 1+r^*= \frac{\mbox{Prob}_y
\{v^c(d',y')\ge v^b(y')\}}{q(d',y)}
\]
Country interest rate: 
$
1+r \equiv \frac1{q(d',y)}
$

Country Spread $= r-r^*$


\end{slide}
\begin{slide}
\centerline{\bf  Section 13.6.5: Calibration and Functional Forms}



Preferences: $$
u(c) = \frac{c^{1-\sigma}-1}{1-\sigma}.
$$

\bigskip 


Output Cost of Default: 
$$
L(y_t) = \max \{0,a_0+a_1y_t+a_2y_t^2\}.
$$


\end{slide}

\begin{slide}

\centerline{\bf Calibration}

$\bullet$ Time unit is a quarter.


$\bullet$ Parameter values: \\
$\sigma=2.$\\
$\theta=0.0385$ probability of reentry.\\
$r^*=1 \%$ per quarter.\\
$\beta=0.85.$\\
$a_1 = -0.36$; parameter of output loss function.\\
$a_2= 0.4403$; parameter of output loss function.

$(\beta, a_1, a_2)$ set to match debt to GDP of 60\% per quarter; 2.6 defaults per century; output cost of default is 7\% per year of autarky. 
\end{slide}
\begin{slide}
\centerline{\bf Asymmetric Output Cost of Default\label{fig:sd_qa_output_loss}}

\centerline{
\includegraphics[width=5in]{sd_qa_output_loss.eps}}
%produced by running output_loss.m in
%c:\data\uribe\book\sovereign_debt\eg
\end{slide}

\begin{slide}
\centerline{\bf \large Section 13.6.6: Computation}

Discretization of State Space

$n_y=200$; Number of output grid points (equally spaced in logs)

$n_d=200$; Number of debt grid points (equally spaced)

$[\underline{y},\overline{y}]=[0.6523,1.5330]$; 4.2 standard deviations

$[\underline{d},\overline{d}]=[0,1.5]$; \\

Transition probability matrix computed using Schmitt-Groh\'e and Uribe (2009) interative procedure, see \verb7tpm.m7

\end{slide}

\begin{slide}
\centering 

{\bf  Section 13.6.7: 

Quantitative Predictions of the Eaton-Gersovitz Model}


\end{slide}

\begin{slide}
\centerline{\bf Selected First and Second Moments: Data and Model Predictions\label{table:sd_qa_results}}

\bigskip

\centerline{\small
\begin{tabular}{lcccccc}
\hline\hline 
&Default&&&&\\
&frequency&E(d/y)&$E(r-r^*)$&$\sigma(r-r^*)$&corr$(r-r^*,y)$&corr$(r-r^*,tb/y)$\\
\hline
Data&  2.6&  58.0&  7.4&  2.9&  -0.64&   0.72\\
Model
&  2.6&  59.0&  3.5&  3.2&  -0.54&   0.81\\
\hline\hline
\end{tabular}
}
{\tiny 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 2014. The variable $d/y$ denotes the quarterly debt-to-GDP ratio in percent, $r-r^*$
denotes the  country  premium, in percent per year, $y$ denotes (quarterly detrended) output, and $tb/y$ denotes the trade-balance-to-GDP ratio. The symbols $E$,  $\sigma$, and corr denote, respectively, the mean, the standard deviation, and the correlation. In the theoretical model, all moments (other than default frequency) are conditional on the country being in good financial standing. Replication file statistics\_model.m in sovereign\_default.zip.\par} 
%produced by running 
%statistics_model.m in
%c:\data\uribe\book\sovereign_debt\eg

Predicted default frequency while in good standing is 3.2\% (which is close to the country spread of 3.5\%). 
\end{slide}
\begin{slide}
{\bf Observations on the Table}\\
$\bullet$ $r$ is countercyclical; when it rains it pours; this feature should increase consumption volatility relative to output; 

$\bullet$ Model explains only half of observed country premium (3.5 versus 7.4 percent). 
\end{slide}
\begin{slide}

By construction, model can either match the default frequency or the spread but not both, because it implies that the spread is equal to the default probablity:
\begin{eqnarray}
r-r^* &\approx &
\ln
\left[
\frac1{q(d',y)(1+r^*)}
\right]
\nonumber\\
& =& \ln
\left[
\frac1
{\mbox{Prob}\{\mbox{repayment in $t+1$ given information in $t$}\}}
\right]
\nonumber\\&=&
\ln\left[
\frac1{1-\mbox{Prob}\{\mbox{default in $t+1$ given information in $t$}\}}
\right]
\nonumber\\
\label{eq:sd_qa_premium}
&\approx&
\mbox{Prob}\{\mbox{default in $t+1$  given information in $t$}\}.
\nonumber
\end{eqnarray}
\end{slide}
\begin{slide}
Q: Can partial default explain the spread-default frequency differential?
Partial default: 
\[
\label{eq:sd_qa_q_partial}
q(d',y) = \frac{\lambda
\mbox{Prob}_y
\{v^c(d',y')< v^b(y')\}+
\mbox{Prob}_y
\{v^c(d',y')\ge v^b(y')\}}{1+r^*}.
\]
This implies that 
\[
\label{eq:sd_qa_q_partial_linearized}
r-r^* \approx (1-\lambda) \mbox{Prob}\{\mbox{default in $t+1$  given information in $t$}\}.
\]
Now spread smaller than default frequency. Thus, allowing for partial default only widens the spread-defaul frequency differential. 
\end{slide}
\begin{slide}
Q: Does making foreign lenders risk averse close the spread-default frequency differential. 

A: Lizarazo (2013), yes. However, as we will show shortly, this result relies on the assumption that default has large negative wealth effects on the foreign lender. If defaulting country is small so that wealth of foreign lender is not affected by default, then allowing for risk aversion, does not help much to close the spread-default frequency differential. (Section 13.9 of USG, 2017) 
\end{slide}
\begin{slide}

\centerline{Data and Model Predictions: Standard Business-Cycle Statistics\label{table:sd_qa_results2}}

\medskip

\centerline{
\begin{tabular}{lcccc}
\hline\hline 
&$\sigma(c)/\sigma(y)$ & $\sigma(tb/y)/\sigma(y)$ & $\mbox{corr}(c,y)$ & $\mbox{corr}(tb/y,y)$\\
\hline
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\\
\hline\hline
\end{tabular}
}

{\tiny Note.  Data moments 
for emerging countries and Argentina are taken from chapter 1, tables 1.6 and 1.9, respectively. The symbols $c$ and $y$ denote the log deviation from trend, $tb/y$ denotes the trade-balance-to-output ratio, and  $\sigma$ and corr denote, respectively,  standard deviation and  correlation.  Replication file for model predictions  simu.m in sovereign\_default.zip.\par}
%model predictions produced by  loading 
%simu_eg_quadratic.mat
%in
%c:\data\uribe\book\sovereign_debt\eg
%which in turn is produced by running
%simu.m in the same directory.
\end{slide}



\begin{slide}
Observations on the table: \\
$\bullet$ model captures excess volatility of consumption. why? in good standing interest rate is countercyclical exacerbating consumption adjustment to negative shocks; in bad standing $c=y$. So overall consumption more volatile than output. 

$\bullet$ Model explains sign but not size of $corr(tb/y, y)$. In the absence of default risk this model would predict $tb/y$ to be procyclical. Recall: finance temporary income shocks, and adjust to permanent ones. 

$\bullet$ Model predicts countercyclical interest rate, this makes savings, and hence the trade balance itself countercyclical. 

\end{slide}


\begin{slide}
\centering 

{\bf  Section 13.6.8: 

Dynamics Around A Typical Default Episode}


\end{slide}
  
\begin{slide}
\centerline{\bf \large Typical Default Episode}

\centerline{\includegraphics[width=7in]{sd_qa_typical_default_episode.eps}}
%Produced by running %typical_default_episode.m in
%c:\data\uribe\book\sovereign_debt\eg

{\tiny Notes: Lines display medians of 25-quarter windows centered on default episodes occurring in
an artificial time series of 1 million quarters. The default date is normalized to 0. Replicaiton file typical\_default\_episode.m in sovereign\_default.zip.


}

\end{slide}
  
\begin{slide}
{\bf Observations on the figure} \\
$\bullet$ When does a country default? After a sudden deep contraction in output. From at mean to 1.3 std below mean in just 3 quarters.  
\\
$\bullet$ model can explain that default coincides with end of contraction and beginning of recovery. 
\\
$\bullet$ consumption falls by more than output (no consumption smoothing!). Why, because spreads increase from 3 to 6 percent. 
\\
$\bullet$ debt fails to increase prior to default. $d/y$ little changed until period of default. in the data, we see $d/y$ increasing. 



\end{slide}


\begin{slide}
\centering 

{\bf  Section 13.6.9: 

Goodness of Approximation of the Eaton-Gersovitz Model}



\end{slide}
  
\begin{slide}

\centerline{Approximating the Eaton-Gersovitz Model: Accuracy Tests\label{table:sd_qa_accuracy}}

\medskip

\centerline{
\small 
\begin{tabular}{lcccccccc}
\hline\hline 
&\multicolumn{2}{c}{Grid Points}&Default&&&&\multicolumn{2}{c}{Correlation}\\
&$n_y$&$n_d$&frequency&E(d/y)&$E(r-r^*)$&$\sigma(r-r^*)$&$(r-r^*,y)$&$(r-r^*,tb/y)$\\
\hline
Data&&&  2.6&  58.0&  7.4&  2.9&  -0.64&  0.72\\
Model*&200&200&  2.65&  59.05&  3.47&  3.21&-0.54&  0.81\\
Model  &25&200& 2.30&  69.43&  3.01&  4.20&  -0.28&  0.44\\
Model&400&200&  2.63&  58.64&  3.43&  3.12&  -0.55&  0.82\\
Model&200&400&  2.65&  59.46&  3.44&  3.13&  -0.55&  0.83\\
Model&400&400&  2.65&  59.46&  3.44&  3.13&  -0.55&  0.83\\
\hline\hline
\end{tabular}
}
{\Tiny 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 2014. The variable $d/y$ denotes the quarterly debt-to-GDP ratio in percent, $r-r^*$
denotes the  country  premium, in percent per year, $y$ denotes (quarterly detrended) output, and $tb/y$ denotes the trade-balance-to-GDP ratio. The symbols $E$ and   $\sigma$ denote, respectively, the mean and  the standard deviation.
The symbols $n_y$ and $n_d$ denote the number of grid points for the endowment and debt, respectively. 
 In the theoretical model, all moments are conditional on the country being in good financial standing. Theoretical moments were computed by running the Matlab script statistics\_model.m after appropriately  adjusting the number of grid points in eg.m.\\
*Baseline grid specification. \par} 
%produced by running 
%statistics_data_model.m in
%c:\data\uribe\book\sovereign_debt\eg

$\bullet$ Hatchondo, Mart\'{\i}nez, and Sapriza (2010) find that the
numerical  solution  of the Eaton-Gersovitz model deteriorates significantly  when the endowment grid is coarsely specified. 
Correlation of country premium with output falls from -0.54 to -0.28 when $n_y$ is reduced from 200 to 25. Std of premium is 1 percentage point higher under coarser grid. 



\end{slide}
  
\begin{slide}
\centering 

{\bf  Section 13.6.10 and 13.6.11: 

The Quantitative Importance of Output Costs of Default

and 

The Quantitative Irrelevance of Exclusion 

}




\end{slide}


\begin{slide}
{\bf Reputation or Direct Output Costs? --- The Quantitative Irrelevance of Exclusion}



Consider no output cost of default, $L(y) = 0$. Leaving financial autarky as the only cost of default. 


What happens?  The debt distribution becomes degenerate.   For all values of $y$ debt is equal to zero.  That is, the model cannot support {\bf any} debt in equilibrium. 
This means that  the benefit of having access to financial markets must  always be smaller than the benefit of defaulting. 


Therefore, the current  model is not really a reputational model of default but instead a sanctions model of default. 
\end{slide}
  
\begin{slide}
But does reputation play any role at all? To answer this question, let's compare the predictions of  the model with output costs of default  and with and without financial exclusion post default. 

The model then becomes: 
\[
v^{gc}(d,y) = \max_{d'}
\left\{
u(y+q^g(d',y)d' -d) + \beta E_yv^g(d',y')
\right\},
\]
The value of  defaulting, $v^{d}(y)$
{\small \[
v^{d}(y) = \max_{d'}
\left\{
u(y-L(y)+q^b(d',y)d' ) + 
\beta \theta E_yv^g(d',y')
+\beta (1-\theta) E_yv^b(d',y')
\right\}
\]}
The value of being in good financial standing
\[
v^g(d,y) = \max\{v^{gc}(d,y),v^d(y)\}.
\]
\[
q^g(d',y) = \frac{\mbox{Prob}_y
\{v^{gc}(d',y')\ge v^{d}(y')\}}{1+r^*},
\]
\end{slide}
  
\begin{slide}

The value of being in bad financial standing and continuing to service the debt,  $v^{bc}$, 
{\small \[
v^{bc}(d,y) = 
\max_{d'} 
\left\{
u(y-L(y)+q^b(d',y)d' -d) + 
\beta \theta E_yv^g(d',y')
+ \beta (1-\theta) E_y v^b(d',y')
\right\}.
\]}
The value of being in bad financial standing 
\[
v^b(d,y) = \max\{v^{bc}(d,y),v^d(y)\}
\]
The reason why $v^{b}(d,y)$ may not
always  be  equal to $v^d(y)$ is that a country in bad standing may have assets $d<0$, in which case it will never default. 

The price of debt in periods of bad financial standing, $q^b(d',y)$
\[
q^b(d',y) = 
\frac{\theta\, \mbox{Prob}_y\{v^{gc}(d',y') \ge v^d(y')\}
+(1-\theta) \mbox{Prob}_y\{v^{bc}(d',y') \ge v^d(y')\}}
{1+r^*}
\]
\end{slide}

\begin{slide}
\centerline{The Quantitative Irrelevance of Exclusion: Selected First and Second Moments\label{table:sd_qa_no_exclusion}}


\centerline{
\small 
\begin{tabular}{lcccccc}
\hline\hline 
&Default&&&&\\
&frequency&E(d/y)&$E(r-r^*)$&$\sigma(r-r^*)$&corr$(r-r^*,y)$&corr$(r-r^*,tb/y)$\\
\hline
Data&  2.6&  58.0&  7.4&  2.9&  -0.64&   0.72\\
Model\\
\,\, Baseline
&  2.6&  59.0&  3.5&  3.2&  -0.54&   0.81\\
\,\, No Exclusion
&  3.0&  53.1&  4.1&  3.6&  -0.61&   0.84
\\
\hline\hline
\end{tabular}
}
%produced by running 
%statistics_data_model_no_exclusion.m in
%c:\data\uribe\book\sovereign_debt\eg\no_exclusion
Observations on the table: 

$\bullet$ The model in which default is not punished by exclusion from financial markets behaves remarkably similar to the baseline model.

$\bullet$  Specifically, the no-exclusion model can support  about the same amount of  debt than the model with exclusion.  The mean debt to output ratio in times of good financial standing  is 53 percent per quarter in the no-exclusion model, slightly below the value of 59 percent predicted by the baseline model. 


\end{slide}

\begin{slide}

$\bullet$ The average country premium in times of good standing is  predicted to be 4.1 percent
in the no-exclusion model 
 compared to 3.5 percent in the baseline case. The default frequency conditional on good standing is 3.7 percent. (In this model, up to first order the spread-default frequency differential is zero.) 

$\bullet$  The volatility of the country premium and the correlation of the country premium with output and the trade balance to output ratio are also little changed. 

$\bullet$ The model predicts that on average the country defaults three times per century compared to a default frequency of 2.6 times per century predicted by the baseline model. 

$\Rightarrow$ We conclude that exclusion from credit markets plays a negligible role for the quantitative  performance of the Eaton-Gersovitz model. The main mechanism supporting debt in equilibrium is the output loss associated with default! 
\end{slide}


\begin{slide}
\centering 

{\bf  Section 13.6.13: 

The Role of Discounting}



\end{slide}


\begin{slide}
\centerline{\bf Varying  the subjective disount factor,  $\beta$}

If $\beta\uparrow$, then agents discount the future less. All else constant the cost of default (exclusion as well as output loss) has a higher present discounted value. This should make countries default less often. 
Lower default frequencies then immediately imply lower country premia. And with more ability to repay, debt should incrase. By this argument $\beta\uparrow \Rightarrow d \uparrow$. 

Yet, $\beta$ does not only affect the present value of the costs of default, it also changes the desired level of debt.  In a model without default, the more patient agents are the lower is the level of debt, thus, by this argument $\beta\uparrow\Rightarrow d\downarrow$. 

Which force dominates in equilibrium? The next table shows that the first force does.
\end{slide}

\begin{slide}

\centerline{\bf Varying $\mathbf{\beta}$
\label{table:sd_qa_higher_betta}}

\medskip

{\tiny
\begin{tabular}{lcccccc}
\hline\hline 
&Default&&&&\\
&frequency&E(d/y)&$E(r-r^*)$&$\sigma(r-r^*)$&corr$(r-r^*,y)$&corr$(r-r^*,tb/y)$\\
\hline
Data&  2.6&  58.0&  7.4&  2.9&  -0.64&   0.72\\
Model\\
\,\,$\beta =0.85^*$&  2.6&  59.0&  3.5&  3.2&  -0.54&   0.81\\
\,\,$\beta =  0.90$&  1.4&  71.4&  1.6&  2.0&  -0.52&  0.78\\
\,\,$\beta =  0.95$&  0.4&  87.8&  0.5&  0.9&  -0.51&  0.71\\
\hline\hline
\end{tabular}

\leftline{$^*$ indicates the baseline calibration. }
}
%produced by running 
%table_higher_betta.m in
%c:\data\uribe\book\sovereign_debt\eg\higher_betta

The larger is $\beta$, all else constant, the more debt can be supported, which is the exact opposite of what happens under committment. 

Intuition, higher $\beta$ increases the present value of the default cost. 

\end{slide}

\begin{slide}
\centering 

{\bf  Section 13.6.15: 

Varying the Persistence of the Output Process}



\end{slide}


\begin{slide}

Varying $\rho$ holding constant the variance of $y$.

\centerline{\small 
\begin{tabular}{lcccccc}
\hline\hline 
&Default&&&&\\
&frequency&E(d/y)&$E(r-r^*)$&$\sigma(r-r^*)$&corr$(r-r^*,y)$&corr$(r-r^*,tb/y)$\\
\hline
Data&  2.6&  58.0&  7.4&  2.9&  -0.64&   0.72\\
Model\\
\,\,$\rho =0$&  0.1&  274.1&  0.1&  0.1&  -0.68&  0.65\\
\,\,$\rho =0.5$&  0.2&  176.5&  0.2&  0.2&  -0.68&  0.67\\
\,\,$\rho =0.75$&  0.7&  104.3&  0.8&  0.6&  -0.57&  0.66\\
\,\,$\rho =0.85$&  1.5&  74.0&  1.7&  1.4&  -0.52&  0.73\\
\,\,$\rho =0.9317^*$&  2.6&  59.0&  3.5&  3.2&  -0.54&   0.81\\
\,\,$\rho =  0.95$&  2.8&  59.7&  3.8&  3.5&  -0.58&  0.85\\
\,\,$\rho =  0.97$&  2.8&  67.3&  3.7&  3.7&  -0.62&  0.85\\
\hline\hline
\end{tabular}
}
{\tiny Note.  ${}^* = $ baseline value. }
%produced by running 
%statistics_model.m in
%c:\data\uribe\book\sovereign_debt\rho\eg\high_rho (rho = 0.97) and in c:\data\uribe\book\sovereign_debt\rho\eg\low_rho (rho = 0.85) and so on.
\\
$\bullet$ the higher is $\rho$ the lower is debt and the higher is the default frequency. Why? Recall that the output cost kicks in only for high levels of output. When $\rho=0$, it is quite likely that output in the near future is high and hence the country has to pay a high default cost. Thus, the country chooses a low default frequency. And with infrequent defaults the country can support more debt. 
\end{slide}

\begin{slide}
\centering 

{\bf  Section 13.7: 

The Welfare Cost of Lack of Commitment}



\end{slide}


\begin{slide}

$\bullet$ If agents could commit to repay, then debt would be {\bf 100 times larger}, 65.88 versus 0.6133, conditional on good standing, or 0.5091 unconditionally. 

Why? Agents are very impatient, $\beta (1+r)=0.8585<1$

$\bullet$ Lack of commitment manifests itself as an endogenous borrowing constraint. 

$\bullet$ And lack of commitment is {\bf welfare reducing}. 

How much would agents be willing to pay to be able to commit to repay?
\end{slide}

\begin{slide}
Value function under commitment: 
\[
v^{\mbox{com}}(d,y) = 
\max_{d'} \left\{u(y+d'(1+r^*)^{-1}-d)
+\beta E_yv^{\mbox{com}}(d',y')\right\}
\]
With $d'$ in hand, we can find equilibrium consumption from 
\[
c^{\mbox{com}}=y+d'/(1+r^*)-d 
\]

The welfare costs of lack of commitment, $\Lambda(d,y)$: 
\[
E_0\sum_{t=0}^{\infty} \beta^t \frac{
\left(c^{\mbox{com}}_t
\right)^{1-\sigma}-1}{1-\sigma}
=
E_0\sum_{t=0}^{\infty} \beta^t \frac{
\left[(1+\Lambda(d_0,y_0))
c^{\mbox{nocom}}_t
\right]
^{1-\sigma}-1}{1-\sigma}.
\]
Solving for $\Lambda(d,y)$ yields
\[
\Lambda(d,y) =
\left[
\frac{
v^{\mbox{com}}(d,y)(1-\sigma)(1-\beta)+1
}
{v^{\mbox{nocom}}(d,y)(1-\sigma)(1-\beta)+1
}\right]^{\frac1{1-\sigma}}-1,
\]
Note that the welfare cost of lack of commitment are state dependent, that is, $\Lambda$ is a function of the current state $(d,y)$. 
\end{slide}

\begin{slide}
Compute $v^{\mbox{nocom}}(d,y)$ and $v^{\mbox{com}}(d,y)$ and then take unconditional expectations using the ergodic distribution of the state $(d,y)$ associacted with the economy displaying lack of commitment. 

The unconditional mean of  the welfare cost of lack of  commitment  is {\bf 273 percent,} that is, 
\[
100\times E\Lambda(d,y)=273
\]

This is an enormous value.
It means that the consumption stream of an  individual living in the economy without commitment must almost {\bf quadruplicate} in order for him to be as well off as living in the economy with commitment to repay debts. 
\end{slide}

\begin{slide}



The totality of this welfare cost is due to the transitional dynamics of switching from no commitment to commitment. Along this transition, debt increases from a mean of 0.50 to a mean of 65.88, and consumption declines from a mean of 0.9873 to a mean of 0.36. Of course, along this transition consumption is temporarily  much higher than 0.9873.

The next figure displays the typical transition from the lack of commitment economy to the commitment economy. 

\end{slide}

\begin{slide}

\centerline{\bf Transition From No Commitment to Commitment\label{fig:sd_commitment_transition}}

\centerline{\includegraphics[width=7.5in]{sd_commitment_transition.eps}}
%Produced with   plot_transitional_dynamics.m
%in directory
%U:\uribe\book\sovereign_debt\eg\cost_of_commitment
{\small 
$\bullet$ The typical transition path is the mean of  10,000 transition paths each starting at a pair $(d,y)$ drawn from the ergodic distribution under lack of commitment. 


$\bullet$ The transitional dynamics are the key determinant of the welfare gains of commitment. Consider a naive approach to welfare evaluation consisting in computing the unconditional welfare in each economy separately. Because in the stationary state average consumption in the commitment economy is {\bf one third} as high as consumption in the no-commitment economy, one would erroneously conclude that
lack of commitment is welfare improving. \par
}
\end{slide}
\begin{slide}

{\bf  Section 13.8: Decentralization Of The Eaton-Gersovitz Model\label{sec:sd_decentralize}}



The Eaton-Gersovitz model is cast in terms of a social planner's problem. A benevolent government aims to maximize the lifetime welfare of households. In doing so, it chooses how much to borrow, when to default, and how much the household should consume each period.  The household itself makes no relevant decision.
It does not participate in financial markets, nor in goods markets, but  
passively consumes the goods it receives from the government each period. 


New environment: 
Private households participate in credit markets and choose optimally how much to consume and save each period. 
Government retains only the decisions to default and to conduct fiscal policy. 

\end{slide}

\begin{slide}

A central question that we will address is whether there exist fiscal instruments that  the government can use to induce households to undertake borrowing and consumption decisions that mimic the social planner's. 

This exercise is known as the decentralization of the social planner's equilibrium. 

$\bullet$ {\bf Externality:} The reason why the government may need fiscal instruments to alter the behavior of private households is that while the former internalizes that the interest rate faced by the country in international financial markets depends on its net external debt position, the latter does not. Individual households are too small to affect with their borrowing the country's credit conditions.

$\bullet$ {\bf Capital Controls}  By applying fiscal distortions, the government makes its borrowing decisions and the private sector's coincide. 
We will show that the social planner's equilibrium can be decentralized via capital controls. 

\end{slide}

\begin{slide}

\leftline{\bf The Decentralized Eaton-Gersovitz Economy}

\leftline{\small (The exposition is based on Na, Schmitt-Groh\'e, Uribe, and Yue, 2014.)}

\bigskip 

{{\it  13.8.1 Households}}
\[
\max E_0 \sum_{t=0}^{\infty}
\beta^t u(c_t)
\]
subject to
\begin{equation}
\label{eq:sd_deg_budget_constraint}
c_t + d_t = (1+\tau^y_t)\tilde{y}_t + (1-\tau^d_t)q^d_t d_{t+1}
\end{equation}
$\tau^y_t=$ is an income subsidy (tax if negative)\\
$\tau^d_t=$ is a tax (subsidy if negative) on debt\\
FOC wrt debt: $u'(c_t) (1-\tau^d_t) q^d_t = \beta E_t u'(c_{t+1})$
\end{slide}

\begin{slide}
{{\it  13.8.2 The Government}}

Default decisions are assumed to be  made by the government. 
Each period the country can be either in good financial standing or in bad financial standing. If it is in good financial standing, it  can choose to honor its  international debts or default.  Let $I_t$ be a binary variable taking the value 1 if the country  is in good standing in period $t$ and chooses to honor its  debt and 0 if it  is in bad standing. If the country defaults in period $t$, it immediately acquires bad financial standing and $I_t$ takes the value 0.  
If the country is in bad standing in
period 
 $t$, it regains good standing in period $t+1$ with constant and exogenous probability $\theta$, and maintains its bad financial standing with probability $1-\theta$. 

When the country is in  bad financial  standing, it is excluded from international financial credit markets and is therefore unable to borrow or lend internationally. 
We then have that
\begin{equation}
\label{eq:sd_deg_I_t=0==>de_t+1=0}
(1-I_t)d_{t+1}=0.
\end{equation}
\end{slide}

\begin{slide}

In periods in which the country is in bad standing ($I_t=0$), the government confiscates any payments of households to foreign lenders and returns the proceeds to households via income subsidies. 
The government also uses the income subsidy to rebate the  proceeds  from the debt tax. 
The resulting sequential budget constraint of the government is then given by 
\begin{equation}
\label{eq:sd_deg_gov_budget_constraint}
\tau^y_t\tilde{y}_t = \tau^d_tq^d_td_{t+1}
+(1-I_t) d_t.
\end{equation}

Let $q_t$ denote the price of debt charged by foreign lenders to domestic borrowers during periods in which the government maintains  good financial standing. 
As before, the price of debt,  $q_t$,  must satisfy  the condition that the expected return of lending to the domestic country equal the opportunity cost of funds. Formally, 
\begin{equation}
\label{eq:q_probability}
q_t = \frac{\mbox{Prob}\{I_{t+1}=1|I_t=1\}}{1+r^*}.
\end{equation}
This expression can be equivalently written as
\[
I_t 
\left[
q_t - \frac{E_tI_{t+1}}{1+r^*}
\right]=0.
\]
\end{slide}

\begin{slide}

{{\it  13.8.3 Competitive Equilibrium\label{sec:sd_seg_equilibrium}}}

Because all domestic households are identical, there is no borrowing or lending among them. This means that in equilibrium the household's net asset position equals the country's net foreign asset position. 
This in turn  implies that the debt tax, $\tau^d_t,$ can be interpreted as a capital control tax. Because when the country is in bad standing  external debt is nil, the value of $\tau^d_t$ in periods of bad standing  is immaterial. Without loss of generality, we set $\tau^d_t=0$ when $I_t=0$, that is,
\begin{equation}
\label{eq:sd_deg_I=0==>tau=0}
(1-I_t)\tau^d_t=0.
\end{equation}

As before, the  endowment
received by the  household, $\tilde{y}_t$,  is given 
by 
\begin{equation}
\label{eq:sd_deg_tildey}
\tilde{y}_t 
= 
\left\{
\begin{array}{ll}
y_t &\mbox{if $I_t=1$}\\
y_t - L(y_t) &\mbox{otherwise}
\end{array}
\right.
.
\end{equation}
\end{slide}

\begin{slide}

In any period $t$ in which the country is in good financial standing, the domestic price of debt, $q^d_t$, must equal the price of debt offered by foreign lenders, $q_t$, that is
\begin{equation}
\label{eq:sd_deg_I_t=1==>q^d=q}
I_t (q^d_t-q_t)=0.
\end{equation}



Combining 
(\ref{eq:sd_deg_budget_constraint})-%(\ref{eq:sd_deg_I_t=0==>de_t+1=0}), 
(\ref{eq:sd_deg_gov_budget_constraint}),
(\ref{eq:sd_deg_tildey}),
and
(\ref{eq:sd_deg_I_t=1==>q^d=q})
yields  the following market-clearing condition
\[
c_t =y_t
-(1-I_t) L(y_t)
 +I_t[ q_td_{t+1}-d_t].
\]



\end{slide}

\begin{slide}

A competitive equilibrium is   a set of stochastic processes 
$\{c_t,$ $d_{t+1}$,  $q_t,$ $q^d_t\}$ satisfying 
\begin{equation}
\label{eq:sd_deg_market-clearing-traded-competitive}
c_t =y_t
-(1-I_t) L(y_t)
 +I_t[ q_td_{t+1}-d_t],
\end{equation}
\begin{equation}
\label{eq:sd_deg_d=0_competitive}
(1-I_t) d_{t+1} = 0,
\end{equation}
\begin{equation}
\label{eq:sd_deg_Euler-competitive}
(1-\tau^d_t) q^d_t u'(c_t) 
=
 \beta E_t
u'(c_{t+1}),
\end{equation}
\begin{equation}
\label{eq:sd_deg_I_t=1==>q^d=q-competitive}
I_t (q^d_t-q_t)=0,
\end{equation}
\begin{equation}
\label{eq:sd_deg_q_expectations}
I_t 
\left[
q_t - \frac{E_tI_{t+1}}{1+r^*}
\right]=0.
\end{equation}
given 
processes $\{y_t,\tau^d_t, I_t\}$ and 
the  initial condition $d_0$. 

\end{slide}

\begin{slide}
\begin{proposition}[Competitive Equilibrium When $\tau^d_t$ Is Unrestricted] \label{proposition:sd_deg_compact} When the government can choose $\tau^d_t$ freely,  stochastic processes $\{c_t, d_{t+1},q_t\}$  can be supported as a  competitive equilibrium if and only if  they satisfy
\begin{equation}
\tag{\ref{eq:sd_deg_market-clearing-traded-competitive}}
c_t =y_t
-(1-I_t) L(y_t)
 +I_t[ q_td_{t+1}-d_t],
\end{equation}
\begin{equation}
\tag{\ref{eq:sd_deg_d=0_competitive}}
(1-I_t) d_{t+1} = 0,
\end{equation}
and
\begin{equation}
\tag{\ref{eq:sd_deg_q_expectations}}
I_t 
\left[
q_t - \frac{E_tI_{t+1}}{1+r^*}
\right]=0,
\end{equation}
given 
processes $\{y_t,I_t\}$ and 
the  initial condition $d_0$. 
\end{proposition}
\end{slide}


\begin{slide}
Proof: 

\begin{equation*}
%\label{eq:sd_deg_market-clearing-traded-competitive}
\fbox{$
c_t =y_t
-(1-I_t) L(y_t)
 +I_t[ q_td_{t+1}-d_t]
$}
\end{equation*}
\begin{equation*}
%\label{eq:sd_deg_d=0_competitive}
\fbox{$
(1-I_t) d_{t+1} = 0
$}
\end{equation*}
\begin{equation*}
%\label{eq:sd_deg_Euler-competitive}
(1-\tau^d_t) q^d_t u'(c_t) 
=
 \beta E_t
u'(c_{t+1}),
\end{equation*}
\begin{equation*}
%\label{eq:sd_deg_I_t=1==>q^d=q-competitive}
I_t (q^d_t-q_t)=0,
\end{equation*}
\begin{equation*}
%\label{eq:sd_deg_q_expectations}
\fbox{$
I_t 
\left[
q_t - \frac{E_tI_{t+1}}{1+r^*}
\right]=0
$}
\end{equation*}
given $I_t$. 
Pick $q^d_t$ and $\tau^d_t$ to satisfy the non-boxed equations. 


\end{slide}

\begin{slide}
In the  Eaton-Gersovitz model 
the government lacks commitment to honor past promises regarding debt payments or defaults. The lack of commitment  opens the door to time inconsistency. For this reason, attention is restricted to Markov perfect equilibria, which are time consistent equilibria in which the equilibrium policy functions are time-invariant functions of the pay-off relevant state variables of the competitive equilibrium of the economy in period $t$. 

The states appearing in the 
conditions of the competitive equilibrium listed in Proposition~\ref{proposition:sd_deg_compact} 
are the endowment, $y_t$, and the stock of net external debt, $d_t$.
Thus, in a Markov perfect equilibrium  the optimal default decision in period $t$ is a time invariant function of $y_t$ and $d_t$.
\end{slide}


\begin{slide}

When $I_t=1$, under the assumption of a Markov perfect equilibrium equation~(\ref{eq:sd_deg_q_expectations}) becomes 
\[
q_t  
=
\frac{E_t I(y_{t+1}, d_{t+1})}{1+r^*}\]
which we can write as 
\[
q_t = q(y_t, d_{t+1})
\]
Using this expression to eliminate $q_t$ from \eqref{eq:sd_deg_market-clearing-traded-competitive}, we have that the constraint set faced by the benevolent government in the decentralized economy are the same as those in the centralized economy. It follows that the allocation must be identical to the one characterized in the Eaton-Gersovitz problem studies in Section 13.6. 
\end{slide}



\begin{slide}

\centerline{\bf Optimal Capital Controls Around The Typical Default Episode\label{fig:sd_deg_capital_controls}}
\centerline{\includegraphics[width=7in]{sd_deg_capital_controls.eps}}

{\tiny Note.  The solid line displays  the median of  
25-quarter windows centered around 
default episodes occurred in an artificial time series of 1 million quarters.  The default date is normalized to 0. The dotted line displays the unconditional median. \par} 
%Produced by running %typical_default_episode.m in
%c:\data\uribe\book\sovereign_debt\eg
\end{slide}
\begin{slide}
Observations: 

The government increases capital controls sharply in the three quarters prior to the default from 9 to 17 percent. This increase in capital control taxes increases the effective interest rate faced by households. In this way, the government makes private agents internalize the increased sensitivity of the interest rate premium with respect to debt as the debt crisis nears. The debt elasticity of the country premium is larger in the run up to the default because foreign lenders understand that the lower is output the higher is the incentive to default, as the output loss that occurs upon default, $L(y_t)$, 
decreases in absolute and relative terms as $y_t$ falls.


{\bf  This capital control tax is implicitly present in every default model \`a la Eaton-Gersovitz. Analyzing the decentralized version of the model, as we did in this section, makes its presence explicit. 
}

If the government does not have access to captial control taxes, then the model with  decentralized borrowing and centralized default
is no longer isomorphic to the social planner's allocation. Kim and Zhang (2012) study this case. Absent the capital control tax, the model features a pecuniary externality. Why? Because household's fail to internalize that their borrowing decisions affect the rate at which they can borrow. 

Kim and Zhang find that the country interst rate increases unambiguously, but that, perhaps surprisingly, the model may or may not lead to  overborrowing. 

\end{slide}

\begin{slide}
\centering

{\bf Section 13.9}


{\bf Risk Averse Lenders}


\end{slide}

\begin{slide}
\leftline{\bf Motivation to allow for risk averse lenders}
$\bullet$ Observed country spreads  tend to be  {\bf larger} than  observed default probabilities. 
\\
$\bullet$ Average spread-default-frequency differential greater {\bf 200 } basis points. 
\\
$\bullet$ By contrast EG model  predicts a {\bf negative or zero} spread-default-frequency differential. 
\\
$\bullet$ Possible solution: introduced {\bf risk averse} lenders into the EG model.
\\
$\bullet$ Why will that help? Spread will then be the sum of default probability and compensation for default risk. 

\end{slide}
\begin{slide}
\leftline{The EG model with risk averse lenders}

Preferences of foreign lenders
\[
E_0\sum_{t=0}^{\infty}\tilde{\beta}^tu(\tilde{c}_t),
\]
$\tilde{\beta}=$  foreign lender's subjective discount factor\\
$\tilde{c}_t=$  consumption of foreign lenders\\
$u(\tilde{c}) = \frac{\tilde{c}^{1-\tilde{\sigma}}-1}{1-\tilde{\sigma}}$, foreign lenders period utility function\\
$\tilde{\sigma}=$  foreign lender's coefficient of relative risk  aversion. 
\end{slide}
\begin{slide}
Pricing kernel 
 \[m'\equiv \tilde{\beta} 
\left(
\frac{
\tilde{c}'}
{
\tilde{c}
}\right)
^{-\tilde{\sigma}}
\]

$\bullet$ Assume that 
the emerging country is {\bf too small to affect the pricing kernel in the rest of the world.}  



$\bullet$ Alternatively, one could assume that the 
emerging country is large enough to affect the world's pricing kernel. Lizarazo (2013) pursues this alternative.  

\end{slide}
\begin{slide}
Let $
g'\equiv 
\frac{
\tilde{c}'}
{\tilde{c}}
$

Assume  an AR(1) process: 
$
\ln
\left(
\frac{g'}
{\bar{g}}
\right)
= \rho_g
\ln \left(
\frac{g}
{\bar{g}}
\right)
 + \mu'
$

The foreign-lender's optimality  condition  is
\begin{equation*}
%\label{eq:sd_ral_q}
q = E\{m'I'|I=1,y, g,d'\}
\end{equation*}
$q=$ price of the emerging country's debt
\\
$y=$ emerging country's endowment \\
$d=$ emerging country's debt\\
$I=$ indicator function that takes the value 1 if the emerging country is in good standing in the current period and chooses to honor its debt and 0 otherwise. 

\end{slide}
\begin{slide}

Pricing equation for risk free bond, $r^*$. 
\begin{equation*}
%\label{eq:sd_ral_r*}
1 = (1+r^*)E\{m'|g\}
\end{equation*}

  $\rightarrow r^*$ is also a random variable. 

If $\tilde{\sigma}=0$, $m=\tilde{\beta}$, which is the case of risk neutrality studies earlier.  
In this case,  $r^*=\tilde{\beta}^{-1}-1$. Thus, the present formulation nests the baseline Eaton-Gersovitz model with risk-neutral lenders studied in  section 13.6 as a special case. 

\end{slide}
\begin{slide}
Derive the country premium: 

Let $1+r=$ gross country interest rate
\[
1+r \equiv \frac1q; \quad \quad \mbox{country premium} \equiv \frac{1+r}{1+r^*}
\] 
If debtor is in good financial standing ($I=1$) 
\[
\frac{1+r}{1+r^*} = \frac{E\{m'|g\}}{
E\{m'I'|y,g,d'\}}
\]
Use $E\{m'I'|y,g,d'\} = \mbox{Cov}(m',I'|y,g,d')+E\{m'|g\}E\{I'|y,g,d'\}$
\[
\frac{1+r}{1+r^*} = \frac{E\{m'|g\}}{\mbox{Cov}(m',I'|y,g,d')+E\{m'|g\}E\{I'|y,g,d'\}}.
\]
\end{slide}

\begin{slide}


Recalling that $E\{m'|g\}=1/(1+r^*)>0$ and that $E\{I'|y,g,d'\}=1-\mbox{Prob} \{\mbox{default in } t+1|y, g, d'\}$, we can write the (gross) country interest rate premium as
\[
\frac{1+r}{1+r^*} = \frac1{(1+r^*)\mbox{Cov}(m',I'|y,g,d')+1-\mbox{Prob} \{\mbox{default in } t+1|y, g, d'\}}
\]

Taking logs on both sides of this expression yields
\[\fbox{$
r-r^* \approx 
\mbox{Prob} \{\mbox{default in } t+1|y, g, d'\} - (1+r^*)\mbox{Cov}(m',I'|y,g,d')$}
\]

which implies that the country
 premium will exceed the probability of default if and only if the conditional covariance between the pricing kernel and the decision to repay is negative. 
\end{slide}

\begin{slide}

Finally, averaging over all states in which the emerging country is in good financial standing and chooses to repay ($I=1$), we obtain
\[
E(r -r^*) > \mbox{Prob} \{\mbox{default in } t+1\} \mbox{ if and only if } \mbox{Cov}(m',I')<0.
\]
According to this expression, the more negative the covariance between the world pricing kernel and the decision to repay, the larger is the
 average 
spread-default-frequency differential. 
 Although the world pricing kernel $m$ is an exogenous stochastic process, its covariance with the decision to repay, $I$, need not be nil. The reason is that $m$ determines the world interest rate, and therefore it affects the emerging country's cost of external funds and its decision to default or repay. 


We find that in the numerical analysis $\mbox{Cov}(m',I')$ is negative 32 percent of the time and thus positive 68 percent of the time. The unconditional mean of $\mbox{Cov}(m',I')$ is 1e-5. This means that this channel will not generate a positive spread-default-frequency differential. 

The next table documents this in detail. 

\end{slide}

 \begin{slide}
{Predictions of the Eaton-Gersovitz Model with Risk-Averse Lenders\label{table:sd_ral_results}}

\medskip

{\tiny 
\begin{tabular}{lccccccc}
\hline\hline 
&\multicolumn{2}{c}{Default Frequency}&&&&\\
\cline{2-3}
&All &Periods in\\
$\tilde{\sigma}$&periods&good standing&E(d/y)&$E(r-r^*)$&$\sigma(r-r^*)$&corr$(r-r^*,y)$&corr$(r-r^*,tb/y)$\\
\hline
0
&   2.6&  3.2&  59.0&  3.5&  3.2&  -0.54&   0.81\\
2&  2.8&  3.4&  58.3&  3.6&  3.5&  -0.54&  0.79\\
5&  2.7&  3.3&  58.0&  3.6&  3.4&  -0.55&  0.80\\
\hline\hline
\end{tabular}
}

{\tiny Note.  The variable $d/y$ denotes the quarterly debt-to-output ratio in percent, $r-r^*$ denotes the  country  premium, in percent per year, $y$ denotes (quarterly detrended) output, and $tb/y$ denotes the trade-balance-to-output ratio. The symbols $E$,  $\sigma$, and corr denote, respectively, the mean, the standard deviation, and the correlation. All moments are conditional on the country being in good financial standing. Theoretical moments were computed by running the Matlab script statistics\_modelral.m. \par} 
 %produced by running 
%statistics_modelral.m in
%c:\data\uribe\book\sovereign_debt\eg\global_factors
\end{slide}

\begin{slide}

$\bullet$ The key message of the table is that the assumption of risk averse foreign lenders has quantitatively negligible effects on the predictions of the Eaton-Gersovitz model. 

$\bullet$ the assumption of risk-averse foreign lenders does not change the prediction of a near-zero spread-default-frequency  differential. 

$\bullet$ The  insensitivity of the endogenous variables of the model to changes in foreign risk aversion occurs eventhough the volatility of the world interest rate  (not shown in the table) increases significantly with $\tilde{\sigma}$.  

Specifically, the standard deviation of $r^*$ is 0, 1.2, and 3.0 percent per year  for  $\tilde{\sigma}$  equal to 0, 2, and 5, respectively.  

Why is it then that this sizable increase in the volatility of the world interest rate does not affect the domestic economy? We conjecture that the reason is that this is an economy with highly impatient agents, who can borrow much less than what they would like to borrow under commitment. As a result, the present model behaves quite similarly to one in which the agent  is up against a borrowing constraint most of the time. In such a setting, the price of credit is little allocative, and hence variation therein  do not affect much consumption or borrowing decisions.  This result may change in a setting with default and more patient consumers. 

\end{slide}


\begin{slide}
\begin{center}

{\bf Section 13.10}

{\bf \large  Long-Term Debt and Default}

[slides not yet written]

\end{center}
\end{slide}

\begin{slide}
\begin{center}

{\bf Section 13.11}

{\bf \large  Debt Renegotiation}

[slides not yet written]

\end{center}
\end{slide}
\begin{slide}
\begin{center}

{\bf Section 13.12}

{\bf \large  Default and Monetary Policy}


\end{center}

\end{slide}
 
\begin{slide}
In this section we 

--- introduce nominal rigidities into the Eaton-Gersovitz model.\\
--- analyze optimal default and devaluation policy. \\
--- document that defaults are accompanied by devaluations.\\
--- study the consequences of suboptimal monetary policy on default. 


This section is based on Na, Schmitt-Groh\'e, Uribe, and Yue (2014). 

\end{slide}




\begin{slide}
{\bf \large The Twin Ds}

There exists a strong empirical link between sovereign default and large devaluations.

$\bullet$ Reinhart (2002) examines data for 
58 countries over the period 
1970 to 1999 and finds that:%113 defaults

-- The unconditional probability of a large devaluation in any 24-month period is  17\%. 

--- The probability of a large devaluation conditional on the 24-month period containing a default is 84\%. 

$\bullet$ Reinhart refers to this phenomenon as the {\bf Twin Ds.} 


Next we show an additional (ie not highlighted by Reinhart) aspect of the Twin D phenomenon, namely that the default is {\bf not} associated with a permanent increase in the devaluation rate. 

\end{slide}

\begin{slide}
{Figure 13.14: Excess Devaluation Around Default, 1975-2013}

\centerline{\includegraphics[width=6in]{sd_default_and_devaluation.eps}}

{\tiny  
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. 
Data sources: Default dates, Uribe and Schmitt-Groh\'e (2015). Exchange rates, WDI.}
%produced by running
%default_X.m in
%c:\data\uribe\book\sovereign_debt\data
\end{slide}

\begin{slide}
Observations on the figure

$\bullet$ the exchange rate is defined so that an increase in the exchange rate is a devaluation of the domestic currency. 

$\bullet$ exchange rate depreciates 40 percent more if window contains default episode than if it does not. 

$\bullet$ post devaluation level of exchange rate stabilizes, hence 
devaluations around default are more akin to  a change in the {\it level} of the nominal exchange rate than to a switch to a higher {\it rate} of depreciation. 


Let's look at some recent defaults in specific countries. 




\end{slide}

\begin{slide}
\begin{center}
{Figure 13.15: The Twin Ds: Six Recent Examples}
\includegraphics[angle=-90,width=8in]{sd_default_exch_rate_slide.eps}
\end{center}


\centerline{ \rule{2cm}{1mm} Nominal Exchange Rate \hspace{0.5in} \rule{0.3cm}{1mm} \rule{0.3cm}{1mm} \rule{0.3cm}{1mm}  \rule{0.3cm}{1mm} Default Date}


{\tiny Note: Exchange rates are nominal dollar exchange rates, annual average, first observation normalized to unity.  } 
%produced by running
%default_after91.m in
%c:\data\uribe\default\eg\data
\end{slide}
 
\begin{slide}
Observations on the figure. 

In each of these 6 examples, we plot the level of the nominal exchange rate. That is, we don't show excess devaluation, but simply the level. 

All 6 cases cobform to the regularity that we wish to highlight, namely, that the devaluation that accompanies the default looks more like a one-time change in the level of the exchange rate than a switch to a permanently higher devaluation rate. 
\end{slide}
 
\begin{slide}
\begin{center}
{\bf \large  Argentina 1996-2006 }\\
\includegraphics[width=6.5in,angle=-0]{sd_arg_unemployment_wage.eps}\\

\medskip

{\tiny Vertical Line 1998, beginning of recession.}

\tiny{Vertical Line 2002, default and devaluation. }




%produced with c:\data\uribe\default\arg_unemployment_wage.m

\end{center}
 
\end{slide}


\begin{slide}
 {\bf Na et al.\ paper:  }

-- develops a model that explains the Twin Ds phenomenon as an optimal policy outcome. 


$\bullet$ {\bf   \large Main  Elements}

-- Imperfect enforcement of debt contracts. 

--  Downward nominal wage rigidity. 


$\bullet$ { \bf \large 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 unemployment.\\
-- The devaluation is necessary to bring real wages down because nominal wages are downwardly rigid. 

\end{slide}

\end{document}


