%slides_irs.tex
%Slides for Chapter 6 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}{4.5in}
\centering 
{\small 
slides 

chapter 6   

Interest Rate Shocks

}
\vspace{1in}

\end{minipage}
\end{slide}

\topleft{\textit{Open Economy Macroeconomics, Chapter 6} }
\topright{M.\ Uribe and S.\ Schmitt-Groh\'e}

\begin{slide}
{\bf Motivation}\\
$\bullet$   Interest-rate shocks are generally believed to be a major source of fluctuations for emerging countries. \\
$\bullet$  The next slide displays country  interest rates and output for 7 emerging economies between 1994:Q1 and 2001:Q4. 
\\
$\bullet$  Why is there one interest rate per country, as opposed to just one world interest rate? One reasons is that  each country has a different default risk, which is reflected in a country-specific interest-rate premium. The most commonly-used measure of country spreads is J.P.\ Morgan's EMBI+ bond index (Emerging Market Bond Index). 
\\
$\bullet$  The figure suggests that  output and country interest rates are negatively correlated. 
\\
$\bullet$ {\bf Primary References:} Neumeyer and Perri (JME, 2005) and Uribe and Yue (JIE, 2006). 
\end{slide}

\begin{slide}{
\centerline{\bf Negative Comovement Between  Interest Rates and Output}
\centerline{\includegraphics[width=10in]{irs_raw_data_slides.eps}}

\centerline{\rule{2cm}{1mm} Output \hspace{1.5cm} \rule{2mm}{1mm} \rule{2mm}{1mm} \rule{2mm}{1mm} \rule{2mm}{1mm}   Country Interest Rate}}
{\tiny Correlations: Argentina -0.67; Brazil -0.51, Ecuador -0.80, Mexico -0.58, Peru -0.37, The Philippines -0.02, South Africa -0.07.}

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\end{slide} 

\begin{slide}

{\bf \large Who Drives Whom?}\\
$\bullet$   The observed negative correlation between output and the interest rate does not necessarily indicate that movements in the interest rate cause movements in output.\\
$\bullet$   Addressing this question requires a combination of  data and theory. \\
$\bullet$  We will study two ways of combining data and theory:\\
(1)  SVAR analysis: here the emphasis is in the S. Converting a simple VAR into an SVAR requires the imposition of identifying assumptions, which are  necessarily theoretical in nature. \\
(2)  Estimated DSGE model. 

The main difference between these two approaches is how much weight they place on data and theory.  We begin with  approach (1).  

\end{slide}


\begin{slide} 
\centerline{\bf \large SVAR Analysis, Uribe and Yue (2006)} 
\bigskip
\centerline{$
A 
\left[ 
\begin{array}{c} 
\hat{y}_t\\ 
\hat{\imath}_t \\ 
tby_t\\ 
\hat{R}^{us}_t\\ 
\hat{R}_t 
\end{array} 
\right] 
= B 
\left[ 
\begin{array}{c} 
\hat{y}_{t-1}\\ 
\hat{\imath}_{t-1} \\ 
tby_{t-1}\\ 
\hat{R}^{us}_{t-1}\\ 
\hat{R}_{t-1} 
\end{array} 
\right] 
+ 
\left[ 
\begin{array}{c} 
\epsilon^y_t\\ 
\epsilon^i_t \\ 
\epsilon^{tby}_t\\ 
\epsilon^{rus}_t\\ 
\epsilon^{r}_t 
\end{array} 
\right] ,
$} 
where $y_t$=output, $i_t$=investment, $tby_t$=trade-balance-to-GDP ratio, $R^{us}_t$=U.S. interest rate, and $R_t$=country interest rate.

$\bullet$ {\bf Identification Assumptions:}
\\
$A$ is lower triangular ($A(i,j)=0$ $\forall  j>i$).\\
$R^{US}_t$ follows a univariate process ($A(4,j)=B(4,j)=0$ $\forall j\neq4$).
\\
$\bullet$ {\bf Countries:} Argentina, Brazil, Ecuador, Mexico, Peru, The Philippines, South Africa.\\ 
$\bullet$ {\bf Sample Period:} 1994:Q1 - 2001:Q4. 
\end{slide} 

\begin{slide}
{\bf \large Comments On Identification}\\
$\bullet$ ${A}$ lower triangular implies that shocks to real variables (output, investment, and the trade balance)
affect the country interest rate contemporaneously, but shocks to the U.S.\ interest rate or to the country interest rate affect real variables with a lag. This makes sense, because real variables (think about starting investment projects, hiring and firing  decisions, etc.)
should respond more slowly than financial variables. \\
$\bullet$  Assuming that $R^{us}_t$ is univariate is sensible because one should not expect individual emerging countries to affect interest rates in the U.S. \\
$\bullet$  {\bf Implications of Identifying Restrictions:}\\
-- $\epsilon^{rus}_t$ and $\epsilon^r_t$ can be interpreted as exogenous U.S.-interest-rate  and country-spread shocks, respectively. \\
-- The identification scheme is vague about the nature of $\epsilon^y_t$, $\epsilon^i_t$, and $\epsilon^{tby}_t$. This is not a problem, because our interest is to understand the effects of interest-rate shocks. 

\end{slide}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\begin{slide} \centering 
\centerline{\bf \large Impulse Response To A Country-Spread Shock, $\epsilon^r_t$} 
{\includegraphics[width=8.5in]{irs_ir_i_data_slides.eps}}
\\{\rule{2cm}{1mm} Point Estimate \hspace{1.5cm} \rule{2mm}{1mm} \rule{2mm}{1mm} \rule{2mm}{1mm} \rule{2mm}{1mm}  2-std.\ Error Band}
%Feb 28, 2015: produced with irband_plot.m 
%in U:\uribe\book\irs\mfiles\JIE_revision
%you must set ei(1) = 1  and pick orient portrait 
\end{slide} 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
\begin{slide}  \centering
\centerline{\bf \large Impulse Response To A U.S.\ Interest-Rate Shock, $\epsilon^{rus}_t$} 
{\includegraphics[width=8.5in]{irs_ir_rus_data_slides.eps}}
\\
{\rule{2cm}{1mm} Point Estimate \hspace{1.5cm} \rule{2mm}{1mm} \rule{2mm}{1mm} \rule{2mm}{1mm} \rule{2mm}{1mm}  2-std.\ Error Band}
%Feb 28, 2015: produced with irband_plot.m 
%in U:\uribe\book\irs\mfiles\JIE_revision
%you must set er(1) = 1  to make the impact shock for the U.S. interest rate equal to 1 and pick orient portrait 

\end{slide} 

\begin{slide}
{\bf Observations on Responses to $\epsilon^{r}_t$ and $\epsilon^{rus}_t$ }

$\bullet$  Country-spread and US-interest-rate shocks cause sizable contractions in   output and investment and a sizable improvement in the trade-balance-to-GDP ratio
(i.e., domestic absorption contracts relatively more than output). \\
$\bullet$ The response to US-interest-rate shocks is estimated with significant uncertainty. One reason is that by  design, $R^{us}_t$ does not vary across countries.  \\
$\bullet$ US-interest-rate shocks cause a large,  delayed overshooting of country spreads. 

\end{slide}


\begin{slide} 
\centering 
\centerline{\bf \large Impulse Response To An Output Shock, $\epsilon^y_t$} 
{\includegraphics[width=8.5in]{irs_ir_y_data_slides.eps}} 
\\
{\rule{2cm}{1mm} Point Estimate \hspace{1.5cm} \rule{2mm}{1mm} \rule{2mm}{1mm} \rule{2mm}{1mm} \rule{2mm}{1mm}  2-std.\ Error Band}
%Feb 28, 2015: produced with irband_plot.m 
%in U:\uribe\book\irs\mfiles\JIE_revision
%you must set ey(1) = 1  (and all the others to 0) to make the impact shock for domestic output equal to 1 and pick orient portrait 
\end{slide} 

\begin{slide}
{\bf Observations on Response to $\epsilon^{y}_t$ }

$\bullet$ An output shock causes expansions in output and investment, and a deterioration of the trade-balance-to-GDP ratio, resembling a technology shock or a terms-of-trade shock in the  SOE-RBC model.\\
$\bullet$ More importantly for the purpose of the present analysis, the output shock drives down the country spread, thus lowering the country's cost of borrowing. \\
$\bullet$ Recall that the present identification scheme is vague with respect to 
the precise nature of $\epsilon^y_t$. It could represent a mix of shocks of diverse natures, such as technology shocks, terms-of-trade shocks, etc. 
\end{slide}

\begin{slide}
{  \bf \large Robustness To Expanding The Temporal And \\Country  Coverage of the Data}


\bigskip

{\bf Expanded Time Span:} 1994:Q1 to 2012:Q4. 

{\bf  Expanded Country Set:} Argentina, 
     Brazil, 
     Bulgaria, 
     Chile, 
     Colombia, 
     Ecuador, 
     Hungary, 
     South Korea, 
     Malaysia, 
     Mexico, 
     Peru, 
     South Africa, 
     Thailand, 
     Turkey,  and 
     Uruguay.
\end{slide}


\begin{slide}
\begin{center}
{\bf Responses to Country-Spread and U.S.-Interest-Rate Shocks: Expanded Data}
%\label{fig:irs_ir_i_data_update}

\centerline{\includegraphics[width=5in]{irs_ir_i_data_update.eps}}
\end{center}
{\tiny 
1\% increase in   country-spread (solid) and   US-int.-rate (broken).
 Output and  investment   in \% dev.\  from  trend; TB/GDP  and    country int.\ rate  in percentage point dev.\ from  mean. }
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%regre.m in
%cd c:\data\uribe\book\irs\data
%this is figure(1)
\end{slide}

\begin{slide}
\begin{center}
{\bf Responses to an Output Shock: Expanded Data}
%\label{fig:irs_ir_y_data_update}

\centerline{\includegraphics[width=5in]{irs_ir_y_data_update.eps}}
\end{center}

{\tiny 
1\% output shock.
 Output and  investment   in \% dev.\  from  trend; TB/GDP  and    country int.\ rate  in percentage point dev.\ from  mean. }
%produced by running 
%regre.m in
%cd c:\data\uribe\book\irs\data
%this is figure(2)
\end{slide}


\begin{slide}
{\bf \large Observations on Robustness Analysis}\\
The preceding two figures show that the baseline empirical results are robust to extending the temporal and cross-sectional dimensions of the panel, especially along the following dimensions:\\
$\bullet$ Increases in the U.S.-interest-rate  and country-spread cause contractions in output and investment. \\
$\bullet$ Increases in the U.S.-interest-rate  and country-spread cause an improvement  in the trade-balance-to-GDP ratio (or, equivalently, a proportionally larger contraction in domestic absorption than in output).\\
$\bullet$  U.S.-interest-rate shocks cause a delayed increase in country spreads.\\
$\bullet$ Output shocks cause an expansion in investment, a deterioration of the trade-balance-to-GDP ratio, and, more importantly, a fall in country spreads.  
\end{slide}

\begin{slide}
\centerline{\bf Decomposition of Forecast-Error Variances}
Let $x_t \equiv [\widehat{y}_t\, \widehat{i}_t \, tby_t\, \widehat{R}^{us}_t \, \widehat{R}_t ]'$. Then the SVAR can be written as
\[
Ax_{t+h} = B x_{t+h-1} + \epsilon_{t+h}
\]
And its MA($\infty$) representation is
\[
x_{t+h} = \sum_{j=0}^{\infty}
C_j\epsilon_{t+h-j}, \mbox{ 
with }
C_j  \equiv \left(
A^{-1}B\right)^jA^{-1}
\]
The forecast of $x_{t+h}$ in $t$ is
$$
E_tx_{t+h} = \sum_{j=h}^{\infty}C_j\epsilon_{t+h-j}
$$
And the associated  forecast error, denoted $FE^h_t$, is
\[
FE^h_t = \sum_{j=0}^{h-1}C_j\epsilon_{t+h-j}
\]
\end{slide}

\begin{slide}
Then the forecast-error variance at horizon $h$, denoted $FEV^h$, is
\[
FEV^h =   \sum_{j=0}^{h-1}C_j
\Sigma_{\epsilon}C_j',\, \mbox{ where }
\Sigma_{\epsilon} \equiv E[\epsilon_t\epsilon_t']
\]
The forecast-error variance attributable to shock $i$ (the $i$-th element of $\epsilon_t$), denoted $FEV^{h,i}$, is
\[
FEV^{h,i} =  \sum_{j=0}^{h-1} (C_j\Lambda_i)
\Sigma_{\epsilon}(C_j\Lambda_i)',
\]
where $\Lambda_i$ is a square conformable matrix with all zeros except for diagonal element $(i,i)$ which equals unity.   
\end{slide}

\begin{slide}
The
share of 
 forecast-error variance of variable $k$ (i.e. $k$-th element of $x_t$) at horizon $h$ attributable to shock $i$, denoted $SFEV^{h,i}_k$, is given by
\[
SFEV^{h,i}_k = \frac{FEV^{h,i}_{kk}}{FEV^h_{kk}},
\]
where $kk$ denotes the $k$-th diagonal element.  This is called a forecast-error variance decomposition. 
As  the horizon become large, $h\rightarrow \infty$, the forecast-error variance of variable $k$ due to shock  $i$ converges to the unconditional variance of $k$ due to $i$.  
The next slide presents the forecast-error variance decomposition implied by the estimated SVAR system. 
\end{slide}


\begin{slide} 
\centerline{\bf \large Estimated Forecast-Error  Variance Decomposition} 
\centerline{\includegraphics[width=9in]{irs_var_decom_data_slides.eps}} 
\centerline{\rule{.2cm}{0.1cm} \rule{.2cm}{0.1cm} \rule{.2cm}{0.1cm} \rule{.2cm}{0.1cm} \rule{.2cm}{0.1cm} $\epsilon^{rus}_t$ \hspace{.5cm} \rule{1cm}{0.1cm}
 $\epsilon^{rus}_t+\epsilon^r_t$}
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%in directory: 
%U:\uribe\book\irs\mfiles\JIE_revision
\end{slide}

\begin{slide}
\centerline{\bf  Observations on  the Forecast-Error Variance Decompositions}

$\bullet$ Jointly,  country-spread and US-interest-rate shocks
($\epsilon^r_t$ and $\epsilon^{rus}_t$)
 explain

-- 30\% of movements in output.\\
-- 32\% of movements in investment.\\
-- 44\% of  movements in the trade-balance-to-GDP ratio.\\
-- 85\% of movements in country-spreads. 

$\bullet$ About 60\% of movements in country spreads is explained by country-spread shocks. 
\end{slide}


\begin{slide}
{\bf Alternative Identification Scheme:} Why Not Place  the Country Spread First in the SVAR System?

{\bf SVAR Prediction Under This Specification:} Output and investment expand in response to an increase in the U.S.\ interest rate.

{\bf Problematic:} It's difficult to rationalize this implication on theoretical grounds. 

\end{slide}


\begin{slide}
{\bf \large DSGE Analysis}

{\bf Motivation}\\
$\bullet$ The SVAR analysis is based on loose theoretical restrictions. 

$\bullet$ Does the propagation mechanism of  interest rate shocks ($\epsilon^{rus}_t$ and $\epsilon^r_t$) implied by the estimated SVAR model concur with the one implied by an optimizing DSGE open economy model? \\
$\bullet$ If so,  the identified interest-rate shocks would be more compelling since the effects they generate would 
be consistent with the optimizing behavior of households and firms. 

{\bf Strategy:} (1) Build a DSGE model of the open economy. (2) Feed the model with the estimated processes for $R^{us}_t$ and $R_t$ (the last 2 equations of the SVAR). (3) Compare the impulse responses predicted by the SVAR and DSGE models. 


\end{slide}


\begin{slide} 
{\bf \large The Theoretical Model (Uribe and Yue, 2006)}

Open economy  model with three frictions:
\begin{itemize}
\item Working-capital constraint on firms
\item Gestation lags and convex adjustment costs in investment
\item Habit formation
\end{itemize} 
\end{slide}

\begin{slide} 
{\bf Firms and Working Capital Constraints} 
\[
\max
 F(k_{t},h_{t}) - u_tk_{t}
- w_th_{t} 
\left[
1 + \frac{\eta (R^d_t-1)}{R^d_t}
\right]
\]
where $F(\cdot,\cdot)$ is a production function,  $h_t=$labor, $k_t=$capital, $w_t=$wage rate, and $R^d_t=$gross interest rate. 
The parameter $\eta$ governs the strength of the working-capital constraint.  The implied demand for labor is
\[
F_h(k_t,h_t) = w_t \left[
1+\eta \left(
\frac{R^d_t-1}{R^d_t}
\right)
\right]
\]
The working-capital constraint is a financial friction that allows for a supply-side effect of interest rate shocks. An increase in the interest rate increases the (financial) cost of labor, inducing a contraction in labor demand.  


 \end{slide}


\begin{slide}
{\bf  Capital Accumulation: Gestation Lags and Convex Adjustment Costs}
\[
i_t = \frac14 \sum_{i=0}^3 s_{it}.
\]
\[
s_{i+1t+1}=s_{it}, \quad i=0,1,2
\]
\[ 
k_{t+1} = 
(1-\delta)k_t 
+k_t \Phi 
\left( 
\frac{s_{3t}}{k_t} 
\right) 
\] 
where $i_t$=investment,  $s_{it}$=number of investment projects started in period $t-i$, for $i=0,1,2,3$ (4-period gestation lag); $k_t$=capital stock. Function $\Phi(\cdot)$ captures convex adjustment costs (note that $\Phi(\cdot)$ must be concave). 
\end{slide}

\begin{slide}
{\bf Households and Habit Formation} 
\[ 
\max E_0 \sum_{t=0}^{\infty} \beta^t\, U(c_t-\mu \tilde{c}_{t-1},h_t), 
\] 
subject to 
\[ 
d_t=R_{t-1} d_{t-1} - w_th_t - u_t k_t +c_t+ i_t + \Psi(d_t) 
\]
\[ 
\lim_{j\rightarrow \infty} E_t \frac{d_{t+j+1} }{\prod_{s=0}^j R_{t+s}}\le 0 
\] 
The function $\Psi(d_t)$ is convex; it  introduces portfolio adjustment costs and gives rise to an effective interest rate, $R^d_t$, satisfying
\[
R^d_t =  
\frac{R_t }
{ 1-\Psi'(d_t)}.
\]


\end{slide} 


\begin{slide}
\vspace{.5cm} 

{\bf \large Driving Forces} 

\begin{eqnarray*} 
\label{eq:R-hat} 
\hat{R}_t 
&=& 0.63 \hat{R}_{t-1} 
+ 0.50 \hat{R}^{us}_t 
+ 0.35 \hat{R}^{us}_{t-1} 
- 0.79 \hat{y}_t\\ 
&+& 0.61 \hat{y}_{t-1} 
+ 0.11 \hat{\imath}_t 
- 0.12 \hat{\imath}_{t-1} 
+ 0.29 tby_t\\ 
&-& 0.19 tby_{t-1} 
+ \epsilon^r_t, 
\end{eqnarray*} 

\[ 
\hat{R}^{us}_t = 
0.83 \hat{R}^{us}_{t-1} 
+ \epsilon^{rus}_t, 
\] 

where $\epsilon^r_t$ and $\epsilon^{rus}_t$ are mean-zero, iid, innovations with standard deviations equal to 0.031 and 0.007, respectively. 



\end{slide} 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{slide}
{\bf Functional Forms}
\[ U(c-\mu \tilde{c},h)=\frac{\left[c - \mu \tilde{c} - \omega^{-1} h^{\omega}\right]^{1-\gamma}-1}{1-\gamma}\]
%
\[F(k,h) = k^\alpha h^{1-\alpha}\]
\[\Phi(x)=x-\frac{\phi}2 (x-\delta)^2; \quad \phi>0\]
\[
\Psi(d)=\frac{\psi}{2}
(d-\bar{d})^2 
\]
\end{slide}
\begin{slide}
{\bf Calibrated Parameters (Quarterly)}
\[\omega=1.45\]
\[\gamma=2\]
\[\alpha=0.32\]
\[R=\beta^{-1}=1.0277\]
\[\delta=0.025\]
\[
\frac{tb}{y} = 0.02
\]
\end{slide}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{slide}
{\bf Estimating $\phi$, $\psi$, $\eta$, and $\mu$}

{\bf Criterion: } Minimize the distance between empirical and theoretical impulse response functions. 

Formally, $\phi$, $\psi$, $\eta$, and $\mu$ are set so as  to minimize
\[
[IR^e-IR^m(\psi,\phi,\eta,\mu)]' \Sigma_{IR^e}^{-1}
[IR^e-IR^m(\psi,\phi,\eta,\mu)], 
\]

Result of estimation: $$\psi=0.00042$$ $$\phi= 72.8$$ $$\eta=1.20$$  $$\mu=0.20$$
\end{slide}

\begin{slide} 
{\bf \large Theoretical and Estimated Impulse Response Functions} \\
\centerline{\includegraphics[width=10in]{irs_fit_habit_slides.eps}} 
%Produced with:  fit_habit.m in directory: 
%U:\uribe\book\irs\mfiles\jie_revision

\centerline{\small \rule{1cm}{.3mm} Empirical IR \hspace{.5cm}  \_ \_ \_ Error Band \hspace{.5cm} -x-x Theoretical IR}
\end{slide} 



\centerline{\bf \large Observations on the Theoretical Impulse Responses}


$\bullet$ The theoretical  model 
replicates well 
a number of key features of the estimated IRFs:\\
--  Output and investment contract in response to an increase in $\epsilon^{rus}_t$ or $\epsilon^r_t$.
\\
-- The trade balance improves in response to an increase in $\epsilon^{rus}_t$ or $\epsilon^r_t$.
\\
-- The country interest rate, $R_t$, displays a hump-shaped response to an increase in  $\epsilon^{rus}_t$.

$\bullet$ These findings suggest that the identification assumptions imposed in  the SVAR analysis are successful in isolating U.S.-interest-rate  and country-spread shocks.  


\begin{slide}
\begin{center}
{\bf  Conditional Standard Deviations\\  Implied by the SVAR and Theoretical Models}
%\label{table:irs_volatility_SVAR_theory}



\begin{tabular}{lccccc}
\hline
\hline
&\multicolumn{2}{c}{$\epsilon^{rus}_t$}&
\multicolumn{2}{c}{$\epsilon^{r}_t$}&Unconditional\\
\cline{2-6}
Variable&SVAR&Theory&SVAR&Theory&SVAR\\
\hline
$\widehat{y}$&  1.5&  1.6&  1.3&  1.3&3.7\\
$\widehat{\imath}$&6.4&3.6&5.0&2.0&14.2\\
$tby$&  2.1&  1.6&  2.0&  0.9&4.4\\
$\widehat{R}^{us}$&  1.3&  1.3&  0&  0&1.3\\
$\widehat{R}$&  3.8&  3.5&  4.7&  4.4&6.5\\
\hline\hline
\end{tabular}
\end{center}
%produced on 3/8/2015 by running 2 scripts, both in the directory
%c:\data\uribe\book\irs\mfiles\JIE_revision
%(1) var_decom1.m
%the variable STD contains columns 1,  3, and 5 of this table (SVAR predictions). 
%(2) var_decom_theory.m 
%STDTH produces columns 2 and 4 of this  table (Theoretical model predictions).
\end{slide}

\begin{slide}
{\bf \large Observations on Conditional Volatilities}\\
$\bullet$ 
 SOE model does well at capturing the importance of U.S.-interest-rate and country-spread shocks in explaining movements in output and country interest rates.\\
$\bullet$ The SOE model does a good job at accounting for variations in the trade balance due to U.S.-interest-rate shocks.\\$\bullet$  But the SOE model  underpredicts the volatilities of investment and the trade balance caused by country-spread shocks.\\
$\bullet$ SOE model implies that   $\epsilon^{rus}_t$ and $\epsilon^r_t$
 jointly explain 32 percent of  fluctuations in output
(($1.6311^2+1.2779^2)/3.6583^2=0.32$), almost same as SVAR ($(1.5274^2+1.3030^2)/3.6583^2=0.30$).
But   SOE model assigns less importance  to $\epsilon^{rus}_t$ and $\epsilon^r_t$ in accounting for variations in
$i_t$ and $tby_t$
 than does the SVAR.\\
$\bullet$ Overall, 
  identified $\epsilon^{rus}_t$ and $\epsilon^r_t$ shocks  are sensible and economically important.
\end{slide}

\begin{slide}
\centerline{\bf \large Shocks to Global  Risk Premia}


$\bullet$ What is the effect of movements in global risk premia on real and financial variables in emerging economies? 

$\bullet$ Akinci (2013) expands the SVAR studied above to include the spread between the U.S. Baa corporate bond rate and the 20-year U.S.\ Treasury bond yield. 

$\bullet$ Baa corporate bonds carry a medium degree of default risk: 13\% cumulative default risk over 20 years, compared with less than 1\% for Aaa rated bonds (highest rating by Moody's) and more than 70\% for C rated bonds (lowest rating). 


\end{slide}

\begin{slide}
{\bf \large The Augmented SVAR}
\begin{equation*}
%\label{eq:irs_Akinci}
A
\left[
\begin{array}{c}
\widehat{y}_t\\
\widehat{\imath}_t \\
tby_t\\
\widehat{R}^{us}_t\\
\widehat{S}^{us}_t\\
\widehat{R}_t
\end{array}
\right]
= B(L)
\left[
\begin{array}{c}
\widehat{y}_{t-1}\\
\widehat{\imath}_{t-1} \\
tby_{t-1}\\
\widehat{R}^{us}_{t-1}\\
\widehat{S}^{us}_{t-1}\\
\widehat{R}_{t-1}
\end{array}
\right]
+
\left[
\begin{array}{c}
\epsilon^y_t\\
\epsilon^i_t \\
\epsilon^{tby}_t\\
\epsilon^{rus}_t\\
\epsilon^{sus}_t\\
\epsilon^{r}_t
\end{array}
\right],
\end{equation*}
$S^{us}_t = $ U.S. corporate bond spread.  \\
{\bf Identification: } same as Uribe and Yue (2006). Pair $[R^{us}_t \, S^{us}_t]'$ follows bivariate process. \\
$\Rightarrow\epsilon^{sus}_t$ can be interpreted as an  innovation to the U.S.\ risk premium. Same interpretation as before for  other innovations. \\
{\bf Countries:} Argentina, Brazil, Mexico, Peru, South Africa, Turkey.\\
{\bf Sample:} 1994:Q1 to 2011:Q3.
\end{slide}

\begin{slide}
{\bf Predictions of SVAR with Global Risk Premium Shocks}

$\bullet$ Interest rate shocks, i.e., $[\epsilon^{rus}_ t\, \epsilon^{sus}_t\,  \epsilon^{r}_t]$,  jointly explain 42\% of the variance of output $\Rightarrow$ reinforces the result obtained by Uribe and Yue (2006).
\\
$\bullet$ The global  risk-premium shock takes over the role previously played by the U.S. interest rate:  $\epsilon^{sus}_t$ explains 18\% of the variance of output whereas $\epsilon^{rus}_t$ explains only 6\%. 
\\
$\bullet$  The country spread shock, $\epsilon^r_t$, continues to be an important driver of aggregate fluctuations in emerging countries, accounting  for 18\% of the observed  variance of output. 
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$\bullet$ Effects of global risk-premium shocks is mediated by the country premium: a 1 percentage point increase in $\epsilon^{sus}_t$ raises the country premium   by 1.3 percentage points. 
\end{slide}

\begin{slide}
{\bf \large Chapter Summary}


$\bullet$ Interest-rate shocks represent an important driver of business cycles in emerging countries, accounting for 30 to 42 percent of the variance of output.
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$\bullet$ Of the 30 to 42 percent of output variance explained by interest rate shocks, half is due to  a global component (U.S.-interest-rate shocks and U.S.-risk-premium shocks)  and the other half is due to  country-specific  spread shocks. 
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$\bullet$ In response to an increase in the interest rate, output and investment contract and the trade balance improves. 
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$\bullet$ An increase in the U.S. interest rate or in the U.S. risk premium produces an overshooting in country spreads, that is, the country spread increases by more than one for one. 
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$\bullet$  The majority of movements in country spreads  (more than 60 percent)  is explained by country spread shocks. 
\end{slide}

\end{document}
