%slides_soe_rbc_emerging.tex 
%Slides for Chapter 5 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 5   

business cycles in emerging
countries: 

productivity shocks
versus financial frictions}
\vspace{1in}

\end{minipage}
\end{slide}

\topleft{\textit{Open Economy Macroeconomics, Chapter 5} }
\topright{M.\ Uribe and S.\ Schmitt-Groh\'e}






\begin{slide}
\centerline{\bf A Quick Reminder Of The OE-RBC Model}
\[
%\label{eq:soe-rbc-utility-edeir}
\max E_0 \sum_{t=0}^{\infty} \beta^t U(c_t,h_t),
\]
subject to
\[
%\label{eq:soe-rbc-bc-combined-edeir}
d_t +
A_tF(k_t,h_t) =(1+r_{t-1})  d_{t-1} +c_t+ k_{t+1}-(1-\delta) k_t + \Phi(k_{t+1}-k_t).
\]
and a no-Ponzi-game constraint. The
driving force is the  productivity  shocks\\
\[
%\label{eq:soe-rbc-productivity-shock}
\ln A_{t+1} = \rho \ln A_t + \tilde{\eta}  \epsilon_{t+1},
\]
A debt-elastic country interest rate to induce stationarity \\
\[
%\label{eq:soe-rbc-r-edeir}
r_t = r^* + p(\tilde{d}_t).
\]
\end{slide}

\begin{slide}
{\bf  From Developed to Less Developed Countries}\\
$\bullet$ We saw that a calibrated version of the SOE-RBC model captures well key empirical regularities of a developed SOE like Canada (chapter 4). \\
$\bullet$  {\bf \large Question:} Can the OE-RBC model also explain business cycles in emerging  and poor economies? \\
$\bullet$ Two important differences between business cycles in developed and emerging and poor economies. \\
-- Emerging and poor economies are  twice as volatile as developed economies (fact~8 in chapter~1).\\
-- In developed economies consumption is less volatile than output, whereas in emerging and poor economies consumption is at least as volatile as output (fact~9 in chapter~1). 

Let's look at each of these two differences  more closely.

\end{slide}

\begin{slide}
 {\bf Emerging and poor economies are  twice as volatile as developed economies } (fact~8, chapter~1).

$\bullet$ In principle, the SOE-RBC model can easily handle this difference. Simply jack up 
(by a factor of around 2)
the standard  deviation of the productivity shock. After all, in the  SOE-RBC  model of  chapter 4,  $\sigma_a$ was calibrated to match the standard deviation of Canadian GDP. \\
$\bullet$  Since not only output but also all of the components of aggregate demand (consumption, investment, net exports) are more volatile in emerging  and poor countries than in rich countries, increasing $\sigma_a$ would help along more than one dimension. \\
$\bullet$  {\bf Problem:} Not all volatilities
 increase in the same proportion as we move from rich to emerging or poor countries. This brings us to the second difference between business cycles in rich and emerging/poor countries \dots
\end{slide}

\begin{slide}
{\bf  In developed economies consumption is less volatile than output, whereas in emerging and poor economies consumption is at least as volatile as output} (fact~9, chapter~1).  

In principle, the OE-RBC model can also handle this fact.  Consider varying the persistence of the productivity shock, governed by the parameter $\rho$. 

\end{slide}

\begin{slide}
\begin{center}
{\bf The Open-Economy RBC Model\\
The Relative Volatility of Consumption as a Function of the Persistence of the Stationary Technology Shock}
%\label{fig:soe-rbc-emerging_sigmac_sigmay}}

\includegraphics[width=6in]{soe_rbc_emerging_sigmac_sigmay.eps}
%produced by running
%edeir_sigmac_sigmay.m in
%c:\data\uribe\teaching\econ366\lecture_notes\edeir
\end{center}
\end{slide}

\begin{slide}
The following figure helps build intuition  for why a more persistent productivity shock increases the volatility of consumption relative to that of output. 
\end{slide}
\begin{slide}
\begin{center}
{\bf  The SOE-RBC Model:
Impulse Response of Output to a  One-Percent Increase in Productivity for High and Low Persistence Of the Stationary Productivity Shock}

%\label{fig:soe-rbc-emerging_ir_y_rho}}

\includegraphics[width=6in]{soe_rbc_emerging_ir_y_rho.eps}
%produced by running
%ir_y_rho.m in
%c:\data\uribe\teaching\econ366\lecture_notes\edeir
\end{center} 
\end{slide}

\begin{slide}
{\bf Intuition}

$\bullet$ With highly persistent productivity shocks, the impulse response of $y_t$ is increasing over time for a number of periods. This makes it possible that at $t=0$, permanent income  is higher than current income. Since consumption depends on permanent income, consumption increases by more than current income. \\
$\bullet$ With less persistent productivity shocks, permanent income increases by  less than current income, so consumption increases by less than current income. \\
$\bullet$  Why?  If productivity increases are expected to last  long, it pays to increase the stock of physical capital. But this takes time. The gradual build-up of the capital stock
dominates the gradual decline of productivity to its steady state, which 
 translates into an increasing path for output (see the analysis of chapter 3). 
\end{slide}

\begin{slide}
{\bf Problem:}

Recall that in the calibration strategy of chaper 4, $\rho$ was picked to match the observed serial correlation of output with the one predicted by the OE-RBC model. 

Thus, there is a tradeoff between using $\rho$ to match the excess volatility of consumption and using it to match the serial correlation of output. 

\end{slide}

\begin{slide}

{\bf The OE-RBC Model with Nonstationary Technology Shocks }

Aguiar and Gopinath (2007) propose solving this problem by adding a second productivity shock. 

The second productivity shock is  nonstationary  as in the closed-economy RBC model of  King, Plosser, and Rebelo (1988, II). 

The analysis of chapter 2 suggests that  even in the context of an endowment economy,  nonstationary endowment shocks have the potential to induce  excess volatility of consumption. 
\end{slide}





\begin{slide}
{\bf The SOE-RBC Model With Nonstationary Technology Shocks}
\[
\max E_0 \sum_{t=0}^{\infty} \beta^t
\frac{[C_t^{\gamma}(1-h_t)^{1-\gamma}]^{1-\sigma}-1}
{1-\sigma}
\]
subject to
\[
\frac{D_{t+1}}{1+r_t}
+Y_t = D_t + C_t + K_{t+1}-(1-\delta)K_t
+ \frac{\phi}2 \left(
\frac{K_{t+1}}{K_t}-g
\right)^2K_t,
\]
\[
Y_t = a_t K_t^{\alpha}(X_th_t)^{1-\alpha}
\]
\[
\lim_{j\rightarrow \infty}
E_t \frac{D_{t+j+1}}{\Pi_{s=0}^j
(1+r_{t+s})} \le 0,
\] 
The country interest rate
\[
r_t = r^* + \psi \left[
e^{\tilde{D}_{t+1}/X_t-\overline{d}}-1
\right],
\]
In equilibrium, $\tilde{D}_{t+1}=D_t$.

\end{slide}

\begin{slide}
{\bf Laws of Motion of Productivity Shocks}

\[
\ln a_t = \rho_a \ln a_{t-1} + \sigma_a \epsilon^a_t
\]
and 
\[
\ln (g_t/g) = \rho_g \ln(g_{t-1}/g) + \sigma_g \epsilon^g_t,
\]
where
\[
g_t \equiv \frac{X_t}{X_{t-1}}
\]

\end{slide}




\begin{slide}
\begin{center}
SOE-RBC Model With Nonstationary Shocks

 Calibrated Parameters
%\label{table:soe-rbc-emerging_AG-calibration}}

\bigskip

\begin{tabular}{c|c|c|c|c|c|c}
\hline\hline
$\beta$&$\gamma$&$\psi$&$\alpha$&$\sigma$&$\delta$&$\overline{d}$\\
0.98&0.36&\fbox{0.001}&0.32&2&0.05&0.1\\
\hline\hline
\end{tabular}

Estimated Parameters (GMM)

\begin{tabular}{c|c|c|c|c|c}
\hline\hline
$\sigma_g$&$\sigma_a$&$\rho_g$&$\rho_a$&$g$&$\phi$\\
0.0213&0.0053&0.00&0.95&1.0066&1.37\\
\hline\hline
\end{tabular}
\end{center}
The time unit is a quarter. Data from Mexico 1980:Q1 to 2003:Q1. Six parameters estimated by matching 10 moments. For moments matched, see next slide.  
\end{slide}


\begin{slide}
\begin{center}
Model Fit

%\label{table:soe-rbc-emerging_AG-model-fit}}

\bigskip

\begin{tabular}{ccc}
\hline\hline
Statistic&Data&Model\\
\hline
$\sigma(y)$&2.40&2.13\\
$\sigma(\Delta y)$&1.52&1.42\\
$\sigma(c)/\sigma(y)$&1.26&1.10\\
$\sigma(i)/\sigma(y)$&4.15&3.83\\
$\sigma(nx)/\sigma(y)$&0.80&0.95\\
$\rho(y)$&0.83&0.82\\
$\rho(\Delta y)$&0.27&0.18\\
$\rho(y,nx)$&-0.75&-0.50\\
$\rho(y,c)$&0.82&0.91\\
$\rho(y,i)$&0.91&0.80\\
\hline
\hline
\end{tabular}
\end{center}

Note. $y$ denotes HP-filtered log output  and $\Delta y$ denotes growth  
rate of output. Same for $c$ and $i$; $nx$ denotes the HP-filtered trade balance. 

\end{slide}


\begin{slide}
\centerline{
{\bf The Implied Importance of \\Nonstationary Productivity Shocks}
}
Let $TFP_t \equiv a_tX_t^{1-\alpha}$ be total factor productivity, and $X_t^{1-\alpha}$ its nonstationary component, which is orthogonal to$a_t$. 
\begin{center}
\begin{eqnarray*}
\label{eq:soe-rbc-emerging_share_of_SR}
\frac{\text{var}\left(\Delta \ln X^{1-\alpha}_t\right)}
{\text{var}\left(\Delta \ln TFP_t\right)}
&=&
\frac{\text{var}((1-\alpha)g_t)}
{\text{var}(\Delta \ln TFP_t)}\\
&=&
\frac{(1-\alpha)^2\sigma_g^2/(1-\rho_g^2)}
{2\sigma_a^2/(1+\rho_a)+(1-\alpha)^2\sigma_g^2/(1-\rho_g^2)} 
\\
\nonumber
&=&
\frac{(1-0.32)^2 \times 0.021^2/(1-0.00^2)}
{2 \times 0.005^2 /(1+0.95)+(1-0.32)^2 \times 0.021^2} 
\\
\nonumber
&=& 0.8793.
\end{eqnarray*}
\end{center}
$\Rightarrow$ The estimated model predicts that TFP growth is driven primarily by nonstationary productivity shocks. 
\end{slide}

\begin{slide}
\begin{center}
{\bf How Should We Interpret This Result?}
\end{center}
Three observations:

$\bullet$ Short sample (1980-2003): problematic if the main goal is to distinguish persistent but transitory productivity shocks from nonstationary productivity shocks. 

$\bullet$ Only productivity shocks are allowed in the horse race. How about other important shocks for emerging countries, such as country-interest-rate shocks? 

$\bullet$ The environment is constrained to be the frictionless neoclassical model. What if   distortions were allowed (financial frictions, nominal rigidities, etc.)?

We turn to this issues next \dots


\end{slide}



\begin{slide}

\centerline{\bf Business Cycles in Latin America: 1900-2005} 
%\label{fig:soe-rbc-emerging_GDP_LA_SDC}


\includegraphics[width=6in]{soe_rbc_emerging_LatinAmerica_gdp.eps}
%produced with c:\data\uribe\trend_cycle\aer_revision\barro_data\plotdata.m, it is figure(1)




$\Rightarrow$ The sample 1980-2003 contains at most one and a half cycles. 

\end{slide}


\begin{slide}
\begin{center}
{\large Addressing  The Three Observations}
\end{center}
$\bullet$ Short sample (1980-2003):  Use  annual data on output, consumption,  investment, and the trade balance from 1900 to 2005. 


$\bullet$ Only productivity shocks are allowed in the horse race: Add more shocks;  country-interest-rate shocks, preference shocks, and government spending shocks. 
 
$\bullet$ The environment is constrained to be the frictionless neoclassical model: add financial frictions, namely, by allowing the data to pick the debt elasticity of the country interest rate and by including a working capital constraint. 
\end{slide}


\begin{slide}
\begin{center}
{\bf A Model With Multiple Shocks and Financial Frictions\\ (GPU, AER 2010) }
\end{center}
\begin{equation*}
%\label{eq:soe-rbc-emerging_gpu-wc-utility-nonstationary} 
\mbox{Households:  }\quad  \max E_0\sum_{t=0}^{\infty} \nu_t\beta^t
\frac{\left[C_t - \omega^{-1}X_{t-1} h_t^{\omega}\right]^{1-\gamma}-1}{1-\gamma},
\end{equation*}
subject to 
\begin{equation*}
%\label{eq:soe-rbc-emerging_gpu-wc-bc-nonstationary}
\frac{D_{t+1}}{1+r_t} = D_t - W_th_t - u_t K_t + C_t + S_t + I_t + \frac{\phi}{2} \left(\frac{K_{t+1}}{K_t}-g\right)^2K_t,
\end{equation*}
\begin{equation*}
%\label{eq:soe-rbc-emerging_gpu-wc-k}
K_{t+1} = (1-\delta) K_t + I_t, 
\end{equation*}
\[
\mbox{Firms:} \quad \max_{\{h_t,K_t\}}
\left\{
a_tK_t^{\alpha} (X_th_t)^{1-\alpha} -u_tK_t - W_th_t\left[
1+ 
\frac{\eta r_t}{1+r_t}
\right]
\right\},
\]
\begin{equation*}
\label{eq:soe-rbc-emerging_gpu-wc-country-premium}
\mbox{Country Interest Rate:} \quad
r_t = 
r^* +  \psi \left(
e^{
\frac{
\widetilde{D}_{t+1}/X_t-\overline{d}}
{\overline{y}}
}
 -1 \right)
+ e^{\mu_t-1}-1,
\end{equation*}

\end{slide}


\begin{slide}
{\bf Five Shocks}
\begin{equation*}
\label{eq:soe-rbc-emerging_gpu-wc-stationary-productivity-shock}
\ln a_{t+1} = \rho_a \ln a_t + \epsilon^a_{t+1}. 
\end{equation*} 
\begin{equation*}
\label{eq:soe-rbc-emerging_gpu-wc-nonstationary-productivity-shock}
\ln (g_{t+1}/g) = \rho_g \ln (g_t/g) + \epsilon^g_{t+1}, \quad \quad
g_t \equiv \frac{X_t}{X_{t-1}} 
\end{equation*}
\begin{equation*}
%\label{eq:soe-rbc-emerging_gpu-wc-preference-shock}
\ln \nu_{t+1} = \rho_{\nu} \ln \nu_t + \epsilon^{\nu}_{t+1},
\end{equation*}  
\[
\ln \mu_{t+1} = \rho_{\mu} \ln \mu_t + \epsilon^{\mu}_{t+1}. 
\]
\begin{equation*}
\label{eq:soe-rbc-emerging_gpu-wc-spending-shock-shock}
\ln (s_{t+1}/\overline{s}) = \rho_s \ln (s_t/\overline{s}) + \epsilon^s_{t+1},  \quad \quad
s_t\equiv \frac{S_t}{X_{t-1}}, 
\end{equation*}

\end{slide}


\begin{slide}
\begin{center}
\singlespacing
{\bf Calibrated Parameters}
%\label{table:soe-rbc-emerging_gpu-wc-calibration}

\medskip

\begin{tabular}{cc}
\hline \hline
Parameter&Value\\
 \hline
$g$ & 1.0107\\
$\overline{d}/\overline{y}$&0.037\\
$\delta$&0.1255\\
$r^*$&0.10\\
$\alpha$&0.32\\
$\gamma$&2\\
$\omega$&1.6\\
$\overline{s}/\overline{y}$ & 0.10\\
\hline \hline
\end{tabular}
\end{center}

\end{slide}


\begin{slide}

\begin{center}
{\bf Bayesian Estimation}
\end{center}

Estimate the model  on 4 time series:  output growth, consumption growth, investment growth, and the trade balance-to-output ratio. 

Estimate 13 structural parameters and 4 nonstructural parameters associated with  measurement errors. 

The structural parameters include 10 defining the processes of the 5 structural shocks, 
$\sigma_g$, 
$\rho_g$, 
$\sigma_a$,
$\rho_a$,
$\sigma_{\nu}$,
$\rho_{\nu}$,
$\sigma_s$,
$\sigma_{\mu}$,
$\rho_{\mu}$ , and the parameters governing capital adjustment costs, 
$\phi$,
the debt elasticity of the country intrest rate, 
$\psi$, and the magnitude of the working-capial constraint, $\eta$. 

The nonstructural parameters are the standard deviations of  measurement errors on output growth, 
$\sigma_{g^Y}^{me}$, 
consumption growth, 
$\sigma_{g^C}^{me}$, 
investment growth, 
$\sigma_{g^I}^{me}$, and 
the trade-balance-to-output ratio,
$\sigma_{TB/Y}^{me}$.


\end{slide}



\begin{slide}
\begin{center}
{\small
{\bf Bayesian Estimation Results}
%\label{table:soe-rbc-emerging_gpu-wc-bayesian-estimation}
\begin{tabular}{cccc|cccc}
\hline\hline
&\multicolumn{3}{c}{Uniform Prior Distributions}&\multicolumn{4}{c}{Posterior Distributions}\\
\cline{2-8}
Parameter&Min&Max&Mean&Mean&Median&5\%&95\%\\
\hline
\fbox{$\sigma_g$}&       0&    0.2&     0.1&  0.0082&  \fbox{0.0067}&  \fbox{0.00058}&   \fbox{0.021}\\
\fbox{$\rho_g$}&   -0.99&   0.99&       0&    0.15&    \fbox{0.21}&    \fbox{-0.69}&    \fbox{0.81}\\
$\sigma_a$&       0&    0.2&     0.1&   0.032&   0.032&    0.027&   0.036\\
$\rho_a$&   -0.99&   0.99&       0&    0.84&    0.84&     0.75&    0.91\\
$\sigma_{\nu}$&       0&      1&     0.5&    0.53&    0.51&     0.39&    0.77\\
$\rho_{\nu}$&   -0.99&   0.99&       0&    0.85&    0.85&     0.76&    0.93\\
$\sigma_s$&       0&    0.2&     0.1&   0.062&   0.064&   0.0059&    0.12\\
$\rho_s$&   -0.99&   0.99&       0&    0.46&    0.56&    -0.42&    0.92\\
$\sigma_{\mu}$&       0&    0.2&     0.1&    0.12&    0.11&    0.067&    0.18\\
$\rho_{\mu}$&   -0.99&   0.99&       0&    0.91&    0.92&     0.83&    0.98\\
$\phi$&       0&      8&       4&     5.6&     5.6&      3.9&     7.5\\
$\psi$&       0&     10&       5&     1.4&     \fbox{1.3}&     0.55&     2.4\\
$\eta$&       0&      5&     2.5&    0.42&     0.4&     0.18&     0.7\\
%$\sigma_{g^Y}^{me}$&  0.0001&  0.013&  0.0067&  0.0045&  0.0042&  0.00051&  0.0096\\
%$\sigma_{g^C}^{me}$&  0.0001&  0.019&  0.0095&  0.0075&  0.0076&  0.00097&   0.014\\
%$\sigma_{g^I}^{me}$&  0.0001&  0.051&   0.025&   0.041&   0.044&    0.022&    0.05\\
%$\sigma_{TB/Y}^{me}$&  0.0001&  0.013&  0.0065&  0.0033&  0.0031&  0.00041&  0.0068\\
\hline\hline
\end{tabular}
}
\end{center}
Note. Based on an  MCMC chain of length 1 million produced using the Metropolis-Hastings algorithm.  Estimates of the standard deviations of measurement errors are presented in chapter 5. 
\end{slide}

\begin{slide}
{\bf \large Observations On Estimation Results}

The parameters defining the process of the nonstationary technology shock are estimated with substantial uncertainty. 

By contrast, the parameters defining the process of the stationary technology shock are more tightly estimated.

The data assigns a value significantly higher than 0 to the debt-elasticity of the  country interest rate, $\psi$. 


\end{slide}


\begin{slide}
\begin{center}
{\bf Empirical and Theoretical Second Moments}
%\label{table:soe-rbc-emerging_gpu-wc-data-model-second-moments}
{\small
\begin{tabular}{lcccc}
\hline\hline
Statistic&$g^Y$&$g^C$&$g^I$&$TB/Y$\\
\hline
\underline{Standard Deviation}\\
Model
&     \fbox{6.2}&      \fbox{8.9}&      18.6&      \fbox{4.9}\\
Data
&     \fbox{5.3}&      \fbox{7.5}&      20.4&      \fbox{5.2}\\
&    (0.43)&      (0.6)&     (1.8)&    (0.57)\\
\underline{Correlation with $g^Y$}\\
Model
&       &   0.80&   0.53&   \fbox{-0.18}\\
Data &       &     0.72&    0.67&   \fbox{-0.04}\\
&       &    (0.07)&   (0.09)&    (0.09)\\
\underline{Correlation with $TB/Y$}\\
Model
& &  -0.37&  -0.31&   \\
Data
& &    -0.27&   -0.19&       \\
& &     (0.07)&    (0.08)&       \\
\underline{Serial Correlation}\\
Model
&   0.04&  -0.06&  -0.098&   0.51\\
Data
&    0.11&  -0.0047&    0.32&    0.58\\
&   (0.09)&    (0.08)&   (0.10)&   (0.07)\\
\hline\hline
\end{tabular}
}
\end{center}
\end{slide}

\begin{slide}
{\bf Observations On Model Fit}

$\bullet$
The model does a good job at capturing a number of second moments of interest.  In particular,

$\bullet$ The high volatility of output growth. 

$\bullet$ The excess volatility of consumption growth relative to output growth. 

$\bullet$ A volatility of the trade-balance-to-output ratio comparable to that of output growth and a mild negative correlation between this variable  and output growth. 

$\bullet$ The model does not capture the positive serial correlation of investment growth. 

\end{slide}

\begin{slide}

\begin{center}
{\bf  \large Variance Decomposition}


%\label{table:soe-rbc-emerging_gpu-wc-var-decomp}
\begin{tabular}{lrrrr}
\hline\hline
Shock&$g^Y$&$g^C$&$g^I$&$TB/Y$\\
\hline
Nonstationary Tech.
&   \fbox{2.6}&   1.1&   0.2&   0.1\\
Stationary Tech.
&  81.8&  42.4&  12.7&   0.5\\
Preference
&   6.8&  27.7&  29.1&   6.2\\
Country Premium
&   6.1&  25.8&  52.0&  92.1\\
Spending
&   0.0&   0.3&   0.3&   0.1\\
Measurement Error
&   0.4&   0.7&   5.2&   0.4\\
\hline\hline
\end{tabular}

Note.  Median of an MCMC chain of length 1 million. 
\end{center}

\end{slide}



\begin{slide}


{\bf  Observations On Variance Decomposition }

$\bullet$ The nonstationary productivity shock explains a small fraction of the variance of output growth and other variables. 

$\bullet$ Much of the variance of output growth is explained by stationary technology shocks. 

$\bullet$ In explaining the excess volatility of consumption, the data appears to prefer a combination of stationary productivity shocks, interest-rate shocks, and preference shocks, rather than nonstationary productivity shocks, as was the case in the RBC model driven solely by  two productivity shocks. 

$\bullet$  Interest-rate shocks are assigned a primary role in explaining movements in investment and the trade-balance-to-output ratio. 
 
\end{slide}


\begin{slide}
\begin{center}
{\bf \large The Implied Importance of \\Nonstationary Productivity Shocks \\
Revisited}
\end{center}


Variance Decomposition of TFP Growth


\begin{eqnarray*}
\frac{\text{var}(\Delta \ln(X_t^{1-\alpha}))}
{\text{var}(\Delta \ln TFP_t)}
&=&
\frac{(1-\alpha)^2\sigma_g^2/(1-\rho_g^2)}
{2\sigma_a^2/(1+\rho_a)+(1-\alpha)^2\sigma_g^2/(1-\rho_g^2)} 
\\
&=& 0.024.
%produced with
%var_decomp_tfp.m in
%c:\data\uribe\book\soe_rbc_emerging\mfiles
\end{eqnarray*}


$\Rightarrow$ The estimated model predicts a negligible contribution of nonstationary productivity shocks to  movements in TFP growth. 
\end{slide}



\begin{slide}
\begin{center}
{\bf The Importance of Financial Frictions}
\end{center}

$\bullet$ Put to choose, the data favors a value of $\psi$, governing the debt-elasticity of the interest rate, much higher than the small vlaue required to induce stationarity. This is an indication of the importance of  that financial frictions. 

$\bullet$ To quantify this importance, the next slide displays observed autocorrelation function of the trade-balance-to-output ratio along with the ones predicted by the model for two values of $\psi$, its posterior median of 1.3 and a small value of 0.001. 

$\bullet$ Why look at the trade balance to output ratio? Because $\psi$ affects the country's ability to borrow internationally, and, as a result, the cyclicality of  the current account, of which the trade balance is a main component. 

\end{slide}


\begin{slide}
\begin{center}
{\bf The Autocorrelation Function of the\\ Trade-Balance-To-Output Ratio}
%\label{fig:soe-rbc-emerging_gpu-wc-financialfrictions_vs_rbc} }
\centering{\includegraphics[width=6in]{soe_rbc_emerging_plot_acf_tby.eps}}
%produced with \uribe\book\soe_rbc_emerging\mfiles\plot_acf_tby.m 
\end{center}
{\tiny
Note. The point estimate and error band of the empirical autocorrelation function was estimated by GMM. After setting $\psi$ to 0.001, the theoretical model was 
reestimated. }
\end{slide}







\end{document}