%slides_tot.tex
%Slides for Chapter 7 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 7   

Importable Goods,

 Exportable Goods,  and 

the Terms of Trade

}
\vspace{1in}

\end{minipage}
\end{slide}

\topleft{\textit{Open Economy Macroeconomics, Chapter 7} }
\topright{M.\ Uribe and S.\ Schmitt-Groh\'e}

\begin{slide}
{\bf \large Motivation}\\
$\bullet$ Thus far, we have studied economies with a single good. The same good is produced, consumed,
sometimes 
 imported, and sometimes exported. \\
$\bullet$ In reality, economies produce, consume, and trade different goods. For example,   copper represents a significant fraction of Chile's exports and GDP, but a small fraction of its consumption and imports. 

\end{slide}

\begin{slide}
{\bf \large Three Categories of Goods Based on International Tradability}\\

$\bullet$
An {\it importable} good is either an  imported good or a good that
is produced domestically but is highly substitutable with a good
that can be  imported.\\
$\bullet$An {\it exportable} good is either an
exported good or a good that is sold domestically but is highly
substitutable with a good that can be  exported. \\
$\bullet$ A {\it nontradable} good is a good that is neither imported nor exported. Nontradables are exclusively produced and  consumed domestically.

\end{slide}

\begin{slide}
{\bf \large Two Important Relative Prices }

The three categories of goods defined in the previous slide give rise to two   important relative prices:

$\bullet$ The {\it Terms of Trade} is the relative price of exportable goods in terms of importable goods. 

$\bullet$ The {\it Real Exchange Rate} is the relative price of a domestic  basket of consumption goods in terms of  foreign baskets of consumption goods. 


These relative prices receive significant attention in Macroeconomics because they either drive or reflect aggregate and sectoral movements in absorption, production, and international trade. 

\end{slide}


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

$\bullet$
Studies open-economy models with  importable and exportable goods. 

$\bullet$ Analyzes empirically and theoretically the aggregate consequences  of movements in the terms of trade. 

$\bullet$ The next chapter introduces nontradable  goods and studies
 the determinants of the real exchange rate. 
\end{slide}

\begin{slide}
{\bf \large The Terms of Trade}

Let $P^x_t$ be a price index of exportable goods and $P^m_t$ a price  index of importable goods for a given country in period $t$. Then, the terms of trade for that country in period $t$, denoted $tot_t$  is  defined as
\[
tot_t = \frac{P^x_t}{P^m_t}.
\]
When $tot_t$ increases, we say that the country experienced an improvement of its terms of trade. 
\end{slide}

\begin{slide}
{\bf \large A Simple Empirical Model of the Terms of Trade}

The typical country is a  small player in the
world markets for the goods it  exports and  imports.


  Thus, it makes sense to assume that 
variations in the terms of trade
represent 
exogenous source of aggregate fluctuations for most countries.  

Accordingly, we postulate that the terms of trade follow a univariate autoregressive process of the form
\begin{equation}
\label{eq:tot_tot_ar1}
\widehat{tot}_t
 = 
\rho \, \widehat{tot}_{t-1}
 + \pi \epsilon_t^{tot},
\end{equation}
where $\widehat{tot}_t$
denotes the log-deviation of 
$tot_t$ 
 from trend (cyclical component of $tot_t$),  
  $\epsilon^{tot}_t\sim (0,1)$ is a white noise,  $\rho\in(-1,1)$ denotes the serial correlation of
the cyclical component of t$tot_t$, and $\pi$ denotes the standard deviation of the innovation in the terms-of-trade process. 
\end{slide}

\begin{slide}
{\bf \large Estimation}

$\bullet$ Obtain $\widehat{tot}_t$ by removing a quadratic trend from the log of $tot_t$.


$\bullet$ Estimate equation~\eqref{eq:tot_tot_ar1}  by OLS.

$\bullet$  Use annual data from 51 poor and emerging countries over the period 1980 to 2011.

$\bullet$ Include only countries with at least 30 consecutive years of data. 

$\bullet$ Data source: World Development Indicators (WDI) from the World Bank. (File n data\_annual.xls in the book's website.)

\end{slide}




\begin{slide}
{\bf \large Terms of Trade Process: Estimation Results}
\singlespacing

\begin{center}
Country-specific estimates of the equation\\
 $\widehat{tot}_t = \rho\, \widehat{tot}_{t-1} + \pi\epsilon^{tot}_t;$ 

{\tiny
\begin{tabular}{lccc}
\hline\hline
Country&$\rho$&$\pi$&$R^2$\\
\hline
\hline
Mean &  0.50&  0.10&  0.30\\
Median &  0.53&  0.09&  0.31\\
Interquartile Range &
$
\left[
\begin{array}{l}
0.41\\0.61
\end{array}
\right]
$&$
\left[
\begin{array}{l}
0.07\\0.11
\end{array}
\right]
$&
$
\left[
\begin{array}{l}
0.19\\0.39
\end{array}
\right]
$
\\
\hline \hline
\end{tabular}}
\end{center}

%produced by running 
%table_ar1_cbc.m in 
%c:\data\uribe\book\tot\data

{\bf Observations}\\
$\bullet$ Terms of trade are moderately volatile:  Implied unconditional standard deviation at median, $\frac{\pi}{\sqrt{1-\rho^2}}$, equal to 0.11 (or 11\% of trend value). \\
$\bullet$  Terms-of-trade shocks die relatively quickly: Half life at median, $\frac{\ln(1/2)}{\ln(\rho)}$, of just one year. \\
$\bullet$  Homogeneity Across Countries:  For half of the countries,  $\rho$ lies in the interval (0.41,0.61) and $\pi$ in the interval $(0.07,0.11)$.\\
$\bullet$ Moderate Fit: Median $R^2$ of  0.31. 

\end{slide}


\begin{slide}
{\bf \large Terms-Of-Trade And  The Trade Balance: Empirics}

Does an improvement of the terms of trade cause an improvement or a deterioration of the trade balance? 

This question is the focus of much research in open economy macroeconomics, and does not have an unambiguous theoretical answer. We begin by addressing it from an empirical perspective. 

Consider the following joint process for the terms of trade and the trade balance:
\begin{equation}
\label{eq:tot_tot}
\widehat{tot}_t = \rho \widehat{tot}_{t-1} + \pi \epsilon^1_t,
\end{equation}
\begin{equation}
\label{eq:tot_tb}
\widehat{tb}_t = \alpha_0\widehat{tot}_t 
+ \alpha_1 \widehat{tot}_{t-1} + \rho_2 \widehat{tb}_{t-1} + \sqrt{\sigma_{22}} 
\epsilon^2_t
\end{equation}
where $\epsilon^1_t$ and $\epsilon^2_t$ are  mean-zero i.i.d.\    innovations,  
 $\widehat{tb}_t$ is  a detrended measure of the trade balance, $\alpha_0$, $\alpha_1$,  $\rho_2$, and $\sigma_{22}$ are  parameters.   As before, we estimate this system by OLS,  country by country,  and equation by equation, on annual data from  51 poor and emerging countries over the period 1980 to 2011.
\end{slide}

\begin{slide}
{\bf Identification}\\
$\bullet$ We adopt the identification assumption that $\epsilon^1_t$ is a terms-of-trade shock.\\
$\bullet$ Because the $\widehat{tot}_t$  appears contemporaneously in equation~\eqref{eq:tot_tb}, 
we have that $\epsilon^1_t$ is orthogonal to $\epsilon^2_t$.\\
$\bullet$  This means that $\epsilon^2_t$ captures  shocks other than terms-of-trade shocks that affect the trade balance contemporaneously.\\
$\bullet$  Solving equations~\eqref{eq:tot_tot} and \eqref{eq:tot_tb} for $[\widehat{tot}_t\,\,\widehat{tb}_t]'$ yields the SVAR system
\begin{equation}
\label{eq:tot_x_2var}
\left[ 
\begin{array}{c}
\widehat{tot}_t\\
\widehat{tb}_t
\end{array}
\right]
= h_x 
\left[ 
\begin{array}{c}
\widehat{tot}_{t-1}\\
\widehat{tb}_{t-1}
\end{array}
\right]
 + \Pi 
\left[ 
\begin{array}{c}
\epsilon^1_t\\
\epsilon^2_t
\end{array}
\right],
\end{equation}
where 
\[
h_x \equiv 
\left[
\begin{array}{cc}
\rho&0\\
\alpha_0\rho+\alpha_1&\rho_2
\end{array}
\right]  \quad  \mbox{ and }  \quad 
\Pi \equiv
\left[
\begin{array}{cc}
\pi&0\\
\alpha_0\pi&\sqrt{\sigma_{22}}
\end{array}
\right].
\]

\end{slide}

\begin{slide}
{\bf \large Does the Trade Balance in Response to an Increase in the Terms of Trade?}\\
The cross-country mean of the estimated  TOT-TB SVAR system is 
\[
\left[
\begin{array}{c}
\widehat{tot}_t\\
\widehat{tb}_t
\end{array}
\right]
=
\left[
\begin{array}{cc}
0.50&0\\
   -0.02    &0.57\\
\end{array}
\right]
\left[
\begin{array}{c}
\widehat{tot}_{t-1}\\
\widehat{tb}_{t-1}
\end{array}
\right]
+
\left[
\begin{array}{cc}
0.10&0\\
    0.008 &   0.032\\
\end{array}
\right]
\left[
\begin{array}{c}
\epsilon_t^{tot}\\
\epsilon^{tb}_t
\end{array}
\right].
%produced by running tot_cbcs.m in
%c:\data\uribe\book\tot\data
%make sure to use the statement nvar = [ntot ntb]; around line 13
\]
The fact that the element $(2,1)$ of $\Pi$ is estimated to be positive on average  means that a positive terms-of-trade shock causes an improvement of the trade balance. 

In particular, a 10 percent improvement in the terms of trade causes an improvement in the trade balance of  0.8 percent of trend GDP.  

Thus, the answer to the question posed at the beginning of the present empirical analysis is {\it yes, the trade balance improves in response to an increase in the terms of trade. }

This is true not only on average across countries, but for most individual countries (38 out of the 51 countries in the sample). 

\end{slide}

\begin{slide}
{\bf \large How Persistent Are the Effects of Terms-of-Trade Shocks on the Trade Balance?}\\
The right panel of the figure displays the response of the trade balance to a +10\% innovation in the terms of trade (average of country-specific impulse responses). 
%\label{fig:tot_ir_cbc_2var} 

\centerline{\includegraphics[width=6.5in]{tot_ir_cbc_2var.eps}}

%produced by running 
%tot_ir_cbc.m (set sizevar=2 in tot_cbcs.m)
%in z:\uribe\book\tot\data

The improvement in the trade balance dies quickly. Less than two years after the improvement in the terms of trade  the trade balance is below trend. \\
{\bf Qualification of the Answer Given in the Previous Slide:} {\it Yes, an  increase  in the terms of trade causes a short-lived   improvement in the trade balance} 

\setcounter{page}{\theslide}
\label{slide:tot_ir_cbc_2var}

\end{slide}

\begin{slide}
{\bf \large The Terms of Trade and  the Trade Balance: Simple Explanations, Old and New}

$\bullet$ {\bf The Harberger-Laursen-Metzler (HLM) 
 Effect} An increase in the terms of trade always improves the trade balance. This result was derived in the context of a Keynesian model and was prevalent between  the early 1950s and the early 1980s. 

$\bullet$
{\bf The Obstfeld-Svensson-Razin (ORS)  Effect}
The effect of the terms of trade on the trade balance depends crucially on the persistence of the terms of trade. The HLM effect holds for low persistence process, but may be reverted at high levels of persistence. This result was derived in the context of a optimizing model of the open economy. 

Let's examine these two theories more closely. 
\end{slide}

\begin{slide}
 {\bf  \large The Harberger-Laursen-Metzler 
 Effect} \\
A classical Keynesian model delivers a positive relationship between $tb_t$ and $tot_t$.  Start with the 
 national accounting identity\\
\centerline{$
y_t = c_t + g_t + i_t + x_t - m_t,
$}
where $y_t$=output, $c_t$= consumption, $g_t$ gov't spending, $i_t$=  investment, $x_t$=
 exports, and $m_t$= imports.  All variables   measured in units of imports. 
Consider the following
behavioral equations \\
\centerline{$g_t = \overline{g}; \quad
i_t = \overline{i}; \quad
[c_t=\overline{c}+\alpha y_t;\quad
m_t=\mu y_t,$}\\
where $\alpha,\mu\in(0,1)$ are known as the marginal propensities to consume and import, and $\overline{c}+\overline{g}+\overline{i}$ as the
autonomous component of domestic absorption.
Let $\overline{q}$ be the quantity of exports; then experts in units of import gods is given by \\
\centerline{$x_t = tot_t \overline{q}.$}\\
The trade balance is  $tb_t l= m_t-x_t$. Combining   all  expressions yields\\
\centerline{$
tb_t = \frac{1-\alpha}{1+\mu-\alpha} tot_t\overline{q} - \frac{\mu(\overline{c}+\overline{g}+\overline{i})}{1+\mu-\alpha} \Rightarrow
\frac{\partial tb_t}
{\partial tot_t} = \frac{1-\alpha}{1+\mu-\alpha} \overline{q}>0$
}\\
This is the HLM effect. Intuition: $tot_t\uparrow\Rightarrow x_t\uparrow\Rightarrow y_t\uparrow\Rightarrow c_t, m_t\uparrow\Rightarrow y_t\uparrow \Rightarrow c_t, m_t
\dots$ but because $\alpha,\mu<1$,  at the end $m_t$ increases by less than $x_t$, so $tb_t\uparrow$.\\
$\bullet$ The  HLM effect appears to be supported by the data (see the figure on slide~\pageref{slide:tot_ir_cbc_2var}).


\end{slide}

\begin{slide}
{\bf Terms-of-Trade Persistence and the HLM Effect}

The HLM effect is mute with respect to how the persistence of $tot_t$. Suppose that the marginal propensity to consume depends positively on the persistence of $tot_t$\\
\centerline{$\alpha(\rho)$ \mbox{ with } $\alpha'(\rho)>0$}
This makes sense: consumption smoothing agents save much of temporary shocks and little of highly persistent shocks. Then we have that 
\[
\frac{\partial tb_t}
{\partial tot_t} = \frac{1-\alpha(\rho)}{1+\mu-\alpha(\rho)} \overline{q},
\]
which suggests that the sensitivity of $tb_t$ to changes in $tot_t$ decreases with the persistence of $tot_t$. This is precisely what the ORS effect is about, in the context in which $\alpha(\rho)$ is endogenously derived in a utility-maximizing framework. 
\end{slide}

\begin{slide}
{\bf \large The Obstfeld-Svensson-Razin   Effect}\\
Consider the endowment open economy of chapter 2. Households consume an importable good,   are endowed with 1 unit of an exportable good, and can borrow or lend at the rate $r>0$. They 
\[
\max_{\{c_t,d_t\}}
E_0-\frac12
\sum_{t=0}^{\infty}\beta^t
(c_t-\bar{c})^2,
\]
subject to
\[
d_t = (1+r) d_{t-1} + c_t - tot_t,
\]
  Assume that $tot_t$ follows the AR(1) process $
tot_t  = \rho \, \, tot_{t-1} + \epsilon^{tot}_t.
$ As we saw in  chapter 2, the equilibrium trade balance is given by
\[
tb_t = rd_{t-1} + \frac{1-\rho}{1+r-\rho} \, \, tot_t,
\]
which implies that  
\begin{equation}
\label{eq:tot_dtb/dtot_ors}
\frac{\partial tb_t}
{\partial tot_t} =
 \frac{1-\rho}{1+r-\rho} .
\end{equation}
The response of the trade balance to terms-of-trade shocks is weaker the more persistent the terms of trade is. This is the ORS effect. 
\end{slide}

\begin{slide}
{\bf \large Testing the ORS Effect}\\


$\bullet$ According to the ORS effect, the response of the trade balance to terms-of-trade shocks is weaker the more persistent the terms of trade are. 

$\bullet$ This is intuitive: a $tot$ shock is like an income shock, and it makes sense that  households save a large fraction of temporary income shocks and a small fraction of permanent income shocks. 

$\bullet$ Is the ORS effect borne out in the data? To see this, use the estimates of the SVAR system  \eqref{eq:tot_x_2var} for each of the 51 poor and emerging countries  of our data set. Then, for each country plot the estimated  impact response of the trade balance to a 10\% increase in the terms of trade 
($\frac{\pi_{21}}{\pi_{11}}\times10$)
as a function of the  estimated persistence parameter $\rho$. 

$\bullet$ If the ORS effect was present in the data, we should observe a negative pattern. 

\end{slide}
\begin{slide}
{\bf Testing for the ORS Effect: Impact Response of the Trade Balance to a Terms of Trade Shock and the Persistence of the Terms of Trade}

\begin{center}

%\label{fig:tot_ors_test}
\includegraphics[width=3.5in]{tot_ors_test.eps}\\
{\tiny Note. Each circle corresponds to a pair $(\rho,\pi_{21}/\pi_{11}\times 10)$ for a particular country, where the parameters $\rho$,  $\pi_{21}$, and  $\pi_{11}$ are  obtained by estimating the SVAR system~\eqref{eq:tot_x_2var}.}

%produced with 
%ors_test.m (set sizevar=2 in tot_cbcs.m)
%z:\uribe\book\tot\data 
\end{center}
The figure displays no clear negative relation between $\rho$ and the size of the impact effect of a terms-of-trade shock on the trade balance, implying that the data does not lend strong support to the ORS effect. 

\end{slide}

\begin{slide}
{\bf \large The ORS Effect in the SOE-RBC Model}

In the  SOE-RBC model of chapter 4, assume that consumption and investment are imported goods and output is exportable. Then, assuming no productivity shocks, output in terms of importable goods is given by $tot_t F(k_t,h_t)$, and the trade balance 
is then given by
\[
tb_t = tot_t F(k_t,h_t)-c_t - i_t - \Phi(k_{t+1}-k_t),
\]
The resulting model is identical to the SOE-RBC model of chapter 4 with $A_t$ renamed $tot_t$. 

Assume that  the log of $tot_t$ follows the AR(1) process $\widehat{tot}_t
 = 
\rho \, \widehat{tot}_{t-1}
 + \pi \epsilon_t^{tot}.$

In this model, an increase in $\rho$ affects not only  the behavior of 
consumption (as in the endowment economy studied thus far)  but also the behavior of investment. The more persistent the terms of trade the larger the effect of a terms-of-trade shock on investment, and therefore the lower the effect on the trade balance. Thus, the presence of investment strengthens  the ORS effect.  The figure on the next slide illustrates this point. 
\end{slide}

\begin{slide}
{\bf Impulse Response of the Trade Balance to a Terms-of-Trade
Shock Implied by the SOE-RBC Model}
%\label{fig:tot_edeir_ir}

\centerline{\includegraphics[width=5in]{tot_edeir_ir.eps}}

{\tiny Note. Response to a one-percent increase in the terms of trade. The calibration of the model is as in chapter 4.}\\
$\bullet$ The more persistent the terms of trade, smaller the impact effect of a terms-of-trade shock on the trade balance. Thus, the ORS effect holds not only in  endowment economies, but also in ones with production and capital.

%produced with 
%edeir_ir.m
%in directory: 
%c:\data\uribe\book\tot\edeir
 \end{slide}

\begin{slide}
{\bf \large Another Test of the ORS Effect}\\
{\small The figure displays 
correlations conditional on terms-of-trade shocks  between the trade balance and the terms of trade implied by the SOE-RBC model (solid line) and by the empirical SVAR model given in equation~\eqref{eq:tot_x_2var} (circles, one for each of the 51 countries in the panel).}

%\label{fig:tot_tot_tb_corr}}
\centerline{\includegraphics[width=4in]{tot_corr_tb_tot_rho.eps}}

%produced by running 
%tot_corr_tb_tot_rho.m 
%in directory: 
%c:\data\uribe\book\tot\data
%recall to set sizevar = 2 in tot_cbcs.m

The SOE-RBC  model is in line with the ORS effect,  as it predicts a negative relation between $\rho$ and the correlation of $tb_t$ with  $tot_t$ conditional on $tot$ shocks. But no such relation is discernible   in the
cloud of circles. This suggests that  
 the data does not  support the  ORS effect from the perspective of conditional correlations. 
\end{slide}

\begin{slide}
{\bf \large How Important Are Terms of Trade Shocks?}

Terms of trade shocks are considered important drivers of business cycles. But how important? We address this questions in two ways:

$\bullet$ Empirically: via a 5-variable SVAR model. 

$\bullet$ Theoretically: the MX model. 
\end{slide}

\begin{slide}
{\bf \large How Important Are Terms-of-Trade Shocks? Empirical Analysis}\\
We study the following   SVAR model in five variables, the terms of trade ($tot_t$), the trade balance ($tb_t$), output ($y_t$), consumption ($c_t$), and investment ($i_t$): 
\begin{eqnarray}
\label{eq:tot_x1}
x^1_t &=& \rho x^1_{t-1} +  u^1_t,
\\
\label{eq:tot_x2}
x^2 _t &=& \alpha_0 x^1_t + \alpha_1 x^1_{t-1} + \rho_2 x^2_{t-1} + u^2_t ,
\end{eqnarray}
\centerline{\mbox{where } $
x_t = 
\left[
\begin{array}{c}
x^1_t \\
x^2_t
\end{array}
\right],$ \mbox{ with } $x^1_t = \widehat{tot}_t \mbox{ and } 
x^2_t =
\left[
\begin{array}{c}
\widehat{tb}_t\\
\widehat{y}_t\\
\widehat{c}_t\\
\widehat{i}_t\\
\end{array}
\right].
$}
The  scalar  innovation  $u^1_t$ and 
the 4-by-1 innovation 
$u^2_t$ are non-structural , i.i.d.  with mean zero, and $E(u^1_t)^2=\pi^2$ and 
$Eu^2_t u^2_t\prime=\Sigma$, 
where $\pi$ is a
 scalar and $\Sigma$ is of order  4-by-4. 

\end{slide}


\begin{slide}
{\bf \large Identification of the Terms-of-Trade Shock}
We assume that the non-structural shock $u_t\equiv [u^1_t\,\,u^2_t]'$ is related to a vector of structural shocks $\epsilon_t=[\epsilon^1_t\,\,\epsilon^2_t]'$ by the expression
\[
\left[
\begin{array}{c}
u^1_t\\
u^2_t
\end{array}
\right]
=
\left[
\begin{array}{cc}
\gamma_{11} & \gamma_{12}\\
\gamma_{21} & \gamma_{22}
\end{array}
\right]
\left[
\begin{array}{c}
\epsilon^1_t\\
\epsilon^2_t
\end{array}
\right]. 
\]
where $\epsilon\sim(\emptyset,I)$, and  $\epsilon^1_t$ and $\epsilon^2_t$  are   1-by-1 and 4-by-1, respectively.

$\bullet$ We impose the restrictions $\gamma_{11}>0$ and $\gamma_{12}=\emptyset$. This means that $\epsilon^1_t$ is the terms of trade shock (the only innovation that affects $tot_t$ contemporaneously).\\
$\bullet$ Because $\widehat{tot}_t$ appears as regressor in~\eqref{eq:tot_x2}, we have   $Eu^1_tu^2_t=\emptyset$, which, together with the identifying assumption of the above bullet,    implies, that $\gamma_{21}=0$. Summarizing, we have\\
\centerline{$u^1_t=\gamma_{11}\epsilon^1_t$ and $u^2_t=\gamma_{22}\epsilon^2_t$, which implies $\gamma_{11}=\pi$ and $\gamma_{22}\gamma_{22}'=\Sigma$}
\end{slide}

\begin{slide}
  Rearranging terms in~\eqref{eq:tot_x1} and \eqref{eq:tot_x2}, we can then write the SVAR system as
\begin{equation}
\label{eq:tot_x}
x_t = h_x x_{t-1} + \Pi 
\epsilon_t,
\end{equation}
\centerline{where  
$
h_x \equiv 
\left[
\begin{array}{cc}
\rho&\emptyset\\
\alpha_0\rho+\alpha_1&\rho_2
\end{array}
\right]$
and 
$\Pi \equiv
\left[
\begin{array}{cc}
\pi&\emptyset\\
\alpha_0\pi&\gamma_{22}
\end{array}
\right].
$}

{\bf Estimation }\\
$\bullet$  We estimate 
\eqref{eq:tot_x1} and \eqref{eq:tot_x2} equation by equation and country by country using the  data set of 51 poor and emerging countries over the period 1980 to 2011. \\
$\bullet$ This delivers country-level estimates of $\rho_1$, $\pi$, $\alpha_0$, $\alpha_1$, $\rho_2$, and $\Sigma$.  \\
$\bullet$Finally, we saw that $\gamma_{22}$ satisfies $\gamma_{22}\gamma_{22}'=\Sigma$. Because we are not interested in identifying the structural innovation $\epsilon^2_t$, any such decomposition of $\Sigma$ is fine. We set $\gamma_{22}$ to be the lower-triangular Cholesky decomposition of
$\Sigma$. 
\end{slide}

\begin{slide}
{\bf  Impulse Response to A Ten-Percent Increase in the Terms of Trade: SVAR Evidence
%\label{fig:tot_ir_cbc_5var}
}\\

\centerline{\includegraphics[width=8in]{tot_ir_cbc_5var_slides.eps}}
%produced by running 
%tot_ir_cbc.m in
%c:\data\uribe\book\tot\data
% set sizevar = 5 and slide=1

{\small Note. For each variable, its impulse response is obtained by first computing  the country-specific impulse responses and then 
averaging  across countries period by period.} 
\end{slide}

\begin{slide}
{\bf Comments on Impulse Responses to a Terms-of-Trade Shock}

In response to a terms-of-trade shock, the following effects are observed:\\
$\bullet$  The trade balance improves. ($\Rightarrow$The HLM effect is supported by the data.)

$\bullet$ Output expands for about 3 years. 

$\bullet$ Consumption falls on impact but recovers quickly.

$\bullet$ Investment expands, albeit with a one-period delay. 
\end{slide}

\begin{slide}

%\label{table:tot_v_share_cbc}
\singlespacing

\begin{center}

{\bf Share of Variance Explained by Terms of Trade Shocks: Country-Level  SVAR Evidence}

\begin{tabular}{llccccc}
\hline\hline
Country & $tot$& $tb$&$y$&  $c$&  $i$\\ 
\hline
Cross-Country Mean &  100&  18&  12&  13&  13\\
Cross-Country Median &  100&  12&  10&  11&  10\\
Median Absolute Deviation & 0 &   11&     9&     9&     8\\
\hline
Using Cross-Country \\ Mean of $h_x$ and $\Pi$ &  100&  7&  3&  1&  2\\
\hline
Panel Estimation &  100&  4&  1&  1&  1\\
\hline
\hline
\end{tabular}

{\tiny Note.  Variance shares are expressed in percent and are based on country-specific estimates of the SVAR system~\eqref{eq:tot_x}. 
 Averages are taken over 51 poor and emerging countries.}
\end{center}
%produced by running table_v_share_cbc.m in
%c:\data\uribe\book\tot\data
\end{slide}

\begin{slide}
{\bf \large Comments on Share of Variances Explained  by Terms-of-Trade Shocks}

$\bullet$ Terms of trade shocks  explain a small share (10 to 12\%) of the variances of   output, consumption, investment, and the trade balance. 

$\bullet$ This result is robust to estimating the variance shares in 3 ways: (1) estimating the variance shares  country by country  and then taking cross-country averages (baseline approach); (2) Computing an average of the country-level SVAR coefficients and using it to compute variance shares; and (3)  estimating an SVAR system on a pooled panel data. 



$\bullet$ There is significant cross-country variation in the estimated variance shares, with median absolute deviations as large as the medians themselves.  
\end{slide}


\begin{slide}
{\bf \large The MX Model}

$\bullet$ Thus far, we have studied one-good models. For example, earlier we used the  open-economy RBC model of chapter 4 and reinterpreted the productivity shock, $A_t$, as a terms-of-trade shock. 

$\bullet$ This approach is problematic, because it implicitly imposes the unrealistic assumption that 100\% of GDP is exported and 100\% of domestic absorption (consumption + investment) is imported. 

$\bullet$ In reality,  the typical country imports only a fraction of the goods it absorbs and exports only a fraction of the goods it produces. Chapter 1 documents that the average trade share (the ratio of exports plus imports to  GDP) is about 40 \% on average.   Under the one-good assumption, the trade share would be around 200\% on average across countries. 

$\bullet$ For this reason, here we study a model economy with two goods, both of which are produced, consumed, and used to produce investment goods.  One good is importable and the other exportable. 
\end{slide}

\begin{slide}
{\bf Households}

\begin{equation*}
\label{eq:tot_mx_utility}
\max E_0 \sum_{t=0}^{\infty} \beta^t
U(c_t,h^m_t,h^x_t),
\end{equation*}
subject to 
\begin{equation*}
\label{eq:tot_mx_bch}
c_t + i^m_t + i^x_t + \Phi_m(k^m_{t+1}-k^m_t) +  \Phi_x(k^x_{t+1}-k^x_t) +  d_t
\end{equation*}
\centerline{$=\frac{d_{t+1}}{1+r_t} + w^m_th^m_t + w^x_t h^x_t + u^m_t k^m_t + u^x_tk^x_t,$}
\begin{equation}
\label{eq:tot_mx_km}
k^m_{t+1} = (1-\delta) k^m_t + i^m_t,
\end{equation}
and
\begin{equation}
\label{eq:tot_mx_kx}
k^x_{t+1} = (1-\delta) k^x_t + i^x_t,
\end{equation}
{\small where $c_t$ is consumption, 
$h^i_t$, $i^j_t$, $k^j_t$, $w^j_t$, and $u^j_t$  hours worked, investment,  capital, the real wage, and the rental rate of capital in sector $j$, for $j=m,x$, with $m,x$  denoting importable and exportable sectors;  $d_t$  is debt due in period $t$,  and  $r_t$ is the interest rate;} $\Phi_i(\cdot)$ for $i=m,x$
are convex capital adjustment costs;    $c_t$, $i^i_t$, $w^i_t$, $u^i_t$ for $i=m,x$, and $\Phi_i(\cdot)$ are  expressed in  units of consumption. 
\end{slide}

\begin{slide}
\singlespacing {\bf Household's Optimality Conditions}\\
{\small $\bullet$ Use  \eqref{eq:tot_mx_km} and \eqref{eq:tot_mx_kx}
to eliminate $i^m_t$ and $i^x_t$ from the sequential budget constraint. \\
$\bullet$ Let $\lambda_t\beta^t$  be the Lagrange multiplier associated with the  budget constraint\\
$\bullet$ Then  the FOCs  with respect
to $c_t$, $h^m_t$, $h^x_t$, $d_{t+1}$, $k^m_{t+1}$, and $k^x_{t+1}$ are, respectively,} \\
\begin{equation}
\label{eq:tot_mx_c_hfoc}
U_1(c_t, h^m_t,h^x_t) =
 \lambda_t,
\end{equation}
\begin{equation}
\label{eq:tot_mx_hm_hfoc}
-U_2(c_t, h^m_t,h^x_t) = \lambda_t w^m_t,
\end{equation}
\begin{equation}
\label{eq:tot_mx_hx_hfoc}
-U_3(c_t, h^m_t,h^x_t) = \lambda_t w^x_t,
\end{equation}
\begin{equation}
\label{eq:tot_mx_d_hfoc}
\lambda_t  =\beta(1+r_t)E_t \lambda_{t+1},
\end{equation}
\begin{equation}
\label{eq:tot_mx_km_hfoc}
\lambda_t 
\left[ 1 + \Phi_m'(k^m_{t+1} - k^m_t)\right] = 
\beta E_t \lambda_{t+1}
\left[u^m_{t+1} + 1 - \delta + \Phi_m'(k^m_{t+2} - k^m_{t+1})\right],
\end{equation}
and 
\begin{equation}
\label{eq:tot_mx_kx_hfoc}
\lambda_t 
\left[ 1 + \Phi_x'(k^x_{t+1} - k^x_t)\right] = 
\beta E_t \lambda_{t+1}
\left[u^x_{t+1} + 1 - \delta + \Phi_x'(k^x_{t+2} - k^x_{t+1})\right].
\end{equation}
\end{slide}

\begin{slide}
{\bf Comments on the Household's Optimality Conditions}

$\bullet$ The optimality conditions are similar to those of the one-sector model of Chapter 4, except that now we have  sector-specific optimality conditions for capital and labor. 

$\bullet$ In the steady state, the rental rates of capital are equalized across sectors, as adjustment costs vanish. 

$\bullet$ Sectoral wage differentials may persist  in the steady state. 

$\bullet$ Sectoral capital adjustment cost and imperfect substitutability of 
sector-specific 
labor are intended to slow down sectoral factor reallocations (to avoid, for example, 
situations such as 
a  tractor  used to produce soybeans on  a farm  be instantaneously flipped to the city  to produce sweaters in response to an increase in the relative price of textiles.)
\end{slide}


\begin{slide}
{\bf \large Production of Final Goods}\\
Final goods are produced by firms in perfectly competitive markets. Profits are given by
\[
A(a^m_t,a^x_t) -p^m_t a^m_t -p^x_t a^x_t,
\]
where $A(a^m_t,a^x_t)$ is the quantity of final goods produced,  
$a^m_t$ and $a^x_t$  importable and exportable goods used as input,  and 
$p^m_t$ and $p^x_t$ are  the relative prices of importables and exportables in terms of units of the final good; 
the Armington aggregator $A(a^m,a^x)$  is increasing, concave, and HD1. \\
Then, profit maximization implies that 
\begin{equation}
\label{eq:tot_mx_am}
A_1(a^m_t,a^x_t) = p^m_t ,
\end{equation}
\begin{equation}
\label{eq:tot_mx_ax}
A_2(a^m_t,a^x_t) = p^x_t .
\end{equation}
Because the Armington aggregator is HD1,   firms make zero profits every period.
\end{slide}

\begin{slide}
{\bf \large Production of Importable and Exportable Goods}
Importable and exportable goods are produced with capital and labor via the technologies
\begin{equation}
\label{eq:tot_mx_ym}
y^m_t =   F^m(k^m_t,h^m_t)
\end{equation}
\begin{equation}
\label{eq:tot_mx_yx}
y^x_t =  F^x(k^x_t,h^x_t),
\end{equation}
where $y^j_t$ is output   in sector $j=m,x$, and $F(\cdot,\cdot)$ is increasing, concave, and HD1. 
Profits  are given by
\[
p^j_tF^j(k^j_t,h^j_t)-w^j_th^j_t
-u^j_tk^j_t,
\] 
for $j=m,x$. 
The optimality conditions are
\begin{equation}
\label{eq:tot_mx_km_ffoc}
p^m_t F^m_1(k^m_t, h^m_t)= u^m_t,
\end{equation}
\begin{equation}
\label{eq:tot_mx_hm_ffoc}
p^m_t F^m_2(k^m_t, h^m_t)= w^m_t,
\end{equation}
\begin{equation}
\label{eq:tot_mx_kx_ffoc}
p^x_t F^x_1(k^x_t, h^x_t)= u^x_t,
\end{equation}
\begin{equation}
\label{eq:tot_mx_hx_ffoc}
p^x_t F^x_2(k^x_t, h^x_t)= w^x_t.
\end{equation}
Because technologies are HD1, firms make no profits. 
\end{slide}

\begin{slide}
{\bf \large Market Clearing}

Equilibrium in the domestic final-goods market
\begin{equation}
\label{eq:tot_mx_market_clearing}
c_t + i^m_t + i^x_t +
\Phi_m(k^m_{t+1}-k^m_t) +  \Phi_x(k^x_{t+1}-k^x_t)
 = A(a^m_t,a^x_t).
\end{equation}


The equilibrium evolution of external debt 
\begin{equation}
\label{eq:tot_mx_d_evolution}
\frac{d_{t+1}}{1+r_t} =  d_t + m_t - x_t,
\end{equation}
where  $m_t$ denotes imports, and $x_t$ denotes exports (both expressed in terms of final goods) and are given by 
\begin{equation}
\label{eq:tot_mx_m}
m_t = p^m_t(a^m_t - y^m_t)
\end{equation}
and
\begin{equation}
\label{eq:tot_mx_x}
x_t = p^x_t(y^x_t-a^x_t ). 
\end{equation}
\end{slide}

\begin{slide}
{\bf \large Two Key Relative Prices}

$\bullet$ The terms of trade ($tot_t$) is  the relative price of exportable goods in terms of importable goods, 
\begin{equation}
\label{eq:tot_mx_tot}
tot_t = \frac{p^x_t}{p^m_t}.
\end{equation}
As in the SVAR model, assume that the country is small  and takes $tot_t$ as exogenous. Also in line with
the SVAR analysis,  assume   an AR(1) structure for $tot_t$:
\begin{equation}
\label{eq:tot_mx_tot_ar1}
\ln
\left(\frac{tot_t}{tot}\right)
= \rho 
\ln
\left(\frac{tot_{t-1}}{tot}\right)
+ \pi \epsilon^{tot}_t,
\end{equation}

$\bullet$
To ensure stationarity, 
 assume that the country interest rate  premium is debt elastic as in
the EDEIR model of Chapter 4:
\begin{equation}
\label{eq:tot_soe_deir}
r_t - r^*=  p(d_{t+1}),
\end{equation}
where $r^*$ denotes the world interest rate    assumed to be constant. The country premium, $p(d)$, is assumed to  
be increasing. 
\end{slide}

\begin{slide}
{\bf \large The Competitive Equilibrium}

\setcounter{page}{\theslide}
\label{slide:competitive_equilibrium}


{\it A competitive equilibrium is then  a set of processes $c_t$, $h^m_t$, $h^x_t$, 
$d_{t+1}$, $i^m_t$, $i^x_t$, $k^m_{t+1}$, $k^x_{t+1}$, $a^m_t$, $a^x_t$, $p^x_t$, $y^m_t$, $y^x_t$, $p^m_t$, $r_t$, $w^m_t$, $w^x_t$, $u^x_t$, $u^m_t$, $\lambda_t$, $m_t$, $x_t$, and $tot_t$  satisfying
equations~\eqref{eq:tot_mx_km}-\eqref{eq:tot_soe_deir}, given initial conditions $k^m_0$, $k^x_0$,  $d_0$, 
and $tot_{-1}$, and the stochastic process $\epsilon^{tot}_t$.  }
\end{slide}

\begin{slide}
{\bf \large Observables}

$\bullet$ How can we measure GDP in models with multiple goods? 

$\bullet$  For a meaningful comparison of  model and data, the theoretical measure of GDP must concur with its empirical counterpart. 

$\bullet$ The WDI, from which we obtained the data for the SVAR analysis,  measures real GDP as the ratio of nominal GDP to a Paasche implicit price deflator. 

$\bullet$ The next slide explains how to obtain the appropriate theoretical counter part of the WDI's measure of real GDP. 
\end{slide}

\begin{slide}
{\bf A Data-Compatible Measure of Real GDP}\\
Real GDP is the ratio of nominal GDP to the price level
\\
\centerline{$
\mbox{real GDP in $t$}=\frac{P^m_t y^m_t + P^x_t y^x_t}{P_t}
$}
{\small A Paasche price index in $t$  (recall we want to comply with the WDI) is the ratio of  the value of  period-$t$ quantities measured in period-$t$ prices  to  the value of period-$t$ quantities  measured in base-period  prices. Denoting  the base period by  0, the Paasche price index is \par}
\centerline{$P_t = \frac{P^m_t y^m_t + P^x_t y^x_t}{P^m_0 y^m_t + P^x_0 y^x_t}
$}
{\small Combining the above two expressions, we obtain}
\[
\mbox{real GDP in $t$}=P^m_0 y^m_t + P^x_0 y^x_t.
\]
{\small Now since, as defined,  real GDP is an {\it index} of real activity, we can scale  its entire path by any constant without changing its meaning. Pick this constant to be the price of consumption in the base year to get \par }
\centerline{$
\mbox{real GDP in $t$}=p^m_0 y^m_t + p^x_0 y^x_t.$
}
Finally, associate the base year with the steady state to obtain
\centerline{$
\mbox{real GDP in $t$}=p^m y^m_t + p^x y^x_t.$
}
This measure of real GDP has two convenient properties: \\(i)  The model has precise predictions for it; and \\(ii) It is as comformable  to its empirical counterpart as the model allows. 
\end{slide}

\begin{slide}
{\bf A Data-Compatible Measure of Other NIPA variables}\\

All NIPA variables in our data set are deflated by the Paasche implicit price index. 

Thus, for example,  the appropriate theoretical counterpart of real consumption is given by
\[
\mbox{real consumption} = 
 \frac{P^c_tc_t}{P_t} 
= c_t \frac{p^my^m_t+p^xy^x_t}
{p^m_ty^m_t+p^x_ty^x_t}. 
\]
This expression makes it clear that comparing $c_t$ to the measure of consumption used in the SVAR analysis would be incorrect. 

Similar transformations  
must be applied to 
  variables listed in the definition of a competitive equilibrium given in slide~\pageref{slide:competitive_equilibrium} 
to obtain the theoretical counterpart of the empirical measures of other NIPA  aggregates, such as investment, imports, and exports. 
\end{slide}

\begin{slide}
{\bf \large Functional Forms for Preferences and Technologies}
GHH preferences 
\[
U(c,h^m, h^x) =\frac{ \left[
c-
G(h^m,h^x)\right]^{1-\sigma} -1 }{1-\sigma};\quad \sigma>0
\]
Imperfect substitutability of sectoral employment
\[
G(h^m,h^x) =  
\frac{\left(h^m\right)^{\omega_m}}{\omega_m}
+
\frac{\left(h^x\right)^{\omega_x}}{\omega_x};
\quad \omega_m,\omega_x>0.
\]
Cobb-Douglas technologies
in the importable and exportable sectors
\[
F^i(k^i,h^i) = A^i \left(k^i\right)^{\alpha_i} \left(h^i\right)^{1-\alpha_i}; \quad i=m,x; 
 A^i>0, \alpha_i\in(0,1).
\]
Exponential  debt-elastic country premium
\[
p(d) = \overline{p} + \psi \left(e^{d-\bar{d}}-1 \right); \quad \psi\ge0.
\]
Quadratic capital adjustment costs,
\[
\Phi_i(x) = \frac{\phi_i}{2}x^2, \quad i=m,x,
 \phi_i\ge0.
\]
CES Armington aggregator of importable and exportable goods,
\[
A(a^m_t,a^x_t) = \left[
\chi 
\left(a^m_t\right)^{1-\frac1{\mu}}
+ (1-\chi)
\left(a^x_t\right)^{1-\frac1{\mu}}
\right]^{\frac{1}{1-\frac{1}{\mu}}};
\quad 
\mu>0,\chi\in(0,1). 
\]
\end{slide}

\begin{slide}
{\bf \large Parameterization of the MX Model}

$\bullet$ We employ a combination of calibration and estimation of the structural parameters of the MX model. 

$\bullet$ The sources of parameter values fall into three groups:

$\star$ Parameter values common to one-good models (e.g., those of  Chapters 4-6). 

$\star$ Parameter values based on sectoral output and trade data. 

$\star$ Parameter values estimated
at the country level 
 to match observed second moments. 
\end{slide}

 \begin{slide}

\begin{center}
{\bf Parameterization of the MX Model}

{\bf \small Parameter Values Common to One-Sector  Models}

%\label{table:tot_mx_calibration}}
\medskip
\begin{tabular}{*{9}{c}}
\hline \hline 
\multicolumn{9}{l}{\underline{Calibrated Structural Parameters}}
\\
$\sigma$&
$\delta$&
$r^*$&
$\overline{p}$&
$\alpha_m,\alpha_x$&
$\omega_m,\omega_x$&
$tot$&
$A^m$&
$\beta$
\\
2 &
0.1&
0.04&
0.07&
0.32&
1.455&
1&
1&
$(1+r^*+\bar{p})^{-1}$\\
\hline
\hline 
\end{tabular}

Note. The time unit is one year. 
\end{center}
\end{slide}


 \begin{slide}

\begin{center}
{\bf Parameterization of the MX Model} \\
{\bf Parameter Values Based on Sectoral Output and Trade Data}

%\label{table:tot_mx_calibration}}
\medskip
\begin{tabular}{*{4}{c}}
\hline \hline 
$\mu$&
$\chi$&
$\overline{d}$&
$A^x$\\
1& 
0.7399&
0.0103&
0.9732\\
\hline
\hline 
\end{tabular}
\end{center}

{\bf Comments :}\\
$\bullet$ $\mu$: estimates at quarterly frequency  $\Rightarrow \mu <1$; estimates at 5-10 year $\Rightarrow \mu<1$. This makes sense, as ability to substitute goods in response to price changes increases with time. The present model is calibrated at annual frequency so $\mu=1$ seems reasonable. 

$\bullet$ $\chi$,$\bar{d}$, $A^x$: match  observed averages across time and countries of the  share of the trade balance in GDP ($s_{tb}=0.01$),
the share of exports in GDP
($s_x=0.21$),
and the share of exportable output in GDP
($s_{yx}=0.47$).
\end{slide}


\begin{slide}
\begin{center}
{\bf Parameterization of the MX Model} \\
{\bf Parameter Values Estimated
Country By Country 
 to \\Match Observed Second Moments }

%\label{table:tot_mx_calibration}}
\medskip
\begin{tabular}{*{5}{c}}
\hline \hline 
$\rho$&
$\pi$&
$\phi_m$&
$\phi_x$&
$\psi$\\
0.53& 
0.09&
1.82&
1.56&
0.18\\
\hline
\hline 
\end{tabular}
\end{center}
Note. Medians across 51 poor and emerging countries over the period 1980-2011. 

{\bf Comments}\\
$\bullet$ $\rho$,$\pi$: estimated using actual  country-specific terms-of-trade data from the WDI.

$\bullet$ $\phi_m$,$\phi_x$,$\psi$: estimated by requiring the model to matches the investment-output volatility ratio and the trade-balance-output volatility ratio for each of the 51 poor and emerging countries in the panel, computed over the period 1980-2011. 
 
\end{slide}

\begin{slide}
\singlespacing
\begin{center}
{\bf Impulse Responses  to a
Ten-Percent Improvement in the\\ Terms-of-Trade  in the MX  Model}\\
%\label{fig:tot_mx_plot_ir_cbc}

\end{center}
\begin{center}


\centerline{\includegraphics[width=11in]
{tot_mx_plot_ir_cbc_slides.eps}}
\begin{quote}
{\small Note. All variables except  for the trade balance and external debt  are expressed  in percent deviations from steady state. The trade balance
and external debt are expressed in level deviations from steady state in percent of steady-state output. 
Cross-country 
medians. \par}
\end{quote}
\end{center}
%produced by running 
%plot_mx_ir_slides.m in
%z:\uribe\book\tot\mx\paasche
\end{slide}

\begin{slide}
{\bf Comments on the Response of the MX model to a Terms-of-Trade Shock}


$\bullet$ There is  a substitution in production away from importable goods and toward exportable goods: 
 employment,  investment, and output increase in the export sector
and decline in the import sector. \\
$\bullet$ There is also a substitution effect on domestic absorption in favor of importable goods. \\
$\bullet$ The elevated demand for importables together with the decline in the production of importables drives up imports. \\
$\bullet$ The decline in the domestic absorption of exportables together with the increase in the domestic production of exportables results in an increase in exports. \\
$\bullet$
Because both imports and exports increase, the response of the trade balance is ambiguous. 
In the figure, 
 the trade balance deteriorates on impact. Thus, the model fails to capture the
HLM effect. \\
$\bullet$ The appreciation of the terms of trade leads to a boom in aggregate output, consumption, and investment.
This is only partially supported by the empirical SVAR model, in which output increases, but consumption and investment fall on impact.
\end{slide}


\begin{slide}

{\bf \large Terms-Of-Trade Shocks: Less Important in Data than in Theory}
%\label{sec:tot_importance_theory}}

How important are terms-of-trade shocks in the MX model? 

And how does this prediction square with that of the empirical SVAR model? 

To address these questions, 
the table on the next slide compares 
the predictions of the MX and SVAR models with respect to the shares of the variances of output and other aggregates of interest 
explained by terms-of-trade shocks. 
\end{slide}

\begin{slide}
\begin{center}
{\bf \large Share of  Variances Explained by Terms-of-Trade Shocks: The MX Model Versus the Empirical SVAR Model}%\label{table:tot_mx_var}

\begin{tabular}{lcc}
\hline\hline
               &&Empirical\\
               &MX     &SVAR\\
              &Model            &Model\\
Variable&      (1)             & (2)\\
\hline
Terms of Trade &  100&  100\\
Trade Balance &   27&   12\\
Output &  18&   10\\
Consumption &   24&   11\\
Investment &   20&   10\\
\hline\hline
\end{tabular}
\end{center}

{\small Note. Each entry 
  is the
cross-country median of the fraction of the variance
of the corresponding indicator
 explained by terms of trade shocks in percent. In column (1)  the 
numerator of the 
fraction is  the 
variance conditional on terms-of-trade shocks   predicted by the MX model for country specific calibrations of $\phi_m$, $\phi_x$, $\psi$, $\rho$, and $\pi$. 
The denominator  is 
the unconditional variance implied by the empirical country-specific SVAR model.  }

%produced by running
%tot_mx_var_cbc.m  in
%c:\data\uribe\book\tot\mx\paasche (see line 46)
\end{slide}

\begin{slide}
{\bf Comments on the Table}


$\bullet$ According to the MX model,  terms of trade shocks explain on average  around 20 percent of the variances of output, consumption, investment, and the trade balance, making them an important source of business cycles in emerging and poor countries. 



$\bullet$ However, the implied role assigned to terms of trade shocks by the MX model is smaller than that reported by Mendoza (1995) and Kose (2002). 


$\bullet$ That is,  the contribution  of terms-of-trade shocks
to business-cycle fluctuations  is 
about twice as large in the MX model than it is in the empirical SVAR model.
We conclude that the 
theoretical model overpredicts the importance of terms of trade shocks as a source of business cycles. 

\end{slide}

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

$\bullet$ An SVAR model estimated on data from emerging and poor countries implies  that  terms-of-trade shocks explain a relatively small share of the variances of output and other macroeconomic aggregates (about 10 percent). 

$\bullet$ A open economy model with exportable and importable goods (the MX model) calibrated to emerging and poor countries predicts that terms-of-trade shocks explain about 20 percent of the variances of output and other macroeconomic aggregates. 

$\bullet$ Thus the MX model overpredicts the importance of terms-of-trade shocks by a factor of 2. 

$\bullet$ How can we reconcile theory and data? An unrealistic assumption of the MX model is that all goods are internationally traded. In reality 2/3 of all goods are not internationally tradable. In the next chapter we fix this problem by expanding the MX model to allow for  nontradable goods. 
\end{slide}

\end{document}
