<p>It seems that a possible explanation is that the productivity shock was too persistent such that capital flow from one country to the other in order to exploit the higher return to capital. Capital is mobile while labor is not. </p>

CC BY-SA 4.0
2020-04-27T14:22:38.310Z
2020-04-27T14:22:38.310Z
Alex Ruiz
<p>I am modeling a two-country world. Within each country there exists a representative infinitely-lived agent, a representative final good producer, a continuum of domestic monopolistic competitive firms (owned by consumers), and a continuum of local retailers that import goods. The representative agent supplies labor and capital to the production process. Domestic firms use labor and capital as inputs to produce intermediate goods; local retailers import differentiated goods. Domestic producers sell to the home and foreign final good producers. Each representative final good producer is a competitive firm that bundles home and foreign intermediate goods into a non-tradable final good, which is consumed and used for investment by the domestic agent. Preferences and technologies are symmetric across both countries.</p>
<p>Domestic producers follow this:</p>
<p><span class="math-container">\begin{gather}
Z_{H,t} + Z^*_{H,t} = Y_t = A_t K_t^\alpha L^{1-\alpha}_t
\end{gather}</span></p>
<p>so for the foreign country, the production process is given by:</p>
<p><span class="math-container">\begin{gather}
Z^*_{F,t} + Z_{F,t} = Y^*_t = A^*_t K^{* \alpha}_t L^{* 1-\alpha}_t
\end{gather}</span></p>
<p>where <span class="math-container">$Z^*_{F,}t$</span> is the intermediate good to produce final good <span class="math-container">$Z^*_t$</span> for foreign country and <span class="math-container">$Z_{F,t}$</span> is the intermediate good that will be exported to the home country.</p>
<p>When shocking the economy with a positive temporary productivity shock, I find that overall <span class="math-container">$Y^*_t$</span> decreases, while <span class="math-container">$Z^*_{F,t}$</span> decreases but <span class="math-container">$Z_{F,t}$</span> increases. However, <span class="math-container">$L^*_t$</span> increases, but <span class="math-container">$K^*_t$</span> decreases.</p>
<p>I understand that <span class="math-container">$Z_{F,t}$</span> increases as a response to the positive shock by the home country, because there is an increase in the demand of goods. My question is, what would be the economic intuition in knowing that <span class="math-container">$Y^*_t$</span> decreases, but <span class="math-container">$L^*_t$</span> increases and <span class="math-container">$K^*_t$</span> decreases? I was thinking that a possible answer would be that, this occurs given that the foreign country needs to produce more <span class="math-container">$Z_{F,t}$</span> to export to the home country, and given that the share of labor needed in the production process is greater than the share of capital, in order to achieve the higher production of <span class="math-container">$Z_{F,t}$</span>, only labor is needed as it is &quot;relatively&quot; more important than capital in the production process (I am assuming that capital share <span class="math-container">$\alpha = 1/3$</span>).</p>

CC BY-SA 4.0
2020-09-24T19:20:45.257Z
How do your input and ouput prices adjust to the shock? What about the output demands in both countries?
Bertrand
<macroeconomics><open-economy-macro><dsge>
Positive productivity shock with a fall in output
Alex Ruiz
# Positive productivity shock with a fall in output

(Asked by: username_0 on 2020-04-14)

I am modeling a two-country world. Within each country there exists a representative infinitely-lived agent, a representative final good producer, a continuum of domestic monopolistic competitive firms (owned by consumers), and a continuum of local retailers that import goods. The representative agent supplies labor and capital to the production process. Domestic firms use labor and capital as inputs to produce intermediate goods; local retailers import differentiated goods. Domestic producers sell to the home and foreign final good producers. Each representative final good producer is a competitive firm that bundles home and foreign intermediate goods into a non-tradable final good, which is consumed and used for investment by the domestic agent. Preferences and technologies are symmetric across both countries.

Domestic producers follow this:

\begin{gather}
Z\_{H,t} + Z^\*\_{H,t} = Y\_t = A\_t K\_t^\alpha L^{1-\alpha}\_t
\end{gather}

so for the foreign country, the production process is given by:

\begin{gather}
Z^\*\_{F,t} + Z\_{F,t} = Y^\*\_t = A^\*\_t K^{\* \alpha}\_t L^{\* 1-\alpha}\_t
\end{gather}

where $Z^\*\_{F,}t$ is the intermediate good to produce final good $Z^\*\_t$ for foreign country and $Z\_{F,t}$ is the intermediate good that will be exported to the home country.

When shocking the economy with a positive temporary productivity shock, I find that overall $Y^\*\_t$ decreases, while $Z^\*\_{F,t}$ decreases but $Z\_{F,t}$ increases. However, $L^\*\_t$ increases, but $K^\*\_t$ decreases.

I understand that $Z\_{F,t}$ increases as a response to the positive shock by the home country, because there is an increase in the demand of goods. My question is, what would be the economic intuition in knowing that $Y^\*\_t$ decreases, but $L^\*\_t$ increases and $K^\*\_t$ decreases? I was thinking that a possible answer would be that, this occurs given that the foreign country needs to produce more $Z\_{F,t}$ to export to the home country, and given that the share of labor needed in the production process is greater than the share of capital, in order to achieve the higher production of $Z\_{F,t}$, only labor is needed as it is "relatively" more important than capital in the production process (I am assuming that capital share $\alpha = 1/3$).

**Tags:** macroeconomics, open-economy-macro, dsge
> **Comments:**
> **username_1**: How do your input and ouput prices adjust to the shock? What about the output demands in both countries?  

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## 1 answers

### Answer by username_0 on 2020-04-27. Score: 0

It seems that a possible explanation is that the productivity shock was too persistent such that capital flow from one country to the other in order to exploit the higher return to capital. Capital is mobile while labor is not.


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