<p>If <span class="math-container">$oil_t$</span> is the worldwide price of oil, neither <span class="math-container">$\rho$</span> nor <span class="math-container">$e_t$</span> are determined in a country specific model (unless the country's economy is so large that it affects global oil demand, which is not the case here).
Because there is no feedback from domestic variables to the worldwide oil price <span class="math-container">$e_t$</span> <em><strong>is</strong></em> the structural shock if AR(1) is an appropriate model of the oil price.The residual of the regression of <span class="math-container">$oil_t$</span> on <span class="math-container">$oil_{t-1}$</span>  <span class="math-container">$\widehat{e_{AR(1),t}}$</span> is already an estimate for the structural shock <span class="math-container">$e_t$</span>. So you can assess the volatility of the structural oil price shock <span class="math-container">$e_t$</span> based on <span class="math-container">$\widehat{e_{AR(1),t}}$</span>. For an AR(1)-process it is possible to do this by looking at a plot of the original series.</p>

CC BY-SA 4.0
2021-02-10T09:46:37.507Z
2021-02-10T10:29:49.523Z
2021-02-10T10:29:49.523Z
Grada Gukovic
<p>Let's consider an exogenous oil price shock (<span class="math-container">$e_t$</span>) as an example in the following equation <span class="math-container">$oil_t = \rho \; oil_{t-1} + e_t$</span>, where <span class="math-container">$oil_t$</span> is one variable in a VAR system. We normally want to recover <span class="math-container">$e_t$</span> based on some structural model we have for some given economy. So I guess that makes <span class="math-container">$e_t$</span> also country-specific, right?</p>
<p>So, for example, we cannot just look visually at oil-price time series data and say that oil price shocks are more volatile or less volatile. Like it depends on the economy of interest?</p>
<p>So although <strong>oil prices</strong> may be more or less volatile in general for a given period, it does not say anything about <strong>oil price shocks</strong> for a given economy, I guess. We need a structural model to recover the oil-price shocks to see how it behaves, right?</p>

<macroeconomics><applied-econometrics>
Structural shocks in economic models are unobservable and country-specific?
Emmanuel Ameyaw
# Structural shocks in economic models are unobservable and country-specific?

(Asked by: username_0 on 2021-02-10)

Let's consider an exogenous oil price shock ($e\_t$) as an example in the following equation $oil\_t = \rho \; oil\_{t-1} + e\_t$, where $oil\_t$ is one variable in a VAR system. We normally want to recover $e\_t$ based on some structural model we have for some given economy. So I guess that makes $e\_t$ also country-specific, right?

So, for example, we cannot just look visually at oil-price time series data and say that oil price shocks are more volatile or less volatile. Like it depends on the economy of interest?

So although **oil prices** may be more or less volatile in general for a given period, it does not say anything about **oil price shocks** for a given economy, I guess. We need a structural model to recover the oil-price shocks to see how it behaves, right?

**Tags:** macroeconomics, applied-econometrics

---

## 1 answers

### Answer by username_1 on 2021-02-10. Score: 4 | Accepted answer

If $oil\_t$ is the worldwide price of oil, neither $\rho$ nor $e\_t$ are determined in a country specific model (unless the country's economy is so large that it affects global oil demand, which is not the case here).
Because there is no feedback from domestic variables to the worldwide oil price $e\_t$ ***is*** the structural shock if AR(1) is an appropriate model of the oil price.The residual of the regression of $oil\_t$ on $oil\_{t-1}$ $\widehat{e\_{AR(1),t}}$ is already an estimate for the structural shock $e\_t$. So you can assess the volatility of the structural oil price shock $e\_t$ based on $\widehat{e\_{AR(1),t}}$. For an AR(1)-process it is possible to do this by looking at a plot of the original series.


---

