Structural shocks in economic models are unobservable and country-specific?
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.