# What is the difference between a transitory and a permanent shock?

In my study of time series regression models in econometrics, we are discussing basic time series regressions and interpreting the effects of shocks in finite distributed lag models. I was wondering what the difference is, in intuitive terms, between a transitory and a permanent shock. According to my understanding at the moment, every shock would be permanent because you cannot undo the past. Wouldn't saying that an effect is transitory be like completely erasing its effect from existence and never accounting for it? I think I am wrong, but I don't know why.

• Suppose the world oil price doubled today and then halved in a year's time: that would be an example of a transitory shock but could have longer-term economic effects – Henry Nov 24 '16 at 9:16
• Just use the explicit economy term, don't turn it into philosophy. Well, in philosophy, shock effect can be wear off (i.e. replace by another events, e.g. technology advances, etc) – mootmoot Nov 24 '16 at 14:51
• @Henry Your comment in this case is misleading at best. If the long term effects do not completely phase out then this would not be a transitory shock. Please post answers as answers. Then users can vote on them and you can also edit them if you find fault in them later. – Giskard Nov 25 '16 at 7:13
• @denesp: whether or not there are long-term effects from transitory shocks is the hysteresis hypothesis. You cannot simply define this issue away either using language or models: it has to be an empirical analysis. – Henry Nov 25 '16 at 8:51
• @Henry Indeed. Which is why a detailed answer would be much better than a short comment. The comment cannot cover all cases, but may mislead the uninformed reader. – Giskard Nov 25 '16 at 14:42

"Permanent shock" is a shock whose effects on current values of a variable never die out in absolute terms. "Transitory shock" is a shock whose effects gradually die out. Consider the simplest one-lag model

$$y_t = \beta y_{t-1} + u_t, \;\;\; y_0 = 0$$

By direct substitution one gets that

$$y_T = \sum_{t=0}^{T-1}\beta^t u_{T-t} = u_T + \beta u_{T-1} + \beta^2u_{T-2} +...+\beta^{T-1}u_1$$

If $|\beta| <1$ the absolute effect of say shock $u_1$ on $y_T$ diminishes as time passes, $T \uparrow$. While mathematically it doesn't die off completely except at infinity, its absolute contribution decays exponentially.

On the other hand, if $\beta =1$ (a "unit root" model) then

$$y_T = \sum_{t=0}^{T-1}u_{T-t}=u_T + u_{T-1} + u_{T-2} +...+u_1$$

and no matter how far we move into the future the shock at period $1$ will fully contribute to the value of $y_T$.

Of course, if autocorrelation is strong (high $\beta$) then a "transitory" shock will influence visibly many periods in the future, so it may be "ignored" when examining "long-term" outcomes, but not when one deals with mid-term effects and policy.

Let me give an example of temporary versus permanent shocks to illustrate my understanding of the question. Consider agriculture production. The adoption of a new production technology will be a permanent supply shock because, e.g. by improving productivity. So, this productivity shock will affect permanently supply conditions (production and prices). In contrast, abnormal rainfall are typically considered as temporary supply shocks because they will only temporary affect production and prices. Their effects are even considered as local.

It's true that previous values influence future ones, and it's hard to show something without math, but here goes a simple, intuitive answer.

If you are studying regressions, you'll know that you build your model and then you calculate your errors/residuals. These residuals have an assumed distribution (say normal distribution centered around 0). A temporary shock can be seen as a spike on a single one of these residuals, at time "t"; a permanent shock can be seen as a change on the structure of all residuals from then on.

In the field, it can be hard to measure how "temporary" a shock is. For permanent shocks, the behavior of your time series has changed and you should build two separate models.