# Idea of errors as 'shocks' to a regression?

So I always understood the error term to be the difference between the observed value from the true, yet unobservable, function value. However, I often here, especially related to the economics fields, articles and people talking about error terms as 'shocks'.

Can anyone offer an intuitive, non-math intensive, explanation?

• The "shock" terminology normally refers to either the innovations or errors in a time series (though you do sometimes see it applied to the errors in a time series) rather than in a regression context. Aug 1, 2014 at 4:28

We are talking about transitory (temporary) shocks. Permanent Shocks create structural shifts, and should not be captured by the error term.

For temporary shocks, take for example a toy-specificaton for demand for money (i.e for liquidity), under controlled interest rates and flexible money supply:

$$M^d = AY^ke^{-a\mathbf i}$$

where $Y$ is output and $\mathbf i$ is the nominal interest rate. In a linearized econometric setting we would get

$$\ln M^d = \ln A +k\ln Y -a\mathbf i +u$$

where $u$ is the error term -excuse me, the shock. What shock?

Our specification by design does not take into account fluctuations in precautionary demand for money. This comes about due to uncertainty / expectations for future events: if, say, news arrive that a banking sector crisis is imminent, people will tend to get their savings out of the banks, thus increasing abruptly the demand for money (interest bearing accounts are not money, they are assets). This abrupt fluctuation will be included in the "error term".

Overall, this reduces the demand for money, for given output and interest rates: it permanently reduces the constant term $A$. In that sense, it is a structural shift, and should not be left to be conceptually captured by the error term, which reflects something that affects the dependent variable only in a certain period. Even if the error term is autocorrelated (=> current shocks propagate into the future), still this propagation will eventually die out, and so strictly speaking, again, it is not the right way to deal with structural shifts