I have a simple question. I want to know the difference between the residuals obtained from a model and idiosyncratic errors.


1 Answer 1


The biggest difference is that residuals is a term used in statistics and "idiosyncratic errors" isn't.

In statistics there is a distinction between error and residuals, where in the model

$$ y = f(x) + \varepsilon $$

$\varepsilon$ is the error term, while

$$ r = y - \hat y $$

where $\hat y$ is the fitted value, is the residual.

I did a quick online search and appears in publications be econometricians, like those slides

The basic panel data model is given by:

$$ y_{it} = \beta_0 + \beta_1 x_{1,it} + \beta_2 x_{2,it} + \dots + \beta_K x_{K,it} + a_i + u_{it}, \qquad (18) $$

with idiosyncratic errors $u_{it}$ [...]

where clearly they mean the error term. Same here where the author also has econometrics background, or discussed on /r/econometrics.

  • $\begingroup$ Great explanation! If the errors in the model are allowed to follow and AR(1) process, does it mean that residuals can also follow an AR(1) process? $\endgroup$
    – Geek_Tech
    Jan 12, 2022 at 8:03
  • 3
    $\begingroup$ If $\hat y$ is a prediction, I would say $r=y-\hat y$ is a prediction error, not a residual. It would be a residual if $\hat y$ were a fitted value. $\endgroup$ Jan 12, 2022 at 8:05
  • 2
    $\begingroup$ @RichardHardy yeah, corrected. $\endgroup$
    – Tim
    Jan 12, 2022 at 8:06

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