In econometrics, why is the error term called the ‘error’ term? The myriad things it captures that influence the independent variable are not errors. They are valid real life phenomena. Is there any historical research or such like that traces the etymology of this term?
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2$\begingroup$ They're the error the model is making in approximating these "real life phenomena", not the other way around. $\endgroup$– Chris HaugCommented Nov 13, 2021 at 19:29
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1$\begingroup$ Etymologically it goes at least back to Gauss's first use of the normal distribution to describe errors in measurements (like positions of stellar objects). Possibly some earlier works might also use the term 'error'. For instance Laplace. $\endgroup$– Sextus EmpiricusCommented Nov 13, 2021 at 21:16
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I have seen this term used in other settings when taking physical measurements on, say, the height or the weight of an object. We would consider there to be a single true value for such a parameter and any deviation from this value in our measurements is considered an error. The population we have sampled from is the population of all possible repeated measurements.
I agree the phrase 'error' may not be suitable for all applications. In, say, medicine we think of randomly selecting people from a target population of people, with repeated experiments being conceptualized on different samples from the population. It would not be fair to consider the subjects in a single sample as mistakes or errors. However, the sample is intended to represent the population but in practice it is not a perfect representation. Additionally, we could think of the deviation between the estimator of the population-level parameter and the true parameter value as an error.
answered Nov 13, 2021 at 19:27