## Econometrics — science built on untestable assumptions

27 May, 2021 at 22:31 | Posted in Statistics & Econometrics | 1 Comment

Just what is the causal content attributed to structural models in econometrics? And what does this imply with respect to the interpretation of the error term? …

Consider briefly the testability of the assumptions brought to light in this section. Given these assumptions directly involve the factors omitted in the error term, testing these empirically seems impossible without information about what is hidden in the error term. But given the error term is unobservable, this places the modeller in a difficult situation: how to know that some important factor has not been left out from the model undermining desired inferences in some way. It also shows that there will always be element of faith in the assumptions about the error term.

Damien Fennell

In econometrics textbooks it is often said that the error term in the regression models used represents the effect of the variables that were omitted from the model. The error term is somehow thought to be a ‘cover-all’ term representing omitted content in the model and necessary to include to ‘save’ the assumed deterministic relation between the other random variables included in the model. Error terms are usually assumed to be orthogonal (uncorrelated) to the explanatory variables. But since they are unobservable, they are also impossible to empirically test. And without justification of the orthogonality assumption, there is as a rule nothing to ensure identifiability.

Distributional assumptions about error terms are a good place to bury things because hardly anyone pays attention to them. Moreover, if a critic does see that this is the identifying assumption, how can she win an argument about the true expected value the level of aether? If the author can make up an imaginary variable, “because I say so” seems like a pretty convincing answer to any question about its properties.

Paul Romer

## 1 Comment »

1. The standard error associated with the samplings and surveys involved in GDP calculations are also simply thrown out. Not to mention the uncalculable errors on outright imputations. GDP should be left out of public policy making; if error terms were reported honestly, GDP would be seen as a uselessly inaccurate measure of well-being.