The perils of calling your pet cat a dog …27 October, 2016 at 11:05 | Posted in Statistics & Econometrics | 1 Comment
Since econometrics doesn’t content itself with only making optimal predictions, but also aspires to explain things in terms of causes and effects, econometricians need loads of assumptions — most important of these are additivity and linearity. Important, simply because if they are not true, your model is invalid and descriptively incorrect. And when the model is wrong — well, then it’s wrong.
The assumption of additivity and linearity means that the outcome variable is, in reality, linearly related to any predictors … and that if you have several predictors then their combined effect is best described by adding their effects together …
This assumption is the most important because if it is not true then even if all other assumptions are met, your model is invalid because you have described it incorrectly. It’s a bit like calling your pet cat a dog: you can try to get it to go in a kennel, or to fetch sticks, or to sit when you tell it to, but don’t be surprised when its behaviour isn’t what you expect because even though you’ve called it a dog, it is in fact a cat. Similarly, if you have described your statistical model inaccurately it won’t behave itself and there’s no point in interpreting its parameter estimates or worrying about significance tests of confidence intervals: the model is wrong.