by From Lars Syll 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
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from Lars Syll
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.
Our admiration for technical virtuosity should not blind us to the fact that we have to have a cautious attitude towards probabilistic inferences in economic contexts. Science should — as Keynes once put it — help us penetrate to “the true process of causation lying behind current events” and disclose “the causal forces behind the apparent facts.” We should look out for causal relations, but econometrics can never be more than a starting point in that endeavour since econometric (statistical) explanations are not explanations in terms of mechanisms, powers, capacities or causes. Firmly stuck in an empiricist tradition, econometrics is only concerned with the measurable aspects of reality. But there is always the possibility that there are other variables — of vital importance and perhaps unobservable and non-additive — that were not considered for the model. Those who were can hence never be guaranteed to be more than potential causes, and not real causes. A rigorous application of econometric methods in economics really presupposes that the phenomena of our real-world economies are ruled by stable causal relations between variables. To warrant that assumption one, however, has to convincingly establish that the targeted acting causes are stable and invariant so that they maintain their parametric status after the bridging. They seldom do.