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Why validating assumptions is so important in science

from Lars Syll

valAn ongoing concern is that excessive focus on formal modeling and statistics can lead to neglect of practical issues and to overconfidence in formal results … Analysis interpretation depends on contextual judgments about how reality is to be mapped onto the model, and how the formal analysis results are to be mapped back into reality. But overconfidence in formal outputs is only to be expected when much labor has gone into deductive reasoning. First, there is a need to feel the labor was justified, and one way to do so is to believe the formal deduction produced important conclusions. Second, there seems to be a pervasive human aversion to uncertainty, and one way to reduce feelings of uncertainty is to invest faith in deduction as a sufficient guide to truth. Unfortunately, such faith is as logically unjustified as any religious creed, since a deduction produces certainty about the real world only when its assumptions about the real world are certain …

Unfortunately, assumption uncertainty reduces the status of deductions and statistical computations to exercises in hypothetical reasoning – they provide best-case scenarios of what we could infer from specific data (which are assumed to have only specific, known problems). Even more unfortunate, however, is that this exercise is deceptive to the extent it ignores or misrepresents available information, and makes hidden assumptions that are unsupported by data …

Despite assumption uncertainties, modelers often express only the uncertainties derived within their modeling assumptions, sometimes to disastrous consequences. Econometrics supplies dramatic cautionary examples in which complex modeling has failed miserably in important applications …

Sander Greenland

Yes, indeed, econometrics fails miserably over and over again.  One reason why it does, is that the error term in the regression models used are thought of as representing the effect of the variables that were omitted from the models. 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:

Paul-Romer-727x727With enough math, an author can be confident that most readers will never figure out where a FWUTV (facts with unknown truth value) is buried. A discussant or referee cannot say that an identification assumption is not credible if they cannot figure out what it is and are too embarrassed to ask.

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. Frank Salter
    November 8, 2019 at 10:25 am

    Again a blog which is presenting a category error instead of discussing what is required. Any arbitrary equation can be fitted to any data set. For theoretical validity, the equation must conform to the quantity calculus. To guess the correct theoretical equation is extremely unlikely as there is a very large number of equation which are not rejected by the quantity calculus. Only by applying first principles analysis will the appropriate equation be found. Unless this fact is accepted and acted upon there will be no possibility of finding the appropriated relationships. Merely reiterating that which is being done is wrong does not advance analysis is any way.

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