## Understanding the limits of statistical inference

6 July, 2017 at 18:35 | Posted in Statistics & Econometrics | 1 Comment

This is indeed an instructive video on what *statistical* inference is all about.

But we have to remember that economics and statistics are two quite different things, and as long as economists cannot identify their statistical theories with real-world phenomena there is no real warrant for taking their statistical inferences seriously.

Just as there is no such thing as a ‘free lunch,’ there is no such thing as a ‘free probability.’ To be able at all to talk about probabilities, you have to specify a model. If there is no chance set-up or model that generates the probabilistic outcomes or events -– in statistics one refers to any process where you observe or measure as an experiment (rolling a die) and the results obtained as the outcomes or events (number of points rolled with the die, being e. g. 3 or 5) of the experiment -– there, strictly seen, is no event at all.

Probability is a relational element. It always must come with a specification of the model from which it is calculated. And then to be of any empirical scientific value it has to be shown to coincide with (or at least converge to) real data generating processes or structures –- something seldom or never done in economics.

And this is the basic problem!

If you have a fair roulette-wheel, you can arguably specify probabilities and probability density distributions. But how do you conceive of the analogous ‘nomological machines’ for prices, gross domestic product, income distribution etc? Only by a leap of faith. And that does not suffice. You have to come up with some really good arguments if you want to persuade people into believing in the existence of socio-economic structures that generate data with characteristics conceivable as stochastic events portrayed by probabilistic density distributions! Not doing that, you simply conflate statistical and economic inferences.

And even worse — some economists using statistical methods think that algorithmic formalisms somehow give them access to causality. That is, however, simply not true. Assuming ‘convenient’ things like faithfulness or stability,is to assume what has to be proven. Deductive-axiomatic methods used in statistics do no produce evidence for causal inferences. The real casuality we are searching for is the one existing in the real-world around us. If there is no warranted connection between axiomatically derived statistical theorems and the real-world, well, then we haven’t really obtained the causation we are looking for.

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Lars, a more basic issue is that statisticians assume that the thing of interest is a genuine property of the members of the population. This is often not the case in economics. Another way to look at is that where probability theory is appropriately applied there is usually some well-defined underlying proportion that underpins the probabilities. This is often not the case in economics.

Your point about models is valid, but mine seem more basic. Regards.

Comment by Dave Marsay— 6 July, 2017 #