You can prove that the moon is made of green cheese with mathematics — IF you start with the wrong initial assumptions and premises. As IT systems designers like to say, rubbish in = rubbish out.
The problem with econometrics doesn’t lie with the maths used, it’s the simplistic initial assumptions that the maths is burdened with and all the little ceteris paribus assumptions that economists use to avoid admitting that they don’t actually understand the chaotic dynamics of real economic flows and processes.
As Steve Keen pointed out some time ago (and his book Debunking Economics: The Naked Emperor Of The Social Sciences should be compulsory reading for all economics students), most of the major pillars of orthodox economics (supply and demand, marginal utility, theory of the firm, etc.) have been contradicted empirically long ago and only entered the canon of ‘acceptable’ economic thought anyway through a mysterious process of cultural osmosis that has nothing to do with hard fact.
Because orthodox economics taught in schools and universities is little more than a discourse, a language of power, a mythical language with the intended purpose of providing capitalism with a falsely structured fixity, a moral purpose and a logical-scientific inevitability.
Except that there isn’t capitalism, there are multiple capitalisms which are manifestations of evolutionary socio-cultural phenomena through which humanity is passing. Just as life evolves, the complex systems humanity invents evolve with it and become something else, the something else ‘just a pause on a way to a becoming’…