I shouldn't even comment on this BS article but here we go, duty calls ( https://xkcd.com/386/ )…

1) First of all, let's make clear that there are no "the economists" and there is no "economics" that could be identified with whatever peeve du jour of "the journalists". Economics as a field, understood as the study of exchange between decision-making agents in more or less large systems[1], is marked by an extreme diversity of approaches and opinions on even basic questions. From my superficial understanding of other fields, this seems to be a big difference between economics and the sciences, and on the other hand rather similar to the humanities. If you're going to criticize something, better make it specific and name names.

2) It is fashionable for "technical" people to scoff at the mathematics used in economic theory (basically, analysis, optimization, linear alg, and measure-theoretic prob), pretending that the problems arise because the tools are too primitive. First, perhaps they should remember that a lot of the foundations of mathematical economics were laid by people way above their paygrade. I'm talking about von Neumann, for example, or Fischer Black. Usually, when smart people do something that does not make sense to you, you take a step back and ask what you might be missing, and usually there is a nontrivial answer to that question. Paul Romer, sorry, is a good economist but he has a BS in math. I would say that's my definition of a "lightweight when it comes to equations". That's not to say he shouldn't criticize, he should! But let's not pretend that there was no reason to "go formal" in economic theorizing or that there were/are easy modeling choices.

3) In my experience, most of the criticism of economic models comes from ignorance of the goal and context of a model and a too literal reading of the math. For example, if you take Markowitz's portfolio optimization (mean vs variance of a linear combination of a multivariate normal), it is correct that individual returns have non-exponentially decaying "heavy" tails, the copula is not (unconditionally) Gaussian, and risk is therefore not captured in variance and correlations (not least because they may in fact be undefined). But that is completely beside the point of the model, which is simply to express the idea that the risk of a portfolio is not necessarily additive and that there is a tradeoff between risk and return. The point being, although it is expressed in mathematical language, it is actually a qualitative model. Once you realize this difference to more descriptive models in the sciences, economic theory starts to make a lot more sense.

4) The real problem of economic theory may be the disconnect between how many people have a stake in it and how many people have the time and leisure and inclination and background to understand what the theorists are actually saying.

5) Side comment and half-reply to ThePhysicist's complaint: The reason to go with the "perfect gas"-type models in economic theory, I think, is that you are dealing with self-interested, utility-maximizing particles or "agents" -> acting particles. The thinking being that if you put in constraints of some form, say a short-sales constraint in a financial market model, you make the model very special. But in the messy real world agents would find a way around this particular constraint eventually. So the unconstrained general equilibrium models are trying to give you a big picture, "this is where the market tends to" type of result. There is so much more to be said on this point but I'm already way above my allocated time for this "duty call"...

6) Last but not least, let me state my opinion that there is nothing inherently noble about science. It is a method to gain knowledge, and it is contingent on the affordances of the field to which it is applied. In economic theory, your basic problem is lack of data. Now that may change in some subfields, and that's great. So the scientific method can be applied in those subfields eventually. But we need answers or opinions today for practical problems. I see economics as akin to philosophy how Russell [2] understood it. Let me quote him:

“Philosophy, as I shall understand the word, is something intermediate between theology and science. Like theology, it consists of speculations on matters as to which definite knowledge has, so far, been unascertainable; but like science, it appeals to human reason rather than to authority, whether that of tradition or that of revelation. All definite knowledge—so I should contend—belongs to science; all dogma as to what surpasses definite knowledge belongs to theology. But between theology and science there is a No Man’s Land, exposed to attack from both sides; this No Man’s Land is philosophy. Almost all the questions of most interest to speculative minds are such as science cannot answer, and the confident answers of theologians no longer seem so convincing as they did in former centuries.”

One should be aware of the limits of this approach but one should also not assume that there was a choice between science and this. If there was, it wouldn't even be a contest! The realm of science may get bigger over time, as more and more data is gathered, but again, we need answers today and in real time, not in 100 years, to decide on regulations, interest rates, portfolios or budgeting decisions. In almost all the big economic questions, your sample size is one and the possibility to experiment is nil. The world is arguably nonstationary on time-scales that matter, economic mechanisms change, and every statistical test and computational experiment is always a joint hypothesis test of your assumptions, about which I said in (1) above that there is and perhaps can be no consensus.

In short, it's not that people don't know there is a problem. It's that there has so far been no better solution.

______________________

[1] I'm just making this definition up on the fly but if someone has a better one, I'm all ears.

[2] B. Russell. A History of Western Philosophy. George Allen & Unwin, 1945.