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After reading this, I am more convinced than ever that macroeconomics has no bloody idea what the hell is going on. We have a bunch of fancy models and then argue over whose model is the least broken.
Yeah.

Macroeconomics is almost entirely faith-based and people generally just believe the version that meshes with their overall political view.

It is pretty easy to see this just watching the back and forth that occurs after someone (whether a random internet forum poster, or a Nobel Prize winner in economics) makes some claim about how policy should be modified (or not) to meet an economic goal. Approximately 50% of people (again, both including random internet people AND those who are highly educated in the field) will nod and the other 50% will be convinced the person who made the claim has no idea how economics works.

While this seems ludicrous when you compare it to "hard" sciences like physics or such I'm not sure it is a repairable situation, because outcomes of different macroeconomic models and policies rely heavily on the perception of reality of people, which is frighteningly close to a random number generator at scale.

That's not entirely true. If you look at something like the Economics Experts Panel: http://www.igmchicago.org/igm-economic-experts-panel, some issues are divisive, some have broad consensus and most are in between.

We tend to only hear about the divisive ones though because those are the only ones that actually make news.

I feel lost when it comes to economics. Yet, I think something of broader importance is at play in the state of economy which is overshadowed by social/cultural/political views. As I see it, the climax of the capitalism/inequality dilemma lies in the fact income follow a long tail distribution. As I said I know pretty much nothing about economics (or maths), but my programming-oriented mind tells me what's really relevant about long tail distributions independently of their current size (for instance the total amount of wealth) is that the head, the peak of the distribution grows exponentially faster than the tail in terms of what percentage of the cake you have in your plate. I'm talking in terms of ratios, not absolute wealth. It is indeed important to distinguish between the two : wealth is redistributed (in terms of percentages) AS wealth (in terms of dollars) increases.

Everybody agrees everyone should be wealthy enough to live decently. To me, figuring out what that bottom income is concentrates most of what is argued about here. If you consider our economic system as a way to level up human condition from the bottom, an algorithm that takes that bottom income and try to reach it, then it seems the root of our economic system (capitalism, shady behaviors commanded by our reptilian cortex, whatever) has a terrific wealth complexity.

Frankly I don't know if this complexity is exponential (seems like it to me, but again, I'm just a programmer), but you get the idea : is income inequality really a political or economic problem ? Or is it just mostly about maths ?