GoKawiilFor the past few months I’ve been working on a theory. It started out as just a fun little data exercise looking at some different types of taxes and benefits and how it effects what people buy and how much they work. During that time I took advantage of opus and later fable to help me get data, but as I was doing that of course opus might interject with some assumption I had wrong or some paper that shows the opposite. This back and forth continued for some time, and, well, it’s culminated in a theory. I’ve since started working alongside my co-author from the Stockholm School of economics on formalizing the theory
My original version, in my voice. Visual, anecdotal, not much in the way of maths or technical details.
The paper. The same theory, but formal. Very similar to the framework developed by nobel prizewinning economist Daron Acemoglu alongside Pascual Restrepo.
The paper uses the same task based model of Acemoglu and Restrepo, and essentially we add the logic of classical economicsand input-output recursion to it to “pin” the wage. That is significant because, well, current economics doesn’t know how wages are set in aggregate. That might sound surprising but essentially all wage models are estimates or they have some free parameters you can change or have to supply some other way. All we did was assume “hey, maybe the classical economists were right, they just didn’t know about how technology can effect the wage”. So, all we need to do is take the scarcity models of classical economists, add on the wage level from the marginal task (Acemoglu and Restrepo) and you just end up with a model that fits history like a glove. Here’s some of the maths:
From Acemoglu and Autor/Restrepo, we get how technology influences the wage:
w = c ⋅ γ ( x ∗ ) w = c \cdot \gamma(x^*)
c c is the rental price of a machine, γ ( x ∗ ) \gamma(x^*) is the “edge at the marginal human task” which is essentially how much better a human is than a machine at something which could be automated. γ ( x ∗ ) \gamma(x^*) you should think of as “technology”, and it can go up or down depending on what kind of technology is invented. During the industrial revolution, we got lots of physical automation (steam engines etc) but not so much cognitive (although, analog-mechanical battleship firing computers are like, super cool counter examples, check it out 1953 instructional video). Anyways steam engines etc caused γ ( x ∗ ) \gamma(x^*) to rise. Conversely, computers caused γ ( x ∗ ) \gamma(x^*) to fall in an interesting specific way, which probably gave us the great stagnation, and, well, AI might make γ ( x ∗ ) \gamma(x^*) fall more generally. That’s γ ( x ∗ ) \gamma(x^*) , what about c c ? In the paper we define c c as:
c = a ⋅ c + λ ⋅ w + b ⋅ r c = a \cdot c + \lambda \cdot w + b \cdot r
a ⋅ c a \cdot c is how much machines cost you need to make a machine λ ⋅ w \lambda \cdot w is how much labor cost you need to make a machine, and b ⋅ r b \cdot r is how much land, oil, ore, other fixed stuff you need to make a machine. So, c c contains itself in its definition, but we can recurse this function, plugging it into itself (and plug our wage definition in too), and then we get:
c = b r / ( 1 − a − λ γ ( x ∗ ) ) c = b r/(1 – a – \lambda \gamma(x^*))
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