(I really like this post, as I said to Issa elsewhere, but) I realized after discussing this earlier that I don’t agree with a key part of the precise vs. imprecise model distinction.
A precise theory is one which can scale to 2+ levels of abstraction/indirection.
An imprecise theory is one which can scale to at most 1 level of abstraction/indirection.
I think this is wrong. More levels of abstraction are worse, not better. Specifically, if a model exactly describes a system on one level, any abstraction will lose predictive power. (Ignoring computational cost—which I’ll get back to,) Quantum theory is more specifically predictive than Newtonian physics. The reason that we can move up and down levels is because we understand the system well enough to quantify how much precision we are losing, not because we can move further without losing precision.
The reason that precise theories are better is because they are tractable enough to quantify how far we can move away from them, and how much we lose by doing so. The problem with economics isn’t that we don’t have accurate enough models of human behavior to aggregate them, but that the inaccuracy isn’t precise enough to allow understanding how the uncertainty from psychology shows up in economics. Fore example, behavioral economics is partly useless because we can’t build equilibrium models—and the reason is because we can’t quantify how they are wrong. For economics, we’re better off with the worse model of rational agents, which we know is wrong, but can kind-of start to quantify by how much, so we can do economic analyses.
(I really like this post, as I said to Issa elsewhere, but) I realized after discussing this earlier that I don’t agree with a key part of the precise vs. imprecise model distinction.
I think this is wrong. More levels of abstraction are worse, not better. Specifically, if a model exactly describes a system on one level, any abstraction will lose predictive power. (Ignoring computational cost—which I’ll get back to,) Quantum theory is more specifically predictive than Newtonian physics. The reason that we can move up and down levels is because we understand the system well enough to quantify how much precision we are losing, not because we can move further without losing precision.
The reason that precise theories are better is because they are tractable enough to quantify how far we can move away from them, and how much we lose by doing so. The problem with economics isn’t that we don’t have accurate enough models of human behavior to aggregate them, but that the inaccuracy isn’t precise enough to allow understanding how the uncertainty from psychology shows up in economics. Fore example, behavioral economics is partly useless because we can’t build equilibrium models—and the reason is because we can’t quantify how they are wrong. For economics, we’re better off with the worse model of rational agents, which we know is wrong, but can kind-of start to quantify by how much, so we can do economic analyses.