Ege Erdil comments on What Do GDP Growth Curves Really Mean?

Ege Erdil 20 Oct 2021 18:39 UTC
3 points
I think in this case omitting the discussion about equivalence under monotonic transformations leads people in the direction of macroeconomic alchemy—they try to squeeze information about welfare from relative prices and quantities even though it’s actually impossible to do it.
The correct way to think about this is probably to use von Neumann’s approach to expected utility: pick three times in history, say $t_{1}, t_{2}, t_{3}$ ; assume that $u (t_{1}) < u (t_{2}) < u (t_{3})$ where $u (t_{i})$ is the utility of living around time $t_{i}$ and ask people for a probability $p$ such that they would be indifferent between a certainty of living in time $t_{2}$ versus a probability $p$ of living in time $t_{3}$ and a probability $1 - p$ of living in time $t_{1}$ . You can then conclude that
$\frac{u (t_{3}) - u (t_{2})}{u (t_{2}) - u (t_{1})} = \frac{1 - p}{p}$
if an expected utility model is applicable to the situation, so you would be getting actual information about the relative differences in how well off people were at various times in history. Obviously we can’t set up a contingent claims market and compare the prices we would get on some assets to infer some value for $p$ , but just imagining having to make this gamble at some odds gives you a better framework to use in thinking about the question “how much have things improved, really?”