As far as I can tell, this sort of consideration is at least somewhat damning for the literal CES model (with poor substitution) in any situation where the inputs have varied by hugely different amounts (many orders of magnitude of difference like in the compute vs labor case) and relative demand remains roughly similar. While this is totally expected under high substitution.
I don’t think this logic is quite right. In particular, the relative price of compute to labor has changed by many orders of magnitude over the same period (compute has decreased in price a lot, wages have grown). Unless compute and labor are perfect complements, you should expect the ratio of compute to labor to be changing as well.
To understand how substitutable compute and labor are, you need to see how the ratio of compute to labor is changing relative to price changes. We try to run through these numbers here.
Yeah, you can get into other fancy tricks to defend it like:
Input-specific technological progress. Even if labour has grown more slowly than capital, maybe the ‘effective labour supply’—which includes tech makes labour more productive (e.g. drinking caffeine, writing faster on a laptop) -- has grown as fast as capital.
Input-specific ‘stepping on toes’ adjustments. If capital grows at 10%/year and labour grows at 5%/year, but (effective labour) = labour^0.5, and (effective capital)=capital, then the growth rates of effective labour and effective capital are equal
As far as I can tell, this sort of consideration is at least somewhat damning for the literal CES model (with poor substitution) in any situation where the inputs have varied by hugely different amounts (many orders of magnitude of difference like in the compute vs labor case) and relative demand remains roughly similar. While this is totally expected under high substitution.
I don’t think this logic is quite right. In particular, the relative price of compute to labor has changed by many orders of magnitude over the same period (compute has decreased in price a lot, wages have grown). Unless compute and labor are perfect complements, you should expect the ratio of compute to labor to be changing as well.
To understand how substitutable compute and labor are, you need to see how the ratio of compute to labor is changing relative to price changes. We try to run through these numbers here.
Yeah, you can get into other fancy tricks to defend it like:
Input-specific technological progress. Even if labour has grown more slowly than capital, maybe the ‘effective labour supply’—which includes tech makes labour more productive (e.g. drinking caffeine, writing faster on a laptop) -- has grown as fast as capital.
Input-specific ‘stepping on toes’ adjustments. If capital grows at 10%/year and labour grows at 5%/year, but (effective labour) = labour^0.5, and (effective capital)=capital, then the growth rates of effective labour and effective capital are equal