>But Nicholas, what about Uzawa’s theorem? Shouldn’t all innovation be labor augmenting in the long run? Thank you, little demon of esotericism, for that objection. I think (to the extent I understand it) that Uzawa’s theorem is based around capital accumulating, but labor not. If there is an optimal ratio of capital to labor, and technology (“A” in the production function) improves, then capital will accumulate until it balances out. However, L in the production function includes human capital as well. Since we do not have a good way to disaggregate things, L is not actually labor, and it’s perfectly plausible for wages to go down due to automation.)
"we prove a generalized version of the multifactor Uzawa theorem. The generalized theorem demonstrates that there is a continuum of representations with capital-augmenting technical change, as long as reproducible capital has a unitary EOS with at least one other factor. From this broader class of factor-augmenting representations, it is possible to choose a representation that matches the empirically observed speed of capital-augmenting technological progress. When we explicitly consider three or more production factors, the factor-augmenting representations can be simultaneously consistent with balanced growth, a nonunitary EOS between capital and labor, and capital-augmenting technical change"
"The generalized Uzawa theorem implies that the labor share is constant on a BGP with a constant rate of capital-augmenting technological change, but the labor share fluctuates when technology deviates from its BGP trend."
"the only reason why capital, Kt, is distinguished from other production factors X1,t, … , XJ,t is that we explicitly specify its linear accumulation process (2). From a theoretical viewpoint, Kt need not be limited to physical capital; Kt can be any combination of factors that can be accumulated linearly with saved output"
"The generalized Uzawa growth theorem considers a hybrid of capital and other non-accumulable inputs, which we call the capital composite. There is a unit EOS between the components of the capital composite. If the capital composite grows slower than output in the absence of technological change, capital-composite-augmenting technical change is necessary for a BGP. Thus, capital-augmenting technical change, which is one component of composite-augmenting technical change, is compatible with balanced growth and a nonunitary EOS between capital and labor."
Do you have an opinion on the relationship between fertility and innovation? Less time on parenting, more time on innovating? Short-term gains, but long-term loss of innovation due to smaller birth cohort over time? Inverted population pyramid requires more spending on elder care, which saps innovation? Older population less able to do innovation?
However, older populations are less violent, therefore, more stability, more innovation?
> it actually increases the patenting rate of the people they worked with before they moved.
Is there a plausible mechanism for this?
They continue collaborating with the people they know in their home country, they’ve just gotten exposed to even more new ideas.
>But Nicholas, what about Uzawa’s theorem? Shouldn’t all innovation be labor augmenting in the long run? Thank you, little demon of esotericism, for that objection. I think (to the extent I understand it) that Uzawa’s theorem is based around capital accumulating, but labor not. If there is an optimal ratio of capital to labor, and technology (“A” in the production function) improves, then capital will accumulate until it balances out. However, L in the production function includes human capital as well. Since we do not have a good way to disaggregate things, L is not actually labor, and it’s perfectly plausible for wages to go down due to automation.)
Possibly relevant: https://www.journals.uchicago.edu/doi/full/10.1086/729034
"we prove a generalized version of the multifactor Uzawa theorem. The generalized theorem demonstrates that there is a continuum of representations with capital-augmenting technical change, as long as reproducible capital has a unitary EOS with at least one other factor. From this broader class of factor-augmenting representations, it is possible to choose a representation that matches the empirically observed speed of capital-augmenting technological progress. When we explicitly consider three or more production factors, the factor-augmenting representations can be simultaneously consistent with balanced growth, a nonunitary EOS between capital and labor, and capital-augmenting technical change"
"The generalized Uzawa theorem implies that the labor share is constant on a BGP with a constant rate of capital-augmenting technological change, but the labor share fluctuates when technology deviates from its BGP trend."
"the only reason why capital, Kt, is distinguished from other production factors X1,t, … , XJ,t is that we explicitly specify its linear accumulation process (2). From a theoretical viewpoint, Kt need not be limited to physical capital; Kt can be any combination of factors that can be accumulated linearly with saved output"
"The generalized Uzawa growth theorem considers a hybrid of capital and other non-accumulable inputs, which we call the capital composite. There is a unit EOS between the components of the capital composite. If the capital composite grows slower than output in the absence of technological change, capital-composite-augmenting technical change is necessary for a BGP. Thus, capital-augmenting technical change, which is one component of composite-augmenting technical change, is compatible with balanced growth and a nonunitary EOS between capital and labor."
Do you have an opinion on the relationship between fertility and innovation? Less time on parenting, more time on innovating? Short-term gains, but long-term loss of innovation due to smaller birth cohort over time? Inverted population pyramid requires more spending on elder care, which saps innovation? Older population less able to do innovation?
However, older populations are less violent, therefore, more stability, more innovation?