âSecond-wave endogenousâ (Iâll write âSWEâ) growth models posit instead that technology grows exponentially with a constant or with a growing population. The idea is that process efficiencyâthe quantity of a given good producible with given labor and/âor capital inputsâgrows exponentially with constant research effort, as in a first-wave endogenous model; but when population grows, we develop more goods, leaving research effort per good fixed.
Only one SWE model avoids a conclusion along these lines: the first one, Young (1998). It avoids the conclusion by positing that vertical innovation faces severely diminishing returns to research labor, so that in effect, a larger population can only be employed productively in research if the range of goods widens.
So does this mean that in the research production function, the exponent on the stock of âideasâ is one, and the exponent on the number of researchers is significantly less than one? It might be nice to see the equation.
Relatedly, isnât endogenous growth a knife-edge case? Intuitively, it seems unlikely to be true, and SWE doesnât seem to address this issue.
In Youngâs case the exponent on ideas is one, and progress looks like log(log(researchers)). (You need to pay a fixed cost to make the good at all in a given period, so only if you go above that do you make positive progress.) See Section 2.2.
Peretto (2018) and Massari and Peretto (2025) have SWE models that I think do successfully avoid the knife-edge issue (or âlinearity critiqueâ), but at the cost of, in some sense, digging the hole deeper when it comes to the excess variety issue.
Thanks for this Phil,
A couple of questions regarding SWE:
So does this mean that in the research production function, the exponent on the stock of âideasâ is one, and the exponent on the number of researchers is significantly less than one? It might be nice to see the equation.
Relatedly, isnât endogenous growth a knife-edge case? Intuitively, it seems unlikely to be true, and SWE doesnât seem to address this issue.
In Youngâs case the exponent on ideas is one, and progress looks like log(log(researchers)). (You need to pay a fixed cost to make the good at all in a given period, so only if you go above that do you make positive progress.) See Section 2.2.
Peretto (2018) and Massari and Peretto (2025) have SWE models that I think do successfully avoid the knife-edge issue (or âlinearity critiqueâ), but at the cost of, in some sense, digging the hole deeper when it comes to the excess variety issue.