I'll try to state in this language what I think is the conceptual flaw.
The stated conclusion is "there is an optimum number of work hours, and it is less than 40."
However, their method of analysis is this:
"We fit a non-linear model that is a quadratic model cognitive ability y ~ ax + b x^2 for x work hours / week, and we found a statistical optimum around 25 hours"
The problem with this is that you're trying to find the best fit of a parabola to the data. And you have tons of samples where the work hours are very few / none (unemployed). Because there is a fairly strong correlation with unemployment and cognitive indicators, the parabola is already being "forced down" near hours worked = 0.
Now in this parabola model of estimated cognitive indicators vs work hours, either you are going to get a minima -- and it goes to infinity at working hours -> infinity (of course in real life it cannot really do this, because we only have so many hours in the week, but the statistical model will suggest it) -- or, you are going to get a maxima, which is what actually happens.
It could well be in the data that the indicators are that there is roughly flat, or even increasing response of cognitive indicators to working hours when the number of working hours is beyond a nominal value, but that the unemployed population has somewhat lower indicators.
In this case the model will automatically become a downward curving, parabola with a maxima, suggesting decline with increasing work hours -- even though this is not what the data directly suggests.
This maxima, the fact that there even is a "work hour optimum" that is a smooth, quadratic curve, is a mirage -- the model is not the data.
A remaining question is why the optimum is less than 40 hours. It is relatively easy to construct a statistical case in which it is a curve fitting artifact, despite that there is no direct data even at at the suggested optimum.
One could in principle check to see if this is the case. The data may be available.
For now, there's few graphs on page 20. It really doesn't seem to me that there is a significant distinction between the part time and full time groups -- in fact, the biggest difference is that more women who have a high reading score are not unemployed. Men who have a higher symbols score are more likely to be full-time employed instead of part-time, slightly -- but the converse is true for men with higher reading scores. The difference is not very distinct.
> Because there is a fairly strong correlation with unemployment and cognitive indicators
You're arguing that there's an endogeneity effect -- that poor cognition causes less working? That's a common problem. The authors discuss their use of an instrumental variable technique to avoid this issue.
> parabola is already being "forced down" near hours worked = 0
Not sure what you mean. Typically a model like this includes a constant to allow for a non-zero dependent variable when all the explanatory variables are zero. To do otherwise in this case would be absurd. The idea that the average non-working person has zero cognitive function...
That's exactly what I'm asking for: a clearer explanation.
I don't believe the paper's conclusion, but I don't understand your criticism of it. If you're saying the estimated curve is inappropriate, a better argument would be that they should include more terms of the work-hours Taylor expansion to get a better fit. Or perhaps there are confounding variables left out of the model.
The stated conclusion is "there is an optimum number of work hours, and it is less than 40."
However, their method of analysis is this:
"We fit a non-linear model that is a quadratic model cognitive ability y ~ ax + b x^2 for x work hours / week, and we found a statistical optimum around 25 hours"
The problem with this is that you're trying to find the best fit of a parabola to the data. And you have tons of samples where the work hours are very few / none (unemployed). Because there is a fairly strong correlation with unemployment and cognitive indicators, the parabola is already being "forced down" near hours worked = 0.
Now in this parabola model of estimated cognitive indicators vs work hours, either you are going to get a minima -- and it goes to infinity at working hours -> infinity (of course in real life it cannot really do this, because we only have so many hours in the week, but the statistical model will suggest it) -- or, you are going to get a maxima, which is what actually happens.
It could well be in the data that the indicators are that there is roughly flat, or even increasing response of cognitive indicators to working hours when the number of working hours is beyond a nominal value, but that the unemployed population has somewhat lower indicators.
In this case the model will automatically become a downward curving, parabola with a maxima, suggesting decline with increasing work hours -- even though this is not what the data directly suggests.
This maxima, the fact that there even is a "work hour optimum" that is a smooth, quadratic curve, is a mirage -- the model is not the data.
A remaining question is why the optimum is less than 40 hours. It is relatively easy to construct a statistical case in which it is a curve fitting artifact, despite that there is no direct data even at at the suggested optimum.
One could in principle check to see if this is the case. The data may be available.
For now, there's few graphs on page 20. It really doesn't seem to me that there is a significant distinction between the part time and full time groups -- in fact, the biggest difference is that more women who have a high reading score are not unemployed. Men who have a higher symbols score are more likely to be full-time employed instead of part-time, slightly -- but the converse is true for men with higher reading scores. The difference is not very distinct.
https://www.melbourneinstitute.com/downloads/working_paper_s...