Some quick point: 1. Thanks for doing this replication! I find the data pretty interesting. 2. I think my main finding here is that the “giving money to those who are the least happy, conditional on being poor” seems much more effective than giving to those who are more happy. Or, the 15 percentile slopes are far higher than the other slopes, below 50k, and this seems more likely to be statistically significant than other outcomes.
I’m really curious why this is. The effect here seems much larger than I would have imagined. Maybe something is going on like, “These very unhappy poor people had expectations of having more money, so they are both particularly miserable, and money is particularly useful to them.”
In theory there could be policy proposals here, but they do seem tricky. A naive one would be, “give money first to the poorest and saddest,” but I’m sure you can do better.
3. From quickly looking at these graphs, I’m skeptical of what you can really takeaway after the 50k pound marks. There seems to be a lot of randomness here, and the 50k threshhold seems arbitrary. I’d also flag that it seems weird to me to extend the red lines so far to the left, when there are so few data points at less than ~3k. I’m very paranoid about outliers here.
4. Instead of doing a simple linear interpolation, split into two sections, I think I’d be excited about other statistical processes you could do. Maybe this could be modeled as a guassian process, or estimated using bayesian techniques. (I realize this could be much more work though).
2) < Or, the 15 percentile slopes are far higher than the other slopes > Agreed, this is probably the most robust finding. I feel pretty uncomfortable about translating this into policy or prescriptions about cash transfers, because this stuff was all correlative; and unearned income might affect happiness differently from earned income.
3) < 50k threshhold seems arbitrary > This is explained in the second footnote. It is worth >$100 USD now, I believe.
< I’d also flag that it seems weird to me to extend the red lines so far to the left, when there are so few data points at less than ~3k > Do you mean from an aesthetic point of view, or a statistical one? The KK (2022) paper uses income groups – and uses the midpoints for the regressions – which is why their lines don’t extend back to very low income.
< I’m skeptical of what you can really takeaway after the 50k pound marks. There seems to be a lot of randomness here >
I think this depends on what claim you are making. I think there is pretty strong evidence for relative levelling off – i.e. significant decrease in the slope for lower percentiles. You can look at the Table for t/p values.
[Editted: didn’t phrase this well]. Though, I agree with you that there is less evidence for absolute levelling off (i.e. 0 slopes above 50k). The fact that the slopes for lower percentiles weren’t significantly positive might be because of a lack of data. 0 slopes for p=10, 30 seems to corroborate this.
Although, if the problem was a generic lack of observations above £50k, then we wouldn’t see significant positive slopes for the higher percentiles. Perhaps, the specific problem was that there wasnt many unhappy rich people in the sample. I will add something to the summary about this.
I haven’t checked for outliers via influence plots or the like.
4) Yeahh, I feel like that would be cool, but would be better to do on the bigger dataset that Killingsworth used. The usefulness here was to use the same methods on different (worse) data.
Do you mean from an aesthetic point of view, or a statistical one?
At least, from one of showing the plot. I’m more skeptical of the line, the further out it goes, especially to a region with only a few points.
I think this depends on what claim you are making. I think there is pretty strong evidence for relative leveling off – i.e. significant decrease in the slope for lower percentiles. You can look at the Table for t/p values.
This data is the part I was nervous about. I don’t see a great indication of “leveling off” in the blue lines. Many have a higher slope than the red lines, and the slope=0 item seems like an anomaly.
At least, from one of showing the plot. I’m more skeptical of the line, the further out it goes, especially to a region with only a few points.
Fair.
This data is the part I was nervous about. I don’t see a great indication of “leveling off” in the blue lines. Many have a higher slope than the red lines, and the slope=0 item seems like an anomaly.
To be clear – there are 2 version of levelling off.
Absolute levelling off: slopes indistinguishable from 0
Relative levelling off: slopes which decrease after the income threshold.
And for both 1) and 2), I am referring to the bottom percentiles. This is the unhappy minority which Kahneman and Killingsworth are referring to. So: the fact that slopes are indistinguishable after the income threshold for p=35, 50, 70 is consistent with the KK findings. The fact the slope increased for the 85th percentile is also consistent with the KK findings. Please look at Figure 1 if you want to double check.
I think there is stronger evidence for 2) than for 1).At percentiles p=5, 10, 15, 20, 25, 30 there was a significant decrease in the slope (2): see below. I agree that occurrences of 1) (i.e. insignificant slopes above £50k) may be because of a lack of data.
I also agree with you that the 0 slope is strange. I found this at the 10th and 30th percentiles. I think the problem might be that there wasnt many unhappy rich people in the sample.
Some quick point:
1. Thanks for doing this replication! I find the data pretty interesting.
2. I think my main finding here is that the “giving money to those who are the least happy, conditional on being poor” seems much more effective than giving to those who are more happy. Or, the 15 percentile slopes are far higher than the other slopes, below 50k, and this seems more likely to be statistically significant than other outcomes.
I’m really curious why this is. The effect here seems much larger than I would have imagined. Maybe something is going on like, “These very unhappy poor people had expectations of having more money, so they are both particularly miserable, and money is particularly useful to them.”
In theory there could be policy proposals here, but they do seem tricky. A naive one would be, “give money first to the poorest and saddest,” but I’m sure you can do better.
3. From quickly looking at these graphs, I’m skeptical of what you can really takeaway after the 50k pound marks. There seems to be a lot of randomness here, and the 50k threshhold seems arbitrary. I’d also flag that it seems weird to me to extend the red lines so far to the left, when there are so few data points at less than ~3k. I’m very paranoid about outliers here.
4. Instead of doing a simple linear interpolation, split into two sections, I think I’d be excited about other statistical processes you could do. Maybe this could be modeled as a guassian process, or estimated using bayesian techniques. (I realize this could be much more work though).
Hey Ozzie!
1) Thank you!
2) < Or, the 15 percentile slopes are far higher than the other slopes > Agreed, this is probably the most robust finding. I feel pretty uncomfortable about translating this into policy or prescriptions about cash transfers, because this stuff was all correlative; and unearned income might affect happiness differently from earned income.
3) < 50k threshhold seems arbitrary > This is explained in the second footnote. It is worth >$100 USD now, I believe.
< I’d also flag that it seems weird to me to extend the red lines so far to the left, when there are so few data points at less than ~3k > Do you mean from an aesthetic point of view, or a statistical one? The KK (2022) paper uses income groups – and uses the midpoints for the regressions – which is why their lines don’t extend back to very low income.
< I’m skeptical of what you can really takeaway after the 50k pound marks. There seems to be a lot of randomness here >
I think this depends on what claim you are making. I think there is pretty strong evidence for relative levelling off – i.e. significant decrease in the slope for lower percentiles. You can look at the Table for t/p values.
[Editted: didn’t phrase this well]. Though, I agree with you that there is less evidence for absolute levelling off (i.e. 0 slopes above 50k). The fact that the slopes for lower percentiles weren’t significantly positive might be because of a lack of data. 0 slopes for p=10, 30 seems to corroborate this.
Although, if the problem was a generic lack of observations above £50k, then we wouldn’t see significant positive slopes for the higher percentiles. Perhaps, the specific problem was that there wasnt many unhappy rich people in the sample. I will add something to the summary about this.
I haven’t checked for outliers via influence plots or the like.
4) Yeahh, I feel like that would be cool, but would be better to do on the bigger dataset that Killingsworth used. The usefulness here was to use the same methods on different (worse) data.
At least, from one of showing the plot. I’m more skeptical of the line, the further out it goes, especially to a region with only a few points.
This data is the part I was nervous about. I don’t see a great indication of “leveling off” in the blue lines. Many have a higher slope than the red lines, and the slope=0 item seems like an anomaly.
Fair.
To be clear – there are 2 version of levelling off.
Absolute levelling off: slopes indistinguishable from 0
Relative levelling off: slopes which decrease after the income threshold.
And for both 1) and 2), I am referring to the bottom percentiles. This is the unhappy minority which Kahneman and Killingsworth are referring to. So: the fact that slopes are indistinguishable after the income threshold for p=35, 50, 70 is consistent with the KK findings. The fact the slope increased for the 85th percentile is also consistent with the KK findings. Please look at Figure 1 if you want to double check.
I think there is stronger evidence for 2) than for 1).At percentiles p=5, 10, 15, 20, 25, 30 there was a significant decrease in the slope (2): see below. I agree that occurrences of 1) (i.e. insignificant slopes above £50k) may be because of a lack of data.
I also agree with you that the 0 slope is strange. I found this at the 10th and 30th percentiles. I think the problem might be that there wasnt many unhappy rich people in the sample.