“If I understand correctly, it sounds like we now agree on the math of my post, and on my arguments around which coefficients from cross-sectional vs longitudinal regressions seem to match? But I think we still disagree about whether the impacts of a gradual increase in gdp across time should be compared to cross-sectional differences?”
Response: Not quite, I agree with some of the calculations you did in the last post, but not with the overall post and conclusions. The quickest justification for this response is that the EVS/WVS coefficients are smaller and even negative for certain country groups. There’s also the statistical significance to consider, which we have not discussed. There is a large amount of uncertainty in the estimates, and while they could be larger, they could also be zero. But regardless of coefficient, yes, we disagree about the implications of time-series (TS) and cross-sectional (CS) differences.
“My first thought on our disagreement is that an income doubling is a fairly arbitrary metric. I think it would be equally reasonable to zoom in on the cross sectional graph, and look at the impact of a 1% increase in income. We can imagine country Y on the cross-section graph which lies a little higher than Ethiopia on the regression line in my post. This country would have $1010 per capital GDP and a SWB of 4+1*.007=4.007, versus Ethiopia at $1000 and 4. If we compare this to what we would expect from a .007 coefficient in one of your alternative regressions, it looks like it’s exactly what we would expect from one year of 1% growth vs the counterfactual for Ethiopia? In this case we don’t need to worry about the amount of time it takes to double income, and TS and CS become more intuitively comparable?”
Response: You’re right that in that case we do not need to worry about the time involved, but what you’re pointing out is how small the relationship actually is in the cross-section. From the figure, the cross-sectional relationship is: y = −2.955 + 0.342*ln(x). Then a 1 percent increase in income is related to an increase in SWB of approximately 0.342*0.01 = 0.003, which of course is actually smaller than the 0.007 coefficient (note the previous post, 0.007 applies to developed not less developed countries. Also, it is statistically insignificant and could also be zero).
“My second thought is that if we assume that TS results are not comparable to CS results because they take a long time, wouldn’t that make the existence of the Easterlin Paradox irrelevant for making any judgements about the world? Isn’t the Easterlin Paradox a paradox precisely because we expect the coefficients to match between CS and TS, but they don’t seem to in some specifications?”
Response: You’re right that the Paradox is about the contrast between the two types of results. However, it’s not just whether the coefficients match. The CS results are statistically significant and the TS results are generally not statistically significant. A second aspect is that the TS results, even if statistically significant, make it clear how long it would take for SWB to increase. The period necessary is not clear in CS results, which makes it look like the CS results are much larger than the TS results. Your calculation above suggests that the CS results are actually quite small too, or that we need larger changes in income to have meaningful changes in SWB, which as the TS results point out, will take a long time. Another aspect, the Paradox is about the contrast, but the surprising result is how small the TS relation is. Whether there’s a contrast or not, this relation is important for thinking about the world.
“we are talking about the Gallup results and ignoring the EVS/WVS results. They are preferred for long-run periods.”
Agreed. I haven’t looked at the EVS/WVS results at all, so there is a good chance that they are less sensitive to the kinds of alternative specifications I tried for the Gallup results.”
Response: the sensitivity isn’t too important, because the relationships are all small. As stated above, even the CS results are quite small, or we need larger changes in income to have meaningful changes in SWB, which as the TS results point out, will take a long time.
“It’s possible that many people on the lower end of the income distribution benefit greatly – indeed many economists, even happiness ones, believe this in their bones. We just need more evidence at scale.”
“I share the same intuition, and find this an interesting area for further exploration. I would be curious to hear your thoughts on why the “Growth X LDC” coefficients in all of your regressions are negative (which is a surprise to me). This seems to imply that people lower down the income distribution are actually benefiting less from % income increases? Re-running your regressions on just the less-developed countries in your Gallup dataset, I also get smaller coefficients than those for the whole dataset.”
Response: The Growth X LDC coefficient applies to lower income countries not strictly lower income people. The distinction is important because we can expect the mechanisms to be different. The impacts of income within a country are absolute and relative, due to social comparison as well as cost of living. Recall that poverty is usually defined in relative terms, i.e., as 60% of the median. While at the country level, I expect income to operate more in absolute terms. It’s not clear to me why growth does not help more in these countries.
(2) Helliwell, J. (2016). Life satisfaction and quality of development. In Bartolini, S., Bilancini, E., Bruni, L., and Porta, P., editors, Policies for Happiness, chapter 7, page 149. Oxford University Press.
There should be others too. For partial explanations (off the top of my head), think income inequality, quality of jobs (security), corruption, work hours, and materialism.
“If I understand correctly, it sounds like we now agree on the math of my post, and on my arguments around which coefficients from cross-sectional vs longitudinal regressions seem to match? But I think we still disagree about whether the impacts of a gradual increase in gdp across time should be compared to cross-sectional differences?”
Response: Not quite, I agree with some of the calculations you did in the last post, but not with the overall post and conclusions. The quickest justification for this response is that the EVS/WVS coefficients are smaller and even negative for certain country groups. There’s also the statistical significance to consider, which we have not discussed. There is a large amount of uncertainty in the estimates, and while they could be larger, they could also be zero. But regardless of coefficient, yes, we disagree about the implications of time-series (TS) and cross-sectional (CS) differences.
“My first thought on our disagreement is that an income doubling is a fairly arbitrary metric. I think it would be equally reasonable to zoom in on the cross sectional graph, and look at the impact of a 1% increase in income. We can imagine country Y on the cross-section graph which lies a little higher than Ethiopia on the regression line in my post. This country would have $1010 per capital GDP and a SWB of 4+1*.007=4.007, versus Ethiopia at $1000 and 4. If we compare this to what we would expect from a .007 coefficient in one of your alternative regressions, it looks like it’s exactly what we would expect from one year of 1% growth vs the counterfactual for Ethiopia? In this case we don’t need to worry about the amount of time it takes to double income, and TS and CS become more intuitively comparable?”
Response: You’re right that in that case we do not need to worry about the time involved, but what you’re pointing out is how small the relationship actually is in the cross-section. From the figure, the cross-sectional relationship is: y = −2.955 + 0.342*ln(x). Then a 1 percent increase in income is related to an increase in SWB of approximately 0.342*0.01 = 0.003, which of course is actually smaller than the 0.007 coefficient (note the previous post, 0.007 applies to developed not less developed countries. Also, it is statistically insignificant and could also be zero).
“My second thought is that if we assume that TS results are not comparable to CS results because they take a long time, wouldn’t that make the existence of the Easterlin Paradox irrelevant for making any judgements about the world? Isn’t the Easterlin Paradox a paradox precisely because we expect the coefficients to match between CS and TS, but they don’t seem to in some specifications?”
Response: You’re right that the Paradox is about the contrast between the two types of results. However, it’s not just whether the coefficients match. The CS results are statistically significant and the TS results are generally not statistically significant. A second aspect is that the TS results, even if statistically significant, make it clear how long it would take for SWB to increase. The period necessary is not clear in CS results, which makes it look like the CS results are much larger than the TS results. Your calculation above suggests that the CS results are actually quite small too, or that we need larger changes in income to have meaningful changes in SWB, which as the TS results point out, will take a long time. Another aspect, the Paradox is about the contrast, but the surprising result is how small the TS relation is. Whether there’s a contrast or not, this relation is important for thinking about the world.
“we are talking about the Gallup results and ignoring the EVS/WVS results. They are preferred for long-run periods.”
Agreed. I haven’t looked at the EVS/WVS results at all, so there is a good chance that they are less sensitive to the kinds of alternative specifications I tried for the Gallup results.”
Response: the sensitivity isn’t too important, because the relationships are all small. As stated above, even the CS results are quite small, or we need larger changes in income to have meaningful changes in SWB, which as the TS results point out, will take a long time.
“It’s possible that many people on the lower end of the income distribution benefit greatly – indeed many economists, even happiness ones, believe this in their bones. We just need more evidence at scale.”
“I share the same intuition, and find this an interesting area for further exploration. I would be curious to hear your thoughts on why the “Growth X LDC” coefficients in all of your regressions are negative (which is a surprise to me). This seems to imply that people lower down the income distribution are actually benefiting less from % income increases? Re-running your regressions on just the less-developed countries in your Gallup dataset, I also get smaller coefficients than those for the whole dataset.”
Response: The Growth X LDC coefficient applies to lower income countries not strictly lower income people. The distinction is important because we can expect the mechanisms to be different. The impacts of income within a country are absolute and relative, due to social comparison as well as cost of living. Recall that poverty is usually defined in relative terms, i.e., as 60% of the median. While at the country level, I expect income to operate more in absolute terms. It’s not clear to me why growth does not help more in these countries.
What I can suggest are two papers that discuss the quality of growth: (1) https://www.sciencedirect.com/science/article/abs/pii/S0305750X17300049
(2) Helliwell, J. (2016). Life satisfaction and quality of development. In Bartolini, S., Bilancini, E., Bruni, L., and Porta, P., editors, Policies for Happiness, chapter 7, page 149. Oxford University Press.
There should be others too. For partial explanations (off the top of my head), think income inequality, quality of jobs (security), corruption, work hours, and materialism.