So, this is a slightly older Fed publication, with the conclusion that:
"For now, the available data do not align to tell a clear, K-shaped story."
There have been newer pieces from other Federal Reserve banks, and it depends on what you view as a K-shape. Do you view it as diverging growth rates? Or do you view it as one group is increasing, one group is decreasing? The former exists; Atlanta calls it a bifurcated economy, while the NYFed calls it "K-shaped". The latter does not exist.
They do find a K-shaped economy, with the following statement: " We find that, since 2023, wealth has increased the most for high-income households, while inflation has risen the most for low-income households, with both factors helping explain the fact that real retail spending rose the most for high-income households."
Now, they also note that earnings data have a more mixed pattern, and therefore may not support the K-shaped hypothesis.
In fact, in another short paper, they confirm the evidence below but still call it K-shaped.
They find that consumer spending growth is highest among higher income groups. This holds across spending categories. They declare it is not K-shaped (since low income spending grew), but bifurcated; consumption inequality is rising, but they are growing at different rates.
What’s interesting is when you dive into the categories. Looking at the last paper is very interesting, specifically the sections on groceries and necessities.
The top quintile doesn’t slow down but they also have the highest disposable income and can absorb prices changes without the need to slow down. Thus their consumption can appear to grow when it’s possible there is some growth but also possible their spending remained steady.
The fourth highest (call it upper middle class) overall saw an increase in spend in 2025 and across their timeline but looking at the macro categories groceries took a sharp drop in 2025 and necessities (which includes groceries) ticked upwards. This suggests a pretty big pull back in reaction to grocery prices and offsetting dollars into energy, housing, medical. So not exactly a story of a willing increase in consumption. Maybe even one where savings/investments increased during 2025 in case things go south.
The middle quintile (essentially middle class) has the more interesting pattern because they tried to hold on to their spend pattern. Though that brings up a question of sustainability.
The bottom two appear to retreat or remain unchanged.
From this paper if you just look at the top line it kinda suggests a K overtime (with some minor uptick by the middle class in 23 & 24). However into 2025 it’s just the highest earners running a game of possible growth. Everyone else is making tradeoffs.
Missing from this analysis (and present in others) is the % of overall spend by quintile because from other papers while the top quintile might be growing they do not account for the majority of dollars.
Here is, I think, a very important caveat that's not being highly discussed. Moody's was the same group who put out that "50% of spending is now being done by the top 10%" stat that made the rounds a while back. While it gathered a ton of traction in online spaces a lot of people in economics raised an eyebrow at the implausible mathematics there.
>Each prior update from Moody’s garnered headlines through 2025, although the methodology and stark findings have drawn skeptics. It is not a direct measure of consumption expenditures by households. Rather, Moody’s works backward from financial and wealth data to estimate the average household savings for each income grouping.1 They count whatever disposable income remains—technically, “personal outlays”— as a broad measure of spending.
>Critics argue that the concentration of spending among the top 10 percent is implausible, and that converting macroeconomic data on financial asset flows to a measure of household spending makes improper assumptions.2 Nonetheless, the findings remain a well-publicized data point in media coverage, staking out the upper bound of the K-shaped consumption story.
The Fed has used this process before, but it results in a relatively small increase in inequality tracing all the way back to the 90s: https://www.dallasfed.org/research/economics/2025/1125-yang-consume
Note - obviously inequality is still high, was then, and is now, but the drastic increase is what's not showing up in most data.
Contrasting to that, the NY Fed's surveys reflect little shift in spending across income ranges over time.
>The New York Fed’s results breaking out gas and groceries are similarly bunched through most of those series, although food and beverage spending growth was notably higher for low-income households in 2025.
>If there is a K-shaped trend since the pandemic, it is subtle. Slightly faster spending growth, on average, for higher- and middle-income households emerges over time as higher cumulative growth in nominal spending (Figure 4). This cumulative view shows these gaps widened primarily in 2023 and have been mostly stable since.
This is a really good read, I'd encourage people to take the time to go through all of it. In addition, if you're wanting to learn about economic trends in general, subscribing to the various regional Fed blogs is a fantastic way to do so.
What's most interesting is a debate on what a K shape is.
I would think that a K shape indicates that outcomes for one group are improving, outcomes for another group are worsening, but that overall things look like they are improving because of the disproportionate weighting occurring in the "improving" group.
However, it appears that the NYFed has taken the belief that divergence in growth rates is K-shape; Atlanta calls it bifurcated.
I think ultimately much of this comes down to how are we wanting to even define economic wellbeing, for instance here we're talking about spending. There does exist a reasonable ceiling for spending among higher income individuals - at some point you're going to see savings rates simply increase while spending moves up modestly.
I think much of this discussion gets lost because the popular thing to do is focus on net worth, which will always reflect rising inequalities as those who have investable assets see returns while those that don't won't. For example, A doctor has an income of $500k and 2MM in invested assets, his assistant has an income of $50k and $5,000 in savings.
The doctor's income goes to 600k while the assistant's goes to 70k, and the market returns 20%. Is this K shaped? The assistant's income gain was double what the doctor's was in percentage terms, but of course the doctor's net worth increased by 400k while the assistant was perhaps able to save maybe another few grand a year.
At it's core, the above scenario is a good one, lower incomes appreciating at a faster pace than higher ones, a flattening of income disparity. But the doctor's spending increase will likely outpace the assistant, the doctor's net worth certainly outpaces the assistant, etc.
Even this article, which relies on measuring spending, to me does miss the point a bit. Ultimately incomes are the thing to focus on, of course fixed basic costs like housing and necessities are as important, but deriving recovery dynamics from spending seems to be once removed already from the real core issue.
>Even this article, which relies on measuring spending, to me does miss the point a bit. Ultimately incomes are the thing to focus on, of course fixed basic costs like housing and necessities are as important, but deriving recovery dynamics from spending seems to be once removed already from the real core issue.
.... Yet you love to quote articles about consumer sentiment using this very metric.
I'm not sure specifically what you're referring to but I think you're confusing a few things here, consumer sentiment historically has been a valuable economic input as it was at one time somewhat predictive of consumer spending and therefore broad consumption trends, that relationship is increasingly inconsistent. Hence discussions around the detachment of consumer sentiment and consumer behavior is very common.
This thread is about inequality of recovery, which is not really tied to consumption per-se, although one could use consumption patterns to attempt to display trends as noted above.
But these two are effectively entirely different topics, I don't know which very metric you're trying to refer to or what quotes, but I'm fairly sure you're misconstruing unrelated items.
The K shape idea doesn't exactly work even though the narrative that the top is pulling further away from the bottom is apt. The unfortunate reality to that is there's not a lot of downward movement available for the lower percentiles. There is a floor to how little one can spend simply living.
Except there has been relatively substantial low income real wage growth between 2019 and 2024 (highest for bottom decile), with 2025 seeing wage growth for all but the bottom decile (but bottom decile real wage growth would still be ~15% between 2019 and 2025).
So, your notion of a "floor" is during an era of pretty substantial improvements in standard of living...
This whole new buzz word thing “K-shaped” is funny. Let’s call it what it is. The top are getting richer and the bottom are getting poorer and can’t even afford food anymore. This is definitely not good news. Hmmmm, I wonder what can possibly go wrong with us plebs being hungry.
Lol I am middle class, as are all my friends. Our purchasing power has decreased and we are literally all struggling. I used to be able to afford basics like milk , eggs and bread, and now struggle to do so. Am I to distrust my reality of what I am experiencing?
> Our purchasing power has decreased and we are literally all struggling. I used to be able to afford basics like milk , eggs and bread, and now struggle to do so.
>Taken together, we show that what consumers have been saying differs from what they have been doing during the post-pandemic period; consumers say they feel worse, but through the end of 2024, they are buying more – not just spending more – than they did in 2019.
/
>In other words, during inflationary episodes, consumers seem to put more weight on higher prices than on higher incomes when assessing their current economic conditions, and as long as income growth remains robust, consumers continue spending even though in sentiment surveys, they say they feel pessimistic about the economy.
The fact of the matter is that almost all data points to the reality that much of this "decrease in purchasing power" is perception, as incomes are up in real terms, and increased spending is also up in real terms - IE people are buying more stuff than they used to and blaming inflation for them spending more.
Your post history is fascinating. We should also acknowledge that you are Canadian, so that's a very different financial circumstance than most Americans. And we're talking about the US here - it's literally in the title of this post and the linked article.
The paper only goes through 2024 when wage growth was keeping up with inflation. 2025 and 2026 have been different, which would explain what you are experiencing now.
Ive been pondering this for some time, but has income inequality gotten so bad that the top 10% (and the next 10% to some extent) now make up so much of the total spending that the bottom for sure 75% are essentially no longer significant in calculation of how much available spending they have to be able to influence change in GDP. The percentage the top 10% per the article since 2020 is an increase in total expenditures by 5% to 45% of all spending. Seems like an insane amount of spending.
I think no, as others said, but also … the rich always spend more than the poor. I think you have to think carefully about what would happen if the rich didn’t spend more than the poor (spoiler warning, the wealth gap would skyrocket because of the basic R>G argument). The two reasons the rich would not spend more than the poor are capital will eat itself (which seems to not actually happen) or there is nothing to buy.
There are kind of two or three or four overlapping questions:
is there a dual economy (à la Temin)? This is a long term question and not a short term question. And arguably a very serious one.
is there a bifurcation (or trifurcation or K-shapedness or E-shaped mess) or whatever to the dynamic/shorter term indicators?
if (2) is yes then the what is the impact on the accuracy of our understanding of the near term health of the economy and what is the impact on the situation in (1)?
> I'm sure if you plotted wealth/income in real inflation adjusted dollars they'll get their damned "K."
That's kinda the issue, the data doesn't really support this.
Wealth, in real terms? Possibly mildly K shaped.
Income, in real terms? No. All income ranges show increases across time, and the level of inequality across those ranges hasn't significantly changed
Now wealth inequality has obviously skyrocketed, part of this is just a long long period of great asset returns (not always the case historically speaking). But another part is that capital gains taxation is just really low in this country, which accelerates that impact.
The difference is whether people on the lower of the curve are actually doing worse or just not doing better to a similar degree to the people on the top. It is a very meaningful difference. If you’re not stuck on zero sum thinking at least.
Explain to me how we reconcile limited supply (both in source material and human capital) with non-zero sum? I get that you can have increases in perceived value, but the quantification (not qualification) of the discourse/process always has limitations of source. No matter the economy of scale, no matter the saturation/market availability, there's ALWAYS a floor and a ceiling...at which point do we reconcile the reality (the limits of labor and material) with the fantasy (perception/qualification of value)?
Everyone wins when someone pushes up the ceiling or the floor. The investor gets the profit, and others get the higher ceiling/floor for basically zero risk. “Limitation of source” is a meaningless term, the very source is constantly changing. Even though your idea is the intuitive idea, it’s the wrong idea
EconomistWithaD | 7 hours ago
So, this is a slightly older Fed publication, with the conclusion that:
"For now, the available data do not align to tell a clear, K-shaped story."
There have been newer pieces from other Federal Reserve banks, and it depends on what you view as a K-shape. Do you view it as diverging growth rates? Or do you view it as one group is increasing, one group is decreasing? The former exists; Atlanta calls it a bifurcated economy, while the NYFed calls it "K-shaped". The latter does not exist.
Explaining the K-Shaped Economy: What’s Behind the Divide? - Liberty Street Economics
They do find a K-shaped economy, with the following statement: " We find that, since 2023, wealth has increased the most for high-income households, while inflation has risen the most for low-income households, with both factors helping explain the fact that real retail spending rose the most for high-income households."
Now, they also note that earnings data have a more mixed pattern, and therefore may not support the K-shaped hypothesis.
In fact, in another short paper, they confirm the evidence below but still call it K-shaped.
K-shaped Economy or Not? Evidence from a Payments Survey - Federal Reserve Bank of Atlanta
They find that consumer spending growth is highest among higher income groups. This holds across spending categories. They declare it is not K-shaped (since low income spending grew), but bifurcated; consumption inequality is rising, but they are growing at different rates.
joepez | 6 hours ago
What’s interesting is when you dive into the categories. Looking at the last paper is very interesting, specifically the sections on groceries and necessities.
The top quintile doesn’t slow down but they also have the highest disposable income and can absorb prices changes without the need to slow down. Thus their consumption can appear to grow when it’s possible there is some growth but also possible their spending remained steady.
The fourth highest (call it upper middle class) overall saw an increase in spend in 2025 and across their timeline but looking at the macro categories groceries took a sharp drop in 2025 and necessities (which includes groceries) ticked upwards. This suggests a pretty big pull back in reaction to grocery prices and offsetting dollars into energy, housing, medical. So not exactly a story of a willing increase in consumption. Maybe even one where savings/investments increased during 2025 in case things go south.
The middle quintile (essentially middle class) has the more interesting pattern because they tried to hold on to their spend pattern. Though that brings up a question of sustainability.
The bottom two appear to retreat or remain unchanged.
From this paper if you just look at the top line it kinda suggests a K overtime (with some minor uptick by the middle class in 23 & 24). However into 2025 it’s just the highest earners running a game of possible growth. Everyone else is making tradeoffs.
Missing from this analysis (and present in others) is the % of overall spend by quintile because from other papers while the top quintile might be growing they do not account for the majority of dollars.
EconomistWithaD | 5 hours ago
Footnote 3; they give you access to the data, if you want to investigate your question.
RIP_Soulja_Slim | 7 hours ago
Here is, I think, a very important caveat that's not being highly discussed. Moody's was the same group who put out that "50% of spending is now being done by the top 10%" stat that made the rounds a while back. While it gathered a ton of traction in online spaces a lot of people in economics raised an eyebrow at the implausible mathematics there.
>Each prior update from Moody’s garnered headlines through 2025, although the methodology and stark findings have drawn skeptics. It is not a direct measure of consumption expenditures by households. Rather, Moody’s works backward from financial and wealth data to estimate the average household savings for each income grouping.1 They count whatever disposable income remains—technically, “personal outlays”— as a broad measure of spending.
>Critics argue that the concentration of spending among the top 10 percent is implausible, and that converting macroeconomic data on financial asset flows to a measure of household spending makes improper assumptions.2 Nonetheless, the findings remain a well-publicized data point in media coverage, staking out the upper bound of the K-shaped consumption story.
The Fed has used this process before, but it results in a relatively small increase in inequality tracing all the way back to the 90s: https://www.dallasfed.org/research/economics/2025/1125-yang-consume
Note - obviously inequality is still high, was then, and is now, but the drastic increase is what's not showing up in most data.
Contrasting to that, the NY Fed's surveys reflect little shift in spending across income ranges over time.
>The New York Fed’s results breaking out gas and groceries are similarly bunched through most of those series, although food and beverage spending growth was notably higher for low-income households in 2025.
>If there is a K-shaped trend since the pandemic, it is subtle. Slightly faster spending growth, on average, for higher- and middle-income households emerges over time as higher cumulative growth in nominal spending (Figure 4). This cumulative view shows these gaps widened primarily in 2023 and have been mostly stable since.
This is a really good read, I'd encourage people to take the time to go through all of it. In addition, if you're wanting to learn about economic trends in general, subscribing to the various regional Fed blogs is a fantastic way to do so.
EconomistWithaD | 7 hours ago
What's most interesting is a debate on what a K shape is.
I would think that a K shape indicates that outcomes for one group are improving, outcomes for another group are worsening, but that overall things look like they are improving because of the disproportionate weighting occurring in the "improving" group.
However, it appears that the NYFed has taken the belief that divergence in growth rates is K-shape; Atlanta calls it bifurcated.
RIP_Soulja_Slim | 6 hours ago
I think ultimately much of this comes down to how are we wanting to even define economic wellbeing, for instance here we're talking about spending. There does exist a reasonable ceiling for spending among higher income individuals - at some point you're going to see savings rates simply increase while spending moves up modestly.
I think much of this discussion gets lost because the popular thing to do is focus on net worth, which will always reflect rising inequalities as those who have investable assets see returns while those that don't won't. For example, A doctor has an income of $500k and 2MM in invested assets, his assistant has an income of $50k and $5,000 in savings.
The doctor's income goes to 600k while the assistant's goes to 70k, and the market returns 20%. Is this K shaped? The assistant's income gain was double what the doctor's was in percentage terms, but of course the doctor's net worth increased by 400k while the assistant was perhaps able to save maybe another few grand a year.
At it's core, the above scenario is a good one, lower incomes appreciating at a faster pace than higher ones, a flattening of income disparity. But the doctor's spending increase will likely outpace the assistant, the doctor's net worth certainly outpaces the assistant, etc.
Even this article, which relies on measuring spending, to me does miss the point a bit. Ultimately incomes are the thing to focus on, of course fixed basic costs like housing and necessities are as important, but deriving recovery dynamics from spending seems to be once removed already from the real core issue.
EconomistWithaD | 6 hours ago
NYFed did do a piece using both spending and income. Spending showed their version of the K-shape; income did not.
But agreed; much of the K-shape seems to be inappropriate (or, at best, partial analysis), while missing a lot of the underlying dynamics.
GhostofBeowulf | 4 hours ago
>Even this article, which relies on measuring spending, to me does miss the point a bit. Ultimately incomes are the thing to focus on, of course fixed basic costs like housing and necessities are as important, but deriving recovery dynamics from spending seems to be once removed already from the real core issue.
.... Yet you love to quote articles about consumer sentiment using this very metric.
RIP_Soulja_Slim | 4 hours ago
I'm not sure specifically what you're referring to but I think you're confusing a few things here, consumer sentiment historically has been a valuable economic input as it was at one time somewhat predictive of consumer spending and therefore broad consumption trends, that relationship is increasingly inconsistent. Hence discussions around the detachment of consumer sentiment and consumer behavior is very common.
This thread is about inequality of recovery, which is not really tied to consumption per-se, although one could use consumption patterns to attempt to display trends as noted above.
But these two are effectively entirely different topics, I don't know which very metric you're trying to refer to or what quotes, but I'm fairly sure you're misconstruing unrelated items.
yrotsihfoedisgnorw | 3 hours ago
The K shape idea doesn't exactly work even though the narrative that the top is pulling further away from the bottom is apt. The unfortunate reality to that is there's not a lot of downward movement available for the lower percentiles. There is a floor to how little one can spend simply living.
EconomistWithaD | 3 hours ago
Except there has been relatively substantial low income real wage growth between 2019 and 2024 (highest for bottom decile), with 2025 seeing wage growth for all but the bottom decile (but bottom decile real wage growth would still be ~15% between 2019 and 2025).
So, your notion of a "floor" is during an era of pretty substantial improvements in standard of living...
yrotsihfoedisgnorw | 3 hours ago
What was it like from ~2007-11?
EconomistWithaD | 3 hours ago
Well, this article is mostly about 2020+ data, so not sure why that's relevant.
https://www.congress.gov/crs-product/R45090
yrotsihfoedisgnorw | 2 hours ago
It's only relevant to your comment about a floor being reasonable because we're looking at a period of substantial improvements in standard of living.
EconomistWithaD | 2 hours ago
Again, this article is post-COVID. With considerable growth in living standards, especially for lower income individuals.
But, I've provided real wage data for you to play around with to test various "timelines".
Sufficient-Bid1279 | 4 hours ago
This whole new buzz word thing “K-shaped” is funny. Let’s call it what it is. The top are getting richer and the bottom are getting poorer and can’t even afford food anymore. This is definitely not good news. Hmmmm, I wonder what can possibly go wrong with us plebs being hungry.
guachi01 | 4 hours ago
The data does not support your claim.
EconomistWithaD | 3 hours ago
Wrong. https://www.epi.org/publication/strong-wage-growth-for-low-wage-workers-bucks-the-historic-trend/
Sufficient-Bid1279 | 3 hours ago
Lol I am middle class, as are all my friends. Our purchasing power has decreased and we are literally all struggling. I used to be able to afford basics like milk , eggs and bread, and now struggle to do so. Am I to distrust my reality of what I am experiencing?
LegSpecialist1781 | 3 hours ago
Yes, that is how economists require you to view the economy.
RIP_Soulja_Slim | 2 hours ago
> Our purchasing power has decreased and we are literally all struggling. I used to be able to afford basics like milk , eggs and bread, and now struggle to do so.
Relevant research: https://www.federalreserve.gov/econres/notes/feds-notes/tracking-consumer-sentiment-versus-how-consumers-are-doing-based-on-verified-retail-purchases-20250424.html
>Taken together, we show that what consumers have been saying differs from what they have been doing during the post-pandemic period; consumers say they feel worse, but through the end of 2024, they are buying more – not just spending more – than they did in 2019.
/
>In other words, during inflationary episodes, consumers seem to put more weight on higher prices than on higher incomes when assessing their current economic conditions, and as long as income growth remains robust, consumers continue spending even though in sentiment surveys, they say they feel pessimistic about the economy.
The fact of the matter is that almost all data points to the reality that much of this "decrease in purchasing power" is perception, as incomes are up in real terms, and increased spending is also up in real terms - IE people are buying more stuff than they used to and blaming inflation for them spending more.
lazydictionary | 3 hours ago
Your post history is fascinating. We should also acknowledge that you are Canadian, so that's a very different financial circumstance than most Americans. And we're talking about the US here - it's literally in the title of this post and the linked article.
gohblu | 3 hours ago
The paper only goes through 2024 when wage growth was keeping up with inflation. 2025 and 2026 have been different, which would explain what you are experiencing now.
EconomistWithaD | 3 hours ago
Wage growth was not just "keeping up with inflation". Wage growth outpaced inflation; substantially.
2025 saw real wage growth for all but the bottom decile (but overall, 2019 to 2025, real wage growth was ~15% for the bottom decile).
https://www.epi.org/blog/low-wage-workers-faced-worsening-affordability-in-2025/
Time_Sorbet_949 | 2 hours ago
Always has been
CautiousOptimism09 | 3 hours ago
Ive been pondering this for some time, but has income inequality gotten so bad that the top 10% (and the next 10% to some extent) now make up so much of the total spending that the bottom for sure 75% are essentially no longer significant in calculation of how much available spending they have to be able to influence change in GDP. The percentage the top 10% per the article since 2020 is an increase in total expenditures by 5% to 45% of all spending. Seems like an insane amount of spending.
[OP] laxnut90 | 3 hours ago
GDP only cares about the value of good and services being exchanged.
One person buying a $500 million dollar yacht has the same GDP impact as 5 million people spending $100 on groceries.
CautiousOptimism09 | 3 hours ago
Right but the US economy for my entire lifetime is built on consumer spending, not necessarily buying yachts. Might be changing
dominiond66 | 42 minutes ago
A "K economy"?
Let's describe the situation in simpler language.
The working class are in an "economic recession"
The rich are thriving!
OnlyHalfBrilliant | 6 hours ago
So the debate is not whether the economy is bifurcation (which is the real problem), but whether the trend lines form a literal letter K?
I'm sure if you plotted wealth/income in real inflation adjusted dollars they'll get their damned "K."
themiracy | 5 hours ago
I think no, as others said, but also … the rich always spend more than the poor. I think you have to think carefully about what would happen if the rich didn’t spend more than the poor (spoiler warning, the wealth gap would skyrocket because of the basic R>G argument). The two reasons the rich would not spend more than the poor are capital will eat itself (which seems to not actually happen) or there is nothing to buy.
There are kind of two or three or four overlapping questions:
RIP_Soulja_Slim | 6 hours ago
> I'm sure if you plotted wealth/income in real inflation adjusted dollars they'll get their damned "K."
That's kinda the issue, the data doesn't really support this.
Wealth, in real terms? Possibly mildly K shaped.
Income, in real terms? No. All income ranges show increases across time, and the level of inequality across those ranges hasn't significantly changed
Now wealth inequality has obviously skyrocketed, part of this is just a long long period of great asset returns (not always the case historically speaking). But another part is that capital gains taxation is just really low in this country, which accelerates that impact.
Rizpam | 6 hours ago
The difference is whether people on the lower of the curve are actually doing worse or just not doing better to a similar degree to the people on the top. It is a very meaningful difference. If you’re not stuck on zero sum thinking at least.
kraeftig | 5 hours ago
Explain to me how we reconcile limited supply (both in source material and human capital) with non-zero sum? I get that you can have increases in perceived value, but the quantification (not qualification) of the discourse/process always has limitations of source. No matter the economy of scale, no matter the saturation/market availability, there's ALWAYS a floor and a ceiling...at which point do we reconcile the reality (the limits of labor and material) with the fantasy (perception/qualification of value)?
THICC_DICC_PRICC | 4 hours ago
Everyone wins when someone pushes up the ceiling or the floor. The investor gets the profit, and others get the higher ceiling/floor for basically zero risk. “Limitation of source” is a meaningless term, the very source is constantly changing. Even though your idea is the intuitive idea, it’s the wrong idea
EconomistWithaD | 6 hours ago
No?
Also, 2019 to 2024, low income workers saw the highest real wage growth; higher than any other group in the income distribution.