Wealth Inequality in the US: The Role of Heterogeneous Returns

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00:05 OK,

00:06 it's 10:31,

00:07 so let's get started,

00:08 everyone.

00:09 Um,

00:09 everybody knows the rules,

00:10 so I don't have to go over them.

00:12 Today,

00:12 we're very happy to have Inne

00:13 Chavier

00:14 from Pompeo Fabre,

00:16 and she's going to talk about uh the role of

00:18 heterogeneous returns and wealth inequality in the United States.

00:22 Um,

00:22 Ines,

00:23 the floor is yours,

00:24 and like I said,

00:25 there'll be no interruptions for the 1st 10 minutes,

00:27 and after that,

00:27 you let me know when's a good time to pause.

00:30 Great.

00:31 Thank you,

00:32 Burke,

00:32 and thank you for having me here today.

00:35 I'm very happy

00:36 to present to you today my job market paper

00:39 which,

00:40 as the title suggests,

00:41 is about understanding what drives wealth inequality and in particular

00:46 what and how can we understand wealth inequality in the United States.

00:50 And so let me start by showing you some evidence on

00:54 how unequal wealth is in the United States,

00:57 and

00:58 here I'm showing,

00:59 I'd like to start with this graph where I'm making essentially two points.

01:04 I'm saying

01:06 I'm going to go into detail,

01:07 but here the main point is to show that

01:09 wealth in the United States is very concentrated

01:12 and in particular is more concentrated than labor income.

01:17 And the way to see this is

01:19 uh first to see that

01:21 when we look at the wealth share that goes to different groups,

01:25 we see that wealth is

01:27 very much concentrated.

01:28 And so

01:29 first I would,

01:30 I would like to draw your attention to the blue bars in this graph

01:33 which are reflecting the share of wealth that goes

01:36 to different groups along the wealth distribution.

01:40 And so for example,

01:41 what you would see here is that in the United States,

01:44 here the the data is from 2019,

01:47 you would see that the richest 1% in the US population

01:52 own a total of 37% of the total wealth.

01:56 And for example,

01:57 if we were to combine the wealth that the top 10% own,

02:03 we would see that the richest 10% own as much as 76% of the total wealth.

02:09 So this is saying that wealth is very much concentrated.

02:14 And the second thing that

02:17 that I would like

02:18 to draw your attention from is the fact that

02:21 while earnings,

02:22 which are reflected in the orange bars in this graph,

02:27 uh,

02:27 while earnings are also concentrated,

02:29 then they are less concentrated than wealth.

02:33 And again,

02:33 the way to see this is,

02:34 for example,

02:35 by noticing that the top 1% earners in the United States

02:40 earn about 14% of the total income.

02:44 But still this is uh much less than the,

02:47 the concentration of wealth that is represented by the blue bars.

02:51 Or uh

02:53 more broadly,

02:53 if we were to compare the size of the top labor income shares with top wealth shares,

02:59 clearly we,

02:59 we see that top wealth shares are

03:01 larger reflecting a larger degree of concentration.

03:05 The reason why I started with this observation is that

03:08 this fact is at odds with the predictions of the workhorse

03:12 model of wealth inequality where the key source of wealth concentration

03:17 is labor income inequality.

03:19 And I say this because there have been different models in the literature

03:24 of of this type

03:26 suggested and proposed,

03:28 and these type of models typically generate too little while concentration

03:32 when compared to the data.

03:34 And more specifically,

03:35 these kinds of models have even a sharper prediction

03:39 for the relationship between the distribution of wealth and earnings,

03:42 and their prediction is that wealth cannot

03:45 be more concentrated than earnings in the sense

03:48 that the right tail of the wealth distribution cannot be fatter

03:53 than the right tail of the labor income distribution.

03:56 Now this,

03:57 uh,

03:57 these facts and these observations have led economists to think that

04:01 there's likely other forces playing a role and,

04:04 uh,

04:05 generating additional wealth concentration

04:07 besides the,

04:08 the labor income heterogeneity.

04:10 And in this project I'm going to focus on one of those mechanisms,

04:15 and this mechanism is the idea that

04:18 besides potentially receiving different labor income,

04:21 households may also receive different rates of return

04:24 on their wealth when they save over time,

04:27 and potentially this mechanism generates some additional wealth concentration.

04:32 Now,

04:33 more specifically,

04:34 what I'm going to do in this project is to start by investigating

04:38 how relevant how empirically relevant this mechanism is in the,

04:42 in US data.

04:44 And so I'm going to uh use

04:46 household level data from the survey of consumer finances

04:50 to document some facts about household finances and rates of return on wealth.

04:54 And by providing this empirical evidence for the United States,

04:57 I'm going to expand on

04:59 the evidence provided by two recent papers which provide

05:02 empirical evidence of return differences into Scandinavian economies.

05:07 Now,

05:07 the kind of data that I'm going to use here is survey data,

05:11 in particular because we do not have the same kind of data,

05:15 in particular administrative data on wealth holdings

05:18 as the one that Scandinavian countries have.

05:21 And so in this project,

05:22 I'm going to propose a methodology based on

05:24 survey data to estimate returns on wealth.

05:28 Now,

05:29 the second thing that I'm going to do then is to

05:32 try to understand

05:33 what are the implications for the wealth distribution

05:37 of the existence of return heterogeneity.

05:40 And the way I'm going to do this

05:42 is through a partial equilibrium model which features

05:46 two main sources of wealth concentration

05:49 labor income inequality on the one hand,

05:51 and in addition,

05:53 I'm also going to consider this return heterogeneity mechanism.

05:58 And

05:59 what I'm going to do more precisely is to build on some

06:01 of the mechanisms proposed in the literature to generate uh return differences,

06:06 and I'm going to introduce this mechanism into a model,

06:09 and I'm going to calibrate returns in my model

06:12 using the empirical evidence that I document in the first part of the paper.

06:17 So

06:18 let me give you a quick preview of the findings.

06:21 The first one is related to the empirical evidence on returns to wealth.

06:27 And

06:27 the first observation is that returns to wealth appear to be heterogeneous,

06:32 and there appears to be a positive correlation

06:36 between the average return on wealth,

06:38 rate of return on wealth and the household's position in the wealth distribution,

06:42 meaning that on average wealthier households tend

06:45 to earn higher returns on their wealth.

06:48 And,

06:49 and I'm going to come back to this graph later,

06:51 uh,

06:51 in,

06:51 in this presentation.

06:53 The second finding of this project is that

06:56 once we take into account this return heterogeneity

06:59 on top of the labor income inequality which

07:01 had been more studied before in the literature,

07:04 once we introduce this mechanism into

07:08 a model and otherwise.

07:09 Standard model of wealth accumulation,

07:11 then we can bring the model much closer to the data and in particular we can generate

07:17 high top wealth shares,

07:18 which is something

07:19 that the previous literature

07:22 on labor income heterogeneity had struggled with.

07:26 So,

07:28 Um,

07:29 I'd like to,

07:30 uh,

07:30 perhaps I,

07:31 I can take,

07:31 uh,

07:32 any question if there,

07:33 uh,

07:33 uh,

07:33 if,

07:34 if there's any question at this point,

07:35 and,

07:36 uh,

07:36 or otherwise,

07:37 I'll,

07:37 I'll start by describing the data set that I used to estimate returns to wealth.

07:43 I see a couple of hands,

07:44 so let's do those.

07:46 Uh,

07:46 thank you,

07:46 Ines.

07:47 Uh,

07:47 Tristan,

07:48 you first.

07:49 Yeah,

07:49 I'm,

07:49 I'm,

07:50 I'm wondering,

07:50 so,

07:51 so if it's the case that

07:53 in the same market,

07:54 you know,

07:54 different households can get different returns,

07:57 you know,

07:57 that's pretty surprising in terms of how we think about,

08:00 you know,

08:01 capital markets being integrated,

08:02 uh,

08:03 but another hypothesis is that this is just different asset classes,

08:06 poorer households,

08:07 you know,

08:08 invest in real estate and other households,

08:11 you know,

08:11 have access to,

08:12 to private equity,

08:13 so so how much of this is just going to be

08:15 differences in asset class holdings.

08:18 Mhm.

08:19 So,

08:20 uh,

08:20 relative to this question,

08:21 I'm,

08:21 I'm going to show precisely some evidence of that,

08:23 and indeed I'm going to find that,

08:25 uh,

08:25 an important driver of these return differences

08:28 is precisely the fact that households own very different kinds of assets.

08:32 Um,

08:33 the,

08:33 in fact,

08:34 the,

08:34 the,

08:34 the fact that different assets have different rates of return over time.

08:38 So this explains,

08:39 uh.

08:40 An important share of the overall return differences.

08:43 Now I'm also going to find,

08:44 especially within some asset classes,

08:46 some additional return heterogeneity

08:49 where

08:50 and here I'm going to focus on just documenting these differences,

08:55 but

08:56 so the literature there has suggested that some of these differences may reflect

09:00 Different in in uh investment ability,

09:03 uh,

09:03 but also some um

09:05 heterogeneity in

09:07 in

09:08 information or,

09:09 or,

09:09 uh,

09:10 for example,

09:10 individuals age reflecting their experience.

09:13 So there,

09:14 there,

09:14 there,

09:14 these two sources of return differences both in portfolio composition

09:18 and uh additional differences within asset classes are going to

09:21 be important to understand the overall return differences that I

09:24 document and that I showed in the previous graph.

09:32 Yeah,

09:32 thank you,

09:33 Tuan,

09:33 you lowered your hand.

09:34 Is,

09:35 is that right?

09:37 No,

09:37 you should just,

09:38 uh,

09:38 I was wondering,

09:39 and maybe that's the question you're going to,

09:41 to address in the next point which is

09:44 What about the participate is the participation rates uh of uh in the,

09:49 in the surveys and the,

09:50 and the reporting bias is not going to be a problem for the whole society.

09:55 Mhm.

09:56 So,

09:56 uh,

09:57 let me,

09:57 let me now describe the,

09:59 the,

09:59 the data set,

10:00 uh,

10:00 that I use and then,

10:02 um,

10:03 so if there is some specific additional question,

10:05 then perhaps I can address it,

10:07 uh,

10:07 in the next round of questions.

10:10 OK,

10:10 so,

10:11 uh,

10:11 the,

10:11 the,

10:12 the data set that I use is,

10:13 as I mentioned before,

10:14 is the survey of consumer finances.

10:16 And so this is going,

10:18 is a survey that is going to cover a period of 30 years from

10:22 1989 to 2019.

10:24 And each wave of the survey,

10:26 which is conducted every 3 years,

10:28 is going to give me information about a cross section of US households,

10:33 and I'm going to have detailed information

10:35 on

10:36 households' income and households' different assets and liabilities.

10:42 Now,

10:42 related to the sampling design of this,

10:44 uh,

10:45 of the survey of consumer finances,

10:46 and one good thing

10:48 about this survey to study issues or questions related to wealth inequality

10:53 is the fact that this sample

10:55 has,

10:55 uh,

10:56 a double,

10:57 a double sampling procedure where on top of a random sample of US households

11:02 it it has a second.

11:04 Second sample of households which are likely to be very wealthy,

11:08 and the benefit of this is because since wealth is extremely concentrated,

11:14 having just a random sample of US households would likely

11:18 not accurately characterize this small group of individuals that hold

11:23 on a disproportionate amount of wealth.

11:26 So this is one advantage of the survey relative to

11:30 other surveys which have information on asset holdings.

11:35 Now at each

11:36 wave of the survey,

11:37 I'm going to have,

11:38 as I said,

11:39 detailed information on individuals' different sources of income,

11:42 and this is going to be,

11:43 for example,

11:45 information on

11:47 individuals' wages,

11:48 individuals' income from dividends,

11:50 individuals' income from

11:52 profits that come from the ownership of firms,

11:54 and so on.

11:56 And in terms of the information on individuals' wealth holdings,

12:00 I'm going to have information on

12:04 the different assets that individuals own.

12:06 So

12:07 this is going to include

12:09 uh deposits,

12:10 ownership of publicly listed stocks,

12:12 ownership of real estate,

12:14 uh,

12:14 bonds,

12:15 and so on.

12:16 And when it comes to asset holdings,

12:19 I'm going to particularly group the,

12:21 the,

12:22 uh,

12:22 assets that individuals own into these seven wealth components or categories.

12:28 And in particular,

12:30 I'm going to consider for one

12:32 broad asset class which is going,

12:34 I'm going to call interest earning assets,

12:36 and this is going to be uh include essentially

12:40 ownership of deposits and bonds.

12:42 Then I'm going to have detailed information

12:45 on the ownership of publicly listed stocks,

12:48 so public equity,

12:50 both directly or indirectly through mutual funds.

12:54 Then in terms of private businesses,

12:56 individuals are going to report whether they own privately

12:59 private businesses which are just so non-publicly listed firms.

13:05 I'm also going to have information on the real estate ownership,

13:09 so both individuals' primary homes where they

13:11 live and other secondary real estate.

13:15 Then there's going to be two residual uh

13:17 categories of other financial and non-financial assets,

13:20 and these are going to be a small share of total wealth between 5 and 6%.

13:26 And finally,

13:26 I'm going to have,

13:27 uh,

13:28 individuals,

13:28 uh,

13:30 so individuals are going to report their liabilities as well,

13:33 and the definition of wealth that I'm going to work with

13:36 is going to be,

13:37 uh,

13:38 wealth is going to be the difference between gross assets and wealth.

13:42 And so,

13:43 uh,

13:43 going back to,

13:44 to one of the previous questions,

13:46 the,

13:46 the,

13:46 the survey of consumer finances,

13:48 the reason why it's also

13:50 popular to study issues of wealth inequality is precisely because it has,

13:54 it's designed

13:56 to capture um

13:57 very detailed groups

13:59 along the wealth distribution

14:01 and being representative of,

14:03 of the households

14:04 that.

14:05 do own the disproportionate amount of wealth,

14:08 and here I'm,

14:09 I'm,

14:09 I'm going to focus on the population

14:12 that does own wealth.

14:13 So if households don't own any assets,

14:16 they are not going to

14:17 be a part of the population in this study.

14:22 OK,

14:22 so,

14:23 uh,

14:23 I'm,

14:24 I'm going to stop here also in case there is any question about the,

14:27 the data before I move on

14:29 to,

14:29 to

14:30 showing the evidence on rates of return.

14:34 Paulo.

14:35 Yes,

14:36 so,

14:36 uh,

14:36 I have a question about,

14:38 uh,

14:38 what are the incentives of people to tell the truth in these surveys,

14:42 and the second is whether taxes come into the picture at any point,

14:46 especially when comparing across countries.

14:48 Mhm.

14:49 Yes,

14:50 so in terms of the first question,

14:52 so the

14:54 one thing,

14:55 so in terms of trying to make sure that houses do not have an incentive to lie,

15:00 one thing that the survey

15:02 is prevented to do is precisely to

15:05 Well,

15:06 first,

15:07 the individual's identity is not revealed,

15:11 and also this,

15:11 the,

15:12 the,

15:12 the survey cannot compare individuals what what they report

15:17 uh

15:18 in terms of their income.

15:19 For example,

15:19 this cannot be compared

15:21 with individuals' tax

15:23 declarations,

15:24 for example.

15:26 So this is

15:27 really the,

15:28 there's,

15:29 these are the kinds of things that are done really to try to um

15:33 uh prevent households from having a clear incentive from lying or for,

15:37 for example,

15:37 from underreporting their,

15:39 their assets or their income.

15:41 Now,

15:41 uh,

15:41 there are studies that have

15:43 compared how this,

15:45 uh,

15:45 household,

15:45 the survey of consumer finances uh matches other data,

15:49 uh,

15:49 in,

15:49 in particular in terms of income and assets.

15:52 And generally in terms of,

15:53 in terms of capital income,

15:55 the survey of consumer finances lines up quite well broadly with,

15:59 uh,

16:00 information on,

16:01 on,

16:02 um.

16:03 Income from,

16:04 from administrative data

16:06 as well as aggregate data on income.

16:09 And in terms of wealth,

16:10 uh,

16:10 the information that they declare ownership of the different assets,

16:15 there is no administrative data on wealth holdings,

16:17 but this data also lines up very well.

16:21 There's some gap that increased that started to exist

16:26 from 2004.

16:27 Onwards,

16:28 where the survey of consumer finances,

16:30 in particular for real estate tends to overstate a little bit

16:34 the the value of real estate relative to aggregate accounts.

16:37 But overall,

16:38 uh,

16:38 this,

16:39 the,

16:39 the,

16:39 the different

16:40 uh

16:41 aggregate

16:42 data sets

16:43 tend to line up quite well,

16:45 suggesting that the,

16:47 the,

16:47 the,

16:47 the values that individuals report are,

16:49 are in line with other sources.

16:54 Uh,

16:54 thank you,

16:55 Yne Pierre.

16:57 Uh,

16:58 Highness,

16:59 I think it's a bit the same question as Tristan,

17:01 but just to clarify,

17:03 is this gonna be important at all,

17:06 or should there be a causal interpretation of wealth on return to wealth?

17:10 Is that important?

17:11 Or do we not care if,

17:12 you know,

17:12 if everything is explained just by the fact that richer people have more

17:16 taste for risk,

17:17 for example?

17:18 Mhm.

17:19 Yeah,

17:19 so

17:20 here,

17:20 um,

17:21 in this,

17:21 in this paper,

17:22 I'm not going to focus on

17:25 the,

17:25 the,

17:26 the

17:27 what.

17:27 Drives these return differences

17:30 and for example,

17:30 one explanation could be a differential exposure to risk

17:34 and this is mainly also one important limitation of the survey of consumer finances

17:39 is the fact that again there is a series of cross sections,

17:43 but I'm not,

17:44 I do not have the panel dimension.

17:46 I do not follow the same individuals over time.

17:48 And so this is going to create a limitation to

17:51 try to disentangle different stories,

17:53 in particular,

17:54 the one of trying to disentangle.

17:58 You know,

17:58 the relative importance of

18:01 how are

18:02 are returns

18:03 higher because individuals are wealthy or are

18:06 individuals wealthy because they have higher returns.

18:08 Now there is some literature suggesting

18:11 that

18:11 both kinds of mechanisms are likely to be a feature of the data.

18:16 But this is not something that here in my paper,

18:19 I'm not going to um

18:21 explore,

18:22 uh,

18:22 for example,

18:23 how,

18:23 how much of the return differences come from the fact that individuals own

18:28 or have different levels of assets in itself.

18:32 Now let me just also go back to one

18:34 previous point where I just didn't mention about taxes

18:37 and it's the fact that so the estimates that I'm going to present here,

18:40 they are going to be

18:42 post corporate

18:44 income taxes

18:45 but pre-capital income taxes and here again.

18:49 This is something that I'm working on,

18:50 on,

18:50 on,

18:51 uh,

18:51 also accounting for,

18:52 uh,

18:53 personal income,

18:54 capital income taxes,

18:55 but the,

18:56 and it's mainly because the survey of consumer finances

18:59 does not have this direct information on households uh payments

19:03 relative to,

19:04 to income taxes.

19:06 Now the idea is that also I I,

19:09 I do not expect that inclusion of personal

19:12 capital income taxes to uh change dramatically the,

19:15 the return differences that I find.

19:17 Essentially,

19:18 because,

19:19 for example,

19:19 we know that from Scandinavian economies,

19:21 we know that including this capital income taxes

19:24 has a very modest effect in

19:27 lowering return differences along the wealth distribution

19:30 and these these estimates for Scandinavian countries.

19:33 not only their

19:35 their income

19:36 tax is more progressive,

19:37 but also these estimates include a wealth tax which is progressive

19:42 and that does not exist in the US,

19:44 but this is something that I'm I'm,

19:46 I'm working on to extend it.

19:49 Um,

19:50 thanks,

19:50 Innes.

19:50 Um,

19:51 we have a few more hands up,

19:52 so let's see if we can get through them quickly.

19:54 Uh,

19:54 Tito,

19:54 you're first.

19:58 Hi,

19:58 Inez,

19:59 uh,

19:59 my question relates to the role that,

20:01 uh,

20:01 entrepreneurship might play in,

20:03 in this divorce between earnings and wealth inequality.

20:07 So if I'm an entrepreneur that pay myself,

20:10 uh,

20:10 I mean,

20:10 I'm,

20:10 I'm a business owner,

20:11 I pay myself a wage,

20:13 and then I reinvest all my

20:15 uh dividends and profits.

20:17 Uh,

20:17 I'm mechanically increasing the rate of return on my assets

20:21 while keeping my wage

20:23 not that big.

20:25 So I wonder whether if you constrain your analysis to wage earners,

20:30 and among the richest wage earners,

20:32 is it the case that also wealth is so more than equally distributed.

20:37 Um,

20:40 So I did not,

20:40 uh,

20:41 so I did not do that exercise in,

20:43 in particular.

20:44 And so

20:45 that I did when I,

20:46 when,

20:47 uh,

20:47 it's true that entrepreneurship plays an important

20:49 role in the overall return differences,

20:51 as I'm going to show that

20:52 very wealthy households own,

20:54 uh,

20:56 a big chunk of their portfolio in the form of private businesses.

20:59 And,

21:00 and so there,

21:01 the 11 adjustment that I made was that

21:04 when house

21:05 So,

21:06 so several or the majority of the household of private

21:08 business owners report to actively work in their firms,

21:12 and so this is an important source of income.

21:14 And there,

21:15 the,

21:15 the concern is to try to account for the labor income that

21:19 these households receive,

21:21 but that they report as a form of profits and not as labor income.

21:25 And so there,

21:26 there,

21:28 there are households who

21:29 report to work on their farms and do declare a wage.

21:32 And so for these people I'm going to consider,

21:35 well,

21:36 this is their wage income and the remaining is profits.

21:39 For the households that do report to own a farm and

21:42 to actively manage it but do not report a wage,

21:45 I am going to Impute a salary to these individuals based on their education,

21:51 their gender,

21:51 and their age,

21:52 and I'm going to deduct

21:54 those estimates of labor income from the reported profits

21:59 to try to account

22:00 for

22:03 what should be reported as or accounted as labor income

22:05 but is instead reported as profits.

22:09 Gotcha.

22:10 Thanks.

22:12 Uh,

22:13 just a very quick clarification question.

22:15 Your,

22:15 your data does include retirement accounts?

22:19 Yes,

22:19 so

22:20 my,

22:20 my data is going to include um

22:23 sponsored,

22:24 uh,

22:24 employee sponsored retirement accounts.

22:27 Yeah,

22:27 so for example,

22:28 the ownership of,

22:29 of stocks or bonds to these accounts is going to be in this data.

22:35 And finally Steven.

22:38 Hi,

22:39 uh,

22:39 thanks.

22:40 I was gonna ask two questions,

22:41 but the first one Roberto already asked.

22:43 Um,

22:44 the second question,

22:45 um,

22:46 is just about

22:48 how,

22:48 how much some of these returns are based on a

22:51 specific period in history.

22:53 I mean,

22:53 it's been a time that stocks have done very well.

22:57 Maybe that's not expected to be repeated again,

22:59 and historically,

23:01 it

23:01 didn't,

23:02 uh,

23:02 you know,

23:03 has not necessarily been always like that,

23:05 so.

23:05 I mean,

23:06 wealth is something that accumulates over time,

23:09 so I was wondering if you have a view on this sort of a steady state finding or this is a,

23:14 a once-off

23:15 thing in history.

23:16 Mhm.

23:17 Yeah,

23:17 so I would,

23:19 thank you.

23:20 Uh,

23:20 so I would say that um

23:22 I,

23:22 I would see it more as a long uh

23:25 run uh difference in returns.

23:27 And the reason why I say this,

23:28 so absolutely during this period,

23:30 there have been uh important fluctuations in asset prices

23:34 and for example,

23:35 if if

23:36 I were to look at the,

23:37 the

23:39 our compute.

23:40 Returns

23:41 focusing up until say the first half of the 2000s,

23:46 then

23:46 I would have found that return differences were

23:50 smaller than if we take into account the overall sample,

23:53 essentially because the first half of the 2000s,

23:56 real estate did particularly well.

23:58 This has benefited

24:00 in particular households in the bottom and in the middle of the distribution.

24:05 But then,

24:05 so

24:06 once we take into account,

24:08 uh,

24:08 so this is if I were to,

24:09 to focus on that particular period of time,

24:12 but if one looks at the overall taking an average

24:15 of asset returns over the whole period of 30 years,

24:19 then there,

24:19 there's not a clear trend in asset prices,

24:24 and it takes,

24:25 so it's kind of the idea is to abstract

24:27 away from these larger price fluctuations and focus more

24:30 on differences in the level of returns in the long run.

24:37 Um,

24:38 OK,

24:38 we still have hands up.

24:39 Chala,

24:40 do you still have a question or you lowered your hand?

24:42 Yeah,

24:43 just a quick follow up on what Anna asked,

24:45 but it might be the case lower income households have more defined

24:49 benefit plans,

24:50 whereas the higher income have defined contribution,

24:52 and if you have a defined benefit,

24:54 you have no idea how well your pension plan is doing.

24:56 So you don't incorporate that wealth

24:59 when you're responding to the survey.

25:02 When might that create a problem?

25:05 So I would say that so that's that's correct.

25:07 At the end this survey

25:09 does not include defined benefit pensions,

25:12 and so this is something that is not included in the

25:14 survey and potentially if this is something that is concentrated in

25:19 the hands of

25:20 households more at the lower or in the middle of the distribution,

25:23 this could potentially.

25:25 Reduce the degree of wealth concentration.

25:29 Now,

25:29 there are some estimates where uh

25:32 if we were to account for uh

25:34 retirement wealth including

25:36 defined benefit pension plans,

25:38 top wealth shares would decrease uh somewhat.

25:41 So for example,

25:42 for

25:42 the,

25:43 the top 10%,

25:44 uh,

25:45 the,

25:45 the wealth share that goes to the top 10% would have decreased

25:49 um

25:50 by about or up to 10% points.

25:53 Now,

25:53 still,

25:54 even

25:54 uh when we take into account these

25:56 these um these kinds of assets and so even if we take into

26:00 account that top wealth inequality might be

26:03 slightly lower than the measured from this

26:06 private wealth definition that I have here.

26:08 Still,

26:09 the,

26:09 the degree of inequality is,

26:11 is still very large and,

26:13 and,

26:14 and so I,

26:14 I think there's still the motivation to try to understand what drives the

26:18 the the the dynamics and what drives the the degree of concentration

26:22 in this definition of wealth,

26:25 but absolutely that,

26:26 uh,

26:27 you know,

26:27 potentially if we take into account.

26:30 These other more difficult to measure uh definitions of wealth,

26:34 then maybe the,

26:35 the exact

26:36 uh degree of wealth concentration would have changed and potentially is,

26:39 is slightly lower than,

26:40 than the one that I'm presenting here.

26:42 OK.

26:43 Great.

26:43 Thank you.

26:44 OK,

26:44 final question,

26:45 then we move on,

26:46 Chuan.

26:47 So clarification,

26:48 so how are stock options

26:50 accounted for?

26:53 So the 11th?

26:55 So stock options here would be,

26:57 uh,

26:57 so there,

26:58 there's a,

26:59 there's a few

27:00 relatively few small share of households who declare to own

27:05 or to have stock options.

27:06 Here in particular,

27:07 they would be accounted as in the,

27:09 in the asset class of non-financial

27:12 assets,

27:13 so they will not be accounted as income.

27:18 OK,

27:19 so

27:20 Perhaps,

27:21 perhaps,

27:22 I

27:22 jump into the,

27:24 to showing you,

27:25 um,

27:25 well,

27:26 the empirical evidence on returns to wealth.

27:28 And so let me start by clarifying what I mean by that.

27:31 So the definition that I'm working with of the return on wealth RW is going to be

27:36 the weighted average of the rate of return

27:39 on the different asset classes or wealth components

27:42 where the weight is given by the share of each asset class in total wealth.

27:48 Now,

27:48 in turn,

27:49 the rate of return on each wealth component is going

27:51 to be given by the sum of two elements,

27:54 a yield component that reflects the dividend income generated by an asset.

27:59 So for example,

27:59 dividend income if one owns stocks,

28:02 and a capital gain component in the case that reflects

28:06 fluctuations in the price of the asset over time.

28:10 Now,

28:11 to estimate the yield component of returns,

28:13 I'm going to use information on from the survey of consumer finances,

28:17 and I'm going to explain in a second more in detail how I do that.

28:20 And in,

28:21 in order to impute the capital gains and losses by asset class,

28:25 I'm going to use aggregate price data.

28:28 And the main reason is because the,

28:30 the US Survey of Consumer Finances

28:32 does not have uh information.

28:34 On the physical quantity of the asset.

28:36 And so I cannot disentangle changes in,

28:38 in

28:39 the,

28:39 the value of each asset.

28:42 I cannot disentangle between changes in the

28:44 price versus changes in the physical quantity.

28:46 So I'm going to use this aggregate price data to impute this part of the return.

28:52 So let me start with the yield component of returns.

28:55 So what I'm going to estimate is average annualized returns over

29:01 the three year intervals that separates two waves of the survey.

29:05 And so here I'm going to give the example of

29:08 the two waves of the survey

29:10 that

29:10 that happened in 1989 and 1992.

29:14 And overall,

29:15 what I'm going to do is I have the information

29:17 on the value of the different assets in 1989.

29:20 And I want to estimate what is the income generated by

29:23 the different assets over the three year period that that separates

29:28 the two waves of the survey.

29:30 And essentially I'm going to use information on the income that individuals report

29:35 at two different points in time,

29:37 um,

29:38 so reflected here in this graph between 1988 and 1999

29:42 and 1991 and 1992.

29:44 So here,

29:45 uh,

29:46 uh,

29:46 I'll just say that also if you were to use information on

29:50 the income uh only from the

29:53 year uh that precedes

29:55 the,

29:55 the survey,

29:56 then the,

29:56 the results will be very,

29:57 very similar.

29:59 So,

30:00 and overall then the aggregate rate of return on,

30:03 on a certain asset class is going to be the geometric average

30:06 between these two rates of return that use information on the

30:10 income generated by the asset at two different points in time.

30:15 Now if we were to do this

30:17 for each of the asset classes that I mentioned before,

30:20 we would have obtained an estimate of the yield return

30:23 of each asset class that is represented in this table.

30:28 And here,

30:28 uh,

30:29 the main point that I wanted to make is that

30:31 there are this is the average uh return over this period,

30:34 1990 to 2019.

30:37 And here the main observation is that there is,

30:40 there are substantial differences in,

30:42 in the yield return of the different assets

30:44 and in particular,

30:45 private businesses

30:46 earn substantially higher returns than the other asset classes that are,

30:51 that are,

30:51 that are included in this survey.

30:54 Now of course

30:55 we don't just care about the yield

30:57 return of each asset,

30:58 we care about the total return.

31:00 And so I'm going to also estimate the capital gain component of returns,

31:05 and this is what I'm showing in this table where

31:08 as I said,

31:09 I'm going to use aggregate price data to impute

31:12 gains.

31:14 And for public equity and real estate,

31:16 I'm going to use Schiller's indexes,

31:19 and for private businesses,

31:21 I'm going to use information from US financial accounts.

31:24 And here again,

31:26 one observation is that there are substantial differences across asset

31:30 classes in the capital gains or losses over the period,

31:34 and clearly equity have earned higher capital gains than the remaining assets.

31:41 Now,

31:41 as I mentioned before,

31:43 uh,

31:43 again,

31:44 the,

31:44 the thing that we care about is the aggregate,

31:46 is the total return,

31:48 not each of these components.

31:50 And so if we were to add this to the yield and the capital gain components of returns,

31:54 we would have obtained the estimates represented in the last column of this table.

32:00 And here,

32:01 uh,

32:01 I'd like to make two observations.

32:03 The first observation is that again,

32:05 there,

32:06 there are substantial differences in the

32:08 average rate of return

32:10 across asset classes,

32:11 and we see that

32:13 private businesses earn substantially higher returns over this period

32:17 than the remaining assets considered in this survey.

32:22 And in,

32:22 besides private businesses,

32:24 also public equity earned on average higher returns than,

32:27 than,

32:27 for example,

32:28 real estate or interest earning assets.

32:31 Now,

32:32 if we were to uh use the the first equation one

32:36 to estimate the overall return on wealth,

32:38 taking into account the weight of

32:41 the class in total wealth,

32:43 we would have found that on average,

32:46 the aggregate wealth portfolio in the in the US earned

32:49 an average rate of return of 6.8% a year.

32:53 So

32:54 the next question that I'm going to ask is whether it's

32:58 fair to say that households at different points of the wealth distribution

33:02 earned markedly different returns on wealth,

33:04 or if it's the case that it's fair to say that the majority or

33:09 all households earned a rate of return on their wealth which was close to 6.8%.

33:14 So

33:15 to answer this question,

33:16 what I'm going to do is to repeat the previous

33:19 calculations but at different points of the wealth distribution.

33:23 And so if we do that,

33:25 then we would have obtained this,

33:27 this,

33:28 we go back to one of the first graphs that I showed

33:30 which where I'm plotting what is the,

33:33 what was the average rate of return on wealth,

33:35 the yearly rate of return

33:37 for households at different percentiles of the wealth distribution.

33:41 And here the first observation is that there

33:44 is a positive correlation between returns and wealth,

33:48 meaning that wealthier households

33:50 earned on average higher returns.

33:52 And these differences can be large in the sense that

33:56 for example,

33:57 if we were to move from the 20th percentile of the wealth distribution

34:00 to the top 1%,

34:02 the yearly rate of return would have risen

34:06 from 3.6% to 8.3% a year,

34:10 so about 4.7% points different.

34:14 Now,

34:15 um,

34:16 going back to 11 point that was made before is one thing that I'm going to ask is

34:21 whether these return differences reflect

34:23 essentially a differential portfolio composition

34:27 and

34:28 And this is exactly one thing that I'm going to find.

34:31 I'm going to find that indeed the,

34:34 the

34:35 composition of wealth portfolios varies systematically with wealth

34:39 and in particular,

34:40 and so this is what I'm showing here in

34:42 this graph where I'm showing the share of each asset

34:45 in the,

34:46 in the gross wealth portfolio,

34:48 so gross asset portfolio

34:50 for households at different percentiles of the wealth distribution.

34:54 And I'm going to observe that as we move towards the top of the wealth distribution,

34:59 the relative importance of equity,

35:03 both public equity and private businesses,

35:05 rises,

35:06 and in particular at the very top of the distribution,

35:09 public businesses,

35:11 or sorry,

35:12 private businesses

35:13 are the main assets

35:15 that

35:16 that very wealthy households own.

35:19 And now,

35:20 of course,

35:20 if we take into account this heterogeneity in,

35:22 in portfolio composition with the,

35:24 the return differences

35:27 in across asset classes that I,

35:29 I showed you before,

35:30 then this helps us,

35:31 will help us understand

35:33 at least in part why wealthier households

35:35 have earned higher returns on their wealth.

35:39 Now,

35:40 in addition to this mechanism,

35:42 I'm going to look at how returns vary or

35:45 I'm going to estimate rates of return on wealth

35:48 within asset classes,

35:49 and again I'm going to do so at different points of the wealth distribution.

35:53 And here I'm going to,

35:55 I'm going to find some evidence of

35:58 additional heterogeneity

36:00 for some asset classes more than others,

36:02 but this is,

36:03 I'm going to still find some evidence that wealthier

36:05 households earn higher rates of return on some assets,

36:10 in particular in real estate,

36:12 and especially when comparing

36:14 the,

36:14 the top 3,

36:15 so the very top of the wealth distribution relative

36:18 to the rest of the wealth distribution.

36:21 And it's also going to be true for private businesses

36:25 where here the relationship between returns and

36:27 wealth is not going to be monotonic,

36:29 but

36:29 I'm going to find that households in the top 10% of the wealth distribution

36:34 are going to earn on average higher returns than the next

36:38 20% in the wealth distribution.

36:40 So again,

36:41 some evidence on return differences

36:43 beyond the composition of asset portfolios.

36:48 Um,

36:49 the,

36:49 the 11 simple exercise that I do is to try to understand

36:53 uh how important these two mechanisms are,

36:55 and here,

36:56 uh,

36:56 I'm,

36:56 I'm plotting in this graph precisely that

36:59 where I do,

37:00 uh,

37:00 two counterfactual exercises

37:03 trying to understand

37:04 how much um

37:06 return differences may reflect heterogeneous

37:08 portfolio composition versus how much

37:11 return differences may reflect additional

37:13 return differences within asset classes.

37:15 And so in this graph,

37:17 I'm showing

37:18 the actual rate of return on wealth by by wealth percentile.

37:22 So this is represented by the red bars.

37:25 And then I'm also showing

37:28 in the green as in the green bars,

37:30 what would be the the rate of return

37:33 on wealth at different points of the wealth distribution

37:36 if all households owned the aggregate wealth portfolio.

37:40 And so here I'm imposing that all households own

37:43 the same kind of assets and in particular,

37:45 I'm saying that

37:46 relative to what they actually own,

37:49 I would be increasing the importance of equity for households

37:53 at the bottom and at the middle of the distribution.

37:56 Whereas for those households at the very top

37:59 or at the top of the distribution,

38:00 I would be reducing the relative importance of equity and would be raising the,

38:05 the relative importance of real estate in particular.

38:08 And so

38:09 perhaps not surprisingly,

38:10 this would lead to a rise in the rate of return on wealth

38:14 for households in the in the bottom and in the middle of distribution,

38:19 and it would lower the rate of return of households at the very top.

38:24 Now,

38:24 in another exercise that I do is to impose that households receive

38:30 the same rate of return within asset classes while potentially owning different

38:35 kinds of assets,

38:37 and this is reflected in the blue bars.

38:40 And here this is saying that if we were to impose that all households on the same

38:46 aggregate return

38:48 within asset classes,

38:50 we would,

38:51 this would increase in particular the return of households

38:54 at the bottom of the distribution and it would break the pattern of

38:59 the increasing pattern between returns and wealth.

39:01 And this is essentially the effect of essentially

39:05 imposing that households at the bottom who are

39:08 especially exposed to real estate

39:10 here

39:12 I'm I'm,

39:12 I'm saying that their returns would have been much higher,

39:15 so they would be equal to the average rate of return.

39:18 And so this is the main effect that you see here.

39:21 And but overall,

39:22 um,

39:23 so

39:23 overall what this is saying is that both kinds of

39:27 sources of return differences

39:29 are important to understand the overall return differences

39:33 and so we need to understand better what are the mechanisms

39:36 underlying both heterogeneous portfolios and portfolio

39:40 return differences within asset class.

39:43 So I'm going to stay,

39:44 to make a,

39:45 a small uh stop here in order and ask if there are any questions.

39:53 Yes.

39:55 Um,

39:56 Chevy first.

39:58 Hi,

39:58 uh,

39:59 yeah,

39:59 couple of questions.

40:00 Um,

40:01 so,

40:01 so the first is,

40:02 um,

40:03 so I guess,

40:04 is the timing of,

40:06 you know,

40:07 wealth and returns,

40:08 uh,

40:10 You,

40:11 you,

40:11 I guess,

40:11 you know,

40:11 so,

40:12 uh,

40:12 proper in the sense that,

40:13 of course,

40:14 you know,

40:15 if I compute report,

40:16 I mean,

40:16 if I compute returns based on,

40:18 based on

40:19 past

40:20 wealth,

40:20 then,

40:21 you know,

40:21 there's clearly an endogeneity,

40:22 right?

40:22 I mean,

40:23 people

40:23 that have had more returns are gonna have more wealth,

40:26 so I presume that the returns are computed,

40:29 you know,

40:29 going forward,

40:30 uh,

40:30 you know,

40:31 given,

40:31 given a wealth.

40:32 So I guess,

40:33 I mean,

40:33 you know,

40:33 that,

40:34 that,

40:34 that's one issue,

40:35 but,

40:35 but then the other issue is.

40:37 So,

40:37 uh,

40:37 uh,

40:38 you know,

40:38 I'm just,

40:39 so,

40:40 you know,

40:41 earnings is,

40:41 is a flow and wealth is a stock,

40:44 and so

40:45 just by compounding over time,

40:47 once you get a more,

40:48 a more skewed distribution of wealth rather than a,

40:51 a distribution of,

40:52 of earnings.

40:53 Uh,

40:54 you know,

40:54 you know,

40:55 even without going to the,

40:56 you know,

40:57 heterogeneity returns,

40:58 I mean,

40:58 it's just,

40:59 you know,

41:00 one wealth over time be more skewed just because you're,

41:03 you know,

41:03 there's the wonders of,

41:04 you know,

41:05 uh,

41:05 compounding interest,

41:06 right?

41:06 I mean,

41:07 you know,

41:08 um,

41:09 yeah,

41:09 sorry.

41:11 Yeah,

41:11 so,

41:11 um,

41:12 I would say,

41:13 so relative to the,

41:14 to the first question,

41:16 so indeed,

41:17 So I'm going to observe households at a certain point in time.

41:20 I'm going to observe where they,

41:22 they,

41:22 they

41:24 land in the wealth distribution.

41:26 And I'm going to estimate the returns based on the,

41:29 the wealth that they report and the income

41:31 that they report associated with each asset.

41:34 Now,

41:34 again,

41:35 since I,

41:35 I cannot observe the same individual over time,

41:39 one thing that I'm not going to be able to disentangle

41:42 or at least it's,

41:43 it's very challenging is

41:45 again,

41:46 how,

41:47 uh,

41:47 so again,

41:48 what part of the returns.

41:50 Or the high returns come from the fact that individuals are wealthy.

41:54 So

41:54 are individuals wealthy because they have higher returns,

41:56 or

41:57 do they have higher returns because they are wealthy?

42:00 So again,

42:00 uh,

42:01 this is something that I cannot,

42:02 um,

42:03 or it's very challenging to do with this data.

42:05 The,

42:06 but the empirical evidence that we have in this literature,

42:09 mainly from Scandinavian economies,

42:11 is saying that

42:13 well,

42:13 there's,

42:14 there's a part of it where,

42:16 uh,

42:18 higher rates of return.

42:20 Reflect the fact that or

42:22 being wealthy

42:23 uh allows individuals to to earn some uh higher rates of return.

42:28 And uh there's a part of it where in some individuals are,

42:32 you know,

42:32 just,

42:33 you can think of this as,

42:34 or one interpretation is some individuals

42:36 are being better at investing than others

42:38 and having higher rates of return.

42:39 And this,

42:40 uh,

42:41 this mechanism allowing individuals to uh end up

42:44 at the top of the wealth distribution.

42:46 So

42:47 exactly this is what's going to happen and in the model,

42:50 this is what's going to happen where some individuals,

42:53 as so it's the mechanism in the model is going to be the the

42:57 the relationship is going to be

42:59 from higher returns

43:01 to higher wealth inequality in the sense that

43:04 I'm going to abstract from the possibility that

43:07 Being wealthier also allows some individuals to earn higher rates of return.

43:12 So here I'm not going to say that this is not potentially one additional mechanism,

43:18 but it's just mainly because of the lack of

43:22 empirical evidence on the strength of this mechanism.

43:28 Um,

43:29 Relative to,

43:30 to your second point of,

43:31 so I'm not sure if I understood very well the,

43:34 the question,

43:34 but,

43:35 so

43:36 if,

43:36 if we have uh a,

43:37 a model,

43:38 for example,

43:38 of labor income inequality.

43:41 And the,

43:42 what is the distribution of wealth implied by that model.

43:45 So,

43:46 did I understood correctly that

43:49 you're asking whether

43:51 isn't it the case that over time

43:53 wealth must be more concentrated in labor income?

43:56 Is that the question?

43:58 Uh,

43:59 again,

43:59 my intuition could be totally wrong,

44:00 but,

44:01 but,

44:01 but yeah,

44:02 I mean,

44:02 you know,

44:02 if I start with,

44:03 uh,

44:04 some,

44:05 some distribution of,

44:05 of earnings,

44:07 and,

44:07 you know,

44:07 some people save a share,

44:09 share,

44:10 and there's,

44:10 you know,

44:11 there's some returns to wealth,

44:13 I mean,

44:13 my sense is,

44:14 you know,

44:14 through compounding,

44:15 uh,

44:17 through compounding,

44:18 you know,

44:18 I mean,

44:18 again,

44:19 wealth is a stock,

44:19 so

44:20 again,

44:21 maybe my intuition is totally wrong,

44:22 but I,

44:22 I would assume that,

44:23 that you would end up with a more skewed distribution,

44:26 um,

44:27 um.

44:28 Because,

44:28 you know,

44:28 you're compounding,

44:29 you're,

44:30 you know,

44:30 you're compounding,

44:32 again,

44:32 you're,

44:32 you're saving a share of,

44:34 of,

44:34 of,

44:35 of your wealth,

44:36 I'm sorry,

44:36 of,

44:36 of your earnings,

44:37 which again,

44:38 I mean,

44:38 this might vary by by

44:40 by earnings,

44:41 so maybe top earners

44:42 presumably uh save more than,

44:44 than,

44:45 than low,

44:45 low earners,

44:46 but even,

44:47 even,

44:47 you know,

44:48 putting a share aside,

44:49 you know,

44:49 even setting that aside,

44:51 and I,

44:52 I,

44:52 you know,

44:52 I would imagine that through compounding.

44:55 Um,

44:55 you know,

44:55 over time,

44:56 yeah,

44:56 you would get a different distribution,

44:58 and in fact you would get a skimer distribution

45:00 again,

45:00 maybe I'm wrong,

45:01 but,

45:02 uh,

45:02 you know,

45:02 this is,

45:03 I mean,

45:04 uh,

45:04 yeah,

45:04 I mean you can just simulate that,

45:05 and,

45:06 and again maybe my intuition is totally wrong,

45:08 um,

45:08 but,

45:08 but I would,

45:09 I would,

45:09 I would.

45:10 Yeah,

45:11 at first pass,

45:12 I would think that,

45:12 you know,

45:13 the,

45:13 the wealth distribution would be more skewed than the,

45:15 than the earnings distribution.

45:18 Yeah,

45:18 exactly.

45:18 So what I meant,

45:20 and let me be more precise,

45:21 is that the literature has shown that in these types of models where the,

45:25 the only source of,

45:26 so everything else being equal and labor income

45:29 heterogeneity being the only source of income,

45:31 then the literature has shown

45:33 that in terms of the implications of this process

45:37 for the stationary distribution of wealth,

45:40 this literature has shown that the,

45:42 the fatness of the distribution tail.

45:46 Cannot be higher

45:47 than the fatness of the labor income scale.

45:51 So it's in that sense that

45:53 top wealth shares cannot be larger than top income shares.

45:56 And so top labor income shares.

45:59 And so this is a result that has been

46:01 established in previous theoretical models in this literature.

46:07 Good,

46:08 thanks,

46:08 Tristan.

46:09 Yeah,

46:10 it's just a clarification question on the private business returns.

46:14 Uh,

46:14 can you say anything about whether those are mostly,

46:18 you know,

46:18 holdings in a,

46:20 a private equity fund,

46:21 or is it mostly,

46:23 you know,

46:23 S corporations and,

46:24 and businesses that the individuals own,

46:26 like,

46:26 you know,

46:26 being a partner in a law firm or a medical practice,

46:30 I think obviously the,

46:31 the second one is,

46:32 is much harder to redistribute,

46:34 um,

46:34 than the first.

46:36 Mhm.

46:37 Exactly.

46:37 So

46:38 I'm,

46:38 I'm,

46:39 I'm not going to look at least in this project specifically on

46:42 the sector or what more detailed what kind of business this is,

46:45 but the majority of these businesses are,

46:47 are,

46:48 uh,

46:48 businesses,

46:49 private businesses in which

46:51 individuals work and,

46:52 and it's their,

46:53 their,

46:54 um,

46:54 so

46:56 the,

46:56 the majority of their wealth,

46:57 the biggest chunk of their wealth is invested in that business

47:00 and they work for it.

47:02 So this is the majority of the cases.

47:06 OK,

47:06 Tatiana.

47:08 Um,

47:08 yeah,

47:08 thanks.

47:09 I had a question about um how if you're adjusting somehow for,

47:12 for the risk of those uh investments and related to that,

47:15 I was wondering.

47:16 Um,

47:16 if there's a lot of churning of people,

47:18 um,

47:18 in that,

47:19 um,

47:19 in these percentiles of that graph that we're seeing.

47:22 So for example,

47:22 if in a given year,

47:24 um,

47:24 especially if investments are very risky,

47:26 if I have very bad returns,

47:27 I might actually move from the ninety-ninth percentile

47:29 in the wealth distribution to the ninety-fifth,

47:31 and that's the year where I'm having

47:32 actually bad returns for my personal portfolio.

47:35 But on the other hand,

47:36 a year where I'm really lucky and if I make a high Risky

47:38 investment if I actually then move up

47:40 from the ninety-fifth to the ninety-ninth percentile

47:43 in that given year where I have the high return,

47:45 it could create a little bit of this mechanical relation between the percentiles

47:49 and the

47:51 the

47:51 the annual average returns,

47:52 but the time series of that person might actually look,

47:54 uh,

47:55 look very different.

47:56 So I was wondering if you know anything about that churning.

47:58 I know you don't have the time series.

48:00 Yeah,

48:01 yeah,

48:01 so,

48:02 uh,

48:02 exactly,

48:03 and

48:04 so again,

48:04 since I cannot

48:06 directly follow the same individuals over time,

48:08 I cannot directly,

48:09 uh,

48:10 with this data,

48:12 I'll measure where,

48:13 where they were along this period

48:15 in the wealth distribution.

48:17 Now,

48:17 there is some churning,

48:18 uh,

48:19 and For example,

48:20 I don't know if you look at

48:22 the top 1%,

48:23 there is some mobility

48:25 for between

48:28 households in the top 1% and the next 4% of the wealth distribution.

48:32 Now,

48:32 we also know that,

48:34 uh,

48:34 so other studies that have looked at the

48:37 wealth mobility,

48:38 especially at the top,

48:39 we also know that

48:40 wealth is quite persistent in the sense that households,

48:43 so they may

48:45 move.

48:46 Agains between these different groups,

48:49 top 1% and the remaining the the next

48:52 2 or 3%,

48:53 but for the majority of households,

48:55 the,

48:56 the,

48:56 their position in the,

48:57 the wealth distribution

48:58 is quite persistent over time.

49:00 But again,

49:01 this is,

49:01 this is something that is difficult to,

49:03 to uh

49:04 measure the,

49:05 the exact

49:06 uh

49:07 or to have an exact measure

49:09 of mobility within this data.

49:12 Um,

49:13 Uh thanks Innes.

49:14 Uh,

49:14 just one second,

49:16 everyone,

49:16 please remember to lower your hands after your question.

49:19 Uh,

49:20 Innes,

49:20 you have 25 minutes,

49:21 so maybe you can aim to have one more pause,

49:24 um,

49:25 and then

49:26 we can,

49:26 we can conclude at,

49:27 uh,

49:28 11:45.

49:29 Thanks.

49:30 OK,

49:31 thank you,

49:32 um.

49:33 OK,

49:33 so let me just quickly

49:35 take stock of what I've shown before,

49:36 before,

49:37 before I move into the model.

49:39 So

49:39 the first,

49:40 the main point of the data so far is that

49:43 there is substantial heterogeneity in rates of return to wealth,

49:46 and the,

49:47 the fact that the average rate of return on wealth.

49:50 In the cross section there is this positive correlation between average

49:53 rates of return and the household's position in the wealth distribution,

49:57 and these differences can be large and they can be understood on the one hand

50:02 because of the fact that households own very different kinds of assets,

50:05 and households,

50:06 and as we move towards the top of the wealth distribution,

50:09 households tend to earn to own assets which earn higher returns.

50:13 And here I'm talking about specifically

50:16 both public equity and in particular private businesses.

50:20 But in addition to this effect,

50:22 there's also some evidence of return differences within asset classes,

50:26 and,

50:26 and

50:28 to understand the overall return differences,

50:30 we have to take into account these two sources of returns,

50:34 of return differences.

50:36 Now,

50:37 as I'm moving to the model now,

50:39 the,

50:39 the main goal is to try to understand

50:42 how important this mechanism of return heterogeneity might be to

50:47 understand the the the high degree of concentration in wealth,

50:50 the high degree of concentration that we observe.

50:53 And I'm going to answer this question through the

50:56 lens of a model of household wealth accumulation.

50:59 And essentially I'm going to

51:01 take the workforce model of earnings inequality

51:04 and I'm going to introduce return heterogeneity to that setting

51:08 to,

51:08 to study this question.

51:10 So the basic building block is going to be a a

51:12 continuous time version of the Beauly Hayagari type of economies,

51:16 and I'm going to describe in more detail in a second.

51:19 And

51:20 uh in addition to this,

51:22 I'm going to uh precisely try to introduce return heterogeneity

51:27 in a way that captures this positive correlation between returns and wealth

51:32 that I find in the data

51:34 and also that captures the,

51:36 the estimated return differences that I documented in the first part.

51:39 And so the way I introduce these return differences in the model is

51:43 going to be motivated by some of the mechanisms proposed in the literature

51:47 and in particular,

51:48 I'm going to consider two sources of return differences,

51:52 and this is going to be on the one

51:54 hand by considering that there are different return types.

51:57 And again,

51:58 I'm going to be more precise in a second what I mean by this,

52:00 but

52:01 you can think of this as a form of

52:03 ex ante return differences.

52:04 Between individuals

52:06 and so differences also that they cannot affect

52:09 and there's going to be also a mechanism of

52:12 generating exposed return differences which is going to be

52:15 the existence of return risk.

52:17 So

52:18 at each point in time some individuals are going to be lucky or luckier than others.

52:23 They're going to receive higher rates of return

52:26 and this potentially allows them to accumulate relatively more wealth.

52:31 But OK,

52:31 let me explain what is the main setting of the model.

52:35 So,

52:35 uh,

52:35 there's going to be a continuum of individuals indexed by I and

52:38 they are going to choose the path of consumption denoted by CI

52:43 that

52:44 uh maximizes their expected lifetime utility.

52:47 And in terms of their preferences,

52:49 I'm going to assume uh very standard preferences in this literature,

52:52 which is

52:53 the,

52:53 the constant relative risk aversion utility.

52:56 And gamma is going to govern the degree of relative risk aversion.

53:00 Now,

53:01 individuals,

53:02 uh,

53:03 they're going to be able

53:04 to,

53:04 to,

53:05 uh to save uh in an asset,

53:08 and the wealth is going in this model is going to be denoted by A.

53:13 And this equation 4 is showing what is the law of motion for individual savings

53:18 and is essentially saying that

53:20 savings of individual I are going to be given

53:24 by the difference between total income and consumption,

53:28 where total income is going to be the sum of labor income and capital income

53:33 which

53:34 potentially reflects some heterogeneity in the rate of

53:37 return on wealth which is potentially individual specific.

53:42 And uh

53:43 also,

53:43 uh,

53:44 I'm going to assume that there

53:44 is some market incompleteness that prevents individuals

53:47 from uh perfectly smoothing consumption over time and this is going to be um

53:53 represented by the fact that individuals face a borrowing

53:55 limit which is represented by a lower bar.

53:59 Now,

54:00 uh,

54:00 in terms of the labor income process,

54:02 I'm going to assume a very,

54:03 uh,

54:03 standard process in the literature,

54:05 and,

54:06 uh,

54:07 this,

54:07 the labor income,

54:08 and the labor income process is going to

54:10 be exogenous from the perspective of individuals,

54:13 and I'm,

54:14 I'm assuming that this process is,

54:16 uh,

54:16 is going to follow a

54:19 Stationary diffusion process

54:20 and I'm going to be more specific about these functional forms,

54:23 but

54:24 here this is just saying that this function

54:27 my is going to determine the mean growth rate of earnings

54:31 and this function sigma Y is going to determine the

54:34 standard deviation of the individual growth rate of earnings.

54:38 Now,

54:39 in terms of the return process that I'm going to assume.

54:43 So I'm also going to assume that returns are stochastic and exogenous,

54:47 and they're also going to follow a

54:49 stationary diffusion process represented by equation 7.

54:53 And here the the key difference is that I'm

54:55 going to allow for some flexibility in this process

54:58 by saying that

55:00 potentially the mean and the standard deviation of

55:02 returns are going to be individual specific.

55:06 And so this is what I mean by allowing for agent types.

55:09 It's in the sense that

55:11 besides the the return heterogeneity that comes

55:14 from the realization of a shock exposed,

55:18 there is also going to be some ex ante heterogeneity

55:21 if individuals have

55:22 a different mean or potentially a different standard deviation

55:27 of their return process.

55:30 Now,

55:31 uh,

55:31 the definition of the equilibrium of the

55:33 stationary equilibrium of this economy is given

55:35 on the one hand by the individual decisions in terms of consumption and savings that

55:40 that solve the individual optimization problem,

55:43 taking as given their processes for labor income and for returns.

55:48 And second is going to be given by a stationary distribution

55:52 over the states of this economy which are wealth,

55:54 labor,

55:55 income,

55:55 and returns,

55:56 and this distribution must be consistent with individual choices on the one hand

56:01 and also with the exogenous processes for labor income and for returns.

56:07 So,

56:07 uh,

56:08 the,

56:08 the calibration of the model is going to be on the first,

56:11 I'm going to calibrate the set of parameters externally and this is,

56:14 um,

56:14 I'm going to follow very standard,

56:16 uh,

56:16 calibration in the literature.

56:18 And here,

56:19 uh,

56:19 is going to be the case for the parameter that

56:21 governs the degree of risk aversion in the utility function,

56:25 the,

56:25 the functional form of labor income,

56:28 which I'm going to assume

56:30 that log

56:31 earnings follow an Ernsteinule process.

56:33 So this is analogous to the

56:35 discrete time AR1 formulation

56:38 where uh earnings are going to be,

56:40 earnings shocks are going to be very persistent

56:43 and in particular the,

56:44 the auto correlation of log earnings is going to be set equal to 0.9

56:49 and the standard deviation of log earnings is going to be set equal to 0.2.

56:53 So again,

56:54 these are uh

56:55 values taken from the literature.

56:57 And finally,

56:58 I just normalize

56:59 um

57:00 the the mean of log earnings such that

57:03 um aggregate earnings sum up to one.

57:06 So the remaining parameters that I need to,

57:09 to um

57:10 calibrate are uh the the individual discount rate,

57:13 which is common across individuals and is denoted by raw,

57:17 the borrowing limit a lower bar,

57:19 and finally,

57:20 the parameters

57:22 that govern individual,

57:23 the individual return process.

57:25 And so in terms of the return process,

57:27 I'm going to assume

57:28 first that individual returns follow an Ernstein-Ullenbeck process.

57:33 And uh the,

57:34 the,

57:34 the parameters that are going to govern this process

57:37 are going to be this theta R which governs the persistence of the process.

57:42 Then I'm also going to calibrate these,

57:45 these parameters that govern the mean and

57:47 the standard deviation of the return process

57:50 of different agent types.

57:52 I'm also going to

57:54 have to,

57:55 to find what is the share of each agent type

57:58 in the economy which is represented by delta J.

58:01 And in the baseline model,

58:03 I'm going to have 3

58:05 different agent uh return types,

58:08 and this is essentially motivated by,

58:10 um,

58:11 well,

58:11 the fact that

58:12 this is,

58:13 uh,

58:14 I found that 3 return types

58:16 uh and return risk is uh,

58:19 a formulation that captures well the amount of heterogeneity that I

58:23 document in the data as I'm going to show next how,

58:25 how this model,

58:27 uh,

58:28 Uh,

58:29 matches the targeted moments.

58:31 But let me just say then,

58:32 what are the targets that I used in order to pin down these parameters.

58:36 So,

58:37 uh,

58:37 in order to pin down the the discount rate,

58:39 I'm going to target an aggregate rate of return of 6.8% a year.

58:44 Uh,

58:44 to pin down the,

58:45 the borrowing constraint parameter in the baseline model,

58:47 I'm going to target the wealth share of the bottom 50.

58:50 And so,

58:51 the,

58:51 the object of interest is going to be

58:53 the,

58:53 the distribution of wealth in the top half of the wealth distribution.

58:57 And finally,

58:58 in order to pin down the different parameters that govern the return process,

59:02 I'm going to target moments of

59:04 how

59:05 returns vary along the wealth distribution in the cross section.

59:12 OK,

59:12 so this,

59:13 this,

59:13 um,

59:14 this slide is just showing how the model does in,

59:17 in fitting

59:18 the,

59:18 the,

59:19 uh,

59:19 the targeted moments and here the fit is quite good,

59:21 in particular in capturing the amount of heterogeneity in returns

59:26 along the wealth distribution

59:28 and in also capturing this positive correlation between

59:31 the rate of return and the household's position in the wealth distribution.

59:35 And now

59:37 the,

59:37 the implied,

59:38 uh,

59:39 the,

59:39 the implied return

59:40 parameters are ones of an economy where the

59:44 majority of households are of the low type,

59:47 and so these are households which have a

59:49 relatively low mean return with low standard deviation.

59:52 Uh,

59:52 and

59:53 then there's going to be,

59:54 uh,

59:55 about 18% of households which are of the mid type,

59:58 and so these households are going to have,

1:00:00 um,

1:00:00 higher rates of or mean rates of return

1:00:03 with more volatility.

1:00:05 And there's going to be a a a minority of households,

1:00:09 about 2%,

1:00:09 which are of the very high type.

1:00:12 Which have much higher mean returns with somewhat lower volatility,

1:00:17 and,

1:00:17 and this is

1:00:19 going to be some of the households that are going to

1:00:21 end up at the very top of the wealth distribution.

1:00:24 Um,

1:00:25 let me,

1:00:25 let me just make a quick comment where I said that in,

1:00:28 in

1:00:29 11 limitation on when uh calibrating the return parameters

1:00:33 is precisely not having the panel dimension and therefore

1:00:36 not having,

1:00:37 um,

1:00:38 not being able to disentangle what

1:00:40 return,

1:00:41 what part of the return differences come from

1:00:43 ex ante return differences potentially in the mean of the process

1:00:47 versus exposed return differences that come simply

1:00:50 from the realization of a return shock.

1:00:54 But it turns out that

1:00:56 this division

1:00:57 into

1:00:58 ex ante versus exposed return differences

1:01:01 uh doesn't matter,

1:01:02 uh,

1:01:03 it's,

1:01:03 it's not important

1:01:05 for the overall distribution of wealth

1:01:08 conditional on matching the targeted moments.

1:01:10 And,

1:01:10 and so,

1:01:11 uh,

1:01:11 this is something that,

1:01:12 uh,

1:01:13 that I,

1:01:14 I look by considering other specifications where I allow for

1:01:18 more or less ex ante heterogeneity by considering.

1:01:22 Or less return types

1:01:24 and

1:01:25 I end up finding that

1:01:27 it's not crucial whether this

1:01:29 so the fact that these parameters are not well pinned down by the targeted moments

1:01:34 is not crucial for the implications of this model for the distribution of wealth.

1:01:41 So,

1:01:41 um,

1:01:43 before I quickly show you the results,

1:01:44 I'm going to stop here to ask if there are any questions.

1:01:50 I'm not seeing any hands right now,

1:01:52 but,

1:01:52 OK,

1:01:53 Tuan.

1:01:55 Yeah,

1:01:55 so,

1:01:55 uh,

1:01:57 in your model,

1:01:57 you,

1:01:57 you assume that

1:01:59 every household has the same,

1:02:01 uh,

1:02:01 list version,

1:02:02 that is,

1:02:03 and you assume,

1:02:04 uh,

1:02:04 uh.

1:02:05 Constant dataset,

1:02:06 uh,

1:02:07 constant risk aversion coefficient.

1:02:09 So isn't that mechanically loading a lot of the

1:02:11 variation onto the returns because you shut down.

1:02:14 It will originating risk aversion.

1:02:16 Mhm,

1:02:18 yeah,

1:02:18 so,

1:02:18 uh,

1:02:18 so I'm,

1:02:19 I'm,

1:02:20 that's correct,

1:02:21 but so I,

1:02:21 I would interpret it more broadly in the sense that

1:02:24 So the return difference is that I,

1:02:26 I,

1:02:27 I,

1:02:27 I target and that the model reflects,

1:02:29 so also reflect the fact that individuals own

1:02:32 very different assets with different rates of return and and potentially,

1:02:37 and so at least some of this heterogeneity in,

1:02:39 in asset portfolios may come from heterogeneity in,

1:02:43 in preferences and risk aversion.

1:02:45 And so to the extent that these heterogeneous portfolios also reflect

1:02:50 uh different degrees of risk aversion,

1:02:53 then you could interpret the differences in rates

1:02:55 of return as also reflecting some of these

1:02:57 um

1:02:58 preference heterogeneity.

1:03:03 So,

1:03:04 um,

1:03:05 uh,

1:03:05 Innes,

1:03:06 just one second,

1:03:07 your namesake has another question,

1:03:09 Xavi.

1:03:11 Yes,

1:03:11 sorry about this.

1:03:12 Uh,

1:03:12 I,

1:03:13 sorry,

1:03:13 quick question,

1:03:13 I,

1:03:14 I,

1:03:14 I think I missed it.

1:03:15 What are you assuming,

1:03:16 um,

1:03:17 about the savings,

1:03:19 uh,

1:03:19 the savings rate?

1:03:20 So

1:03:20 does everybody save the same from the earnings or,

1:03:24 or is there a variation there?

1:03:26 So the,

1:03:27 the saving rate,

1:03:28 individual saving rate is going to be an endogenous object and it's going to be,

1:03:32 um,

1:03:32 it's going to depend on,

1:03:33 in particular,

1:03:34 it's going to depend on their labor income and the rate of return.

1:03:39 So

1:03:40 depending on households uh realization of their labor income and of their returns,

1:03:44 they're going to

1:03:45 optimally decide how much to save and to consume

1:03:49 and this,

1:03:49 so this is going to be an endogenous object

1:03:52 and the optimal behavior is going to be such that,

1:03:55 uh,

1:03:55 so the,

1:03:56 the saving rate of individuals is not constant along the distribution.

1:04:00 So for example,

1:04:01 when

1:04:02 Uh,

1:04:02 so,

1:04:03 sorry,

1:04:03 just,

1:04:03 just then,

1:04:04 so I mean if you shut down the heterogeneity returns

1:04:08 and you just have this heterogeneity in savings rate because presumably,

1:04:12 you know,

1:04:12 people that,

1:04:12 you know,

1:04:13 make $3 million

1:04:14 are gonna save a lot more than people that make,

1:04:16 you know,

1:04:16 $20,000 a year.

1:04:18 So

1:04:19 I mean,

1:04:19 so if you,

1:04:19 if you just have this,

1:04:21 you know,

1:04:21 heterogeneity and savings rate and,

1:04:23 and shut down heterogeneity in returns,

1:04:26 I mean,

1:04:26 are you getting the same kind of distributions or you actually need

1:04:29 the heterogeneity returns?

1:04:33 Well,

1:04:33 um,

1:04:34 I,

1:04:34 I'm,

1:04:34 I'm perhaps we,

1:04:36 we can

1:04:36 talk more at the end,

1:04:37 but the,

1:04:38 I'm not sure what exactly you mean by different saving rates,

1:04:42 but I would say so

1:04:44 the thing is that the individual saving rates is

1:04:47 going to depend endogenously on the rate of return.

1:04:51 Right?

1:04:52 So,

1:04:54 When I,

1:04:55 if I shut down or introduce rate of return heterogeneity,

1:04:58 this is going to

1:05:00 affect individuals' saving rates.

1:05:02 Now,

1:05:03 if I'm not sure if this,

1:05:04 if this is your question,

1:05:05 and please interrupt me if it's not,

1:05:06 but I'm going to show the results of a model where Individuals,

1:05:12 so I'm going to shut down all return differences,

1:05:14 and individuals are going to still face labor income heterogeneity,

1:05:17 and they are going to still decide optimally how much to save and to consume.

1:05:22 And so there's going to be some heterogeneity in saving rates,

1:05:25 but only due to labor income.

1:05:28 And there I'm going to show that this model generates some wealth concentration

1:05:32 but cannot generate

1:05:34 very high top wealth shares,

1:05:36 and this is in line with the previous findings of the literature of,

1:05:39 of the inability of this mechanism to generate very high wealth concentration.

1:05:45 So I,

1:05:46 I'm not sure if this addressed your point.

1:05:48 Um,

1:05:48 no,

1:05:48 it,

1:05:48 it does,

1:05:49 it does.

1:05:49 So what you,

1:05:49 you said is just,

1:05:50 you know,

1:05:51 what you said is

1:05:52 clearly,

1:05:53 um,

1:05:54 uh,

1:05:54 earnings heterogeneity is gonna generate different,

1:05:57 uh,

1:05:57 savings rates,

1:05:58 but that's not enough,

1:05:59 uh,

1:06:00 if you,

1:06:00 if you,

1:06:01 if you keep the same,

1:06:02 um,

1:06:03 uh,

1:06:03 returns,

1:06:04 he,

1:06:04 I mean,

1:06:04 sorry,

1:06:04 if you keep the same returns to,

1:06:06 to wealth,

1:06:07 that's not enough to just.

1:06:08 Generate the,

1:06:09 the,

1:06:10 you know,

1:06:10 the patterns that you see in the data,

1:06:11 right,

1:06:11 so that you do need,

1:06:13 uh,

1:06:13 you,

1:06:13 you,

1:06:14 you do need wealth heterogeneity,

1:06:15 uh,

1:06:16 sorry,

1:06:16 the returns to heterogen,

1:06:17 the returns to wealth be to be heterogeneous

1:06:20 to explain the returns in the,

1:06:22 the,

1:06:22 the,

1:06:22 the patterns in the data,

1:06:23 right,

1:06:24 exactly.

1:06:25 So,

1:06:26 yeah,

1:06:27 exactly.

1:06:27 Thank you,

1:06:28 and,

1:06:28 and exactly,

1:06:28 I'm going to show this in,

1:06:30 in a couple of slides.

1:06:32 So let me show you first what are the implications

1:06:34 of this model that features labor income and return heterogeneity.

1:06:38 How,

1:06:39 what are,

1:06:39 what is the equilibrium distribution of wealth implied by that model?

1:06:43 And here I'm showing just that by showing what

1:06:46 is the Lorentz curve implied by the baseline model

1:06:50 which is reflected in the yellow line.

1:06:52 And the Lorentz curve,

1:06:54 what it's telling us is what is the share of wealth

1:06:57 on the y axis

1:06:58 that goes to different percentiles of the population.

1:07:03 And so

1:07:04 the closer we get to the 45 degree line,

1:07:07 the more equal is the distribution of wealth.

1:07:09 And as we move

1:07:11 to the southwest of this graph,

1:07:14 then the degree of wealth concentration increases

1:07:17 as the share of wealth that goes to smaller groups at the top increases.

1:07:22 And so here the,

1:07:24 the,

1:07:24 the main point that I want to make is how,

1:07:26 how

1:07:27 this line,

1:07:28 the yellow line

1:07:29 follows very closely the blue dashed line,

1:07:32 saying that

1:07:33 the model implied distribution of wealth

1:07:36 is very close to the one that you observe

1:07:38 in the data and in particular this model can generate

1:07:42 high top wealth shares

1:07:43 and perhaps this high will become clearer when I show this

1:07:47 other counterfactual exercise where I shut down these return differences.

1:07:51 But here,

1:07:52 the main point is the ability of this model to generate

1:07:55 wealth shares which are

1:07:56 very close to the ones that we observe in the

1:07:58 data and in particular the ability of this model to generate

1:08:02 high top wealth shares,

1:08:03 um,

1:08:04 which is also reflected here in,

1:08:06 in this table as I compare the,

1:08:08 the wealth shares

1:08:09 implied by the model and the ones that we observe in the data.

1:08:13 Now,

1:08:14 uh,

1:08:14 going back to some of one point,

1:08:16 uh,

1:08:17 that was previously discussed is,

1:08:19 uh,

1:08:19 to try to understand what is the importance

1:08:21 of this mechanism in generating wealth concentration.

1:08:25 So in order to answer this question,

1:08:27 what I'm going to do is a counterfactual exercise where

1:08:30 I'm going to

1:08:32 solve the same model,

1:08:33 but now I'm going to completely shut down all sources.

1:08:36 Of return differences,

1:08:38 both

1:08:39 ex ante

1:08:40 return differences that come from the existence of different types

1:08:44 as well as return differences that come from the existence of some return risk.

1:08:49 And so if we were to solve this model,

1:08:52 we would have the

1:08:53 the wealth shares

1:08:54 implied by that model are depicted here in this table in the first column.

1:09:00 And then we compare it,

1:09:01 we can compare it to the wealth shares supplied by the baseline model and the data.

1:09:05 And overall,

1:09:06 if we were to shut down all return differences,

1:09:08 we would have found that the,

1:09:10 the,

1:09:10 the top wealth shares implied by that,

1:09:12 that model,

1:09:13 uh,

1:09:13 fall substantially.

1:09:15 And in particular,

1:09:15 for example,

1:09:16 for the top 10%,

1:09:17 the,

1:09:18 the wealth share that they own would fall to about half

1:09:22 um as compared to the baseline and also compared to the data.

1:09:26 And so overall these results are in line with the,

1:09:29 the previous evidence of the literature that

1:09:33 while uh labor income inequality generates some wealth concentration,

1:09:37 this,

1:09:37 this mechanism cannot generate as much wealth

1:09:40 concentration as we observe in the data.

1:09:43 And,

1:09:43 and here return differences are key uh into,

1:09:46 into being able to

1:09:49 explain and generate

1:09:50 very high top wealth shares.

1:09:52 And another way of seeing this is again through the Lorentz curve,

1:09:56 where now to the previous graph I'm adding this green dotted line which represents

1:10:02 the Lorentz curve implied by this previous model where

1:10:06 households face labor income heterogeneity,

1:10:09 but the rate of return on wealth is identical for all individuals

1:10:13 and again here.

1:10:14 Uh,

1:10:15 when we look at the top half of the distribution,

1:10:17 what we see

1:10:18 again is that the Lorentz curve

1:10:20 implied by that model

1:10:21 is,

1:10:22 um,

1:10:23 well,

1:10:23 it is much closer to the,

1:10:24 the full equality line

1:10:26 and,

1:10:26 and also is,

1:10:27 is unable to match

1:10:28 the,

1:10:29 the,

1:10:30 the

1:10:30 top wealth concentration

1:10:33 that is observed in the data and represented by the blue dashed line.

1:10:37 So

1:10:38 Uh,

1:10:39 I would like to,

1:10:40 to just briefly conclude by saying that the main point that

1:10:45 I would like you to take from this presentation is that,

1:10:48 uh,

1:10:49 and I hope I have convinced you that in order,

1:10:51 if you want to understand

1:10:53 wealth inequality in the US and in particular why wealth is so concentrated,

1:10:58 we need to take into account.

1:11:00 Uh,

1:11:00 return this mechanism of return heterogeneity,

1:11:04 and we need to take into account these differences

1:11:06 first because they are empirically relevant and in the data we observe that

1:11:12 there are return differences and they can be large

1:11:15 and I have documented that in this paper by showing that

1:11:19 the average return on wealth increases with

1:11:21 wealth and these differences can be large.

1:11:24 And now going forward,

1:11:25 uh,

1:11:26 we need to understand better and uh I,

1:11:28 I,

1:11:28 I,

1:11:29 that's part also of my research agenda is to try to understand better

1:11:32 what mechanisms are underlying these return differences,

1:11:36 not only in,

1:11:37 in differential portfolio compositions,

1:11:39 also

1:11:40 in return differences within asset classes.

1:11:44 And,

1:11:45 uh,

1:11:46 but so we also need to take into account this return heterogeneity,

1:11:49 not only because it's uh empirically relevant but

1:11:52 also because it potentially the implications of this mechanism

1:11:56 in generating wealth concentration are large

1:11:59 and

1:12:00 I,

1:12:01 I say this because

1:12:03 I've shown that if we have a simple model that features

1:12:07 labor income heterogeneity and return heterogeneity

1:12:09 in a way that is consistent with the amount of heterogeneity in these

1:12:13 of these two sources that we see in US data in particular,

1:12:17 then this model can track very closely the degree

1:12:19 of wealth concentration that we observe in the US.

1:12:22 And so

1:12:23 we now need to pay

1:12:25 more attention to heterogeneity in household finances

1:12:28 in particular and rates of return on wealth

1:12:30 beyond the heterogenetic labor income that was more studied

1:12:34 if we want to understand better what what drives wealth concentration

1:12:39 and then potentially what if we want to do something about it.

1:12:44 And so I'm going to stop here.

1:12:46 Uh,

1:12:46 I want to,

1:12:47 to thank you,

1:12:48 uh,

1:12:49 for your questions and,

1:12:50 um,

1:12:50 I'm,

1:12:51 I'm also happy to answer a few more

1:12:53 if there are still questions left.

1:12:56 Thank you.

showAllTimestamps

no

transcript

OK, it's 10:31, so let's get started, everyone. Um, everybody knows the rules, so I don't have to go over them. Today, we're very happy to have Inne Chavier from Pompeo Fabre, and she's going to talk about uh the role of heterogeneous returns and wealth inequality in the United States. Um, Ines, the floor is yours, and like I said, there'll be no interruptions for the 1st 10 minutes, and after that, you let me know when's a good time to pause. Great. Thank you, Burke, and thank you for having me here today. I'm very happy to present to you today my job market paper which, as the title suggests, is about understanding what drives wealth inequality and in particular what and how can we understand wealth inequality in the United States. And so let me start by showing you some evidence on how unequal wealth is in the United States, and here I'm showing, I'd like to start with this graph where I'm making essentially two points. I'm saying I'm going to go into detail, but here the main point is to show that wealth in the United States is very concentrated and in particular is more concentrated than labor income. And the way to see this is uh first to see that when we look at the wealth share that goes to different groups, we see that wealth is very much concentrated. And so first I would, I would like to draw your attention to the blue bars in this graph which are reflecting the share of wealth that goes to different groups along the wealth distribution. And so for example, what you would see here is that in the United States, here the the data is from 2019, you would see that the richest 1% in the US population own a total of 37% of the total wealth. And for example, if we were to combine the wealth that the top 10% own, we would see that the richest 10% own as much as 76% of the total wealth. So this is saying that wealth is very much concentrated. And the second thing that that I would like to draw your attention from is the fact that while earnings, which are reflected in the orange bars in this graph, uh, while earnings are also concentrated, then they are less concentrated than wealth. And again, the way to see this is, for example, by noticing that the top 1% earners in the United States earn about 14% of the total income. But still this is uh much less than the, the concentration of wealth that is represented by the blue bars. Or uh more broadly, if we were to compare the size of the top labor income shares with top wealth shares, clearly we, we see that top wealth shares are larger reflecting a larger degree of concentration. The reason why I started with this observation is that this fact is at odds with the predictions of the workhorse model of wealth inequality where the key source of wealth concentration is labor income inequality. And I say this because there have been different models in the literature of of this type suggested and proposed, and these type of models typically generate too little while concentration when compared to the data. And more specifically, these kinds of models have even a sharper prediction for the relationship between the distribution of wealth and earnings, and their prediction is that wealth cannot be more concentrated than earnings in the sense that the right tail of the wealth distribution cannot be fatter than the right tail of the labor income distribution. Now this, uh, these facts and these observations have led economists to think that there's likely other forces playing a role and, uh, generating additional wealth concentration besides the, the labor income heterogeneity. And in this project I'm going to focus on one of those mechanisms, and this mechanism is the idea that besides potentially receiving different labor income, households may also receive different rates of return on their wealth when they save over time, and potentially this mechanism generates some additional wealth concentration. Now, more specifically, what I'm going to do in this project is to start by investigating how relevant how empirically relevant this mechanism is in the, in US data. And so I'm going to uh use household level data from the survey of consumer finances to document some facts about household finances and rates of return on wealth. And by providing this empirical evidence for the United States, I'm going to expand on the evidence provided by two recent papers which provide empirical evidence of return differences into Scandinavian economies. Now, the kind of data that I'm going to use here is survey data, in particular because we do not have the same kind of data, in particular administrative data on wealth holdings as the one that Scandinavian countries have. And so in this project, I'm going to propose a methodology based on survey data to estimate returns on wealth. Now, the second thing that I'm going to do then is to try to understand what are the implications for the wealth distribution of the existence of return heterogeneity. And the way I'm going to do this is through a partial equilibrium model which features two main sources of wealth concentration labor income inequality on the one hand, and in addition, I'm also going to consider this return heterogeneity mechanism. And what I'm going to do more precisely is to build on some of the mechanisms proposed in the literature to generate uh return differences, and I'm going to introduce this mechanism into a model, and I'm going to calibrate returns in my model using the empirical evidence that I document in the first part of the paper. So let me give you a quick preview of the findings. The first one is related to the empirical evidence on returns to wealth. And the first observation is that returns to wealth appear to be heterogeneous, and there appears to be a positive correlation between the average return on wealth, rate of return on wealth and the household's position in the wealth distribution, meaning that on average wealthier households tend to earn higher returns on their wealth. And, and I'm going to come back to this graph later, uh, in, in this presentation. The second finding of this project is that once we take into account this return heterogeneity on top of the labor income inequality which had been more studied before in the literature, once we introduce this mechanism into a model and otherwise. Standard model of wealth accumulation, then we can bring the model much closer to the data and in particular we can generate high top wealth shares, which is something that the previous literature on labor income heterogeneity had struggled with. So, Um, I'd like to, uh, perhaps I, I can take, uh, any question if there, uh, uh, if, if there's any question at this point, and, uh, or otherwise, I'll, I'll start by describing the data set that I used to estimate returns to wealth. I see a couple of hands, so let's do those. Uh, thank you, Ines. Uh, Tristan, you first. Yeah, I'm, I'm, I'm wondering, so, so if it's the case that in the same market, you know, different households can get different returns, you know, that's pretty surprising in terms of how we think about, you know, capital markets being integrated, uh, but another hypothesis is that this is just different asset classes, poorer households, you know, invest in real estate and other households, you know, have access to, to private equity, so so how much of this is just going to be differences in asset class holdings. Mhm. So, uh, relative to this question, I'm, I'm going to show precisely some evidence of that, and indeed I'm going to find that, uh, an important driver of these return differences is precisely the fact that households own very different kinds of assets. Um, the, in fact, the, the, the fact that different assets have different rates of return over time. So this explains, uh. An important share of the overall return differences. Now I'm also going to find, especially within some asset classes, some additional return heterogeneity where and here I'm going to focus on just documenting these differences, but so the literature there has suggested that some of these differences may reflect Different in in uh investment ability, uh, but also some um heterogeneity in in information or, or, uh, for example, individuals age reflecting their experience. So there, there, there, these two sources of return differences both in portfolio composition and uh additional differences within asset classes are going to be important to understand the overall return differences that I document and that I showed in the previous graph. Yeah, thank you, Tuan, you lowered your hand. Is, is that right? No, you should just, uh, I was wondering, and maybe that's the question you're going to, to address in the next point which is What about the participate is the participation rates uh of uh in the, in the surveys and the, and the reporting bias is not going to be a problem for the whole society. Mhm. So, uh, let me, let me now describe the, the, the data set, uh, that I use and then, um, so if there is some specific additional question, then perhaps I can address it, uh, in the next round of questions. OK, so, uh, the, the, the data set that I use is, as I mentioned before, is the survey of consumer finances. And so this is going, is a survey that is going to cover a period of 30 years from 1989 to 2019. And each wave of the survey, which is conducted every 3 years, is going to give me information about a cross section of US households, and I'm going to have detailed information on households' income and households' different assets and liabilities. Now, related to the sampling design of this, uh, of the survey of consumer finances, and one good thing about this survey to study issues or questions related to wealth inequality is the fact that this sample has, uh, a double, a double sampling procedure where on top of a random sample of US households it it has a second. Second sample of households which are likely to be very wealthy, and the benefit of this is because since wealth is extremely concentrated, having just a random sample of US households would likely not accurately characterize this small group of individuals that hold on a disproportionate amount of wealth. So this is one advantage of the survey relative to other surveys which have information on asset holdings. Now at each wave of the survey, I'm going to have, as I said, detailed information on individuals' different sources of income, and this is going to be, for example, information on individuals' wages, individuals' income from dividends, individuals' income from profits that come from the ownership of firms, and so on. And in terms of the information on individuals' wealth holdings, I'm going to have information on the different assets that individuals own. So this is going to include uh deposits, ownership of publicly listed stocks, ownership of real estate, uh, bonds, and so on. And when it comes to asset holdings, I'm going to particularly group the, the, uh, assets that individuals own into these seven wealth components or categories. And in particular, I'm going to consider for one broad asset class which is going, I'm going to call interest earning assets, and this is going to be uh include essentially ownership of deposits and bonds. Then I'm going to have detailed information on the ownership of publicly listed stocks, so public equity, both directly or indirectly through mutual funds. Then in terms of private businesses, individuals are going to report whether they own privately private businesses which are just so non-publicly listed firms. I'm also going to have information on the real estate ownership, so both individuals' primary homes where they live and other secondary real estate. Then there's going to be two residual uh categories of other financial and non-financial assets, and these are going to be a small share of total wealth between 5 and 6%. And finally, I'm going to have, uh, individuals, uh, so individuals are going to report their liabilities as well, and the definition of wealth that I'm going to work with is going to be, uh, wealth is going to be the difference between gross assets and wealth. And so, uh, going back to, to one of the previous questions, the, the, the survey of consumer finances, the reason why it's also popular to study issues of wealth inequality is precisely because it has, it's designed to capture um very detailed groups along the wealth distribution and being representative of, of the households that. do own the disproportionate amount of wealth, and here I'm, I'm, I'm going to focus on the population that does own wealth. So if households don't own any assets, they are not going to be a part of the population in this study. OK, so, uh, I'm, I'm going to stop here also in case there is any question about the, the data before I move on to, to showing the evidence on rates of return. Paulo. Yes, so, uh, I have a question about, uh, what are the incentives of people to tell the truth in these surveys, and the second is whether taxes come into the picture at any point, especially when comparing across countries. Mhm. Yes, so in terms of the first question, so the one thing, so in terms of trying to make sure that houses do not have an incentive to lie, one thing that the survey is prevented to do is precisely to Well, first, the individual's identity is not revealed, and also this, the, the, the survey cannot compare individuals what what they report uh in terms of their income. For example, this cannot be compared with individuals' tax declarations, for example. So this is really the, there's, these are the kinds of things that are done really to try to um uh prevent households from having a clear incentive from lying or for, for example, from underreporting their, their assets or their income. Now, uh, there are studies that have compared how this, uh, household, the survey of consumer finances uh matches other data, uh, in, in particular in terms of income and assets. And generally in terms of, in terms of capital income, the survey of consumer finances lines up quite well broadly with, uh, information on, on, um. Income from, from administrative data as well as aggregate data on income. And in terms of wealth, uh, the information that they declare ownership of the different assets, there is no administrative data on wealth holdings, but this data also lines up very well. There's some gap that increased that started to exist from 2004. Onwards, where the survey of consumer finances, in particular for real estate tends to overstate a little bit the the value of real estate relative to aggregate accounts. But overall, uh, this, the, the, the different uh aggregate data sets tend to line up quite well, suggesting that the, the, the, the values that individuals report are, are in line with other sources. Uh, thank you, Yne Pierre. Uh, Highness, I think it's a bit the same question as Tristan, but just to clarify, is this gonna be important at all, or should there be a causal interpretation of wealth on return to wealth? Is that important? Or do we not care if, you know, if everything is explained just by the fact that richer people have more taste for risk, for example? Mhm. Yeah, so here, um, in this, in this paper, I'm not going to focus on the, the, the what. Drives these return differences and for example, one explanation could be a differential exposure to risk and this is mainly also one important limitation of the survey of consumer finances is the fact that again there is a series of cross sections, but I'm not, I do not have the panel dimension. I do not follow the same individuals over time. And so this is going to create a limitation to try to disentangle different stories, in particular, the one of trying to disentangle. You know, the relative importance of how are are returns higher because individuals are wealthy or are individuals wealthy because they have higher returns. Now there is some literature suggesting that both kinds of mechanisms are likely to be a feature of the data. But this is not something that here in my paper, I'm not going to um explore, uh, for example, how, how much of the return differences come from the fact that individuals own or have different levels of assets in itself. Now let me just also go back to one previous point where I just didn't mention about taxes and it's the fact that so the estimates that I'm going to present here, they are going to be post corporate income taxes but pre-capital income taxes and here again. This is something that I'm working on, on, on, uh, also accounting for, uh, personal income, capital income taxes, but the, and it's mainly because the survey of consumer finances does not have this direct information on households uh payments relative to, to income taxes. Now the idea is that also I I, I do not expect that inclusion of personal capital income taxes to uh change dramatically the, the return differences that I find. Essentially, because, for example, we know that from Scandinavian economies, we know that including this capital income taxes has a very modest effect in lowering return differences along the wealth distribution and these these estimates for Scandinavian countries. not only their their income tax is more progressive, but also these estimates include a wealth tax which is progressive and that does not exist in the US, but this is something that I'm I'm, I'm working on to extend it. Um, thanks, Innes. Um, we have a few more hands up, so let's see if we can get through them quickly. Uh, Tito, you're first. Hi, Inez, uh, my question relates to the role that, uh, entrepreneurship might play in, in this divorce between earnings and wealth inequality. So if I'm an entrepreneur that pay myself, uh, I mean, I'm, I'm a business owner, I pay myself a wage, and then I reinvest all my uh dividends and profits. Uh, I'm mechanically increasing the rate of return on my assets while keeping my wage not that big. So I wonder whether if you constrain your analysis to wage earners, and among the richest wage earners, is it the case that also wealth is so more than equally distributed. Um, So I did not, uh, so I did not do that exercise in, in particular. And so that I did when I, when, uh, it's true that entrepreneurship plays an important role in the overall return differences, as I'm going to show that very wealthy households own, uh, a big chunk of their portfolio in the form of private businesses. And, and so there, the 11 adjustment that I made was that when house So, so several or the majority of the household of private business owners report to actively work in their firms, and so this is an important source of income. And there, the, the concern is to try to account for the labor income that these households receive, but that they report as a form of profits and not as labor income. And so there, there, there are households who report to work on their farms and do declare a wage. And so for these people I'm going to consider, well, this is their wage income and the remaining is profits. For the households that do report to own a farm and to actively manage it but do not report a wage, I am going to Impute a salary to these individuals based on their education, their gender, and their age, and I'm going to deduct those estimates of labor income from the reported profits to try to account for what should be reported as or accounted as labor income but is instead reported as profits. Gotcha. Thanks. Uh, just a very quick clarification question. Your, your data does include retirement accounts? Yes, so my, my data is going to include um sponsored, uh, employee sponsored retirement accounts. Yeah, so for example, the ownership of, of stocks or bonds to these accounts is going to be in this data. And finally Steven. Hi, uh, thanks. I was gonna ask two questions, but the first one Roberto already asked. Um, the second question, um, is just about how, how much some of these returns are based on a specific period in history. I mean, it's been a time that stocks have done very well. Maybe that's not expected to be repeated again, and historically, it didn't, uh, you know, has not necessarily been always like that, so. I mean, wealth is something that accumulates over time, so I was wondering if you have a view on this sort of a steady state finding or this is a, a once-off thing in history. Mhm. Yeah, so I would, thank you. Uh, so I would say that um I, I would see it more as a long uh run uh difference in returns. And the reason why I say this, so absolutely during this period, there have been uh important fluctuations in asset prices and for example, if if I were to look at the, the our compute. Returns focusing up until say the first half of the 2000s, then I would have found that return differences were smaller than if we take into account the overall sample, essentially because the first half of the 2000s, real estate did particularly well. This has benefited in particular households in the bottom and in the middle of the distribution. But then, so once we take into account, uh, so this is if I were to, to focus on that particular period of time, but if one looks at the overall taking an average of asset returns over the whole period of 30 years, then there, there's not a clear trend in asset prices, and it takes, so it's kind of the idea is to abstract away from these larger price fluctuations and focus more on differences in the level of returns in the long run. Um, OK, we still have hands up. Chala, do you still have a question or you lowered your hand? Yeah, just a quick follow up on what Anna asked, but it might be the case lower income households have more defined benefit plans, whereas the higher income have defined contribution, and if you have a defined benefit, you have no idea how well your pension plan is doing. So you don't incorporate that wealth when you're responding to the survey. When might that create a problem? So I would say that so that's that's correct. At the end this survey does not include defined benefit pensions, and so this is something that is not included in the survey and potentially if this is something that is concentrated in the hands of households more at the lower or in the middle of the distribution, this could potentially. Reduce the degree of wealth concentration. Now, there are some estimates where uh if we were to account for uh retirement wealth including defined benefit pension plans, top wealth shares would decrease uh somewhat. So for example, for the, the top 10%, uh, the, the wealth share that goes to the top 10% would have decreased um by about or up to 10% points. Now, still, even uh when we take into account these these um these kinds of assets and so even if we take into account that top wealth inequality might be slightly lower than the measured from this private wealth definition that I have here. Still, the, the degree of inequality is, is still very large and, and, and so I, I think there's still the motivation to try to understand what drives the the the the dynamics and what drives the the degree of concentration in this definition of wealth, but absolutely that, uh, you know, potentially if we take into account. These other more difficult to measure uh definitions of wealth, then maybe the, the exact uh degree of wealth concentration would have changed and potentially is, is slightly lower than, than the one that I'm presenting here. OK. Great. Thank you. OK, final question, then we move on, Chuan. So clarification, so how are stock options accounted for? So the 11th? So stock options here would be, uh, so there, there's a, there's a few relatively few small share of households who declare to own or to have stock options. Here in particular, they would be accounted as in the, in the asset class of non-financial assets, so they will not be accounted as income. OK, so Perhaps, perhaps, I jump into the, to showing you, um, well, the empirical evidence on returns to wealth. And so let me start by clarifying what I mean by that. So the definition that I'm working with of the return on wealth RW is going to be the weighted average of the rate of return on the different asset classes or wealth components where the weight is given by the share of each asset class in total wealth. Now, in turn, the rate of return on each wealth component is going to be given by the sum of two elements, a yield component that reflects the dividend income generated by an asset. So for example, dividend income if one owns stocks, and a capital gain component in the case that reflects fluctuations in the price of the asset over time. Now, to estimate the yield component of returns, I'm going to use information on from the survey of consumer finances, and I'm going to explain in a second more in detail how I do that. And in, in order to impute the capital gains and losses by asset class, I'm going to use aggregate price data. And the main reason is because the, the US Survey of Consumer Finances does not have uh information. On the physical quantity of the asset. And so I cannot disentangle changes in, in the, the value of each asset. I cannot disentangle between changes in the price versus changes in the physical quantity. So I'm going to use this aggregate price data to impute this part of the return. So let me start with the yield component of returns. So what I'm going to estimate is average annualized returns over the three year intervals that separates two waves of the survey. And so here I'm going to give the example of the two waves of the survey that that happened in 1989 and 1992. And overall, what I'm going to do is I have the information on the value of the different assets in 1989. And I want to estimate what is the income generated by the different assets over the three year period that that separates the two waves of the survey. And essentially I'm going to use information on the income that individuals report at two different points in time, um, so reflected here in this graph between 1988 and 1999 and 1991 and 1992. So here, uh, uh, I'll just say that also if you were to use information on the income uh only from the year uh that precedes the, the survey, then the, the results will be very, very similar. So, and overall then the aggregate rate of return on, on a certain asset class is going to be the geometric average between these two rates of return that use information on the income generated by the asset at two different points in time. Now if we were to do this for each of the asset classes that I mentioned before, we would have obtained an estimate of the yield return of each asset class that is represented in this table. And here, uh, the main point that I wanted to make is that there are this is the average uh return over this period, 1990 to 2019. And here the main observation is that there is, there are substantial differences in, in the yield return of the different assets and in particular, private businesses earn substantially higher returns than the other asset classes that are, that are, that are included in this survey. Now of course we don't just care about the yield return of each asset, we care about the total return. And so I'm going to also estimate the capital gain component of returns, and this is what I'm showing in this table where as I said, I'm going to use aggregate price data to impute gains. And for public equity and real estate, I'm going to use Schiller's indexes, and for private businesses, I'm going to use information from US financial accounts. And here again, one observation is that there are substantial differences across asset classes in the capital gains or losses over the period, and clearly equity have earned higher capital gains than the remaining assets. Now, as I mentioned before, uh, again, the, the thing that we care about is the aggregate, is the total return, not each of these components. And so if we were to add this to the yield and the capital gain components of returns, we would have obtained the estimates represented in the last column of this table. And here, uh, I'd like to make two observations. The first observation is that again, there, there are substantial differences in the average rate of return across asset classes, and we see that private businesses earn substantially higher returns over this period than the remaining assets considered in this survey. And in, besides private businesses, also public equity earned on average higher returns than, than, for example, real estate or interest earning assets. Now, if we were to uh use the the first equation one to estimate the overall return on wealth, taking into account the weight of the class in total wealth, we would have found that on average, the aggregate wealth portfolio in the in the US earned an average rate of return of 6.8% a year. So the next question that I'm going to ask is whether it's fair to say that households at different points of the wealth distribution earned markedly different returns on wealth, or if it's the case that it's fair to say that the majority or all households earned a rate of return on their wealth which was close to 6.8%. So to answer this question, what I'm going to do is to repeat the previous calculations but at different points of the wealth distribution. And so if we do that, then we would have obtained this, this, we go back to one of the first graphs that I showed which where I'm plotting what is the, what was the average rate of return on wealth, the yearly rate of return for households at different percentiles of the wealth distribution. And here the first observation is that there is a positive correlation between returns and wealth, meaning that wealthier households earned on average higher returns. And these differences can be large in the sense that for example, if we were to move from the 20th percentile of the wealth distribution to the top 1%, the yearly rate of return would have risen from 3.6% to 8.3% a year, so about 4.7% points different. Now, um, going back to 11 point that was made before is one thing that I'm going to ask is whether these return differences reflect essentially a differential portfolio composition and And this is exactly one thing that I'm going to find. I'm going to find that indeed the, the composition of wealth portfolios varies systematically with wealth and in particular, and so this is what I'm showing here in this graph where I'm showing the share of each asset in the, in the gross wealth portfolio, so gross asset portfolio for households at different percentiles of the wealth distribution. And I'm going to observe that as we move towards the top of the wealth distribution, the relative importance of equity, both public equity and private businesses, rises, and in particular at the very top of the distribution, public businesses, or sorry, private businesses are the main assets that that very wealthy households own. And now, of course, if we take into account this heterogeneity in, in portfolio composition with the, the return differences in across asset classes that I, I showed you before, then this helps us, will help us understand at least in part why wealthier households have earned higher returns on their wealth. Now, in addition to this mechanism, I'm going to look at how returns vary or I'm going to estimate rates of return on wealth within asset classes, and again I'm going to do so at different points of the wealth distribution. And here I'm going to, I'm going to find some evidence of additional heterogeneity for some asset classes more than others, but this is, I'm going to still find some evidence that wealthier households earn higher rates of return on some assets, in particular in real estate, and especially when comparing the, the top 3, so the very top of the wealth distribution relative to the rest of the wealth distribution. And it's also going to be true for private businesses where here the relationship between returns and wealth is not going to be monotonic, but I'm going to find that households in the top 10% of the wealth distribution are going to earn on average higher returns than the next 20% in the wealth distribution. So again, some evidence on return differences beyond the composition of asset portfolios. Um, the, the 11 simple exercise that I do is to try to understand uh how important these two mechanisms are, and here, uh, I'm, I'm plotting in this graph precisely that where I do, uh, two counterfactual exercises trying to understand how much um return differences may reflect heterogeneous portfolio composition versus how much return differences may reflect additional return differences within asset classes. And so in this graph, I'm showing the actual rate of return on wealth by by wealth percentile. So this is represented by the red bars. And then I'm also showing in the green as in the green bars, what would be the the rate of return on wealth at different points of the wealth distribution if all households owned the aggregate wealth portfolio. And so here I'm imposing that all households own the same kind of assets and in particular, I'm saying that relative to what they actually own, I would be increasing the importance of equity for households at the bottom and at the middle of the distribution. Whereas for those households at the very top or at the top of the distribution, I would be reducing the relative importance of equity and would be raising the, the relative importance of real estate in particular. And so perhaps not surprisingly, this would lead to a rise in the rate of return on wealth for households in the in the bottom and in the middle of distribution, and it would lower the rate of return of households at the very top. Now, in another exercise that I do is to impose that households receive the same rate of return within asset classes while potentially owning different kinds of assets, and this is reflected in the blue bars. And here this is saying that if we were to impose that all households on the same aggregate return within asset classes, we would, this would increase in particular the return of households at the bottom of the distribution and it would break the pattern of the increasing pattern between returns and wealth. And this is essentially the effect of essentially imposing that households at the bottom who are especially exposed to real estate here I'm I'm, I'm saying that their returns would have been much higher, so they would be equal to the average rate of return. And so this is the main effect that you see here. And but overall, um, so overall what this is saying is that both kinds of sources of return differences are important to understand the overall return differences and so we need to understand better what are the mechanisms underlying both heterogeneous portfolios and portfolio return differences within asset class. So I'm going to stay, to make a, a small uh stop here in order and ask if there are any questions. Yes. Um, Chevy first. Hi, uh, yeah, couple of questions. Um, so, so the first is, um, so I guess, is the timing of, you know, wealth and returns, uh, You, you, I guess, you know, so, uh, proper in the sense that, of course, you know, if I compute report, I mean, if I compute returns based on, based on past wealth, then, you know, there's clearly an endogeneity, right? I mean, people that have had more returns are gonna have more wealth, so I presume that the returns are computed, you know, going forward, uh, you know, given, given a wealth. So I guess, I mean, you know, that, that, that's one issue, but, but then the other issue is. So, uh, uh, you know, I'm just, so, you know, earnings is, is a flow and wealth is a stock, and so just by compounding over time, once you get a more, a more skewed distribution of wealth rather than a, a distribution of, of earnings. Uh, you know, you know, even without going to the, you know, heterogeneity returns, I mean, it's just, you know, one wealth over time be more skewed just because you're, you know, there's the wonders of, you know, uh, compounding interest, right? I mean, you know, um, yeah, sorry. Yeah, so, um, I would say, so relative to the, to the first question, so indeed, So I'm going to observe households at a certain point in time. I'm going to observe where they, they, they land in the wealth distribution. And I'm going to estimate the returns based on the, the wealth that they report and the income that they report associated with each asset. Now, again, since I, I cannot observe the same individual over time, one thing that I'm not going to be able to disentangle or at least it's, it's very challenging is again, how, uh, so again, what part of the returns. Or the high returns come from the fact that individuals are wealthy. So are individuals wealthy because they have higher returns, or do they have higher returns because they are wealthy? So again, uh, this is something that I cannot, um, or it's very challenging to do with this data. The, but the empirical evidence that we have in this literature, mainly from Scandinavian economies, is saying that well, there's, there's a part of it where, uh, higher rates of return. Reflect the fact that or being wealthy uh allows individuals to to earn some uh higher rates of return. And uh there's a part of it where in some individuals are, you know, just, you can think of this as, or one interpretation is some individuals are being better at investing than others and having higher rates of return. And this, uh, this mechanism allowing individuals to uh end up at the top of the wealth distribution. So exactly this is what's going to happen and in the model, this is what's going to happen where some individuals, as so it's the mechanism in the model is going to be the the the relationship is going to be from higher returns to higher wealth inequality in the sense that I'm going to abstract from the possibility that Being wealthier also allows some individuals to earn higher rates of return. So here I'm not going to say that this is not potentially one additional mechanism, but it's just mainly because of the lack of empirical evidence on the strength of this mechanism. Um, Relative to, to your second point of, so I'm not sure if I understood very well the, the question, but, so if, if we have uh a, a model, for example, of labor income inequality. And the, what is the distribution of wealth implied by that model. So, did I understood correctly that you're asking whether isn't it the case that over time wealth must be more concentrated in labor income? Is that the question? Uh, again, my intuition could be totally wrong, but, but, but yeah, I mean, you know, if I start with, uh, some, some distribution of, of earnings, and, you know, some people save a share, share, and there's, you know, there's some returns to wealth, I mean, my sense is, you know, through compounding, uh, through compounding, you know, I mean, again, wealth is a stock, so again, maybe my intuition is totally wrong, but I, I would assume that, that you would end up with a more skewed distribution, um, um. Because, you know, you're compounding, you're, you know, you're compounding, again, you're, you're saving a share of, of, of, of your wealth, I'm sorry, of, of your earnings, which again, I mean, this might vary by by by earnings, so maybe top earners presumably uh save more than, than, than low, low earners, but even, even, you know, putting a share aside, you know, even setting that aside, and I, I, you know, I would imagine that through compounding. Um, you know, over time, yeah, you would get a different distribution, and in fact you would get a skimer distribution again, maybe I'm wrong, but, uh, you know, this is, I mean, uh, yeah, I mean you can just simulate that, and, and again maybe my intuition is totally wrong, um, but, but I would, I would, I would. Yeah, at first pass, I would think that, you know, the, the wealth distribution would be more skewed than the, than the earnings distribution. Yeah, exactly. So what I meant, and let me be more precise, is that the literature has shown that in these types of models where the, the only source of, so everything else being equal and labor income heterogeneity being the only source of income, then the literature has shown that in terms of the implications of this process for the stationary distribution of wealth, this literature has shown that the, the fatness of the distribution tail. Cannot be higher than the fatness of the labor income scale. So it's in that sense that top wealth shares cannot be larger than top income shares. And so top labor income shares. And so this is a result that has been established in previous theoretical models in this literature. Good, thanks, Tristan. Yeah, it's just a clarification question on the private business returns. Uh, can you say anything about whether those are mostly, you know, holdings in a, a private equity fund, or is it mostly, you know, S corporations and, and businesses that the individuals own, like, you know, being a partner in a law firm or a medical practice, I think obviously the, the second one is, is much harder to redistribute, um, than the first. Mhm. Exactly. So I'm, I'm, I'm not going to look at least in this project specifically on the sector or what more detailed what kind of business this is, but the majority of these businesses are, are, uh, businesses, private businesses in which individuals work and, and it's their, their, um, so the, the majority of their wealth, the biggest chunk of their wealth is invested in that business and they work for it. So this is the majority of the cases. OK, Tatiana. Um, yeah, thanks. I had a question about um how if you're adjusting somehow for, for the risk of those uh investments and related to that, I was wondering. Um, if there's a lot of churning of people, um, in that, um, in these percentiles of that graph that we're seeing. So for example, if in a given year, um, especially if investments are very risky, if I have very bad returns, I might actually move from the ninety-ninth percentile in the wealth distribution to the ninety-fifth, and that's the year where I'm having actually bad returns for my personal portfolio. But on the other hand, a year where I'm really lucky and if I make a high Risky investment if I actually then move up from the ninety-fifth to the ninety-ninth percentile in that given year where I have the high return, it could create a little bit of this mechanical relation between the percentiles and the the the annual average returns, but the time series of that person might actually look, uh, look very different. So I was wondering if you know anything about that churning. I know you don't have the time series. Yeah, yeah, so, uh, exactly, and so again, since I cannot directly follow the same individuals over time, I cannot directly, uh, with this data, I'll measure where, where they were along this period in the wealth distribution. Now, there is some churning, uh, and For example, I don't know if you look at the top 1%, there is some mobility for between households in the top 1% and the next 4% of the wealth distribution. Now, we also know that, uh, so other studies that have looked at the wealth mobility, especially at the top, we also know that wealth is quite persistent in the sense that households, so they may move. Agains between these different groups, top 1% and the remaining the the next 2 or 3%, but for the majority of households, the, the, their position in the, the wealth distribution is quite persistent over time. But again, this is, this is something that is difficult to, to uh measure the, the exact uh or to have an exact measure of mobility within this data. Um, Uh thanks Innes. Uh, just one second, everyone, please remember to lower your hands after your question. Uh, Innes, you have 25 minutes, so maybe you can aim to have one more pause, um, and then we can, we can conclude at, uh, 11:45. Thanks. OK, thank you, um. OK, so let me just quickly take stock of what I've shown before, before, before I move into the model. So the first, the main point of the data so far is that there is substantial heterogeneity in rates of return to wealth, and the, the fact that the average rate of return on wealth. In the cross section there is this positive correlation between average rates of return and the household's position in the wealth distribution, and these differences can be large and they can be understood on the one hand because of the fact that households own very different kinds of assets, and households, and as we move towards the top of the wealth distribution, households tend to earn to own assets which earn higher returns. And here I'm talking about specifically both public equity and in particular private businesses. But in addition to this effect, there's also some evidence of return differences within asset classes, and, and to understand the overall return differences, we have to take into account these two sources of returns, of return differences. Now, as I'm moving to the model now, the, the main goal is to try to understand how important this mechanism of return heterogeneity might be to understand the the the high degree of concentration in wealth, the high degree of concentration that we observe. And I'm going to answer this question through the lens of a model of household wealth accumulation. And essentially I'm going to take the workforce model of earnings inequality and I'm going to introduce return heterogeneity to that setting to, to study this question. So the basic building block is going to be a a continuous time version of the Beauly Hayagari type of economies, and I'm going to describe in more detail in a second. And uh in addition to this, I'm going to uh precisely try to introduce return heterogeneity in a way that captures this positive correlation between returns and wealth that I find in the data and also that captures the, the estimated return differences that I documented in the first part. And so the way I introduce these return differences in the model is going to be motivated by some of the mechanisms proposed in the literature and in particular, I'm going to consider two sources of return differences, and this is going to be on the one hand by considering that there are different return types. And again, I'm going to be more precise in a second what I mean by this, but you can think of this as a form of ex ante return differences. Between individuals and so differences also that they cannot affect and there's going to be also a mechanism of generating exposed return differences which is going to be the existence of return risk. So at each point in time some individuals are going to be lucky or luckier than others. They're going to receive higher rates of return and this potentially allows them to accumulate relatively more wealth. But OK, let me explain what is the main setting of the model. So, uh, there's going to be a continuum of individuals indexed by I and they are going to choose the path of consumption denoted by CI that uh maximizes their expected lifetime utility. And in terms of their preferences, I'm going to assume uh very standard preferences in this literature, which is the, the constant relative risk aversion utility. And gamma is going to govern the degree of relative risk aversion. Now, individuals, uh, they're going to be able to, to, uh to save uh in an asset, and the wealth is going in this model is going to be denoted by A. And this equation 4 is showing what is the law of motion for individual savings and is essentially saying that savings of individual I are going to be given by the difference between total income and consumption, where total income is going to be the sum of labor income and capital income which potentially reflects some heterogeneity in the rate of return on wealth which is potentially individual specific. And uh also, uh, I'm going to assume that there is some market incompleteness that prevents individuals from uh perfectly smoothing consumption over time and this is going to be um represented by the fact that individuals face a borrowing limit which is represented by a lower bar. Now, uh, in terms of the labor income process, I'm going to assume a very, uh, standard process in the literature, and, uh, this, the labor income, and the labor income process is going to be exogenous from the perspective of individuals, and I'm, I'm assuming that this process is, uh, is going to follow a Stationary diffusion process and I'm going to be more specific about these functional forms, but here this is just saying that this function my is going to determine the mean growth rate of earnings and this function sigma Y is going to determine the standard deviation of the individual growth rate of earnings. Now, in terms of the return process that I'm going to assume. So I'm also going to assume that returns are stochastic and exogenous, and they're also going to follow a stationary diffusion process represented by equation 7. And here the the key difference is that I'm going to allow for some flexibility in this process by saying that potentially the mean and the standard deviation of returns are going to be individual specific. And so this is what I mean by allowing for agent types. It's in the sense that besides the the return heterogeneity that comes from the realization of a shock exposed, there is also going to be some ex ante heterogeneity if individuals have a different mean or potentially a different standard deviation of their return process. Now, uh, the definition of the equilibrium of the stationary equilibrium of this economy is given on the one hand by the individual decisions in terms of consumption and savings that that solve the individual optimization problem, taking as given their processes for labor income and for returns. And second is going to be given by a stationary distribution over the states of this economy which are wealth, labor, income, and returns, and this distribution must be consistent with individual choices on the one hand and also with the exogenous processes for labor income and for returns. So, uh, the, the calibration of the model is going to be on the first, I'm going to calibrate the set of parameters externally and this is, um, I'm going to follow very standard, uh, calibration in the literature. And here, uh, is going to be the case for the parameter that governs the degree of risk aversion in the utility function, the, the functional form of labor income, which I'm going to assume that log earnings follow an Ernsteinule process. So this is analogous to the discrete time AR1 formulation where uh earnings are going to be, earnings shocks are going to be very persistent and in particular the, the auto correlation of log earnings is going to be set equal to 0.9 and the standard deviation of log earnings is going to be set equal to 0.2. So again, these are uh values taken from the literature. And finally, I just normalize um the the mean of log earnings such that um aggregate earnings sum up to one. So the remaining parameters that I need to, to um calibrate are uh the the individual discount rate, which is common across individuals and is denoted by raw, the borrowing limit a lower bar, and finally, the parameters that govern individual, the individual return process. And so in terms of the return process, I'm going to assume first that individual returns follow an Ernstein-Ullenbeck process. And uh the, the, the parameters that are going to govern this process are going to be this theta R which governs the persistence of the process. Then I'm also going to calibrate these, these parameters that govern the mean and the standard deviation of the return process of different agent types. I'm also going to have to, to find what is the share of each agent type in the economy which is represented by delta J. And in the baseline model, I'm going to have 3 different agent uh return types, and this is essentially motivated by, um, well, the fact that this is, uh, I found that 3 return types uh and return risk is uh, a formulation that captures well the amount of heterogeneity that I document in the data as I'm going to show next how, how this model, uh, Uh, matches the targeted moments. But let me just say then, what are the targets that I used in order to pin down these parameters. So, uh, in order to pin down the the discount rate, I'm going to target an aggregate rate of return of 6.8% a year. Uh, to pin down the, the borrowing constraint parameter in the baseline model, I'm going to target the wealth share of the bottom 50. And so, the, the object of interest is going to be the, the distribution of wealth in the top half of the wealth distribution. And finally, in order to pin down the different parameters that govern the return process, I'm going to target moments of how returns vary along the wealth distribution in the cross section. OK, so this, this, um, this slide is just showing how the model does in, in fitting the, the, uh, the targeted moments and here the fit is quite good, in particular in capturing the amount of heterogeneity in returns along the wealth distribution and in also capturing this positive correlation between the rate of return and the household's position in the wealth distribution. And now the, the implied, uh, the, the implied return parameters are ones of an economy where the majority of households are of the low type, and so these are households which have a relatively low mean return with low standard deviation. Uh, and then there's going to be, uh, about 18% of households which are of the mid type, and so these households are going to have, um, higher rates of or mean rates of return with more volatility. And there's going to be a a a minority of households, about 2%, which are of the very high type. Which have much higher mean returns with somewhat lower volatility, and, and this is going to be some of the households that are going to end up at the very top of the wealth distribution. Um, let me, let me just make a quick comment where I said that in, in 11 limitation on when uh calibrating the return parameters is precisely not having the panel dimension and therefore not having, um, not being able to disentangle what return, what part of the return differences come from ex ante return differences potentially in the mean of the process versus exposed return differences that come simply from the realization of a return shock. But it turns out that this division into ex ante versus exposed return differences uh doesn't matter, uh, it's, it's not important for the overall distribution of wealth conditional on matching the targeted moments. And, and so, uh, this is something that, uh, that I, I look by considering other specifications where I allow for more or less ex ante heterogeneity by considering. Or less return types and I end up finding that it's not crucial whether this so the fact that these parameters are not well pinned down by the targeted moments is not crucial for the implications of this model for the distribution of wealth. So, um, before I quickly show you the results, I'm going to stop here to ask if there are any questions. I'm not seeing any hands right now, but, OK, Tuan. Yeah, so, uh, in your model, you, you assume that every household has the same, uh, list version, that is, and you assume, uh, uh. Constant dataset, uh, constant risk aversion coefficient. So isn't that mechanically loading a lot of the variation onto the returns because you shut down. It will originating risk aversion. Mhm, yeah, so, uh, so I'm, I'm, that's correct, but so I, I would interpret it more broadly in the sense that So the return difference is that I, I, I, I target and that the model reflects, so also reflect the fact that individuals own very different assets with different rates of return and and potentially, and so at least some of this heterogeneity in, in asset portfolios may come from heterogeneity in, in preferences and risk aversion. And so to the extent that these heterogeneous portfolios also reflect uh different degrees of risk aversion, then you could interpret the differences in rates of return as also reflecting some of these um preference heterogeneity. So, um, uh, Innes, just one second, your namesake has another question, Xavi. Yes, sorry about this. Uh, I, sorry, quick question, I, I, I think I missed it. What are you assuming, um, about the savings, uh, the savings rate? So does everybody save the same from the earnings or, or is there a variation there? So the, the saving rate, individual saving rate is going to be an endogenous object and it's going to be, um, it's going to depend on, in particular, it's going to depend on their labor income and the rate of return. So depending on households uh realization of their labor income and of their returns, they're going to optimally decide how much to save and to consume and this, so this is going to be an endogenous object and the optimal behavior is going to be such that, uh, so the, the saving rate of individuals is not constant along the distribution. So for example, when Uh, so, sorry, just, just then, so I mean if you shut down the heterogeneity returns and you just have this heterogeneity in savings rate because presumably, you know, people that, you know, make $3 million are gonna save a lot more than people that make, you know, $20,000 a year. So I mean, so if you, if you just have this, you know, heterogeneity and savings rate and, and shut down heterogeneity in returns, I mean, are you getting the same kind of distributions or you actually need the heterogeneity returns? Well, um, I, I'm, I'm perhaps we, we can talk more at the end, but the, I'm not sure what exactly you mean by different saving rates, but I would say so the thing is that the individual saving rates is going to depend endogenously on the rate of return. Right? So, When I, if I shut down or introduce rate of return heterogeneity, this is going to affect individuals' saving rates. Now, if I'm not sure if this, if this is your question, and please interrupt me if it's not, but I'm going to show the results of a model where Individuals, so I'm going to shut down all return differences, and individuals are going to still face labor income heterogeneity, and they are going to still decide optimally how much to save and to consume. And so there's going to be some heterogeneity in saving rates, but only due to labor income. And there I'm going to show that this model generates some wealth concentration but cannot generate very high top wealth shares, and this is in line with the previous findings of the literature of, of the inability of this mechanism to generate very high wealth concentration. So I, I'm not sure if this addressed your point. Um, no, it, it does, it does. So what you, you said is just, you know, what you said is clearly, um, uh, earnings heterogeneity is gonna generate different, uh, savings rates, but that's not enough, uh, if you, if you, if you keep the same, um, uh, returns, he, I mean, sorry, if you keep the same returns to, to wealth, that's not enough to just. Generate the, the, you know, the patterns that you see in the data, right, so that you do need, uh, you, you, you do need wealth heterogeneity, uh, sorry, the returns to heterogen, the returns to wealth be to be heterogeneous to explain the returns in the, the, the, the patterns in the data, right, exactly. So, yeah, exactly. Thank you, and, and exactly, I'm going to show this in, in a couple of slides. So let me show you first what are the implications of this model that features labor income and return heterogeneity. How, what are, what is the equilibrium distribution of wealth implied by that model? And here I'm showing just that by showing what is the Lorentz curve implied by the baseline model which is reflected in the yellow line. And the Lorentz curve, what it's telling us is what is the share of wealth on the y axis that goes to different percentiles of the population. And so the closer we get to the 45 degree line, the more equal is the distribution of wealth. And as we move to the southwest of this graph, then the degree of wealth concentration increases as the share of wealth that goes to smaller groups at the top increases. And so here the, the, the main point that I want to make is how, how this line, the yellow line follows very closely the blue dashed line, saying that the model implied distribution of wealth is very close to the one that you observe in the data and in particular this model can generate high top wealth shares and perhaps this high will become clearer when I show this other counterfactual exercise where I shut down these return differences. But here, the main point is the ability of this model to generate wealth shares which are very close to the ones that we observe in the data and in particular the ability of this model to generate high top wealth shares, um, which is also reflected here in, in this table as I compare the, the wealth shares implied by the model and the ones that we observe in the data. Now, uh, going back to some of one point, uh, that was previously discussed is, uh, to try to understand what is the importance of this mechanism in generating wealth concentration. So in order to answer this question, what I'm going to do is a counterfactual exercise where I'm going to solve the same model, but now I'm going to completely shut down all sources. Of return differences, both ex ante return differences that come from the existence of different types as well as return differences that come from the existence of some return risk. And so if we were to solve this model, we would have the the wealth shares implied by that model are depicted here in this table in the first column. And then we compare it, we can compare it to the wealth shares supplied by the baseline model and the data. And overall, if we were to shut down all return differences, we would have found that the, the, the top wealth shares implied by that, that model, uh, fall substantially. And in particular, for example, for the top 10%, the, the wealth share that they own would fall to about half um as compared to the baseline and also compared to the data. And so overall these results are in line with the, the previous evidence of the literature that while uh labor income inequality generates some wealth concentration, this, this mechanism cannot generate as much wealth concentration as we observe in the data. And, and here return differences are key uh into, into being able to explain and generate very high top wealth shares. And another way of seeing this is again through the Lorentz curve, where now to the previous graph I'm adding this green dotted line which represents the Lorentz curve implied by this previous model where households face labor income heterogeneity, but the rate of return on wealth is identical for all individuals and again here. Uh, when we look at the top half of the distribution, what we see again is that the Lorentz curve implied by that model is, um, well, it is much closer to the, the full equality line and, and also is, is unable to match the, the, the top wealth concentration that is observed in the data and represented by the blue dashed line. So Uh, I would like to, to just briefly conclude by saying that the main point that I would like you to take from this presentation is that, uh, and I hope I have convinced you that in order, if you want to understand wealth inequality in the US and in particular why wealth is so concentrated, we need to take into account. Uh, return this mechanism of return heterogeneity, and we need to take into account these differences first because they are empirically relevant and in the data we observe that there are return differences and they can be large and I have documented that in this paper by showing that the average return on wealth increases with wealth and these differences can be large. And now going forward, uh, we need to understand better and uh I, I, I, that's part also of my research agenda is to try to understand better what mechanisms are underlying these return differences, not only in, in differential portfolio compositions, also in return differences within asset classes. And, uh, but so we also need to take into account this return heterogeneity, not only because it's uh empirically relevant but also because it potentially the implications of this mechanism in generating wealth concentration are large and I, I say this because I've shown that if we have a simple model that features labor income heterogeneity and return heterogeneity in a way that is consistent with the amount of heterogeneity in these of these two sources that we see in US data in particular, then this model can track very closely the degree of wealth concentration that we observe in the US. And so we now need to pay more attention to heterogeneity in household finances in particular and rates of return on wealth beyond the heterogenetic labor income that was more studied if we want to understand better what what drives wealth concentration and then potentially what if we want to do something about it. And so I'm going to stop here. Uh, I want to, to thank you, uh, for your questions and, um, I'm, I'm also happy to answer a few more if there are still questions left. Thank you.

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