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ECON 20110 Fall 2013 - Lecture 13: Redistribution — Transcript

by Glen Weyl · 10,611 words · 1,558 segments · language en · Watch on YouTube

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0:01okay let's get started so
0:05um today we're going to apply Monopoly
0:08Theory to I think a very important
0:10social problem which is the growing
0:13inequality uh in the United States uh um
0:17as well as many other countries and I'm
0:19going to talk about why one might be
0:21concerned about this um even from sort
0:25of a Libertarian perspective why
0:27redistribution might be valuable because
0:30it provides insurance against risks that
0:33people would have chosen to insure
0:35themselves against if they had the
0:36opportunity to do so but that they don't
0:38have the opportunity to
0:40do um and I'll talk about from that
0:43perspective what
0:45optimal Insurance should try to do
0:48maximizing people's expected
0:50utilities and that uh concave utility as
0:54a function of wealth means that the poor
0:57value a marginal dollar more than the
0:58rich do and therefore that
1:00redistribution is valuable and we'll
1:02talk about logarithmic utility as a good
1:04approximation to this we'll then build a
1:06framework for analyzing optimal
1:09Taxation and we'll analyze two things in
1:12that context first uh the optimal linear
1:16or sort of average tax rate that people
1:18pay so you know in reality tax schedules
1:21are like you know you pay a certain rate
1:23on the first certain amount of income
1:25more on the next certain amount etc
1:28etc um but you can think of the optimal
1:31linear tax as a measure of um sort of
1:35what the average tax rate should be and
1:37we'll calibrate that using a log
1:40logistic distribution of income which is
1:42a reasonably good fit to the US income
1:44distribution then we'll also talk about
1:46the optimal special sear charge for the
1:48rich so I don't know if you guys
1:50remember but a few years ago Obama was
1:52talking about introducing an extra tax
1:54on people earning over a million dollar
1:56and we'll talk about uh what what that
1:58should be and we'll calibrate that using
2:01the fact that at the top end of the
2:02income Spectrum the distribution of
2:04incomes is roughly
2:06Paro um like those fat tail
2:08distributions we talked about and then
2:10we'll talk about evidence on labor
2:12Supply elasticity which is the other key
2:14parameter other than inequality in
2:17determining optimal
2:18redistribution and then finally I'll
2:20talk a little bit about an alternative
2:22theory of optimal income taxation that
2:25um that I've been developing with some
2:28co-authors recently okay so income
2:31inequality uh can be measured in roughly
2:35three broad types of ways one is income
2:38inequality at the very bottom of the
2:39distribution the second is income
2:41inequality throughout the main part of
2:42the distribution and the third is at the
2:44very top so poverty me measures
2:47inequality at the very bottom and this
2:49is typically measured by the fraction of
2:50individuals who are below some line um
2:54so there's a global poverty line of $1
2:57per day but uh that's not really a
3:01reasonable or useful measure in the
3:02United States where people are so much
3:04richer so in the United States there's
3:06also sort of a relative poverty line
3:08which measures this inequality at the
3:10bottom and the interesting thing is
3:12despite the fact that we'll talk about
3:14um how inequality is been growing uh
3:17poverty in the United States has not
3:19been growing in fact it's been declining
3:22so uh inequality at the bottom end of
3:24the spectrum has not been grown on the
3:26other hand inequality in the mid-range
3:29is usually measured by the Genny
3:31coefficient which is a measure of how
3:34far from perfect equality the economy is
3:36and let me just show you what that looks
3:38like so um this curve here is called the
3:43Loren curve this says if we consider the
3:46bottom say 50% of people in the
3:49population what fraction of all of the
3:52income do they earn if there was perfect
3:54equality that would be 50% right then
3:57you can get you know at the bottom 7 %
4:00what fraction do they earn Etc that
4:02draws out this thing called Loren curve
4:04and then the geny coefficient is the
4:07area above the Loren's curve and below
4:09the line of perfect equality divided by
4:12the total area of this
4:15triangle yep has there been any Research
4:17into what is the optimal level of
4:21inequality on any kind of meure uh yeah
4:24there's a ton of stuff about that um
4:26there's a whole literature on whether
4:28inequality or to what extent inequality
4:30might increase or decrease growth one
4:33way of thinking about that is exactly
4:34what we're going to study today which is
4:37how much redistribution should you do
4:40but you know the question when you say
4:42optimal is optimal with respect to what
4:44intervention you know what I mean
4:46because like how would one change
4:48inequality well one way you could do it
4:50is by taxing and redistributing another
4:53way you could do it is by killing off
4:56all the poor
4:57people another way you could do it is by
5:00not killing off all the poor people but
5:01stopping any poor people from having
5:03children so I mean there are many
5:05different interventions and to really
5:07talk about the optimal extent of
5:09inequality you need to say optimal with
5:11respect to like what particular policy
5:13intervention that could change it so
5:15yeah I guess a related question is why
5:17is it that when they that um you're
5:21measuring this so when you do your gain
5:23coition it's with respect to perfect
5:24equality so why is it necessarily that
5:27as close to a some level of inequality
5:29well because it's just trying to measure
5:31how much inequality there
5:33is it's not attempting to say what it
5:37should be it's just measuring the degree
5:39of inequality so it's a it's a purely
5:41positive measure not a normative
5:45measure okay so
5:48um the the second uh the last measure is
5:54top income
5:56shares so this is what part of income
5:59does the do the richest people take so
6:03you might ask what fraction does the top
6:0410% take of all income top 1% and this
6:08measures inequality at the very uh high
6:11end of the spectrum as well so this has
6:14been growing radically in recent years
6:17in the United States and it's mostly at
6:19the very very top so this shows over the
6:22years what fraction of national income
6:25is acing to the top 1% the top 5 to 1%
6:30and the top 10 to 5% and as you'll
6:32notice there's been a little bit of
6:33increase in the top 5 to 1% hardly any
6:36increase in the top 10 to 5% and the top
6:391% has just
6:42skyrocketed but in other countries
6:46that's not uh true so if you look at the
6:49top 1%
6:51share in France it's come down and
6:54stayed down in Japan it's come down and
6:57stayed down Etc
7:02okay um
7:05and if you look at inequality at a a
7:08global
7:09scale the only part of it that's been
7:12increasing is the number of people that
7:14are super
7:16rich whereas overall geny coefficient
7:18has increased a little bit uh but not
7:21very much um especially not in recent
7:25years and um uh the fraction
7:30uh Super Rich that are coming from the
7:32United States is actually not increased
7:34because there come to be a lot more
7:36super rich people in other uh
7:38countries okay so many Libertarians and
7:43conservatives tend to oppose
7:45redistribution and I used to be uh one
7:48of these so I sort of emphathize with
7:50these ideas uh and let me go through
7:53what some of their standard arguments
7:55against redistribution are so one the
7:58most common one is that you know rich
7:59people earn their money so who has the
8:01right to take it away from them another
8:03argument that you hear a lot is social
8:05Darwinism which is that rich people are
8:08better than other people uh that's why
8:11they got rich and if we want the society
8:13to be healthy to work you know Etc we
8:15need to have more uh of them that could
8:18either mean that we want them to have
8:19more children and we think if they have
8:20more money they'll have more children it
8:22could also be that we think that they're
8:24better at using that money in a
8:26productive way poor people will just
8:27piss that money away or whatever the
8:29rich people use it for productive
8:32Investments another argument from Robert
8:36nosek uh is that um if they got their
8:41money in a fair way who has the right to
8:43take it away from them like if we
8:44started with an initially Fair situation
8:47and we enforced Fair rules along the way
8:49and some people got rich that well
8:51that's just the outcome of a bunch of
8:53fair things happening and so it couldn't
8:55be unfair another argument is that
9:00a Protestant argument is that the
9:02wealthy are wealthy because they were
9:04chosen by God and you know man should
9:06not undo what God
9:08chose Ein Rand argues that taxation is a
9:11form of violence and that property is
9:13basically inviable it's another standard
9:16libertarian perspective there are sort
9:19of fascistic arguments for uh against
9:22redistribution that basically
9:24redistribution encourages people to have
9:26conflicts between classes and that it's
9:28important to like Unity within a society
9:31and in order to do that uh we have to um
9:34avoid uh redistribution conservatives
9:38tend to argue that every like element of
9:41society has a role to play Within
9:43society and that redistribution can
9:45upset the ability of those traditional
9:48groups to play their relevant roles now
9:51um I think some of these arguments are
9:53quite interesting and powerful and I'm
9:55going to try to return a little bit to
9:57them later um
10:00and a lot of them haven't really been
10:01modeled that well by
10:03economists uh but I think that there's a
10:06pretty compelling argument even for a
10:09Libertarian for redistribution and in
10:11fact when I was a Libertarian it was
10:13this argument that originally persuaded
10:15me that redistribution might be
10:18desirable and it's very related to a
10:21classic Christian saying by John
10:24Bradford so he saw poor people being led
10:28through the streets uh to like a
10:30workhouse and he said there but for the
10:34grace of God go I and that is sort of
10:38the idea behind uh John
10:41haran uh and rs's argument for
10:44redistribution so you read the piece by
10:45John har this idea I've learned recently
10:48actually shows up even earlier in a
10:51paper by William vicory who won the
10:53Nobel prize in economics um and they
10:57gave sort of a Libertarian or
10:59choice-based approach to why we should
11:02have uh uh
11:05redistribution and can anyone tell me
11:08what what the basic idea of that is yeah
11:09Adam well um pretty much uh because
11:12people are too young in that situation
11:16to like make a decision about like
11:17insurance but because people are usually
11:20risk averse they would choose in that
11:22situation to lower their income in like
11:25the wealthy State and raise it in the
11:27poor State as a form of insurance so the
11:29government should do you do that
11:32redistribution because they obviously
11:34can't yeah so the idea is you know
11:36people almost always seek re uh
11:39insurance against bad things that might
11:41happen to them major risks in their life
11:43like medical insurance auto insurance
11:45Etc and the reason is because money is
11:47worth more to you when you have a lot of
11:49it than when you don't have as much of
11:51it and you know one of the biggest risks
11:54you face in life is what position you're
11:56going to end up in are you going to be a
11:57brilliant person who makes a lot of
11:59money money or you going to be a um poor
12:02person who makes a lot less money right
12:04which parents will you have will you
12:05have good parents or will you have
12:06crappy parents who don't take good care
12:09of you um what country or town are you
12:12born into Etc and people can't buy
12:15insurance against these things because
12:16they're too young or not even born yet
12:19and therefore the government should act
12:20as an insurance agent CH giving people
12:23the insurance that they would have
12:25chosen to get had they been able to
12:27choose to do so um and that's exactly
12:30what redistributive spending does so um
12:34this Advocates the idea that we should
12:36implement the policy that people would
12:38have chosen behind the veil of ignorance
12:40about who they are within
12:43Society um another way of putting it is
12:47Adam Smith so rather than the veil of
12:50ignorance he said imagine you were an
12:51impartial Outsider looking at people
12:54what would you think of as the
12:57distribution that you would you would
12:58choose yeah can so on about the John R
13:01said about this the here whole thing of
13:04the max Min principle which is Rel
13:06that's an extreme version of this and I
13:09think it's not a very plausible version
13:10of this or very consistent with his own
13:13logic because behind the veil of
13:14ignorance why would people suddenly have
13:16this Max Min uh preference rather than
13:19the risk preferences we see them
13:21actually having in the world which are
13:23not completely maxmen yeah that's
13:25basically exactly what I was ask about
13:27why yeah so I I I'm not I don't find
13:29rs's version of this very compelling I
13:32find the vicory and harani versions much
13:34more compelling yeah my um would this uh
13:38leg justification have like in itself
13:40moral hazard problems well but the thing
13:43is we didn't say that that necessarily
13:45means that you should redistribute
13:48everything because there might be
13:50consequences if I redistribute that I'll
13:52work less hard that's the reason why we
13:54don't give perfect Insurance to people
13:56because we want to retain some incentive
13:58that theyy to avoid the bad events right
14:02the idea is we wouldn't just like
14:03perfectly yeah and that's what the rest
14:05of the class is going to be about is the
14:06tradeoff between Insurance versus
14:08incentives
14:10okay um yeah that's up people who are
14:14highly
14:15talented like before like even before
14:17the veil of even with the veil of
14:19ignorance and even um like before
14:22knowing their position in life if
14:23they're like inly talented say that
14:26there is well but maybe their talent you
14:28can step back to a step before they know
14:30what their talent is that's sort of the
14:32idea I mean I don't know if you think
14:34you can step back to such a state and in
14:36fact that's like a big debate uh whether
14:38like there are things which even behind
14:40the veil of ignorance you already know
14:41about yourself but you know because I
14:44mean in no way that's like the classic
14:46argument against fre distribution right
14:48because some people like some I don't
14:51necessarily believe this but some people
14:52believe you know people who are inly
14:54talented the called and so if they're
14:57yeah so I mean if you basically believe
14:58that there are certain things like that
15:00it's just that certain types of people
15:02have more than other types of people
15:04because like say even behind there's no
15:07situation in which they didn't know that
15:10Noble sess that they had right and in
15:12some sense that's like the Protestant
15:15idea as well right it's the idea that
15:16like certain people are sort of chosen
15:18by God to be more talented so if you
15:21believe that then you wouldn't want this
15:23and in fact you know I think a really
15:25interesting research program that hasn't
15:27really been worked out in economics is
15:30like what would optimal taxes be in a
15:32world where there's some properties that
15:34we don't want to redistribute and others
15:36that we do so like for example when when
15:39like there's a ugly person we don't
15:41usually say oh it's so unlucky for them
15:44that they were ugly right whereas when
15:46there's a beautiful person that gets hit
15:48by a car and now is ugly we say it was
15:50so unlucky that such a beautiful person
15:51ended up ugly right so people might
15:54approach these some things is more like
15:56about luck and some things more about
15:58what you Des erve or what you earned
16:00Yeah Austin not strictly do any like
16:03political science research into the
16:05decline of religion Europe trying to
16:06connect that to the rise of the
16:08distribution so I feel like that yes
16:10there definitely has been I don't know
16:11it that well but I could definitely
16:13direct you to somebody who would know it
16:14I have a friend who like knows the
16:15redistributive literature like better
16:17than anybody in political science so um
16:21yeah right um this is like still like
16:24ultimately like a philosophical sort of
16:26judgment right yeah I mean lots of
16:29things that we build our theories up
16:30from our philosophical
16:32judgments pretty much everything is
16:34because in the
16:36end you can only deductively bring
16:39things back to some fundamental
16:41principles that you just have to accept
16:42on faith
16:44so um okay so this perspective would say
16:48that we should try to maximize average
16:50utility and that's called
16:53utilitarianism uh Jeremy benam uh
16:56described it as trying to create the
16:57greatest good for the greatest number of
17:00people um and usually the way that we
17:03model this is that people have some
17:05utility that depend on income plus some
17:07value that they get from everything else
17:11like Leisure their identity enjoyable
17:13work
17:14etc so for utilitarian social welfare is
17:19the sum of all these individual welfares
17:22and people are waited equally because
17:24you don't know uh which individual
17:26you're going to be you're equally likely
17:27to be any of them so from this
17:29perspective inequality is just another
17:31form of inefficiency it's an
17:33inefficiency from the failure to provide
17:35Insurance um because the rich don't
17:37value money as much as the poor do and
17:40the reason is risk aversion and that's
17:42what we're going to go through now yeah
17:44Tanner in that equation what is the uh F
17:47of little i what does that function mean
17:48that's the number of people with that
17:51income I yeah EV should U should U of I
17:55plus v of X be in parentheses
18:00yeah yeah that's right I mean I yeah
18:04exactly uh yeah Adam um so in this
18:08equation like then um redistribution
18:11isn't solely like monetary based like
18:13someone finds work more enjoyable then
18:15they might have like we distribute less
18:17income to them they get utility from
18:20other areas
18:22or yeah so that's actually a really good
18:24question so um this is really assuming
18:27that everyone has the same utility
18:28function over
18:30income and if that's true then this is
18:32going to be the right formulation but
18:34we'll talk a little bit I think at the
18:35end of the class about a model where
18:37people could vary both in terms of how
18:40much they like
18:41money versus other things and how
18:45talented they are right and depending on
18:50whether you think you should
18:51redistribute that or how you should
18:52think you should redistribute that that
18:54could affect so a lot of people think
18:56that there's like a basic principle that
18:58we should redistribute differences in
19:00ability but we shouldn't redistribute
19:02the fact that like one person likes to
19:04work harder than another person does or
19:06like cares more about money than another
19:08person does so yeah Tanner doesn't this
19:11assume that utility is Cardinal not
19:13ordinal well but but I think that people
19:17view it that way because they have to
19:19make like when people buy insurance
19:21they're saying that money is worth more
19:23to them when they're poor than when
19:24they're rich right and if you want to
19:27say like what would be my value for
19:28being various different people in the
19:30world you have to have some Cardinal
19:32isation of your utility for that so like
19:35when you have when you think about
19:36Choice over uncertainty that creates
19:38that has to create a calization of
19:42utility okay so utility is assumed to be
19:45concave in income and the idea behind
19:48this is risk aversion roughly you start
19:51as you get more money running out of
19:53good uses of that money so like when
19:55you're poor money is great because it
19:57allows you to buy like a house that
19:58doesn't fall down and food that you need
20:01and health basic health care as you
20:02start get getting richer what do you do
20:04with all the money I guess you can have
20:05like you know Justin Bieber come and
20:07sing for your daughter whatever but it
20:10maybe that's not as valuable per dollar
20:12as the other things right
20:15um okay now if you don't believe in risk
20:18aversion uh let let me give you a little
20:21example that hopefully will persuade you
20:23uh to believe in risk aversion okay so
20:26imagine that we flip a coin
20:29um and you get $2 if it comes up heads
20:32and if it comes up sorry if it comes up
20:34tails and if it comes up heads you flip
20:36it again if if it comes up tails you get
20:39$4 and if it comes up heads you flip it
20:41again etc etc etc doubling each time
20:46right so uh Austin how much would you be
20:50willing to pay in order for me to offer
20:52you this bet if you flip a coin can you
20:55explain that here okay I flip a coin if
20:58it comes up tails you get $2 if it comes
21:00up heads you get to flip again if it
21:03comes up tails you get $4 if it comes up
21:05heads you flip it again if it comes up
21:08taals you get 16 $8 yeah Etc let's see
21:11here it would be the value would be the
21:14sum
21:16of 2 n * 1 2
21:21N so
21:24$2 is that the sum of hold on 2 to the n
21:281 what's the sum from I = 1 to Infinity
21:33of 2 the I * 1 2 the i 2
21:38I what is 2 the I over 1 * 1 over 2 the
21:44i 2 I over
21:472 yeah what's that one one so it's the
21:51sum of one + 1 + 1 + 1 + 1 + 1 + 1
21:56infinitely so how much would you you
21:59personally be willing to pay in order to
22:01get me to do
22:03this you know I feel like there's some
22:08Inc yeah maybe yeah what would you what
22:13would you be willing to pay for this
22:14I'll put in 100 bucks 100 bucks is
22:17anyone here willing to pay more than 100
22:19bucks raise your
22:21hand um uh is anyone here willing to pay
22:26more than 200 bucks more than than a
22:28th000 bucks more than 10,000 bucks no I
22:33didn't think so okay uh so clearly you
22:35guys are not okay how much would a risk
22:38neutral person be willing to pay for
22:40this uh yes so well like
22:44an expected the
22:47expected exactly is
22:50this what no sorry you going say I was
22:53just thinking this kind of reminds me of
22:54like a physics question where like
22:56theoretically the tales are infinite but
22:58just because of like quantization is
22:59practic it seems like you got a similar
23:02thing no but I mean I could give you
23:03things that like didn't literally sum to
23:05an infinite amount but sub to something
23:07enormous and you still wouldn't be
23:08willing to pay you know a very large
23:11amount for it yeah M so every time it it
23:15lands heads you get to flip again yeah
23:17so why wouldn't anybody pay $10,000 for
23:20this because you keep getting larger
23:21payouts and then you know that it's
23:23going to come up taals like infly many
23:25times right if you but you only get to
23:27do it once oh
23:29okay so yeah yeah re so I mean in this
23:34it's possible you flip it once and get
23:36once you paid $10,000 for it you flip at
23:38ones it lands tails and you get two both
23:41yeah okay so you could
23:43lose
23:489,000 okay so apparently you guys are
23:50not risk
23:51neutral right and it's hard to imagine
23:54any reasonable person paying all that
23:56much for this thing right and and so
23:58therefore it seems reasonable to think
24:01that people are risk averse so imagine
24:03that people had log
24:05utility you could just go through and
24:07compute how much people are willing to
24:09pay for this uh starting from zero they
24:12should be willing to pay the log of all
24:13these things which is rather than
24:16doubling it it's only adding a constant
24:18so it would die off exponentially and
24:21you would be willing to pay very little
24:22for this yeah uh doesn't it depend on
24:25how much income you're currently at
24:28depend
24:29it does yeah so the more income you're
24:31currently at the more you should be
24:32willing to pay for this for
24:35sure um yeah so uh like even a gambler
24:41or like somebody who's considered
24:45um risk loving yeah they wouldn't like
24:49CU they're not really risk loving over
24:51the full range that's the point right
24:53like they might be risk lugging for a
24:55little bit but they wouldn't really take
24:57this big of a risk you know so they're
25:00like Risk loving for certain levels
25:03maybe I don't even think they're really
25:04risk loving I think that they like they
25:06they just are over optimistic about
25:08their chances of winning I mean that's
25:09my basic view yeah Tanner I actually
25:12want a guy who trades through for J
25:14Morgan say that he would want to bet on
25:15Cor if he could like in his job well of
25:19course that's true because he's betting
25:21with the government's
25:22money person like he loves to gamble
25:25that's people do I don't believe it
25:27maybe it's because he's used to
25:28something with a much lower expect no I
25:31I think that he's saying that like with
25:32the company's money he would want to do
25:34that because then in the end like you
25:37know if if it loses a lot of money the
25:39worst thing that happens is he get fired
25:41and if he makes a lot of money he gets
25:4230% of that he was talking about this in
25:44conjunction with his like gambling habit
25:46so like his personal I think he would do
25:48it for both time both but I would
25:49certainly wouldn't do it for like this
25:52much you know no but for some for some
25:54measure he was risk buing yeah maybe
25:57yeah I don't isn't it possible to be
25:59like purely risk averse and be a gambler
26:02you just also derive like utility from
26:04like the adrenaline or whatever maybe
26:06yeah I mean I think that it's mostly
26:08that people like misestimate the chance
26:11that they are going to win or they trick
26:15themselves into the kingdom yeah okay so
26:20um risk
26:21aversion um alone uh therefore gives
26:25some motive for redistribution
26:28but the if we're more specific about the
26:30form of utility we can get a much more
26:32useful uh
26:34measure um and luckily there's some
26:37pretty powerful evidence about this the
26:39same way there was for Zip's law in
26:41partic in particular a lot of uh
26:44evidence points us to The View that
26:45people's utility is roughly logarithmic
26:47which is kind of amazing because this
26:49form for utility was first proposed in
26:51the 17th century and basically nothing
26:53we've done since then has convinced us
26:55that there's any better approximation to
26:57people's utility since then um and this
27:00is super intuitive to think about it
27:02basically says the value of a certain
27:04percentage increase in your income is
27:06constant no matter what income you're at
27:07so like d like someone is just as happy
27:10to move from $50,000 of income to
27:12100,000 as from 100,000 to2 200,000 as
27:15from 200,000 to 400,000 Etc it's
27:18mathematically very convenient and has a
27:20lot of empirical support so my favorite
27:23support for this comes from uh paper by
27:25uh Dan sax and co-authors and they
27:28studied subjective wellbeing measures
27:31these are when we run a survey and we
27:33ask people on a ladder of life from zero
27:36being like the worst life you can
27:38imagine living to 10 being the best life
27:40you can imagine living where would you
27:42put yourself and let's let H be the
27:45number that people report and I be the
27:47income that they earn yeah philli um
27:50don't if you survey someone with
27:52sufficiently high income uh might you
27:55have a problem fitting this to a log
27:57data because if it was log outa they
27:59would want to report above a 10 but they
28:02can't because it's yeah I mean I don't
28:04think that you in a random sample very
28:07often get such people that's true
28:09because like yeah there's not that many
28:13people who are 10 log points higher than
28:17like a average person in the
28:19population it's it has to be even more
28:21than 10 log points here because the
28:23coefficient turns out to be33 so they'd
28:26have to be 30 log points out
28:30so that's a
28:31lot uh let me figure out exactly what
28:34that
28:41is but still isn't that kind of like
28:44somewhat fla
28:46measurement well hold on one second let
28:48me just figure this out e to the 30
28:52times let's say that someone who's at
28:54one is at one right so
28:59yeah it can't even tell me what that is
29:00it's some like ungodly large number
29:03about 10 to the it's on the order of
29:05about 10
29:1015 because e is approximately theare of
29:1310 so it's something like that yeah
29:17that's like that's like trillions of
29:20trillions of dollars right
29:23so um okay 1.07 * 10 the
29:2913 what's 10 the 13th so we take three
29:31off of that to get thousand three off of
29:33that nine off of that gets us to
29:36billions right take another three off
29:39that gets us to trillions so that's like
29:42hund tens or hundreds of trillions of
29:44dollars or something so yeah you're not
29:45going to get someone like that in exle
29:48okay uh so this is what they find fits
29:51incredibly well so this if you run this
29:55regression you get H is equal to35 * the
29:58log of income plus Epsilon so just to
30:00show you how powerful this is here are
30:03200 countries and each one of these
30:05countries they ran the regression within
30:07the country of income and here are the
30:10regression coefficients like given by
30:13these lines
30:14right and here is the cross country
30:16regression so you see these things are
30:18like all pretty much the same and
30:20they're all pretty much parallel to the
30:21cross country relationship so I think
30:24that shows pretty compelling evidence
30:26that um BAS basically logiic income does
30:30a good job of explaining uh yeah right
30:33but um doesn't like sort of measure of
30:37your wellbeing like run the same
30:39problems like a con valuation surve you
30:41would think so wouldn't
30:44you but I think the data speaks louder
30:47than the theory I mean like the fact
30:50that people that this does such a good
30:53job explaining the data I think answers
30:56a lot of the objections that you could
30:58happen too but what if like everybody
31:00has the same sort of bies like but then
31:03why does it line up so perfectly with
31:05the logarithm of their
31:11income I mean it's just like you know
31:13yeah I agree there th This Is Right
31:15without having any right to be right but
31:17still it is seems to be right yeah
31:20Austin what about like relative income
31:22effects exactly that's what you would
31:23think if it was relative income effects
31:25then you would expect the relationship
31:27cross countries to be much flatter than
31:28the Rel relationship within countries
31:31because the rich countries would
31:32everyone would have a higher Baseline
31:34and you wouldn't expect them to be any
31:35happier but that's not what
31:38happens yeah um is there any data on
31:42risk preferences that also support yes
31:45there's like a ton of data there's a
31:47nice paper by Raj cheddy that looks at
31:49like 10 different ways of measuring risk
31:51aversion they all line up really well
31:52with logarithmic
31:55utility okay so all the things together
31:58mean that I think especially given that
32:00it's so convenient we can just go run
32:02with logarithmic utility okay so
32:05designing an optimal tax system involves
32:07a wide range of issues you have to
32:09decide what you're going to tax is it
32:10going to be income consumption Capital
32:13how is the um how do we redistribute the
32:16money that's
32:17collected um what deductions do we give
32:21people and what is the base for the
32:23taxes uh do we give just uniform
32:26deductions or do we give them targeted
32:28to particular groups for doing
32:29particular things do we have inheritance
32:32taxes you know how do we tax different
32:34Generations how many brackets do we have
32:38and where at what income thresholds what
32:40rate do we have over each of these
32:42brackets we have to make decisions about
32:44the administrative process what
32:46government programs to spend the money
32:48on to give subsidies maybe over some
32:51range just for people getting into the
32:53workforce at all so these are really
32:55important issues but today we're only
32:57going to focus on two of them that have
32:59been sort of very important to economics
33:01as well as in the news one is how high
33:05should overall tax rates be and how flat
33:08or Progressive should things be on the
33:10Super Rich should we have like a higher
33:12rate on the Super Rich than on the rest
33:13of the population or not okay
33:16so you know if we if the poor value uh
33:22money more than the rich do why should
33:24we not just redistribute everything
33:26until we have perfect to Quality can
33:29someone uh yeah Julian uh because then
33:32nobody would have any incentive to work
33:34CU they can do not work and then they're
33:36still the same amount of money exactly
33:38because if you tax people more they have
33:40less marginal incentive to work so in
33:42particular Beyond some point more taxes
33:44are counterproductive because you'll
33:46actually raise less total revenue and
33:48this is uh called the equity efficiency
33:50tradeoff or the insurance incentives
33:53trade-off and the basic goal in this
33:55problem is to maximize average utility
33:58given that we can only use let's say a
34:00simple instrument we have like a linear
34:03tax on everyone's income and then we
34:06redistribute that back to people and
34:08then maybe we have the search charge on
34:09the rich and that raising taxes causes
34:12less work because people substitute down
34:15to doing less work and all revenue is
34:17given back lump sum to everyone now to
34:20keep things simple we're going to ignore
34:22income effects because
34:25um a lot of reseearch has shown that
34:28those aren't all that important to
34:29determining this problem we can
34:31incorporate them of course but the
34:33formulas get a uh
34:36Messier uh and it doesn't make much of a
34:38difference right so in that case all the
34:40reduction comes from What's called the
34:41labor Supply
34:42elasticity which is the percent Fallen
34:45work when your wages Fall by a percent
34:48and let's say that people who are
34:50currently earning income I have an
34:53average labor Supply elasticity of
34:55Epsilon bar
34:58okay now people's income after we have
35:01taxes and transfers are going to be
35:04they'll get one minus the tax rate times
35:07their income plus the tax rate times the
35:09average income because we're going to
35:11redistribute that average income that we
35:13tax away back to people lump some okay
35:17so um the post tax wage that people earn
35:22is one minus the tax rate times their
35:24wage
35:25right and so if we raise taxes by uh one
35:31unit how much is that going to cause
35:35people's earnings to Fall by if they
35:37have an elasticity of Epsilon Tanner can
35:40you derive
35:42that Bo yeah
35:44sure so the remember that the labor
35:47Supply elasticity was the
35:50elasticity of um like how much your
35:54income changed when your wage Changed by
35:571%
35:59%
36:25yep the post test which is that so you
36:28want to find the change in that as the
36:30tax changes yes exactly no the change
36:33the change in the total amount of income
36:35you're going to earn we also have to do
36:37that yeah so we'll have to figure out
36:39how much this changes how much the
36:40elasticity Chang yeah and then the
36:41elasticity will do the rest for us okay
37:14[Applause]
37:22so tea only shows up once in there right
37:24yeah so I'm
37:34yeah that's it and then you need to
37:37multiply so to get that turn that into
37:39an elas uh to to okay so then the
37:44elasticity says uh if you take that
37:48number uh and you divide it by the
37:53current uh wage which is W * 1 -
37:59T then you can multiply it by the
38:05elasticity and and then yeah and that
38:09should give you um how
38:13much uh how much the income by what uh
38:18percentage the amount that people work
38:20changes so it's just this
38:25yeah exactly
38:31so when we raise um the income when we
38:36raise
38:37taxes they'll uh the amount that people
38:40work will fall by the labor Supply
38:42elasticity averaged at that income tax
38:45level times 1 minus uh the T divided by
38:491 minus the tax rate okay and this is
38:54the income weighted average elasticity
38:57of Labor
38:59Supply uh and imagine that there is a
39:02density of people over different incomes
39:05of f ofi so like that's the number of
39:07people earning a given income that's
39:08what we were talking about before again
39:11we're going to ignore income effects so
39:14then total welfare remember is going to
39:17be the integral over the incomes of the
39:20logarithm of the income right now each
39:24individual by the envelope theorem the
39:27the only cost to them of taxing them is
39:30the amount of money that they
39:32lose times whatever their marginal
39:34valuation of that money is because any
39:37amount that they go into working uh into
39:41reducing the amount of work right
39:43they're choosing the optimal amount of
39:45work given um given uh the tax rate
39:49right so we can now take the derivative
39:52of this and what do we
39:55get well uh derivative of the logarithm
39:59is one over the inside right times the
40:03number of people at that income and then
40:05what happens to uh what happens to my
40:09income by the envelope theorem I can
40:11hold fixed but the average income is
40:14going to change because people other
40:15people are going to work less when we
40:17tax more right and what's that going to
40:21change by well I'm going to raise this
40:24by one because I'm collecting more taxes
40:29and then I'm going to reduce it by um
40:35the amount of
40:36taxes times however much the income
40:39changes which is the elasticity Time 1
40:42minus the tax rate and then these people
40:45also lose directly by the envelope
40:47theorem their
40:51income and that gives us this formula
40:55here which is 1
40:59minus the tax rate times the
41:02elasticity ID 1us the tax rate times the
41:06average income and the average welfare
41:08weight that's one o this is the amount
41:11of like value that the person gets from
41:13an additional dollar that's one over
41:15their post tax
41:17income minus the average value of the
41:20product of income and the welfare weight
41:24right now I'm going to define a variable
41:28Sigma which is going to be the negative
41:31co-variance of income divided by average
41:34income with welfare weight divided by
41:36average welfare weight now why should
41:38this be a negative number well the
41:41Richer someone is the less they value an
41:43additional dollar and this is sort of a
41:45measure of
41:47inequality why because if everyone had
41:50the same income there would be no
41:51covariance there right the more
41:54covariance there is there the more
41:56inequality there
41:58right the more that people's income are
42:01moving around and therefore the more
42:03their welfare rates are moving around
42:04now obviously if we have higher taxes
42:07that's reducing inequality and leading
42:09to less variation in the welfare weights
42:10and therefore less Co negative
42:12co-variance with income yes you well can
42:15you explain why um you Define welfare
42:16weight as one over the because that's
42:19the marginal utility that someone gets
42:21from an additional unit of uh dollar and
42:24that's therefore the weight the society
42:25should place on them getting an addition
42:27so if everybody has the same log
42:29function then isn't the coherence always
42:31going to
42:33be the same um no because it depends on
42:36the degree of inequality right because
42:38the thing is that um if someone has
42:40higher income then their weight is going
42:42to be lower because they value income
42:45they value money less right and if you
42:47make things more equal by having higher
42:49tax rates then these are going to be
42:50closer to being equal and there will be
42:52less co-variance
42:54there okay so
43:00um optimization
43:03then is going to
43:05be that uh
43:091us T average elasticity over 1 minus t
43:13is equal to this
43:16co-variance and so we can just solve out
43:19that the optimal tax rate is going to be
43:21equal to this measure of inequality
43:24which depends on the tax rate divided by
43:26the average elasticity times this
43:28measure of inequality which depends on
43:30the tax
43:31rate okay so the tax is going to be
43:37increasing in Sigma and decreasing in
43:41epsilon and how does that uh capture the
43:44trade-off between equity and efficiency
43:46can someone explain that yeah joh this
43:49it's increasing that means the equity is
43:53increasing along the perance rate sorry
43:56say that again it's becom more evitable
43:58because the sigma is
44:00increasing well so Sigma is a measure of
44:03inequality right sorry so it's becom
44:04more inequitable uhhuh so but okay so
44:09what this is saying is that the more the
44:11bigger Sigma is the bigger the optimal
44:13tax rate should be and the bigger
44:15Epsilon is the lower the optimal tax
44:18rate should be so how does that reflect
44:20this logic we were discussing before
44:23that Julian was pointing out of the
44:24trade-off between trying to get greater
44:26equal quity and greater uh efficiency so
44:31if Sigma is greater that means the tax
44:34be greater at the same time that because
44:36why why because why should it be greater
44:40because well no I I agree but but why
44:43why intuitively how does that correspond
44:45to the intuitive logic we were talking
44:46about before about the trade-off between
44:48equality and
44:52efficiency anybody else uh yep um bar uh
44:59so uh as the elasticity increases the
45:02tax rate should be lower because um if
45:06the elasticity is higher that means
45:08people are more responsive to a higher
45:10tax rate will work less yes and
45:12therefore there's more efficiency cost
45:15because of the moral hazard issues right
45:17yeah and and what about Sigma why when
45:19that's higher should there be higher T
45:22um because in that case if Sig higher is
45:25more inquality yeah so a higher tax is
45:28necessary
45:29to distribute that because poor value
45:32exactly
45:35exactly
45:37um okay so this is a simple
45:39formalization of the equity efficiency
45:41tradeoff and if Sigma is getting very
45:44very large except near T equals 1 then
45:48we're going to want tax rate of one or
45:51if the elasticity goes to zero we're
45:52going to want a tax rate of one and vice
45:54versa so the more inequality there is
45:57and the less elasticity is the higher
45:59the optimal tax rate is okay so that
46:03average tax rate covers um like the tax
46:08that is going to be faced by most
46:09Americans or most people in a given
46:12country but Obama has now not that
46:15recently caused uh called for a sear
46:18charge on the super rich and when taxing
46:23the super rich the amount of money that
46:25they lose as a result of that tax
46:27doesn't matter that much to see that
46:29notice that um one over a million dollar
46:34is only about 1 12th of one over the
46:37median income in the United States and
46:39so therefore like the marginal value of
46:41an additional uh dollar for the rich
46:44people is hardly anything compared to
46:46for a typical person right and so a
46:49simple way to think about this is that
46:50we should just try to maximize revenues
46:54um on on the wealthy right so imagine
46:58that we had a tax rate for those earning
47:01over a million dollar uh which we called
47:05uh T sub 10 6 and let's let uh I bar sub
47:1010 the 6 be the average income of those
47:12who are earning over a million dollar
47:15right now if we raise this tax rate
47:18that's going to cause uh two effects can
47:20someone describe to me what those two
47:22effects will
47:23be uh yeah um you're going to have a
47:27higher a tax take mechanically cuz we
47:31are raising uh we're taxing more heavily
47:34but they are going to respond by working
47:36less and that's going to have a opposite
47:39effect exactly so there's a mechanical
47:42increase in the revenue that we earn
47:44which is that for every dollar that
47:46these people earn over a million dollars
47:48we'll get one more Dollar in tax revenue
47:51but also there will be for everyone
47:53earning an income Above This their
47:55incomes will fall by this this amount
47:57which will reduce the tax taxes that we
47:59get by this amount yeah how is this so
48:03when you say that increase revenue from
48:05I by IUS 106 does that mean you're
48:07taking every no it's only we don't get
48:10money that's below a million these
48:13people earn right because the tax ratees
48:15only charged above a million do so it's
48:18a marginal tax rate above a million doar
48:20okay oh so you're just saying that we
48:22get T * IUS well we get we're changing T
48:26right so we get for every unit change in
48:28t This Much from each
48:30person yeah
48:34re was what T der that's the percent
48:37change yeah
48:39exactly anybody
48:42else okay so the total effect on revenue
48:47is therefore we get i - 10 6 * 1 minus
48:52this
48:53reduction uh in in taxes is from the
48:58effect we talked about and the optimal
49:00tax is going to equate this to zero on
49:02average for people above a million
49:05dollar and this was the formula derived
49:08by Emanuel Siz in 2001 so if we take
49:11averages we just can put bars over all
49:13this stuff right where again e bar sub
49:1710 6 is the a average income weighted
49:20elasticity of people earning an income
49:22above uh a million dollar and I bar the
49:266 again is the average income of those
49:28who are earning over a
49:30million okay so now let's define Alpha
49:33to be I bar sub 10 6 divided I bar sub
49:3810 6 minus 10 6 so that's the average
49:41income that people earning above a
49:42million are doing divided by on average
49:45how much more than a million dollar are
49:47they
49:47earning okay so by the same logic as
49:51before um what are we going to uh get as
49:55the optimal tax formula Adam you could
49:57you derive that on board yeah
50:13sure so you'd set that equal to zero
50:16yeah exactly and then try to use that
50:19Alpha thing that
50:20I find
50:28o
51:14C
51:32[Applause]
51:38[Applause]
51:48yes so you've got to get all the t's on
51:50one side so you can divide through and
51:52solve for it right yeah so I just divide
51:54by oh you've got another one on that
51:57right so I actually don't think you did
51:59a very good job isolating it there yeah
52:02forgot about that too uh
52:19so how about isolating the left hand
52:22side
52:23thing this over here yeah
52:27and so subtracting one from subtract one
52:29from both sides
52:50yeah okay now before you do anything
52:53else try turning the right hand side
52:54into something that's related to
52:55something I have on the
52:57board
52:59um
53:01so this
53:20equals so that would be one over Alpha
53:23good okay so try putting that in that's
53:25going to make your life easier
53:43um now you need to isolate T sub 10 6
53:59multiply both sides by the denominator
54:01right
54:17yeah okay
54:32+ one
54:36yeah what that uh okay try doing it this
54:40way try just bringing the other t to the
54:43other side of the equation so you'll
54:45have t * 10 6 * EP Epsilon + 1 over
54:50Alpha is equal to 1
54:52Alpha what you say again try bringing
54:55the T term t Alpha to that side of the
54:57equation and factoring out the T the sub
55:0110
55:026 bring this one to the side and then
55:04factor out the T sub 6 on the
55:13left no no don't divide don't divide
55:17okay just just bring this over and then
55:20factor of T so you can then divide so
55:24does setal zer this saying subtract
55:41this okay
55:54plus off
55:56and now you got it
56:14yeah okay nicely done Adam so that's
56:18what Adam got 1 over Alpha + 1 Alpha
56:21plus e sub 10 6 now remember that Alpha
56:26uh what where do we use Alpha
56:28before well it turns out that this thing
56:33up here is equal exactly to the Proto
56:36coefficient of the upper tail of the
56:37income
56:39distribution
56:41um so uh what this says is that the
56:47lower is
56:48Alpha right the higher should be taxes
56:52and the higher is the elasticity the
56:54lower should be taxes right
56:57in
56:58particular if 1 over Alpha is greater
57:02than the our other measure of inequality
57:06then we're going to tend to make taxes
57:09more Progressive that is the rate at the
57:10top should be higher than it is
57:13throughout and it will tend to be more
57:16Progressive if the rich have lower
57:18elasticity than most Americans
57:20do
57:21right so those are the conditions under
57:24which things are progressive okay
57:26so to get a sense for uh Sigma let's
57:31first assume that the distribution of
57:33income is log
57:34logistic um that means that it takes
57:37this form turns out then that beta is
57:39equal to one over the Genny coefficient
57:42which is about 045 in the United States
57:44and the mean income turns out to be
57:47equal to this which uh mean income is
57:50about 46,000 in the US and that gives us
57:54that the alpha coefficient sorry this is
57:56a little bit confusing this is the alpha
57:57for the log logistic distribution not
57:59the alpha for the upper tail of the
58:01income distribution is uh that and so
58:05then you get that Sigma is a function of
58:07T looks approximately like this so um
58:13if uh we
58:16then uh plug that into our previous
58:19equation Sigma over the elasticity plus
58:22uh Sigma we get curves looking like this
58:26that determine what the optimal tax rate
58:28is so if the elasticity is .1 optimal
58:32taxes are about uh SE
58:3765% or so if elasticity is.3 optimal
58:41taxes are about um uh 40 uh 7% and as
58:48elasticity increases optimal taxes
58:51fall okay calcul yes well sorry so you
58:54used um Ed a measure of inequality and
58:57average income to determine like the
58:58spread of income ranges yeah but um how
59:01did you like how did you choose that
59:03this still be like the distri
59:05distribution function to be log logistic
59:07you mean or like why would it be log
59:09logistic well just because that seems to
59:11be good approximation if you look at
59:12more detailed data about the US income
59:14distribution the log logistic
59:16distribution over most of the range
59:17seems to be pretty good it's not good at
59:19the top part of the income distribution
59:21at
59:22all but um this is mostly like our
59:25average tax rate so it's mostly going to
59:27be dependent on the things like the
59:29Genny that determine the average income
59:31not uh income inequality over the main
59:34range not over the very top was like one
59:37of the reasons you chose it because it
59:38just includes the Gen coefficient was
59:40that yeah I mean you can also do that
59:42with log normal but it's a slightly more
59:44complicated transformation but yeah
59:47right sorry on that last slide like uh
59:50what do what does each line
59:54mean so each of these Cur curves
59:56represents Sigma of T divided by the
59:59elasticity plus Sigma of T okay which
1:00:02was what we said was the right hand side
1:00:04of the optimal tax formula so and the
1:00:07left hand side is the tax rate so we
1:00:08just intersect this with the 45° line to
1:00:10get the optimal
1:00:12taxes okay calculating Alpha is even
1:00:17easier so the upper part of the income
1:00:19distribution has a Proto tail which
1:00:21let's say is equal to 1.5 though it's
1:00:24somewhere between 1.5 and 3
1:00:27if you then just go through and
1:00:28calculate what I bar is under a Proto
1:00:32distribution uh you get that it's equal
1:00:34to 10
1:00:366 * Alpha over 1 + Alpha and so that
1:00:40gives you that I bar 10 6 over I 10 6 -
1:00:4310 6 is exactly equal to Alpha so I
1:00:46named it Alpha because it was the upper
1:00:48tail of a prto
1:00:51distribution prto distributions always
1:00:53have the property that if you take the
1:00:55average value of income above some level
1:00:58divided by that average value minus that
1:01:00level you always get a constant which is
1:01:02equal to Alpha okay so if you then plug
1:01:06into the formula with the elasticities
1:01:07of
1:01:080.13.5 and 1 you get optimal taxes of
1:01:1187. 6957 and4 as compared to Optimal
1:01:16taxes for the same elasticities of 6748
1:01:2038 and
1:01:2126 uh under for the main part of the
1:01:25income distribution
1:01:26now of course the elasticity is for
1:01:28these different groups is going to be
1:01:29crucial but this tends to lean us
1:01:31towards having Progressive taxes and the
1:01:33main reason is because inequality is so
1:01:35high at the top end of the income
1:01:36distribution if we hadn't been having
1:01:38this dramatic increase of inequality at
1:01:40the top end then we wouldn't have wanted
1:01:42to have more Progressive taxes so the
1:01:45reason why you tend to have this is
1:01:48because inequality has been growing more
1:01:50at the top end of the distribution than
1:01:52uh throughout the middle range of the
1:01:54jny coefficient
1:01:57okay now there yeah Adam I just a
1:02:00question so is this pretty much like
1:02:02with the look of the elasticity and the
1:02:03fact that this pretty much just like
1:02:05static view attack is like not the
1:02:06effect of like increase productivity
1:02:09over time well okay remember that when
1:02:12we talked about static models we can
1:02:14have short-run static models and long
1:02:16run static models so the issue is not
1:02:17really about whether it's static not
1:02:19it's about how longterm you're thinking
1:02:21about things and that's what I'm about
1:02:23to bring in so almost all the evidence
1:02:25that we have about the effects of taxes
1:02:28is based on short run changes right um
1:02:33and this can either bias things upward
1:02:37or downward so a really short run change
1:02:40might lead people to work less but they
1:02:42might just work more the next year or
1:02:43more importantly they might like
1:02:44manipulate their taxes to make it look
1:02:47like they had less income this year and
1:02:48then that it came in the next year right
1:02:50to take advantage of the lower taxes but
1:02:52on the other hand as you're pointing out
1:02:54at them there might be longer term
1:02:56things that higher taxes do for example
1:02:58it might change the types of careers
1:03:00people do it might change whether people
1:03:02get a good education in order to get a
1:03:05higher paying job it might change
1:03:07whether people go into the labor force
1:03:08at all until they get older it might
1:03:11change uh like the whole culture of a
1:03:13country that people are just like lazy
1:03:15in Europe because and everything thinks
1:03:19that's acceptable because taxes are
1:03:20lower right are higher right okay so
1:03:24these measures has shown that the labor
1:03:27Supply elasticity of the rich is very
1:03:30low but their taxable income elasticity
1:03:33that is the total amount that they're
1:03:35reporting earning e even though they
1:03:37don't work less when taxes rise at least
1:03:39in the short term they do report earning
1:03:42a lot uh less and uh why might that be
1:03:46the case uh is Kim here I don't think he
1:03:48is no um Can somebody else guess why
1:03:52that might be the case uh yeah myy uh
1:03:56like loopholes in the tax system
1:03:58basically yeah they can shift their
1:04:00income over time they can make it look
1:04:02like they earned
1:04:04income later right or they might just uh
1:04:09put more effort when taxes are higher
1:04:10into evading taxes that's another thing
1:04:13right yeah so could it also be that
1:04:16because they value income more in the
1:04:18present they just underreports that then
1:04:20when they're paying taxes on more in the
1:04:22future it's still discounted
1:04:26sorry say that again so if they
1:04:28underreport their income in the short
1:04:31run yeah it could just be because they
1:04:33value it more now so if they have to
1:04:34report it in the future even though
1:04:36they're paying taxes on on that what do
1:04:39you mean by value it more now in other
1:04:41words it's not discounted
1:04:43now yeah I mean but that's why they're
1:04:45substituting they're like making it look
1:04:47like they earned the income later in
1:04:49order to try to pay less taxes right
1:04:52yeah isn't that ask asking why
1:04:56well no but I mean of course the reason
1:04:58why they're doing that is to pay less
1:04:59taxes right um yeah so uh you
1:05:06know so I think a lot of people think
1:05:09the right number here is at highest
1:05:11about. 3 and maybe closer to 0.1 on the
1:05:14other hand on the middle class labor
1:05:15Supply elasticity seems to be a bit
1:05:17higher because more middle class people
1:05:21uh tend to say for example women uh in
1:05:25the labor force might stay at home if
1:05:27the taxes get higher
1:05:29um and that leads to about 40% average
1:05:33income tax rising to about 80% at the
1:05:35top which is really quite Progressive
1:05:38right so one possible interpretation
1:05:41that Emanuel sias and uh Peter diamond
1:05:43and uh Toma come take from this is
1:05:46that we should have a much higher and
1:05:48more progressive tax system but some
1:05:51have also argued that the long run labor
1:05:53Supply elasticity is much higher than
1:05:54this uh as Adam was sort of suggesting
1:05:58okay so let me talk a little bit about
1:06:00some of these long run things and
1:06:02whether they actually mean that we
1:06:03should have uh lower taxes or not okay
1:06:08my view is that basically no ambitious
1:06:11intelligent person is ever going to
1:06:12slack off and just not work hard because
1:06:14of incentives and that's why these labor
1:06:16Supply elasticities are so low but on
1:06:18the other hand the choice of the career
1:06:20that you go into is very affected by
1:06:22incentives so for example in the 1950s
1:06:25most PE there used to be a large number
1:06:27of people going into Academia government
1:06:30and
1:06:31engineering and today almost everybody
1:06:33goes into Finance right from top schools
1:06:35right and the I think an important
1:06:38reason is the relative wage that you
1:06:39earn in finance over a lifetime is about
1:06:41three or four times higher now relative
1:06:44to uh those other professions than it
1:06:46was in the
1:06:471950s and uh so that increased by about
1:06:51three or four times those relative wages
1:06:53but in response the relative proportion
1:06:55of people going into Finance compared to
1:06:57those other things changed by about 10
1:06:59times so that suggest a giant
1:07:01elasticity right um and so under the
1:07:05standard theory that would say giant
1:07:07elasticity we should have low taxes
1:07:09because if we don't have low taxes
1:07:10everyone's going to waste society's
1:07:12money by becoming academics government
1:07:15you know everyone all these people who
1:07:16could be so productive being in finance
1:07:18are instead going to do all these low
1:07:20productivity professions like
1:07:22engineering Academia and government
1:07:24right so the the question is do you
1:07:26really believe that logic uh you know is
1:07:29the world would the world really be
1:07:30better if we had lower taxes so that
1:07:32everyone went into Finance perhaps you
1:07:35know maybe professions get paid
1:07:37something that's not exactly the same as
1:07:39their social value right um and so this
1:07:42is an alternative basis for optimal
1:07:44taxation not redistribution but charging
1:07:47people a tax rate uh that reflects the
1:07:50externalities created by their
1:07:52profession and in fact I think this does
1:07:54a good job matching what you hear Karl
1:07:57Marx writing so Karl Marx doesn't say we
1:07:59should tax the rich because they'll keep
1:08:02working despite the fact that we tax
1:08:05them which is what this model would
1:08:07require and Ein Rand doesn't write in
1:08:09fact she writes the opposite that oh
1:08:11don't tax the rich because they won't
1:08:12work if you tax them right uh instead
1:08:17the Ein Rand writes that the rich are
1:08:18doing wonderful things that they're
1:08:19making the world a better place and that
1:08:21the poor are you know not doing anything
1:08:24good and uh and Marx writes that the
1:08:27rich are parasites and that's why we
1:08:28should tax them right um and so what we
1:08:32did in this paper that I recently wrote
1:08:34called Taxation and the allocation of
1:08:36talent is that we tried to calibrate all
1:08:40of these
1:08:41things based on uh the distribution of
1:08:44incomes that exist in different
1:08:46professions and the views of different
1:08:48groups about how much externalities
1:08:50different professions have so uh here we
1:08:54don't care at all about about
1:08:55redistribution we're just trying to
1:08:57charge different incomes the
1:08:59externalities that they're likely to be
1:09:00creating and if you take a view of
1:09:02someone from the tea party that leads to
1:09:04basically no taxes or even slightly
1:09:06negative taxes whereas for Occupy Wall
1:09:09Street views you can look at what they
1:09:11are this leads to quite high taxes uh
1:09:14for my personal views which are very
1:09:16similar to my co-author Ben Lockwood it
1:09:17leads to pretty modest but positive
1:09:19taxes and for my very skeptical
1:09:21co-author who doesn't believe that
1:09:22there's any externalities it leads to
1:09:24near zero taxes but you can just go
1:09:26online plug in your own views about the
1:09:29productivity of different professions on
1:09:31our applet and it will tell you what you
1:09:33think optimal taxes should be so this is
1:09:34a very different view of of what optimal
1:09:37taxation is yeah philli
1:09:39um what do you want to look closer to
1:09:43the margin of the profession than the
1:09:46average because when you change a tax
1:09:48rates you're mostly going to be
1:09:50eliminating or at least just for small
1:09:52changes you're going to be mostly
1:09:54eliminating or adding margin yeah I mean
1:09:56the the the right way to think about the
1:09:57numbers that you plug in is not the
1:09:59average externality of people but the
1:10:01average externality of the marginal
1:10:02people people who just drop in or drop
1:10:05out should we look at the Marg average
1:10:08exality of marginal home sure yeah
1:10:11that's the right way to think about
1:10:14it good thanks guys

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