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Lecture 3: Key theories — Transcript

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0:05So I think we'll go ahead and start. I'd
0:08like to say good morning, good
0:09afternoon, good evening to you all and
0:12welcome to today's lecture in the course
0:14on key concepts in macro development.
0:17This course is organized as part of the
0:19STEG program. STEG is an acronym for
0:23structural transformation and economic
0:25growth. And the STEG program is a
0:27multi-year research initiative led by
0:29the Center for Economic Policy Research
0:31in London and funded and we're grateful
0:34for this by the United Kingdom's Foreign
0:37Commonwealth and Development Office as
0:39part of the UK aid effort. I'm Doug Gan.
0:43My colleague Joe Kabosi and I are the
0:45academic leads for the STEG program and
0:48along with a whole set of amazing
0:49colleagues at many universities around
0:51the world, we're excited to be offering
0:54this course.
0:56One of the explicit goals of the STEG
0:58program is to increase the number of
1:01researchers working on structural
1:02transformation of low and middle inome
1:05economies and to increase the quantity,
1:08quality and relevance of their research.
1:11That's where you all come in. The world
1:13needs a lot of smart, motivated,
1:16energetic people who can help us
1:18understand the really challenging
1:20questions that we face in relation to
1:22the the sources and patterns of economic
1:25growth and development.
1:27So with this course, we hope to share
1:29with all of you and and anyone else with
1:31an interest what we know and maybe more
1:35important, what we don't know about the
1:37topic. We're grateful that a lot of our
1:40colleagues have come together to
1:41contribute their time and their
1:43knowledge to putting together the course
1:45and we really appreciate their goodwill
1:47and generosity.
1:49I'm particularly delighted that today we
1:51have Berthold Herendorf a professor at
1:53Arizona State University to lecture on
1:56the topic key theories of structural
1:58transformation.
2:00Having started with some facts and
2:02descriptions of the patterns of
2:04structural transformation, Berthold is
2:06going to help us think about the broad
2:08classes of theories that might serve as
2:10frameworks for our thinking. So just a
2:13word or two about ground rules. Those of
2:16you who are in the virtual front row
2:18should please feel free to ask questions
2:20during the course of the lecture.
2:22Berthold has said he's happy to handle
2:25those questions. Others, please enter
2:28your questions in the Q&A section and um
2:32I and others will try to answer as many
2:34of those as possible. Please be aware
2:36that if you use the the hand button and
2:39try to put your hand up, the lecturer
2:41won't be able to see you. The lecture is
2:44being recorded and it'll be available on
2:46the STEG website and on YouTube for
2:48watching later. The presentation slides
2:51are available and I think the link is
2:54already in the chat window. So if you
2:56haven't already downloaded the slides
2:58and would like to have them to follow
3:00along, please um take a look in the chat
3:03window. And on that note and without any
3:05further ado, I'll turn things over to
3:07Burkeold. And thanks again.
3:11Yeah, thank you everybody.
3:13Let me share my
3:17screen. So you should be seeing the
3:20slides now, do you?
3:22Yes.
3:23Okay, that's good.
3:28Let me start with a few organizational
3:30details. I have chosen a teaching
3:31assistant.
3:33His name is Santiago Garcia Palto. He's
3:35a PhD student here at ASU. Was on the
3:38market and you will join Georgetown
3:41Qatar in the summer. So, if you want to
3:42go to the World Cup next year, there's
3:44your guy on the ground who already is
3:47talking about getting tickets for me.
3:49Anyway, more professionally, his email
3:52is Santiago Garcia at ASU.edu.
3:55Any questions you have, please contact
3:57him. There will be a tutorial session
4:00that Santiago holds on Monday, February
4:0422nd, that's the coming Monday, at 400
4:06p.m. UK time. I unfortunately will not
4:09be able to participate because that's
4:11exactly my teaching time for the
4:12undergraduates. But Santiago will be
4:14there. If you want him to answer any of
4:17your questions, just send him an email
4:19by 8:00 p.m. Sunday night UK time and he
4:22will organize those for the session.
4:25Otherwise, he will talk about a problem
4:27set which I've put at the end of the
4:29slides. The purpose of this problem set
4:32is to try and bring everybody up to
4:34speed because I will be the first person
4:37who probably talks about a dynamic
4:40channel equilibrium model. So far it was
4:42about facts and accounting. So the
4:45technical demand of this lecture is
4:47somewhat higher and I'm aware that we
4:50have a very heterogeneous group of
4:51people listening to the lecture. The
4:54purpose of the tutorial session is to
4:56help you catch up with what is in my
4:59lecture and give you some basic tools.
5:02The problem set is basically your way of
5:05practicing and then learning about the
5:08most basic version of the model that I'm
5:10going to discuss. Mine will be slightly
5:13more general, but that basic version has
5:17everything that you need to know if you
5:19want to solve a structural
5:20transformation model. Now Santi got that
5:23same type of lecture from me five years
5:25ago. So he should know how to do it.
5:27Probably he knows it better than I do
5:30and he will go through the derivations
5:32and answer questions in on Monday's in
5:34Monday's tutorial session.
5:39The background paper for today's lecture
5:41is a handbook chapter that I wrote
5:43together with Richard Rogers and Anakage
5:45Valentini. It's called growth and
5:47structural transformation and that's
5:49from the handbook of economic growth in
5:512014.
5:53So this was kind of a stupid little
5:55thing because Akosh and I got confused
5:58about the literature in 2008 and we
6:01wrote lecture notes. Lecture notes which
6:04basically were of the nature. We don't
6:06understand exactly what's going on.
6:07Everybody uses a different type of
6:09framework. There's so many different
6:11little effects. So what are the main
6:14forces behind structural transformation?
6:17And then luckily for everybody, Richard
6:19got asked to write a handbook chapter
6:21about structural transformation. And he
6:23asked me and said, "Do you have any idea
6:24what we should write or are you
6:26interested in participating?" And I
6:28said, "Yeah, I got these lecture notes
6:29here." And then Richard turned them into
6:32a very nice chapter with our help that I
6:36think has become a standard reference on
6:39growth and structural transformation. So
6:41I'm going to present core material from
6:43this handbook chapter. If you want more
6:46detail, please go to the printed
6:48version. In particular, I'm going to
6:51introduce the topic. Then I talk about
6:53some stylized facts, a background model,
6:57then what we perceive as a benchmark
6:59model of structural transformation, and
7:01then I'm going to conclude.
7:06Introduction. It's always good to define
7:08what you're talking about.
7:11Structural transformation is the
7:12reallocation of economic activity across
7:17broad sectors of the economy.
7:20Kusnits 50 60 years ago listed
7:23structural transformation as a key
7:25feature of modern economic growth.
7:30The typical split in sectors that people
7:33consider is agriculture,
7:36manufacturing and services.
7:40Agriculture and manufacturing are both
7:42producing goods. So they're tangible
7:46services produce intangible output. And
7:49then the difference between agriculture
7:51and manufacturing is that you presumably
7:53can eat agricultural output but not
7:55manufacturing output which uh is true
7:59for everything except for processed
8:00food. So that's very progressive. So the
8:03notion is you can't eat processed food
8:05or you shouldn't at least eat it. But
8:06anyway uh so this broad distinction in
8:10different sectors has proven very useful
8:14and it has turned out that structural
8:16transformation the reallocation between
8:18these three sectors has important
8:20aggregate implications
8:23when and if the sectoral composition
8:25matters. So for example,
8:28important implications have been found
8:30for labor market outcomes, productivity,
8:33the skill premium, urbanization etc.
8:38So the standard paper that is written on
8:42this in this theme is of the nature
8:46women don't do so well in agriculture
8:48but do way better in services. What are
8:51the implications of a dramatic
8:54transformation from agriculture into a
8:57service industry for the labor force
9:00participation of women or the wage
9:03premium, the wage gap between male and
9:07female salaries etc. This is a subject
9:10on which I think Rachel will
9:13pick up and and talk a lot about in the
9:15next lecture. So I'm just throwing this
9:18out here. The general way in which these
9:21papers are written is something differs
9:22across these sectors. Hence a change in
9:26the composition has aggregate
9:28implications.
9:33Now I'm going to focus on models with
9:35balanced growth and structural
9:37transformation.
9:39I will first present the stylized facts
9:42of structural transformation
9:44then develop a multis- sector extension
9:46of the one sector growth model that is
9:49consistent with these stylized facts and
9:51that serves as a natural benchmark model
9:54to start study structural
9:55transformation.
9:58Lastly, I asked whether it's possible to
10:00simultaneously deliver balance growth in
10:03structural transformation.
10:05Now that's actually harder than it
10:08sounds
10:09and I uh will report some success but
10:12also some models where this doesn't
10:15work. You might wonder why do we worry
10:18about balance grows at all. Uh the main
10:21reason is it's not only a feature that
10:24seems to come out of the data but it
10:27also implies that you can solve the
10:28models much more easily. It's like cop
10:31Douglas production functions. Balance
10:32grows in cop Douglas production
10:34functions. They're your friend. Whenever
10:35that's in the model, you're in business.
10:38Whenever it's not, well, you can still
10:40do it. But for an old guy like me, you
10:42have to simulate stuff. And I like
10:46balance growth because you can
10:48characterize the equilibrium
10:50analytically.
10:56Do interrupt me if you have questions or
10:58things don't make sense.
11:00Let's turn to the stylized facts of
11:02structure transformation. Before you
11:05talk about the facts, you always have to
11:08clarify how you measure the phenomenon
11:10you're after. So how to measure
11:11structural change or transformation?
11:16The three most common measures of
11:18sectoral economic activity are
11:21employment
11:23value added and final expenditure
11:26produced by a sector.
11:30Perhaps the most common one is
11:32employment shares because it's most
11:33commonly available and they are
11:36calculated either by using workers or
11:39hours worked if you have better data by
11:42a sector depending on what's there.
11:47Value added shares and final consumption
11:51expenditure shares are typically
11:52expressed in current prices. I call them
11:55nominal shares.
11:57The advantage of using current prices is
11:59that everything is the same unit and
12:01naturally shares make sense. If you use
12:05constant prices, everything is still in
12:07the same units. But often it's debatable
12:10what constant prices to use and how good
12:12they are. So if you have current prices,
12:16the most natural thing or perhaps the
12:19first thing to do is to calculate
12:21nominal shares.
12:23Now, if there are three measures, you
12:25wonder whether they all give the same
12:27answer. In a very broad brush sense,
12:30yes. But there are at least two reasons
12:33for differences among these three
12:35different measures.
12:37One is that investment and international
12:40trade
12:42imply that production and consumption
12:45don't necessarily coincide.
12:48and I can consume a lot of stuff that's
12:50produced in Europe like my car, the wine
12:53I drink, etc., etc. And so the
12:56consumption measure might differ from
12:59the production measure.
13:01The second reason why these measures
13:04might differ is that value added is a
13:07distinct concept from final expenditure.
13:10Now, usually I say that assume that
13:12everybody knows and then everybody knots
13:14and I move on. And over the years I
13:16found out nobody has the foggiest idea
13:17what I'm really talking about when I
13:19talk about value added and final
13:20expenditure. So I shouldn't say nobody
13:22but many people don't. So let's do one
13:25slide with some basic background
13:27concepts just to make sure we are all on
13:30the same page. Let's start really basic.
13:33What is an industry?
13:35It's a collection of establishments that
13:37produce similar goods or services. For
13:40example, the agricultural industry.
13:43They all produce edible tangible output.
13:49Now, establishments in these industries
13:52produce gross output
13:55by using the production factors,
13:57capital,
13:59labor, and intermediate goods.
14:05The establishments then sell the output
14:08either to final users for example
14:10households
14:12to other establishments or to
14:14themselves.
14:18What's a sector?
14:20Sectors sectors are aggregates of
14:23industries with similar characteristics.
14:25So the agricultural sector is all
14:28industries forestry, fishing,
14:32uh a livestock production etc. that are
14:37similar and can be summarized as
14:39agriculture.
14:42Now notice so far there's nothing that
14:45relates to value added. I've talked
14:47about final uses and I've talked about
14:49gross output which is final uses plus
14:52intermediate inputs for yourself and for
14:55others
14:56but I haven't talked about value added.
14:58So value added is somewhat of an
14:59artificial concept. If you really look
15:01at the data it doesn't immediately come
15:04out of the data. You have to take the
15:06value of gross output and subtract from
15:08it the value of intermediate inputs.
15:12Having said that, you should be aware
15:14that while it sounds obvious,
15:17it's often challenging in the data to
15:19find
15:21information on both and in particular to
15:24find constant prices for both if you're
15:27interested in real value added.
15:30Other than that, value added is the
15:32value added over the use of the
15:34intermediate inputs and uh you subtract
15:38get it by subtracting gross output. from
15:41gross output intermediate inputs.
15:45Distinct from that is final expenditure.
15:48It's not how much value you add but how
15:51much you actually deliver as a sector in
15:55terms of gross output to final users.
15:57This would be households or exports or
16:00anything that doesn't get further
16:03entered in the production process and
16:05modified.
16:08So final expenditure therefore are
16:10composite of the value added from
16:12different sectors
16:15and the uh composition of the final
16:19expenditure can be inferred from
16:22so-called total requirement matrix and
16:25we did that in a paper with the same
16:27co-authors in a in 2013. So if you're
16:30interested in the details go to that
16:31paper. I'm not going to have the time
16:34today to talk about that in this
16:36lecture.
16:39Instead, what I'm going to do is I'm
16:40going to focus on the production
16:42measures of structural change in
16:45particular employment shares and value
16:48added shares and give you some facts.
16:56Let's start with currently rich
16:58countries in particular Belgium, Spain,
17:02Finland, France, Japan, Korea,
17:04Netherlands, Sweden, the UK, and the
17:06United States. Why these countries?
17:09Because we found data for these
17:11countries reaching back till 1800.
17:15So what you see here is six plots,
17:19two for each of the three big sectors,
17:21agriculture, manufacturing and services.
17:25On the x-axis is always the share in the
17:28top three it's the employment share and
17:32the bottom three it's the value added
17:34share in current prices. So this is
17:36nominal shares.
17:39On the yaxis is the log of GDP per
17:42capita in 1990 international dollars.
17:46Richard talked about this. We want to
17:48use a unit that's the same in all
17:51countries so that we can compare GDP
17:54across countries and we want to take
17:56into account purchasing power par
17:59differences across countries. So
18:01international dollars do that.
18:05In the top three, as I said, it's the
18:08share of employment. And every dot is an
18:11observation from some year, which we
18:14don't care about. Important to us is
18:16that we have observations when these
18:18economies were rel relatively poor and
18:22observations when they were relatively
18:24rich. So each dot is an observation for
18:27a country and they're all put together.
18:30You can see a very clear pattern that is
18:34coming out of almost all documentations
18:38of the structural transformation facts.
18:40Namely, the employment share and
18:43agriculture is very large when you are
18:45poor
18:46and it falls to almost zero when you are
18:49rich.
18:51At the same time, the employment share
18:53of services is small when you are poor
18:57and it increases
18:59to around 80% when you are rich. So,
19:02agriculture is declining, services are
19:05increasing as GDP per capita increases.
19:10Manufacturing is somewhat of a weird
19:12sector because first it is increasing in
19:15employment shares but then there's a
19:18peak in the countries we have here Korea
19:23is included so the peak is fairly high
19:25at 04.5
19:28but afterwards the employment share of
19:31manufacturing falls.
19:35This is often referred to as a hump
19:37shape or an inverted U shape.
19:42If you go one, Was there a question?
19:46If you go one down, you see similar
19:49patterns for the value added shares. The
19:53agricultural shares fall, the
19:56manufacturing share follows a hump
19:57shape, and the services share increases.
20:02Now while they are similar there are
20:04some differences. One prominent one is
20:08that the value added shares of
20:10agriculture for poor countries tend to
20:13be considerably smaller than the
20:15employment shares.
20:17Which means that if you take value added
20:20per employed person the productivity of
20:24agriculture is low in poor countries.
20:27Now, Duck has important work on this,
20:29many other people, which wonders why so
20:33many people are in agriculture in poor
20:35countries, although they're really bad
20:37at producing it in terms of
20:39productivity.
20:42The second common feature is that the
20:44peak in manufacturing is around nine of
20:47lock GDP in 1990 international dollars.
20:52And that is also a GDP at which the
20:57value added share of services starts to
21:00increase. So you can think of this as
21:04not so much increasing and then an
21:06acceleration which happens here right
21:08around when the
21:11um peak of the manufacturing share
21:13happens.
21:15Lastly, it's important to recognize that
21:18even in very poor countries, there are
21:20market services
21:22and they seem to be reasonably
21:24productive at it, at least compared to
21:27agriculture, which I conclude from
21:29dividing this by this.
21:33Now, these are currently rich countries
21:36and a very long time series. If you want
21:38to convincingly document facts, it's
21:40always a good idea to not only look at
21:43the time series of a few rich countries,
21:45but also at the cross-section. And this
21:48is exactly what the next slide does. It
21:51uses the world development indicators
21:53because that has sectoral employment
21:55shares and the United Nations national
21:59accounts cross-sections between 1980 and
22:032000 in the upper case and 1975
22:07and 2005 in the lower case. Not going to
22:10go into the details.
22:13As you go away from currently rich
22:16countries who have even historically
22:18often fairly good data quality, stuff
22:21becomes a little more blurred and you
22:23get more outliers. But I think I can
22:26convince you with these two um panels
22:29here that similar patterns as before
22:32hold also in the cross-sections
22:35that is agriculture falls, manufacturing
22:38follows a hump shape and services
22:41increases.
22:44Now the noise around that is important
22:47if you look at a single country or group
22:50of countries but I would interpret this
22:52not as invalidating the facts but as
22:55being a deviation from the average which
22:58then might be worth exploring.
23:01So you might ask why is it that India
23:03has a large high-tech service sector
23:07which is not that usual for a country of
23:10its GDP per capita.
23:13But don't get confused and view
23:15everything as one data point that has
23:17nothing to do with anything else. I
23:19think it's good to have two things in
23:21mind. One thing is what are the stylized
23:25facts that hold very broadly across time
23:27and countries and what is the particular
23:30situation in the country that I'm
23:32studying and why would this be different
23:36from the broad facts in order to be able
23:39to do this one first has to understand
23:42what the forces behind the broad facts
23:44might be
23:47so summary when GDP per capita increases
23:52The shares of employment and nominal
23:54value added, nominal being incurrent
23:57prices,
23:58decrease in agriculture,
24:01increase in services
24:04and follow a hump shape in
24:05manufacturing.
24:08For low levels of development, meaning
24:12low GDP per capita,
24:15the value added share in agriculture is
24:17considerably lower than the employment
24:20share.
24:21that is agriculture is relatively
24:24unproductive.
24:28The employment share and the nominal
24:30value added share for the services
24:32sector are bounded away from zero even
24:36at very low levels of development.
24:40And for a log GDP per capita around 9,
24:44the increase in the nominal value added
24:47share in services accelerates
24:50and the nominal value added share for
24:52manufacturing peaks.
24:56Now the number nine is a little bit
24:58arbitrary you should be aware of because
25:01it depends on what prices I choose. This
25:03is in 1990 international dollars. If you
25:06move to more recent prices that might be
25:10underlying the current pen world table,
25:13the nine might change. The key thing is
25:16there is a middle income GDP, however
25:19you measure it, at which manufacturing
25:22peaks and services accelerate.
25:28So this is as much as I wanted to say
25:30about the stylized facts of structural
25:32change in the handbook chapter. I looked
25:35at it yesterday. Again, there's much
25:37more lengthy and detailed discussion. If
25:39you're interested, go there. It also
25:42includes measures of final expenditure.
25:45The basic broadbrush conclusions don't
25:48change. They the three key patterns
25:51namely decrease in agriculture, increase
25:53in services, some shape in
25:54manufacturing. And these are the three
25:58features that we would like a model to
26:00replicate.
26:11In order to be able to deliver such a
26:13model, it's useful to do a few
26:16background steps and look first at a two
26:20sector version of the growth model.
26:23Now, why two sectors? Well, the standard
26:26version of the gross model has one
26:28sector. If I talk about the reallocation
26:30across broad sectors, that's a
26:32non-starter.
26:33There's no reallocation in the standard
26:35gross model. That's why we use it often
26:37because it's so convenient. There's no
26:39role for relative prices to do anything
26:42interesting either because every
26:43relative price is one or constant.
26:49A two sector version is the first step
26:51of disagregating it. And this is going
26:55to be useful because it links what the
26:57structural transformation literature
26:58does to what the previous literature has
27:01done that focused on consumption and
27:03investment. I will briefly go through
27:06that and then I will disagregate
27:08consumption and look at structural
27:10change or structural transformation
27:12within consumption
27:14but keeping the structure of the two
27:17sector model the same. So this thing
27:19won't be thrown away. It's useful to go
27:21with me through that two sector model.
27:24It will just be the upper layer of a
27:26further disagregate structure into
27:28agriculture manufacturing and services.
27:31The model goes back to Ozava and I'll
27:33present a version building on Greenwood
27:35Heracowitz Cressel
27:40environment
27:42preferences and endowments. There is an
27:44infinitely life representative household
27:48who has preferences over consumption
27:50sequences
27:52that are described by the following
27:55separable utility function. The sum from
27:58time 0 to infinity
28:00of beta to the t
28:03time log of consumption.
28:06Beta is between 0 and one and is the
28:09discount factor. We need that to keep
28:11this infinite sum finite.
28:16Endowments. There's one unit of time in
28:18each period and there's a positive
28:20initial stock of capital K0 which is
28:24larger than zero. So to otherwise you
28:26won't get this economy off the ground.
28:32technology consumption C and investment
28:36X are produced from capital K and labor
28:40N.
28:42I'm going to follow the convention that
28:44uppercase let us refer to aggregate
28:47variables and lowerase variables to
28:50sectoral variables. So consumption and
28:53investment I'm going to call that
28:55aggregate and then capital is in each
28:57sector and labor in each sector.
29:01Production takes place in two separate
29:03sectors and the production functions are
29:05of the cog douglas form with the same
29:07exponents.
29:09So for example consumption is the
29:11capital in the consumption sector KC to
29:14the power theta
29:17time AC * N C which is technical
29:22progress in the consumption sector time
29:25labor to the power 1 minus DA.
29:30Technical progress here in the way it's
29:31written is labor augmenting. We probably
29:34all know that it doesn't matter for a
29:36cop Douglas production function because
29:38you could bring it up in front. But here
29:40it's written as augmenting labor.
29:44Changes in in a represent exogenous
29:48labor augmenting technical progress in
29:50that sector. And notice that the changes
29:53in A don't have to be the same and they
29:56will in general not be the same.
30:00What is the same here is the exponents
30:02theta on capital in the consumption and
30:07in the invest in the investment sector.
30:11Now at the beginning this usually takes
30:14some getting used to because most people
30:16say how plausible is that is that true
30:18in the data and the answer is no.
30:22But it turns out that
30:24first of all it's extremely convenient
30:26as I will show you in a minute and
30:29second you can still get the major
30:33developments of structural
30:35transformation
30:36if you assume this counterfactual equal
30:39exponents.
30:41So it's not true in the data but it's
30:43not of first order importance for what
30:44we want to do and it's convenient to
30:46assume these. So why is it convenient? I
30:50will uh come to that in a second by
30:53showing you the results for this two
30:54sector model. Let me describe the
30:56environment first.
31:01Capital accumulates as usual. You start
31:03with a capital stock KT, use it for
31:06production in period T. Then delta of it
31:10depreciates. So you're left with one
31:12minus delta KT. You add to that
31:14investment X and you get the capital
31:17stock in the next period. The
31:19depreciation rate is between zero and
31:21one
31:23as is usually the case.
31:27Capital and labor can be used in both
31:30sectors implying that feasibility
31:32requires that the total capital stock is
31:36at least as large as the sum of the two
31:38sectoral capital stocks and total labor
31:41which is normalized to one because
31:42there's a measure one of households
31:45is at least as large as the total labor
31:48in the two sectors NC and NX. X
31:56competitive equilibrium. I want to
31:59emphasize the role of relative prices
32:02and I therefore consider a sequence of
32:04markets competitive equilibrium as
32:06opposed to a planner problem. I could
32:08write down a planner problem where I
32:10only use preferences, technology, and
32:12feasibility. But that by construction
32:15would not contain any prices and there's
32:17important information in what the prices
32:20do. Therefore, I write down a
32:22competitive equilibrium.
32:25The investment good is going to be the
32:27numer that means its price is equal to
32:29one in each period.
32:31And I'm going to denote the price of
32:33consumption relative to the investment
32:35good by P.
32:38The rental prices for capital and labor
32:41are denoted by R and W. I'm following
32:44the notation that everything aggregate
32:48is uppercase letter. So that's why R and
32:50W are uppercase. I'm not sure it's
32:52ideal, but that's what we did in the
32:53handbook chapter. And one rule is if you
32:55did something in the past, don't change
32:57it because you get confused.
32:59Um, so R and W are rental prices for
33:03capital and labor.
33:06I assume that the household accumulates
33:07capital and rents it to the firm. So the
33:09household owns everything capital labor
33:12the firms here which is the most natural
33:14way of writing down the gross model
33:20characterization of equilibrium. Now if
33:23I was teaching at ASU I would go to the
33:26board and do a few derivations and
33:28explain the steps. Since I only have an
33:31hour and 15 minutes, I'm not going to be
33:34able to do that here. So, I'm just going
33:36to state main results in this model and
33:39I'm going to refer you to Santiago's
33:42tutorial session on Monday. So, he's
33:44going to through the steps and hopefully
33:46derive everything if you are interested.
33:49If you have seen these models, this is
33:51fairly standard, but it needs to be said
33:53nonetheless at least once.
33:56First the capital to labor ratios are
33:59equalized across the sectors at each
34:01point in time.
34:04So KCN C equal KXNX
34:07equal the aggregate KN and since labor
34:10is equal to one equal the aggregate
34:12capital stock. That's crucial because it
34:16means that you can do a lot of things in
34:19this economy that you couldn't otherwise
34:21do.
34:23This comes directly from the fact that I
34:25assumed that the exponents in the Cob
34:28Douglas production functions here are
34:31equal. If they're not equal, I would not
34:34get this result.
34:36with equal capital labor ratios. I can
34:40also show that the equilibrium value of
34:43the relative price
34:45of consumption to investment is pinned
34:47down by technology and equal to the
34:49inverse of the two labor augmenting
34:52technical changes.
34:54So if the
34:58excuse me if
35:01if the technical change term AX is very
35:05large
35:07relative to AC that means labor is very
35:11productive in investment production
35:13relative to consumption production then
35:16the price of investment is low relative
35:18to consumption or P which is the price
35:21of consumption to investment is high. So
35:24it's the inverse. The price of something
35:26is high if the a technical change term
35:30in the production of the item is low. So
35:35if you're very productive doing
35:36something, it's cheap. If you're not so
35:38productive, it's expensive relative to
35:40the other one.
35:42Second,
35:44equal capital to labor ratios mean that
35:47the model aggregates on the production
35:49side. By which I mean if you add
35:52investment and consumption in current in
35:55the same units
35:57namely investment which is the numerica
36:01then you get output Y in this economy
36:05and output Y is produced by an aggregate
36:08production function of the same form as
36:10the sectoral ones with the same theta
36:14but now plugged in aggregate capital K
36:18and aggregate labor one.
36:22So if you express everything in terms of
36:24investment, you need the investment
36:27augmenting technical change term. If you
36:30did it the other way around and
36:31expressed everything in units of
36:32consumption, you would have the
36:34consumption augmenting technical change
36:36here. Santi is going to talk more about
36:38that. I'm just going to state that and
36:39you have to take it at face value from
36:41me.
36:43So capital labor ratios are the same.
36:45prices are the inverse of the technical
36:47change terms and the production side
36:50aggregates.
36:55It is also true in this economy that the
36:58sectoral expenditure shares
37:01equal the sectoral employment shares.
37:06Now that's very convenient because it
37:08means that if I get the right behavior
37:11of the expenditure share then I'm also
37:14going to get the right behavior of the
37:16employment share. We have seen in the
37:17data that they behave similarly in the
37:20model they are the same. So we don't
37:21have to worry about that.
37:24Lastly, I get the standard oiler
37:26equation from the household problem
37:27which says consumption growth in terms
37:31of the numerator PCC or I should say
37:35consumption expenditure growth in terms
37:37of the numerator equals the discount
37:40factor plus 1 minus delta plus the
37:43rental price for capital.
37:47Again, Santi is going to derive all of
37:49this on Monday.
37:53We are interested in balanced growth and
37:55since this is a multis sector model I
37:57will focus on aggregate balance growth
37:59where balance growth refers to the
38:01aggregate variable but underneath there
38:03may be some changes.
38:06So I talk about an aggregate balance
38:08growth pass as an equilibrium pass along
38:11which the cult effects hold for
38:13aggregate variables that is constant
38:15growth of GDP per capita and capital per
38:18capita and constant capital GDP ratio
38:23real interest rate and capital income
38:25share and total income.
38:29Now for practical purposes and also to
38:32construct an aggregate balance gross
38:34path I'm going to assume that the
38:37sectoral TFP growth rates are constant.
38:41So ait + 1 / ait in each sector c or x
38:47is going to grow at a constant rate
38:49gamma i. Notice that these constant
38:53rates may well be different and in fact
38:56they should be different because we know
38:58that equipment in particular but
39:01investment more general has fallen in
39:03price relative to consumption. This
39:06would be captured here by having gamma
39:08for investment larger than gamma for
39:11consumption. Right? There's more growth
39:13in technical change in investment.
39:18The relative price does the opposite. it
39:20falls when the A's grow a lot.
39:26Now under these assumptions you can show
39:27that a unique aggregate balance gross
39:30pass exists in this two sector model.
39:36Sorry. Can I ask question?
39:38Of course you can.
39:39Yeah. So um we said earlier that the two
39:41sectors have different growth rate. So
39:43for instance the investment so the
39:45growth rate in investment sector is
39:47higher than the growth rate of
39:48consumption sector. Then why do we get
39:50the constant growth rate for the whole
39:52economy? Is it because of the bulos
39:54bulos disease we talked about before? Is
39:57it because because investment sector is
39:59higher uh tip growth then the pro and
40:03the relative price of investment will
40:05decrease so that the uh proportion of
40:08the investment sector in GDP has
40:10decreased is is it because of that or
40:13could you it's a good question. Uh let's
40:16go back to slide 16 at the bottom which
40:19defines GDP. It says GDP is X + P plus C
40:25time C. Now you point out correctly
40:29what's going to happen is there's
40:31stronger growth in X than in C. But GDP
40:35is not X plus C because I have to add it
40:37in the same units. GDP is X plus P * C.
40:42So the
40:44the weaker growth in consumption is
40:47going to get offset by the fact that the
40:49relative price of consumption is going
40:50to increase.
40:53Right? Look at the relative price. If
40:56consumption doesn't grow much but a
40:59investment grows a lot then this
41:00relative price grows a lot. And what's
41:03going to happen is that X and the
41:05expenditure on consumption, they grow at
41:08the same rate,
41:10but X and C don't. So the trick is the
41:14relative price that converts C into
41:17units of X is going to make sure that
41:19they're both on the same footing and
41:21grow at the same rate.
41:24Does that make sense?
41:25Yeah, thank you.
41:26So Santi is going to talk more about
41:28this. It is a good question and at the
41:30beginning when you haven't seen many
41:31multis sector models you get confused by
41:33this. Some people get still confused
41:36although they have seen a lot of those
41:38but the key thing is always make sure
41:40that everything is in the same units and
41:42you take into account both the real
41:45growth of the item you look at and the
41:48growth of its price.
41:52Let's put it differently. We are getting
41:54this massive increase of equipment. Why
41:57isn't that blowing up our GDP? Well, at
41:59the same time, the price of equipment is
42:01falling so much. So, my computer is
42:04always $1,500. Although the computer
42:06becomes better every four years
42:07dramatically, right? The computer
42:09becomes better, but the price falls. I
42:11always spend the same. So, that's the
42:13basic idea.
42:15Other questions?
42:18It's not the case. Let me then talk
42:21about structural change. So far, there's
42:22no structural change. there's just
42:25consumption and investment as and as
42:27Jean Lung has has pointed out they grow
42:30at the same rate if expressed in the
42:32same units.
42:35Now I'm going to now present a benchmark
42:38model of structural change which is
42:40going to disagregate consumption and
42:43focus on structural change within
42:45consumption.
42:46I will present three classes of
42:48preferences that give you structural
42:50change and then assess whether they're
42:52consistent with aggregate balance growth
42:54paths as defined before.
42:59Now I should say a couple of more
43:01sentences. This is a benchmark model
43:04that focuses on structural change within
43:06consumption
43:08which is a natural first step to take
43:10because consumption is roughly 80 85% of
43:14total GDP in most developed economies.
43:18It does leave the question open what
43:20happens to the rest and I'll get a
43:22little bit to that as we go through. But
43:24first let's talk about how you might
43:26generate structural change within
43:28consumption. The first class of
43:30preference is the generalized stiri
43:32preferences that Richard Akosh and I
43:34used in the AER paper that we had in
43:372013
43:39where you disagregate the sea from
43:41before
43:42into
43:44an aggregator
43:46that depends on consumption of
43:48agricultural goods, manufactured goods
43:51and services.
43:53In front there are weights omega a, m
43:57and s. And the exponents here, don't let
43:59them distract you. They're there so that
44:01the limits of these specifications
44:05are the right ones. More importantly,
44:09epsilon minus one over epsilon is the
44:12exponent on all three uh consumption
44:15items. And then you take it the inverse.
44:17So that's a CES production um utility
44:21function with an elasticity of
44:23substitution between the three that's
44:26equal to epsilon.
44:28Now it's not a CES in the strict sense
44:31because there are additional terms here
44:33C bar A and C bar S which are constant
44:37terms both positive
44:39and they imply that this utility
44:42function is not homothetic.
44:45What's a homothetic utility function is
44:47one you can scale up and down. If you
44:50double all expenditure, you double all
44:53the um util all the consumption of each
44:57of the different categories.
44:59So if the bar terms here were zero, this
45:02would be homothetic.
45:06Non-zero bar terms introduce
45:10non-homotheticities
45:12which is a fancy way of saying you
45:15consume more of some goods than others
45:19and it changes as income changes. The
45:22income elasticity in other words of
45:24these different goods is not one.
45:27This can be best illustrated if you look
45:29at the implied demand system and I've
45:31written it here at agriculture over
45:33manufacturing expenditure services over
45:36manufacturing expenditure first it's a
45:40familiar term from CES utility functions
45:44that just depends on the relative price
45:48it's fixed ideas if epsilon is one then
45:50I have log special case up there the
45:54relative price doesn't matter the
45:56expenditure shares are constant. If
45:58epsilon is larger than one, you
46:00substitute. What that means? If the
46:02relative price of something goes up, the
46:05expenditure share is going to go down.
46:08And if epsilon is smaller one, the
46:09opposite happens. You have compliments.
46:11If the price goes up, the expenditure
46:14share goes up because you don't
46:15substitute as much as the price
46:17increased or more. So that's the
46:20standard CS here.
46:24The nonometheticity
46:26constants add additional terms here CA
46:29bar and CS bar that are deviations from
46:34the standard CS. In particular, in the
46:37case of agriculture, there's a constant
46:39term that you add. So if you
46:42decide what to do in agriculture, you
46:44first have to satisfy that constant term
46:47and then the CES comes. The same is done
46:50in services but you subtract that term.
46:55Often the interpretation is this is
46:57subsistence consumption. You have to eat
46:59a minimum amount of calories otherwise
47:01you die. Think of this as CA bar. The C
47:05bar is often interpreted as home
47:07production. Even if you don't purchase
47:10any services in the market, you still
47:12get some for free so to speak from a
47:14market perspective. And these are the
47:15ones which you produce yourself. So what
47:18that means is that if you are poor, you
47:20first satisi want to satisfy your
47:22subsistence consumption of agriculture.
47:26You are happy with your um home
47:29production of services. So you subtract
47:31something. So if you're poor, you will
47:33spend relatively much on agriculture and
47:36relatively less on services.
47:39If you then increase your expenditure,
47:43you will increase the expenditure on
47:45manufactured goods and ultimately these
47:48two terms will converge to zero and you
47:50go to a CES. So this is a very simple
47:52and cheap way of generating
47:55nonomoticities
47:57which imply that when you're poor your
48:00composition is biased towards
48:01agriculture and when you're rich it goes
48:04more and more into services. You can
48:06already see how structural
48:07transformation is almost hardwired into
48:09this specification.
48:12Now I want to um for those of you who
48:15have seen more in this literature make a
48:17few remarks of two recent papers that uh
48:21generalized this specification. So we
48:23were perfectly happy with this
48:24specification and then as always in life
48:26somebody comes out and says it doesn't
48:28always work and there's some
48:29shortcomings and you get slightly pissed
48:32off. I discussed this paper. I didn't
48:34like it at the beginning. Now I like it.
48:36So obviously progress means somebody
48:38points out something better and one
48:40better specification is kumin lashkari
48:44mysteria that's in the fourth fifth or
48:45sixth round I don't know of econometrica
48:48I lost track.
48:50They basically use what's called the
48:52nonomothetic ces the same as before the
48:55weights.
48:57Then there is the consumption
48:59agriculture manufacturing. Oh, sorry.
49:02And services.
49:04And now they introduce nonomaticities in
49:07a different way. Not through constant
49:09terms as we did and many people before
49:12us. So I shouldn't claim here that's the
49:15invention of this paper but we used it.
49:18They introduced nonomaticities by
49:20putting consumption with an exponent in
49:23front of agriculture and services. So
49:25intuitively what that does is as
49:28consumption grows you can have different
49:31weights depending on how much
49:33consumption you have on agriculture and
49:36services. So in particular if you want
49:39that services get more and more of the
49:43expenditure as you become richer you're
49:46going to make the weight on this C here
49:48large and you make it on this C small.
49:52The implied demand system is the same as
49:55before in the first part which is the
49:58relative price effect. And then you can
50:00see there is the consumption term that
50:04is in front here and it depends on how
50:07you choose the sigmas whether a good
50:10becomes more or less important as
50:12consumption grows.
50:14And then there's another paper by Tim
50:17Bapad that does something similar. He
50:20uses piggle preferences.
50:22I can never remember what piggle stands
50:24for. It's price independent generalized
50:26linearity which doesn't tell you much
50:29but the demand function people use this.
50:32I'm not going to go into the details of
50:34this specification much. I just mention
50:36it. It's an indirect utility function
50:39which depends on expenditure and the
50:41prices of goods and services. and he
50:44again gets a demand system which depends
50:46on relative prices and on expenditure.
50:52So a similar a different way of getting
50:56something similar the share of your
50:58expenditure on goods here depends on
51:01relative prices and it depends on how
51:03much expenditure you have.
51:06Now if you are interested in that
51:07there's an excellent recent paper by
51:09Teimo Bart himself and then Alder and
51:12Müller in the AJ macro where they
51:14generalize it to many goods. The
51:16original paper just had goods and
51:17services. I just flag this for those who
51:21are particularly interested or somewhat
51:22more advanced. If you didn't understand
51:24the word I said when I discussed this
51:26slide that's fine just ignore it for
51:30now. We have three different
51:32specifications and the key thing is as
51:34already in the simplest specification
51:37there's relative price effects and
51:39there's effects of income that come
51:42through nonomotheticity terms in the
51:44simplest form the constants CA and CS.
51:54So I need to also specify technology.
51:57I'm going to stick to the cob daggers
51:59production functions with equal shares.
52:02But now I'm going to assume that there's
52:05production functions for each
52:07consumption category. Agriculture,
52:09manufacturing and services separately.
52:12Right? Before it was consumption,
52:13investment. Now it's agriculture,
52:16manufacturing, services and investment.
52:19But the functional forms are the same.
52:22And since the equal shares in the equal
52:25exponents in the cob douglas worked so
52:27well before I'm going to use them again
52:31for those who want some further hints on
52:34the literature there are three
52:36generalizations of that in an important
52:39paper in JPEG
52:42generalized the
52:45technology to allowing for different
52:48exponents on the different production
52:50functions.
52:52And then we uh I mean we Akos and Chris
52:56Harrington and I wrote a paper in the HA
52:59macro where we estimated CES production
53:02function and explored what that does to
53:04structural change and a full-blown
53:08model analysis of that is in Alvarez
53:10Guard and Poshka which is in theoretical
53:12economics in 2017. Again, this is not
53:15meant as essential for this lecture, but
53:18just as some suggestions for further
53:20readings for those who are more
53:22interested. So, you can generalize this,
53:25but it's tedious. The most
53:27straightforward thing is to work with
53:28these
53:32remarks. The literature often works with
53:35only three production functions,
53:38assuming that all investment is produced
53:40in the manufacturing sector. Instead I
53:44have here used four
53:47distinguishing agriculture manufacturing
53:49and services and that's just consumption
53:51and then there's one investment sector
53:53where nothing interesting happens in
53:55structural change.
53:57Why have I done that?
54:00Assuming that all investment is produced
54:02in the manufacturing sector is not
54:04supported by the data. An easy way of
54:06showing that is that
54:09in the last 10 years, US investment
54:11exceeded the value added the total value
54:15added of US manufacturing.
54:18So you can't possibly assume that all
54:20investment is produced in manufacturing
54:21because investment is more than
54:23manufacturing value added. Why can that
54:26be? Think of software.
54:28Software is an investment. it's not
54:30produced in the manufacturing sector and
54:33it's becoming a bigger and bigger part.
54:37I have therefore left investment
54:39separate so that structural change
54:41happens only within consumption.
54:45Having said that view that is a natural
54:47first step as always you got to start
54:50somewhere and you better start somewhere
54:52simple otherwise you don't understand
54:53what you what you get. We since then
54:57have continued working and in a recent
54:59paper with Richard and Akosh which I
55:02think is coming out in the review of
55:03economic studies sometime this year we
55:07characterize structural change within
55:09investment as well and we focus as in
55:12this paper on the aggregate balance
55:14growth pass I should mention there's a
55:17companion paper that was independent of
55:19ours by Garcia Puan Masia Corta which
55:22again takes gazillions of rounds in
55:25econom Metrica and they do the same that
55:29we did but they characterize investment
55:31the structural change in investment
55:33along transition path to the aggregate
55:36balance growth pass. So our paper is
55:37aggregate balance growth theirs is the
55:39transition path which I admit is a lot
55:42harder to do uh because you don't have
55:44analytical solutions anymore. So if
55:47you're interested in structure change
55:48within investment there are two papers
55:50that are currently at the frontier and
55:53that talk about this. I should add it's
55:56very messy. It took us forever to
55:58understand how to characterize it along
56:00the aggregate balance growth path. Uh
56:03but it's done. I don't want to do it in
56:06this lecture because I want to focus on
56:08the essentials. So let's go back
56:10structural change within consumption
56:15and then there are some stupid
56:16feasibility constraints as before. So in
56:20this benchmark model I have
56:24the same key properties from before
56:27continue to hold.
56:29In particular the capital to labor
56:31ratios are going to be equal to the
56:33aggregate capital labor ratio as before.
56:37Why? Because I have fork of Douglas
56:39instead of two but the exponents are all
56:41the same.
56:43Still the relative prices are determined
56:45by technology. So relative price of two
56:48things is the inverse of the technical
56:51change terms.
56:53Again the four sectors aggregate on the
56:56production side. So I have an aggregate
56:58production function of aggregate output.
57:01And this was Jinglong's question. Why?
57:04Because I'm taking the product for each
57:07sector of price and output. And output
57:09does whatever it does. But prices offset
57:13this. So I can aggregate everything up.
57:16the four sector model aggregates on the
57:18production side and the sectoral
57:20employment shares continue to equal the
57:23sectoral expenditure shares which is
57:24convenient. So I have just to look at
57:26one and I know I characterize the other.
57:32I can then analyze this more complicated
57:35model with four sectors
57:38by breaking the household problem into
57:40two subpros. One is the intertemporal
57:42problem from before. I allocate total
57:45income
57:46among the composite consumption good C
57:49and savings which turn into investment
57:53and then there's a static problem where
57:56I allocate the period consumption
57:58expenditure PC PTCT
58:02among the three different consumption
58:03goods agriculture manufacturing and
58:05services
58:08so going through the two sector model
58:10before is useful to understand the
58:13intertemporal problem.
58:15What's new is the composition of
58:18consumption follows from a static
58:21problem. Now the structural
58:24transformation that I'm trying to
58:25generate and we'll show you in a second
58:27how it results is going to happen within
58:32consumption where the two sector
58:34structure is totally unaffected but
58:36within consumption there's reallocation
58:38and the patterns that I showed you
58:39before will happen.
58:42Before
58:46I show you the two key results, are
58:48there any questions or things I should
58:50clarify better
58:52before I move on?
58:55Excuse me. Uh yeah, I have a question
58:58about the like total investment existing
59:01uh the manufacturing. Uh how about if we
59:04kind of uh add the durable consumptions
59:07that treat like uh non-durable and uh
59:10durable consumptions and uh separately a
59:14separate sectors would would that help
59:16like explaining and also taking out
59:18inventories from investment uh
59:21measurement how how much to what extent
59:23would that help
59:25um so it's a good question what you are
59:29referring to if I understand correctly
59:31is that in the national pounds.
59:34The stock of durable consumption goods
59:37like washing machines, furniture, etc.
59:40is not capitalized. It's not part of the
59:42capital stock. Okay? And the investment
59:45in durables is expensed
59:48not expensed is counted as consumption
59:50expenditure but not as investment that
59:53leads to a stock. If you reallocate the
59:57investment in durables and add them to
59:59the total investment that's otherwise
1:00:02out in the economy, you make the problem
1:00:05worse because you increase investment
1:00:07even further. The manufacturing sector
1:00:10is what it is already. Without durables,
1:00:12the total investment exceeds
1:00:15manufacturing value added. So if you add
1:00:17some more, you make it worse.
1:00:19Inventories won't help you. It's
1:00:22actually very stark. What happens
1:00:24basically is that about half of
1:00:27investment is services
1:00:30and you have to take that into account
1:00:33if you want to match the composition of
1:00:36investment seriously to the data. Now I
1:00:38I already talked about software. Think
1:00:40of other things. When you build a house,
1:00:44there's design services, architectural
1:00:48services, there's transportation
1:00:49services, there's hotel and retail
1:00:51services of all the materials that you
1:00:54put in the house. So the house looks
1:00:55like a physical thing and you say, well,
1:00:57that was produced by the manufacturing
1:00:59sector. In particular, where I live in
1:01:01Phoenix, every house looks the same
1:01:02standardized manufacturing sector. But
1:01:05you overlook when you do that that
1:01:06there's a huge service component in
1:01:09these physical things because you for
1:01:12starters have to get them from where
1:01:13they were produced
1:01:15to where you sell the house. I have a
1:01:19stove for being pretentious from Italy.
1:01:22So it was expensive to ship it over and
1:01:24then there was a wholesaler here and
1:01:26then there was a retailer here and then
1:01:28it was put into my house. So there is
1:01:30even in that physical house is a large
1:01:33service component and what we argue in
1:01:35the paper you have to take that into
1:01:37account. It's it's an excellent question
1:01:39but it's it's it's hard to weasel out
1:01:42there
1:01:43and it's so stark that if you really
1:01:46want to do this you you should think
1:01:48about structural change within
1:01:49investing.
1:01:51Other questions?
1:01:52Thank you. That's very helpful.
1:01:54May I ask a question sir?
1:01:57Oh go ahead.
1:01:58Yeah. uh I know this is a benchmark
1:02:00model but uh I wonder that if we can
1:02:04handle this issue within the
1:02:06heterogeneous agent framework because
1:02:08when I think about uh structural
1:02:11transformation
1:02:13uh what comes to my mind is that uh the
1:02:16the switch of the labor market within
1:02:18the ind different industries
1:02:22so
1:02:26to to fix ideas. So this is a
1:02:29representative h agent model or
1:02:32representative household model. So
1:02:34there's no heterogeneity within the
1:02:36households.
1:02:38But what happens is that each household
1:02:40is going to allocate its labor among
1:02:43producing investment, agriculture,
1:02:45manufacturing and services.
1:02:47So within the household you can allocate
1:02:51different shares of your total time
1:02:53endowment of one two different sectors
1:02:55and that can change over time.
1:02:58Now another question that I sense from
1:03:01your uh excellent question is what
1:03:04happens if I have different households?
1:03:07Maybe some are educated or not so
1:03:09educated. Some are single, some are
1:03:12married.
1:03:13Some have a comparative advantage for
1:03:16agriculture for some reason. Others have
1:03:18a comparative advantage for services
1:03:20perhaps of education.
1:03:23You can extend this model and ask
1:03:25questions in this context
1:03:28because the production side is going to
1:03:30be similar but now you have to work on
1:03:31the
1:03:33uh on the preference side on the
1:03:35household side and make it more
1:03:36complicated. Some people have started to
1:03:38do this. I don't want to do it here
1:03:41because I want to give you the benchmark
1:03:43model and it's kind of hard. And it's
1:03:45not hard, but it's I always find it
1:03:47useful to think of the most simple
1:03:49framework that has the essence of the
1:03:51key effects. Once you understand that
1:03:53you can complicate. If you start with a
1:03:56complicated one, chances are you never
1:03:58get the simple effects and that's why
1:04:00I'm not I'm not doing that. Okay? But
1:04:03it's a good question and um you can uh
1:04:06check some people have worked on it. I
1:04:08think Rachel is going to talk in the
1:04:09next lecture about um such distinction
1:04:14between men and women or skilled and
1:04:16unskilled. I don't do it in in this
1:04:19basic framework.
1:04:24Well, if that's not the case, I have
1:04:26about 10 minutes left. Let me come to
1:04:29the key results then. Key results. The
1:04:32first key result as I see it is from a
1:04:34paper of Konamote rebell in the review
1:04:37of economic studies and I'm going to
1:04:38have labeled this income effects
1:04:44take the utility function that we used
1:04:47in our a paper
1:04:51here it was
1:04:54and impose that epsilon is equal to one.
1:04:57If epsilon is equal to one, this utility
1:04:59function reduces to a special case which
1:05:02is called stone giri and that's lock
1:05:05utility and here it is
1:05:09where is it here.
1:05:14So if epsilon is equal one the cs goes
1:05:17away and I have a log utility in
1:05:19agricultural consumption minus the
1:05:21constant term manufacturer consumption
1:05:24and services consumption.
1:05:27On top of that assume that all sectors
1:05:30counterfactually but just for the
1:05:32purpose of this proposition have the
1:05:35same growth rate of technical change. So
1:05:37the gamma eyes are all the same.
1:05:40If this is the case then there is an
1:05:42aggregate balance growth path and along
1:05:45the aggregate balance growth path
1:05:47employment and expenditure shares are
1:05:49constant for investment.
1:05:51They decrease for agriculture.
1:05:54they increase for services and they're
1:05:56constant for manufacturing.
1:06:00So under these stark assumptions
1:06:04you get structural change out of
1:06:06agriculture into services
1:06:09but you don't get the hump shape in
1:06:12manufacturing
1:06:14at the same time you still get an
1:06:16aggregate balance growth bus. So why is
1:06:17that the case? Essentially everything is
1:06:20growing at the same rate but these
1:06:23constant terms CA and CS going to lead
1:06:26to reallocation.
1:06:28Think about it as follows. If CA is
1:06:30close to C bar A,
1:06:34this number is very small and the
1:06:37curvature is very steep here. So you
1:06:39want to allocate a lot to agriculture.
1:06:42If you're poor and your consumption of
1:06:45agriculture is close to C bar, you don't
1:06:48worry much about services because you
1:06:50get that constant turn for free. So even
1:06:52if your service purchases were zero, you
1:06:55would still not be at a corner. Now take
1:06:58that economy and let it grow. The
1:07:01relative importance of this bar term
1:07:03here and this bar term there diminishes
1:07:07as you grow and ultimately you go
1:07:10towards a cog daggers function where
1:07:13it's lock consumption of agriculture
1:07:15manufacturing and services. So you go
1:07:17through a composition omega a omega m
1:07:21and omega s in the limit. Hence you go
1:07:24out of agriculture towards omega A you
1:07:26go into services towards omega s and you
1:07:29get structural change but not in
1:07:32manufacturing.
1:07:35Second key result my emperor is relative
1:07:38price effects.
1:07:41Suppose that the growth rates of
1:07:43technical progress are strongest in
1:07:44agriculture second in manufacturing and
1:07:47third in services.
1:07:49Suppose that the nonomaticity terms C
1:07:52bar A and C bar S are zero
1:07:56and suppose that the elasticity of
1:07:58substitution between these different
1:08:01consumption goods is smaller than one.
1:08:04There is an aggregate balance gross pass
1:08:06again along which employment and
1:08:09expenditure shares are constant for
1:08:10investment. They decrease for
1:08:13agriculture. the increase for services
1:08:15and there lies somewhere in between the
1:08:18other two shares for manufacturing.
1:08:21So as before I get structural
1:08:24transformation out of agriculture and
1:08:26into services.
1:08:28I don't get a constant share of
1:08:30manufacturing necessarily anymore but
1:08:31it's not clear that I get a hump shape
1:08:33either.
1:08:35So these were the two first models that
1:08:38broke the ground and that highlighted
1:08:42the two main effects namely income
1:08:45effects in conjunction with non-homothic
1:08:48utility functions that lead to
1:08:49reallocation even if there's no price
1:08:51changes. Notice here if all the gamas
1:08:54are the same, the relative prices won't
1:08:55change
1:08:57or different gamas that lead to relative
1:09:00price changes
1:09:02but no income effects because the
1:09:05utility function is homothetic. All the
1:09:07bar terms are zero and then I get
1:09:10reallocation
1:09:11within consumption just from price
1:09:14effects. In order to form intuition,
1:09:17it's useful to go to the extreme case.
1:09:19Think of a leontf.
1:09:22If gamma a is the strongest in all
1:09:26sectors, that means agriculture has the
1:09:28strongest
1:09:30techn technological progress, which
1:09:32means that the relative price of
1:09:34agriculture is falling. You're not
1:09:36changing anything in your real
1:09:38consumption bundle. The relative price
1:09:40is falling. What happens with a share?
1:09:41It's going down.
1:09:45Similarly,
1:09:46gamma s is the smallest. So the relative
1:09:48price of services is increasing. You're
1:09:51not changing your bundle in the Leontf
1:09:53case which is the extreme form of
1:09:55epsilon smaller than one. So services
1:09:59become more and more expensive. The
1:10:00share you spend on services is
1:10:02increasing.
1:10:03So that's a very mechanical and simple
1:10:05way of getting you move out of
1:10:08agriculture and you move into services.
1:10:10The Hump shape is more challenging.
1:10:16Additional results about the hump shape.
1:10:19The paper by commenceri
1:10:22shows that over very long periods our
1:10:25utility function wasn't useful because
1:10:27the income effects are persistent
1:10:30and with our nonomothetic CES utility
1:10:33function the income effects come for
1:10:36constants. So basically what happens if
1:10:38you go back to our uh demand system here
1:10:45the nonomoticities come from constant
1:10:47terms
1:10:49and as PMC cm grows and grows and grows
1:10:53these things converge to zero. So in the
1:10:55limit they disappear. What they point
1:10:57out is that income effects seem to be
1:11:00persistent over long periods of time. So
1:11:03their specification is more useful
1:11:05because the income effect doesn't go
1:11:06away. So you have that C here all the
1:11:09time no matter how rich you are. And
1:11:12then they do similar things as I just
1:11:16discussed. They show that persistent and
1:11:19income effects and the usual relative
1:11:20price effects can replicate agricultural
1:11:23and service shares over the long
1:11:25horizon. But there's some challenge
1:11:27still with the hump shape in
1:11:29manufacturing. they no longer get an
1:11:31aggregate balance gross path but an
1:11:33asmtotic aggregate balance gross path.
1:11:37And then a recent paper by Alder Müller
1:11:40Bart uses the generalized pickle
1:11:43preferences. It's going to be in print
1:11:45in AJ macro I think this year. Again
1:11:49they model persistent income effects
1:11:51over long horizons and the usual price
1:11:54effects and they get everything.
1:11:57They replicate all shares including the
1:11:59H shape in manufacturing over long
1:12:01horizons and they have an aggregate
1:12:03balance cross.
1:12:06So in terms of achieving this what we
1:12:10want namely aggregate balance growth and
1:12:12the stylized facts stats as it stands
1:12:14the gold standard
1:12:16a little bit
1:12:18um little bit unfortunate is that they
1:12:21use an indirect utility function namely
1:12:23this generalized piggle specification
1:12:26which is not always the most intuitive
1:12:28way of getting things. It's flexible, so
1:12:31you can generate what you see in the
1:12:33data, but it's a little bit hard
1:12:35sometimes to keep track where the
1:12:37effects come from. Still, I think if you
1:12:39want the best model to replicate the
1:12:42stylized facts, it's this one,
1:12:47which leads me to conclude.
1:12:51I've shown you that there are clear
1:12:53stylized facts of structural
1:12:54transformation.
1:12:56Agriculture shrinks, manufacturing
1:12:59follows a hump shape and services
1:13:01expand.
1:13:04I've illustrated in a benchmark model of
1:13:07structural change two main forces.
1:13:10One is relative prices change with a low
1:13:13elasticity of substitution meaning the
1:13:16different goods are complements in the
1:13:19extreme case leontf
1:13:21and so the sector with a low
1:13:23productivity growth will expand
1:13:26because you don't substitute much and
1:13:28the share you spend on this will go up
1:13:31and the sector with a high productivity
1:13:33growth will contract. Why? again you
1:13:36don't change the composition much and
1:13:38the share you spend on it will decrease
1:13:40in the model the expenditure and the
1:13:44employment shares do the same thing so
1:13:45once I have the expenditure shares I
1:13:47know it's true also for employment
1:13:48shares
1:13:50the second effect that I've highlighted
1:13:52is that income changes
1:13:55can lead to structural change when there
1:13:57are different income elasticities
1:14:00luxury goods which are the ones that
1:14:02have increasing shares and higher Income
1:14:05elasticities expand when you develop. So
1:14:09these are the services and necessities
1:14:11as agricultural goods contract because
1:14:14they have an income elasticity smaller
1:14:16one. So the share goes down as you
1:14:19develop.
1:14:22The cess and the piggle utility generate
1:14:25these forces and are consistent with
1:14:27aggregate balance growth pass and the
1:14:30nonomothetic sess which I forgot to
1:14:32mention here can generate these forces
1:14:34as well but is not consistent with
1:14:38aggregate balance gross path instead it
1:14:41asmtotically has aggregate balance grows
1:14:44but along the transition it won't
1:14:49now there's many different ways in which
1:14:51you could generalize The results I've
1:14:53shown you, I've hinted at some
1:14:56developments which took place since we
1:14:59published that handbook chapter in 2014,
1:15:01which is already almost six, seven years
1:15:03ago.
1:15:05There's many more. We also have a
1:15:07discussion in the handbook chapter about
1:15:09future research and what we think might
1:15:11be useful.
1:15:13If you want a updated version, we have
1:15:16uh Richard Akos and I published a paper
1:15:19in uh the review of the Federal Reserve
1:15:22of St. Louis. I believe it was in 2019
1:15:27where we talk about some future de some
1:15:30more current developments. So there's a
1:15:32lot of work being done currently. I
1:15:34think it's fair to say that the
1:15:35benchmark model is still a useful
1:15:38starting place, but lots of stuff and
1:15:41exciting stuff has happened since and
1:15:43Rachel in the follow-up lecture will
1:15:45talk about some of it and the other you
1:15:48will find in the journals. So that's all
1:15:50I had to say. I think I did exactly an
1:15:53hour 15 minutes given I started a little
1:15:55late and I'm open for questions until
1:15:5810:30.
1:16:02Fantastic. Thank you so much, Berthold,
1:16:04and thanks for being so prompt. Please,
1:16:06um, those of you with cameras and mics,
1:16:09please feel free to go ahead and pepper
1:16:13Bertold with questions for the next 10
1:16:14minutes.
1:16:17Don't be shy,
1:16:19guys. Another question.
1:16:22Yeah, you know, but you only got two.
1:16:23Okay.
1:16:24Okay. What is the So, we saw that the
1:16:28manufacturing is ham shipped. What is
1:16:30your most preferred explanation for this
1:16:32hamship? What is the intuition behind?
1:16:38That's actually a good question and I'm
1:16:39not sure I have an answer. So there's
1:16:42there's different ways of of generating
1:16:45it.
1:16:47One the only one I covered in this
1:16:50lecture was the alder, but there it
1:16:52comes from
1:16:54flexible income effects.
1:16:57And so somewhat by construction, you can
1:17:00get it if you free up your preferences
1:17:04and you have strong and then weaker
1:17:06income effects. So imagine if you're
1:17:08relatively poor, you want a lot of
1:17:10manufacturing goods no matter what they
1:17:12cost. If you get richer, you want less
1:17:14and less manufacturing goods. So that
1:17:16that's one way. Another way is to um
1:17:22free up the constraint that
1:17:25technological progress grows at constant
1:17:27rates.
1:17:29Okay. So it it I don't know the exact uh
1:17:34facts out of the top of my head but I'm
1:17:36under the impression that that's a good
1:17:38a reasonable assumption say for the
1:17:41postwar US but not a reasonable
1:17:42assumption over 200 years.
1:17:45Okay. But I think it's I just refereed
1:17:48on the weekend the paper that was
1:17:50exactly about the hump shape and I think
1:17:53uh there is a lot of interesting work
1:17:55but it's not ultimately settled where it
1:17:58comes from. I've always in my own work
1:18:00I've stayed away from it somewhat
1:18:03wimping out saying this is kind of
1:18:05difficult and and messy and I I haven't
1:18:08dealt with it. But I think it must have
1:18:10to do with the fact that the technical
1:18:13progress is not constant over a very
1:18:15long horizon in manufacturing and that
1:18:18the nature of the manufacturing goods
1:18:19that you consume and how much you want
1:18:21of it changes over time. Right? Think
1:18:23about it. You're very poor in
1:18:24agriculture. You want some basic
1:18:26furniture, you want some basic housing
1:18:28and everybody goes into that. Now we sit
1:18:31in big houses. We have everything. You
1:18:32want a somewhat better computer,
1:18:34somewhat better car. maybe you want some
1:18:37services much more than the additional
1:18:40manufactured goods. So I think that's
1:18:42what essentially the preferences that
1:18:44are flexible capture and my hunch is
1:18:47that drives it but I'm not an expert on
1:18:49that question but it's again the second
1:18:51excellent question Jingle
1:18:54thank you
1:18:55anybody
1:18:57may question so uh I was uh wondering so
1:19:02as the GDP per capita increases
1:19:06uh do poor countries move to
1:19:09manufacturing before they move new
1:19:11services or is it like uh like if we go
1:19:15from very less to very high can we
1:19:17directly hit manufacturing and jump into
1:19:21services?
1:19:22Sorry I had some trouble getting the
1:19:25connection. Can you ask the question
1:19:26again please?
1:19:28Sure. Uh I was asking if the GDP per
1:19:31capita increases uh does a exaculture
1:19:34heavy economy
1:19:36does it can it move from exulture to
1:19:40services directly or is that translation
1:19:43always through manufacturing?
1:19:47If I understand correctly and I
1:19:48apologize if I don't because there was
1:19:50some disturbances in the in the
1:19:53connection. If I understand correctly,
1:19:56there are exceptions where economies
1:19:58have not developed the manufacturing
1:20:00sector as much as others and jump to
1:20:03services directly. I don't know where
1:20:06you are from but this is sometimes
1:20:08something people say about India
1:20:12that the service sector is unusually
1:20:14large in India compared to the average
1:20:18um experience
1:20:20and the manufacturing sector is not so
1:20:22large. Now if you want to understand
1:20:24developments like this, one way to think
1:20:27about it is that in Germany where I come
1:20:30from the manufacturing sector is still
1:20:32unusually large although we are fairly
1:20:34developed and the reason is we are just
1:20:35pretty good at producing cars and
1:20:37machinery and equipment and we export a
1:20:40lot of it.
1:20:42In other countries like Britain which is
1:20:44at a similar level of development with
1:20:48all due respect they're not very good at
1:20:50producing cars. I had one once. I will
1:20:52never buy one again. And they don't
1:20:53exist anymore. And if they exist,
1:20:55they're run by German companies. So
1:20:57their manufacturing sector is relatively
1:20:59small, but they have the city of London,
1:21:02right? So they export a lot of financial
1:21:04services. They are very good at this. We
1:21:06are not so good at this. If you ever
1:21:07been to Frankfurt, you know why. It's
1:21:09kind of a boring dull place.
1:21:12And we don't have a comparative
1:21:13advantage in that. So if you take trait
1:21:16into account which I've completely
1:21:17blocked out here you can get fairly
1:21:21sizable deviations from the average
1:21:23behavior
1:21:24right because you don't have to produce
1:21:26every let me put it differently to you I
1:21:29assumed that everything that you consume
1:21:31you have to produce yourself
1:21:34with trade that's not the case and so
1:21:36with trade the consumption composition
1:21:38may differ to a sizable extent from the
1:21:41production composition now this is an
1:21:43insight that can Inori Matsuyama had
1:21:46about 15 years ago
1:21:48and again it's something that's not in
1:21:51the benchmark model but that's important
1:21:53to think about and there's some work on
1:21:55that where people uh Kui comes to mind
1:21:58in the journal monetary economics 2013
1:22:00has a nice paper on that but that's
1:22:03that's a good question if that was your
1:22:04question I hope I didn't butcher it and
1:22:07it's an important question
1:22:08yeah that was my question so yeah I was
1:22:11thinking about uh yeah I I'm from India
1:22:14And I was thinking about India and I was
1:22:16also thinking about the comparative
1:22:18advantage uh sign. So yes. Yeah.
1:22:24Um could I ask something about uh
1:22:28nesting this model in sort of an
1:22:29international
1:22:30Can you speak up a little bit Holt?
1:22:32Sorry. Could I could I ask something
1:22:33about putting this into into an
1:22:35international framework? It kind of
1:22:36builds on something that uh was being
1:22:38said in the comments, but uh all of
1:22:40these models have just exogenous TFP
1:22:43growth. But if you look at the current
1:22:45situation where some countries clearly
1:22:47have much higher productivity, let's say
1:22:49in agriculture than others, what are
1:22:51some of the barriers that keep countries
1:22:54with very low agricultural productivity
1:22:56from essentially adopting the TFP of
1:22:59much more agriculturally productive uh
1:23:02regions?
1:23:04I mean that's an excellent question
1:23:06which is almost too excellent in the
1:23:07sense that it goes way way beyond the
1:23:10structural change model
1:23:12and you're exactly right the structural
1:23:14change model is a framework in which
1:23:17I do not answer why TFP is what it is I
1:23:21say given what TFP is what is the
1:23:24composition of the economy so a whole
1:23:27set of other questions and I think that
1:23:29would be probably much more of an expert
1:23:31in those than I am is Why are poor
1:23:34countries
1:23:35relatively
1:23:37inefficient in doing agriculture? And
1:23:40there's a huge literature gigia and many
1:23:42others have contributed to that.
1:23:46And it's I think we understand a little
1:23:48more why that is.
1:23:52There are certainly some barriers.
1:23:54There's certainly human capital
1:23:55differences.
1:23:57There's the perils of subsistence
1:24:01farming and inefficient use and
1:24:03allocation of land to people. But I
1:24:07don't want to go into the details of
1:24:08that. First of all, I haven't prepared
1:24:10for it. But it's also somewhat of a
1:24:12separate issue. I like to think of what
1:24:15determines TFP and then take TFP and ask
1:24:18what determines the composition of the
1:24:20economy as a result of TFP. And mine has
1:24:22entirely been about the second question.
1:24:25takes away it doesn't take away from the
1:24:27first question being very interesting
1:24:30but I have really nothing to say about
1:24:32this here right I've assumed everything
1:24:34is coming from heaven and it is what it
1:24:36is and now let's see what happens
1:24:40I think shar
1:24:42ask a question
1:24:42thank you
1:24:45um prof so you um in the last part of
1:24:49your section you make a lot of
1:24:51recommendation on this paper and I think
1:24:54one that resonates to an African
1:24:56perspective in terms of um our structure
1:25:00of the structural transformation is
1:25:02industrial policy and there hasn't been
1:25:05a lot of papers that do this work in um
1:25:08in a theoretical format. So I was
1:25:11thinking um of industrial policy in sort
1:25:14of like a theoretical format uh and
1:25:17looking at the consumption function that
1:25:19you've put to ask if someone was to play
1:25:21around with the consumption function and
1:25:24particular on the manufacturing side and
1:25:26probably um maybe allocate the constant
1:25:30consumption somewhere um along that
1:25:32manufacturing uh constant consumption.
1:25:35would that also assist to probably ramp
1:25:37up the efficiency in which the the
1:25:42manufacturing sector operates because
1:25:44industrial policy is quite an important
1:25:47sector. I mean an important um factor in
1:25:52in determining what happens uh within
1:25:54growing the manufacturing sector in
1:25:56Africa and we speak about a lot but we
1:25:59have not tried to model that and include
1:26:02it in the framework of structural
1:26:04transformation. So uh perhaps can you
1:26:07can I ask that you at least talk about
1:26:09that a little and assist how does one
1:26:11even try and include it in the models
1:26:13that we're trying to work with here.
1:26:14Thank you. And another excellent
1:26:17question. I have to admit it's one that
1:26:20I heard before. I gave uh essentially
1:26:23this talk at an IMF training session
1:26:26about 12 months ago and they asked me
1:26:29exactly this question and I said it's a
1:26:30great question. I have nothing to say
1:26:32about it but we will work on it over the
1:26:34summer. Well then the corona virus
1:26:36happened and lots of other things
1:26:37distracted me. I don't think I think
1:26:40you're completely right Sharon. There's
1:26:42not much work on that. This framework
1:26:44cannot as it is tell you much about it
1:26:47because it says given what the
1:26:49productivities are what is the
1:26:50composition but it doesn't say again and
1:26:53this is related to hold as well where
1:26:56the productivities come from if you want
1:27:00to think about industrial policy that's
1:27:02the focus of the analysis and we have
1:27:05very little on that we tried to make
1:27:07some progress and we got stuck I can
1:27:09only say uh um Richard Akosh and I have
1:27:12agreed to meet again in April and that
1:27:14will be the subject about we think
1:27:16namely
1:27:18um what types of policies
1:27:21are interesting to consider in these
1:27:23models. Now notice one thing the
1:27:25equilibrium of the model that I have
1:27:27characterized is efficient. There is no
1:27:29room for policy here therefore to
1:27:32improve it.
1:27:34So what that means is I have a model
1:27:36that fits the data
1:27:39but the government should stay out of it
1:27:40given this model. Now I'm not thinking
1:27:43that uh necessarily that industrial
1:27:46policy is bad and should always be
1:27:49avoided. I'm just saying this model
1:27:50cannot speak about it to it at all. So I
1:27:53agree with you Sharon bleak situation
1:27:57but that's one subject on which you
1:28:00could focus and I think it's an
1:28:02important subject because in the
1:28:03practical world if you talk to the IMF
1:28:05guys that's all they care about. If you
1:28:07tell them the world is efficient the
1:28:09next conclusion is why are you here?
1:28:11your rent because you don't do anything
1:28:13good. They don't like that conclusion,
1:28:15you know, by the fact that they make a
1:28:16lot of money. They think they're
1:28:17important. Therefore, you have to write
1:28:19a model in which they are important to
1:28:20speak to them. And we are going to try
1:28:22and do that because I want to get
1:28:24invited again to the IMF.
1:28:27Listen, I'm going to intervene here
1:28:28because I know that Berthold um has in
1:28:33fact an important appointment to get to
1:28:35and I just want to thank you, Berthold.
1:28:37I wonder if those of you in the front
1:28:38row um would be willing to unmute your
1:28:41microphones and so that we can give
1:28:43Berthold a kind of old-fashioned round
1:28:45of applause out loud. And uh just thank
1:28:49you again, Berthold, for making the time
1:28:51and for and for a great and clear
1:28:53lecture.
1:28:55Thank you. That's an impressive round of
1:28:57applause. It was a pleasure.
1:28:59I like the I like the icon, the applause
1:29:01icon, but it doesn't resonate in quite
1:29:03the same way. and thank you again for
1:29:06the time. Um, I'll pass along your
1:29:09comments about the British automaking
1:29:11industry. Um,
1:29:15and I want to thank everyone for taking
1:29:18part for the questions from the front
1:29:20row for the questions from everyone um,
1:29:24in the Q&A. We're trying to figure out a
1:29:27way to post the Q&A content along with
1:29:30the slides and other things um on the
1:29:33website and to provide as much of the
1:29:35material as we can. But Berthold, thank
1:29:37you so very very much and great
1:29:40appreciation to you. I would also like
1:29:42once again to thank uh Mandy and Kirsty
1:29:46and Lauren and the team at CR for
1:29:49putting this together and for sticking
1:29:50around late on a Friday evening. So many
1:29:54thanks and uh we look forward to seeing
1:29:56you all next week when we continue on
1:29:59and um for those of you in the front row
1:30:02who are going to be available um for the
1:30:05TA session on Monday, we look forward to
1:30:07seeing you there. Couple of people
1:30:09commented in the Q&A. We really haven't
1:30:11figured out a good way to do the to make
1:30:14the TA sessions available for we're kind
1:30:17of wrestling with the challenge that a
1:30:20TA session is necessarily small and we
1:30:23haven't quite figured out a way to
1:30:25provide more than basic content. So
1:30:28we'll keep working on that and see what
1:30:29we can do. But um again thanks to
1:30:32everyone and we look forward to your
1:30:34feedback. Please let us know if there's
1:30:36if you have comments or feedback for us.
1:30:38Just one question.
1:30:40One, one last question. So, is the TA
1:30:43session also going to be posted the
1:30:45video so that those who can't attend it
1:30:47can see it?
1:30:48I I think um I think that's a question
1:30:51for Santi and also for the participants
1:30:53themselves. We don't want to smother
1:30:54participation
1:30:56um if people are nervous about having
1:30:57their questions um going to the world.
1:31:00But maybe that's something we can figure
1:31:02out.
1:31:03I mean, it would be nice for those who
1:31:04are excluded if they want to see what he
1:31:07said. agree.
1:31:08I don't know. I want to I haven't talked
1:31:09to Santi. But knowing him is
1:31:10well on on my end you have Yeah. You
1:31:13have the approval. So if you want to do
1:31:15it and the participants agree with that
1:31:16then we are
1:31:18All right. Well, we'll try to sort that
1:31:19out before before we go live and we'll
1:31:21let people know.
1:31:23But thank you all.
1:31:24Okay. Thank you very much and have a
1:31:27nice day. Bye bye.
1:31:28Bye. And thanks again, Bert.

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