okay let's uh let's start um So the plan
for today is to wrap up this growth uh
Theory section of the of the course and
um I I I want to sort of
conclude by showing you what we can and
cannot explain with the mods we have
looked up to now and almost as a matter
of accounting I will tell you what do we
need to fill which gaps do we need to
fill in order to explain sort of the
great dispersion we see in income per
capita across the world um but before I
do that I need to finish the previous
lecture and so let me let me do that H I
had shown you this table remember in the
in the complete model the model that has
a a productivity growth unemployment and
and and population growth um we
concluded that imbalanced growth H the
following happened no uh obviously if we
pick the right normalization the right
normalization here was ER effective
workers so that productivity
productivity times a population or
workers and so if we normalize the
variables by that H we get obviously
zero growth that's what it means to have
a balanced growth in which all the
relevant variables are growing at the
same rate H so Capital per effective
worker will will be a state that's
that's a diagram we plot remember the
diagram we plot was output per effective
worker against Capital per effective
worker and that diagram has a steady
state okay and that steady state at the
steady state or the balance growth point
then we have that H the normalized
variables grow at the rate of zero
Capital per worker has to grow at the
rate G GA because Capital per effective
worker is not growing so Capital per
worker will be growing at the rate GA
the same applies for output per worker
output per effective worker is not
growing that's balanced growth but
therefore output per worker will be
growing at the rate
GA um
these are the exogenous drivers a you
know output per worker we assume no a
well sorry labor is is GA is exogenous
in this model and so is GM population
growth is some constant we take it's not
something we try to explain within the
model okay but the two drivers of
absolute growth will be GA and GN and so
capital in the St state will be growing
at the rate GA plus GN output will be
growing at the rate GA plus GN so that's
balance grow okay now let me give you an
example so you can do see that suppose
that our production function is is this
we call that the a cop Douglas
production
function K to the 1 minus Alpha a n to
the alpha does this function have
constant
returns to scale yes the sum of the
exponents is one okay anyways but so uh
take the log of both sides the change in
the log is the rate of growth and so you
get that the rate of growth of output is
equal to 1 minus Alpha the rate of
growth of capital plus Alpha time the
rate of growth of effective workers okay
so in balanced growth GK will be growing
at the rate GA plus GN and therefore
output will also be growing at the rate
GA plus GN okay so that's what you have
in the table and if you want to look at
a variable like this Capital per worker
then output per worker then you you need
G gy minus GN
H so subtract the GN and you can
subtract both sides then it's going to
be equal to GA okay I subtract GM from
the right hand side H this one and that
one cancel and I get GA on the right
hand side that's the way you use that
expression to fill all this all these
blanks okay that's the that's St so I I
think I stopped right before that this
this slide or at this slide which is you
know if I look at this the table GN is
pretty easy to compute in most places
there are places in the world where we
sort of cannot even measure birth and
death so it's difficult but in most
places H you can measure GN the rate of
FR of population H quite accurately and
the question we have though is how do we
measure technological progress It's also
easy to measure the growth in the stock
of capital it's investment minus
depreciation uh but how do we measure H
GA no the rate of technological progress
and uhh the first proposal on how to do
it was also by Bob solo H that was a
second contribution he had in this in
growth Theory well it was also growth
measurement how do we measure GA it
turns out that the only way you're going
to have output per capita growing over
time outut person growing over time is
due to GA so we might as well try to
measure that since it's such an
important variable for sort of the
growth of er the growth of uh happiness
if you get one indicator of happiness is
output per C per worker well such an
important driver we need to be able to
measure it and and the basic idea that
Bob solo had is is essentially something
you could have taken from
1401 it's extremely simple it says ER
there are some assumptions behind this
but you know in in the basic competitive
model you have that that um you can
compute the contribution of each each
factor of production to to Output H by
the payment it receives okay so under
this assumption no suppose that that
you're spending in workers
$30,000 a
year so that means in a competitive
equilibrium in the labor market and so
on that the worker is contributing to
production
$30,000 okay I'm not going to deal with
markups and things like that here but
that's a basic idea you can adjust all
these formulas to include markups but
let me not do that so that also tells
you that if you increase
um er employment by 10% you'll also
going to increase output by 10% times
whatever is the contribution of Labor to
Output okay and that's what I have here
the contribution of H to Output of
adding workers is going to be that times
Delta n i can divide by H by y both
sides and here multiply and divide by n
and I get that the the the rate of the
the the rate of growth in
output due to a a a rate of growth in
employment is equal to the labor share
that's called the labor share is the
wage Bill W * n divided by total total
uh Revenue uh sales and uh uh times the
rate of growth of H population or
workers is the same here so I'm going to
call this GYN it's the rate of growth of
output due to the rate of growth in
population is equal to this this labor
share which I'm going to call that Alpha
times GM okay I can do exactly the same
with capital
and you can do if you have more factor
of production you can do the same for
each factor of production so but in this
simple example we have only two factors
of production labor and capital so I can
do the same for Capital and I can say
the contribution of of Capital Growth to
Output growth is going to be equal to
the capital share which is the compl of
the labor share so it's it's total
revenue minus the wage wage payment the
wage Bill divided by total revenue h
times the rate of growth of capital okay
so the contribution of H to Output
growth of the rate of growth of capital
is is 1 minus Alpha which is the share
of capital times uh the rate of growth
of capital okay so that means if I sum
the
contribution of Labor and capital I have
I I'm left with the residual which is
whatever is the rate of growth I have in
output I know how much I'm getting from
labor I know how much I'm getting for
Capital if there is any difference it
must be due to that thing I don't not
observe which is technological progress
okay that's the logic of all this
stuff go back for example to this
production function I'm saying I know
the contribution that K has to Output
growth I know the contribution that n
has to Output growth well the only thing
I'm missing is the contribution that a
has to Output growth which say don't
observe but I observe output growth I
observe Capital Growth I observe
employment growth so I can solve out
what
is the technological technological
progress a growth okay and that's that's
called it's called the solo residual by
the way okay but that's the way the rate
of growth of GA of a is measured the
rate of growth of output minus the
contribution to growth of er employment
population and capital
any question about
that no makees
sense
somewhat okay good so anyway so there's
a huge industry of measuring these kind
of things of course uh let me give you
an
example h on how to use this accounting
um so China 78 2017 that's an episode in
which China was growing very very
strongly
ER on
average China grew at over 7% out
progress over
7% now by the formula I showed you
before if I ask you the question well
what was behind that growth how much was
a contribution of Labor how much was a
contribution of capital and how much was
a contribution of technological progress
well there are some things we can
measure fairly well population growth
during this period in China was around
1.7% per
year there was a massive amount of
investment the Capital stock was growing
at a rate of
99.2% per year and the residual you can
compute it using the solo approach H is
around
4.2% okay so that 7.2% is a result of
the weighted average of these three
things okay so that's basic explanation
of ER the growth in China during that
that period now just looking at this not
don't look at at the
diagram what jumps immediately just if
you just look at this
part what jumps to you
immediately let me ask you differently
does it look like balanced
growth do you think that that that's
balanced growth that in other words do
you think that China had a arrived to
its state and and that growth is a
result of what was happening in that
stady
state
no but what is it that
looks that tells you that that that's
not the same
state balanc growth is when everything
everything is growing at the same rate
no everything you have you know
meaning all the endogenous
variables ER unnormalized are growing at
the same at the same rate as the
exogenous
variables so what is it that it would
nearly jump to me here is say
7.2% that's less than than the rate of
growth of capital
so so I know that there Capital over
output was Rising so that's not a state
state I know that I can see it in a
different way I know that in a steady
state in balanced
growth the rate of growth of output and
of capital should be the sum of the rate
of growth of population plus the rate of
technological
progress okay that's
5.9% but capital was growing at
99.2% not
5.9% so I do know that that's a period
in which China was growing
Beyond its steady state or balanced
growth rate of
growth and I know more than that I know
that the reason that was happening is
because there was more capital
accumulation than you would expect in
the stady
state when are you likely to see a
situation like that in which capital
accumulation is faster than the rate of
growth of capital in the St State and
it's faster than the rate of growth of
output that is that's a a period in
which we have transitional growth been
pulled you know growth above the state
state growth is being pulled by capital
accumulation when does that
happen do to mind first is economies are
like transitioning from command market
economies I believe and also the second
thing that comes to mind is potentially
um um countries recovering from like War
periods okay that's a deep deep deep
answer I wanted something simpler which
is
what I I want to say so the economy is
not in a state state that's clear but
what do we also know we know that the
Capital stock is below its stady state
level and that could be as a result of
of the the things you described you had
a war so your Capital stock was wiped
out or H you had a period in which
saving rate was very low and now you're
going to high saving rate episode with
that a lot of that is what happened in
in souis Asia in particular actually was
a fast increase in the rate of in the
say a sharp rise in this in the saving
rate but the bottom what I so what I had
in mind is for one of these reasons
that's a situation where the initial
Capital stock was below the stady state
and so you have a period of transitional
growth in which investment rate is more
than you need to do to maintain the
stock of capital per effective worker
know there's a positive gap between the
the green line and the and and the and
the red line and that's what leads you
transitional growth until you reach a c
state if things do not change meaning
population growth remain the same as in
that period and the and the the rate of
technological progress Remains the Same
As in that period we know that the
balanced growth rate of China is
5.9%
okay it's 5.9 because it's 07 plus
0.42 now so so that 7.2% average there
you're likely to see it and actually
there's an average that has numbers like
15 % very early on H to close to 6% or
so on the last stage H so that's that's
would be a stady state now that I think
is an
overestimate because H uh we know the
rate of population growth is declining
very rapidly in China it's turning
negative okay so so so for the rate of
growth of output China is going to is
unless there's a big change in
technological progress in the process of
technological progress it's going to be
pretty difficult for China to grow a lot
more than 5% I think going forward and
that creates some problems but but
that's what it is that's what this model
tells you you need to change something
and the things you can change in this
model are what well you could induce
higher saving rate you would get more
transitional growth out of that more
capital accumulation that's costly that
means less consumption and so on H or it
could be some technological breakthrough
but that's a probably would affect the
whole world in any event but that's the
kind of things you
okay good so that's that's
uh so
so is is the models we have developed
here sort of are quite good to explain
you know uh catching up processes
catching up growth and and and to
understand what are the where are
economies converging o over
time what I want to next is I I want to
end up trying to explain remember one of
the plots I showed you very early on is
that there's great
dispersion H in income per per person
per capita across the world and also
some countries are sort of not catching
up and which is especially in Africa and
so on and I want to try to understand so
people have put lots of effort in trying
to
understand why do we have these
differences and so I'm going to expand a
little bit the model we have H to show
you few things people have explored and
and then I'm going to conclude that
those things that people have explored
sort of can't explain it either and then
as I'm going to go back sort of to
growth accounting so sort of thing I did
for China there and try to explain what
what what seems to be ER behind all
these big disparities we have in the
world so the first thing I'm going to do
is just it's useful as an exercise even
I'm going to start with h I'm going to
modify the the solo mod a little bit so
this is like the production function I
showed you before but rather than having
n here I'm going to have H and H is just
n our old n population labor for there
but a scale up by this human capital
Factor okay so what this says is that
that human
capital is
really is the population
times something that controls for the
level of schooling of that population
okay so a big candidate for difference
across the world is that you know that
certain populations are far more
educated than others so so
this does exactly that s is an
increasing function of the numbers of
years of schooling and there is a big
micro evidence literature trying to
estimate what is the value of thats what
is the value of an extra unit of
schooling for a human capital and so on
and sort of the estimate depends on what
kind of a schooling are we talking about
is primary secondary thary whatever but
on average that's a number around 0.1
okay so one extra year of schooling
raises sort of human capital by about
10% so the whole population increases
the average by one year
year um that adds about 10% to human
capital so is as if you had increased
population by 10% so it makes a
difference now is it's pretty hard to
raise for a country one year of
schooling for the average takes a lot of
time but when you look in the
crosssection there's huge difference
across the world between numbers of
years of schooling and that accounts for
a big part of the difference in income
per
capita anyways so let me um do a balanc
growth exercise with this this expanded
Model H and see how far we can get so so
the first thing I'm going to do is I'm
going to normalize everything by
effective work sorry by workers okay so
I'm going to divide every all the
variables I'm going to show you are
going to be divided by
n
now notice that I'm dividing by n not by
a * n or a *
H
or so so there's a difference with the
previous analysis and I I can always
divide and the model we had I can always
divide by whatever I want all my
variables I divided by effective workers
because I wanted to have a diagram where
the curves were not moving around but I
can divide by whatever I want and and
and I will divide by different things
depending on the analysis I want to
conduct now I know that once I divide by
population only not by a times
population and education perhaps H I
cannot draw my previous diagram the the
diagram with the saving uh output per
per effect per worker and so on because
those curves are going to be moving so
it's not very friendly but I can divide
by whatever I want and I had I'm I want
to divide here by just population so
little H will be simply a big H divided
by n okay remember that big H was just e
to U time n so that's that output per
worker will be just the will be K
Capital divided by n and here is Big H
divided by n which is little H okay so
all this now is measured as output per
worker or per
population per
person now remember what I can do here
is then I know that the rate of growth
of output per person is going to be
equal to 1 minus Alpha times the rate of
growth of capital per person plus Alpha
time the rate of growth of a Time the
rate of growth of age in which age is is
this H years of schooling
transformation okay now if you think
about the steady state H it doesn't make
any sense that GH at some point will
become zero I mean we can increase
education but at some point we cannot be
all going to you know 150 years of
education so that is unlike capital and
things like that you can increase for a
while education but but at some point
there's a limit I mean you're not going
to do a post post post post PhD blah
blah blah okay so in the stady state we
know that eventually in the long run
this GH is equal to zero so this this
economy we expanded to include years of
schooling has the same sort of balanced
growth characteristics of the economy I
just showed you before okay so that that
in that economy Capital per person will
grow at the rate GA and output per
person will grow at the rate GA output
will grow at the rate GA plus GN so
exactly the same as we had before not
not not so up to now adding human
capital doesn't change our conclusions
about balanced growth it will change
some conclusions that are important
that's the reason I'm introducing this
variable but doesn't change this this
conclusion so this model which is a
little expansion of the previous model
we had has the same balanced growth
characteristics as the model I show you
before
so let me do a little bit of algebra
with it h so from the capital
accumulation equation I know that so let
me remember the capital accumulation now
written in in
per in per per person will be H you
know KT + one this is remember little K
minus
KT equal to
s * y
d
minus Delta plus
n
k
t wait why do I have a Delta plus n
minus plus GA there remember that in the
previous mod I have a Delta plus n plus
GA
there did I make a mistake
actually this is a useful exercise for
you you remember they had a Delta plus n
plus plus G there
no what's
wrong I just told you that this economy
at least in balanced growth is exactly
the
same so you make a mistake
no the reason I had the ga there is
because I was looking at the change in
capital per effective worker I'm looking
now at the change in capital per worker
not per effective worker so I don't have
that a in the denominator so I don't
need to account for the rate of growth
of the denominator due to an increase in
technology I don't need that so but I
that also means well and and so what I
can do is you know divide both sides by
KT that's
KT and this
is the rate of growth of K no is the
rate of growth of
K but in a steady state the rate of
growth of K Capital per worker is equal
to what
GA is the rate of growth of Technology
that's the so this in a state state this
is equal to
G
okay and so what I wrote there is I
think should be exactly
that is it yes good okay that's what I
did and what did I do why did I do this
for well because now I can you know you
know that I can know I can measure Delta
Del Delta is a yeah I can measure Delta
I can measure n
h um and I can measure
GA so this implies that I can solve out
in a steady state for what is the level
of capital per ER effective worker okay
that I can solve from this equation and
it's equal to this expression here
notice a few interesting things here is
capital per effective worker each of
them is divided by n so I can also look
at Big K over a times big h no h is
increasing in the saving
rate that you already had in the model
we discussed before if the saving rate
is higher then the you're going to end
up with a higher Capital ER perir
effective worker ratio in yesterday's St
is decreasing in population growth you
all these things you already saw before
okay so now that I have this expression
for K Over H I can go back to my
production
function to this and sticking
there this this value and I get that
output at time T once you're in the
balance growth path is equal to a t time
h
time K over a h to 1us Alpha just just
solve for that and the point being is
that now I can write this as YT is equal
to a times e to so human capital times
this expression here so human the point
is human capital doesn't affect the
stady state growth but it does affect
the income per capita that you have have
and it makes a big difference I'll show
you
okay so when people try to explain
difference across the world they notice
that they were missing a big component
and and that big component is
education so let's compare what I want
to do next is you know I can do this for
every country in the world okay and I
can compare it with the
US okay I can do this for every every
country in the world and let's compare
it with and I can compare it with any
other country in the world but just you
know let's compare it with the largest
country in the world in terms of output
that's a us so let's let's see what we
get so so I'm going to take output per
capita in everywhere and divided by the
same expression for the
US and I'm going to Define that variable
as y i hat so for Country I say
Singapore okay we take output per capita
and we divide it by output per capita
per person in in the
us assume big if you see is a huge if
that but you can do that for you know
the US versus Singapore probably is not
a crazy assumption to make H assume that
they have the same rate of technological
progress and the same technology and so
on well the same rate of technological
progress I'm going to assume that for
now so then this why I had a you can
write this it's just a this for
Singapore divided by this for the
US it shows it turns out to be this
expression here
okay
so solo did something like this and said
okay H assume that technology is the
same across the world because you know
at least for major Economist technology
sort of can be imported and and and can
we can have the same the same uh
um more or less the same technology
across the world so assume that this guy
is equal to one and that both Singapore
and and the US have the same rate of
growth okay and so that means
er um that you know countries that have
higher saving rate will tend to have we
know that in Bal go will tend to have
higher output per capita so if Singapore
has a higher saving rate than the US
that will tend to give Singapore a
higher income per capita okay if country
has a a higher population growth then it
will tend to have a lower income per
capita and and so on so forth and so the
question is well suppose you make this
Assumption of equal technology and take
this take the the we can measure the
saving rate in different parts of the
world the population rates in different
part of the world and we're assuming
that the same rate of technological
progress everywhere how much of the
difference we observe in income per
capita across the world can be accounted
by that okay so that's that was the
first question is well suppose that that
the technology is the same but we
measured all these other things saving
rate population growth H common rate of
technological progress common
depreciation across the world and so on
how much can we explain of the income
disparity and the conclusion is the
following the conclusion of that
experiment is that if that if if the
only difference
behind PE incomes per capita were sort
of years of schooling sorry a key thing
that I me that I forgot to measure is
years of schooling so know if a country
has more years of schooling will tend to
have a higher income per capita and so
on so if you try to explain the
differences in income per capita across
the world using variables like years of
schooling H difference in Saving rate
difference in population growth and so
on the world would be a lot more
egalitarian than it actually is it would
look a lot more flatter okay so this is
how much you can account here you put a
bunch of lots of countries you know
Africa and so on here and if you just
stick in the in the equation their
corresponding saving rate education
levels and so on the world would be a
lot more similar there wouldn't be the
kind of disparities we see between some
African countries and and and Singapore
say we're talking about Singapore okay
but the world doesn't look like that
that's the point so so if you take all
these things that make a lot of sense
education saving rate blah you're going
to explain a small share of the of the
differences in income per capita across
the world ah sorry in this this plot
here L is our
n l labor is our n so this y Over N our
little Y in this
so so not so we can't get so far we need
something else so what else do we need
to uh to add to really explain the
amount of disparity we
have
well this the answer is again the solo
residual it turns out that the
assumption that A's are the same across
the world that the level and the rate of
grows are the same around around the
world is just
a very bad assumption okay the level of
Technologies are very different across
different parts of the world so the next
step was say okay let's measure the
difference in Technologies across the
world and it turns out that if you try
to explain so if you go out there and
you measure the level of Technology
across the world different places no uh
Zimbabwe
Singapore South Korea and so on so forth
well and then you plot that the level of
Technology the countries have visis
their output per capita per worker you
expain a big share of it okay so here is
what you have is the relative a so
everything is related to the US here
okay so the the a that we measure the
level of a that we measure I don't
remember which year was this
19 I don't remember when it was that
doesn't matter H so if you measure the
the relative level of technology in
country ey relative to the
US and then you measure the relative
output per capita in that country
related to the US and forget about
everything else educational so on so
forth you can get a pretty good
relationship between the two okay so
between one one half and two third of
the difference in output per worker
across different countries in the world
can be attributed to the difference in
technology level okay so that's the
conclusion that we
have now let me revisit the the this
issue of
convergence ER and and so if you if you
what you do is you take countries that
have more or less the same
a and that have more or less the same
levels of
education then and you look at sort of
their their the path of their output per
capita you get that the models we have
been discussing here work St well okay
so here you see that you know they're
more or less growing together there are
Wars and stuff like that here so so
there are great recessions and things
like that but on average you see sort of
the countries that that were behind sort
of cut up and so on okay big dispers
here they were all growing together and
as more time passes the closer they get
to each other because you know they're
converging these guys the US and the UK
were already sort of very close to the
stady state very in 1870s while Japan
was way behind but it was sort of in the
same class of countries in terms of
technology and in terms of H education
levels and so
on so it works pretty well H this is H
for for more
countries and you you plot per capita
income in 1870 again for countries that
have similar A's and K's uh
A A and H and you look at the rate of
growth and you get exactly what you
would expect countries that were further
behind CAU up that's Japan very fast
rate of growth and you get this very
negative relationship okay so this is
the convergence model it works extremely
well conditional on having the same a
and AG so that's the contribution of
this lecture it tells you I already told
you that this convergence model Works
quite well the point is now that it
works very well and I had told you early
on I think in the first lecture on
growth that this work very well for
certain kind of countries but then when
we put all of them together there were
some countries that were clearly off and
they were mostly in Africa but you had
countries that had low per capita income
and they grew very little during that
the sample I show you so here I'm
refining that I'm saying okay now I'm
going to tell you a little bit more what
I mean by countries being similar and
what I mean here is that they have
similar A and H okay so when I look at
countries that have similar A and H they
work the models we have discussed work
extremely
well this is over a shorter period of
time so you have more fluctuations and
more countries but still and you know
you can argue that Mexico and Chile
probably do not belong with many of
these other countries but you still get
this negative relationship is quite
clear now if you don't control by A and
H you put everything together then the
plot looks like the plot I showed you
earlier okay so if I control by A A and
H the moles work very well if I don't
control for a andh then the M do not
look that nice
okay so this led to a literature which
is called the conditional convergence
literature and the idea it's almost
accounting but the idea is the following
so so the question that that that was
behind this literature is well why is it
that we have some countries
say here no that have a very low income
per capita and grow very slowly that's a
puzzle how can it happen that we have
that and the the the the story but again
it's more accounting than an explanation
in my view is is what is called
conditional convergence says for some
reason probably has to be explained in
terms of you know institutions political
instability or whatever for some reason
some countries have just lower steady
state levels of Technology lower steady
States because they they have lower
Technologies and they're stuck with
lower Technologies and so on okay uh
so so what this literature does is says
okay let's compute the St state so let's
accept that some countries will have
lower level of Technology that's what it
is maybe at some point they'll flip from
there but you know they have been for a
long time in in in a stock that let's
assume that they have have a different
level of technology so that means let's
compute for each country its steady
state its own steady state using its own
technology and its own level of
Education
okay
so so in particular this in this plot
I'm going to show you er er take the
values the value of a for 1970
that's the plot I'm going to show you
the Valu that each country had in 1970
compute the state state level of output
corresponding to that
a
okay a and over time it will be growing
at GA whatever but but take the a of
1970 compute the state value of
that compare it with the current output
over that if the current output is below
that that means that the this country
still needs to catch up have not with
respect to some Universal stady state
but with respect to its own stady state
with its lower technology and whatever
okay and
then look at whether we see convergence
or not and the answer is that you start
recovering a this downward sloping curve
so what does this say what is the the
big story is telling us it's saying look
some countries for reasons that are
Beyond this mold just simply have much
Lower State States
yeah they have lower Technologies they
don't know how to use more complicated
technology I don't know well but that's
what it is they have lower Technologies
and so they have their own stady states
which can be stady states with very low
levels of income per
capita now for those countries it still
applies and that's what this picture
shows that if they are not at their
state state still have lower Capital per
war effect worker than they need to have
in their stady state that they will have
transitional growth so they will grow
faster than their growth in the in in in
in their own steady
state and that's what this picture shows
you you know these are countries that
that grew very little look at we have
Japan here together with bwan I think
ER and maybe Taiwan in the same in the
same place okay so these are countries
that still have lots of grows to do
relative to their own stady State and
they did grow a lot we know how do I
know that well because the output I
compute the output I compute relative to
a steady state at the beginning of my
sample was much lower than one that
means that that you're not at your St
State
no so this variable here is the output
you have at the beginning of the sample
relative to what the steady state your
steady state is how do you compute the
stady state well you input the level of
Technology you input the saving rate you
input the population growth and all
these kind of things so you have a
number lower than one means you still
have catching up growth to do not with
respect to the global Universal aady
state but with respect to your own aady
State and when you do that you see that
some countries that in the s in the
total sample look like they're not
growing and so on so forth they are
growing they're just
growing you know relative to their own
stady state which has little growth and
it has low levels of technology and so
on and so that's a conclusion of this
conditional convergence literature now
it turns out that that that the world
has become very unequal also on this
Dimension over time this this shows you
the ratio of GDP per worker of the 90th
percentile to the 10th percentile
country and so you have not only big
difference in technology across the
world but also you have very different
rates of growth in techn technology
across different countries on the world
so this difference is sort of increasing
quite dramatically
okay I don't know what happened
here but
uh I mean I'm saying so the world
started with with count this is telling
you it started with countries that you
know were richer than others and that
distance has been rising over
time but sort of towards the end we
began to change
here I think that has a lot to do with
China that was a poor economy that grew
very fast During the period and it
wasn't very large here so it didn't
matter as much but then it began to
count a lot I think I'm not completely
sure that's it anyways but that's the
state of knowledge in this I mean
obviously there's a big literature
around follow of this and and very
complex even literature but but there's
we understand we know that that that we
have a you know good ways of explaining
how a country converges to its own EST
State ER that we have very poor models
certainly within economics if go
to um within growth Theory per
se there there a l institutions and
stuff like that explain some of that but
we have very poor models in general H to
understand sort of what
gives rise to this big
disparity in in the in technology
adoption and so
on so that's all that I want to say
about growth the next topic is we're
going to open the economy we're going to
go back to the type of models we had
very early on but now in the context of
an open economy