Advertisement
47:01
Lecture 16: Convergence and Cross-Country Variation
MIT OpenCourseWare
·
May 11, 2026
Open on YouTube
Transcript
0:17
okay let's uh let's start um So the plan
0:21
for today is to wrap up this growth uh
0:25
Theory section of the of the course and
0:28
um I I I want to sort of
0:31
conclude by showing you what we can and
0:34
cannot explain with the mods we have
0:35
looked up to now and almost as a matter
0:38
of accounting I will tell you what do we
Advertisement
0:41
need to fill which gaps do we need to
0:43
fill in order to explain sort of the
0:45
great dispersion we see in income per
0:48
capita across the world um but before I
0:51
do that I need to finish the previous
0:57
lecture and so let me let me do that H I
1:01
had shown you this table remember in the
1:03
in the complete model the model that has
1:05
a a productivity growth unemployment and
1:09
and and population growth um we
Advertisement
1:13
concluded that imbalanced growth H the
1:16
following happened no uh obviously if we
1:19
pick the right normalization the right
1:21
normalization here was ER effective
1:24
workers so that productivity
1:27
productivity times a population or
1:30
workers and so if we normalize the
1:32
variables by that H we get obviously
1:35
zero growth that's what it means to have
1:37
a balanced growth in which all the
1:39
relevant variables are growing at the
1:40
same rate H so Capital per effective
1:44
worker will will be a state that's
1:47
that's a diagram we plot remember the
1:48
diagram we plot was output per effective
1:52
worker against Capital per effective
1:54
worker and that diagram has a steady
1:56
state okay and that steady state at the
1:59
steady state or the balance growth point
2:01
then we have that H the normalized
2:04
variables grow at the rate of zero
2:07
Capital per worker has to grow at the
2:09
rate G GA because Capital per effective
2:12
worker is not growing so Capital per
2:14
worker will be growing at the rate GA
2:17
the same applies for output per worker
2:19
output per effective worker is not
2:21
growing that's balanced growth but
2:23
therefore output per worker will be
2:25
growing at the rate
2:27
GA um
2:29
these are the exogenous drivers a you
2:32
know output per worker we assume no a
2:36
well sorry labor is is GA is exogenous
2:40
in this model and so is GM population
2:42
growth is some constant we take it's not
2:45
something we try to explain within the
2:46
model okay but the two drivers of
2:49
absolute growth will be GA and GN and so
2:52
capital in the St state will be growing
2:54
at the rate GA plus GN output will be
2:57
growing at the rate GA plus GN so that's
2:59
balance grow okay now let me give you an
3:02
example so you can do see that suppose
3:04
that our production function is is this
3:07
we call that the a cop Douglas
3:09
production
3:10
function K to the 1 minus Alpha a n to
3:14
the alpha does this function have
3:15
constant
3:17
returns to scale yes the sum of the
3:20
exponents is one okay anyways but so uh
3:25
take the log of both sides the change in
3:27
the log is the rate of growth and so you
3:30
get that the rate of growth of output is
3:32
equal to 1 minus Alpha the rate of
3:33
growth of capital plus Alpha time the
3:36
rate of growth of effective workers okay
3:39
so in balanced growth GK will be growing
3:42
at the rate GA plus GN and therefore
3:44
output will also be growing at the rate
3:46
GA plus GN okay so that's what you have
3:48
in the table and if you want to look at
3:51
a variable like this Capital per worker
3:54
then output per worker then you you need
3:57
G gy minus GN
3:59
H so subtract the GN and you can
4:02
subtract both sides then it's going to
4:03
be equal to GA okay I subtract GM from
4:06
the right hand side H this one and that
4:09
one cancel and I get GA on the right
4:12
hand side that's the way you use that
4:14
expression to fill all this all these
4:16
blanks okay that's the that's St so I I
4:21
think I stopped right before that this
4:24
this slide or at this slide which is you
4:27
know if I look at this the table GN is
4:30
pretty easy to compute in most places
4:33
there are places in the world where we
4:34
sort of cannot even measure birth and
4:36
death so it's difficult but in most
4:39
places H you can measure GN the rate of
4:42
FR of population H quite accurately and
4:45
the question we have though is how do we
4:47
measure technological progress It's also
4:48
easy to measure the growth in the stock
4:51
of capital it's investment minus
4:53
depreciation uh but how do we measure H
4:56
GA no the rate of technological progress
5:00
and uhh the first proposal on how to do
5:03
it was also by Bob solo H that was a
5:07
second contribution he had in this in
5:09
growth Theory well it was also growth
5:11
measurement how do we measure GA it
5:13
turns out that the only way you're going
5:14
to have output per capita growing over
5:16
time outut person growing over time is
5:19
due to GA so we might as well try to
5:21
measure that since it's such an
5:23
important variable for sort of the
5:26
growth of er the growth of uh happiness
5:31
if you get one indicator of happiness is
5:33
output per C per worker well such an
5:36
important driver we need to be able to
5:37
measure it and and the basic idea that
5:40
Bob solo had is is essentially something
5:42
you could have taken from
5:43
1401 it's extremely simple it says ER
5:49
there are some assumptions behind this
5:51
but you know in in the basic competitive
5:53
model you have that that um you can
5:57
compute the contribution of each each
5:59
factor of production to to Output H by
6:04
the payment it receives okay so under
6:08
this assumption no suppose that that
6:11
you're spending in workers
6:13
$30,000 a
6:15
year so that means in a competitive
6:18
equilibrium in the labor market and so
6:20
on that the worker is contributing to
6:22
production
6:24
$30,000 okay I'm not going to deal with
6:26
markups and things like that here but
6:28
that's a basic idea you can adjust all
6:30
these formulas to include markups but
6:32
let me not do that so that also tells
6:36
you that if you increase
6:41
um er employment by 10% you'll also
6:45
going to increase output by 10% times
6:50
whatever is the contribution of Labor to
6:52
Output okay and that's what I have here
6:54
the contribution of H to Output of
6:59
adding workers is going to be that times
7:02
Delta n i can divide by H by y both
7:07
sides and here multiply and divide by n
7:10
and I get that the the the rate of the
7:13
the the rate of growth in
7:16
output due to a a a rate of growth in
7:22
employment is equal to the labor share
7:24
that's called the labor share is the
7:26
wage Bill W * n divided by total total
7:30
uh Revenue uh sales and uh uh times the
7:36
rate of growth of H population or
7:39
workers is the same here so I'm going to
7:42
call this GYN it's the rate of growth of
7:45
output due to the rate of growth in
7:48
population is equal to this this labor
7:51
share which I'm going to call that Alpha
7:54
times GM okay I can do exactly the same
7:58
with capital
8:00
and you can do if you have more factor
8:01
of production you can do the same for
8:02
each factor of production so but in this
8:05
simple example we have only two factors
8:07
of production labor and capital so I can
8:09
do the same for Capital and I can say
8:12
the contribution of of Capital Growth to
8:16
Output growth is going to be equal to
8:18
the capital share which is the compl of
8:20
the labor share so it's it's total
8:23
revenue minus the wage wage payment the
8:26
wage Bill divided by total revenue h
8:29
times the rate of growth of capital okay
8:32
so the contribution of H to Output
8:35
growth of the rate of growth of capital
8:38
is is 1 minus Alpha which is the share
8:40
of capital times uh the rate of growth
8:44
of capital okay so that means if I sum
8:48
the
8:49
contribution of Labor and capital I have
8:53
I I'm left with the residual which is
8:56
whatever is the rate of growth I have in
8:57
output I know how much I'm getting from
8:59
labor I know how much I'm getting for
9:02
Capital if there is any difference it
9:03
must be due to that thing I don't not
9:05
observe which is technological progress
9:08
okay that's the logic of all this
9:12
stuff go back for example to this
9:14
production function I'm saying I know
9:16
the contribution that K has to Output
9:20
growth I know the contribution that n
9:22
has to Output growth well the only thing
9:25
I'm missing is the contribution that a
9:27
has to Output growth which say don't
9:29
observe but I observe output growth I
9:32
observe Capital Growth I observe
9:34
employment growth so I can solve out
9:36
what
9:37
is the technological technological
9:39
progress a growth okay and that's that's
9:43
called it's called the solo residual by
9:45
the way okay but that's the way the rate
9:48
of growth of GA of a is measured the
9:50
rate of growth of output minus the
9:52
contribution to growth of er employment
9:56
population and capital
10:01
any question about
10:03
that no makees
10:05
sense
10:07
somewhat okay good so anyway so there's
10:11
a huge industry of measuring these kind
10:13
of things of course uh let me give you
10:17
an
10:18
example h on how to use this accounting
10:22
um so China 78 2017 that's an episode in
10:27
which China was growing very very
10:28
strongly
10:30
ER on
10:32
average China grew at over 7% out
10:36
progress over
10:37
7% now by the formula I showed you
10:40
before if I ask you the question well
10:43
what was behind that growth how much was
10:46
a contribution of Labor how much was a
10:48
contribution of capital and how much was
10:50
a contribution of technological progress
10:53
well there are some things we can
10:55
measure fairly well population growth
10:57
during this period in China was around
10:59
1.7% per
11:01
year there was a massive amount of
11:05
investment the Capital stock was growing
11:07
at a rate of
11:08
99.2% per year and the residual you can
11:12
compute it using the solo approach H is
11:15
around
11:17
4.2% okay so that 7.2% is a result of
11:21
the weighted average of these three
11:24
things okay so that's basic explanation
11:28
of ER the growth in China during that
11:32
that period now just looking at this not
11:36
don't look at at the
11:38
diagram what jumps immediately just if
11:42
you just look at this
11:46
part what jumps to you
11:49
immediately let me ask you differently
11:51
does it look like balanced
11:56
growth do you think that that that's
11:59
balanced growth that in other words do
12:02
you think that China had a arrived to
12:05
its state and and that growth is a
12:08
result of what was happening in that
12:11
stady
12:16
state
12:18
no but what is it that
12:20
looks that tells you that that that's
12:23
not the same
12:26
state balanc growth is when everything
12:29
everything is growing at the same rate
12:30
no everything you have you know
12:34
meaning all the endogenous
12:37
variables ER unnormalized are growing at
12:41
the same at the same rate as the
12:44
exogenous
12:47
variables so what is it that it would
12:49
nearly jump to me here is say
12:54
7.2% that's less than than the rate of
12:57
growth of capital
12:59
so so I know that there Capital over
13:02
output was Rising so that's not a state
13:04
state I know that I can see it in a
13:08
different way I know that in a steady
13:12
state in balanced
13:14
growth the rate of growth of output and
13:17
of capital should be the sum of the rate
13:19
of growth of population plus the rate of
13:22
technological
13:24
progress okay that's
13:27
5.9% but capital was growing at
13:31
99.2% not
13:34
5.9% so I do know that that's a period
13:36
in which China was growing
13:40
Beyond its steady state or balanced
13:42
growth rate of
13:44
growth and I know more than that I know
13:47
that the reason that was happening is
13:48
because there was more capital
13:50
accumulation than you would expect in
13:52
the stady
13:54
state when are you likely to see a
13:56
situation like that in which capital
13:59
accumulation is faster than the rate of
14:01
growth of capital in the St State and
14:03
it's faster than the rate of growth of
14:04
output that is that's a a period in
14:08
which we have transitional growth been
14:10
pulled you know growth above the state
14:14
state growth is being pulled by capital
14:18
accumulation when does that
14:27
happen do to mind first is economies are
14:31
like transitioning from command market
14:33
economies I believe and also the second
14:36
thing that comes to mind is potentially
14:39
um um countries recovering from like War
14:44
periods okay that's a deep deep deep
14:47
answer I wanted something simpler which
14:49
is
14:51
what I I want to say so the economy is
14:54
not in a state state that's clear but
14:57
what do we also know we know that the
14:59
Capital stock is below its stady state
15:01
level and that could be as a result of
15:04
of the the things you described you had
15:07
a war so your Capital stock was wiped
15:09
out or H you had a period in which
15:12
saving rate was very low and now you're
15:14
going to high saving rate episode with
15:17
that a lot of that is what happened in
15:19
in souis Asia in particular actually was
15:21
a fast increase in the rate of in the
15:23
say a sharp rise in this in the saving
15:26
rate but the bottom what I so what I had
15:28
in mind is for one of these reasons
15:32
that's a situation where the initial
15:33
Capital stock was below the stady state
15:35
and so you have a period of transitional
15:37
growth in which investment rate is more
15:39
than you need to do to maintain the
15:41
stock of capital per effective worker
15:44
know there's a positive gap between the
15:47
the green line and the and and the and
15:49
the red line and that's what leads you
15:51
transitional growth until you reach a c
15:54
state if things do not change meaning
15:58
population growth remain the same as in
16:01
that period and the and the the rate of
16:05
technological progress Remains the Same
16:07
As in that period we know that the
16:09
balanced growth rate of China is
16:12
5.9%
16:15
okay it's 5.9 because it's 07 plus
16:20
0.42 now so so that 7.2% average there
16:25
you're likely to see it and actually
16:26
there's an average that has numbers like
16:28
15 % very early on H to close to 6% or
16:33
so on the last stage H so that's that's
16:38
would be a stady state now that I think
16:40
is an
16:41
overestimate because H uh we know the
16:45
rate of population growth is declining
16:46
very rapidly in China it's turning
16:48
negative okay so so so for the rate of
16:51
growth of output China is going to is
16:53
unless there's a big change in
16:54
technological progress in the process of
16:56
technological progress it's going to be
16:58
pretty difficult for China to grow a lot
17:00
more than 5% I think going forward and
17:04
that creates some problems but but
17:07
that's what it is that's what this model
17:08
tells you you need to change something
17:10
and the things you can change in this
17:11
model are what well you could induce
17:13
higher saving rate you would get more
17:15
transitional growth out of that more
17:17
capital accumulation that's costly that
17:19
means less consumption and so on H or it
17:23
could be some technological breakthrough
17:25
but that's a probably would affect the
17:27
whole world in any event but that's the
17:30
kind of things you
17:32
okay good so that's that's
17:36
uh so
17:38
so is is the models we have developed
17:41
here sort of are quite good to explain
17:44
you know uh catching up processes
17:47
catching up growth and and and to
17:49
understand what are the where are
17:51
economies converging o over
17:54
time what I want to next is I I want to
17:58
end up trying to explain remember one of
18:00
the plots I showed you very early on is
18:02
that there's great
18:04
dispersion H in income per per person
18:07
per capita across the world and also
18:09
some countries are sort of not catching
18:11
up and which is especially in Africa and
18:15
so on and I want to try to understand so
18:17
people have put lots of effort in trying
18:19
to
18:20
understand why do we have these
18:22
differences and so I'm going to expand a
18:24
little bit the model we have H to show
18:27
you few things people have explored and
18:30
and then I'm going to conclude that
18:32
those things that people have explored
18:34
sort of can't explain it either and then
18:37
as I'm going to go back sort of to
18:39
growth accounting so sort of thing I did
18:42
for China there and try to explain what
18:46
what what seems to be ER behind all
18:49
these big disparities we have in the
18:51
world so the first thing I'm going to do
18:53
is just it's useful as an exercise even
18:57
I'm going to start with h I'm going to
18:59
modify the the solo mod a little bit so
19:01
this is like the production function I
19:03
showed you before but rather than having
19:05
n here I'm going to have H and H is just
19:10
n our old n population labor for there
19:14
but a scale up by this human capital
19:17
Factor okay so what this says is that
19:22
that human
19:23
capital is
19:26
really is the population
19:29
times something that controls for the
19:31
level of schooling of that population
19:34
okay so a big candidate for difference
19:36
across the world is that you know that
19:37
certain populations are far more
19:38
educated than others so so
19:42
this does exactly that s is an
19:45
increasing function of the numbers of
19:47
years of schooling and there is a big
19:49
micro evidence literature trying to
19:52
estimate what is the value of thats what
19:54
is the value of an extra unit of
19:56
schooling for a human capital and so on
20:00
and sort of the estimate depends on what
20:02
kind of a schooling are we talking about
20:03
is primary secondary thary whatever but
20:05
on average that's a number around 0.1
20:08
okay so one extra year of schooling
20:11
raises sort of human capital by about
20:14
10% so the whole population increases
20:16
the average by one year
20:19
year um that adds about 10% to human
20:22
capital so is as if you had increased
20:25
population by 10% so it makes a
20:27
difference now is it's pretty hard to
20:30
raise for a country one year of
20:33
schooling for the average takes a lot of
20:35
time but when you look in the
20:37
crosssection there's huge difference
20:38
across the world between numbers of
20:40
years of schooling and that accounts for
20:42
a big part of the difference in income
20:44
per
20:46
capita anyways so let me um do a balanc
20:51
growth exercise with this this expanded
20:53
Model H and see how far we can get so so
20:58
the first thing I'm going to do is I'm
20:59
going to normalize everything by
21:00
effective work sorry by workers okay so
21:05
I'm going to divide every all the
21:06
variables I'm going to show you are
21:08
going to be divided by
21:09
n
21:12
now notice that I'm dividing by n not by
21:16
a * n or a *
21:19
H
21:22
or so so there's a difference with the
21:24
previous analysis and I I can always
21:27
divide and the model we had I can always
21:30
divide by whatever I want all my
21:32
variables I divided by effective workers
21:34
because I wanted to have a diagram where
21:36
the curves were not moving around but I
21:39
can divide by whatever I want and and
21:42
and I will divide by different things
21:43
depending on the analysis I want to
21:45
conduct now I know that once I divide by
21:47
population only not by a times
21:50
population and education perhaps H I
21:53
cannot draw my previous diagram the the
21:56
diagram with the saving uh output per
21:59
per effect per worker and so on because
22:01
those curves are going to be moving so
22:03
it's not very friendly but I can divide
22:05
by whatever I want and I had I'm I want
22:07
to divide here by just population so
22:09
little H will be simply a big H divided
22:14
by n okay remember that big H was just e
22:17
to U time n so that's that output per
22:22
worker will be just the will be K
22:26
Capital divided by n and here is Big H
22:31
divided by n which is little H okay so
22:33
all this now is measured as output per
22:37
worker or per
22:40
population per
22:42
person now remember what I can do here
22:45
is then I know that the rate of growth
22:47
of output per person is going to be
22:49
equal to 1 minus Alpha times the rate of
22:52
growth of capital per person plus Alpha
22:55
time the rate of growth of a Time the
22:58
rate of growth of age in which age is is
23:02
this H years of schooling
23:05
transformation okay now if you think
23:07
about the steady state H it doesn't make
23:10
any sense that GH at some point will
23:12
become zero I mean we can increase
23:14
education but at some point we cannot be
23:16
all going to you know 150 years of
23:19
education so that is unlike capital and
23:22
things like that you can increase for a
23:25
while education but but at some point
23:27
there's a limit I mean you're not going
23:28
to do a post post post post PhD blah
23:31
blah blah okay so in the stady state we
23:34
know that eventually in the long run
23:36
this GH is equal to zero so this this
23:40
economy we expanded to include years of
23:43
schooling has the same sort of balanced
23:46
growth characteristics of the economy I
23:47
just showed you before okay so that that
23:50
in that economy Capital per person will
23:54
grow at the rate GA and output per
23:57
person will grow at the rate GA output
23:59
will grow at the rate GA plus GN so
24:01
exactly the same as we had before not
24:04
not not so up to now adding human
24:06
capital doesn't change our conclusions
24:09
about balanced growth it will change
24:12
some conclusions that are important
24:14
that's the reason I'm introducing this
24:15
variable but doesn't change this this
24:18
conclusion so this model which is a
24:20
little expansion of the previous model
24:21
we had has the same balanced growth
24:23
characteristics as the model I show you
24:27
before
24:28
so let me do a little bit of algebra
24:31
with it h so from the capital
24:33
accumulation equation I know that so let
24:38
me remember the capital accumulation now
24:41
written in in
24:43
per in per per person will be H you
24:49
know KT + one this is remember little K
24:54
minus
24:56
KT equal to
25:00
s * y
25:04
d
25:06
minus Delta plus
25:09
n
25:11
k
25:14
t wait why do I have a Delta plus n
25:17
minus plus GA there remember that in the
25:20
previous mod I have a Delta plus n plus
25:23
GA
25:26
there did I make a mistake
25:33
actually this is a useful exercise for
25:37
you you remember they had a Delta plus n
25:40
plus plus G there
25:43
no what's
25:46
wrong I just told you that this economy
25:48
at least in balanced growth is exactly
25:50
the
25:51
same so you make a mistake
26:01
no the reason I had the ga there is
26:04
because I was looking at the change in
26:07
capital per effective worker I'm looking
26:10
now at the change in capital per worker
26:12
not per effective worker so I don't have
26:13
that a in the denominator so I don't
26:16
need to account for the rate of growth
26:17
of the denominator due to an increase in
26:21
technology I don't need that so but I
26:24
that also means well and and so what I
26:27
can do is you know divide both sides by
26:32
KT that's
26:37
KT and this
26:43
is the rate of growth of K no is the
26:47
rate of growth of
26:51
K but in a steady state the rate of
26:54
growth of K Capital per worker is equal
26:56
to what
27:01
GA is the rate of growth of Technology
27:04
that's the so this in a state state this
27:09
is equal to
27:12
G
27:14
okay and so what I wrote there is I
27:17
think should be exactly
27:18
that is it yes good okay that's what I
27:24
did and what did I do why did I do this
27:27
for well because now I can you know you
27:31
know that I can know I can measure Delta
27:34
Del Delta is a yeah I can measure Delta
27:36
I can measure n
27:39
h um and I can measure
27:43
GA so this implies that I can solve out
27:49
in a steady state for what is the level
27:52
of capital per ER effective worker okay
27:57
that I can solve from this equation and
28:00
it's equal to this expression here
28:02
notice a few interesting things here is
28:05
capital per effective worker each of
28:07
them is divided by n so I can also look
28:09
at Big K over a times big h no h is
28:14
increasing in the saving
28:16
rate that you already had in the model
28:18
we discussed before if the saving rate
28:20
is higher then the you're going to end
28:21
up with a higher Capital ER perir
28:25
effective worker ratio in yesterday's St
28:28
is decreasing in population growth you
28:31
all these things you already saw before
28:33
okay so now that I have this expression
28:38
for K Over H I can go back to my
28:40
production
28:42
function to this and sticking
28:46
there this this value and I get that
28:49
output at time T once you're in the
28:52
balance growth path is equal to a t time
28:56
h
28:58
time K over a h to 1us Alpha just just
29:01
solve for that and the point being is
29:03
that now I can write this as YT is equal
29:06
to a times e to so human capital times
29:10
this expression here so human the point
29:13
is human capital doesn't affect the
29:15
stady state growth but it does affect
29:17
the income per capita that you have have
29:21
and it makes a big difference I'll show
29:23
you
29:26
okay so when people try to explain
29:29
difference across the world they notice
29:31
that they were missing a big component
29:33
and and that big component is
29:36
education so let's compare what I want
29:39
to do next is you know I can do this for
29:42
every country in the world okay and I
29:45
can compare it with the
29:48
US okay I can do this for every every
29:51
country in the world and let's compare
29:53
it with and I can compare it with any
29:54
other country in the world but just you
29:56
know let's compare it with the largest
29:58
country in the world in terms of output
30:00
that's a us so let's let's see what we
30:03
get so so I'm going to take output per
30:06
capita in everywhere and divided by the
30:10
same expression for the
30:12
US and I'm going to Define that variable
30:15
as y i hat so for Country I say
30:20
Singapore okay we take output per capita
30:23
and we divide it by output per capita
30:26
per person in in the
30:28
us assume big if you see is a huge if
30:34
that but you can do that for you know
30:35
the US versus Singapore probably is not
30:37
a crazy assumption to make H assume that
30:41
they have the same rate of technological
30:44
progress and the same technology and so
30:46
on well the same rate of technological
30:48
progress I'm going to assume that for
30:50
now so then this why I had a you can
30:54
write this it's just a this for
30:58
Singapore divided by this for the
31:00
US it shows it turns out to be this
31:04
expression here
31:06
okay
31:08
so solo did something like this and said
31:12
okay H assume that technology is the
31:16
same across the world because you know
31:19
at least for major Economist technology
31:22
sort of can be imported and and and can
31:26
we can have the same the same uh
31:28
um more or less the same technology
31:30
across the world so assume that this guy
31:33
is equal to one and that both Singapore
31:35
and and the US have the same rate of
31:38
growth okay and so that means
31:43
er um that you know countries that have
31:46
higher saving rate will tend to have we
31:49
know that in Bal go will tend to have
31:51
higher output per capita so if Singapore
31:54
has a higher saving rate than the US
31:56
that will tend to give Singapore a
31:59
higher income per capita okay if country
32:04
has a a higher population growth then it
32:07
will tend to have a lower income per
32:10
capita and and so on so forth and so the
32:13
question is well suppose you make this
32:15
Assumption of equal technology and take
32:18
this take the the we can measure the
32:20
saving rate in different parts of the
32:21
world the population rates in different
32:23
part of the world and we're assuming
32:24
that the same rate of technological
32:26
progress everywhere how much of the
32:28
difference we observe in income per
32:31
capita across the world can be accounted
32:34
by that okay so that's that was the
32:36
first question is well suppose that that
32:39
the technology is the same but we
32:42
measured all these other things saving
32:44
rate population growth H common rate of
32:47
technological progress common
32:49
depreciation across the world and so on
32:51
how much can we explain of the income
32:54
disparity and the conclusion is the
32:56
following the conclusion of that
32:58
experiment is that if that if if the
33:03
only difference
33:05
behind PE incomes per capita were sort
33:08
of years of schooling sorry a key thing
33:11
that I me that I forgot to measure is
33:13
years of schooling so know if a country
33:15
has more years of schooling will tend to
33:17
have a higher income per capita and so
33:18
on so if you try to explain the
33:21
differences in income per capita across
33:22
the world using variables like years of
33:25
schooling H difference in Saving rate
33:28
difference in population growth and so
33:30
on the world would be a lot more
33:32
egalitarian than it actually is it would
33:34
look a lot more flatter okay so this is
33:38
how much you can account here you put a
33:40
bunch of lots of countries you know
33:43
Africa and so on here and if you just
33:47
stick in the in the equation their
33:49
corresponding saving rate education
33:51
levels and so on the world would be a
33:53
lot more similar there wouldn't be the
33:56
kind of disparities we see between some
33:58
African countries and and and Singapore
34:00
say we're talking about Singapore okay
34:03
but the world doesn't look like that
34:05
that's the point so so if you take all
34:07
these things that make a lot of sense
34:09
education saving rate blah you're going
34:12
to explain a small share of the of the
34:15
differences in income per capita across
34:16
the world ah sorry in this this plot
34:19
here L is our
34:21
n l labor is our n so this y Over N our
34:26
little Y in this
34:29
so so not so we can't get so far we need
34:32
something else so what else do we need
34:34
to uh to add to really explain the
34:39
amount of disparity we
34:41
have
34:44
well this the answer is again the solo
34:47
residual it turns out that the
34:49
assumption that A's are the same across
34:51
the world that the level and the rate of
34:54
grows are the same around around the
34:56
world is just
34:58
a very bad assumption okay the level of
35:01
Technologies are very different across
35:04
different parts of the world so the next
35:07
step was say okay let's measure the
35:09
difference in Technologies across the
35:12
world and it turns out that if you try
35:15
to explain so if you go out there and
35:16
you measure the level of Technology
35:18
across the world different places no uh
35:23
Zimbabwe
35:24
Singapore South Korea and so on so forth
35:29
well and then you plot that the level of
35:32
Technology the countries have visis
35:35
their output per capita per worker you
35:38
expain a big share of it okay so here is
35:41
what you have is the relative a so
35:44
everything is related to the US here
35:46
okay so the the a that we measure the
35:49
level of a that we measure I don't
35:51
remember which year was this
35:53
19 I don't remember when it was that
35:58
doesn't matter H so if you measure the
36:01
the relative level of technology in
36:03
country ey relative to the
36:05
US and then you measure the relative
36:07
output per capita in that country
36:09
related to the US and forget about
36:11
everything else educational so on so
36:13
forth you can get a pretty good
36:15
relationship between the two okay so
36:18
between one one half and two third of
36:21
the difference in output per worker
36:23
across different countries in the world
36:26
can be attributed to the difference in
36:28
technology level okay so that's the
36:30
conclusion that we
36:32
have now let me revisit the the this
36:36
issue of
36:37
convergence ER and and so if you if you
36:41
what you do is you take countries that
36:43
have more or less the same
36:44
a and that have more or less the same
36:47
levels of
36:49
education then and you look at sort of
36:51
their their the path of their output per
36:53
capita you get that the models we have
36:56
been discussing here work St well okay
36:59
so here you see that you know they're
37:01
more or less growing together there are
37:03
Wars and stuff like that here so so
37:05
there are great recessions and things
37:07
like that but on average you see sort of
37:09
the countries that that were behind sort
37:13
of cut up and so on okay big dispers
37:16
here they were all growing together and
37:20
as more time passes the closer they get
37:22
to each other because you know they're
37:24
converging these guys the US and the UK
37:27
were already sort of very close to the
37:29
stady state very in 1870s while Japan
37:33
was way behind but it was sort of in the
37:35
same class of countries in terms of
37:37
technology and in terms of H education
37:40
levels and so
37:42
on so it works pretty well H this is H
37:47
for for more
37:49
countries and you you plot per capita
37:52
income in 1870 again for countries that
37:55
have similar A's and K's uh
37:58
A A and H and you look at the rate of
38:01
growth and you get exactly what you
38:02
would expect countries that were further
38:04
behind CAU up that's Japan very fast
38:07
rate of growth and you get this very
38:09
negative relationship okay so this is
38:11
the convergence model it works extremely
38:13
well conditional on having the same a
38:16
and AG so that's the contribution of
38:18
this lecture it tells you I already told
38:20
you that this convergence model Works
38:22
quite well the point is now that it
38:24
works very well and I had told you early
38:28
on I think in the first lecture on
38:29
growth that this work very well for
38:32
certain kind of countries but then when
38:33
we put all of them together there were
38:35
some countries that were clearly off and
38:37
they were mostly in Africa but you had
38:38
countries that had low per capita income
38:41
and they grew very little during that
38:44
the sample I show you so here I'm
38:47
refining that I'm saying okay now I'm
38:49
going to tell you a little bit more what
38:50
I mean by countries being similar and
38:53
what I mean here is that they have
38:54
similar A and H okay so when I look at
38:57
countries that have similar A and H they
39:00
work the models we have discussed work
39:02
extremely
39:04
well this is over a shorter period of
39:06
time so you have more fluctuations and
39:08
more countries but still and you know
39:11
you can argue that Mexico and Chile
39:12
probably do not belong with many of
39:14
these other countries but you still get
39:16
this negative relationship is quite
39:19
clear now if you don't control by A and
39:22
H you put everything together then the
39:24
plot looks like the plot I showed you
39:26
earlier okay so if I control by A A and
39:30
H the moles work very well if I don't
39:34
control for a andh then the M do not
39:37
look that nice
39:40
okay so this led to a literature which
39:42
is called the conditional convergence
39:45
literature and the idea it's almost
39:48
accounting but the idea is the following
39:51
so so the question that that that was
39:53
behind this literature is well why is it
39:55
that we have some countries
39:58
say here no that have a very low income
40:03
per capita and grow very slowly that's a
40:05
puzzle how can it happen that we have
40:08
that and the the the the story but again
40:13
it's more accounting than an explanation
40:15
in my view is is what is called
40:17
conditional convergence says for some
40:20
reason probably has to be explained in
40:23
terms of you know institutions political
40:26
instability or whatever for some reason
40:30
some countries have just lower steady
40:32
state levels of Technology lower steady
40:34
States because they they have lower
40:36
Technologies and they're stuck with
40:37
lower Technologies and so on okay uh
40:42
so so what this literature does is says
40:45
okay let's compute the St state so let's
40:49
accept that some countries will have
40:51
lower level of Technology that's what it
40:53
is maybe at some point they'll flip from
40:55
there but you know they have been for a
40:57
long time in in in a stock that let's
41:01
assume that they have have a different
41:03
level of technology so that means let's
41:05
compute for each country its steady
41:08
state its own steady state using its own
41:12
technology and its own level of
41:14
Education
41:15
okay
41:17
so so in particular this in this plot
41:20
I'm going to show you er er take the
41:23
values the value of a for 1970
41:28
that's the plot I'm going to show you
41:30
the Valu that each country had in 1970
41:33
compute the state state level of output
41:35
corresponding to that
41:37
a
41:39
okay a and over time it will be growing
41:42
at GA whatever but but take the a of
41:45
1970 compute the state value of
41:49
that compare it with the current output
41:52
over that if the current output is below
41:54
that that means that the this country
41:56
still needs to catch up have not with
41:58
respect to some Universal stady state
42:00
but with respect to its own stady state
42:02
with its lower technology and whatever
42:04
okay and
42:06
then look at whether we see convergence
42:08
or not and the answer is that you start
42:11
recovering a this downward sloping curve
42:14
so what does this say what is the the
42:16
big story is telling us it's saying look
42:19
some countries for reasons that are
42:22
Beyond this mold just simply have much
42:25
Lower State States
42:28
yeah they have lower Technologies they
42:30
don't know how to use more complicated
42:32
technology I don't know well but that's
42:35
what it is they have lower Technologies
42:38
and so they have their own stady states
42:40
which can be stady states with very low
42:42
levels of income per
42:44
capita now for those countries it still
42:47
applies and that's what this picture
42:49
shows that if they are not at their
42:53
state state still have lower Capital per
42:56
war effect worker than they need to have
42:58
in their stady state that they will have
43:00
transitional growth so they will grow
43:03
faster than their growth in the in in in
43:07
in their own steady
43:09
state and that's what this picture shows
43:11
you you know these are countries that
43:14
that grew very little look at we have
43:16
Japan here together with bwan I think
43:20
ER and maybe Taiwan in the same in the
43:23
same place okay so these are countries
43:26
that still have lots of grows to do
43:27
relative to their own stady State and
43:30
they did grow a lot we know how do I
43:32
know that well because the output I
43:34
compute the output I compute relative to
43:37
a steady state at the beginning of my
43:38
sample was much lower than one that
43:41
means that that you're not at your St
43:43
State
43:44
no so this variable here is the output
43:48
you have at the beginning of the sample
43:51
relative to what the steady state your
43:53
steady state is how do you compute the
43:56
stady state well you input the level of
43:58
Technology you input the saving rate you
44:00
input the population growth and all
44:02
these kind of things so you have a
44:04
number lower than one means you still
44:05
have catching up growth to do not with
44:08
respect to the global Universal aady
44:11
state but with respect to your own aady
44:13
State and when you do that you see that
44:15
some countries that in the s in the
44:17
total sample look like they're not
44:19
growing and so on so forth they are
44:21
growing they're just
44:22
growing you know relative to their own
44:24
stady state which has little growth and
44:26
it has low levels of technology and so
44:28
on and so that's a conclusion of this
44:32
conditional convergence literature now
44:35
it turns out that that that the world
44:38
has become very unequal also on this
44:41
Dimension over time this this shows you
44:44
the ratio of GDP per worker of the 90th
44:47
percentile to the 10th percentile
44:49
country and so you have not only big
44:51
difference in technology across the
44:53
world but also you have very different
44:55
rates of growth in techn technology
44:57
across different countries on the world
44:59
so this difference is sort of increasing
45:01
quite dramatically
45:04
okay I don't know what happened
45:07
here but
45:10
uh I mean I'm saying so the world
45:14
started with with count this is telling
45:15
you it started with countries that you
45:18
know were richer than others and that
45:20
distance has been rising over
45:24
time but sort of towards the end we
45:26
began to change
45:29
here I think that has a lot to do with
45:31
China that was a poor economy that grew
45:34
very fast During the period and it
45:36
wasn't very large here so it didn't
45:37
matter as much but then it began to
45:39
count a lot I think I'm not completely
45:42
sure that's it anyways but that's the
45:44
state of knowledge in this I mean
45:47
obviously there's a big literature
45:50
around follow of this and and very
45:53
complex even literature but but there's
45:57
we understand we know that that that we
46:01
have a you know good ways of explaining
46:04
how a country converges to its own EST
46:07
State ER that we have very poor models
46:11
certainly within economics if go
46:14
to um within growth Theory per
46:18
se there there a l institutions and
46:20
stuff like that explain some of that but
46:22
we have very poor models in general H to
46:26
understand sort of what
46:27
gives rise to this big
46:29
disparity in in the in technology
46:31
adoption and so
46:33
on so that's all that I want to say
46:37
about growth the next topic is we're
46:40
going to open the economy we're going to
46:42
go back to the type of models we had
46:44
very early on but now in the context of
46:46
an open economy
— end of transcript —
Advertisement
