[00:17] okay let's uh let's start um So the plan
[00:21] for today is to wrap up this growth uh
[00:25] Theory section of the of the course and
[00:28] um I I I want to sort of
[00:31] conclude by showing you what we can and
[00:34] cannot explain with the mods we have
[00:35] looked up to now and almost as a matter
[00:38] of accounting I will tell you what do we
[00:41] need to fill which gaps do we need to
[00:43] fill in order to explain sort of the
[00:45] great dispersion we see in income per
[00:48] capita across the world um but before I
[00:51] do that I need to finish the previous
[00:57] lecture and so let me let me do that H I
[01:01] had shown you this table remember in the
[01:03] in the complete model the model that has
[01:05] a a productivity growth unemployment and
[01:09] and and population growth um we
[01:13] concluded that imbalanced growth H the
[01:16] following happened no uh obviously if we
[01:19] pick the right normalization the right
[01:21] normalization here was ER effective
[01:24] workers so that productivity
[01:27] productivity times a population or
[01:30] workers and so if we normalize the
[01:32] variables by that H we get obviously
[01:35] zero growth that's what it means to have
[01:37] a balanced growth in which all the
[01:39] relevant variables are growing at the
[01:40] same rate H so Capital per effective
[01:44] worker will will be a state that's
[01:47] that's a diagram we plot remember the
[01:48] diagram we plot was output per effective
[01:52] worker against Capital per effective
[01:54] worker and that diagram has a steady
[01:56] state okay and that steady state at the
[01:59] steady state or the balance growth point
[02:01] then we have that H the normalized
[02:04] variables grow at the rate of zero
[02:07] Capital per worker has to grow at the
[02:09] rate G GA because Capital per effective
[02:12] worker is not growing so Capital per
[02:14] worker will be growing at the rate GA
[02:17] the same applies for output per worker
[02:19] output per effective worker is not
[02:21] growing that's balanced growth but
[02:23] therefore output per worker will be
[02:25] growing at the rate
[02:27] GA um
[02:29] these are the exogenous drivers a you
[02:32] know output per worker we assume no a
[02:36] well sorry labor is is GA is exogenous
[02:40] in this model and so is GM population
[02:42] growth is some constant we take it's not
[02:45] something we try to explain within the
[02:46] model okay but the two drivers of
[02:49] absolute growth will be GA and GN and so
[02:52] capital in the St state will be growing
[02:54] at the rate GA plus GN output will be
[02:57] growing at the rate GA plus GN so that's
[02:59] balance grow okay now let me give you an
[03:02] example so you can do see that suppose
[03:04] that our production function is is this
[03:07] we call that the a cop Douglas
[03:09] production
[03:10] function K to the 1 minus Alpha a n to
[03:14] the alpha does this function have
[03:15] constant
[03:17] returns to scale yes the sum of the
[03:20] exponents is one okay anyways but so uh
[03:25] take the log of both sides the change in
[03:27] the log is the rate of growth and so you
[03:30] get that the rate of growth of output is
[03:32] equal to 1 minus Alpha the rate of
[03:33] growth of capital plus Alpha time the
[03:36] rate of growth of effective workers okay
[03:39] so in balanced growth GK will be growing
[03:42] at the rate GA plus GN and therefore
[03:44] output will also be growing at the rate
[03:46] GA plus GN okay so that's what you have
[03:48] in the table and if you want to look at
[03:51] a variable like this Capital per worker
[03:54] then output per worker then you you need
[03:57] G gy minus GN
[03:59] H so subtract the GN and you can
[04:02] subtract both sides then it's going to
[04:03] be equal to GA okay I subtract GM from
[04:06] the right hand side H this one and that
[04:09] one cancel and I get GA on the right
[04:12] hand side that's the way you use that
[04:14] expression to fill all this all these
[04:16] blanks okay that's the that's St so I I
[04:21] think I stopped right before that this
[04:24] this slide or at this slide which is you
[04:27] know if I look at this the table GN is
[04:30] pretty easy to compute in most places
[04:33] there are places in the world where we
[04:34] sort of cannot even measure birth and
[04:36] death so it's difficult but in most
[04:39] places H you can measure GN the rate of
[04:42] FR of population H quite accurately and
[04:45] the question we have though is how do we
[04:47] measure technological progress It's also
[04:48] easy to measure the growth in the stock
[04:51] of capital it's investment minus
[04:53] depreciation uh but how do we measure H
[04:56] GA no the rate of technological progress
[05:00] and uhh the first proposal on how to do
[05:03] it was also by Bob solo H that was a
[05:07] second contribution he had in this in
[05:09] growth Theory well it was also growth
[05:11] measurement how do we measure GA it
[05:13] turns out that the only way you're going
[05:14] to have output per capita growing over
[05:16] time outut person growing over time is
[05:19] due to GA so we might as well try to
[05:21] measure that since it's such an
[05:23] important variable for sort of the
[05:26] growth of er the growth of uh happiness
[05:31] if you get one indicator of happiness is
[05:33] output per C per worker well such an
[05:36] important driver we need to be able to
[05:37] measure it and and the basic idea that
[05:40] Bob solo had is is essentially something
[05:42] you could have taken from
[05:43] 1401 it's extremely simple it says ER
[05:49] there are some assumptions behind this
[05:51] but you know in in the basic competitive
[05:53] model you have that that um you can
[05:57] compute the contribution of each each
[05:59] factor of production to to Output H by
[06:04] the payment it receives okay so under
[06:08] this assumption no suppose that that
[06:11] you're spending in workers
[06:13] $30,000 a
[06:15] year so that means in a competitive
[06:18] equilibrium in the labor market and so
[06:20] on that the worker is contributing to
[06:22] production
[06:24] $30,000 okay I'm not going to deal with
[06:26] markups and things like that here but
[06:28] that's a basic idea you can adjust all
[06:30] these formulas to include markups but
[06:32] let me not do that so that also tells
[06:36] you that if you increase
[06:41] um er employment by 10% you'll also
[06:45] going to increase output by 10% times
[06:50] whatever is the contribution of Labor to
[06:52] Output okay and that's what I have here
[06:54] the contribution of H to Output of
[06:59] adding workers is going to be that times
[07:02] Delta n i can divide by H by y both
[07:07] sides and here multiply and divide by n
[07:10] and I get that the the the rate of the
[07:13] the the rate of growth in
[07:16] output due to a a a rate of growth in
[07:22] employment is equal to the labor share
[07:24] that's called the labor share is the
[07:26] wage Bill W * n divided by total total
[07:30] uh Revenue uh sales and uh uh times the
[07:36] rate of growth of H population or
[07:39] workers is the same here so I'm going to
[07:42] call this GYN it's the rate of growth of
[07:45] output due to the rate of growth in
[07:48] population is equal to this this labor
[07:51] share which I'm going to call that Alpha
[07:54] times GM okay I can do exactly the same
[07:58] with capital
[08:00] and you can do if you have more factor
[08:01] of production you can do the same for
[08:02] each factor of production so but in this
[08:05] simple example we have only two factors
[08:07] of production labor and capital so I can
[08:09] do the same for Capital and I can say
[08:12] the contribution of of Capital Growth to
[08:16] Output growth is going to be equal to
[08:18] the capital share which is the compl of
[08:20] the labor share so it's it's total
[08:23] revenue minus the wage wage payment the
[08:26] wage Bill divided by total revenue h
[08:29] times the rate of growth of capital okay
[08:32] so the contribution of H to Output
[08:35] growth of the rate of growth of capital
[08:38] is is 1 minus Alpha which is the share
[08:40] of capital times uh the rate of growth
[08:44] of capital okay so that means if I sum
[08:48] the
[08:49] contribution of Labor and capital I have
[08:53] I I'm left with the residual which is
[08:56] whatever is the rate of growth I have in
[08:57] output I know how much I'm getting from
[08:59] labor I know how much I'm getting for
[09:02] Capital if there is any difference it
[09:03] must be due to that thing I don't not
[09:05] observe which is technological progress
[09:08] okay that's the logic of all this
[09:12] stuff go back for example to this
[09:14] production function I'm saying I know
[09:16] the contribution that K has to Output
[09:20] growth I know the contribution that n
[09:22] has to Output growth well the only thing
[09:25] I'm missing is the contribution that a
[09:27] has to Output growth which say don't
[09:29] observe but I observe output growth I
[09:32] observe Capital Growth I observe
[09:34] employment growth so I can solve out
[09:36] what
[09:37] is the technological technological
[09:39] progress a growth okay and that's that's
[09:43] called it's called the solo residual by
[09:45] the way okay but that's the way the rate
[09:48] of growth of GA of a is measured the
[09:50] rate of growth of output minus the
[09:52] contribution to growth of er employment
[09:56] 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