WEBVTT

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okay let's uh let's start um So the plan

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for today is to wrap up this growth uh

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Theory section of the of the course and

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um I I I want to sort of

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conclude by showing you what we can and

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cannot explain with the mods we have

00:00:35.878 --> 00:00:41.079
looked up to now and almost as a matter

00:00:38.479 --> 00:00:43.599
of accounting I will tell you what do we

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need to fill which gaps do we need to

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fill in order to explain sort of the

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great dispersion we see in income per

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capita across the world um but before I

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do that I need to finish the previous

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lecture and so let me let me do that H I

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had shown you this table remember in the

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in the complete model the model that has

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a a productivity growth unemployment and

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and and population growth um we

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concluded that imbalanced growth H the

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following happened no uh obviously if we

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pick the right normalization the right

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normalization here was ER effective

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workers so that productivity

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productivity times a population or

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workers and so if we normalize the

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variables by that H we get obviously

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zero growth that's what it means to have

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a balanced growth in which all the

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relevant variables are growing at the

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same rate H so Capital per effective

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worker will will be a state that's

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that's a diagram we plot remember the

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diagram we plot was output per effective

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worker against Capital per effective

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worker and that diagram has a steady

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state okay and that steady state at the

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steady state or the balance growth point

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then we have that H the normalized

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variables grow at the rate of zero

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Capital per worker has to grow at the

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rate G GA because Capital per effective

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worker is not growing so Capital per

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worker will be growing at the rate GA

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the same applies for output per worker

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output per effective worker is not

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growing that's balanced growth but

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therefore output per worker will be

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growing at the rate

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GA um

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these are the exogenous drivers a you

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know output per worker we assume no a

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well sorry labor is is GA is exogenous

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in this model and so is GM population

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growth is some constant we take it's not

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something we try to explain within the

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model okay but the two drivers of

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absolute growth will be GA and GN and so

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capital in the St state will be growing

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at the rate GA plus GN output will be

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growing at the rate GA plus GN so that's

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balance grow okay now let me give you an

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example so you can do see that suppose

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that our production function is is this

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we call that the a cop Douglas

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production

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function K to the 1 minus Alpha a n to

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the alpha does this function have

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constant

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returns to scale yes the sum of the

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exponents is one okay anyways but so uh

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take the log of both sides the change in

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the log is the rate of growth and so you

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get that the rate of growth of output is

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equal to 1 minus Alpha the rate of

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growth of capital plus Alpha time the

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rate of growth of effective workers okay

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so in balanced growth GK will be growing

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at the rate GA plus GN and therefore

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output will also be growing at the rate

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GA plus GN okay so that's what you have

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in the table and if you want to look at

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a variable like this Capital per worker

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then output per worker then you you need

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G gy minus GN

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H so subtract the GN and you can

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subtract both sides then it's going to

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be equal to GA okay I subtract GM from

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the right hand side H this one and that

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one cancel and I get GA on the right

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hand side that's the way you use that

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expression to fill all this all these

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blanks okay that's the that's St so I I

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think I stopped right before that this

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this slide or at this slide which is you

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know if I look at this the table GN is

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pretty easy to compute in most places

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there are places in the world where we

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sort of cannot even measure birth and

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death so it's difficult but in most

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places H you can measure GN the rate of

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FR of population H quite accurately and

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the question we have though is how do we

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measure technological progress It's also

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easy to measure the growth in the stock

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of capital it's investment minus

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depreciation uh but how do we measure H

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GA no the rate of technological progress

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and uhh the first proposal on how to do

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it was also by Bob solo H that was a

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second contribution he had in this in

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growth Theory well it was also growth

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measurement how do we measure GA it

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turns out that the only way you're going

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to have output per capita growing over

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time outut person growing over time is

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due to GA so we might as well try to

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measure that since it's such an

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important variable for sort of the

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growth of er the growth of uh happiness

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if you get one indicator of happiness is

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output per C per worker well such an

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important driver we need to be able to

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measure it and and the basic idea that

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Bob solo had is is essentially something

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you could have taken from

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1401 it's extremely simple it says ER

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there are some assumptions behind this

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but you know in in the basic competitive

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model you have that that um you can

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compute the contribution of each each

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factor of production to to Output H by

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the payment it receives okay so under

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this assumption no suppose that that

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you're spending in workers

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$30,000 a

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year so that means in a competitive

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equilibrium in the labor market and so

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on that the worker is contributing to

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production

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$30,000 okay I'm not going to deal with

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markups and things like that here but

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that's a basic idea you can adjust all

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these formulas to include markups but

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let me not do that so that also tells

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you that if you increase

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um er employment by 10% you'll also

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going to increase output by 10% times

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whatever is the contribution of Labor to

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Output okay and that's what I have here

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the contribution of H to Output of

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adding workers is going to be that times

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Delta n i can divide by H by y both

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sides and here multiply and divide by n

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and I get that the the the rate of the

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the the rate of growth in

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output due to a a a rate of growth in

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employment is equal to the labor share

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that's called the labor share is the

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wage Bill W * n divided by total total

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uh Revenue uh sales and uh uh times the

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rate of growth of H population or

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workers is the same here so I'm going to

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call this GYN it's the rate of growth of

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output due to the rate of growth in

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population is equal to this this labor

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share which I'm going to call that Alpha

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times GM okay I can do exactly the same

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with capital

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and you can do if you have more factor

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of production you can do the same for

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each factor of production so but in this

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simple example we have only two factors

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of production labor and capital so I can

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do the same for Capital and I can say

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the contribution of of Capital Growth to

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Output growth is going to be equal to

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the capital share which is the compl of

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the labor share so it's it's total

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revenue minus the wage wage payment the

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wage Bill divided by total revenue h

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times the rate of growth of capital okay

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so the contribution of H to Output

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growth of the rate of growth of capital

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is is 1 minus Alpha which is the share

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of capital times uh the rate of growth

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of capital okay so that means if I sum

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the

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contribution of Labor and capital I have

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I I'm left with the residual which is

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whatever is the rate of growth I have in

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output I know how much I'm getting from

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labor I know how much I'm getting for

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Capital if there is any difference it

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must be due to that thing I don't not

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observe which is technological progress

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okay that's the logic of all this

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stuff go back for example to this

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production function I'm saying I know

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the contribution that K has to Output

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growth I know the contribution that n

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has to Output growth well the only thing

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I'm missing is the contribution that a

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has to Output growth which say don't

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observe but I observe output growth I

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observe Capital Growth I observe

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employment growth so I can solve out

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what

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is the technological technological

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progress a growth okay and that's that's

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called it's called the solo residual by

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the way okay but that's the way the rate

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of growth of GA of a is measured the

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rate of growth of output minus the

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contribution to growth of er employment

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population and capital

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any question about

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that no makees

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sense

00:10:07.480 --> 00:10:13.639
somewhat okay good so anyway so there's

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a huge industry of measuring these kind

00:10:13.639 --> 00:10:18.360
of things of course uh let me give you

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an

00:10:18.360 --> 00:10:27.200
example h on how to use this accounting

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um so China 78 2017 that's an episode in

00:10:27.200 --> 00:10:30.040
which China was growing very very

00:10:28.879 --> 00:10:32.000
strongly

00:10:30.039 --> 00:10:36.240
ER on

00:10:32.000 --> 00:10:37.679
average China grew at over 7% out

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progress over

00:10:37.679 --> 00:10:43.559
7% now by the formula I showed you

00:10:40.919 --> 00:10:46.278
before if I ask you the question well

00:10:43.559 --> 00:10:48.119
what was behind that growth how much was

00:10:46.278 --> 00:10:50.480
a contribution of Labor how much was a

00:10:48.120 --> 00:10:53.519
contribution of capital and how much was

00:10:50.480 --> 00:10:55.680
a contribution of technological progress

00:10:53.519 --> 00:10:57.959
well there are some things we can

00:10:55.679 --> 00:10:59.719
measure fairly well population growth

00:10:57.958 --> 00:11:01.919
during this period in China was around

00:10:59.720 --> 00:11:05.399
1.7% per

00:11:01.919 --> 00:11:07.599
year there was a massive amount of

00:11:05.399 --> 00:11:08.720
investment the Capital stock was growing

00:11:07.600 --> 00:11:12.159
at a rate of

00:11:08.720 --> 00:11:15.720
99.2% per year and the residual you can

00:11:12.159 --> 00:11:17.078
compute it using the solo approach H is

00:11:15.720 --> 00:11:21.440
around

00:11:17.078 --> 00:11:24.799
4.2% okay so that 7.2% is a result of

00:11:21.440 --> 00:11:28.839
the weighted average of these three

00:11:24.799 --> 00:11:32.240
things okay so that's basic explanation

00:11:28.839 --> 00:11:36.480
of ER the growth in China during that

00:11:32.240 --> 00:11:38.639
that period now just looking at this not

00:11:36.480 --> 00:11:42.920
don't look at at the

00:11:38.639 --> 00:11:45.839
diagram what jumps immediately just if

00:11:42.919 --> 00:11:45.838
you just look at this

00:11:46.480 --> 00:11:51.800
part what jumps to you

00:11:49.320 --> 00:11:55.680
immediately let me ask you differently

00:11:51.799 --> 00:11:55.679
does it look like balanced

00:11:56.120 --> 00:12:02.799
growth do you think that that that's

00:11:59.360 --> 00:12:05.680
balanced growth that in other words do

00:12:02.799 --> 00:12:08.838
you think that China had a arrived to

00:12:05.679 --> 00:12:11.359
its state and and that growth is a

00:12:08.839 --> 00:12:13.800
result of what was happening in that

00:12:11.360 --> 00:12:13.800
stady

00:12:16.198 --> 00:12:20.759
state

00:12:18.399 --> 00:12:23.120
no but what is it that

00:12:20.759 --> 00:12:25.838
looks that tells you that that that's

00:12:23.120 --> 00:12:25.839
not the same

00:12:26.799 --> 00:12:30.559
state balanc growth is when everything

00:12:29.159 --> 00:12:34.679
everything is growing at the same rate

00:12:30.559 --> 00:12:37.719
no everything you have you know

00:12:34.679 --> 00:12:41.359
meaning all the endogenous

00:12:37.720 --> 00:12:44.278
variables ER unnormalized are growing at

00:12:41.360 --> 00:12:46.839
the same at the same rate as the

00:12:44.278 --> 00:12:46.838
exogenous

00:12:47.278 --> 00:12:54.278
variables so what is it that it would

00:12:49.879 --> 00:12:57.078
nearly jump to me here is say

00:12:54.278 --> 00:12:59.240
7.2% that's less than than the rate of

00:12:57.078 --> 00:13:02.638
growth of capital

00:12:59.240 --> 00:13:04.639
so so I know that there Capital over

00:13:02.639 --> 00:13:08.278
output was Rising so that's not a state

00:13:04.639 --> 00:13:12.240
state I know that I can see it in a

00:13:08.278 --> 00:13:14.799
different way I know that in a steady

00:13:12.240 --> 00:13:17.560
state in balanced

00:13:14.799 --> 00:13:19.838
growth the rate of growth of output and

00:13:17.559 --> 00:13:22.838
of capital should be the sum of the rate

00:13:19.839 --> 00:13:24.360
of growth of population plus the rate of

00:13:22.839 --> 00:13:27.600
technological

00:13:24.360 --> 00:13:31.278
progress okay that's

00:13:27.600 --> 00:13:34.159
5.9% but capital was growing at

00:13:31.278 --> 00:13:36.919
99.2% not

00:13:34.159 --> 00:13:40.120
5.9% so I do know that that's a period

00:13:36.919 --> 00:13:42.679
in which China was growing

00:13:40.120 --> 00:13:44.440
Beyond its steady state or balanced

00:13:42.679 --> 00:13:47.000
growth rate of

00:13:44.440 --> 00:13:48.839
growth and I know more than that I know

00:13:47.000 --> 00:13:50.600
that the reason that was happening is

00:13:48.839 --> 00:13:52.920
because there was more capital

00:13:50.600 --> 00:13:54.079
accumulation than you would expect in

00:13:52.919 --> 00:13:56.759
the stady

00:13:54.078 --> 00:13:59.120
state when are you likely to see a

00:13:56.759 --> 00:14:01.000
situation like that in which capital

00:13:59.120 --> 00:14:03.320
accumulation is faster than the rate of

00:14:01.000 --> 00:14:04.720
growth of capital in the St State and

00:14:03.320 --> 00:14:08.199
it's faster than the rate of growth of

00:14:04.720 --> 00:14:10.600
output that is that's a a period in

00:14:08.198 --> 00:14:14.120
which we have transitional growth been

00:14:10.600 --> 00:14:18.480
pulled you know growth above the state

00:14:14.120 --> 00:14:22.198
state growth is being pulled by capital

00:14:18.480 --> 00:14:22.199
accumulation when does that

00:14:27.559 --> 00:14:33.599
happen do to mind first is economies are

00:14:31.360 --> 00:14:36.039
like transitioning from command market

00:14:33.600 --> 00:14:39.519
economies I believe and also the second

00:14:36.039 --> 00:14:44.039
thing that comes to mind is potentially

00:14:39.519 --> 00:14:47.278
um um countries recovering from like War

00:14:44.039 --> 00:14:49.480
periods okay that's a deep deep deep

00:14:47.278 --> 00:14:51.120
answer I wanted something simpler which

00:14:49.480 --> 00:14:54.278
is

00:14:51.120 --> 00:14:57.720
what I I want to say so the economy is

00:14:54.278 --> 00:14:59.600
not in a state state that's clear but

00:14:57.720 --> 00:15:01.959
what do we also know we know that the

00:14:59.600 --> 00:15:04.560
Capital stock is below its stady state

00:15:01.958 --> 00:15:07.359
level and that could be as a result of

00:15:04.559 --> 00:15:09.439
of the the things you described you had

00:15:07.360 --> 00:15:12.680
a war so your Capital stock was wiped

00:15:09.440 --> 00:15:14.639
out or H you had a period in which

00:15:12.679 --> 00:15:17.239
saving rate was very low and now you're

00:15:14.639 --> 00:15:19.079
going to high saving rate episode with

00:15:17.240 --> 00:15:21.399
that a lot of that is what happened in

00:15:19.078 --> 00:15:23.679
in souis Asia in particular actually was

00:15:21.399 --> 00:15:26.078
a fast increase in the rate of in the

00:15:23.679 --> 00:15:28.559
say a sharp rise in this in the saving

00:15:26.078 --> 00:15:32.078
rate but the bottom what I so what I had

00:15:28.559 --> 00:15:33.559
in mind is for one of these reasons

00:15:32.078 --> 00:15:35.919
that's a situation where the initial

00:15:33.559 --> 00:15:37.479
Capital stock was below the stady state

00:15:35.919 --> 00:15:39.318
and so you have a period of transitional

00:15:37.480 --> 00:15:41.839
growth in which investment rate is more

00:15:39.318 --> 00:15:44.318
than you need to do to maintain the

00:15:41.839 --> 00:15:47.160
stock of capital per effective worker

00:15:44.318 --> 00:15:49.879
know there's a positive gap between the

00:15:47.159 --> 00:15:51.879
the green line and the and and the and

00:15:49.879 --> 00:15:54.958
the red line and that's what leads you

00:15:51.879 --> 00:15:58.439
transitional growth until you reach a c

00:15:54.958 --> 00:16:01.239
state if things do not change meaning

00:15:58.440 --> 00:16:05.319
population growth remain the same as in

00:16:01.240 --> 00:16:07.240
that period and the and the the rate of

00:16:05.318 --> 00:16:09.318
technological progress Remains the Same

00:16:07.240 --> 00:16:12.720
As in that period we know that the

00:16:09.318 --> 00:16:15.198
balanced growth rate of China is

00:16:12.720 --> 00:16:20.680
5.9%

00:16:15.198 --> 00:16:25.159
okay it's 5.9 because it's 07 plus

00:16:20.679 --> 00:16:26.879
0.42 now so so that 7.2% average there

00:16:25.159 --> 00:16:28.559
you're likely to see it and actually

00:16:26.879 --> 00:16:33.559
there's an average that has numbers like

00:16:28.559 --> 00:16:38.198
15 % very early on H to close to 6% or

00:16:33.559 --> 00:16:40.239
so on the last stage H so that's that's

00:16:38.198 --> 00:16:41.159
would be a stady state now that I think

00:16:40.240 --> 00:16:45.120
is an

00:16:41.159 --> 00:16:46.679
overestimate because H uh we know the

00:16:45.120 --> 00:16:48.240
rate of population growth is declining

00:16:46.679 --> 00:16:51.758
very rapidly in China it's turning

00:16:48.240 --> 00:16:53.600
negative okay so so so for the rate of

00:16:51.759 --> 00:16:54.959
growth of output China is going to is

00:16:53.600 --> 00:16:56.600
unless there's a big change in

00:16:54.958 --> 00:16:58.318
technological progress in the process of

00:16:56.600 --> 00:17:00.680
technological progress it's going to be

00:16:58.318 --> 00:17:04.599
pretty difficult for China to grow a lot

00:17:00.679 --> 00:17:07.240
more than 5% I think going forward and

00:17:04.599 --> 00:17:08.558
that creates some problems but but

00:17:07.240 --> 00:17:10.599
that's what it is that's what this model

00:17:08.558 --> 00:17:11.959
tells you you need to change something

00:17:10.599 --> 00:17:13.759
and the things you can change in this

00:17:11.959 --> 00:17:15.759
model are what well you could induce

00:17:13.759 --> 00:17:17.640
higher saving rate you would get more

00:17:15.759 --> 00:17:19.679
transitional growth out of that more

00:17:17.640 --> 00:17:23.400
capital accumulation that's costly that

00:17:19.679 --> 00:17:25.280
means less consumption and so on H or it

00:17:23.400 --> 00:17:27.519
could be some technological breakthrough

00:17:25.279 --> 00:17:30.038
but that's a probably would affect the

00:17:27.519 --> 00:17:32.519
whole world in any event but that's the

00:17:30.038 --> 00:17:36.400
kind of things you

00:17:32.519 --> 00:17:38.400
okay good so that's that's

00:17:36.400 --> 00:17:41.280
uh so

00:17:38.400 --> 00:17:44.480
so is is the models we have developed

00:17:41.279 --> 00:17:47.200
here sort of are quite good to explain

00:17:44.480 --> 00:17:49.519
you know uh catching up processes

00:17:47.200 --> 00:17:51.720
catching up growth and and and to

00:17:49.519 --> 00:17:54.918
understand what are the where are

00:17:51.720 --> 00:17:58.319
economies converging o over

00:17:54.919 --> 00:18:00.320
time what I want to next is I I want to

00:17:58.319 --> 00:18:02.639
end up trying to explain remember one of

00:18:00.319 --> 00:18:04.038
the plots I showed you very early on is

00:18:02.640 --> 00:18:07.360
that there's great

00:18:04.038 --> 00:18:09.640
dispersion H in income per per person

00:18:07.359 --> 00:18:11.879
per capita across the world and also

00:18:09.640 --> 00:18:15.240
some countries are sort of not catching

00:18:11.880 --> 00:18:17.640
up and which is especially in Africa and

00:18:15.240 --> 00:18:19.480
so on and I want to try to understand so

00:18:17.640 --> 00:18:20.520
people have put lots of effort in trying

00:18:19.480 --> 00:18:22.679
to

00:18:20.519 --> 00:18:24.839
understand why do we have these

00:18:22.679 --> 00:18:27.798
differences and so I'm going to expand a

00:18:24.839 --> 00:18:30.879
little bit the model we have H to show

00:18:27.798 --> 00:18:32.720
you few things people have explored and

00:18:30.880 --> 00:18:34.200
and then I'm going to conclude that

00:18:32.720 --> 00:18:37.519
those things that people have explored

00:18:34.200 --> 00:18:39.080
sort of can't explain it either and then

00:18:37.519 --> 00:18:42.639
as I'm going to go back sort of to

00:18:39.079 --> 00:18:46.199
growth accounting so sort of thing I did

00:18:42.640 --> 00:18:49.640
for China there and try to explain what

00:18:46.200 --> 00:18:51.279
what what seems to be ER behind all

00:18:49.640 --> 00:18:53.880
these big disparities we have in the

00:18:51.279 --> 00:18:57.038
world so the first thing I'm going to do

00:18:53.880 --> 00:18:59.159
is just it's useful as an exercise even

00:18:57.038 --> 00:19:01.599
I'm going to start with h I'm going to

00:18:59.159 --> 00:19:03.360
modify the the solo mod a little bit so

00:19:01.599 --> 00:19:05.678
this is like the production function I

00:19:03.359 --> 00:19:10.639
showed you before but rather than having

00:19:05.679 --> 00:19:14.480
n here I'm going to have H and H is just

00:19:10.640 --> 00:19:17.440
n our old n population labor for there

00:19:14.480 --> 00:19:22.440
but a scale up by this human capital

00:19:17.440 --> 00:19:23.840
Factor okay so what this says is that

00:19:22.440 --> 00:19:26.080
that human

00:19:23.839 --> 00:19:29.359
capital is

00:19:26.079 --> 00:19:31.399
really is the population

00:19:29.359 --> 00:19:34.399
times something that controls for the

00:19:31.400 --> 00:19:36.320
level of schooling of that population

00:19:34.400 --> 00:19:37.640
okay so a big candidate for difference

00:19:36.319 --> 00:19:38.918
across the world is that you know that

00:19:37.640 --> 00:19:42.520
certain populations are far more

00:19:38.919 --> 00:19:45.480
educated than others so so

00:19:42.519 --> 00:19:47.519
this does exactly that s is an

00:19:45.480 --> 00:19:49.798
increasing function of the numbers of

00:19:47.519 --> 00:19:52.759
years of schooling and there is a big

00:19:49.798 --> 00:19:54.599
micro evidence literature trying to

00:19:52.759 --> 00:19:56.240
estimate what is the value of thats what

00:19:54.599 --> 00:20:00.000
is the value of an extra unit of

00:19:56.240 --> 00:20:02.319
schooling for a human capital and so on

00:20:00.000 --> 00:20:03.720
and sort of the estimate depends on what

00:20:02.319 --> 00:20:05.798
kind of a schooling are we talking about

00:20:03.720 --> 00:20:08.960
is primary secondary thary whatever but

00:20:05.798 --> 00:20:11.798
on average that's a number around 0.1

00:20:08.960 --> 00:20:14.000
okay so one extra year of schooling

00:20:11.798 --> 00:20:16.079
raises sort of human capital by about

00:20:14.000 --> 00:20:19.038
10% so the whole population increases

00:20:16.079 --> 00:20:22.359
the average by one year

00:20:19.038 --> 00:20:25.119
year um that adds about 10% to human

00:20:22.359 --> 00:20:27.279
capital so is as if you had increased

00:20:25.119 --> 00:20:30.319
population by 10% so it makes a

00:20:27.279 --> 00:20:33.119
difference now is it's pretty hard to

00:20:30.319 --> 00:20:35.599
raise for a country one year of

00:20:33.119 --> 00:20:37.119
schooling for the average takes a lot of

00:20:35.599 --> 00:20:38.759
time but when you look in the

00:20:37.119 --> 00:20:40.439
crosssection there's huge difference

00:20:38.759 --> 00:20:42.919
across the world between numbers of

00:20:40.440 --> 00:20:44.720
years of schooling and that accounts for

00:20:42.919 --> 00:20:46.080
a big part of the difference in income

00:20:44.720 --> 00:20:51.079
per

00:20:46.079 --> 00:20:53.599
capita anyways so let me um do a balanc

00:20:51.079 --> 00:20:58.199
growth exercise with this this expanded

00:20:53.599 --> 00:20:59.319
Model H and see how far we can get so so

00:20:58.200 --> 00:21:00.919
the first thing I'm going to do is I'm

00:20:59.319 --> 00:21:05.158
going to normalize everything by

00:21:00.919 --> 00:21:06.600
effective work sorry by workers okay so

00:21:05.159 --> 00:21:08.080
I'm going to divide every all the

00:21:06.599 --> 00:21:09.918
variables I'm going to show you are

00:21:08.079 --> 00:21:12.639
going to be divided by

00:21:09.919 --> 00:21:16.200
n

00:21:12.640 --> 00:21:19.600
now notice that I'm dividing by n not by

00:21:16.200 --> 00:21:22.240
a * n or a *

00:21:19.599 --> 00:21:24.558
H

00:21:22.240 --> 00:21:27.679
or so so there's a difference with the

00:21:24.558 --> 00:21:30.038
previous analysis and I I can always

00:21:27.679 --> 00:21:32.240
divide and the model we had I can always

00:21:30.038 --> 00:21:34.839
divide by whatever I want all my

00:21:32.240 --> 00:21:36.558
variables I divided by effective workers

00:21:34.839 --> 00:21:39.278
because I wanted to have a diagram where

00:21:36.558 --> 00:21:42.359
the curves were not moving around but I

00:21:39.278 --> 00:21:43.679
can divide by whatever I want and and

00:21:42.359 --> 00:21:45.079
and I will divide by different things

00:21:43.679 --> 00:21:47.679
depending on the analysis I want to

00:21:45.079 --> 00:21:50.439
conduct now I know that once I divide by

00:21:47.679 --> 00:21:53.840
population only not by a times

00:21:50.440 --> 00:21:56.360
population and education perhaps H I

00:21:53.839 --> 00:21:59.558
cannot draw my previous diagram the the

00:21:56.359 --> 00:22:01.759
diagram with the saving uh output per

00:21:59.558 --> 00:22:03.119
per effect per worker and so on because

00:22:01.759 --> 00:22:05.119
those curves are going to be moving so

00:22:03.119 --> 00:22:07.079
it's not very friendly but I can divide

00:22:05.119 --> 00:22:09.719
by whatever I want and I had I'm I want

00:22:07.079 --> 00:22:14.000
to divide here by just population so

00:22:09.720 --> 00:22:17.720
little H will be simply a big H divided

00:22:14.000 --> 00:22:22.319
by n okay remember that big H was just e

00:22:17.720 --> 00:22:26.679
to U time n so that's that output per

00:22:22.319 --> 00:22:31.359
worker will be just the will be K

00:22:26.679 --> 00:22:33.840
Capital divided by n and here is Big H

00:22:31.359 --> 00:22:37.079
divided by n which is little H okay so

00:22:33.839 --> 00:22:40.038
all this now is measured as output per

00:22:37.079 --> 00:22:42.599
worker or per

00:22:40.038 --> 00:22:45.519
population per

00:22:42.599 --> 00:22:47.278
person now remember what I can do here

00:22:45.519 --> 00:22:49.960
is then I know that the rate of growth

00:22:47.278 --> 00:22:52.480
of output per person is going to be

00:22:49.960 --> 00:22:55.840
equal to 1 minus Alpha times the rate of

00:22:52.480 --> 00:22:58.159
growth of capital per person plus Alpha

00:22:55.839 --> 00:23:02.240
time the rate of growth of a Time the

00:22:58.159 --> 00:23:05.000
rate of growth of age in which age is is

00:23:02.240 --> 00:23:07.278
this H years of schooling

00:23:05.000 --> 00:23:10.359
transformation okay now if you think

00:23:07.278 --> 00:23:12.519
about the steady state H it doesn't make

00:23:10.359 --> 00:23:14.558
any sense that GH at some point will

00:23:12.519 --> 00:23:16.918
become zero I mean we can increase

00:23:14.558 --> 00:23:19.678
education but at some point we cannot be

00:23:16.919 --> 00:23:22.640
all going to you know 150 years of

00:23:19.679 --> 00:23:25.120
education so that is unlike capital and

00:23:22.640 --> 00:23:27.559
things like that you can increase for a

00:23:25.119 --> 00:23:28.839
while education but but at some point

00:23:27.558 --> 00:23:31.158
there's a limit I mean you're not going

00:23:28.839 --> 00:23:34.359
to do a post post post post PhD blah

00:23:31.159 --> 00:23:36.278
blah blah okay so in the stady state we

00:23:34.359 --> 00:23:40.240
know that eventually in the long run

00:23:36.278 --> 00:23:43.919
this GH is equal to zero so this this

00:23:40.240 --> 00:23:46.200
economy we expanded to include years of

00:23:43.919 --> 00:23:47.880
schooling has the same sort of balanced

00:23:46.200 --> 00:23:50.679
growth characteristics of the economy I

00:23:47.880 --> 00:23:54.278
just showed you before okay so that that

00:23:50.679 --> 00:23:57.000
in that economy Capital per person will

00:23:54.278 --> 00:23:59.798
grow at the rate GA and output per

00:23:57.000 --> 00:24:01.839
person will grow at the rate GA output

00:23:59.798 --> 00:24:04.079
will grow at the rate GA plus GN so

00:24:01.839 --> 00:24:06.959
exactly the same as we had before not

00:24:04.079 --> 00:24:09.879
not not so up to now adding human

00:24:06.960 --> 00:24:12.480
capital doesn't change our conclusions

00:24:09.880 --> 00:24:14.080
about balanced growth it will change

00:24:12.480 --> 00:24:15.640
some conclusions that are important

00:24:14.079 --> 00:24:18.278
that's the reason I'm introducing this

00:24:15.640 --> 00:24:20.320
variable but doesn't change this this

00:24:18.278 --> 00:24:21.798
conclusion so this model which is a

00:24:20.319 --> 00:24:23.918
little expansion of the previous model

00:24:21.798 --> 00:24:27.079
we had has the same balanced growth

00:24:23.919 --> 00:24:28.880
characteristics as the model I show you

00:24:27.079 --> 00:24:31.000
before

00:24:28.880 --> 00:24:33.760
so let me do a little bit of algebra

00:24:31.000 --> 00:24:38.000
with it h so from the capital

00:24:33.759 --> 00:24:41.079
accumulation equation I know that so let

00:24:38.000 --> 00:24:43.240
me remember the capital accumulation now

00:24:41.079 --> 00:24:49.839
written in in

00:24:43.240 --> 00:24:54.640
per in per per person will be H you

00:24:49.839 --> 00:24:56.519
know KT + one this is remember little K

00:24:54.640 --> 00:25:00.320
minus

00:24:56.519 --> 00:25:00.319
KT equal to

00:25:00.798 --> 00:25:06.079
s * y

00:25:04.519 --> 00:25:09.639
d

00:25:06.079 --> 00:25:11.639
minus Delta plus

00:25:09.640 --> 00:25:14.159
n

00:25:11.640 --> 00:25:17.759
k

00:25:14.159 --> 00:25:20.799
t wait why do I have a Delta plus n

00:25:17.759 --> 00:25:23.558
minus plus GA there remember that in the

00:25:20.798 --> 00:25:26.079
previous mod I have a Delta plus n plus

00:25:23.558 --> 00:25:26.079
GA

00:25:26.359 --> 00:25:30.319
there did I make a mistake

00:25:33.000 --> 00:25:36.679
actually this is a useful exercise for

00:25:37.480 --> 00:25:43.558
you you remember they had a Delta plus n

00:25:40.398 --> 00:25:46.119
plus plus G there

00:25:43.558 --> 00:25:48.879
no what's

00:25:46.119 --> 00:25:50.278
wrong I just told you that this economy

00:25:48.880 --> 00:25:51.520
at least in balanced growth is exactly

00:25:50.278 --> 00:25:57.079
the

00:25:51.519 --> 00:25:57.079
same so you make a mistake

00:26:01.798 --> 00:26:07.759
no the reason I had the ga there is

00:26:04.720 --> 00:26:10.399
because I was looking at the change in

00:26:07.759 --> 00:26:12.319
capital per effective worker I'm looking

00:26:10.398 --> 00:26:13.879
now at the change in capital per worker

00:26:12.319 --> 00:26:16.278
not per effective worker so I don't have

00:26:13.880 --> 00:26:17.840
that a in the denominator so I don't

00:26:16.278 --> 00:26:21.278
need to account for the rate of growth

00:26:17.839 --> 00:26:24.519
of the denominator due to an increase in

00:26:21.278 --> 00:26:27.079
technology I don't need that so but I

00:26:24.519 --> 00:26:32.359
that also means well and and so what I

00:26:27.079 --> 00:26:32.359
can do is you know divide both sides by

00:26:32.599 --> 00:26:35.879
KT that's

00:26:37.480 --> 00:26:40.960
KT and this

00:26:43.200 --> 00:26:50.038
is the rate of growth of K no is the

00:26:47.278 --> 00:26:50.038
rate of growth of

00:26:51.319 --> 00:26:56.678
K but in a steady state the rate of

00:26:54.398 --> 00:26:59.918
growth of K Capital per worker is equal

00:26:56.679 --> 00:26:59.919
to what

00:27:01.558 --> 00:27:09.879
GA is the rate of growth of Technology

00:27:04.000 --> 00:27:12.640
that's the so this in a state state this

00:27:09.880 --> 00:27:14.399
is equal to

00:27:12.640 --> 00:27:17.159
G

00:27:14.398 --> 00:27:18.879
okay and so what I wrote there is I

00:27:17.159 --> 00:27:24.159
think should be exactly

00:27:18.880 --> 00:27:27.440
that is it yes good okay that's what I

00:27:24.159 --> 00:27:31.240
did and what did I do why did I do this

00:27:27.440 --> 00:27:34.000
for well because now I can you know you

00:27:31.240 --> 00:27:36.640
know that I can know I can measure Delta

00:27:34.000 --> 00:27:39.558
Del Delta is a yeah I can measure Delta

00:27:36.640 --> 00:27:43.679
I can measure n

00:27:39.558 --> 00:27:49.759
h um and I can measure

00:27:43.679 --> 00:27:52.080
GA so this implies that I can solve out

00:27:49.759 --> 00:27:57.480
in a steady state for what is the level

00:27:52.079 --> 00:28:00.079
of capital per ER effective worker okay

00:27:57.480 --> 00:28:02.480
that I can solve from this equation and

00:28:00.079 --> 00:28:05.158
it's equal to this expression here

00:28:02.480 --> 00:28:07.558
notice a few interesting things here is

00:28:05.159 --> 00:28:09.960
capital per effective worker each of

00:28:07.558 --> 00:28:14.240
them is divided by n so I can also look

00:28:09.960 --> 00:28:16.360
at Big K over a times big h no h is

00:28:14.240 --> 00:28:18.759
increasing in the saving

00:28:16.359 --> 00:28:20.199
rate that you already had in the model

00:28:18.759 --> 00:28:21.839
we discussed before if the saving rate

00:28:20.200 --> 00:28:25.360
is higher then the you're going to end

00:28:21.839 --> 00:28:28.119
up with a higher Capital ER perir

00:28:25.359 --> 00:28:31.079
effective worker ratio in yesterday's St

00:28:28.119 --> 00:28:33.798
is decreasing in population growth you

00:28:31.079 --> 00:28:38.079
all these things you already saw before

00:28:33.798 --> 00:28:40.639
okay so now that I have this expression

00:28:38.079 --> 00:28:42.319
for K Over H I can go back to my

00:28:40.640 --> 00:28:46.240
production

00:28:42.319 --> 00:28:49.558
function to this and sticking

00:28:46.240 --> 00:28:52.079
there this this value and I get that

00:28:49.558 --> 00:28:56.440
output at time T once you're in the

00:28:52.079 --> 00:28:58.158
balance growth path is equal to a t time

00:28:56.440 --> 00:29:01.159
h

00:28:58.159 --> 00:29:03.760
time K over a h to 1us Alpha just just

00:29:01.159 --> 00:29:06.640
solve for that and the point being is

00:29:03.759 --> 00:29:10.919
that now I can write this as YT is equal

00:29:06.640 --> 00:29:13.159
to a times e to so human capital times

00:29:10.919 --> 00:29:15.120
this expression here so human the point

00:29:13.159 --> 00:29:17.600
is human capital doesn't affect the

00:29:15.119 --> 00:29:21.678
stady state growth but it does affect

00:29:17.599 --> 00:29:23.599
the income per capita that you have have

00:29:21.679 --> 00:29:26.440
and it makes a big difference I'll show

00:29:23.599 --> 00:29:26.439
you

00:29:26.720 --> 00:29:31.480
okay so when people try to explain

00:29:29.240 --> 00:29:33.839
difference across the world they notice

00:29:31.480 --> 00:29:36.360
that they were missing a big component

00:29:33.839 --> 00:29:39.839
and and that big component is

00:29:36.359 --> 00:29:42.398
education so let's compare what I want

00:29:39.839 --> 00:29:45.798
to do next is you know I can do this for

00:29:42.398 --> 00:29:48.199
every country in the world okay and I

00:29:45.798 --> 00:29:51.158
can compare it with the

00:29:48.200 --> 00:29:53.080
US okay I can do this for every every

00:29:51.159 --> 00:29:54.519
country in the world and let's compare

00:29:53.079 --> 00:29:56.319
it with and I can compare it with any

00:29:54.519 --> 00:29:58.200
other country in the world but just you

00:29:56.319 --> 00:30:00.038
know let's compare it with the largest

00:29:58.200 --> 00:30:03.038
country in the world in terms of output

00:30:00.038 --> 00:30:06.679
that's a us so let's let's see what we

00:30:03.038 --> 00:30:10.119
get so so I'm going to take output per

00:30:06.679 --> 00:30:12.519
capita in everywhere and divided by the

00:30:10.119 --> 00:30:15.719
same expression for the

00:30:12.519 --> 00:30:20.079
US and I'm going to Define that variable

00:30:15.720 --> 00:30:23.759
as y i hat so for Country I say

00:30:20.079 --> 00:30:26.558
Singapore okay we take output per capita

00:30:23.759 --> 00:30:28.480
and we divide it by output per capita

00:30:26.558 --> 00:30:34.038
per person in in the

00:30:28.480 --> 00:30:35.960
us assume big if you see is a huge if

00:30:34.038 --> 00:30:37.879
that but you can do that for you know

00:30:35.960 --> 00:30:41.919
the US versus Singapore probably is not

00:30:37.880 --> 00:30:44.200
a crazy assumption to make H assume that

00:30:41.919 --> 00:30:46.640
they have the same rate of technological

00:30:44.200 --> 00:30:48.558
progress and the same technology and so

00:30:46.640 --> 00:30:50.159
on well the same rate of technological

00:30:48.558 --> 00:30:54.879
progress I'm going to assume that for

00:30:50.159 --> 00:30:58.200
now so then this why I had a you can

00:30:54.880 --> 00:31:00.919
write this it's just a this for

00:30:58.200 --> 00:31:04.120
Singapore divided by this for the

00:31:00.919 --> 00:31:06.519
US it shows it turns out to be this

00:31:04.119 --> 00:31:08.278
expression here

00:31:06.519 --> 00:31:12.880
okay

00:31:08.278 --> 00:31:16.119
so solo did something like this and said

00:31:12.880 --> 00:31:19.399
okay H assume that technology is the

00:31:16.119 --> 00:31:22.719
same across the world because you know

00:31:19.398 --> 00:31:26.158
at least for major Economist technology

00:31:22.720 --> 00:31:28.639
sort of can be imported and and and can

00:31:26.159 --> 00:31:30.840
we can have the same the same uh

00:31:28.638 --> 00:31:33.079
um more or less the same technology

00:31:30.839 --> 00:31:35.638
across the world so assume that this guy

00:31:33.079 --> 00:31:38.119
is equal to one and that both Singapore

00:31:35.638 --> 00:31:43.638
and and the US have the same rate of

00:31:38.119 --> 00:31:46.638
growth okay and so that means

00:31:43.638 --> 00:31:49.439
er um that you know countries that have

00:31:46.638 --> 00:31:51.119
higher saving rate will tend to have we

00:31:49.440 --> 00:31:54.240
know that in Bal go will tend to have

00:31:51.119 --> 00:31:56.558
higher output per capita so if Singapore

00:31:54.240 --> 00:31:59.000
has a higher saving rate than the US

00:31:56.558 --> 00:32:04.200
that will tend to give Singapore a

00:31:59.000 --> 00:32:07.679
higher income per capita okay if country

00:32:04.200 --> 00:32:10.679
has a a higher population growth then it

00:32:07.679 --> 00:32:13.880
will tend to have a lower income per

00:32:10.679 --> 00:32:15.240
capita and and so on so forth and so the

00:32:13.880 --> 00:32:18.120
question is well suppose you make this

00:32:15.240 --> 00:32:20.359
Assumption of equal technology and take

00:32:18.119 --> 00:32:21.798
this take the the we can measure the

00:32:20.359 --> 00:32:23.439
saving rate in different parts of the

00:32:21.798 --> 00:32:24.679
world the population rates in different

00:32:23.440 --> 00:32:26.120
part of the world and we're assuming

00:32:24.679 --> 00:32:28.440
that the same rate of technological

00:32:26.119 --> 00:32:31.479
progress everywhere how much of the

00:32:28.440 --> 00:32:34.000
difference we observe in income per

00:32:31.480 --> 00:32:36.880
capita across the world can be accounted

00:32:34.000 --> 00:32:39.638
by that okay so that's that was the

00:32:36.880 --> 00:32:42.559
first question is well suppose that that

00:32:39.638 --> 00:32:44.158
the technology is the same but we

00:32:42.558 --> 00:32:47.240
measured all these other things saving

00:32:44.159 --> 00:32:49.440
rate population growth H common rate of

00:32:47.240 --> 00:32:51.880
technological progress common

00:32:49.440 --> 00:32:54.120
depreciation across the world and so on

00:32:51.880 --> 00:32:56.880
how much can we explain of the income

00:32:54.119 --> 00:32:58.959
disparity and the conclusion is the

00:32:56.880 --> 00:33:03.039
following the conclusion of that

00:32:58.960 --> 00:33:05.319
experiment is that if that if if the

00:33:03.038 --> 00:33:08.200
only difference

00:33:05.319 --> 00:33:11.319
behind PE incomes per capita were sort

00:33:08.200 --> 00:33:13.038
of years of schooling sorry a key thing

00:33:11.319 --> 00:33:15.720
that I me that I forgot to measure is

00:33:13.038 --> 00:33:17.278
years of schooling so know if a country

00:33:15.720 --> 00:33:18.759
has more years of schooling will tend to

00:33:17.278 --> 00:33:21.079
have a higher income per capita and so

00:33:18.759 --> 00:33:22.759
on so if you try to explain the

00:33:21.079 --> 00:33:25.558
differences in income per capita across

00:33:22.759 --> 00:33:28.278
the world using variables like years of

00:33:25.558 --> 00:33:30.240
schooling H difference in Saving rate

00:33:28.278 --> 00:33:32.798
difference in population growth and so

00:33:30.240 --> 00:33:34.599
on the world would be a lot more

00:33:32.798 --> 00:33:38.158
egalitarian than it actually is it would

00:33:34.599 --> 00:33:40.638
look a lot more flatter okay so this is

00:33:38.159 --> 00:33:43.639
how much you can account here you put a

00:33:40.638 --> 00:33:47.079
bunch of lots of countries you know

00:33:43.638 --> 00:33:49.158
Africa and so on here and if you just

00:33:47.079 --> 00:33:51.480
stick in the in the equation their

00:33:49.159 --> 00:33:53.919
corresponding saving rate education

00:33:51.480 --> 00:33:56.000
levels and so on the world would be a

00:33:53.919 --> 00:33:58.080
lot more similar there wouldn't be the

00:33:56.000 --> 00:34:00.919
kind of disparities we see between some

00:33:58.079 --> 00:34:03.519
African countries and and and Singapore

00:34:00.919 --> 00:34:05.200
say we're talking about Singapore okay

00:34:03.519 --> 00:34:07.759
but the world doesn't look like that

00:34:05.200 --> 00:34:09.280
that's the point so so if you take all

00:34:07.759 --> 00:34:12.000
these things that make a lot of sense

00:34:09.280 --> 00:34:15.000
education saving rate blah you're going

00:34:12.000 --> 00:34:16.800
to explain a small share of the of the

00:34:15.000 --> 00:34:19.838
differences in income per capita across

00:34:16.800 --> 00:34:21.599
the world ah sorry in this this plot

00:34:19.838 --> 00:34:26.799
here L is our

00:34:21.599 --> 00:34:29.440
n l labor is our n so this y Over N our

00:34:26.800 --> 00:34:32.599
little Y in this

00:34:29.440 --> 00:34:34.679
so so not so we can't get so far we need

00:34:32.599 --> 00:34:39.039
something else so what else do we need

00:34:34.679 --> 00:34:41.519
to uh to add to really explain the

00:34:39.039 --> 00:34:44.519
amount of disparity we

00:34:41.519 --> 00:34:47.440
have

00:34:44.519 --> 00:34:49.079
well this the answer is again the solo

00:34:47.440 --> 00:34:51.358
residual it turns out that the

00:34:49.079 --> 00:34:54.320
assumption that A's are the same across

00:34:51.358 --> 00:34:56.279
the world that the level and the rate of

00:34:54.320 --> 00:34:58.320
grows are the same around around the

00:34:56.280 --> 00:35:01.560
world is just

00:34:58.320 --> 00:35:04.000
a very bad assumption okay the level of

00:35:01.559 --> 00:35:07.078
Technologies are very different across

00:35:04.000 --> 00:35:09.800
different parts of the world so the next

00:35:07.079 --> 00:35:12.800
step was say okay let's measure the

00:35:09.800 --> 00:35:15.079
difference in Technologies across the

00:35:12.800 --> 00:35:16.880
world and it turns out that if you try

00:35:15.079 --> 00:35:18.480
to explain so if you go out there and

00:35:16.880 --> 00:35:23.358
you measure the level of Technology

00:35:18.480 --> 00:35:24.920
across the world different places no uh

00:35:23.358 --> 00:35:29.639
Zimbabwe

00:35:24.920 --> 00:35:32.960
Singapore South Korea and so on so forth

00:35:29.639 --> 00:35:35.480
well and then you plot that the level of

00:35:32.960 --> 00:35:38.679
Technology the countries have visis

00:35:35.480 --> 00:35:41.639
their output per capita per worker you

00:35:38.679 --> 00:35:44.239
expain a big share of it okay so here is

00:35:41.639 --> 00:35:46.000
what you have is the relative a so

00:35:44.239 --> 00:35:49.279
everything is related to the US here

00:35:46.000 --> 00:35:51.119
okay so the the a that we measure the

00:35:49.280 --> 00:35:53.200
level of a that we measure I don't

00:35:51.119 --> 00:35:58.318
remember which year was this

00:35:53.199 --> 00:35:58.318
19 I don't remember when it was that

00:35:58.358 --> 00:36:03.559
doesn't matter H so if you measure the

00:36:01.159 --> 00:36:05.358
the relative level of technology in

00:36:03.559 --> 00:36:07.679
country ey relative to the

00:36:05.358 --> 00:36:09.400
US and then you measure the relative

00:36:07.679 --> 00:36:11.559
output per capita in that country

00:36:09.400 --> 00:36:13.440
related to the US and forget about

00:36:11.559 --> 00:36:15.719
everything else educational so on so

00:36:13.440 --> 00:36:18.480
forth you can get a pretty good

00:36:15.719 --> 00:36:21.598
relationship between the two okay so

00:36:18.480 --> 00:36:23.318
between one one half and two third of

00:36:21.599 --> 00:36:26.000
the difference in output per worker

00:36:23.318 --> 00:36:28.119
across different countries in the world

00:36:26.000 --> 00:36:30.480
can be attributed to the difference in

00:36:28.119 --> 00:36:32.760
technology level okay so that's the

00:36:30.480 --> 00:36:36.760
conclusion that we

00:36:32.760 --> 00:36:37.800
have now let me revisit the the this

00:36:36.760 --> 00:36:41.599
issue of

00:36:37.800 --> 00:36:43.119
convergence ER and and so if you if you

00:36:41.599 --> 00:36:44.838
what you do is you take countries that

00:36:43.119 --> 00:36:47.720
have more or less the same

00:36:44.838 --> 00:36:49.199
a and that have more or less the same

00:36:47.719 --> 00:36:51.759
levels of

00:36:49.199 --> 00:36:53.960
education then and you look at sort of

00:36:51.760 --> 00:36:56.079
their their the path of their output per

00:36:53.960 --> 00:36:59.358
capita you get that the models we have

00:36:56.079 --> 00:37:01.480
been discussing here work St well okay

00:36:59.358 --> 00:37:03.039
so here you see that you know they're

00:37:01.480 --> 00:37:05.639
more or less growing together there are

00:37:03.039 --> 00:37:07.519
Wars and stuff like that here so so

00:37:05.639 --> 00:37:09.679
there are great recessions and things

00:37:07.519 --> 00:37:13.318
like that but on average you see sort of

00:37:09.679 --> 00:37:16.838
the countries that that were behind sort

00:37:13.318 --> 00:37:20.079
of cut up and so on okay big dispers

00:37:16.838 --> 00:37:22.358
here they were all growing together and

00:37:20.079 --> 00:37:24.280
as more time passes the closer they get

00:37:22.358 --> 00:37:27.559
to each other because you know they're

00:37:24.280 --> 00:37:29.000
converging these guys the US and the UK

00:37:27.559 --> 00:37:33.279
were already sort of very close to the

00:37:29.000 --> 00:37:35.679
stady state very in 1870s while Japan

00:37:33.280 --> 00:37:37.560
was way behind but it was sort of in the

00:37:35.679 --> 00:37:40.960
same class of countries in terms of

00:37:37.559 --> 00:37:42.599
technology and in terms of H education

00:37:40.960 --> 00:37:47.480
levels and so

00:37:42.599 --> 00:37:49.318
on so it works pretty well H this is H

00:37:47.480 --> 00:37:52.318
for for more

00:37:49.318 --> 00:37:55.079
countries and you you plot per capita

00:37:52.318 --> 00:37:58.239
income in 1870 again for countries that

00:37:55.079 --> 00:38:01.280
have similar A's and K's uh

00:37:58.239 --> 00:38:02.519
A A and H and you look at the rate of

00:38:01.280 --> 00:38:04.560
growth and you get exactly what you

00:38:02.519 --> 00:38:07.559
would expect countries that were further

00:38:04.559 --> 00:38:09.318
behind CAU up that's Japan very fast

00:38:07.559 --> 00:38:11.519
rate of growth and you get this very

00:38:09.318 --> 00:38:13.800
negative relationship okay so this is

00:38:11.519 --> 00:38:16.880
the convergence model it works extremely

00:38:13.800 --> 00:38:18.440
well conditional on having the same a

00:38:16.880 --> 00:38:20.358
and AG so that's the contribution of

00:38:18.440 --> 00:38:22.079
this lecture it tells you I already told

00:38:20.358 --> 00:38:24.880
you that this convergence model Works

00:38:22.079 --> 00:38:28.400
quite well the point is now that it

00:38:24.880 --> 00:38:29.880
works very well and I had told you early

00:38:28.400 --> 00:38:32.440
on I think in the first lecture on

00:38:29.880 --> 00:38:33.838
growth that this work very well for

00:38:32.440 --> 00:38:35.200
certain kind of countries but then when

00:38:33.838 --> 00:38:37.039
we put all of them together there were

00:38:35.199 --> 00:38:38.838
some countries that were clearly off and

00:38:37.039 --> 00:38:41.639
they were mostly in Africa but you had

00:38:38.838 --> 00:38:44.078
countries that had low per capita income

00:38:41.639 --> 00:38:47.000
and they grew very little during that

00:38:44.079 --> 00:38:49.039
the sample I show you so here I'm

00:38:47.000 --> 00:38:50.280
refining that I'm saying okay now I'm

00:38:49.039 --> 00:38:53.318
going to tell you a little bit more what

00:38:50.280 --> 00:38:54.560
I mean by countries being similar and

00:38:53.318 --> 00:38:57.800
what I mean here is that they have

00:38:54.559 --> 00:39:00.358
similar A and H okay so when I look at

00:38:57.800 --> 00:39:02.920
countries that have similar A and H they

00:39:00.358 --> 00:39:04.000
work the models we have discussed work

00:39:02.920 --> 00:39:06.480
extremely

00:39:04.000 --> 00:39:08.079
well this is over a shorter period of

00:39:06.480 --> 00:39:11.000
time so you have more fluctuations and

00:39:08.079 --> 00:39:12.519
more countries but still and you know

00:39:11.000 --> 00:39:14.119
you can argue that Mexico and Chile

00:39:12.519 --> 00:39:16.239
probably do not belong with many of

00:39:14.119 --> 00:39:19.200
these other countries but you still get

00:39:16.239 --> 00:39:22.118
this negative relationship is quite

00:39:19.199 --> 00:39:24.480
clear now if you don't control by A and

00:39:22.119 --> 00:39:26.519
H you put everything together then the

00:39:24.480 --> 00:39:30.838
plot looks like the plot I showed you

00:39:26.519 --> 00:39:34.239
earlier okay so if I control by A A and

00:39:30.838 --> 00:39:37.358
H the moles work very well if I don't

00:39:34.239 --> 00:39:40.000
control for a andh then the M do not

00:39:37.358 --> 00:39:42.759
look that nice

00:39:40.000 --> 00:39:45.280
okay so this led to a literature which

00:39:42.760 --> 00:39:48.560
is called the conditional convergence

00:39:45.280 --> 00:39:51.040
literature and the idea it's almost

00:39:48.559 --> 00:39:53.519
accounting but the idea is the following

00:39:51.039 --> 00:39:55.838
so so the question that that that was

00:39:53.519 --> 00:39:58.800
behind this literature is well why is it

00:39:55.838 --> 00:40:03.119
that we have some countries

00:39:58.800 --> 00:40:05.720
say here no that have a very low income

00:40:03.119 --> 00:40:08.838
per capita and grow very slowly that's a

00:40:05.719 --> 00:40:13.439
puzzle how can it happen that we have

00:40:08.838 --> 00:40:15.000
that and the the the the story but again

00:40:13.440 --> 00:40:17.639
it's more accounting than an explanation

00:40:15.000 --> 00:40:20.679
in my view is is what is called

00:40:17.639 --> 00:40:23.358
conditional convergence says for some

00:40:20.679 --> 00:40:26.440
reason probably has to be explained in

00:40:23.358 --> 00:40:30.199
terms of you know institutions political

00:40:26.440 --> 00:40:32.440
instability or whatever for some reason

00:40:30.199 --> 00:40:34.439
some countries have just lower steady

00:40:32.440 --> 00:40:36.240
state levels of Technology lower steady

00:40:34.440 --> 00:40:37.599
States because they they have lower

00:40:36.239 --> 00:40:42.838
Technologies and they're stuck with

00:40:37.599 --> 00:40:45.720
lower Technologies and so on okay uh

00:40:42.838 --> 00:40:49.799
so so what this literature does is says

00:40:45.719 --> 00:40:51.838
okay let's compute the St state so let's

00:40:49.800 --> 00:40:53.800
accept that some countries will have

00:40:51.838 --> 00:40:55.960
lower level of Technology that's what it

00:40:53.800 --> 00:40:57.560
is maybe at some point they'll flip from

00:40:55.960 --> 00:41:01.199
there but you know they have been for a

00:40:57.559 --> 00:41:03.000
long time in in in a stock that let's

00:41:01.199 --> 00:41:05.639
assume that they have have a different

00:41:03.000 --> 00:41:08.679
level of technology so that means let's

00:41:05.639 --> 00:41:12.400
compute for each country its steady

00:41:08.679 --> 00:41:14.118
state its own steady state using its own

00:41:12.400 --> 00:41:15.800
technology and its own level of

00:41:14.119 --> 00:41:17.400
Education

00:41:15.800 --> 00:41:20.640
okay

00:41:17.400 --> 00:41:23.760
so so in particular this in this plot

00:41:20.639 --> 00:41:28.078
I'm going to show you er er take the

00:41:23.760 --> 00:41:30.000
values the value of a for 1970

00:41:28.079 --> 00:41:33.000
that's the plot I'm going to show you

00:41:30.000 --> 00:41:35.679
the Valu that each country had in 1970

00:41:33.000 --> 00:41:37.679
compute the state state level of output

00:41:35.679 --> 00:41:39.239
corresponding to that

00:41:37.679 --> 00:41:42.159
a

00:41:39.239 --> 00:41:45.719
okay a and over time it will be growing

00:41:42.159 --> 00:41:49.078
at GA whatever but but take the a of

00:41:45.719 --> 00:41:52.519
1970 compute the state value of

00:41:49.079 --> 00:41:54.720
that compare it with the current output

00:41:52.519 --> 00:41:56.400
over that if the current output is below

00:41:54.719 --> 00:41:58.239
that that means that the this country

00:41:56.400 --> 00:42:00.240
still needs to catch up have not with

00:41:58.239 --> 00:42:02.118
respect to some Universal stady state

00:42:00.239 --> 00:42:04.639
but with respect to its own stady state

00:42:02.119 --> 00:42:06.280
with its lower technology and whatever

00:42:04.639 --> 00:42:08.879
okay and

00:42:06.280 --> 00:42:11.119
then look at whether we see convergence

00:42:08.880 --> 00:42:14.880
or not and the answer is that you start

00:42:11.119 --> 00:42:16.720
recovering a this downward sloping curve

00:42:14.880 --> 00:42:19.720
so what does this say what is the the

00:42:16.719 --> 00:42:22.558
big story is telling us it's saying look

00:42:19.719 --> 00:42:25.959
some countries for reasons that are

00:42:22.559 --> 00:42:28.720
Beyond this mold just simply have much

00:42:25.960 --> 00:42:30.559
Lower State States

00:42:28.719 --> 00:42:32.519
yeah they have lower Technologies they

00:42:30.559 --> 00:42:35.440
don't know how to use more complicated

00:42:32.519 --> 00:42:38.119
technology I don't know well but that's

00:42:35.440 --> 00:42:40.480
what it is they have lower Technologies

00:42:38.119 --> 00:42:42.559
and so they have their own stady states

00:42:40.480 --> 00:42:44.079
which can be stady states with very low

00:42:42.559 --> 00:42:47.480
levels of income per

00:42:44.079 --> 00:42:49.480
capita now for those countries it still

00:42:47.480 --> 00:42:53.000
applies and that's what this picture

00:42:49.480 --> 00:42:56.639
shows that if they are not at their

00:42:53.000 --> 00:42:58.599
state state still have lower Capital per

00:42:56.639 --> 00:43:00.759
war effect worker than they need to have

00:42:58.599 --> 00:43:03.920
in their stady state that they will have

00:43:00.760 --> 00:43:07.359
transitional growth so they will grow

00:43:03.920 --> 00:43:09.519
faster than their growth in the in in in

00:43:07.358 --> 00:43:11.679
in their own steady

00:43:09.519 --> 00:43:14.239
state and that's what this picture shows

00:43:11.679 --> 00:43:16.039
you you know these are countries that

00:43:14.239 --> 00:43:20.039
that grew very little look at we have

00:43:16.039 --> 00:43:23.558
Japan here together with bwan I think

00:43:20.039 --> 00:43:26.358
ER and maybe Taiwan in the same in the

00:43:23.559 --> 00:43:27.839
same place okay so these are countries

00:43:26.358 --> 00:43:30.598
that still have lots of grows to do

00:43:27.838 --> 00:43:32.519
relative to their own stady State and

00:43:30.599 --> 00:43:34.920
they did grow a lot we know how do I

00:43:32.519 --> 00:43:37.119
know that well because the output I

00:43:34.920 --> 00:43:38.800
compute the output I compute relative to

00:43:37.119 --> 00:43:41.599
a steady state at the beginning of my

00:43:38.800 --> 00:43:43.599
sample was much lower than one that

00:43:41.599 --> 00:43:44.640
means that that you're not at your St

00:43:43.599 --> 00:43:48.559
State

00:43:44.639 --> 00:43:51.400
no so this variable here is the output

00:43:48.559 --> 00:43:53.920
you have at the beginning of the sample

00:43:51.400 --> 00:43:56.480
relative to what the steady state your

00:43:53.920 --> 00:43:58.760
steady state is how do you compute the

00:43:56.480 --> 00:44:00.679
stady state well you input the level of

00:43:58.760 --> 00:44:02.359
Technology you input the saving rate you

00:44:00.679 --> 00:44:04.039
input the population growth and all

00:44:02.358 --> 00:44:05.759
these kind of things so you have a

00:44:04.039 --> 00:44:08.400
number lower than one means you still

00:44:05.760 --> 00:44:11.040
have catching up growth to do not with

00:44:08.400 --> 00:44:13.119
respect to the global Universal aady

00:44:11.039 --> 00:44:15.679
state but with respect to your own aady

00:44:13.119 --> 00:44:17.400
State and when you do that you see that

00:44:15.679 --> 00:44:19.318
some countries that in the s in the

00:44:17.400 --> 00:44:21.079
total sample look like they're not

00:44:19.318 --> 00:44:22.599
growing and so on so forth they are

00:44:21.079 --> 00:44:24.680
growing they're just

00:44:22.599 --> 00:44:26.480
growing you know relative to their own

00:44:24.679 --> 00:44:28.919
stady state which has little growth and

00:44:26.480 --> 00:44:32.920
it has low levels of technology and so

00:44:28.920 --> 00:44:35.880
on and so that's a conclusion of this

00:44:32.920 --> 00:44:38.480
conditional convergence literature now

00:44:35.880 --> 00:44:41.240
it turns out that that that the world

00:44:38.480 --> 00:44:44.760
has become very unequal also on this

00:44:41.239 --> 00:44:47.558
Dimension over time this this shows you

00:44:44.760 --> 00:44:49.280
the ratio of GDP per worker of the 90th

00:44:47.559 --> 00:44:51.760
percentile to the 10th percentile

00:44:49.280 --> 00:44:53.280
country and so you have not only big

00:44:51.760 --> 00:44:55.599
difference in technology across the

00:44:53.280 --> 00:44:57.720
world but also you have very different

00:44:55.599 --> 00:44:59.519
rates of growth in techn technology

00:44:57.719 --> 00:45:01.639
across different countries on the world

00:44:59.519 --> 00:45:04.519
so this difference is sort of increasing

00:45:01.639 --> 00:45:07.039
quite dramatically

00:45:04.519 --> 00:45:10.559
okay I don't know what happened

00:45:07.039 --> 00:45:10.558
here but

00:45:10.679 --> 00:45:15.879
uh I mean I'm saying so the world

00:45:14.119 --> 00:45:18.240
started with with count this is telling

00:45:15.880 --> 00:45:20.280
you it started with countries that you

00:45:18.239 --> 00:45:24.118
know were richer than others and that

00:45:20.280 --> 00:45:26.319
distance has been rising over

00:45:24.119 --> 00:45:28.960
time but sort of towards the end we

00:45:26.318 --> 00:45:28.960
began to change

00:45:29.119 --> 00:45:34.079
here I think that has a lot to do with

00:45:31.679 --> 00:45:36.440
China that was a poor economy that grew

00:45:34.079 --> 00:45:37.839
very fast During the period and it

00:45:36.440 --> 00:45:39.119
wasn't very large here so it didn't

00:45:37.838 --> 00:45:42.119
matter as much but then it began to

00:45:39.119 --> 00:45:44.760
count a lot I think I'm not completely

00:45:42.119 --> 00:45:47.318
sure that's it anyways but that's the

00:45:44.760 --> 00:45:50.119
state of knowledge in this I mean

00:45:47.318 --> 00:45:53.079
obviously there's a big literature

00:45:50.119 --> 00:45:57.519
around follow of this and and very

00:45:53.079 --> 00:46:01.160
complex even literature but but there's

00:45:57.519 --> 00:46:04.559
we understand we know that that that we

00:46:01.159 --> 00:46:07.358
have a you know good ways of explaining

00:46:04.559 --> 00:46:11.599
how a country converges to its own EST

00:46:07.358 --> 00:46:14.119
State ER that we have very poor models

00:46:11.599 --> 00:46:18.160
certainly within economics if go

00:46:14.119 --> 00:46:20.960
to um within growth Theory per

00:46:18.159 --> 00:46:22.879
se there there a l institutions and

00:46:20.960 --> 00:46:26.000
stuff like that explain some of that but

00:46:22.880 --> 00:46:27.440
we have very poor models in general H to

00:46:26.000 --> 00:46:29.440
understand sort of what

00:46:27.440 --> 00:46:31.960
gives rise to this big

00:46:29.440 --> 00:46:33.960
disparity in in the in technology

00:46:31.960 --> 00:46:37.639
adoption and so

00:46:33.960 --> 00:46:40.800
on so that's all that I want to say

00:46:37.639 --> 00:46:42.400
about growth the next topic is we're

00:46:40.800 --> 00:46:44.640
going to open the economy we're going to

00:46:42.400 --> 00:46:46.400
go back to the type of models we had

00:46:44.639 --> 00:46:49.838
very early on but now in the context of

00:46:46.400 --> 00:46:49.838
an open economy