so after doing aslm in the first part of
the course and where we took prices
completely sticky and output was fully
determined by aggregate demand uh we
said well that minates in the very very
short run but but over time at some
point the supply side start showing up
there are constraints the labor market
gets very tight and so on and and so we
added a block that started from wage
determination and then we look at the
impact of wages on
prices and then we related inflation
rate use that to relate inflation rate
to economic activity so output above or
below the potential output or or the
natural level of output and things of
that kind so remember the starting point
was a um a wage
demand equations so what what workers
demand for a wage this period depends on
how what's the price level they expect
for the period because they set the wage
today and they have to leave through the
year or to whatever is the Contracting
period H with that nominal wage so
naturally if if they expect higher price
level in the future they're going to
demand the higher nominal wage today and
then we said that's a funion that is
also going to be decreasing in the level
of unemployment because the obviously
that weakens bargaining for power for
workers or makes makes actually becoming
unemployed or not having a job H more
costly because it's very difficult to
exit out of unemployment and then we
made us an normalization this function
also an increasing function on this
variable Z which captures a bunch of
Labor Market institutions including wage
labor bargaining power so more
bargaining power means that for any
given level of unemployment workers
would tend to demand a higher wage okay
so that's what the Z variable was all
about then we wanted to go from wages to
prices H because the ultimate goal was
to bring inflation into the picture and
and for that we have to produce a we we
introduce a production function H
because uh in particular out we made
output a function of employment and and
that very naturally will connect wage
pressure to price pressure because you
know you need labor to produce output so
the labor market is very tight that
means also it's going to be more
expensive to produce output and we
simplifi this production function a lot
we made it output equal to employment
and that meant also that one unit of
Labor in order to produce one extra unit
of output you need one extra unit of
label which means you need to pay a wage
okay one one one unit of the wage and so
then we said suppose that the price
setting from the side of the firms
simply takes this cost which is the wage
and adds a markup to it to pay for a
bunch of other things that we haven't
introduced in this model okay so the
price charged by firms is equal to the
wage times one plus some positive
numbers 8.2 or something like that so
1.2 H and we can write rewrite this
price setting equation as a wage the
real wage the firms are willing to offer
and it's just equal to that okay so when
the markup goes up that means the real
wage the firms are willing to offer is
lower than
otherwise okay that took us to the
concept of the natural rate of
unemployment and and and what the
natural what I said no is there's
nothing natural about the natural rate
of unemployment it's simply a definition
that says that's an employment that
results when the price expected price is
equal to the actual price that's that's
what that's all that that is and if when
when we have that condition then we can
think of the real wage demanded by work
because I can replace expected price for
actual price and divide both sides by
price so the actual wage demanded by
workers is equal to a function of the
natural rate of unemployment and I stick
the end there precisely because I
replace expected price or P for no other
reason okay but now we have two
equations for the real wage the real
wage that firms are willing to pay and
the real weight of workers need to
demand and we can make them both equal
and that determines the natural rate of
unemployment okay so remember this from
the point of view of the firm this is
equal to one over one plus a marup the
only endogenous variable the marup is a
constant the Z is also a parameter is
exogenous and so from the here we can
solve the natural rate of unemployment 1
over 1 plus M and we can solve the
natural rate of unemployment and if you
do the algebra right you you're going to
get to a point like that that pins down
natural rate of unemployment again there
is nothing natural about the natural
rate of unemployment it depends on a
bunch of parameters okay which for
example it clearly depends on the markup
it depends on things that we took as
constant here as given here all the
things that wear in Z those are part of
that and so we then we look at things
that change and that's just done with
equations we look at things that change
the natural rate of unemployment that's
one example if bargaining Power by
workers goes up they're going to demand
a higher wage at the initial natural
rate of unemployment well that obviously
that higher wage is inconsistent with
what firms are willing to pay the only
way equilibrium can be restor in this
model that's the medium run equilibrium
is for the natural rate of unemployment
to rise to un Prime okay
so there you have it nothing natural the
natural rate of employ is not constant
it depends on institutional parameters
such as bargaining power another example
is markups it depends on markups as well
the degree of competition if you will in
the Goods Market if if we are in some
equilibrium like this one and now
suddenly firms for whatever
reason choose or need to charge a higher
markup that h means that that at this
level of unemploy the wage that workers
would demand is higher than the wage
that firms are willing to pay the real
wage and the only thing that can clear
the market in this case here in the
medium run is for the natural rate of
unemployment to rise okay so here we got
two experiments where we move some
parameter one the bargaining power of
workers and the other one the the markup
of the firms and both increase the
natural rate of unemployment
good The Next Step was
to look at things that happen outside
the natural rate of unemployment and
particular what happens to prices there
okay we look so what we did is we took
the we went back to the
model with the expected price here that
means an employment that comes out from
this equilibrium is not is not going to
be necessarily the natural rate of an
employment that will be the case only if
P happens to be equal to p h then we
simplify this function f here for
something linear like this very simple
but again decreasing in unemployment
increasing in this institutional
parameters
z h we replace this wage here from this
expression here and rearrange so we got
this
here okay and the next step was just to
go from here to rate of inflation and we
did it through a SE several steps and
approximations and we ended up with what
is known as the Philips curve okay so
this say inflation is increasing an
expected inflation on these
institutional parameters if the markups
go up that will tend to
increase inflation H if bargaining Power
by workers go up then that's the same
but most importantly is negatively
related to unemployment and that's the
reason that today nowadays you know
there's lots of discussion about the
tightness in the labor market and and
whether that's really necessary do we
need to cause a recession a situation
where an employment goes up a lot in
order to really finally bring down
inflation yeah that's was
question is
alha oh remember that I made up this
function we said this function is
decreasing
unemployment I just
uh replace that function for that
okay so it's a sensitivity of wage
Demand by workers to their employment
rate Alpha that is very high means that
wage demand is very sensitive very
responsive to unemployment y intuition
for like an expected price like could
you connect that back to like I don't
know some sort of like a commodity or
something or so what is the intuition
for for this yeah like just like a price
feels tactile but like an expected price
I don't well I mean imagine that workers
and firms bargain for a wage that will
live through the year you're buying by
you're bargaining for the wage nominal
wage today you don't set a real wage you
set the nominal wage say $100 whatever
well the wage demand will depend a lot
on on what I expect inflation to be
during this period if I expect inflation
to be 10% you're very likely to demand a
higher nominal wage because you have to
leave an average with higher prices so
that's that's the role of that is the
price I mean I I would prefer and there
are countries where that's done to set
my wage in real terms so I don't need to
worry about that but in practice you in
economies with low inflation like the US
you don't do that you you get a nominal
wage and you have to leave for a year or
until the next negotiation for your wage
contract with that level of of wages
okay with the interest rate or with the
the inflation rate whereas the I guess
the regular price is defined by the wage
is depend on the market no no they're
both the same but one is the only thing
is
that this price here is not sort of the
current is what you really expect the
price to be during the year is that is
this is here just because at the moment
in which you set the wage you don't know
the price you're going to face as a as a
worker but it's it's the price so you
don't know the price that you're going
to actually face so the only the best
you can do is calculate well I think
inflation is going to be 10% so give me
know what I would have had in mind with
inflation equal to zero plus 5% so on
average I'm about right that's sort of
the
logic but this expected price is meant
to be your best proxy you have at the
moment in which you're bargaining for
your wage for what the actual price will
be during the life of that particular
wage
okay
um okay so we end up with that that that
uh Philips curve here importantly this
an decreasing function of
unemployment er um and then we' made
different assumptions about expectations
if expected inflation for example is a
constant that's when we say expected
infl inflation is very well anchored
then you get a Philips curve that looks
like this in which inflation it has a
constant here and it's decreasing on the
rate of unemployment and and during the
60s H that that relationship sort of
held fairly well it was a downward slope
in relationship it got to be steeper and
steeper as we moved into higher and
higher inflation levels and then I said
but in the 70s the whole thing broke
loose you nothing like a downward
sloping curve here that happened for two
reasons there were some cause push
shocks you can think of lots of shocks
to M but more interesting H expected
inflation became an anchor and then we
changed then H the expected inflation
mod for rather than being a constant
being the some weighted average like
this and we said look during the
70s essentially that that Theta was
equal to one okay so inflation expected
inflation was really whatever was
inflation last year people expected that
level of inflation to stay the next year
rather than going back to that whatever
was the constant or inflation Target or
historical constant pi and and that
meant that the the during that period
really the Philips curve looked more
like a relationship of the change in the
inflation rate as a decrease in function
of unemployment so that means that when
you increase an employment here you
reduce a rate at which unemployment is
inflation is rising okay that's the goal
of
the situation in in a case in
which expected inflation is an an anchor
and the last step we had there is we
replace we notice we said well what
happens if we stick in here the natural
rate of unemployment then that will give
us that will happen only when expected
price is equal to actual prices so that
means that when inflation is equal to
expected inflation from here we can
solve the natural rate of unemployment
as a function of these structural
parameters and once we have that we
could go back to our Philips curve and
rewrite it in this way okay so you can
think of the Philips curve in this way
and this is the the the way you
typically we typically write it down in
which it says H inflation is decreasing
in the unemployment
Gap
so so if the unemployment is above the
natural rate of unemployment that means
inflation will tend to be below expected
inflation if expected inflation happen
to be equal to lag inflation that means
if an employment is above the natural
rate of unemployment then inflation will
be falling
okay any questions good you need to know
this
okay how to derive these things I mean
not so much yeah you should know how to
WR but you need to understand this
relationship between the out the
unemployment Gap and
inflation relative to spected
inflation yep
unor versus de unored inflation expected
inflation it's just a statement
about ER what is the model we have H for
expected
inflation
so suppose we have the following model
for expected inflation one minus Theta
Theta some number between Z and one
times a constant
inflation plus something that is a
function of plus Thea times whatever is
previous
inflation central banks try to set a
target for the inflation rate in the US
is around 2% and ideally people will
tend to believe they may see an tempor
inflation that that is above say 2% but
as long as as as people expect that to
be undone in the in the in the next
period then inflations we say they're
very well anchored so that's a case in
which very well anchored means th equal
to Z here and you always sticking there
in the case of the US at 2% and and
there's a lot of there's a lot of that's
the way the econom is behaving right now
inflation today is 5% but if you ask
people what do you expect inflation to
be two and two years from now people
tell you me look around 2% two and a
half percent or so unanchor expectation
is when when you don't have that anchor
that 2% that the FED told you is
whatever was the previous inflation
that's what people extrapolate will be
inflation for Next Period and that's a
lot harder when you get into an
inflationary episode in that context is
very difficult because you at 5% people
are still expecting 5% for next year so
you need to is much harder to bring
inflation down you need to create much
more unemployment to bring inflation
back to the 2% 2% Target okay that's
that's what it means to an so anchor
means Theta very close to zero an anchor
Theta very close to one that's a a
formal definition
we then move
[Music]
to what I think is probably the most
important model you'll see in this
course which is the islm PC which is
just the islm plus the Philips curve and
that allow us to talk about the short
run which is what we did in the slm and
then all the way to the medium Run Okay
in medium understood as when you go back
to the Natural rate of unemployment
natural level of output and so on
oh we got a banking crisis there but
that's
oh this you may find useful here here I
was trying to explain the banking crisis
and and so and I said we have a model
for that already remember we had this x
this spreads in the investment function
I said well you can think of a negative
Financial shock something like a a
credit spread shock as an increasing X
and that will shift to left okay just
saying
good
uh islm PC model was just going back to
the islm model we're going to simplify
things by not by just assuming that the
Central Bank sets the real interest rate
and the real interest rate is that okay
ER and uh and to that we added a Philips
curve but we didn't like that Philips
curve because you know we have
everything is a function of output here
and interest rate and now we have
inflation and then employment rate so
yet another variable to carry around so
we went from H the output Gap to an
employment R an employment gap to an
output Gap and and we did that just by
noticing that output is equal to the
labor force time one minus unemployment
rate equivalently similar you can Define
potential output or the natural output
level as employment Time 1 minus the
natural rate of unemployment subtract
these two no and I you get that the
output Gap is equal to minus L times the
unemployment Gap and so we replace this
for that expression divided by L and we
end up with a Philips curve written in
the form of an increasing function of
the output Gap so when the output Gap is
positive then inflation will exceed
expected inflation if expected inflation
is an anchor that is expected inflation
is equal to lag inflation then that
means that a positive output Gap leads
to an increase in inflation inflation R
okay so we look at an example here H you
know this is the type of but now we're
going to have the real interest rate
here just makes it simpler to think
about Central monetary policy in terms
of the real interest rate otherwise too
many things move at once so this is what
we had done for quiz one here you have
some particular equilibrium the islm
with this real interest rate we
got some equilibrium output equal to Y
the new part the contribution of this
block of the course is that now we need
to also check whether this Y is is
consistent with potential output or not
with natural level of output and that
for that we need to uh see whether this
level of output H is consider again is
above or below the natural rate of
output and for that we need to look at
the Philips curve okay okay and in this
particular case that's not the the case
because output is above the natural rate
of output you put now given that
observation you you put right draw here
the the Philips curve you know that
because output is above the natural rate
of output the natural level of output
that means inflation is above expected
inflation if expected inflation happens
to be an anchor equal to Pi minus one
that means that at this output Gap that
there's an inflation that is rising okay
H now inflation Rising means the central
bank will have to react and the way we
so you'll have to do something up here
you need to bring output down and how
can you bring output
down so so this economy is is engaging
in an inflationary spiral actually given
this mod of expectation how do you stop
that if you are the fed and you you
raise the interest rate no because you
need to bring the L back so the
equilibrium level of output you need
increase the real rate up to a point in
which um the level equilibrium level of
output is equal to the Natural rate of
output um and you may have to do more
than that if inflation was an anchor and
you find yourself with 5% inflation you
may have to temporarily actually to
bring inflation back down to 2% you may
have to overshoot raise interest rate a
lot generate a negative output gap for a
while and then once you reach the level
of inflation you like the 2% then you
can go back uh to the Natural level of
output okay so that's the reason central
banks worry a lot about unanchor
expectations because then they know that
they find themselves an inflation above
their target is not going to be enough
to bring the output Gap to zero they're
going to have to overshoot in the way
down in order to re re-anchor expect
well in order to bring inflation back
down to the Target of
2% but in any event even if inflation
are expect well anchor you still have to
bring output down because at the very
least you need to close this pos
positive output Gap and that if you're
the FED in the US or any Central Bank
you do it by increasing the real
interest rate now in practice central
banks really don't control the real
interest they control the nominal
interest ratees so there's a little
fight there between inflation and and
what they do to the nominal interest
rate but let's ignore that complication
for now okay now H suppose that the FED
is is is in vacation
and and and so and and somebody someone
else you know decides in the government
decides that no we cannot have this very
high level of inflation so what else
could you
do and you're not the FED fed in
vacation who else can make
policy the government the central
government the treasury and so on no
what is the instrument they have what do
they need to do
the problem they have is output is too
high and that's what is leading to lots
of inflation so
what do you think they should
do c govern expend raise taxes something
of that kind okay but they need a fiscal
contraction because that will bring the
yes down and so equilibrium
output will be lower okay so that's an
alternative you have you should know
this
and here I just did what we just
discussed just in in a steps these
things happen slowly the F doesn't hike
interest rate in one shot and so on it
takes a while before you get to the
final
equilibrium oh I I show you the
deflationary spiral said sometimes
things can get very
complicated ER because you may hit the
zero lower bound the FED can bring the
nominal interest R to zero but if
inflation is already low that may not
give you the real interest that you need
in order to get output equal to the
Natural rate of output I me here was one
example in which you need a negative
real interest rate to get output to be
equal to Natural rate of output but that
may not happen because you you you hit
the zero lower bound H and so at that
point the problem you have is that and
that's was the trag tragedy of Japan for
so long is that not
only you cannot bring the interest rate
the nominal interest rate below zero but
you start getting into deflationary
inflation below expectation and
expectation goes to number very close to
zero because of an anchor deflation
expectations then you start getting
negative expected inflation and when you
get Negative expected inflation even if
you're at the zero lower Bound in the
nominal interest rate that means a
positive real interest rate so
effectively you're increasing interest
rate at the same time and that can be a
very complicated thing to get out of
again that's what happened to Japan for
a long
time what would you do if as a
government if you fall into a situation
like
that and Japan did a lot of
that well you can do lots of things but
but in particular of the kind of things
you know what what would you do if you
are in a situation like this in which
the zero lower bound is binding and and
inflation is actually falling here I had
a benign case in which inflation
expectation was well anchor that's not
what happened to Japan after they
experienced a long period of
deflationary forces the then the people
began to expect more deflation more
deflation and so on so what else can you
do let me give you a hint Japan is one
of the countries has the highest levels
of public debt
how do you accumulate public
debt yeah you you need to borrow a lot
you have big fiscal deficit so that's
the way you can fight this you know you
can shift the yes to the right by having
an expansionary fiscal policy that's the
only tool really you have you lose the
power of monetary policy against the
zero lower bound but you still have
fiscal policy and they did a lot of
fiscal policy
not
interesting this is this is interesting
ER that's a different kind of shock
suppose you are at your medium run
equilibrium and then all of a sudden
markups go up perhaps for example
because the price of oil went up a lot
and something like that so then what you
then that's a different kind of shock
from the previous one from from any
fiscal sh or anything like that that's
an aggregate demand this is an agre
supply problem because the first thing I
know of a permanent at least change in m
is that the natural rate of unemployment
has to
rise if the natural rate of unemployment
has to rise that mean my Philips Curve
will shift
now okay in that particular case I know
the Philips Curve will shift to the left
how do I know that well because I know
that that the natural rate of
unemployment went up which means the
natural rate of natural level of output
has to come down and the natural level
of output coming down means simply that
that the level at which is expected
inflation and inflation are
equal happens at a lower level of output
so the Philips can move to the left so
suppose you were in this equilibrium
here I'm doing for the case of an anchor
expectations but the same logic goes for
the case of anchor expectation ER so
suppose you were at some equilibrium
like this it was your medium run
equilibrium but now the price of energy
goes up a lot and and and you expect
that to last for a while that means the
Philips curve moves up so that means
that if output with output at this level
now you get you have a problem because
you start getting inflation out of this
okay because this this level of output
is too high relative to the new level of
the natural the new level of natural
level of output so you have a positive
output Gap positive output Gap means
inflation above expected inflation if
you have an anchor expectations means
inflation starts
rising
up so that means the FED now needs to
react to that and needs to tighten
interest rate in order to to go to a new
level of H natural level of output okay
and that's the response but if the F
that's not react and a little bit of
this is what happened we had some Supply
shocks and so on that were considered to
be temporary well they weren't as
temporary so there was no reaction but
it turns out that that they lasted a lot
longer than the fair expected and so so
so now they had to catch up
okay that was part of the reason we got
into a high inflation episode
that was the main reason in
Europe the US is a mixture of aggregate
demand lots of fiscal policy and so on
and ER and supply side in Europe was
very much a story of this
kind well a financial Panic you need to
upset it with a decline in in in real
interest rate and a little bit of that
has been happening it's not the FED that
has cut their rates but but the markets
have anticipated the FED will not raise
interest rate as much as they expected
before we got we got into this banking
mess so we had already sort of studied
the short run the medium run and now we
want to look at the long run okay and
that's what economic growth is about
economic growth Theory and facts and so
on let me go to so one of the things I
I highlighted is that we tend to
see among countries that are fairly
similar
along education and variables like that
systems economic systems and political
systems and so on you tend to find
relationship like this that is countries
with a lower per capita income at the
beginning of the sample tend to grow
faster in the sample and that captures
very much the idea that there's a
convergence there's a force towards
convergence of H income per capita if
you will okay that's another
illustration of that phenomenon lots of
dispersion here ER 70 years later a lot
less
dispersion but we also said that some
countries that do not match that and but
we focus most of what we did in
growth on understanding this process the
process of convergence and how it
happened with without technological
progress and so on and then we spent a
little bit of a lecture say at most 10
10 points worth in a quiz or seven
points talking about sort of anomalies
and things like that no five points or
something so the key ER object here one
of the key objects there there are a
couple but but one of them was well now
we need to be a little bit more serious
about the production function we said
because for the short it's okay to take
Capital as given and just worry about
most of the fluctuation in output will
come from fluctuations in
employment that's not so over long
periods of time capital accumulation
plays a huge role and so we need to be
explicit about the fact that Capital
matters a lot for production
okay and so we postulated a production
function like this output as increas
increasing function of cap and of
capital and labor and now we said for
this part of the course we're not going
to worry about unemployment and so on
employment labor force population
they're all the same for us here for
this part of the course and then said
this production function has some
important
properties one is it has constant
returns to scale things change quite a
bit if you don't have constant return to
scale so we have constant return to
scale which means you should know this
that if you scale all output all input
all the factors of Productions by the
same factor output Also Rises by the
same factor okay so a production
function we use a lot was aob Douglas
you know output equal square root of K *
the square root of n well the sum of
those exponents is one so that's a a
production function with constant return
to scale okay so anything that has the
exponents add up to one then you're
that's a constant return to scale
technology but importantly and it also
has decreasing returns with each of its
factor of production
that means as you rather than moving
both factors of production up you move
only one well you're going to increase
output but as just keep increasing that
factor alone you're going to increase
output by less and less and less and
less because essentially has fewer and
fewer of the
other factor of production to work with
okay and so that's decreasing returns to
Capital or labor I mean if you fix the
other factor of production you move up
it's going to increase at a decreasing
rate so one normalization that we start
with was well a scaling Factor could be
a population one over population okay
that's a scaling factor and if I do that
I multiply both everything by one / n
would go into output per person is an
increasing function of a increasing
function but at a increasing rate of
capital per person okay we plot that
function here and and this conc is
increasing but it's concave that shows
the decreasing returns of capital no h
and we got that function there then the
SEC uh and we talk
well we said H so so so when you move in
this you can increase output per person
per per person by simply increasing
Capital per person and the more you
increase Capital per person output will
increase more and more but but but at a
decreasing rate you can see that moving
a the distance between A and B is the
same as the distance between C and D
however the increasing output when you
go from A to B is enormous compar when
compare with the increasing output that
you get from the increasing capitals
over per per person from C to D okay
decreasing returns this there is another
way of of increasing output per person
which is with technological progress
when the function f shifting up over
time and we split the two main lectures
in grow both into one part one in which
we just we shut down the second Channel
and then the second important lecture
here had we focus on this channel so
that's a that's what we
have so let's go to when I shut down
this channel for now and focus on on the
case without technological progress
first okay so so we put things together
we said this is comes from the previous
lecture we can write a output per
uh per person as an increasing function
of um Capital per person second key
equation is well this is a proper it has
to be if you in a closed economy no over
expenditure or anything like we could
add that but it's not important for the
message then investment has to be equal
so investment is going to be very
important here because it's what will
make the Capital stock grow but there
has to be funed fing for that and the
funding come from saving okay and we
simplify things by assuming that the
saving function is just proportional to
the level of output which is reasonable
when you think about long run all these
things scale up when you're thinking
about very shortterm no we have some
constants and so on floating around but
but but over the long run things do
scale up and so we can write investment
in equilibrium investment has to be
equal to saving saving is proportional
to Output so we get that investment in
this economy is increasing in output
this is an constant somewhere between
zero and one okay and the last key
equation here is the capital
accumulation equation the capital
accumulation equation says that Capital
t+ One is equal to Capital today minus
the depreciation some a fraction of the
machines break down in every period but
plus the new investment plus I okay and
we rote things and replace the saving
function and so on and we end up in in
in qu an expression like this that says
Capital per person here grows with
investment which is funded by savings
which is an increasing function of
output which in turn is an increasing
function of capital per person minus
whatever is the depreciation and what we
did then the the start diagram in in in
the solo model is is we plot this
function and that function we know that
the state state is when these two things
are equal that pins down the K star of
over n k Over N start of this economy
but we also know that to the left of
that point in in capital
space this term is greater than that and
therefore H the Capital stock is rising
to the right we get that this term is
greater than that and therefore the
Capital stock is falling okay and that's
what we have in this diagram so that's
the state of the economy when when the
depreciation per worker which is the
require in the minimum in you need to
keep the Capital stock constant is
whatever is depreciation per worker no
anything else you do it will grow the
stock of capital anything less you do
you're not maintaining enough of your
Capital stock is declining and that's
exactly what happens here that's State
you have Capital below that then then uh
Capital stock will be rising because you
have lots of saving and therefore lots
of investment relative to what you need
in order to maintain the stock of the
small stock of capital you have until
you reach a c state
and the and you know the this model
alone can explain really the that
pattern we have that that you know that
the poorer economies tended to grow
faster than the Richer economies if you
think of poorer economies as economies
that are otherwise similar but that have
low a low stock of capital to start with
well those economies are going to be to
the left of the stady state and
therefore they're going to tend to grow
at whatever is the steady state rate of
growth plus this catching up growth okay
and so this is a very powerful little
model it can explain a lot of that those
convergence the convergence that we saw
in in the data
okay do you understand
this this is
important
okay then we did some experiments what
happens if you increase the saving rate
at the time when solo was writing this
model many people said that what was
behind growth was saving well in this
model we show that indeed if a saving
rate Rises then you at any given level
of capital suppose that was the oldest
state if now the saving rate Rises that
will increase H increase investment
above what you need to maintain that
level of the stock of capital so the
stock stock of capital going to start
growing when that happens output per
capita will grow faster than in a state
state because you're going to go be
going from here to there but eventually
you'll converge to the same whole rate
of growth so the point here is that the
saving rate cannot change per se does
not change the rate of growth in the
long run but it gives you transitional
growth and a lot of the the Asian
Miracle of the very fast rates of growth
from the 60s and 70s and 80s has to do
with this kind of thing very sudden
increasing saving rates plus other
institutional changes and so on but High
increase in the saving rate that also Le
led to very fast growth okay so again
this little model can explain a lot as
well it can explain when you see those
growth Miracles often is associated to
some for some
reason varies a lot across different
scenarios the saving rate went up quite
a
bit but point is so that gives you very
fast growth in the short term but
eventually pets out
okay so the the the next thing we all
that we did for a fixed population it
said well so suppose now the population
is
growing H I said the diagram we had
before would be very unpleasant because
all these curves would be shifting so
what we need well what we need to do is
divide not by a constant we need to
divide by whatever is the population at
that point in time and that will give us
the same diagram we had with one little
twist so I went through sort of a little
algebra here to arrive to a capital
accumulation equation Capital per person
equ an equation for the change in the
capital per person which is very similar
to what we had the only difference is
that the required capital investment
required to maintain the stock of
capital per person has an extra term
here
GM and I said that GM so let's think
about this
term so Delta so think of this as the
required
investment in order to maintain the
stock of capital where it
was ER if if h this Delta comes from the
fact that well you have a stock of
capital you lose a fraction of that well
you need an investment equal to that
fraction that you lost in order to
maintain the stock of capital the same
that's that's that's that's
clear but that's not enough to maintain
the capital per person constant if if
per person is rising population is
rising because even if you maintain the
stock of capital constant the
denominator is rising at the rate of
population growth
so in order to maintain the capital per
person constant you need to deal with
the growth of denominator as well and
that means you need a little you need
also investment to match the increase in
population so they can keep the capital
per person constant okay so that's a
that's a modification so in terms of our
diagram all that happened here I have
technological progress as well set it to
zero for now all that happened relative
to the previous diagram is that now this
I rotated this curve up upward a little
bit okay
GN but then you conduct analysis exactly
in the same way the only thing that is
different now is that in the previous
model we had that the rate of growth the
stady state rate of growth was equal to
zero and the state state rate of growth
of output per person was also equal to
zero population was not growing output
was not growing the ratio wasn't growing
either here is still the case that in a
steady state output per person is is not
growing okay but that also means since
population is growing at the rate GN or
N I don't know how I call it here H that
means output must be also growing at the
rate GN that's what will keep output per
person not growing okay so so for the
output itself a very important factor in
in in in in the in growth is population
growth and if you look at rates of
growth in general in the world s
certainly in the developed World H
they're falling for a variety of reasons
and one of them is because population
growth is
falling okay but per person that doesn't
make a difference but but but for the
level the rate of growth it does and
then we we added technological progress
which we model as a effective as
enhancing labor so having a better
technology means is as you had more
workers so for any given level of
workers having a better technology we
model it as having more workers okay and
you can model it exactly that way you
can use exactly the same diagram we had
before but now we will divide our
scaling Factor rather than being one
over population is going to be one over
effective population effective workers
one over again and you conduct exactly
the same analysis you do exactly the
same approximations I did before H but
the difference now is
that ER is that here you have a rather
than GN you have
G why is that well because if I want to
maintain the capital per effective
worker constant then I need to First
make up for the depreciation of the
stock of capital that's I have to
stabilize the numerator but then I have
to take into account that the
denominator is growing for two reasons
because population is growing and
because technology is growing and in
order to maintain the ratio constant I'm
going to have to investment so so to
maintain that ratio constant and that's
the reason now we
have this this line here rotates even
further and we get Delta plus GA plus GN
okay and you should play with these
things what happen in this diagram if I
you know if I increase GA or stuff like
that and notice that here now still you
have a steady state but it's a steady
state in the space of output per
effective worker in capital per
effective worker that means for example
that so that means that these quantities
are not growing in the stady state but
output will be growing at which rate in
the stady state in any state state here
what is the rate of growth of
output if output Over N is constant in
in the today
State how can that happen output has to
be growing at which rate at the same
rate as the
denominator so it's GA plus
GN what about that's a tricker question
what happens to Output per person in
this stady state what rate is it growing
at output per
person sorry somebody said the right
thing but ga exactly I want to keep this
ratio constant I'm asking the question
at which Pace does this need to rise in
order to maintain this constant well at
the same rate as a is growing
good here we also did we asked the
question well could it be that here if
we change the saving rate we get some
extra kick in the long run and the
answer is no for the same logic as we
had before you're going to get
transitional growth but you're
eventually you're going to convert to a
stady state and the rate of growth in
the long run is not going to be a
function of the saving rate is going to
be equal to GA plus GN
okay
good do here measuring technological
progress blah blah told you the story of
China
good oh we run out of time so let me
just say the the the last thing uh that
I want to say so the last thing we
discussed you say well what happen if
you add education to this and and try to
no I make what am I doing yeah I
expanded the model a little bit I had
education and said does this change
conclusions a lot I said no not really I
mean it it doesn't change the conclusion
with respect to the long run it affects
the level of output per capita if you
have more education but it want a che
affect the rate of growth in the long
run and the last point I made is that
look H in this model if you expand it
and you try to assume the technology the
technology is the same and the rate of
technological progress is the same
across the world you stick those
parameters in the mod population growth
education levels and all that then you
don't explain the amount of inequality
we see in the world the world will look
a lot flatter if if it was just H
differences in population growth
depreciation
education level and things like that but
with the same technology so if you want
to account for so this model the
mod doesn't produce enough
inequality in the world you need to add
something else that explains that we
have some countries in Africa that are
not growing that they're growing at a
very low levels rate and we said that
something else technology for whatever
reason it happens that there's a pocket
of countries that that seem to have a
lower sort of permanently lower level of
technology and both level and growth
rate and that's what explains sort of a
subset of countries that are sort of
seem stack they are not consistent with
this convergence type thing so that's
the reason it's called conditional
convergence those countries themselves
are converging to something but they're
converging to something much lower and
with much lower rate of growth than most
of the rest of the world but for the
final lesson is for the average country
on
average it's clear that poorer countries
grow faster than richer countries that's
a that's that's a dominant Force but you
need a little more if you want to
explain certain pockets of the world
okay