Advertisement
50:23
Transcript
0:18
so after doing aslm in the first part of
0:20
the course and where we took prices
0:22
completely sticky and output was fully
0:25
determined by aggregate demand uh we
0:27
said well that minates in the very very
0:30
short run but but over time at some
0:34
point the supply side start showing up
0:35
there are constraints the labor market
Advertisement
0:37
gets very tight and so on and and so we
0:40
added a block that started from wage
0:44
determination and then we look at the
0:46
impact of wages on
0:48
prices and then we related inflation
0:51
rate use that to relate inflation rate
0:53
to economic activity so output above or
0:56
below the potential output or or the
1:00
natural level of output and things of
1:02
that kind so remember the starting point
Advertisement
1:05
was a um a wage
1:08
demand equations so what what workers
1:11
demand for a wage this period depends on
1:13
how what's the price level they expect
1:16
for the period because they set the wage
1:18
today and they have to leave through the
1:19
year or to whatever is the Contracting
1:22
period H with that nominal wage so
1:25
naturally if if they expect higher price
1:27
level in the future they're going to
1:29
demand the higher nominal wage today and
1:32
then we said that's a funion that is
1:34
also going to be decreasing in the level
1:35
of unemployment because the obviously
1:39
that weakens bargaining for power for
1:41
workers or makes makes actually becoming
1:45
unemployed or not having a job H more
1:49
costly because it's very difficult to
1:50
exit out of unemployment and then we
1:53
made us an normalization this function
1:55
also an increasing function on this
1:56
variable Z which captures a bunch of
1:59
Labor Market institutions including wage
2:02
labor bargaining power so more
2:03
bargaining power means that for any
2:05
given level of unemployment workers
2:07
would tend to demand a higher wage okay
2:10
so that's what the Z variable was all
2:13
about then we wanted to go from wages to
2:16
prices H because the ultimate goal was
2:18
to bring inflation into the picture and
2:22
and for that we have to produce a we we
2:24
introduce a production function H
2:27
because uh in particular out we made
2:30
output a function of employment and and
2:33
that very naturally will connect wage
2:36
pressure to price pressure because you
2:37
know you need labor to produce output so
2:40
the labor market is very tight that
2:42
means also it's going to be more
2:43
expensive to produce output and we
2:46
simplifi this production function a lot
2:48
we made it output equal to employment
2:51
and that meant also that one unit of
2:54
Labor in order to produce one extra unit
2:57
of output you need one extra unit of
3:00
label which means you need to pay a wage
3:03
okay one one one unit of the wage and so
3:07
then we said suppose that the price
3:08
setting from the side of the firms
3:10
simply takes this cost which is the wage
3:13
and adds a markup to it to pay for a
3:14
bunch of other things that we haven't
3:16
introduced in this model okay so the
3:19
price charged by firms is equal to the
3:21
wage times one plus some positive
3:23
numbers 8.2 or something like that so
3:25
1.2 H and we can write rewrite this
3:28
price setting equation as a wage the
3:32
real wage the firms are willing to offer
3:34
and it's just equal to that okay so when
3:36
the markup goes up that means the real
3:39
wage the firms are willing to offer is
3:41
lower than
3:44
otherwise okay that took us to the
3:46
concept of the natural rate of
3:48
unemployment and and and what the
3:50
natural what I said no is there's
3:52
nothing natural about the natural rate
3:53
of unemployment it's simply a definition
3:56
that says that's an employment that
3:58
results when the price expected price is
4:01
equal to the actual price that's that's
4:04
what that's all that that is and if when
4:07
when we have that condition then we can
4:09
think of the real wage demanded by work
4:13
because I can replace expected price for
4:16
actual price and divide both sides by
4:17
price so the actual wage demanded by
4:21
workers is equal to a function of the
4:23
natural rate of unemployment and I stick
4:26
the end there precisely because I
4:28
replace expected price or P for no other
4:31
reason okay but now we have two
4:33
equations for the real wage the real
4:34
wage that firms are willing to pay and
4:37
the real weight of workers need to
4:39
demand and we can make them both equal
4:42
and that determines the natural rate of
4:44
unemployment okay so remember this from
4:47
the point of view of the firm this is
4:48
equal to one over one plus a marup the
4:51
only endogenous variable the marup is a
4:53
constant the Z is also a parameter is
4:56
exogenous and so from the here we can
4:59
solve the natural rate of unemployment 1
5:01
over 1 plus M and we can solve the
5:03
natural rate of unemployment and if you
5:05
do the algebra right you you're going to
5:07
get to a point like that that pins down
5:10
natural rate of unemployment again there
5:12
is nothing natural about the natural
5:14
rate of unemployment it depends on a
5:15
bunch of parameters okay which for
5:19
example it clearly depends on the markup
5:21
it depends on things that we took as
5:23
constant here as given here all the
5:26
things that wear in Z those are part of
5:28
that and so we then we look at things
5:31
that change and that's just done with
5:33
equations we look at things that change
5:35
the natural rate of unemployment that's
5:37
one example if bargaining Power by
5:40
workers goes up they're going to demand
5:41
a higher wage at the initial natural
5:43
rate of unemployment well that obviously
5:46
that higher wage is inconsistent with
5:47
what firms are willing to pay the only
5:49
way equilibrium can be restor in this
5:52
model that's the medium run equilibrium
5:54
is for the natural rate of unemployment
5:56
to rise to un Prime okay
6:00
so there you have it nothing natural the
6:02
natural rate of employ is not constant
6:04
it depends on institutional parameters
6:05
such as bargaining power another example
6:09
is markups it depends on markups as well
6:12
the degree of competition if you will in
6:13
the Goods Market if if we are in some
6:17
equilibrium like this one and now
6:18
suddenly firms for whatever
6:21
reason choose or need to charge a higher
6:24
markup that h means that that at this
6:28
level of unemploy the wage that workers
6:31
would demand is higher than the wage
6:32
that firms are willing to pay the real
6:34
wage and the only thing that can clear
6:36
the market in this case here in the
6:38
medium run is for the natural rate of
6:40
unemployment to rise okay so here we got
6:43
two experiments where we move some
6:46
parameter one the bargaining power of
6:47
workers and the other one the the markup
6:50
of the firms and both increase the
6:53
natural rate of unemployment
6:56
good The Next Step was
7:00
to look at things that happen outside
7:01
the natural rate of unemployment and
7:03
particular what happens to prices there
7:06
okay we look so what we did is we took
7:09
the we went back to the
7:11
model with the expected price here that
7:15
means an employment that comes out from
7:16
this equilibrium is not is not going to
7:18
be necessarily the natural rate of an
7:20
employment that will be the case only if
7:22
P happens to be equal to p h then we
7:25
simplify this function f here for
7:27
something linear like this very simple
7:30
but again decreasing in unemployment
7:32
increasing in this institutional
7:34
parameters
7:35
z h we replace this wage here from this
7:40
expression here and rearrange so we got
7:43
this
7:44
here okay and the next step was just to
7:47
go from here to rate of inflation and we
7:50
did it through a SE several steps and
7:52
approximations and we ended up with what
7:55
is known as the Philips curve okay so
7:58
this say inflation is increasing an
8:00
expected inflation on these
8:02
institutional parameters if the markups
8:05
go up that will tend to
8:07
increase inflation H if bargaining Power
8:11
by workers go up then that's the same
8:14
but most importantly is negatively
8:16
related to unemployment and that's the
8:18
reason that today nowadays you know
8:21
there's lots of discussion about the
8:23
tightness in the labor market and and
8:25
whether that's really necessary do we
8:27
need to cause a recession a situation
8:28
where an employment goes up a lot in
8:30
order to really finally bring down
8:32
inflation yeah that's was
8:35
question is
8:37
alha oh remember that I made up this
8:39
function we said this function is
8:41
decreasing
8:43
unemployment I just
8:46
uh replace that function for that
8:50
okay so it's a sensitivity of wage
8:54
Demand by workers to their employment
8:57
rate Alpha that is very high means that
9:00
wage demand is very sensitive very
9:02
responsive to unemployment y intuition
9:05
for like an expected price like could
9:07
you connect that back to like I don't
9:08
know some sort of like a commodity or
9:10
something or so what is the intuition
9:12
for for this yeah like just like a price
9:15
feels tactile but like an expected price
9:18
I don't well I mean imagine that workers
9:21
and firms bargain for a wage that will
9:24
live through the year you're buying by
9:26
you're bargaining for the wage nominal
9:28
wage today you don't set a real wage you
9:30
set the nominal wage say $100 whatever
9:34
well the wage demand will depend a lot
9:36
on on what I expect inflation to be
9:38
during this period if I expect inflation
9:41
to be 10% you're very likely to demand a
9:43
higher nominal wage because you have to
9:44
leave an average with higher prices so
9:46
that's that's the role of that is the
9:48
price I mean I I would prefer and there
9:51
are countries where that's done to set
9:53
my wage in real terms so I don't need to
9:55
worry about that but in practice you in
9:57
economies with low inflation like the US
9:59
you don't do that you you get a nominal
10:01
wage and you have to leave for a year or
10:03
until the next negotiation for your wage
10:05
contract with that level of of wages
10:10
okay with the interest rate or with the
10:14
the inflation rate whereas the I guess
10:17
the regular price is defined by the wage
10:19
is depend on the market no no they're
10:21
both the same but one is the only thing
10:23
is
10:24
that this price here is not sort of the
10:28
current is what you really expect the
10:29
price to be during the year is that is
10:32
this is here just because at the moment
10:33
in which you set the wage you don't know
10:36
the price you're going to face as a as a
10:37
worker but it's it's the price so you
10:41
don't know the price that you're going
10:42
to actually face so the only the best
10:44
you can do is calculate well I think
10:46
inflation is going to be 10% so give me
10:49
know what I would have had in mind with
10:50
inflation equal to zero plus 5% so on
10:53
average I'm about right that's sort of
10:55
the
10:56
logic but this expected price is meant
10:58
to be your best proxy you have at the
11:01
moment in which you're bargaining for
11:02
your wage for what the actual price will
11:04
be during the life of that particular
11:07
wage
11:10
okay
11:15
um okay so we end up with that that that
11:19
uh Philips curve here importantly this
11:22
an decreasing function of
11:24
unemployment er um and then we' made
11:27
different assumptions about expectations
11:29
if expected inflation for example is a
11:31
constant that's when we say expected
11:33
infl inflation is very well anchored
11:36
then you get a Philips curve that looks
11:38
like this in which inflation it has a
11:41
constant here and it's decreasing on the
11:42
rate of unemployment and and during the
11:45
60s H that that relationship sort of
11:47
held fairly well it was a downward slope
11:50
in relationship it got to be steeper and
11:52
steeper as we moved into higher and
11:54
higher inflation levels and then I said
11:56
but in the 70s the whole thing broke
11:58
loose you nothing like a downward
12:01
sloping curve here that happened for two
12:03
reasons there were some cause push
12:05
shocks you can think of lots of shocks
12:06
to M but more interesting H expected
12:10
inflation became an anchor and then we
12:12
changed then H the expected inflation
12:15
mod for rather than being a constant
12:17
being the some weighted average like
12:18
this and we said look during the
12:22
70s essentially that that Theta was
12:24
equal to one okay so inflation expected
12:28
inflation was really whatever was
12:30
inflation last year people expected that
12:32
level of inflation to stay the next year
12:34
rather than going back to that whatever
12:36
was the constant or inflation Target or
12:38
historical constant pi and and that
12:42
meant that the the during that period
12:43
really the Philips curve looked more
12:45
like a relationship of the change in the
12:47
inflation rate as a decrease in function
12:50
of unemployment so that means that when
12:52
you increase an employment here you
12:54
reduce a rate at which unemployment is
12:56
inflation is rising okay that's the goal
12:58
of
12:59
the situation in in a case in
13:02
which expected inflation is an an anchor
13:06
and the last step we had there is we
13:08
replace we notice we said well what
13:10
happens if we stick in here the natural
13:12
rate of unemployment then that will give
13:14
us that will happen only when expected
13:16
price is equal to actual prices so that
13:18
means that when inflation is equal to
13:20
expected inflation from here we can
13:22
solve the natural rate of unemployment
13:24
as a function of these structural
13:26
parameters and once we have that we
13:28
could go back to our Philips curve and
13:30
rewrite it in this way okay so you can
13:34
think of the Philips curve in this way
13:36
and this is the the the way you
13:37
typically we typically write it down in
13:39
which it says H inflation is decreasing
13:43
in the unemployment
13:45
Gap
13:47
so so if the unemployment is above the
13:50
natural rate of unemployment that means
13:52
inflation will tend to be below expected
13:54
inflation if expected inflation happen
13:56
to be equal to lag inflation that means
13:59
if an employment is above the natural
14:01
rate of unemployment then inflation will
14:02
be falling
14:05
okay any questions good you need to know
14:08
this
14:11
okay how to derive these things I mean
14:14
not so much yeah you should know how to
14:16
WR but you need to understand this
14:18
relationship between the out the
14:19
unemployment Gap and
14:23
inflation relative to spected
14:26
inflation yep
14:29
unor versus de unored inflation expected
14:33
inflation it's just a statement
14:35
about ER what is the model we have H for
14:40
expected
14:42
inflation
14:44
so suppose we have the following model
14:47
for expected inflation one minus Theta
14:51
Theta some number between Z and one
14:53
times a constant
14:56
inflation plus something that is a
14:58
function of plus Thea times whatever is
15:01
previous
15:02
inflation central banks try to set a
15:04
target for the inflation rate in the US
15:06
is around 2% and ideally people will
15:10
tend to believe they may see an tempor
15:12
inflation that that is above say 2% but
15:16
as long as as as people expect that to
15:19
be undone in the in the in the next
15:22
period then inflations we say they're
15:24
very well anchored so that's a case in
15:26
which very well anchored means th equal
15:28
to Z here and you always sticking there
15:30
in the case of the US at 2% and and
15:33
there's a lot of there's a lot of that's
15:35
the way the econom is behaving right now
15:37
inflation today is 5% but if you ask
15:39
people what do you expect inflation to
15:41
be two and two years from now people
15:43
tell you me look around 2% two and a
15:45
half percent or so unanchor expectation
15:49
is when when you don't have that anchor
15:51
that 2% that the FED told you is
15:53
whatever was the previous inflation
15:54
that's what people extrapolate will be
15:56
inflation for Next Period and that's a
15:58
lot harder when you get into an
15:59
inflationary episode in that context is
16:01
very difficult because you at 5% people
16:03
are still expecting 5% for next year so
16:05
you need to is much harder to bring
16:08
inflation down you need to create much
16:09
more unemployment to bring inflation
16:11
back to the 2% 2% Target okay that's
16:14
that's what it means to an so anchor
16:17
means Theta very close to zero an anchor
16:19
Theta very close to one that's a a
16:21
formal definition
16:31
we then move
16:32
[Music]
16:35
to what I think is probably the most
16:37
important model you'll see in this
16:39
course which is the islm PC which is
16:41
just the islm plus the Philips curve and
16:45
that allow us to talk about the short
16:46
run which is what we did in the slm and
16:49
then all the way to the medium Run Okay
16:52
in medium understood as when you go back
16:54
to the Natural rate of unemployment
16:56
natural level of output and so on
17:00
oh we got a banking crisis there but
17:05
that's
17:08
oh this you may find useful here here I
17:11
was trying to explain the banking crisis
17:14
and and so and I said we have a model
17:17
for that already remember we had this x
17:19
this spreads in the investment function
17:20
I said well you can think of a negative
17:22
Financial shock something like a a
17:25
credit spread shock as an increasing X
17:27
and that will shift to left okay just
17:32
saying
17:34
good
17:36
uh islm PC model was just going back to
17:39
the islm model we're going to simplify
17:42
things by not by just assuming that the
17:44
Central Bank sets the real interest rate
17:47
and the real interest rate is that okay
17:50
ER and uh and to that we added a Philips
17:54
curve but we didn't like that Philips
17:56
curve because you know we have
17:57
everything is a function of output here
17:59
and interest rate and now we have
18:02
inflation and then employment rate so
18:05
yet another variable to carry around so
18:07
we went from H the output Gap to an
18:10
employment R an employment gap to an
18:13
output Gap and and we did that just by
18:16
noticing that output is equal to the
18:18
labor force time one minus unemployment
18:21
rate equivalently similar you can Define
18:25
potential output or the natural output
18:27
level as employment Time 1 minus the
18:30
natural rate of unemployment subtract
18:32
these two no and I you get that the
18:36
output Gap is equal to minus L times the
18:40
unemployment Gap and so we replace this
18:42
for that expression divided by L and we
18:45
end up with a Philips curve written in
18:46
the form of an increasing function of
18:49
the output Gap so when the output Gap is
18:51
positive then inflation will exceed
18:54
expected inflation if expected inflation
18:56
is an anchor that is expected inflation
18:58
is equal to lag inflation then that
19:00
means that a positive output Gap leads
19:03
to an increase in inflation inflation R
19:07
okay so we look at an example here H you
19:11
know this is the type of but now we're
19:13
going to have the real interest rate
19:14
here just makes it simpler to think
19:16
about Central monetary policy in terms
19:17
of the real interest rate otherwise too
19:19
many things move at once so this is what
19:22
we had done for quiz one here you have
19:23
some particular equilibrium the islm
19:26
with this real interest rate we
19:29
got some equilibrium output equal to Y
19:33
the new part the contribution of this
19:35
block of the course is that now we need
19:38
to also check whether this Y is is
19:40
consistent with potential output or not
19:42
with natural level of output and that
19:45
for that we need to uh see whether this
19:47
level of output H is consider again is
19:51
above or below the natural rate of
19:53
output and for that we need to look at
19:54
the Philips curve okay okay and in this
19:57
particular case that's not the the case
20:00
because output is above the natural rate
20:02
of output you put now given that
20:04
observation you you put right draw here
20:08
the the Philips curve you know that
20:10
because output is above the natural rate
20:11
of output the natural level of output
20:14
that means inflation is above expected
20:15
inflation if expected inflation happens
20:18
to be an anchor equal to Pi minus one
20:20
that means that at this output Gap that
20:23
there's an inflation that is rising okay
20:27
H now inflation Rising means the central
20:30
bank will have to react and the way we
20:32
so you'll have to do something up here
20:33
you need to bring output down and how
20:37
can you bring output
20:39
down so so this economy is is engaging
20:42
in an inflationary spiral actually given
20:44
this mod of expectation how do you stop
20:55
that if you are the fed and you you
20:58
raise the interest rate no because you
21:00
need to bring the L back so the
21:02
equilibrium level of output you need
21:03
increase the real rate up to a point in
21:07
which um the level equilibrium level of
21:09
output is equal to the Natural rate of
21:12
output um and you may have to do more
21:15
than that if inflation was an anchor and
21:17
you find yourself with 5% inflation you
21:19
may have to temporarily actually to
21:21
bring inflation back down to 2% you may
21:23
have to overshoot raise interest rate a
21:25
lot generate a negative output gap for a
21:27
while and then once you reach the level
21:30
of inflation you like the 2% then you
21:33
can go back uh to the Natural level of
21:35
output okay so that's the reason central
21:39
banks worry a lot about unanchor
21:40
expectations because then they know that
21:42
they find themselves an inflation above
21:43
their target is not going to be enough
21:46
to bring the output Gap to zero they're
21:48
going to have to overshoot in the way
21:49
down in order to re re-anchor expect
21:52
well in order to bring inflation back
21:54
down to the Target of
21:56
2% but in any event even if inflation
21:58
are expect well anchor you still have to
22:01
bring output down because at the very
22:03
least you need to close this pos
22:04
positive output Gap and that if you're
22:07
the FED in the US or any Central Bank
22:09
you do it by increasing the real
22:10
interest rate now in practice central
22:12
banks really don't control the real
22:14
interest they control the nominal
22:15
interest ratees so there's a little
22:17
fight there between inflation and and
22:19
what they do to the nominal interest
22:20
rate but let's ignore that complication
22:22
for now okay now H suppose that the FED
22:27
is is is in vacation
22:29
and and and so and and somebody someone
22:32
else you know decides in the government
22:35
decides that no we cannot have this very
22:38
high level of inflation so what else
22:40
could you
22:42
do and you're not the FED fed in
22:46
vacation who else can make
22:50
policy the government the central
22:52
government the treasury and so on no
22:54
what is the instrument they have what do
22:57
they need to do
22:59
the problem they have is output is too
23:00
high and that's what is leading to lots
23:02
of inflation so
23:04
what do you think they should
23:09
do c govern expend raise taxes something
23:12
of that kind okay but they need a fiscal
23:15
contraction because that will bring the
23:17
yes down and so equilibrium
23:20
output will be lower okay so that's an
23:23
alternative you have you should know
23:25
this
23:32
and here I just did what we just
23:34
discussed just in in a steps these
23:37
things happen slowly the F doesn't hike
23:39
interest rate in one shot and so on it
23:41
takes a while before you get to the
23:43
final
23:53
equilibrium oh I I show you the
23:55
deflationary spiral said sometimes
23:57
things can get very
23:59
complicated ER because you may hit the
24:02
zero lower bound the FED can bring the
24:04
nominal interest R to zero but if
24:06
inflation is already low that may not
24:09
give you the real interest that you need
24:10
in order to get output equal to the
24:12
Natural rate of output I me here was one
24:14
example in which you need a negative
24:16
real interest rate to get output to be
24:18
equal to Natural rate of output but that
24:20
may not happen because you you you hit
24:23
the zero lower bound H and so at that
24:26
point the problem you have is that and
24:28
that's was the trag tragedy of Japan for
24:31
so long is that not
24:35
only you cannot bring the interest rate
24:38
the nominal interest rate below zero but
24:40
you start getting into deflationary
24:41
inflation below expectation and
24:43
expectation goes to number very close to
24:45
zero because of an anchor deflation
24:47
expectations then you start getting
24:49
negative expected inflation and when you
24:51
get Negative expected inflation even if
24:53
you're at the zero lower Bound in the
24:54
nominal interest rate that means a
24:56
positive real interest rate so
24:57
effectively you're increasing interest
24:59
rate at the same time and that can be a
25:00
very complicated thing to get out of
25:02
again that's what happened to Japan for
25:04
a long
25:05
time what would you do if as a
25:07
government if you fall into a situation
25:09
like
25:12
that and Japan did a lot of
25:16
that well you can do lots of things but
25:18
but in particular of the kind of things
25:21
you know what what would you do if you
25:23
are in a situation like this in which
25:25
the zero lower bound is binding and and
25:27
inflation is actually falling here I had
25:29
a benign case in which inflation
25:31
expectation was well anchor that's not
25:34
what happened to Japan after they
25:35
experienced a long period of
25:36
deflationary forces the then the people
25:39
began to expect more deflation more
25:40
deflation and so on so what else can you
25:51
do let me give you a hint Japan is one
25:55
of the countries has the highest levels
25:57
of public debt
25:59
how do you accumulate public
26:02
debt yeah you you need to borrow a lot
26:05
you have big fiscal deficit so that's
26:07
the way you can fight this you know you
26:08
can shift the yes to the right by having
26:11
an expansionary fiscal policy that's the
26:12
only tool really you have you lose the
26:15
power of monetary policy against the
26:16
zero lower bound but you still have
26:18
fiscal policy and they did a lot of
26:19
fiscal policy
26:28
not
26:29
interesting this is this is interesting
26:33
ER that's a different kind of shock
26:36
suppose you are at your medium run
26:38
equilibrium and then all of a sudden
26:40
markups go up perhaps for example
26:43
because the price of oil went up a lot
26:45
and something like that so then what you
26:49
then that's a different kind of shock
26:50
from the previous one from from any
26:51
fiscal sh or anything like that that's
26:53
an aggregate demand this is an agre
26:54
supply problem because the first thing I
26:56
know of a permanent at least change in m
27:00
is that the natural rate of unemployment
27:01
has to
27:02
rise if the natural rate of unemployment
27:05
has to rise that mean my Philips Curve
27:07
will shift
27:09
now okay in that particular case I know
27:12
the Philips Curve will shift to the left
27:13
how do I know that well because I know
27:16
that that the natural rate of
27:17
unemployment went up which means the
27:20
natural rate of natural level of output
27:22
has to come down and the natural level
27:24
of output coming down means simply that
27:26
that the level at which is expected
27:28
inflation and inflation are
27:30
equal happens at a lower level of output
27:32
so the Philips can move to the left so
27:35
suppose you were in this equilibrium
27:36
here I'm doing for the case of an anchor
27:38
expectations but the same logic goes for
27:41
the case of anchor expectation ER so
27:44
suppose you were at some equilibrium
27:46
like this it was your medium run
27:47
equilibrium but now the price of energy
27:49
goes up a lot and and and you expect
27:51
that to last for a while that means the
27:53
Philips curve moves up so that means
27:56
that if output with output at this level
27:58
now you get you have a problem because
28:00
you start getting inflation out of this
28:02
okay because this this level of output
28:05
is too high relative to the new level of
28:07
the natural the new level of natural
28:09
level of output so you have a positive
28:11
output Gap positive output Gap means
28:13
inflation above expected inflation if
28:16
you have an anchor expectations means
28:18
inflation starts
28:20
rising
28:21
up so that means the FED now needs to
28:24
react to that and needs to tighten
28:26
interest rate in order to to go to a new
28:29
level of H natural level of output okay
28:32
and that's the response but if the F
28:35
that's not react and a little bit of
28:37
this is what happened we had some Supply
28:38
shocks and so on that were considered to
28:41
be temporary well they weren't as
28:42
temporary so there was no reaction but
28:44
it turns out that that they lasted a lot
28:46
longer than the fair expected and so so
28:50
so now they had to catch up
28:52
okay that was part of the reason we got
28:56
into a high inflation episode
28:59
that was the main reason in
29:01
Europe the US is a mixture of aggregate
29:04
demand lots of fiscal policy and so on
29:07
and ER and supply side in Europe was
29:10
very much a story of this
29:19
kind well a financial Panic you need to
29:22
upset it with a decline in in in real
29:24
interest rate and a little bit of that
29:27
has been happening it's not the FED that
29:29
has cut their rates but but the markets
29:31
have anticipated the FED will not raise
29:33
interest rate as much as they expected
29:36
before we got we got into this banking
29:38
mess so we had already sort of studied
29:41
the short run the medium run and now we
29:43
want to look at the long run okay and
29:45
that's what economic growth is about
29:47
economic growth Theory and facts and so
29:53
on let me go to so one of the things I
29:58
I highlighted is that we tend to
30:01
see among countries that are fairly
30:04
similar
30:07
along education and variables like that
30:11
systems economic systems and political
30:13
systems and so on you tend to find
30:15
relationship like this that is countries
30:18
with a lower per capita income at the
30:21
beginning of the sample tend to grow
30:22
faster in the sample and that captures
30:24
very much the idea that there's a
30:26
convergence there's a force towards
30:28
convergence of H income per capita if
30:31
you will okay that's another
30:34
illustration of that phenomenon lots of
30:36
dispersion here ER 70 years later a lot
30:40
less
30:41
dispersion but we also said that some
30:43
countries that do not match that and but
30:46
we focus most of what we did in
30:50
growth on understanding this process the
30:53
process of convergence and how it
30:55
happened with without technological
30:57
progress and so on and then we spent a
30:59
little bit of a lecture say at most 10
31:02
10 points worth in a quiz or seven
31:04
points talking about sort of anomalies
31:07
and things like that no five points or
31:12
something so the key ER object here one
31:16
of the key objects there there are a
31:18
couple but but one of them was well now
31:21
we need to be a little bit more serious
31:22
about the production function we said
31:24
because for the short it's okay to take
31:27
Capital as given and just worry about
31:28
most of the fluctuation in output will
31:30
come from fluctuations in
31:32
employment that's not so over long
31:34
periods of time capital accumulation
31:36
plays a huge role and so we need to be
31:39
explicit about the fact that Capital
31:41
matters a lot for production
31:44
okay and so we postulated a production
31:47
function like this output as increas
31:50
increasing function of cap and of
31:52
capital and labor and now we said for
31:54
this part of the course we're not going
31:56
to worry about unemployment and so on
31:57
employment labor force population
31:59
they're all the same for us here for
32:02
this part of the course and then said
32:04
this production function has some
32:06
important
32:07
properties one is it has constant
32:10
returns to scale things change quite a
32:12
bit if you don't have constant return to
32:14
scale so we have constant return to
32:15
scale which means you should know this
32:18
that if you scale all output all input
32:21
all the factors of Productions by the
32:23
same factor output Also Rises by the
32:26
same factor okay so a production
32:29
function we use a lot was aob Douglas
32:32
you know output equal square root of K *
32:36
the square root of n well the sum of
32:38
those exponents is one so that's a a
32:41
production function with constant return
32:42
to scale okay so anything that has the
32:46
exponents add up to one then you're
32:48
that's a constant return to scale
32:50
technology but importantly and it also
32:54
has decreasing returns with each of its
32:57
factor of production
32:58
that means as you rather than moving
33:01
both factors of production up you move
33:04
only one well you're going to increase
33:05
output but as just keep increasing that
33:08
factor alone you're going to increase
33:10
output by less and less and less and
33:11
less because essentially has fewer and
33:13
fewer of the
33:14
other factor of production to work with
33:17
okay and so that's decreasing returns to
33:19
Capital or labor I mean if you fix the
33:22
other factor of production you move up
33:23
it's going to increase at a decreasing
33:25
rate so one normalization that we start
33:28
with was well a scaling Factor could be
33:32
a population one over population okay
33:35
that's a scaling factor and if I do that
33:37
I multiply both everything by one / n
33:40
would go into output per person is an
33:44
increasing function of a increasing
33:47
function but at a increasing rate of
33:49
capital per person okay we plot that
33:52
function here and and this conc is
33:56
increasing but it's concave that shows
33:58
the decreasing returns of capital no h
34:03
and we got that function there then the
34:05
SEC uh and we talk
34:07
well we said H so so so when you move in
34:12
this you can increase output per person
34:16
per per person by simply increasing
34:18
Capital per person and the more you
34:20
increase Capital per person output will
34:23
increase more and more but but but at a
34:25
decreasing rate you can see that moving
34:27
a the distance between A and B is the
34:29
same as the distance between C and D
34:31
however the increasing output when you
34:32
go from A to B is enormous compar when
34:35
compare with the increasing output that
34:38
you get from the increasing capitals
34:39
over per per person from C to D okay
34:43
decreasing returns this there is another
34:45
way of of increasing output per person
34:49
which is with technological progress
34:51
when the function f shifting up over
34:54
time and we split the two main lectures
34:57
in grow both into one part one in which
34:59
we just we shut down the second Channel
35:02
and then the second important lecture
35:05
here had we focus on this channel so
35:09
that's a that's what we
35:14
have so let's go to when I shut down
35:17
this channel for now and focus on on the
35:19
case without technological progress
35:21
first okay so so we put things together
35:24
we said this is comes from the previous
35:26
lecture we can write a output per
35:29
uh per person as an increasing function
35:33
of um Capital per person second key
35:37
equation is well this is a proper it has
35:41
to be if you in a closed economy no over
35:43
expenditure or anything like we could
35:46
add that but it's not important for the
35:48
message then investment has to be equal
35:50
so investment is going to be very
35:52
important here because it's what will
35:54
make the Capital stock grow but there
35:57
has to be funed fing for that and the
35:58
funding come from saving okay and we
36:01
simplify things by assuming that the
36:02
saving function is just proportional to
36:04
the level of output which is reasonable
36:06
when you think about long run all these
36:08
things scale up when you're thinking
36:10
about very shortterm no we have some
36:12
constants and so on floating around but
36:14
but but over the long run things do
36:17
scale up and so we can write investment
36:20
in equilibrium investment has to be
36:21
equal to saving saving is proportional
36:24
to Output so we get that investment in
36:26
this economy is increasing in output
36:30
this is an constant somewhere between
36:31
zero and one okay and the last key
36:35
equation here is the capital
36:36
accumulation equation the capital
36:38
accumulation equation says that Capital
36:41
t+ One is equal to Capital today minus
36:45
the depreciation some a fraction of the
36:47
machines break down in every period but
36:50
plus the new investment plus I okay and
36:54
we rote things and replace the saving
36:56
function and so on and we end up in in
36:59
in qu an expression like this that says
37:02
Capital per person here grows with
37:04
investment which is funded by savings
37:06
which is an increasing function of
37:08
output which in turn is an increasing
37:09
function of capital per person minus
37:12
whatever is the depreciation and what we
37:14
did then the the start diagram in in in
37:17
the solo model is is we plot this
37:20
function and that function we know that
37:22
the state state is when these two things
37:23
are equal that pins down the K star of
37:27
over n k Over N start of this economy
37:31
but we also know that to the left of
37:33
that point in in capital
37:35
space this term is greater than that and
37:39
therefore H the Capital stock is rising
37:41
to the right we get that this term is
37:44
greater than that and therefore the
37:46
Capital stock is falling okay and that's
37:49
what we have in this diagram so that's
37:51
the state of the economy when when the
37:53
depreciation per worker which is the
37:55
require in the minimum in you need to
37:58
keep the Capital stock constant is
38:00
whatever is depreciation per worker no
38:03
anything else you do it will grow the
38:05
stock of capital anything less you do
38:07
you're not maintaining enough of your
38:08
Capital stock is declining and that's
38:10
exactly what happens here that's State
38:13
you have Capital below that then then uh
38:17
Capital stock will be rising because you
38:18
have lots of saving and therefore lots
38:20
of investment relative to what you need
38:22
in order to maintain the stock of the
38:23
small stock of capital you have until
38:26
you reach a c state
38:29
and the and you know the this model
38:34
alone can explain really the that
38:36
pattern we have that that you know that
38:39
the poorer economies tended to grow
38:41
faster than the Richer economies if you
38:43
think of poorer economies as economies
38:45
that are otherwise similar but that have
38:48
low a low stock of capital to start with
38:51
well those economies are going to be to
38:52
the left of the stady state and
38:54
therefore they're going to tend to grow
38:55
at whatever is the steady state rate of
38:57
growth plus this catching up growth okay
39:00
and so this is a very powerful little
39:03
model it can explain a lot of that those
39:06
convergence the convergence that we saw
39:08
in in the data
39:11
okay do you understand
39:14
this this is
39:17
important
39:20
okay then we did some experiments what
39:22
happens if you increase the saving rate
39:24
at the time when solo was writing this
39:26
model many people said that what was
39:27
behind growth was saving well in this
39:30
model we show that indeed if a saving
39:33
rate Rises then you at any given level
39:36
of capital suppose that was the oldest
39:38
state if now the saving rate Rises that
39:40
will increase H increase investment
39:44
above what you need to maintain that
39:46
level of the stock of capital so the
39:48
stock stock of capital going to start
39:50
growing when that happens output per
39:52
capita will grow faster than in a state
39:54
state because you're going to go be
39:56
going from here to there but eventually
39:58
you'll converge to the same whole rate
40:00
of growth so the point here is that the
40:02
saving rate cannot change per se does
40:04
not change the rate of growth in the
40:06
long run but it gives you transitional
40:08
growth and a lot of the the Asian
40:10
Miracle of the very fast rates of growth
40:12
from the 60s and 70s and 80s has to do
40:15
with this kind of thing very sudden
40:17
increasing saving rates plus other
40:19
institutional changes and so on but High
40:22
increase in the saving rate that also Le
40:24
led to very fast growth okay so again
40:27
this little model can explain a lot as
40:29
well it can explain when you see those
40:31
growth Miracles often is associated to
40:34
some for some
40:35
reason varies a lot across different
40:37
scenarios the saving rate went up quite
40:40
a
40:41
bit but point is so that gives you very
40:44
fast growth in the short term but
40:46
eventually pets out
40:49
okay so the the the next thing we all
40:53
that we did for a fixed population it
40:55
said well so suppose now the population
40:58
is
40:59
growing H I said the diagram we had
41:02
before would be very unpleasant because
41:04
all these curves would be shifting so
41:05
what we need well what we need to do is
41:07
divide not by a constant we need to
41:08
divide by whatever is the population at
41:11
that point in time and that will give us
41:13
the same diagram we had with one little
41:15
twist so I went through sort of a little
41:17
algebra here to arrive to a capital
41:20
accumulation equation Capital per person
41:24
equ an equation for the change in the
41:26
capital per person which is very similar
41:28
to what we had the only difference is
41:30
that the required capital investment
41:33
required to maintain the stock of
41:35
capital per person has an extra term
41:37
here
41:39
GM and I said that GM so let's think
41:43
about this
41:44
term so Delta so think of this as the
41:49
required
41:51
investment in order to maintain the
41:52
stock of capital where it
41:54
was ER if if h this Delta comes from the
41:58
fact that well you have a stock of
42:00
capital you lose a fraction of that well
42:01
you need an investment equal to that
42:03
fraction that you lost in order to
42:04
maintain the stock of capital the same
42:07
that's that's that's that's
42:10
clear but that's not enough to maintain
42:12
the capital per person constant if if
42:16
per person is rising population is
42:18
rising because even if you maintain the
42:21
stock of capital constant the
42:23
denominator is rising at the rate of
42:25
population growth
42:28
so in order to maintain the capital per
42:30
person constant you need to deal with
42:32
the growth of denominator as well and
42:35
that means you need a little you need
42:36
also investment to match the increase in
42:38
population so they can keep the capital
42:42
per person constant okay so that's a
42:45
that's a modification so in terms of our
42:47
diagram all that happened here I have
42:49
technological progress as well set it to
42:50
zero for now all that happened relative
42:52
to the previous diagram is that now this
42:55
I rotated this curve up upward a little
42:57
bit okay
43:00
GN but then you conduct analysis exactly
43:03
in the same way the only thing that is
43:05
different now is that in the previous
43:07
model we had that the rate of growth the
43:09
stady state rate of growth was equal to
43:12
zero and the state state rate of growth
43:14
of output per person was also equal to
43:16
zero population was not growing output
43:18
was not growing the ratio wasn't growing
43:21
either here is still the case that in a
43:24
steady state output per person is is not
43:28
growing okay but that also means since
43:32
population is growing at the rate GN or
43:34
N I don't know how I call it here H that
43:38
means output must be also growing at the
43:41
rate GN that's what will keep output per
43:44
person not growing okay so so for the
43:48
output itself a very important factor in
43:50
in in in in the in growth is population
43:53
growth and if you look at rates of
43:55
growth in general in the world s
43:57
certainly in the developed World H
44:00
they're falling for a variety of reasons
44:03
and one of them is because population
44:04
growth is
44:05
falling okay but per person that doesn't
44:08
make a difference but but but for the
44:11
level the rate of growth it does and
44:14
then we we added technological progress
44:16
which we model as a effective as
44:20
enhancing labor so having a better
44:23
technology means is as you had more
44:26
workers so for any given level of
44:27
workers having a better technology we
44:29
model it as having more workers okay and
44:33
you can model it exactly that way you
44:35
can use exactly the same diagram we had
44:37
before but now we will divide our
44:39
scaling Factor rather than being one
44:41
over population is going to be one over
44:43
effective population effective workers
44:45
one over again and you conduct exactly
44:47
the same analysis you do exactly the
44:49
same approximations I did before H but
44:52
the difference now is
44:54
that ER is that here you have a rather
44:59
than GN you have
45:01
G why is that well because if I want to
45:06
maintain the capital per effective
45:09
worker constant then I need to First
45:12
make up for the depreciation of the
45:13
stock of capital that's I have to
45:16
stabilize the numerator but then I have
45:18
to take into account that the
45:20
denominator is growing for two reasons
45:21
because population is growing and
45:23
because technology is growing and in
45:24
order to maintain the ratio constant I'm
45:26
going to have to investment so so to
45:28
maintain that ratio constant and that's
45:30
the reason now we
45:33
have this this line here rotates even
45:36
further and we get Delta plus GA plus GN
45:42
okay and you should play with these
45:44
things what happen in this diagram if I
45:46
you know if I increase GA or stuff like
45:51
that and notice that here now still you
45:54
have a steady state but it's a steady
45:55
state in the space of output per
45:57
effective worker in capital per
45:59
effective worker that means for example
46:02
that so that means that these quantities
46:04
are not growing in the stady state but
46:07
output will be growing at which rate in
46:09
the stady state in any state state here
46:12
what is the rate of growth of
46:23
output if output Over N is constant in
46:26
in the today
46:28
State how can that happen output has to
46:31
be growing at which rate at the same
46:33
rate as the
46:34
denominator so it's GA plus
46:39
GN what about that's a tricker question
46:43
what happens to Output per person in
46:45
this stady state what rate is it growing
46:48
at output per
46:52
person sorry somebody said the right
46:54
thing but ga exactly I want to keep this
46:58
ratio constant I'm asking the question
47:00
at which Pace does this need to rise in
47:03
order to maintain this constant well at
47:04
the same rate as a is growing
47:09
good here we also did we asked the
47:11
question well could it be that here if
47:13
we change the saving rate we get some
47:14
extra kick in the long run and the
47:16
answer is no for the same logic as we
47:18
had before you're going to get
47:18
transitional growth but you're
47:21
eventually you're going to convert to a
47:22
stady state and the rate of growth in
47:24
the long run is not going to be a
47:25
function of the saving rate is going to
47:27
be equal to GA plus GN
47:31
okay
47:41
good do here measuring technological
47:44
progress blah blah told you the story of
47:46
China
47:50
good oh we run out of time so let me
47:55
just say the the the last thing uh that
47:58
I want to say so the last thing we
48:00
discussed you say well what happen if
48:03
you add education to this and and try to
48:06
no I make what am I doing yeah I
48:09
expanded the model a little bit I had
48:11
education and said does this change
48:13
conclusions a lot I said no not really I
48:16
mean it it doesn't change the conclusion
48:18
with respect to the long run it affects
48:20
the level of output per capita if you
48:22
have more education but it want a che
48:24
affect the rate of growth in the long
48:26
run and the last point I made is that
48:29
look H in this model if you expand it
48:34
and you try to assume the technology the
48:36
technology is the same and the rate of
48:38
technological progress is the same
48:39
across the world you stick those
48:41
parameters in the mod population growth
48:43
education levels and all that then you
48:46
don't explain the amount of inequality
48:48
we see in the world the world will look
48:50
a lot flatter if if it was just H
48:54
differences in population growth
48:56
depreciation
48:57
education level and things like that but
48:59
with the same technology so if you want
49:01
to account for so this model the
49:05
mod doesn't produce enough
49:08
inequality in the world you need to add
49:10
something else that explains that we
49:12
have some countries in Africa that are
49:14
not growing that they're growing at a
49:15
very low levels rate and we said that
49:17
something else technology for whatever
49:19
reason it happens that there's a pocket
49:21
of countries that that seem to have a
49:25
lower sort of permanently lower level of
49:27
technology and both level and growth
49:30
rate and that's what explains sort of a
49:32
subset of countries that are sort of
49:34
seem stack they are not consistent with
49:36
this convergence type thing so that's
49:38
the reason it's called conditional
49:39
convergence those countries themselves
49:41
are converging to something but they're
49:43
converging to something much lower and
49:44
with much lower rate of growth than most
49:47
of the rest of the world but for the
49:49
final lesson is for the average country
49:51
on
49:52
average it's clear that poorer countries
49:55
grow faster than richer countries that's
49:57
a that's that's a dominant Force but you
49:59
need a little more if you want to
50:01
explain certain pockets of the world
50:03
okay
— end of transcript —
Advertisement
