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49:04
Transcript
0:16
So, today I'm going to talk about the
0:18
Phillips curve and inflation. Um
0:22
Now, as I said in the previous lecture,
0:24
uh
0:25
the material that is specific to this
0:27
lecture will not enter this quiz.
0:30
It's the beginning of what is perhaps
0:31
the most important model you'll see in
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0:33
the in in this in this uh class, but
0:37
it will take us uh three or four
0:38
lectures to to develop. So, I'm going to
0:42
say things that certainly will
0:44
um
0:45
may help you understand a little better
0:46
the previous lecture, and so
0:49
if you're only concerned about the next
0:51
quiz,
0:52
uh there will be a sort of uh small
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0:55
review of the previous lecture here. Uh
0:57
but again, anything that's specific to
1:00
this lecture and was not in the previous
1:02
one
1:03
won't be part of of this quiz.
1:06
So, what is this Phillips curve? Well,
1:08
in in uh
1:10
in 1958, an an economist uh at LSE, the
1:14
London School of Economics,
1:16
came up with some just an empirical
1:17
relationship. This is A.W. Phillips. He
1:20
found that using historical data
1:24
uh for the US, I think he did it. Um
1:28
uh there was a negative relation up to
1:30
sort of the '50s, I think. Uh
1:33
the there was a negative relation
1:35
between uh the unemployment rate and the
1:37
rate of inflation.
1:39
And then our very own Paul Samuelson and
1:42
Robert Solow
1:44
labeled this relationship the Phillips
1:46
curve in honor of uh
1:48
A.W. Phillips.
1:49
And nowadays it's sort of is a central
1:52
concept uh in macroeconomics, and
1:55
uh and uh it's certainly very, very
1:58
relevant to understand what is going on
2:00
uh right now in not only in the US
2:02
economy, but in most economies around
2:04
the world.
2:06
So, let me
2:07
show you sort of this is not the one
2:08
that uh
2:10
that Phillips uh plotted. I think this
2:12
is the one that uh
2:14
uh
2:15
Samuelson and Solow plotted for data
2:17
from between 1900 and 1960 uh
2:20
for the US, you found you find sort of
2:23
this sort of negative correlation. I
2:25
think it's reasonable.
2:27
Uh
2:28
um
2:29
there's negative correlation between
2:31
uh the unemployment rate and inflation
2:34
rate, no? At very low levels of
2:36
unemployment, you typically see very
2:37
high levels of inflation.
2:39
Conversely, sort of at very high levels
2:41
of unemployment, you tend to receive low
2:44
levels of inflation or even deflation.
2:46
In fact, this period includes the the
2:49
Great Depression, for example.
2:52
So,
2:53
that's sort of the data. And and again,
2:56
this was just an empirical regularity.
2:59
But we can build some theory about this
3:00
relationship using the ingredients most
3:03
of the ingredients that
3:05
I mean, essentially we can build a
3:07
relationship that is downward sloping
3:10
from the ingredients we already have.
3:13
And this is the part that is a little
3:14
bit of a review
3:15
of the previous lecture.
3:17
Remember that we had um um
3:20
actually the previous two lectures. We
3:22
had a wage setting equation
3:25
W equal expected prices
3:28
and then a decreasing function of
3:29
unemployment and an increasing function
3:31
of uh these labor market supporting
3:34
institutions or
3:36
worker supporting institutions, that
3:38
institutional variables, I should say.
3:40
And um and then we had a price setting
3:43
equation, which was simply the wage uh
3:46
marked up.
3:48
M is a positive constant. So, let me
3:50
start from these two what So, what I'm
3:53
trying to do is derive a Phillips curve.
3:55
Again, this was only an empirical
3:57
relationship, but it turns out that even
3:59
with theory we knew by the time of, you
4:01
know, Samuelson and and and Solow, we
4:03
could sort of come up with a with a
4:05
theory of that relationship. And that
4:07
theory builds on the ingredients we have
4:09
been looking at. So, these are the price
4:11
set the wage setting equation, the price
4:12
setting equation. I'm going to just
4:14
simplify things and assume that this
4:16
this relationship here, this function f
4:19
of u z, is some linear function, at
4:22
least locally linear function, uh which
4:24
is decreasing in unemployment and
4:26
increasing in z.
4:28
Why is it decreasing in unemployment?
4:35
This says, no, that that if unemployment
4:37
goes up,
4:39
for any given expected price,
4:41
wage demand is lower.
4:43
Okay? And that's essentially because uh
4:46
for the worker is is sort of is a
4:49
becoming unemployed is a scary
4:50
situation.
4:52
Conversely, for firms it's higher it's
4:54
easier to find uh
4:56
uh
4:56
a worker and and uh
4:59
and uh So, as we said, a worker is
5:01
scared for two reasons. One is that it's
5:04
more likely it gets fired when
5:05
unemployment is high, typically that's a
5:07
recession. It's also likely they know
5:10
that that worker knows that if she were
5:13
to fall into the unemployment pool, it
5:15
would take a longer time to get out of
5:17
it. Okay? And the firms are seeing the
5:19
opposite side. It's pretty easy for them
5:21
to replace a worker if they were to
5:24
dismiss a worker because there's lots of
5:26
available workers in unemployment. Okay?
5:28
So, that's the reason that's negative.
5:30
So, I'm going to stick this function
5:32
back in here.
5:34
And then I'm going to replace this W
5:37
with this function in there in the price
5:39
setting equation, and I end up with an
5:42
equation for P. Okay? So, this says that
5:46
the price, given the expected price,
5:50
is decreasing in unemployment and
5:52
increasing in z and increasing in the
5:54
markup.
5:55
So, again, why is this price decreasing
5:58
in unemployment?
6:02
This is the part that is review of the
6:04
previous lecture.
6:05
Previous today. Because
6:07
the wages go down and then the labor uh
6:09
factors of production are cheaper. Okay,
6:10
perfect. Because wages go down, since uh
6:14
our firm needs one worker to produce one
6:16
unit of a good, then the cost of
6:17
production of one unit goes down with
6:19
the wage, and and therefore the price
6:22
goes down. Because the firm is asking
6:24
for a constant markup over that wage,
6:26
the wage declines, and the price drops.
6:31
Good. So, that's all review. So,
6:35
this equation you had seen just without
6:37
an explicit functional form here. What I
6:39
want to do is to go from here. This is
6:42
still not the Phillips curve. Remember,
6:43
the Phillips curve was a relationship
6:44
between inflation
6:46
and unemployment. Here we have a
6:48
relationship between the price level
6:51
and unemployment. Okay? So, we want to
6:53
take one
6:55
one derivative higher. We want to go to
6:57
relation between
6:58
inflation and unemployment. And
7:00
inflation is is the rate of change of P.
7:03
No?
7:04
It's not it's not a level of P.
7:07
So, to do that, all that we'll do is So,
7:09
this when I don't have a subscript here,
7:11
I mean
7:12
the price at time t.
7:14
Okay? And this is the expected price for
7:16
next period, that's what we have.
7:18
Uh
7:18
but today for next period.
7:21
What I'm going to do, I'm going to
7:22
divide both sides by P minus 1. By that,
7:25
I mean the price in the previous period.
7:27
Okay? So, both sides. I'm going to
7:29
divide this side by P minus 1.
7:32
And and and this one by P minus 1.
7:34
So, I get that expression. Okay? That's
7:36
exactly the same equation we had before.
7:39
All that I did is I divided by P minus
7:41
1. Remember remember what this means.
7:44
So, if this is the price for the
7:46
beginning for January 2023,
7:49
uh
7:50
this is the price for, say, where we're
7:51
using annual data, for January 2022.
7:54
Okay? So, I'm dividing by the price of
7:56
January 2022 both sides.
8:00
Now, notice that remember that I can
8:03
that P over P minus 1 is equal to 1 plus
8:06
the inflation rate. Remember where
8:08
inflation rate is just
8:10
P minus P minus 1 over P minus 1. So,
8:14
this is just straightforward algebra,
8:16
no?
8:17
Remember our definition of inflation.
8:33
That's P minus that's inflation. Okay?
8:36
So, 1 plus pi is just
8:39
P minus uh
8:41
over P minus 1. Okay? And that's what
8:43
you have there.
8:44
I can do the same for expected
8:45
inflation.
8:48
Notice that
8:53
sometimes people get confused, but
8:56
expected inflation
8:58
is equal to P
9:00
expected
9:02
not minus P expected minus 1. It's P
9:05
minus 1.
9:07
P minus 1.
9:10
And the reason I'm not subtracting the
9:12
expectation here is because at time t,
9:15
which is when you're forming that
9:16
expectation, you already know what
9:18
happened at t minus 1.
9:21
Okay? So, that's the reason this is
9:22
expected inflation. I don't I don't need
9:25
uh uh
9:26
um
9:28
to put expectations in here. Okay? So,
9:31
that's pi e.
9:33
And so, what we get is
9:35
uh I can replace
9:37
this guy here for 1 plus pi, this guy
9:40
here for 1 plus pi e,
9:42
and I get the following relationship.
9:45
Okay?
9:47
All that I've done is substituting this
9:49
for that, that for that.
9:52
So, that's our price setting equation
9:54
now expressed in terms of inflation rate
9:58
unexpected inflation rate
10:00
and now you know
10:02
if not we're not in Argentina we're in
10:04
the US
10:05
inflation if expected inflation is a
10:07
small numbers
10:09
and the log of 1 plus a small number is
10:11
approximately that number
10:15
so
10:17
I'm going to use this approximation
10:19
which again is valid for X small
10:23
and and so I can replace this 1 plus pi
10:26
for pi and this 1 plus pi e for pi e
10:30
this 1 plus m for m
10:33
plus no and this term here if these
10:36
numbers are not too large again plus
10:39
minus alpha u
10:41
plus z
10:43
and that I do all that and I end up with
10:45
this expression
10:51
all that I've done is I took logs of
10:53
this so I get log of 1 plus pi equal to
10:56
log of 1 plus pi e plus log of 1 plus m
10:59
plus log of 1 minus alpha u plus alpha z
11:02
I'm saying if pi pi e m alpha u plus z
11:07
are not very large numbers which we're
11:09
going to assume then this is
11:11
approximately right so I can rewrite
11:13
that expression as that
11:16
approximately I should have put an
11:17
approximately
11:22
okay so now we have something that looks
11:23
a lot more than like the empirical
11:25
relationship we were talking about we
11:27
have a relationship between inflation
11:29
and unemployment so this says that
11:32
for any given expected inflation and
11:34
markups and and labor market
11:35
institutions
11:37
higher unemployment means lower
11:39
inflation
11:40
why is that
11:43
so that curve tells you that's a
11:44
negative relation we wanted no it says
11:47
higher unemployment lower inflation
11:53
why is that
12:02
look you had it very clear when we talk
12:04
about this no
12:05
you you understood very clearly why an
12:07
increase in unemployment lower the wage
12:10
you understood very clearly why
12:13
therefore an increase in unemployment
12:15
lower the price
12:18
I haven't done anything but algebra in
12:20
the two steps so the same economics
12:22
behind the explanations that you had
12:23
before apply to this curve here
12:26
so the reason inflation will be lower
12:29
when you unemployment is higher given
12:31
all the rest
12:33
is because there's really less wage wage
12:35
pressure workers will demand lower wages
12:38
that means lower prices and therefore
12:39
inflation will be lower the economics
12:41
hasn't changed at all I only I only
12:43
divided both sides
12:45
by p minus 1 and I took the logs and I
12:47
approximated so so the economics has not
12:49
changed
12:50
it just did a little bit of
12:53
basic math okay
12:55
so all the what I'm trying to say is all
12:57
the intuitions that you can already you
12:59
already had from the wage setting price
13:02
setting equations and so on you can
13:03
apply to the Phillips curve as well
13:06
okay
13:08
good so now we have something that
13:11
in principle could explain the type of
13:13
relationship that Phillips
13:16
found and then Samuelson Solo
13:17
corroborated with extended data
13:23
so
13:26
let's let's see how do we get to
13:27
something that looks like what
13:30
these people run as a
13:31
they run a regression essentially
13:34
or they correlated and inflation
13:38
inflation with unemployment
13:40
and they found a downward sloping
13:42
relationship
13:44
well
13:45
look what if that happens here suppose
13:47
that
13:48
that we assume that expected inflation
13:51
is equal to some constant
13:54
in in economics we say when that's the
13:56
case
13:58
and especially if pi is a low number
14:00
inflation expectations are well anchored
14:03
meaning you know any single year they
14:06
can be a price of oil is high or
14:07
something happens and inflation will
14:09
deviate from that
14:10
but people are all the time expecting
14:12
for inflation sort of to go back to the
14:15
what is a normal level
14:17
nowadays
14:18
or at least
14:19
a few years ago in the US the normal
14:22
level was around 2% say okay so people
14:25
say well this year inflation was 1.8 but
14:28
we expect next year 2% the next year we
14:31
got surprises on the upside price of
14:33
food went up something like that we got
14:35
inflation of 2.3% but you ask people how
14:38
do you what much do you expect for next
14:40
year they say well 2%
14:42
so so that's what a model of expectation
14:45
like this means is that you know you're
14:47
always expecting something which is
14:49
some historical value on that we have
14:51
agreed is a reasonable level for our
14:54
economy or something like that okay
14:56
so you see that if I replace expected
14:58
inflation for a constant here pi bar
15:01
then I have then my Phillips curve is
15:04
really this is inflation then I have a
15:06
constant minus alpha u
15:09
that's the simplest of the
15:11
downward sloping relationship I can have
15:12
that case is a line downward sloping
15:14
line no that's it
15:17
of course you know it could be
15:19
non-linear and so on but but this
15:20
captures the essence so that's the
15:22
theory for why
15:24
Phillips was finding what he was finding
15:27
our theory of the
15:29
wage of the labor market if you will and
15:31
the price setting
15:33
behavior of firms gives us a Phillips
15:35
curve of the kind that he had in mind
15:39
and if you look in the 60s in the US
15:43
then you see this negative relationship
15:45
that eventually become sort of became a
15:47
steeper it wasn't linear like this it
15:49
was a little convex but but it's
15:51
downward sloping
15:53
and in fact
15:55
to some extent
15:58
our own very our very own Bob Solo and
16:02
Paul Samuelson
16:04
were advising the US government at the
16:06
time and they said well you know let's
16:08
exploit this stuff a little
16:10
we like to have lower unemployment we
16:13
can live with a little less more
16:14
inflation but we know there's a negative
16:16
trade-off there's a negative trade-off
16:18
between these two things okay so
16:20
if we like to lower unemployment it's
16:22
fine we get a little more of inflation
16:24
and initially the deal was very good
16:26
because this curve was very flat
16:29
you see you could cut him unemployment a
16:31
lot you can see the dates here cutting
16:33
unemployment a lot and you're not
16:35
getting a lot of inflation
16:37
eventually the deal the deal turned into
16:39
a much rather deal much more rather deal
16:41
because
16:42
then to lower a little bit more
16:43
unemployment we start getting a lot more
16:45
of inflation okay so people for a while
16:48
you know were okay with this model
16:50
assuming that inflation was low but when
16:53
they realized that this thing was being
16:54
exploited then they began to sort of
16:57
change the expectations they made I
16:59
think that's what we had here but but
17:01
the the reason held pretty well
17:03
during this time and again it became
17:05
steeper and steeper as we
17:07
pushed it more and more towards sort of
17:09
very low levels of unemployment
17:12
so that's the story but again there is
17:14
your model of the Phillips curve and
17:15
that
17:17
it's a very very good model for the
17:18
times where Phillips also estimated his
17:21
his Phillips curve
17:23
now
17:25
if you sort of turn the page and look at
17:27
the same data in the 70s
17:30
look how it looks
17:32
okay
17:33
so from 1970 to 1995 that's the data you
17:36
have there there's no negative
17:37
relationship thing is all over the place
17:40
okay
17:41
so had Mr. Phillips been born a few
17:43
years
17:44
few decades later and had he estimated
17:47
his regression he would have found
17:49
nothing
17:50
there would be no curve in his honor at
17:52
least if he had run that same regression
17:54
maybe he would have run a different
17:55
regression but
17:56
nothing
17:57
okay so what happened
18:00
well our theory can explain as well what
18:03
happened there
18:04
remember the theory is not that
18:07
inflation is equal to a constant minus
18:09
the
18:11
minus
18:13
alpha u
18:14
the theory says
18:16
this is a constant only if
18:18
the model of expectation is this
18:20
constant
18:21
but if expectation is moving around
18:24
or if anything in this constant is
18:26
moving around then then there's another
18:29
source of variation
18:31
okay for example what happens suppose
18:34
that you're here in 1965 and all of the
18:36
sudden you get a the price of oil goes
18:39
up a lot and I'm telling you capture the
18:41
price of oil with an increase in m firms
18:43
need to sort of mark up things more in
18:44
order to cover higher energy energy
18:46
costs
18:48
well look at what m does m says that for
18:50
any given level of unemployment now I
18:52
get higher inflation that's what an oil
18:54
shock does no you get an oil shock then
18:57
for any given level of unemployment now
18:58
you get find yourself with more
18:59
inflation
19:00
so that moves you in the opposite
19:02
direction moves you up there and that's
19:04
one of the reasons
19:06
for these points around here
19:08
we got lots of inflation because we got
19:10
massive oil shocks
19:12
during the 70s and early 80s okay
19:18
we had wars in the Middle East and so on
19:20
that that led to to those shocks so that
19:23
so that was one of the reasons
19:25
we got shocks here
19:27
to this term here
19:29
and that sort of
19:31
muddied the relationship
19:33
but the other reason which is more
19:35
interesting I think and that you already
19:37
began to see that something was
19:38
happening here
19:40
is that
19:41
as inflation went up
19:44
people sort of stopped believing in this
19:45
model so the expectation formation
19:48
mechanism changed
19:52
okay so this guy
19:54
began to react
19:56
to
19:57
endogenous variables. And I'm going to
19:58
explain more precisely what So, that's
20:01
what we mean by expected inflation
20:03
became the anchor. It was no longer
20:06
anchored around this constant of 2%
20:09
but but but it became the anchor. It
20:11
began to follow the data. So, if if the
20:13
data came with more inflation, then
20:15
people believed that next year we would
20:17
have more inflation as well. Okay, not
20:19
back to 2% but if we got 5% inflation
20:22
today, people began to say, "Well, okay,
20:24
I don't think that next year my best
20:26
estimate is 2% is probably closer to
20:28
5%." Okay, that's what it means
20:30
de-anchoring. That's what has the Fed
20:33
and most central banks around the world
20:34
terrified today.
20:36
Inflation is very is much higher than 2%
20:39
and they're very worried about this guy
20:42
becoming
20:43
the anchor or an anchor. Okay.
20:46
I'll get back to that in a second.
20:48
Anyway, so but let me let me explain
20:50
this
20:51
how this expected inflation term work
20:53
here.
20:54
So, let me replace the model of
20:56
expected inflation
20:59
for something which is some weighted
21:00
average of a constant.
21:02
That's
21:03
and
21:05
the most recent inflation.
21:07
Okay. So, this model says, "What is my
21:09
expected inflation for next year? Well,
21:12
it's an average of this long-run target
21:13
that we have,
21:15
say 2%,
21:17
and whatever was the most recent
21:18
inflation."
21:20
If theta in the model I showed you
21:22
before, the one that applied to the '60s
21:24
and so on,
21:25
up to the '60s, had essentially theta
21:28
equal to zero.
21:30
So, this guy didn't show up there
21:32
and and expected inflation was very well
21:35
anchored.
21:36
What we began to happen
21:39
as we began to move that way
21:41
and then we got hit by oil shocks so we
21:43
So, people began to see much higher
21:45
inflation numbers than they were used
21:46
to,
21:48
then this theta
21:50
began to
21:51
increase. Okay. So, people began to sort
21:54
of change the model of expectation and
21:55
began to think that
21:57
inflation was going to be more
21:58
persistent than they used to think in
22:00
the past. So, in high inflation today
22:02
means high inflation tomorrow. That's
22:03
what it means more persistent. In the
22:05
past was high inflation today was was a
22:07
back draw, we'll go back to sort of the
22:10
normal long-run average. Now, that's no
22:12
longer the case. And so, if I replace
22:15
this more general model of expected
22:16
inflation
22:18
here in the Phillips curve, I get this
22:20
expression which now has this extra
22:22
term.
22:23
So, the
22:24
we used to have theta equal to zero but
22:26
during the '70s and '80s and even early
22:29
'90s, actually that theta got to be very
22:31
close to one.
22:33
Okay, if you estimate these models, you
22:35
get that theta was very close to one.
22:37
And look at what happens when theta gets
22:39
very close to one.
22:41
So, when theta is is one literally, then
22:43
the best forecast for inflation is the
22:45
previous inflation.
22:47
Okay, so this year is 5% and I think
22:49
next year is 5%, not 2%, 5%.
22:53
If this year is 7%, I think next year is
22:55
7% again.
22:57
And so, if you do that, then my expected
23:00
inflation becomes lag inflation pi t
23:02
minus one. So, if I stick in replace the
23:04
expected inflation for pi t minus one, I
23:07
get to this Phillips curve
23:09
which I can rewrite
23:11
as the change in inflation in relation
23:14
as as a relationship between the change
23:16
in inflation and the level of
23:18
unemployment.
23:20
So, now what you have is that if
23:22
unemployment is very low, then inflation
23:25
is is picking up, you know, it's going
23:28
there. So, if inflation if unemployment
23:30
is very low, not only inflation is high,
23:33
but it's also growing
23:34
over time.
23:36
Okay.
23:37
That's the reason sometimes people refer
23:39
to this formulation of the Phillips
23:41
curve as the accelerationist Phillips
23:44
curve because now there's a relation
23:45
between unemployment and the change in
23:47
inflation. And if you estimate
23:50
this Phillips curve, this
23:51
accelerationist Phillips curve on the
23:54
data I just showed you of the '70s and
23:57
'80s, you get a much better
23:59
relationship. Okay, you still have the
24:00
oil shocks that messed things up
24:03
but but you can start seeing recovering
24:05
this negative relationship. But again,
24:07
it's between the change in inflation and
24:09
the level of unemployment. And that's a
24:10
very scary situation for a central bank
24:12
to find itself in because it's very easy
24:14
to for things to escalate.
24:19
Okay.
24:22
So, by the mid-'90s,
24:25
we had re-anchored expectations. There
24:27
was a sort of very aggressive
24:30
policy to control inflation by Paul
24:32
Volcker
24:33
in the US and it was imitated around the
24:37
world with some lag,
24:39
but but inflation became re-anchored.
24:41
So, we went back to this theta equal to
24:43
zero type model. The expected inflation
24:46
in the US, the target inflation of the
24:48
central bank was around 2% that became
24:51
what people expected for the next year
24:53
and and that re-anchored. So, we went
24:56
back in other words
25:00
to that sort of Phillips curve.
25:03
Okay, and that's what central banks want
25:04
to be at. They want to have inflation
25:06
expectation very well anchored.
25:09
And they were very successful after the
25:10
'90s. And so, we got
25:12
into again now Look, I'm I'm now I'm not
25:15
running the accelerations. I'm again
25:17
running inflation against unemployment
25:19
and you again can see this downward
25:21
sloping relationship. Okay.
25:24
So, that was very good news. Was great
25:26
success of monetary policy
25:28
during the '90s and later was the
25:31
re-anchoring of expected inflation again
25:34
all around the developed world and many
25:36
of the include even
25:37
Latin America, many economies in Latin
25:39
America saw re-anchored expectation,
25:41
Asia and so on. So,
25:43
so it was a good time for central banks.
25:51
Okay.
25:59
So, the next
26:00
thing I want to do, this will connect
26:01
more with the with the the previous
26:03
lecture. This is the last thing I want
26:05
to say
26:07
for this lecture then I'm I may start
26:10
the review afterwards.
26:12
Um
26:13
is that I want to connect now this
26:16
Phillips curve with something we
26:17
discussed in the previous lecture which
26:19
is the natural rate of unemployment
26:20
because that's the way
26:22
you'll typically see the Phillips curve
26:23
written and and that's
26:26
also the way
26:27
that sort of uh you know, when Chairman
26:30
Powell is talking about the labor market
26:32
tightness and so on, he's not talking
26:34
relative to M and Z and things like
26:37
that, he's talking relative to what is
26:38
called the natural rate of unemployment.
26:39
So, I want to go from a Phillips curve
26:42
that looks like that,
26:46
you know, like that, to one that has the
26:48
natural rate of unemployment in there.
26:50
And so, that's the last step
26:53
in this lecture.
26:54
So,
26:55
remember the definition of the natural
26:57
rate of unemployment. What was the
26:59
definition of the natural rate of
27:00
unemployment?
27:04
Was it the unemployment rate that God
27:07
gave us?
27:10
Any God?
27:15
No.
27:17
It had a very precise meaning for us.
27:24
And remember, we used exactly that model
27:27
to figure it out.
27:30
Remember?
27:34
We we solved the Actually, we solved the
27:36
natural rate of unemployment from
27:38
something like this. I think we had the
27:39
function still generic function f of U
27:41
Z. But we solved from an expression like
27:44
this.
27:46
We said,
27:47
"Under one assumption,
27:50
we can call this
27:51
U
27:52
U N, the natural rate of unemployment.
27:55
What was that assumption?"
27:57
And that's the only thing
27:59
Expected price Okay, expected price is
28:01
equal to the actual price. Okay, so we
28:03
said if this is equal to that, then you
28:05
solve out that's the natural rate of
28:07
unemployment. And that's the only thing
28:08
that that it that means that that that
28:12
natural rate of unemployment means
28:14
simply that when when the
28:15
when the price is equal to the expected
28:17
price.
28:20
But if the price
28:23
is equal to the expected price,
28:26
what else is equal?
28:33
I pointed at the right expressions
28:35
there.
28:37
Inflation is equal to expected
28:39
inflation.
28:41
So, I can use the same logic I used here
28:44
for the natural rate of unemployment
28:45
using the Phillips curve.
28:47
I can say, "Okay,
28:49
my I can solve out for the natural rate
28:51
of unemployment here simply by setting
28:53
the expected inflation equal to actual
28:55
inflation."
28:58
Okay.
28:59
And if I do this, I can solve for the
29:01
natural rate of unemployment from here.
29:04
U N.
29:05
I mean, I'm going to give I'm going to
29:06
put the superscript N here when I when
29:08
you let me replace pi e for pi. That's a
29:11
That's what I
29:12
That's what I
29:13
The fact that I replace this pi e for pi
29:16
is what allows me to put the superscript
29:17
N there. Call it the natural rate of
29:19
unemployment. And now I can solve it.
29:21
Well, obviously that cancels with that
29:22
and I can solve the natural rate of
29:23
unemployment and it's equal to this
29:25
function here.
29:28
So, why is the natural rate of
29:30
unemployment increasing in M?
29:33
A question like that can come up in the
29:35
quiz.
29:38
I'm not going to use the Phillips curve
29:39
to ask you if I ask you about that, but
29:41
I can ask you that. What
29:42
What happens to the natural rate of
29:43
unemployment if M goes up?
29:47
You know that.
29:49
UN will go up, but what is the
29:50
mechanism?
29:59
So, why does the natural rate of
30:00
unemployment go up when
30:02
the markup goes up?
30:06
Yep. If the real cost is constant, wages
30:08
have to go down, right?
30:10
I mean, another way of saying it is that
30:12
the firms are not willing to pay they
30:14
want to pay a lower real wage.
30:16
At the original level of unemployment
30:19
before the change in M,
30:22
workers would not take that lower real
30:24
wage.
30:26
No, it's not an equilibrium real wage
30:27
because workers say, "No, no, at this
30:29
level of unemployment we need a higher
30:31
real wage."
30:32
So, the only way to restore equilibrium
30:34
in that model we had was to increase
30:37
unemployment because that will lower the
30:39
bargaining power of workers and they
30:40
will end up accepting the lower real
30:42
wage that firms are willing to offer
30:44
now. Okay.
30:46
So, that's the reason
30:48
uh we get this this markup effect.
30:53
Z is
30:55
same logic. It's a little easier to see
30:57
it there, but Z means, well, at any
31:00
given level of unemployment
31:02
an increase in Z means workers want a
31:04
higher real wage.
31:06
Firms are not willing to pay a higher
31:07
real wage,
31:09
so you have to bring down the real wage
31:11
that workers demand and the only way
31:13
that can happen is with a higher
31:14
unemployment.
31:15
Okay. That's the reason the natural rate
31:17
of unemployment is also increasing in Z.
31:23
Okay.
31:24
And now the last step.
31:26
The last step is to
31:29
You see, I can go back to my Phillips
31:31
curve.
31:34
Say that.
31:36
And I'm going to replace M plus Z
31:40
for alpha UN. I can do that, you see?
31:45
I can replace this M plus C Z for alpha
31:48
times UN.
31:52
How do I know that? Well, M plus C Z is
31:55
equal to UN times alpha.
31:58
I can replace in the Phillips curve
32:01
M plus C by alpha UN and I can re
32:04
I can therefore
32:06
rewrite the Phillips curve in the
32:08
following form.
32:10
Inflation is equal to expected inflation
32:12
minus alpha times the gap between the
32:16
unemployment rate and the natural rate
32:18
of unemployment.
32:20
Okay. So,
32:22
so
32:23
when
32:25
Chairman Powell is worried about labor
32:27
market being very tight, what he's
32:29
saying is, well, unemployment is likely
32:31
to be below the natural rate of
32:33
unemployment.
32:34
Because if unemployment is below the
32:36
natural rate of unemployment, that's
32:37
putting upward pressure on inflation.
32:41
Okay.
32:44
So, that's a
32:45
So, that's what it means. This gap is
32:47
very important uh for macroeconomists
32:50
and certainly for central bankers that
32:52
are very worried about inflation. Okay?
32:54
That gap here.
32:55
Problem is is this this is a difficult
32:58
object to estimate, so you have to have
32:59
estimates as
33:02
The truth is that it's very difficult to
33:04
know what it is, although there are
33:05
estimates out there and I'm going to
33:06
show you one.
33:09
You notice that something is wrong when
33:10
this guy starts picking up. It's a It's
33:12
a little bit the other way around, you
33:14
know?
33:15
Uh uh
33:16
the US in fact had a the opposite
33:18
problem
33:20
um
33:21
before COVID. It's a somehow
33:23
unemployment was very low relative to
33:25
historical levels, but inflation was not
33:27
picking up.
33:28
So, that was implicitly telling us that
33:30
for some reason, not fully understood,
33:33
the natural rate of unemployment was
33:34
declining.
33:36
Okay.
33:38
So, here is one picture that looks
33:40
is one estimate uh again, I I don't
33:43
trust any particular estimate, but
33:45
it tells a story. That's one particular
33:48
estimate of the natural rate of
33:49
unemployment in the US, that blue line.
33:52
And what you see in red the red is the
33:54
actual rate of unemployment in the US.
33:57
So,
33:58
what happens when when in situations
34:00
like these?
34:04
So, what do you think what's happening
34:05
to inflation in in this episode, which
34:08
is right after the global financial
34:09
crisis or the great recession?
34:15
So, what what what do you need to read
34:17
here? Well,
34:18
the unemployment rate was a lot higher
34:19
than the
34:21
natural rate of unemployment.
34:24
Does that put upward or downward
34:25
pressure on inflation?
34:28
Downward pressure on inflation. No,
34:29
unemployment is very high relative to
34:30
natural rate of unemployment. It's minus
34:32
alpha times U minus UN.
34:34
So, and that's what happened. We had
34:36
lots of problem with inflation.
34:37
Inflation was going very low. We even
34:39
had negative inflation there, a little
34:41
deflation for a while.
34:43
Okay. So, that was a problem.
34:46
Here is the period that they described
34:48
before is a little mysterious because we
34:49
went unemployment went below what we
34:51
thought it was a natural rate of
34:52
unemployment and inflation wasn't really
34:54
picking up a lot. At the end began to
34:55
pick up a little, but it wasn't picking
34:57
up a lot and that was a little bit of a
34:59
mystery.
35:00
Now, we're in this situation here,
35:03
which
35:04
we have extremely low unemployment
35:07
and very high inflation. So, so this I
35:10
think this captures well the situation
35:12
right now. We have a
35:13
negative gap between unemployment and
35:15
the natural rate of unemployment and
35:17
that's the reason that's putting a lot
35:18
of pressure on inflation.
35:20
We also have other things that are
35:22
putting pressure on inflation that come
35:23
from the supply side of the economy and
35:25
so on.
35:26
So, that combination is pretty bad for
35:29
for the
35:31
inflation outcomes and outlook
35:35
as well.
35:36
Okay.
35:38
So, that's where we're at.
35:40
We're going to talk a lot more about
35:41
this because this is what is going on
35:43
right now.
35:45
Any questions about that? Otherwise, I
35:47
want to start sort of reviewing things,
35:48
although I don't know.
35:51
Any question about this? Yep.
35:54
Is correction to increase unemployment?
35:57
Sorry? Is the only way to fix, I guess,
35:59
the inflationary expectations? Well,
36:01
that's a very good question.
36:03
That's a very good question.
36:09
I'm I'm trying to decide what to
36:14
answer what with what do we have.
36:17
Um
36:23
There are two views
36:24
at this moment.
36:27
There's one view
36:29
that says there's no way around that.
36:32
They just look at these curves and say,
36:33
"Look,
36:34
there's no way around that. That's the
36:35
reason we need a recession."
36:38
Okay.
36:38
Because otherwise we were not going to
36:40
control inflation.
36:43
And a recession means high unemployment.
36:45
Okay, that's one view.
36:47
At this moment, it's becoming the
36:50
dominant view.
36:51
It has gone in cycles, but at this
36:53
moment it's the dominant view.
36:57
There is a another view,
36:59
which is the one that the central bank
37:01
the Fed adopted for a while,
37:04
that said, "Well, this is not the only
37:06
indicator of tightness of the labor
37:08
market. There is other things as well."
37:11
And those indicators are moving in the
37:13
right direction.
37:14
And so, we may be able not to create a
37:16
big mess here because these other
37:18
factors are moving in the right right
37:21
direction.
37:22
Some of those factors are as I said,
37:24
other measures of of labor market
37:26
tightness and and hiring, the flows.
37:28
Remember I showed you flows between
37:29
employment and unemployment, out of
37:31
employment and so on. Those flows look
37:33
extremely tight and now they're
37:35
improving. So, the gaps in those
37:36
dimensions are better. And the other one
37:38
is the what's a big cost push component,
37:40
which is what I said before, the supply
37:42
chains and so on created extra
37:44
inflation, abnormal inflation like
37:46
increasing markups, like M was very
37:48
high.
37:49
And some of that is subsiding as well.
37:50
So, so there are dynamics that suggest
37:53
that inflation is declining even without
37:54
unemployment.
37:56
But, I would say
37:58
the medium voter
38:00
in this space of, you know, forecast of
38:02
inflation and so on,
38:04
thinks that that that we will need some
38:06
some adjustment through this this part
38:08
as well. Okay.
38:11
My main concern I I think that
38:15
the the Fed the the path the Fed is
38:17
forecasting is feasible,
38:19
but a very narrow path. I mean, it may
38:21
happen.
38:22
And and to me, whether it they're
38:24
successful at not creating a big mess
38:26
here, I mean, bringing unemployment very
38:29
high in order to bring inflation down,
38:31
has a lot to do with whether
38:34
somehow we manage to keep expected
38:35
inflation anchored.
38:37
And there there was some evidence, I
38:39
think I said that a few lectures ago,
38:41
there was some evidence that in the
38:42
summer of
38:45
uh summer of 2022, I'm from the southern
38:49
hemisphere, so I get always confused
38:50
with summers and and so on.
38:52
So, the in in the summer of 2022, US
38:55
summer of 2022, inflation was becoming
38:57
very unanchored. This guy
38:59
one year expected inflation was creeping
39:01
up to 6% and that was very scary. Okay?
39:04
Because think what happened. If if if
39:07
you get expected inflation at 6%,
39:10
then it's not enough to bring
39:12
unemployment to the natural rate of
39:13
unemployment to get inflation back to
39:15
the 2% we like because you need to bring
39:17
expected inflation down now. And that
39:19
means you need to sort of bring the
39:22
unemployment rate very very high in
39:24
order to re-anchor expectations. So,
39:26
that's a very scary situation. They were
39:28
very persuasive though at the end of the
39:29
summer with very hawkish speeches and so
39:32
on
39:33
and they managed to re-anchor expected
39:35
inflation. So, expected inflation very
39:37
quickly came down to two two and a half
39:38
percent one year out to
39:41
But, now it been picking up again and
39:43
now we are around 3% again, so it's a
39:44
little bit scary for where we are. So,
39:47
to me this is going to be very important
39:49
in that. So,
39:51
if inflation keeps lingering around 6%
39:53
and so on, and eventually the expected
39:55
inflation becomes an anchor, then
39:57
there's almost no way around but to have
39:59
a recession to get out of that.
40:02
If that doesn't happen, if they succeed
40:04
convincing a ton of people that that,
40:06
you know, they're very serious about
40:07
about this stuff and they they re-anchor
40:09
expectation expected inflation, then we
40:11
don't need to create a large recession.
40:14
Still they may create it, cause it
40:15
because, you know, accidents happen, but
40:17
but but but they don't need to.
40:20
But they will need to if this guy gets
40:22
an anchor.
40:24
Actually, maybe I can use even this
40:26
expression here
40:28
to explain what I'm trying to say and I
40:30
realize that this is again, this is
40:31
material really for
40:33
for the next lecture.
40:35
What I'm trying to say is that if they
40:36
manage
40:38
to keep this theta very close to zero,
40:42
okay?
40:43
Then, in order to bring inflation back
40:46
to their target of pi bar, 2% or so,
40:50
all that they really need to do is to
40:52
sort of bring unemployment to the
40:53
natural rate of unemployment. So, they
40:55
only need to really
40:57
uh
40:59
fix this gap.
41:01
Okay? They need to raise unemployment so
41:03
so it closes that gap. But it's a small
41:05
change.
41:06
That's if they succeed keeping expected
41:09
inflation at around 2%.
41:12
If they don't,
41:16
say suppose that that
41:18
that
41:19
theta becomes very far from from zero,
41:24
then we have a problem because then
41:25
expected inflation is above the target,
41:28
no? Because we have 6%, so suppose theta
41:30
is equal to one, we have 6%, then
41:32
expected inflation
41:33
is 6%.
41:35
That means that if you if your expected
41:38
inflation
41:40
is
41:41
6%,
41:43
then in order to bring bring the
41:44
inflation if you bring unemployment just
41:47
to the natural rate of unemployment, so
41:48
the red line to the blue line, you
41:50
haven't made a lot of progress. All that
41:52
you have done is
41:53
you have brought down inflation
41:55
to 6%, which is expected inflation.
41:58
So, if you are have expected inflation
42:00
of 6%, you need to bring unemployment
42:03
much higher than the natural rate of
42:05
unemployment in order to bring inflation
42:07
back to the target of 2%.
42:10
That's the reason I say
42:11
to me
42:13
the fight will be
42:15
the battle will be won or lost
42:18
on that term there.
42:21
Yep.
42:23
How much
42:24
of this current like inflationary
42:26
pressure is caused by unemployment? How
42:28
much of it is caused on the supply side?
42:30
Cuz it feels like a lot of this stuff
42:31
like CPI going up, energy prices going
42:33
up, it's like how much can the Fed keep
42:35
control of something like Well, it
42:36
varies a little from different
42:40
This is around the world, but but in the
42:41
US,
42:42
uh for a while a big component of
42:44
inflation was all that stuff.
42:47
Uh you know, bottlenecks in the ports
42:49
and and stuff like that.
42:51
That's almost all gone.
42:52
There's very little of that left. So,
42:54
now is
42:56
is aggregate demand. People feel very
42:57
rich
42:59
for a variety of reasons, they're
43:00
spending a lot and that's the reason
43:01
unemployment is very low.
43:04
It's not unemployment per se, it's just
43:05
the aggregate demand is very high.
43:07
You know?
43:09
Uh and that translates into very low
43:10
unemployment and that feeds into
43:12
inflation this way
43:13
through wages and so on.
43:15
But
43:17
in the US, the component of aggregate
43:18
demand is much larger than in Europe. In
43:20
Europe, those supply side factors are
43:22
much more important. So,
43:25
you know, around the
43:29
Yeah, the summer of 2022, you could say
43:33
both both Europe and the US had about
43:36
the same amount of excess inflation.
43:37
They were all with about 10% inflation.
43:41
But in the US was 2/3 excess aggregate
43:44
demand,
43:45
while in Europe was 2/3 problems on the
43:48
supply side, especially because of the
43:49
war and stuff like that.
43:51
Okay?
43:51
So,
43:52
so but it for the US today is mostly an
43:54
aggregate demand problem. We're not
43:56
going to get a lot of
43:57
Obviously, if the war stops, that's
43:59
going to help,
44:01
but it's not going to be enough. We we
44:02
we need to
44:04
just the economy is too hot. It's too
44:05
much aggregate demand out there.
44:07
That's the that's the fundamental
44:09
problem. Yeah.
44:11
Can you explain again why an increase in
44:13
Z would increase the natural rate of
44:16
unemployment? An increase in Z? Yeah.
44:19
So,
44:20
uh
44:21
um
44:23
for that the basis the previous slide
44:25
diagram, but remember what Z does.
44:27
Actually, let me go to
44:30
this equation here.
44:34
So, we can figure out in this in this
44:36
two equations here. If Z goes up, that
44:39
means for any given level of
44:40
unemployment
44:42
and expected inflation,
44:45
wages go up. Workers demand higher wage.
44:50
But
44:51
remember that that the firms
44:55
uh
44:56
So, so let me let me let me we're
44:58
talking about the natural rate of
44:58
unemployment, so let me replace this PE
45:00
for P first of all.
45:02
Okay?
45:03
So, I'm going to divide
45:05
W by P both sides. So, I get
45:09
if if Z goes up, the workers want a
45:12
higher real wage.
45:14
No? If because
45:17
if Z goes up, then W over P, I'm
45:20
dividing by P both sides, goes up.
45:23
Workers demand a higher wage.
45:25
But the firms, from here you can see
45:27
that I can divide by P both sides, W
45:29
over P that the firms offer is equal to
45:32
1 over 1 + M.
45:35
Okay? So, the the firms are not going to
45:37
offer a higher real wage. The workers
45:40
want a higher real wage.
45:42
The only thing that can restore
45:43
equilibrium that the workers end up
45:45
demanding the same real wage as the
45:47
firms are willing to pay
45:49
is that somehow the hands of the worker
45:51
gets weakened. And the only variable
45:53
here that can weaken their hand is a
45:56
higher unemployment.
45:58
Okay?
45:59
So,
46:00
let me put it all in
46:05
So, at the natural rate,
46:07
I know that PE is equal to P.
46:10
So, that means the wage setting equation
46:13
the wage setting equation implies
46:16
W over P
46:19
equal F U Z.
46:22
Okay?
46:24
From the price setting equation,
46:28
I have that
46:29
W over P
46:32
is equal to 1 over 1 + M.
46:35
So, in this very simple model, this is
46:37
given.
46:38
If this guy goes up,
46:40
these guys want a higher real wage, but
46:42
that cannot happen because that would be
46:43
inconsistent with the price setting, so
46:45
you need to bring down this guy down.
46:48
The only thing that can bring it down is
46:49
for unemployment to go up.
46:52
And that's at P, we call that the
46:54
natural rate of unemployment.
46:56
Okay.
46:59
Yeah.
47:01
So, like last lecture we talked about
47:03
the labor force participation rate. Um
47:07
is there like any reason to try and like
47:10
increase that to increase Oh,
47:12
fantastic. Yes.
47:16
Well, I mean
47:19
there are sort of negative policies as
47:21
well.
47:22
You know, Z reduction in a sense does
47:24
that because
47:25
the the was a emergency unemployment
47:28
benefits and emergency
47:30
income supplements and so on as a result
47:32
of the pandemic that are disappearing
47:34
slowly. And that's very naturally so
47:36
it's it's going to bring
47:39
uh participation back up and it is
47:41
beginning to pick up. So,
47:43
so yeah, you need to incentivize return
47:46
to work. And now there are some people
47:48
that
47:48
there's nothing that
47:50
they've retired essentially or, you
47:52
know, they have health problems and they
47:54
they just cannot return. We lost that.
47:57
And the other margin which is very
47:58
important is immigration. So, that's a
48:00
big issue
48:01
because immigration obviously that we
48:03
lost I think in the US, I'm not a labor
48:05
economist, but we lost
48:07
I think a flow of the order of the order
48:09
of 500,000 people a year
48:11
during COVID.
48:13
And and and that's that's a big chunk of
48:15
the decline in
48:17
in the labor No, what you need is more
48:19
employment. That's going to that puts
48:21
downward pressure on wages for the same
48:23
amount of aggregate demand.
48:25
And that's what you need, but but
48:28
Yeah, we're taking that's a very good
48:29
point. We're taking all that as given
48:31
here. Remember, we're fixing all that,
48:33
but but if you don't, then then you
48:36
other terms will start appearing in this
48:38
expression and so on.
48:40
Good.
48:42
Obviously, I'm not going to start the
48:43
review. We have only 1 minute, but so in
48:45
the next lecture I I'll just review
48:48
uh the material for the quiz.
— end of transcript —
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