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Lecture 9: The Phillips Curve and Inflation — Transcript

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0:16So, today I'm going to talk about the
0:18Phillips curve and inflation. Um
0:22Now, as I said in the previous lecture,
0:24uh
0:25the material that is specific to this
0:27lecture will not enter this quiz.
0:30It's the beginning of what is perhaps
0:31the most important model you'll see in
0:33the in in this in this uh class, but
0:37it will take us uh three or four
0:38lectures to to develop. So, I'm going to
0:42say things that certainly will
0:44um
0:45may help you understand a little better
0:46the previous lecture, and so
0:49if you're only concerned about the next
0:51quiz,
0:52uh there will be a sort of uh small
0:55review of the previous lecture here. Uh
0:57but again, anything that's specific to
1:00this lecture and was not in the previous
1:02one
1:03won't be part of of this quiz.
1:06So, what is this Phillips curve? Well,
1:08in in uh
1:10in 1958, an an economist uh at LSE, the
1:14London School of Economics,
1:16came up with some just an empirical
1:17relationship. This is A.W. Phillips. He
1:20found that using historical data
1:24uh for the US, I think he did it. Um
1:28uh there was a negative relation up to
1:30sort of the '50s, I think. Uh
1:33the there was a negative relation
1:35between uh the unemployment rate and the
1:37rate of inflation.
1:39And then our very own Paul Samuelson and
1:42Robert Solow
1:44labeled this relationship the Phillips
1:46curve in honor of uh
1:48A.W. Phillips.
1:49And nowadays it's sort of is a central
1:52concept uh in macroeconomics, and
1:55uh and uh it's certainly very, very
1:58relevant to understand what is going on
2:00uh right now in not only in the US
2:02economy, but in most economies around
2:04the world.
2:06So, let me
2:07show you sort of this is not the one
2:08that uh
2:10that Phillips uh plotted. I think this
2:12is the one that uh
2:14uh
2:15Samuelson and Solow plotted for data
2:17from between 1900 and 1960 uh
2:20for the US, you found you find sort of
2:23this sort of negative correlation. I
2:25think it's reasonable.
2:27Uh
2:28um
2:29there's negative correlation between
2:31uh the unemployment rate and inflation
2:34rate, no? At very low levels of
2:36unemployment, you typically see very
2:37high levels of inflation.
2:39Conversely, sort of at very high levels
2:41of unemployment, you tend to receive low
2:44levels of inflation or even deflation.
2:46In fact, this period includes the the
2:49Great Depression, for example.
2:52So,
2:53that's sort of the data. And and again,
2:56this was just an empirical regularity.
2:59But we can build some theory about this
3:00relationship using the ingredients most
3:03of the ingredients that
3:05I mean, essentially we can build a
3:07relationship that is downward sloping
3:10from the ingredients we already have.
3:13And this is the part that is a little
3:14bit of a review
3:15of the previous lecture.
3:17Remember that we had um um
3:20actually the previous two lectures. We
3:22had a wage setting equation
3:25W equal expected prices
3:28and then a decreasing function of
3:29unemployment and an increasing function
3:31of uh these labor market supporting
3:34institutions or
3:36worker supporting institutions, that
3:38institutional variables, I should say.
3:40And um and then we had a price setting
3:43equation, which was simply the wage uh
3:46marked up.
3:48M is a positive constant. So, let me
3:50start from these two what So, what I'm
3:53trying to do is derive a Phillips curve.
3:55Again, this was only an empirical
3:57relationship, but it turns out that even
3:59with theory we knew by the time of, you
4:01know, Samuelson and and and Solow, we
4:03could sort of come up with a with a
4:05theory of that relationship. And that
4:07theory builds on the ingredients we have
4:09been looking at. So, these are the price
4:11set the wage setting equation, the price
4:12setting equation. I'm going to just
4:14simplify things and assume that this
4:16this relationship here, this function f
4:19of u z, is some linear function, at
4:22least locally linear function, uh which
4:24is decreasing in unemployment and
4:26increasing in z.
4:28Why is it decreasing in unemployment?
4:35This says, no, that that if unemployment
4:37goes up,
4:39for any given expected price,
4:41wage demand is lower.
4:43Okay? And that's essentially because uh
4:46for the worker is is sort of is a
4:49becoming unemployed is a scary
4:50situation.
4:52Conversely, for firms it's higher it's
4:54easier to find uh
4:56uh
4:56a worker and and uh
4:59and uh So, as we said, a worker is
5:01scared for two reasons. One is that it's
5:04more likely it gets fired when
5:05unemployment is high, typically that's a
5:07recession. It's also likely they know
5:10that that worker knows that if she were
5:13to fall into the unemployment pool, it
5:15would take a longer time to get out of
5:17it. Okay? And the firms are seeing the
5:19opposite side. It's pretty easy for them
5:21to replace a worker if they were to
5:24dismiss a worker because there's lots of
5:26available workers in unemployment. Okay?
5:28So, that's the reason that's negative.
5:30So, I'm going to stick this function
5:32back in here.
5:34And then I'm going to replace this W
5:37with this function in there in the price
5:39setting equation, and I end up with an
5:42equation for P. Okay? So, this says that
5:46the price, given the expected price,
5:50is decreasing in unemployment and
5:52increasing in z and increasing in the
5:54markup.
5:55So, again, why is this price decreasing
5:58in unemployment?
6:02This is the part that is review of the
6:04previous lecture.
6:05Previous today. Because
6:07the wages go down and then the labor uh
6:09factors of production are cheaper. Okay,
6:10perfect. Because wages go down, since uh
6:14our firm needs one worker to produce one
6:16unit of a good, then the cost of
6:17production of one unit goes down with
6:19the wage, and and therefore the price
6:22goes down. Because the firm is asking
6:24for a constant markup over that wage,
6:26the wage declines, and the price drops.
6:31Good. So, that's all review. So,
6:35this equation you had seen just without
6:37an explicit functional form here. What I
6:39want to do is to go from here. This is
6:42still not the Phillips curve. Remember,
6:43the Phillips curve was a relationship
6:44between inflation
6:46and unemployment. Here we have a
6:48relationship between the price level
6:51and unemployment. Okay? So, we want to
6:53take one
6:55one derivative higher. We want to go to
6:57relation between
6:58inflation and unemployment. And
7:00inflation is is the rate of change of P.
7:03No?
7:04It's not it's not a level of P.
7:07So, to do that, all that we'll do is So,
7:09this when I don't have a subscript here,
7:11I mean
7:12the price at time t.
7:14Okay? And this is the expected price for
7:16next period, that's what we have.
7:18Uh
7:18but today for next period.
7:21What I'm going to do, I'm going to
7:22divide both sides by P minus 1. By that,
7:25I mean the price in the previous period.
7:27Okay? So, both sides. I'm going to
7:29divide this side by P minus 1.
7:32And and and this one by P minus 1.
7:34So, I get that expression. Okay? That's
7:36exactly the same equation we had before.
7:39All that I did is I divided by P minus
7:411. Remember remember what this means.
7:44So, if this is the price for the
7:46beginning for January 2023,
7:49uh
7:50this is the price for, say, where we're
7:51using annual data, for January 2022.
7:54Okay? So, I'm dividing by the price of
7:56January 2022 both sides.
8:00Now, notice that remember that I can
8:03that P over P minus 1 is equal to 1 plus
8:06the inflation rate. Remember where
8:08inflation rate is just
8:10P minus P minus 1 over P minus 1. So,
8:14this is just straightforward algebra,
8:16no?
8:17Remember our definition of inflation.
8:33That's P minus that's inflation. Okay?
8:36So, 1 plus pi is just
8:39P minus uh
8:41over P minus 1. Okay? And that's what
8:43you have there.
8:44I can do the same for expected
8:45inflation.
8:48Notice that
8:53sometimes people get confused, but
8:56expected inflation
8:58is equal to P
9:00expected
9:02not minus P expected minus 1. It's P
9:05minus 1.
9:07P minus 1.
9:10And the reason I'm not subtracting the
9:12expectation here is because at time t,
9:15which is when you're forming that
9:16expectation, you already know what
9:18happened at t minus 1.
9:21Okay? So, that's the reason this is
9:22expected inflation. I don't I don't need
9:25uh uh
9:26um
9:28to put expectations in here. Okay? So,
9:31that's pi e.
9:33And so, what we get is
9:35uh I can replace
9:37this guy here for 1 plus pi, this guy
9:40here for 1 plus pi e,
9:42and I get the following relationship.
9:45Okay?
9:47All that I've done is substituting this
9:49for that, that for that.
9:52So, that's our price setting equation
9:54now expressed in terms of inflation rate
9:58unexpected inflation rate
10:00and now you know
10:02if not we're not in Argentina we're in
10:04the US
10:05inflation if expected inflation is a
10:07small numbers
10:09and the log of 1 plus a small number is
10:11approximately that number
10:15so
10:17I'm going to use this approximation
10:19which again is valid for X small
10:23and and so I can replace this 1 plus pi
10:26for pi and this 1 plus pi e for pi e
10:30this 1 plus m for m
10:33plus no and this term here if these
10:36numbers are not too large again plus
10:39minus alpha u
10:41plus z
10:43and that I do all that and I end up with
10:45this expression
10:51all that I've done is I took logs of
10:53this so I get log of 1 plus pi equal to
10:56log of 1 plus pi e plus log of 1 plus m
10:59plus log of 1 minus alpha u plus alpha z
11:02I'm saying if pi pi e m alpha u plus z
11:07are not very large numbers which we're
11:09going to assume then this is
11:11approximately right so I can rewrite
11:13that expression as that
11:16approximately I should have put an
11:17approximately
11:22okay so now we have something that looks
11:23a lot more than like the empirical
11:25relationship we were talking about we
11:27have a relationship between inflation
11:29and unemployment so this says that
11:32for any given expected inflation and
11:34markups and and labor market
11:35institutions
11:37higher unemployment means lower
11:39inflation
11:40why is that
11:43so that curve tells you that's a
11:44negative relation we wanted no it says
11:47higher unemployment lower inflation
11:53why is that
12:02look you had it very clear when we talk
12:04about this no
12:05you you understood very clearly why an
12:07increase in unemployment lower the wage
12:10you understood very clearly why
12:13therefore an increase in unemployment
12:15lower the price
12:18I haven't done anything but algebra in
12:20the two steps so the same economics
12:22behind the explanations that you had
12:23before apply to this curve here
12:26so the reason inflation will be lower
12:29when you unemployment is higher given
12:31all the rest
12:33is because there's really less wage wage
12:35pressure workers will demand lower wages
12:38that means lower prices and therefore
12:39inflation will be lower the economics
12:41hasn't changed at all I only I only
12:43divided both sides
12:45by p minus 1 and I took the logs and I
12:47approximated so so the economics has not
12:49changed
12:50it just did a little bit of
12:53basic math okay
12:55so all the what I'm trying to say is all
12:57the intuitions that you can already you
12:59already had from the wage setting price
13:02setting equations and so on you can
13:03apply to the Phillips curve as well
13:06okay
13:08good so now we have something that
13:11in principle could explain the type of
13:13relationship that Phillips
13:16found and then Samuelson Solo
13:17corroborated with extended data
13:23so
13:26let's let's see how do we get to
13:27something that looks like what
13:30these people run as a
13:31they run a regression essentially
13:34or they correlated and inflation
13:38inflation with unemployment
13:40and they found a downward sloping
13:42relationship
13:44well
13:45look what if that happens here suppose
13:47that
13:48that we assume that expected inflation
13:51is equal to some constant
13:54in in economics we say when that's the
13:56case
13:58and especially if pi is a low number
14:00inflation expectations are well anchored
14:03meaning you know any single year they
14:06can be a price of oil is high or
14:07something happens and inflation will
14:09deviate from that
14:10but people are all the time expecting
14:12for inflation sort of to go back to the
14:15what is a normal level
14:17nowadays
14:18or at least
14:19a few years ago in the US the normal
14:22level was around 2% say okay so people
14:25say well this year inflation was 1.8 but
14:28we expect next year 2% the next year we
14:31got surprises on the upside price of
14:33food went up something like that we got
14:35inflation of 2.3% but you ask people how
14:38do you what much do you expect for next
14:40year they say well 2%
14:42so so that's what a model of expectation
14:45like this means is that you know you're
14:47always expecting something which is
14:49some historical value on that we have
14:51agreed is a reasonable level for our
14:54economy or something like that okay
14:56so you see that if I replace expected
14:58inflation for a constant here pi bar
15:01then I have then my Phillips curve is
15:04really this is inflation then I have a
15:06constant minus alpha u
15:09that's the simplest of the
15:11downward sloping relationship I can have
15:12that case is a line downward sloping
15:14line no that's it
15:17of course you know it could be
15:19non-linear and so on but but this
15:20captures the essence so that's the
15:22theory for why
15:24Phillips was finding what he was finding
15:27our theory of the
15:29wage of the labor market if you will and
15:31the price setting
15:33behavior of firms gives us a Phillips
15:35curve of the kind that he had in mind
15:39and if you look in the 60s in the US
15:43then you see this negative relationship
15:45that eventually become sort of became a
15:47steeper it wasn't linear like this it
15:49was a little convex but but it's
15:51downward sloping
15:53and in fact
15:55to some extent
15:58our own very our very own Bob Solo and
16:02Paul Samuelson
16:04were advising the US government at the
16:06time and they said well you know let's
16:08exploit this stuff a little
16:10we like to have lower unemployment we
16:13can live with a little less more
16:14inflation but we know there's a negative
16:16trade-off there's a negative trade-off
16:18between these two things okay so
16:20if we like to lower unemployment it's
16:22fine we get a little more of inflation
16:24and initially the deal was very good
16:26because this curve was very flat
16:29you see you could cut him unemployment a
16:31lot you can see the dates here cutting
16:33unemployment a lot and you're not
16:35getting a lot of inflation
16:37eventually the deal the deal turned into
16:39a much rather deal much more rather deal
16:41because
16:42then to lower a little bit more
16:43unemployment we start getting a lot more
16:45of inflation okay so people for a while
16:48you know were okay with this model
16:50assuming that inflation was low but when
16:53they realized that this thing was being
16:54exploited then they began to sort of
16:57change the expectations they made I
16:59think that's what we had here but but
17:01the the reason held pretty well
17:03during this time and again it became
17:05steeper and steeper as we
17:07pushed it more and more towards sort of
17:09very low levels of unemployment
17:12so that's the story but again there is
17:14your model of the Phillips curve and
17:15that
17:17it's a very very good model for the
17:18times where Phillips also estimated his
17:21his Phillips curve
17:23now
17:25if you sort of turn the page and look at
17:27the same data in the 70s
17:30look how it looks
17:32okay
17:33so from 1970 to 1995 that's the data you
17:36have there there's no negative
17:37relationship thing is all over the place
17:40okay
17:41so had Mr. Phillips been born a few
17:43years
17:44few decades later and had he estimated
17:47his regression he would have found
17:49nothing
17:50there would be no curve in his honor at
17:52least if he had run that same regression
17:54maybe he would have run a different
17:55regression but
17:56nothing
17:57okay so what happened
18:00well our theory can explain as well what
18:03happened there
18:04remember the theory is not that
18:07inflation is equal to a constant minus
18:09the
18:11minus
18:13alpha u
18:14the theory says
18:16this is a constant only if
18:18the model of expectation is this
18:20constant
18:21but if expectation is moving around
18:24or if anything in this constant is
18:26moving around then then there's another
18:29source of variation
18:31okay for example what happens suppose
18:34that you're here in 1965 and all of the
18:36sudden you get a the price of oil goes
18:39up a lot and I'm telling you capture the
18:41price of oil with an increase in m firms
18:43need to sort of mark up things more in
18:44order to cover higher energy energy
18:46costs
18:48well look at what m does m says that for
18:50any given level of unemployment now I
18:52get higher inflation that's what an oil
18:54shock does no you get an oil shock then
18:57for any given level of unemployment now
18:58you get find yourself with more
18:59inflation
19:00so that moves you in the opposite
19:02direction moves you up there and that's
19:04one of the reasons
19:06for these points around here
19:08we got lots of inflation because we got
19:10massive oil shocks
19:12during the 70s and early 80s okay
19:18we had wars in the Middle East and so on
19:20that that led to to those shocks so that
19:23so that was one of the reasons
19:25we got shocks here
19:27to this term here
19:29and that sort of
19:31muddied the relationship
19:33but the other reason which is more
19:35interesting I think and that you already
19:37began to see that something was
19:38happening here
19:40is that
19:41as inflation went up
19:44people sort of stopped believing in this
19:45model so the expectation formation
19:48mechanism changed
19:52okay so this guy
19:54began to react
19:56to
19:57endogenous variables. And I'm going to
19:58explain more precisely what So, that's
20:01what we mean by expected inflation
20:03became the anchor. It was no longer
20:06anchored around this constant of 2%
20:09but but but it became the anchor. It
20:11began to follow the data. So, if if the
20:13data came with more inflation, then
20:15people believed that next year we would
20:17have more inflation as well. Okay, not
20:19back to 2% but if we got 5% inflation
20:22today, people began to say, "Well, okay,
20:24I don't think that next year my best
20:26estimate is 2% is probably closer to
20:285%." Okay, that's what it means
20:30de-anchoring. That's what has the Fed
20:33and most central banks around the world
20:34terrified today.
20:36Inflation is very is much higher than 2%
20:39and they're very worried about this guy
20:42becoming
20:43the anchor or an anchor. Okay.
20:46I'll get back to that in a second.
20:48Anyway, so but let me let me explain
20:50this
20:51how this expected inflation term work
20:53here.
20:54So, let me replace the model of
20:56expected inflation
20:59for something which is some weighted
21:00average of a constant.
21:02That's
21:03and
21:05the most recent inflation.
21:07Okay. So, this model says, "What is my
21:09expected inflation for next year? Well,
21:12it's an average of this long-run target
21:13that we have,
21:15say 2%,
21:17and whatever was the most recent
21:18inflation."
21:20If theta in the model I showed you
21:22before, the one that applied to the '60s
21:24and so on,
21:25up to the '60s, had essentially theta
21:28equal to zero.
21:30So, this guy didn't show up there
21:32and and expected inflation was very well
21:35anchored.
21:36What we began to happen
21:39as we began to move that way
21:41and then we got hit by oil shocks so we
21:43So, people began to see much higher
21:45inflation numbers than they were used
21:46to,
21:48then this theta
21:50began to
21:51increase. Okay. So, people began to sort
21:54of change the model of expectation and
21:55began to think that
21:57inflation was going to be more
21:58persistent than they used to think in
22:00the past. So, in high inflation today
22:02means high inflation tomorrow. That's
22:03what it means more persistent. In the
22:05past was high inflation today was was a
22:07back draw, we'll go back to sort of the
22:10normal long-run average. Now, that's no
22:12longer the case. And so, if I replace
22:15this more general model of expected
22:16inflation
22:18here in the Phillips curve, I get this
22:20expression which now has this extra
22:22term.
22:23So, the
22:24we used to have theta equal to zero but
22:26during the '70s and '80s and even early
22:29'90s, actually that theta got to be very
22:31close to one.
22:33Okay, if you estimate these models, you
22:35get that theta was very close to one.
22:37And look at what happens when theta gets
22:39very close to one.
22:41So, when theta is is one literally, then
22:43the best forecast for inflation is the
22:45previous inflation.
22:47Okay, so this year is 5% and I think
22:49next year is 5%, not 2%, 5%.
22:53If this year is 7%, I think next year is
22:557% again.
22:57And so, if you do that, then my expected
23:00inflation becomes lag inflation pi t
23:02minus one. So, if I stick in replace the
23:04expected inflation for pi t minus one, I
23:07get to this Phillips curve
23:09which I can rewrite
23:11as the change in inflation in relation
23:14as as a relationship between the change
23:16in inflation and the level of
23:18unemployment.
23:20So, now what you have is that if
23:22unemployment is very low, then inflation
23:25is is picking up, you know, it's going
23:28there. So, if inflation if unemployment
23:30is very low, not only inflation is high,
23:33but it's also growing
23:34over time.
23:36Okay.
23:37That's the reason sometimes people refer
23:39to this formulation of the Phillips
23:41curve as the accelerationist Phillips
23:44curve because now there's a relation
23:45between unemployment and the change in
23:47inflation. And if you estimate
23:50this Phillips curve, this
23:51accelerationist Phillips curve on the
23:54data I just showed you of the '70s and
23:57'80s, you get a much better
23:59relationship. Okay, you still have the
24:00oil shocks that messed things up
24:03but but you can start seeing recovering
24:05this negative relationship. But again,
24:07it's between the change in inflation and
24:09the level of unemployment. And that's a
24:10very scary situation for a central bank
24:12to find itself in because it's very easy
24:14to for things to escalate.
24:19Okay.
24:22So, by the mid-'90s,
24:25we had re-anchored expectations. There
24:27was a sort of very aggressive
24:30policy to control inflation by Paul
24:32Volcker
24:33in the US and it was imitated around the
24:37world with some lag,
24:39but but inflation became re-anchored.
24:41So, we went back to this theta equal to
24:43zero type model. The expected inflation
24:46in the US, the target inflation of the
24:48central bank was around 2% that became
24:51what people expected for the next year
24:53and and that re-anchored. So, we went
24:56back in other words
25:00to that sort of Phillips curve.
25:03Okay, and that's what central banks want
25:04to be at. They want to have inflation
25:06expectation very well anchored.
25:09And they were very successful after the
25:10'90s. And so, we got
25:12into again now Look, I'm I'm now I'm not
25:15running the accelerations. I'm again
25:17running inflation against unemployment
25:19and you again can see this downward
25:21sloping relationship. Okay.
25:24So, that was very good news. Was great
25:26success of monetary policy
25:28during the '90s and later was the
25:31re-anchoring of expected inflation again
25:34all around the developed world and many
25:36of the include even
25:37Latin America, many economies in Latin
25:39America saw re-anchored expectation,
25:41Asia and so on. So,
25:43so it was a good time for central banks.
25:51Okay.
25:59So, the next
26:00thing I want to do, this will connect
26:01more with the with the the previous
26:03lecture. This is the last thing I want
26:05to say
26:07for this lecture then I'm I may start
26:10the review afterwards.
26:12Um
26:13is that I want to connect now this
26:16Phillips curve with something we
26:17discussed in the previous lecture which
26:19is the natural rate of unemployment
26:20because that's the way
26:22you'll typically see the Phillips curve
26:23written and and that's
26:26also the way
26:27that sort of uh you know, when Chairman
26:30Powell is talking about the labor market
26:32tightness and so on, he's not talking
26:34relative to M and Z and things like
26:37that, he's talking relative to what is
26:38called the natural rate of unemployment.
26:39So, I want to go from a Phillips curve
26:42that looks like that,
26:46you know, like that, to one that has the
26:48natural rate of unemployment in there.
26:50And so, that's the last step
26:53in this lecture.
26:54So,
26:55remember the definition of the natural
26:57rate of unemployment. What was the
26:59definition of the natural rate of
27:00unemployment?
27:04Was it the unemployment rate that God
27:07gave us?
27:10Any God?
27:15No.
27:17It had a very precise meaning for us.
27:24And remember, we used exactly that model
27:27to figure it out.
27:30Remember?
27:34We we solved the Actually, we solved the
27:36natural rate of unemployment from
27:38something like this. I think we had the
27:39function still generic function f of U
27:41Z. But we solved from an expression like
27:44this.
27:46We said,
27:47"Under one assumption,
27:50we can call this
27:51U
27:52U N, the natural rate of unemployment.
27:55What was that assumption?"
27:57And that's the only thing
27:59Expected price Okay, expected price is
28:01equal to the actual price. Okay, so we
28:03said if this is equal to that, then you
28:05solve out that's the natural rate of
28:07unemployment. And that's the only thing
28:08that that it that means that that that
28:12natural rate of unemployment means
28:14simply that when when the
28:15when the price is equal to the expected
28:17price.
28:20But if the price
28:23is equal to the expected price,
28:26what else is equal?
28:33I pointed at the right expressions
28:35there.
28:37Inflation is equal to expected
28:39inflation.
28:41So, I can use the same logic I used here
28:44for the natural rate of unemployment
28:45using the Phillips curve.
28:47I can say, "Okay,
28:49my I can solve out for the natural rate
28:51of unemployment here simply by setting
28:53the expected inflation equal to actual
28:55inflation."
28:58Okay.
28:59And if I do this, I can solve for the
29:01natural rate of unemployment from here.
29:04U N.
29:05I mean, I'm going to give I'm going to
29:06put the superscript N here when I when
29:08you let me replace pi e for pi. That's a
29:11That's what I
29:12That's what I
29:13The fact that I replace this pi e for pi
29:16is what allows me to put the superscript
29:17N there. Call it the natural rate of
29:19unemployment. And now I can solve it.
29:21Well, obviously that cancels with that
29:22and I can solve the natural rate of
29:23unemployment and it's equal to this
29:25function here.
29:28So, why is the natural rate of
29:30unemployment increasing in M?
29:33A question like that can come up in the
29:35quiz.
29:38I'm not going to use the Phillips curve
29:39to ask you if I ask you about that, but
29:41I can ask you that. What
29:42What happens to the natural rate of
29:43unemployment if M goes up?
29:47You know that.
29:49UN will go up, but what is the
29:50mechanism?
29:59So, why does the natural rate of
30:00unemployment go up when
30:02the markup goes up?
30:06Yep. If the real cost is constant, wages
30:08have to go down, right?
30:10I mean, another way of saying it is that
30:12the firms are not willing to pay they
30:14want to pay a lower real wage.
30:16At the original level of unemployment
30:19before the change in M,
30:22workers would not take that lower real
30:24wage.
30:26No, it's not an equilibrium real wage
30:27because workers say, "No, no, at this
30:29level of unemployment we need a higher
30:31real wage."
30:32So, the only way to restore equilibrium
30:34in that model we had was to increase
30:37unemployment because that will lower the
30:39bargaining power of workers and they
30:40will end up accepting the lower real
30:42wage that firms are willing to offer
30:44now. Okay.
30:46So, that's the reason
30:48uh we get this this markup effect.
30:53Z is
30:55same logic. It's a little easier to see
30:57it there, but Z means, well, at any
31:00given level of unemployment
31:02an increase in Z means workers want a
31:04higher real wage.
31:06Firms are not willing to pay a higher
31:07real wage,
31:09so you have to bring down the real wage
31:11that workers demand and the only way
31:13that can happen is with a higher
31:14unemployment.
31:15Okay. That's the reason the natural rate
31:17of unemployment is also increasing in Z.
31:23Okay.
31:24And now the last step.
31:26The last step is to
31:29You see, I can go back to my Phillips
31:31curve.
31:34Say that.
31:36And I'm going to replace M plus Z
31:40for alpha UN. I can do that, you see?
31:45I can replace this M plus C Z for alpha
31:48times UN.
31:52How do I know that? Well, M plus C Z is
31:55equal to UN times alpha.
31:58I can replace in the Phillips curve
32:01M plus C by alpha UN and I can re
32:04I can therefore
32:06rewrite the Phillips curve in the
32:08following form.
32:10Inflation is equal to expected inflation
32:12minus alpha times the gap between the
32:16unemployment rate and the natural rate
32:18of unemployment.
32:20Okay. So,
32:22so
32:23when
32:25Chairman Powell is worried about labor
32:27market being very tight, what he's
32:29saying is, well, unemployment is likely
32:31to be below the natural rate of
32:33unemployment.
32:34Because if unemployment is below the
32:36natural rate of unemployment, that's
32:37putting upward pressure on inflation.
32:41Okay.
32:44So, that's a
32:45So, that's what it means. This gap is
32:47very important uh for macroeconomists
32:50and certainly for central bankers that
32:52are very worried about inflation. Okay?
32:54That gap here.
32:55Problem is is this this is a difficult
32:58object to estimate, so you have to have
32:59estimates as
33:02The truth is that it's very difficult to
33:04know what it is, although there are
33:05estimates out there and I'm going to
33:06show you one.
33:09You notice that something is wrong when
33:10this guy starts picking up. It's a It's
33:12a little bit the other way around, you
33:14know?
33:15Uh uh
33:16the US in fact had a the opposite
33:18problem
33:20um
33:21before COVID. It's a somehow
33:23unemployment was very low relative to
33:25historical levels, but inflation was not
33:27picking up.
33:28So, that was implicitly telling us that
33:30for some reason, not fully understood,
33:33the natural rate of unemployment was
33:34declining.
33:36Okay.
33:38So, here is one picture that looks
33:40is one estimate uh again, I I don't
33:43trust any particular estimate, but
33:45it tells a story. That's one particular
33:48estimate of the natural rate of
33:49unemployment in the US, that blue line.
33:52And what you see in red the red is the
33:54actual rate of unemployment in the US.
33:57So,
33:58what happens when when in situations
34:00like these?
34:04So, what do you think what's happening
34:05to inflation in in this episode, which
34:08is right after the global financial
34:09crisis or the great recession?
34:15So, what what what do you need to read
34:17here? Well,
34:18the unemployment rate was a lot higher
34:19than the
34:21natural rate of unemployment.
34:24Does that put upward or downward
34:25pressure on inflation?
34:28Downward pressure on inflation. No,
34:29unemployment is very high relative to
34:30natural rate of unemployment. It's minus
34:32alpha times U minus UN.
34:34So, and that's what happened. We had
34:36lots of problem with inflation.
34:37Inflation was going very low. We even
34:39had negative inflation there, a little
34:41deflation for a while.
34:43Okay. So, that was a problem.
34:46Here is the period that they described
34:48before is a little mysterious because we
34:49went unemployment went below what we
34:51thought it was a natural rate of
34:52unemployment and inflation wasn't really
34:54picking up a lot. At the end began to
34:55pick up a little, but it wasn't picking
34:57up a lot and that was a little bit of a
34:59mystery.
35:00Now, we're in this situation here,
35:03which
35:04we have extremely low unemployment
35:07and very high inflation. So, so this I
35:10think this captures well the situation
35:12right now. We have a
35:13negative gap between unemployment and
35:15the natural rate of unemployment and
35:17that's the reason that's putting a lot
35:18of pressure on inflation.
35:20We also have other things that are
35:22putting pressure on inflation that come
35:23from the supply side of the economy and
35:25so on.
35:26So, that combination is pretty bad for
35:29for the
35:31inflation outcomes and outlook
35:35as well.
35:36Okay.
35:38So, that's where we're at.
35:40We're going to talk a lot more about
35:41this because this is what is going on
35:43right now.
35:45Any questions about that? Otherwise, I
35:47want to start sort of reviewing things,
35:48although I don't know.
35:51Any question about this? Yep.
35:54Is correction to increase unemployment?
35:57Sorry? Is the only way to fix, I guess,
35:59the inflationary expectations? Well,
36:01that's a very good question.
36:03That's a very good question.
36:09I'm I'm trying to decide what to
36:14answer what with what do we have.
36:17Um
36:23There are two views
36:24at this moment.
36:27There's one view
36:29that says there's no way around that.
36:32They just look at these curves and say,
36:33"Look,
36:34there's no way around that. That's the
36:35reason we need a recession."
36:38Okay.
36:38Because otherwise we were not going to
36:40control inflation.
36:43And a recession means high unemployment.
36:45Okay, that's one view.
36:47At this moment, it's becoming the
36:50dominant view.
36:51It has gone in cycles, but at this
36:53moment it's the dominant view.
36:57There is a another view,
36:59which is the one that the central bank
37:01the Fed adopted for a while,
37:04that said, "Well, this is not the only
37:06indicator of tightness of the labor
37:08market. There is other things as well."
37:11And those indicators are moving in the
37:13right direction.
37:14And so, we may be able not to create a
37:16big mess here because these other
37:18factors are moving in the right right
37:21direction.
37:22Some of those factors are as I said,
37:24other measures of of labor market
37:26tightness and and hiring, the flows.
37:28Remember I showed you flows between
37:29employment and unemployment, out of
37:31employment and so on. Those flows look
37:33extremely tight and now they're
37:35improving. So, the gaps in those
37:36dimensions are better. And the other one
37:38is the what's a big cost push component,
37:40which is what I said before, the supply
37:42chains and so on created extra
37:44inflation, abnormal inflation like
37:46increasing markups, like M was very
37:48high.
37:49And some of that is subsiding as well.
37:50So, so there are dynamics that suggest
37:53that inflation is declining even without
37:54unemployment.
37:56But, I would say
37:58the medium voter
38:00in this space of, you know, forecast of
38:02inflation and so on,
38:04thinks that that that we will need some
38:06some adjustment through this this part
38:08as well. Okay.
38:11My main concern I I think that
38:15the the Fed the the path the Fed is
38:17forecasting is feasible,
38:19but a very narrow path. I mean, it may
38:21happen.
38:22And and to me, whether it they're
38:24successful at not creating a big mess
38:26here, I mean, bringing unemployment very
38:29high in order to bring inflation down,
38:31has a lot to do with whether
38:34somehow we manage to keep expected
38:35inflation anchored.
38:37And there there was some evidence, I
38:39think I said that a few lectures ago,
38:41there was some evidence that in the
38:42summer of
38:45uh summer of 2022, I'm from the southern
38:49hemisphere, so I get always confused
38:50with summers and and so on.
38:52So, the in in the summer of 2022, US
38:55summer of 2022, inflation was becoming
38:57very unanchored. This guy
38:59one year expected inflation was creeping
39:01up to 6% and that was very scary. Okay?
39:04Because think what happened. If if if
39:07you get expected inflation at 6%,
39:10then it's not enough to bring
39:12unemployment to the natural rate of
39:13unemployment to get inflation back to
39:15the 2% we like because you need to bring
39:17expected inflation down now. And that
39:19means you need to sort of bring the
39:22unemployment rate very very high in
39:24order to re-anchor expectations. So,
39:26that's a very scary situation. They were
39:28very persuasive though at the end of the
39:29summer with very hawkish speeches and so
39:32on
39:33and they managed to re-anchor expected
39:35inflation. So, expected inflation very
39:37quickly came down to two two and a half
39:38percent one year out to
39:41But, now it been picking up again and
39:43now we are around 3% again, so it's a
39:44little bit scary for where we are. So,
39:47to me this is going to be very important
39:49in that. So,
39:51if inflation keeps lingering around 6%
39:53and so on, and eventually the expected
39:55inflation becomes an anchor, then
39:57there's almost no way around but to have
39:59a recession to get out of that.
40:02If that doesn't happen, if they succeed
40:04convincing a ton of people that that,
40:06you know, they're very serious about
40:07about this stuff and they they re-anchor
40:09expectation expected inflation, then we
40:11don't need to create a large recession.
40:14Still they may create it, cause it
40:15because, you know, accidents happen, but
40:17but but but they don't need to.
40:20But they will need to if this guy gets
40:22an anchor.
40:24Actually, maybe I can use even this
40:26expression here
40:28to explain what I'm trying to say and I
40:30realize that this is again, this is
40:31material really for
40:33for the next lecture.
40:35What I'm trying to say is that if they
40:36manage
40:38to keep this theta very close to zero,
40:42okay?
40:43Then, in order to bring inflation back
40:46to their target of pi bar, 2% or so,
40:50all that they really need to do is to
40:52sort of bring unemployment to the
40:53natural rate of unemployment. So, they
40:55only need to really
40:57uh
40:59fix this gap.
41:01Okay? They need to raise unemployment so
41:03so it closes that gap. But it's a small
41:05change.
41:06That's if they succeed keeping expected
41:09inflation at around 2%.
41:12If they don't,
41:16say suppose that that
41:18that
41:19theta becomes very far from from zero,
41:24then we have a problem because then
41:25expected inflation is above the target,
41:28no? Because we have 6%, so suppose theta
41:30is equal to one, we have 6%, then
41:32expected inflation
41:33is 6%.
41:35That means that if you if your expected
41:38inflation
41:40is
41:416%,
41:43then in order to bring bring the
41:44inflation if you bring unemployment just
41:47to the natural rate of unemployment, so
41:48the red line to the blue line, you
41:50haven't made a lot of progress. All that
41:52you have done is
41:53you have brought down inflation
41:55to 6%, which is expected inflation.
41:58So, if you are have expected inflation
42:00of 6%, you need to bring unemployment
42:03much higher than the natural rate of
42:05unemployment in order to bring inflation
42:07back to the target of 2%.
42:10That's the reason I say
42:11to me
42:13the fight will be
42:15the battle will be won or lost
42:18on that term there.
42:21Yep.
42:23How much
42:24of this current like inflationary
42:26pressure is caused by unemployment? How
42:28much of it is caused on the supply side?
42:30Cuz it feels like a lot of this stuff
42:31like CPI going up, energy prices going
42:33up, it's like how much can the Fed keep
42:35control of something like Well, it
42:36varies a little from different
42:40This is around the world, but but in the
42:41US,
42:42uh for a while a big component of
42:44inflation was all that stuff.
42:47Uh you know, bottlenecks in the ports
42:49and and stuff like that.
42:51That's almost all gone.
42:52There's very little of that left. So,
42:54now is
42:56is aggregate demand. People feel very
42:57rich
42:59for a variety of reasons, they're
43:00spending a lot and that's the reason
43:01unemployment is very low.
43:04It's not unemployment per se, it's just
43:05the aggregate demand is very high.
43:07You know?
43:09Uh and that translates into very low
43:10unemployment and that feeds into
43:12inflation this way
43:13through wages and so on.
43:15But
43:17in the US, the component of aggregate
43:18demand is much larger than in Europe. In
43:20Europe, those supply side factors are
43:22much more important. So,
43:25you know, around the
43:29Yeah, the summer of 2022, you could say
43:33both both Europe and the US had about
43:36the same amount of excess inflation.
43:37They were all with about 10% inflation.
43:41But in the US was 2/3 excess aggregate
43:44demand,
43:45while in Europe was 2/3 problems on the
43:48supply side, especially because of the
43:49war and stuff like that.
43:51Okay?
43:51So,
43:52so but it for the US today is mostly an
43:54aggregate demand problem. We're not
43:56going to get a lot of
43:57Obviously, if the war stops, that's
43:59going to help,
44:01but it's not going to be enough. We we
44:02we need to
44:04just the economy is too hot. It's too
44:05much aggregate demand out there.
44:07That's the that's the fundamental
44:09problem. Yeah.
44:11Can you explain again why an increase in
44:13Z would increase the natural rate of
44:16unemployment? An increase in Z? Yeah.
44:19So,
44:20uh
44:21um
44:23for that the basis the previous slide
44:25diagram, but remember what Z does.
44:27Actually, let me go to
44:30this equation here.
44:34So, we can figure out in this in this
44:36two equations here. If Z goes up, that
44:39means for any given level of
44:40unemployment
44:42and expected inflation,
44:45wages go up. Workers demand higher wage.
44:50But
44:51remember that that the firms
44:55uh
44:56So, so let me let me let me we're
44:58talking about the natural rate of
44:58unemployment, so let me replace this PE
45:00for P first of all.
45:02Okay?
45:03So, I'm going to divide
45:05W by P both sides. So, I get
45:09if if Z goes up, the workers want a
45:12higher real wage.
45:14No? If because
45:17if Z goes up, then W over P, I'm
45:20dividing by P both sides, goes up.
45:23Workers demand a higher wage.
45:25But the firms, from here you can see
45:27that I can divide by P both sides, W
45:29over P that the firms offer is equal to
45:321 over 1 + M.
45:35Okay? So, the the firms are not going to
45:37offer a higher real wage. The workers
45:40want a higher real wage.
45:42The only thing that can restore
45:43equilibrium that the workers end up
45:45demanding the same real wage as the
45:47firms are willing to pay
45:49is that somehow the hands of the worker
45:51gets weakened. And the only variable
45:53here that can weaken their hand is a
45:56higher unemployment.
45:58Okay?
45:59So,
46:00let me put it all in
46:05So, at the natural rate,
46:07I know that PE is equal to P.
46:10So, that means the wage setting equation
46:13the wage setting equation implies
46:16W over P
46:19equal F U Z.
46:22Okay?
46:24From the price setting equation,
46:28I have that
46:29W over P
46:32is equal to 1 over 1 + M.
46:35So, in this very simple model, this is
46:37given.
46:38If this guy goes up,
46:40these guys want a higher real wage, but
46:42that cannot happen because that would be
46:43inconsistent with the price setting, so
46:45you need to bring down this guy down.
46:48The only thing that can bring it down is
46:49for unemployment to go up.
46:52And that's at P, we call that the
46:54natural rate of unemployment.
46:56Okay.
46:59Yeah.
47:01So, like last lecture we talked about
47:03the labor force participation rate. Um
47:07is there like any reason to try and like
47:10increase that to increase Oh,
47:12fantastic. Yes.
47:16Well, I mean
47:19there are sort of negative policies as
47:21well.
47:22You know, Z reduction in a sense does
47:24that because
47:25the the was a emergency unemployment
47:28benefits and emergency
47:30income supplements and so on as a result
47:32of the pandemic that are disappearing
47:34slowly. And that's very naturally so
47:36it's it's going to bring
47:39uh participation back up and it is
47:41beginning to pick up. So,
47:43so yeah, you need to incentivize return
47:46to work. And now there are some people
47:48that
47:48there's nothing that
47:50they've retired essentially or, you
47:52know, they have health problems and they
47:54they just cannot return. We lost that.
47:57And the other margin which is very
47:58important is immigration. So, that's a
48:00big issue
48:01because immigration obviously that we
48:03lost I think in the US, I'm not a labor
48:05economist, but we lost
48:07I think a flow of the order of the order
48:09of 500,000 people a year
48:11during COVID.
48:13And and and that's that's a big chunk of
48:15the decline in
48:17in the labor No, what you need is more
48:19employment. That's going to that puts
48:21downward pressure on wages for the same
48:23amount of aggregate demand.
48:25And that's what you need, but but
48:28Yeah, we're taking that's a very good
48:29point. We're taking all that as given
48:31here. Remember, we're fixing all that,
48:33but but if you don't, then then you
48:36other terms will start appearing in this
48:38expression and so on.
48:40Good.
48:42Obviously, I'm not going to start the
48:43review. We have only 1 minute, but so in
48:45the next lecture I I'll just review
48:48uh the material for the quiz.

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