[00:16] So, today I'm going to talk about the
[00:18] Phillips curve and inflation. Um
[00:22] Now, as I said in the previous lecture,
[00:24] uh
[00:25] the material that is specific to this
[00:27] lecture will not enter this quiz.
[00:30] It's the beginning of what is perhaps
[00:31] the most important model you'll see in
[00:33] the in in this in this uh class, but
[00:37] it will take us uh three or four
[00:38] lectures to to develop. So, I'm going to
[00:42] say things that certainly will
[00:44] um
[00:45] may help you understand a little better
[00:46] the previous lecture, and so
[00:49] if you're only concerned about the next
[00:51] quiz,
[00:52] uh there will be a sort of uh small
[00:55] review of the previous lecture here. Uh
[00:57] but again, anything that's specific to
[01:00] this lecture and was not in the previous
[01:02] one
[01:03] won't be part of of this quiz.
[01:06] So, what is this Phillips curve? Well,
[01:08] in in uh
[01:10] in 1958, an an economist uh at LSE, the
[01:14] London School of Economics,
[01:16] came up with some just an empirical
[01:17] relationship. This is A.W. Phillips. He
[01:20] found that using historical data
[01:24] uh for the US, I think he did it. Um
[01:28] uh there was a negative relation up to
[01:30] sort of the '50s, I think. Uh
[01:33] the there was a negative relation
[01:35] between uh the unemployment rate and the
[01:37] rate of inflation.
[01:39] And then our very own Paul Samuelson and
[01:42] Robert Solow
[01:44] labeled this relationship the Phillips
[01:46] curve in honor of uh
[01:48] A.W. Phillips.
[01:49] And nowadays it's sort of is a central
[01:52] concept uh in macroeconomics, and
[01:55] uh and uh it's certainly very, very
[01:58] relevant to understand what is going on
[02:00] uh right now in not only in the US
[02:02] economy, but in most economies around
[02:04] the world.
[02:06] So, let me
[02:07] show you sort of this is not the one
[02:08] that uh
[02:10] that Phillips uh plotted. I think this
[02:12] is the one that uh
[02:14] uh
[02:15] Samuelson and Solow plotted for data
[02:17] from between 1900 and 1960 uh
[02:20] for the US, you found you find sort of
[02:23] this sort of negative correlation. I
[02:25] think it's reasonable.
[02:27] Uh
[02:28] um
[02:29] there's negative correlation between
[02:31] uh the unemployment rate and inflation
[02:34] rate, no? At very low levels of
[02:36] unemployment, you typically see very
[02:37] high levels of inflation.
[02:39] Conversely, sort of at very high levels
[02:41] of unemployment, you tend to receive low
[02:44] levels of inflation or even deflation.
[02:46] In fact, this period includes the the
[02:49] Great Depression, for example.
[02:52] So,
[02:53] that's sort of the data. And and again,
[02:56] this was just an empirical regularity.
[02:59] But we can build some theory about this
[03:00] relationship using the ingredients most
[03:03] of the ingredients that
[03:05] I mean, essentially we can build a
[03:07] relationship that is downward sloping
[03:10] from the ingredients we already have.
[03:13] And this is the part that is a little
[03:14] bit of a review
[03:15] of the previous lecture.
[03:17] Remember that we had um um
[03:20] actually the previous two lectures. We
[03:22] had a wage setting equation
[03:25] W equal expected prices
[03:28] and then a decreasing function of
[03:29] unemployment and an increasing function
[03:31] of uh these labor market supporting
[03:34] institutions or
[03:36] worker supporting institutions, that
[03:38] institutional variables, I should say.
[03:40] And um and then we had a price setting
[03:43] equation, which was simply the wage uh
[03:46] marked up.
[03:48] M is a positive constant. So, let me
[03:50] start from these two what So, what I'm
[03:53] trying to do is derive a Phillips curve.
[03:55] Again, this was only an empirical
[03:57] relationship, but it turns out that even
[03:59] with theory we knew by the time of, you
[04:01] know, Samuelson and and and Solow, we
[04:03] could sort of come up with a with a
[04:05] theory of that relationship. And that
[04:07] theory builds on the ingredients we have
[04:09] been looking at. So, these are the price
[04:11] set the wage setting equation, the price
[04:12] setting equation. I'm going to just
[04:14] simplify things and assume that this
[04:16] this relationship here, this function f
[04:19] of u z, is some linear function, at
[04:22] least locally linear function, uh which
[04:24] is decreasing in unemployment and
[04:26] increasing in z.
[04:28] Why is it decreasing in unemployment?
[04:35] This says, no, that that if unemployment
[04:37] goes up,
[04:39] for any given expected price,
[04:41] wage demand is lower.
[04:43] Okay? And that's essentially because uh
[04:46] for the worker is is sort of is a
[04:49] becoming unemployed is a scary
[04:50] situation.
[04:52] Conversely, for firms it's higher it's
[04:54] easier to find uh
[04:56] uh
[04:56] a worker and and uh
[04:59] and uh So, as we said, a worker is
[05:01] scared for two reasons. One is that it's
[05:04] more likely it gets fired when
[05:05] unemployment is high, typically that's a
[05:07] recession. It's also likely they know
[05:10] that that worker knows that if she were
[05:13] to fall into the unemployment pool, it
[05:15] would take a longer time to get out of
[05:17] it. Okay? And the firms are seeing the
[05:19] opposite side. It's pretty easy for them
[05:21] to replace a worker if they were to
[05:24] dismiss a worker because there's lots of
[05:26] available workers in unemployment. Okay?
[05:28] So, that's the reason that's negative.
[05:30] So, I'm going to stick this function
[05:32] back in here.
[05:34] And then I'm going to replace this W
[05:37] with this function in there in the price
[05:39] setting equation, and I end up with an
[05:42] equation for P. Okay? So, this says that
[05:46] the price, given the expected price,
[05:50] is decreasing in unemployment and
[05:52] increasing in z and increasing in the
[05:54] markup.
[05:55] So, again, why is this price decreasing
[05:58] in unemployment?
[06:02] This is the part that is review of the
[06:04] previous lecture.
[06:05] Previous today. Because
[06:07] the wages go down and then the labor uh
[06:09] factors of production are cheaper. Okay,
[06:10] perfect. Because wages go down, since uh
[06:14] our firm needs one worker to produce one
[06:16] unit of a good, then the cost of
[06:17] production of one unit goes down with
[06:19] the wage, and and therefore the price
[06:22] goes down. Because the firm is asking
[06:24] for a constant markup over that wage,
[06:26] the wage declines, and the price drops.
[06:31] Good. So, that's all review. So,
[06:35] this equation you had seen just without
[06:37] an explicit functional form here. What I
[06:39] want to do is to go from here. This is
[06:42] still not the Phillips curve. Remember,
[06:43] the Phillips curve was a relationship
[06:44] between inflation
[06:46] and unemployment. Here we have a
[06:48] relationship between the price level
[06:51] and unemployment. Okay? So, we want to
[06:53] take one
[06:55] one derivative higher. We want to go to
[06:57] relation between
[06:58] inflation and unemployment. And
[07:00] inflation is is the rate of change of P.
[07:03] No?
[07:04] It's not it's not a level of P.
[07:07] So, to do that, all that we'll do is So,
[07:09] this when I don't have a subscript here,
[07:11] I mean
[07:12] the price at time t.
[07:14] Okay? And this is the expected price for
[07:16] next period, that's what we have.
[07:18] Uh
[07:18] but today for next period.
[07:21] What I'm going to do, I'm going to
[07:22] divide both sides by P minus 1. By that,
[07:25] I mean the price in the previous period.
[07:27] Okay? So, both sides. I'm going to
[07:29] divide this side by P minus 1.
[07:32] And and and this one by P minus 1.
[07:34] So, I get that expression. Okay? That's
[07:36] exactly the same equation we had before.
[07:39] All that I did is I divided by P minus
[07:41] 1. Remember remember what this means.
[07:44] So, if this is the price for the
[07:46] beginning for January 2023,
[07:49] uh
[07:50] this is the price for, say, where we're
[07:51] using annual data, for January 2022.
[07:54] Okay? So, I'm dividing by the price of
[07:56] January 2022 both sides.
[08:00] Now, notice that remember that I can
[08:03] that P over P minus 1 is equal to 1 plus
[08:06] the inflation rate. Remember where
[08:08] inflation rate is just
[08:10] P minus P minus 1 over P minus 1. So,
[08:14] this is just straightforward algebra,
[08:16] no?
[08:17] Remember our definition of inflation.
[08:33] That's P minus that's inflation. Okay?
[08:36] So, 1 plus pi is just
[08:39] P minus uh
[08:41] over P minus 1. Okay? And that's what
[08:43] you have there.
[08:44] I can do the same for expected
[08:45] inflation.
[08:48] Notice that
[08:53] sometimes people get confused, but
[08:56] expected inflation
[08:58] is equal to P
[09:00] expected
[09:02] not minus P expected minus 1. It's P
[09:05] minus 1.
[09:07] P minus 1.
[09:10] And the reason I'm not subtracting the
[09:12] expectation here is because at time t,
[09:15] which is when you're forming that
[09:16] expectation, you already know what
[09:18] happened at t minus 1.
[09:21] Okay? So, that's the reason this is
[09:22] expected inflation. I don't I don't need
[09:25] uh uh
[09:26] um
[09:28] to put expectations in here. Okay? So,
[09:31] that's pi e.
[09:33] And so, what we get is
[09:35] uh I can replace
[09:37] this guy here for 1 plus pi, this guy
[09:40] here for 1 plus pi e,
[09:42] and I get the following relationship.
[09:45] Okay?
[09:47] All that I've done is substituting this
[09:49] for that, that for that.
[09:52] So, that's our price setting equation
[09:54] now expressed in terms of inflation rate
[09:58] 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.