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