so today I'm going to talk about the Philips curve and inflation um now as I said in the previous lecture uh the material that is specific to this lecture will not enter this quiz is the beginning of what is perhaps the most important model you'll see in the in in this in this uh class but it will take us three or four lectures to to develop so I'm going to say things that certainly will um may help you understand a little better the previous lecture and so if you are only concerned about the next Quiz there will be a sort of a small review of the previous lecture here H but again anything that's specific to this lecture and was not in the previous one won't be part of of this quiz so what is this Philips SC well in in in 1958 an an economist and at LSC London School of Economics came out with some just an empirical relationship this is aw Phillips he found that using historical data for the US I think he did it um there was a negative relation up to sort of the 50s I think the there was a negative relationship between the employment rate and the rate of inflation and then our very own Paul samelson and Robert solo labeled this relationship the Philips curve in honor of aw Phillips and nowadays is sort of is a central Concept in macroeconomics and uh and uh it's certainly very very relevant to understand what is going on right now in not only in the US economy but in most economies around the world so let me show you sort of this is not the one that that Phillips plotted I think this is the one that some solo ploted for data from between 1900 1960 for the US you found you find sort of this sort of negative correlation I think it's reasonable um there correlation between the unemployment rate and inflation rate no at very low levels of unemployment you typically see very high levels of inflation conversely sort of a very high levels of unemployment you tend to see low levels of inflations or even deflation in fact this period includes the the Great Depression for example so that's sort of the data and and again this was just an empirical regularity but we can build some theory about this relationship using the ingredients most of the ingredients that I mean essentially we can build a relationship that is downward sloping from the ingredients we already have and this is the part that is a little bit of a review of the previous lecture remember that we had um um actually the previous two lectures we had a weight setting equation W equal expected prices and then a decreasing function of an employment and an increasing function of uh these labor market supporting institutions or workers supporting institutions institutional variables I should say and um and then we had a price setting equation which was simply the wage H marked up m is a positive constant so let me start from these two what so what I'm trying to do is derive a Philips curve again this was only an empirical relationship but it turns out that even with Theory We Knew by the time of you know Samson and and solo we could sort of come up with a with a theory of that relationship that theory Builds on the ingredients we have been looking at so these are the price set the weight set in equation the price set in equation I'm going to just simplify things and assume that this this relationship here this function f of u z is some linear function at least locally linear function H which is decreasing in unemployment and increasing in Z why is it decreasing in employment this says no that that if an employment goes up for any given expected price wage demand is lower okay and that's essentially because for the workers is sort of becoming an employee is a scary situation conversely for firms it's higher it's easier to find a a worker and and uh and the so as we say that worker is scared for two reasons one is that it's more likely it gets fired when an employment is high typically that's a recession it's also like it knows that that worker knows that if she were to fall into the unemployment pool it will take a longer time to get out of it okay and the firms are seeing the opposite side it's pretty easy for them to replace a worker if they were to dismiss a worker because there's lots of available workers in an employment okay so that's the reason that negative so I'm going to stick this function back in here and then I'm going to replace this W with this function in there in the price setting equation and I end up with an equation for p okay so this says that the price given the expected price is decreasing in unemployment and increasing in Z and increasing in the markup so again why is this price decreasing in unemployment this is the part that is review of the previous lecture previous to wages go down and then factors of production okay perfect because wages go down since our firm needs one worker to produce one unit of the good then the cost of production of one unit goes down with a wage and and therefore the price goes down because the firm is asking for a constant markup over that wage the wage declines and the price drops good so that's all review so this equation you had seen just without an explicit functional form here what I want to do is to go from here this is still not the Philips curve remember the Philips curve was a relationship between inflation and unemployment here we have a relationship between the price level and unemployment okay so we want to take one one derivative higher we want to go to relation between an inflation and unemployment inflation is is the rate of change of p no it's not it's not the level of P so to do that all that will do is so this when I don't have a subscript here I mean the price at time T okay and this is the expected price for Next Period that's what you have H but today for Next Period what I'm going to do I'm going to divide both sides by P minus one by that I mean the price in the previous period okay so both sides I'm going to divide by this side by P minus one and and and this one by P minus one so I get that expression okay that's exactly same equation we had before all that I did is I divide by P minus one remember remember what this means so if this is the price for the begin for January 2023 ER this is the price for say where we're using annual data for January 2022 okay so I'm dividing by the price of January 2022 both sides now notice that remember that I can that P over P minus one is equal to 1 plus the inflation rate remember where inflation rate is just P minus P minus one over P minus one so this is just straightforward algebra no remember our definition of inflation that's P that's inflation okay so 1 plus pi is just P minus over P minus one okay and that's what you have there I can do the same for expect the inflation notice that sometimes people get confused but expected inflation is equal to p P expected not minus P expected minus one it's p minus one p minus one and the reason I'm not subtracting the expectation here is because at time T which is when you're forming that expectation you already know what happened at T minus one okay so that's the reason this is expected inflation I don't I don't need a a um to put expectation in here okay so that's Pi e and so what we get is H I can replace this guy here for 1 plus pi this guy here for 1+ pi e and I get the following relationship okay so all that I've done is substituting this for that that for that so that's our price setting equation now Express in terms of inflation rates unexpected inflation rate and now you know if not we're not in Argentina we're in the US inflation expected inflations are small numbers no and the log of one plus a small number is approximately that number okay so I'm going to use this approximation which again is valid for X small no and and so I can replace this 1+ Pi for pi and this 1 + Pi E for for pi e this 1 + M for M plus no and this term here if these numbers are not too large again plus minus Alpha U plus Z and that I do all that and I end up with this expression okay all I've done is I took logs of this so I get log of 1 + pi equal to log of 1 + Pi e+ log of 1 + m Plus plus log of 1 - Alpha U plus Alp Z I'm saying if Pi Pi e m alpha U + z are not very large numbers which we assume then this is approximately right so I can rewrite that expression as that approximately I should have put an approximately okay okay so now we have something that looks a lot more than like the empirical relationship we were talking about we have a relationship between inflation and unemployment so this says that for any given expected inflation and markups and and labor market institutions higher unemployment means lower inflation why is that so that curve tells you that's a negative relation we wanted no it says higher unemployment lower inflation why is that look you had it very clear when we talk about this no you you understood very clearly why an increase in unemployment lower the wage you understood very clearly why therefore an increase in unemployment lower the price I haven't done anything but algebra in the two steps so the same economics behind the explanations that you had before apply to this curve here so the reason inflation will be lower where when an employment is higher given all the rest is because there will be less W wage pressure workers will demand lower wages that means lower prices and therefore inflation will be lower the economics hasn't changed at all I only I only divided both sides by P minus one and I took the logs and I approximated so so the economics has not changed just did a little bit of basic math okay so all the what I'm trying to say is all the intuitions that you can already you already had from the weight setting price setting equation and so on you can apply to the Philips curve as well okay good so now we have something that in principle could explain the type of relationship that Phillips found and then samon solo corroborated H with extended data so let's let's see how do we get to something that looks like what these people run as a regression remember they run a regression essentially or they correlated an inflation inflation with unemployment okay and they found a downward slope in relationship well look at what happens here suppose that that we assume that expected inflation is equal to some constant in in economics we say when that's the case and especially if Pi is a low number inflation expectations are well anchor meaning you know any single year there can be a price of oil is high or something happens and inflation will deviate from that but people are all the time expecting for inflation sort of to go back to the what is a normal level nowadays or at least a few years ago in the US the normal level was around 2% say okay so people say well this year inflation was 1.8 but we spend next year 2% the next year we got s prices on the upside price of food went up something like that we got inflation of 2.3% but you ask people how do you what amount you expect for next year say well 2% so so that's what a model of expectation like this means is that you know you always expecting something which is some historical value and that we have agre a reasonable level for our economy or something like that okay so you see that if I replace expected inflation infation for a constant here Pi Bar then I have then my Philips curve is really this is inflation then I have a constant minus Alpha U that's the simplest of the downward sloping relationship I can have in that case it's a line downward sloping line no that's it of course you know it could be nonlinear and so on but but this captures the essence so that's a theory for why Phillips was Finding what it was finding our theory of the wage of the labor market if you will and the price setting behavior of firms gives us a Philips curve of the kind that he had in mind and if you look in the 60s in the US then you see this negative relationship that eventually become sort of became a steeper it wasn't linear like this it was a little convex but but it's downward sloping and in fact to some extent ER I were own very our very own Bob solo and and Paul samelson were advising the US government at the time and they say well you know let's exploit this stuff a little okay we like to have lower unemployment we can live with a little less more inflation but we know there it's a negative trade-off there's a negative trade-off between these two things okay so if we like to lower unemployment it's fine we get a little more of inflation and initially the deal was very good because the curve was very flat you see so you could cut unemployment a lot you can see the dates here you're cutting unemployment a lot and you're not getting a lot of inflation eventually the the deal turned into a much roten deal much more roten deal because then to lower a little bit more employment we start getting a lot more of inflation okay so people for a while you know were okay with this model assuming that inflation was low but when they realized that this thing was being exploited then they began to sort of change the expectations they made I think that's what we had here but but the the region held pretty well during this time and again it became steeper and steeper as we push it more and more towards sort of very low levels of unemployment so that's the story but again there is your model of the Philips curve and that is a very very good model for the Times where Phillips also estimated his his Philips curve now if you sort of Turn the page and look at the same data in the' 70s look how it looks okay so from 1970 to 1995 that's the data you have there there's no negative relationship thing is all over the place okay so had Mr Phillips been born a few years few decades later and had he estimated his regression he would have found nothing okay there would be no curve in his honor at least he had run that same regression maybe he would have run a different regression but nothing okay so what happen well our Theory can explain as well what happened there remember the theory is not that inflation is equal to a constant minus the minus Alpha U the theory says this is a constant only if the model of expectation is this constant but if expectation is moving around or if anything in this constant is moving around then then there's another source of variation okay for example what happens suppose you here in 1965 and all of a sudden you get a the price of oil goes up a lot and I'm telling you capture the price of oil with an increas in M firms need to sort of Mark up things more in order to cover higher en energy cost well look at what M does m says that for any given level of unemployment now I get higher inflation that's what an oil shock does no you get an oil shock then for any given L of employment now you get find yourself with more inflation so that moves you in the opposite direction moves you up there and that's one of the reasons for these points around here we got lots of inflation because we got massive oil shocks H during the 70s and early 80s okay we had wars in the Middle East and so on that that led to to those shock so that so that was one of the reasons we got shocks here to this term here and and that sort of mudded the relationship but the other reason which is more interesting I think and that you already began to see that something was happening here is that as inflation went up people sort of Stop Believing in this model so the expectation formation mechanism change okay so this guy began to react to endogenous variables and I'm going to explain more precisely what so that's what we mean by expected inflation became the anchor was no longer anchor around this constant of 2% but but but it became the anchor it began to follow the data so if the data came with more inflation then people believe that next year we would have more inflation as well okay not back to two 2% but if we got 5% inflation today people be to say well okay I don't think that next year my best estimate is 2% is probably closer to 5% % okay that's what it means the anchoring that's what has the fed and most central banks around the world terrified today inflation is very is much higher than 2% and they're very worried about this guy becoming the Anor or an anle okay I'll get back to that in a second anyway so but let me let me explain this how this expected inflation term work here so let me replace the model of expected inflation for something which is some weighted average of a constant that's and the most recent inflation okay so this model says what is my expected inflation for next year well it's an average of this long run Target that we have say 2% and whatever was the most recent inflation if Theta and the model I show you before the one that applied to the 60s and so on up to the 60s had essentially Thal to zero so this guy didn't show up there and and and expected inflation was very well anchored what began to happen as we began to move that way and then we got hit by oil shock so we so people began to see much higher inflation numbers than they were used to then this Theta began to increase okay so people began to sort of change the mod of expectation and began to think that the inflation was going to be more persistent than they used to think in the past so in high inflation today means High inflation tomorrow that's what it means more persistent in the past was high inflation today what was a backdraw we go back to sort of the normal long run average now that's no longer the case and so if I replace this more General model of expected inflation here in the Philips curve I get this expression which now has this extra term so the we used to have the equal to zero but during the 70s and 80s and even early 90s actually that Theta got to be very close to one okay you estimate these models you get that Theta was very close to one and look at what happens when Theta gets very close to one so when Theta is one literally then the best forast for inflation is the previous inflation okay so this year is 5% and I think next year is 5% not 2% 5% if this year is 7% I think next year is 7% again and so if you do that then my expected inflation becomes lag inflation Pi T minus one so if I stick in replace the expected inflation for pi T minus one I get to this Philip curve which I can rewrite as the change in inflation been Rel as a as a relationship between the change in inflation and the level of unemployment so now what you have is that if an employment is very low then inflation is is picking up you know it's going so if inflation if an employment is very low not only inflation is high but it's also growing over time okay that's the reason sometimes people refer to this formulation of the Philips curve as the accelerationist Phillips curve because now there a relation between unemployment and the change in inflation and if you estimate this Philips curve this acceleration is Philips curve on the data I just show you of the 70s and 80s you get get a much better relationship okay you still have the old shocks that mess things up but but you start see recovering this negative relationship but again it's between the change in inflation and the level of unemployment and that's a very scary situation for the central bank to find itself in because it's very easy to for thing to escalate okay so by the mid90s we had reanchored expectations there was sort of very AG Rive policy to control inflation by Paul vulker in the US and it was imitated around the world with some lag but but inflation became re-anchor so we went back to this Theta equal to zero type model the expected inflation in the US the target inflation of the Central Bank was around 2% that became what people expected for the next year and and and that reanchored so we went back in other words to that sort of Philips Cur okay and that's what central banks want to be at they want to have inflation expectation very well anchored and they were very successful after the 90s and so we got into again now look I'm now I'm not running deceleration I'm again running inflation against unemployment and you again see this downward sloping relationship okay so that was very good news was great success of monetary policy and during the '90s and later was the re-anchoring of expected inflation again all around the developed world and many of the incl even Latin America many economies in Latin americaas of reanchored expectation Asia and so on so so it was a good time for central banks okay so the next thing I want to do this will connect more with the with the the previous lecture it's the last thing I want to say for this H lecture then I may start the review afterwards um is that I want to connect now this Philips curve with something we discussed in the previous lecture which is the natural rate of unemployment because that's the way you'll typically see the Philips Cur written and and that's also the way that sort of you know when chairman Powell is talking about the labor market ESS and so on is not talking relative to M and z and things like that it's talking relative to what is called the natural rate of unemployment so I want to go from a Philips curve that looks like that like that to one that has the natural rate of unemployment in there and so that's the last step in this lecture so remember the definition of the natural rate of unemployment what was the definition of the natural rate of unemployment was it the unemployment rate that God gave us any God no it had a very precise meaning for us and remember we use exactly that model to figure it out we we sold the actually we sold the natural rate of unemployment from something like this I think we had the function still generic function f of u z but we Sol from an expression like this we we said under one assumption we can call this U un the natural rate of unemployment what was that assumption and that's the only thing expected price expected price is equal to the actual price okay so we said if this is equal to that then you solve out L naturual rate of unemployment and that's the only thing that that it that means that that that naturual rate of unemployment means simply that one when the when the price is equal to the expected price but if the price is equal to expected price what else is equal I I pointed at the right Expressions inflation is equal to expected inflation so I can use the same logic I use here for the natural rate of unemployment using the Philips curve I can say okay my I can solve out for the natural rate of unemployment here simply by setting the spected inflation equal to actual inflation okay and if I do this I can solve for the natural rate of unemployment from here un I mean I'm going to give I put the superscript in here when I when you let me replace Pi for pi that's a that's what that's what I the fact that I replace this Pi for pi is what allows me to put the superscript N there call it the natural rate of unemployment and now I can solve it well obviously that canist with that and I can solve the natural rate of unemployment and it's equal to this function here so why is the natural rate of unemployment increasing in m a question like that can come up in the quiz I'm not going to use the Philips curve to ask you if I ask you about that but I can ask you that what what happens to Natural rate of an employment if M goes up you know that you will go up but what is the mechanism so why does the natural rate of unemployment go up when the markup goes up yep remain constant wages have to go down right I mean another way of saying it is that the firms are not willing to pay they want to pay a lower real wage at the original level of unemployment before the change in M workers would not take that lower real wage no it's not an equilibrium real wage because workers said no no at this level of unemployment we need that higher real wage so the only way to restore equilibrium in that model we had was to increase unemployment because that will lower the bargaining power of workers and they will end up accepting the lower real wage that firms are willing to offer now okay so that's a reason H we get this this markup effect Z is same logic it's a little easier to see it there but Z means well at any given level of unemployment an increasing Z means workers want a higher real wage firms are not willing to pay a higher real wage so you have to bring down the real wage of workers demand and the only way that can happen is with a higher unemployment okay that's the reason the natural rate of unemployment is also increasing in Z okay and now the last step the last step is to you see I can go back to my Philips curve say that and I'm going to replace M plus Z for Alpha unu I can do that see I can replace this M plus c z for Alpha time unu n how do I know that well M plus z z is equal to un * Alpha I can replace in the Philips curve M plus C by Alpha un and I can re I can therefore rewrite the Philips curve in the following form inflation is equal to expected inflation minus Alpha times the gap between the unemployment rate and the natural rate of unemployment okay so so when chairman Powell is worried about Labor Market very tight what is saying is Well unemployment is likely to be below the natural rate of unemployment because if unemployment is below the natural rate of unemployment that's putting upward pressure on inflation okay so that's a so that's what it mean this Gap is very important for microeconomist and certainly for Central Bankers that are very worried about inflation okay that Gap here problem is is this is s difficult object to estimate so you have to have estimates is the truth is that it's very difficult to know what it is although there are estimates out there and going I show you one you notice that something is wrong when this guy starts speaking up it's a little bit the other way around you know the US in fact had the opposite problem um before covid is that somehow unemployment was very low relative to historical levels but inflation was not picking up so that was implicitly telling us that for some reason not fully understood the natural rate of unemployment was declining okay so here is one picture that looks is one estimate again I don't trust any particular estimate but it tells the story that's one particular estimate of the natural rate of unemployment in the US that blue line and what you see in red the red is the actual rate of unemployment in the US so so what happens when in situations like this so what do you think was happening to inflation in in this episode which is right after the global financial crisis or the Great Recession so what what what do you need to read here well the unemployment rate was a lot higher than the natural rate of unemployment does that put upward or downward pressure on inflation downward pressure on inflation unemployment is very high Rel to Natural rate of unemployment it's minus Alpha time uus un so and that's what happened we had lots of problem with inflation inflation was going very low we even had negative inflation there a little deflation for a while okay so that was a problem here is the period that I described before is a little mysterious because we went unemployment went beow we thought it was a natural rlo and inflation wasn't really picking up a lot at the end began to pick up a little but it wasn't picking have a lot and that was a little bit of a mystery now we're in this situation here which we have extremely low unemployment and very high inflation so so this I think this captures well the situation right now we have a negative gap between unemployment and the natural rate of unemployment and that's the reason that's putting a lot of pressure on inflation we also have other things that are putting pressure on inflation that come from the supply side of the economy and so on so that combination is pretty bad for for the inflation outcomes and and Outlook as well okay so that's where we're at we're want to talk a lot more about this because this is what is going on right now any questions about that otherwise I want to start sort of reviewing things although I don't know any question about these y this direction to increase unemployment sorry is the only way to fix I guess the inflationary well that's a very good question that's a very good question and I'm trying to decide what to answer what with what we have um there are two views at this moment there's one view that says there's no way around that that just look at this curve says look there's no way around that that's the reason we need a recession okay because otherwise we're not going to control inflation and recession means higher employment okay that's one view at this moment it's becoming the dominant view has going in Cycles but at this moment is the dominant view there is another view which is the one that the Central Bank the FED adopted for a while that said well this is not the only indicator of tightness of the labor market there is other things as well and those indicators are moving in the right direction and so we may be able not to create a big mess here because these other factors are moving in the right right direction some of those factors are as I said other measures of of Labor Market tightness and and high the flows remember I showed you flows between employment and employment out of employment so on those flows look extremely tight and now they're improving so the gaps in those dimensions are better and the other one is there was a big cost push component which is what I said before the supply chains and so on created extra inflation abnormal inflation like increasing markups like M was very high and some of that is subsiding as well so so there are dynamics that suggest that inflation is declining even without unemployment but I would say the median voter in this space of you know forecast of inflation and so on thinks that that we will need some some adjustment through this this part as well okay my main concern I I think that the the fed the path the FED is forecasting is feasible but a very narrow path I mean it may happen and and to me whether they're successful at not creating a big mess here that mean bringing an employment very high in order to bring inflation down has a lot to do with whether somehow we manage to keep expected inflation anchor and uh there was some evence I think I said that a few lectures ago there was some evidence that in the summer of er er Summit of 2022 I'm from the southern hemisphere so I get always confused with Summers and and so on so the in in the summer of 2022 us summer of 222 inflation was becoming very an anchor this guy one year expected inflation was creeping up to 6% and that was very scary okay because think what happened if if if you get expected inflation at 6% then it's not enough to bring an employment to the Natural rate of unemployment to get inflation back to the 2% we like because you need to bring expected inflation down now and that means you need to sort of bring the employment rate very very high in order to re-anchor expectation so that's a very scary situation they were very persuasive though at the end of the summer with very hawkish speeches and so on and they managed to re anchor expected inflation expected inflation very quickly came down to two two and a half per one year out even but now it has been picking up again and now we're around 3% again so it's a little scary where we are so to me this is going to be very important in that so if inflation keeps lingering around 6% and so on and eventually this expected inflation becomes an anchor then there's almost no way around but to have a recession to get out of that if that doesn't happen if this convincing of people that that you know they're very serious about this stuff and they they re anchor expect expect the inflation then we don't need to create a large recession still they may create it cause it because you know accidents happen but but but they don't need to but they will need to if this guy gets an anchor actually maybe I can use even this expression here to explain what I'm trying to say and I realize that this is again this is material really for for the next lecture what I'm trying to say is that if they manage to keep this data very close to zero okay then in order to BR inflation back to their target of Pi Bar 2% or so all that they really need to do is to sort of bring an employment to the Natural rate of unemployment so they only need to really ER fix this Gap okay they need to clim raise an employment so so it closes that Gap but it's a small change that's is they succeed keeping expected inflation at around 2% if they don't say suppose that that that Theta becomes very far from from zero then we have a problem because then expected inflation is above the Target no because we have 6% so suppose that is equal to one we have 6% then expected inflation is 6% that means that if you if your expected inflation is 6% then in order to bring bring the inflation if you bring an employment just to the Natural rate of unemployment so the red line to the Blue Line you haven't made a lot of progress all that you have done is you have brought down inflation to 6% which is expect inflation so if you have expected inflation of 6% you need to bring an employment much higher than the actual rate of unemployment in order to bring inflation back to the Target of 2% that's the reason I say to me the fight will be the battle will be won or lost on that term there yep how much of this current like inflationary pressure is caused by unemployment how much would it cause on the supply side cuz it feels like a lot of the stuff like CPI going up Energy prices going up like how much can p control well it varies at different part different places around the world but but in the US H for a while a big component of inflation was all that stuff H you know bottlenecks in the ports and and stuff like that that's almost all gone there's very little of that left so now is is aggregate demand people feel very rich for a variety of reasons they're spending a lot and that's the reason unemployment is very low it's not an employment per se it's just an aggregate demand is very high no ER and that translate into very low unemployment and that fits into inflation this way through wages and so on but in the US the component of aggregate demand is much larger than in Europe in Europe those supply side factors are much more important so you know around the yeah the summer of 2022 you could say both both Europe and the US had about the same amount of excess inflation they were all with around 10% inflation but in the US was to3d excess aggregate demand while in Europe was two third problems on the supply side especially because of the war and stuff like that okay so so but for the us today is mostly an aggregate demand problem we're not going to get a lot of obviously if the war stops that's going to help but it's not going to be enough we we we need to just the economy is too hot it's too much aggregate demand out there that's that's the fundamental problem yeah please explain again why and increase in Z would increase the natural rate of increase in Z yeah so um for that the best is the previous slide diagram but remember what Z does actually let me go to this equation here so we can figure out in this in these two equations here if Z goes up that means for any given level of unemployment an expected inflation wages go up workers demand higher wage but remember that that the firms ER so soor let me let me let me we're talking about the natural rate of unemployment so let me replace this PE for p first of all okay so I'm going to divide W by P both sides so I get if if Z goes up the workers want a higher real wage no if because if Z goes up then W over p and dividing by people side goes up workers demand the higher wage but the firms from here you can see that I can divide by P both sides W over P that the firms offer is equal to 1 over 1 + m okay so the the firms are not going to offer a higher real wage the workers want a higher real wage the only thing that can restore equilibrium that the workers end up demanding the same real wage as the firms are willing to pay is that somehow the hands of the worker gets weakened and the only variable here that can weaken their hand is higher deployment okay so let me put it all in So at the natural rate I know that P is equal to P so that means the weight setting equation the weight setting equation implies W over P equal f u z okay from the price setting equation I have that W over p is equal to 1 over 1 + m so in this very simple mod this is given if this guy goes up these guys want a higher real wage but that cannot happen because that would be consistent with the price setting so you need to bring down this guy now the only thing that can bring it down is for an employment to go up and that's at P we call that the natural rate of unemployment okay so like last lecture we talked about the labor force participation rate um is there like any reason to try and like increase that to increase oh that would fantastic [Music] yes well I mean there are sort of negative policies as well you know Z reduction in a sense does that because there was a emergency unemployment benefits e emergency income supplements and so on as a result of the pandemia that are disappearing slowly and that very naturate so is going to bring a a a participation back up and it is beginning to pick up so so yeah you need to incentivize return to work and now there are some people that there's nothing that they retire essentially or you know or they have health problems and they they just cannot return we lost that and the other margin which is very important is immigration so that's a big issue because immigration obviously we lost I think in the US and not a labor economy but we lost I think a flow for the of the order of 500,000 people a year during covid and and and that's that's a big chunk of the decline in in the label no what you need is more employment that's going to that puts downward pressure on wages for the same amount of aggregate demand and that's what you need but but the yeah we're take that's a very good point we're taking all that as given here remember we're fixing all that but but if you don't then then other terms will start appearing in this expression and so on good obviously I'm not going to start the review we have only one minute but so in the next lecture I I'll just review the material for the quiz