Lecture 30: New Keynesian Sticky Prices IV

[Music] [Music] welcome back so we are going to start the new session and in this session as i discussed in the last session that we were talking about the we have finished the new classical understanding and now we are moving towards the new topic which is about the the the output gap about the monetary policy stand how the central bank decides about what will be the appropriate rate of uh policy rate which can be in the form of either increasing or decreasing the policy rate so how central bank decides about this thing when i mention about so let me give you the background what we are going to discuss about the monetary policy in today's session in in this session is about how we can understand the the role of monetary policy or we can think about what will be the appropriate rate of policy rate so in case of india we have the repo rate and reverse rate rate repo rate is the rate at which central bank lends to the commercial banks and the scheduled commercial banks so you can think about the lending happening from the central bank to the banks when banks are having excess liquidity and they feel that they have excess reserves excess cash and the central bank also feels that they have excess liquidity in the economy then it allows the commercial banks to keep money with this central bank so central bank will be offering some rate of interest on that so that is what we call it the reverse repo rate let us first understand about the reaper rate because rape rate is always higher than the reverse reparate and and report plays very important role so in case of india we have something called the liquidity adjustment facility so l a f under liquidity adjustment facility typically at it happens that the central bank decides about increasing or decreasing the money supply based on increasing and decreasing the policy rate uh rape on reverse repo and they adjust the liquidity in the economy through these two rates whenever they feel that you have less liquid in the economy so they decrease the rate of interest and pump the money through the the repair rate and whenever they see that their excess liquidity then they will be going for either increasing the reverse repair rate so reverse report means either banks will be incentivized to save or they will be simply increasing other parameters for example cash reject ratio and slr requirements but in typical case the policy rate matters a lot because on this you have the money supply decided so if your money supply is moving around the rep rate or the policy rate then it becomes really important that what will be the the appropriate rate and which all parameters will determine this rate when the central bank or rbi reserve bank of india is going to decide about the rate of interest that the rape rate which is 4 percent this time so if it is going to be four percent then this four percent will be based on which all indicators where which all indicators will play a very important role that understanding is crucial in the macroeconomic setup and in this particular setup we will try to understand that which all factors specifically the parameters play important role in deciding about the appropriate policy rate in case of u.s you have the federal fund rate so maybe we will be having examples from that but it will be really interesting to see that in real life how it works the reference book remains same here this stephen d williamson and will be also covering the chapter 15 but here we will be also focusing on the williamson part and also we will be referring the man cube book of macroeconomics and there will be talking about the dynamic system under that you have the quick adjustment in the economy the short run adjustment so nuke nigerian school of economic thought is more about the new canadian idea right team cringing school of economic thought is more about the short run adjustment in equilibrium so we will be talking about those things otherwise the objectives remain same not much change right so here we will be talking about the the condition under which we are discussing this part so here we are talking about the taylor rule so john taylor ah developed this idea that what will be the appropriate policy monetary policy rule through which central bank will decide about the appropriate rate about the policy rate so taylor rule for monetary policy increase in nominal interest rate when inflation too high normally we one of the main objectives of the the central bank is that it has to go for price stability so when i say about price stability then it implies that the rate of inflation has to be lower most of the countries have gone for inflation targeting mechanism under that they they have certain rule of thumb or certain i would say targets fixed for the central bank so in case of india as per the monetary policy committee they they have decided about four plus minus two so four plus minus two that the upper range will be six percent and lower range will be two percent below this central bank if it will go the central bank has to react if inflation touches six percent or beyond then central bank will react normally we find that there is direct relationship between the policy rate and inflation so if inflation is going up policy rate will go up if inflation is coming down policy rate will come down so that's the under understanding and here we find that here we have the inflation so here what what it means that here if i am talking about r which is the the real rate of interest so here we say that here it is 2.0 plus 1.2 i right minus 1.5 gap so this output gap this this i will be discussing in the subsequent slides in detail but let us understand what is the value of this 1.2 and 1.5 if you have a one percent increase in inflation which is i is the inflation here and a gap is the output gap if you have one percent increase in inflation then the the rate of interest increase by the central bank we will be around uh 1.2 percent if you have the output gap output gap here we we are mentioning about gap this shows about the output gap if output gap is around if if a output gap which shows the relationship between the unemployment rate at the equilibrium and how much ah unemployment rate you have actual so deviation from that or you can say that the actual and potential output with the full capacity how much output an economy can produce and how much it is producing route right now so if it is lower then of course it means that you have the slowdown if you are producing higher than the potential then it means that you are utilizing all of the resources your employment and everything will be better so unemployment will reduce so that kind of dimension i am talking about so let us first think about the nominal interest rate if you have a inflation increasing by 1 percent your nominal interest rate will increase by 1.2 if the output gap increases by 1 percent your nominal interest rate will have the inverse relationship that it will decrease by 1.5 and these relationships are having very important role in the economy if you have i inflation 0 if you have no output gap your nominal rate of interest will be equivalent to what you have the two percent which is the natural rate of interest so this can be called as the natural data vendor natural rate of interest at which the rate at which you have the full employment in the economy or equilibrium output in the economy so you do not see any deviation so these two variables play very important role one is the inflation and one is the output gap and if you have a output gap as zero so zero multiplied by one point two it becomes zero and zero multiplied one point five it zero so these two will be zero which means that your nominal interest rate is equivalent to the natural rate of interest and this ah is the ideal scenario but in real life it may not be the same let's talk about how we can understand this so this particular part we are discussing from man cube so there we have first start with the basic premise of the taylor rule derivation so this equation is widely popular and being used by the fed reserve for this policy stand on the monetary policy so here here we have a yt which is the output and here you have the natural rate of output and isolate of output is the rate at which if everything goes well ah set is paribus then this is the output that the economy will achieve so if everything equals then and if the economy utilizes the resources available in the economy optimally then this is the output that the economy is going to get then here you have the real rate of interest this is what we have the r t right and row here is the natural rate of interest so the real rate of interest is this right and here you have the epsilon t and this epsilon t is having ah some kind of shock so this is from demand side so demands are in the sense that you have a sudden change in some macroeconomic scenario in flow of capital or something that has created some ah some shock or maybe a unwanted shock has happened in the economy so because of that the decrease in demand so this random variable will have both upside and down side capturing in the economy from demand side so and mean of this is 0 and variance is 1. so this is how we go about it the alpha is greater than 0 so right and rho is also greater than 0 the row is important row is the natural rate of interest it is the real interest rate at which in the absence of any shock the demand for goods and services equals the natural level of output so this is what i mentioned at the full employment equilibrium level so this is the ideal situation this should be the rate of interest actually in the economy but due to deviations either because of this epsilon or because of this alpha you have some parameters not coming exactly to the natural rate of interest so real interest of interest is not equal if real rate of interest equal to natural interest rate this becomes 0 right which means that your y t is equal to y t bar and if you are just taking the expectation then this is also zero so this is the ideal situation that if you have a real rate of interest equivalent to rho which is the natural rate of interest then you do not have to worry about the moment you have a deviation then it matters a lot so if r t is greater than rho then what will be the scenario if r t is less than rho then what will be the scenario but overall since it is having the inverse relationship between the output and real interest rate so this is directly linked with what we call it the is lm scenario that we have already i think those who have done the macroeconomics one that you must be knowing about is lm framework the hexane idea so there it is linked with ah this so y t is equal to y t bar the full employment potential output minus alpha rt minus rho plus epsilon t is nothing but the equation of i s curve i s line which is downward sloping inverse relationship between output and interest rate right so here we will be talking about this alpha value will matter a lot that what is the alpha value here we have so this is what we measures the interest sensitivity of demand if it is higher then it means that you are having a more sensitive the rate of interest with output if it is lower than it is less sensitive so this is what natural rate of interest if you have r t is equal to rho right so this will become zero and then you have y t is equal to y t bar so this is the ideal situation for most of the economy this is the demand shock that i have already mentioned let's talk about the rate of interest and here rate of interest will have lot of importance here will be so fisherian idea works here so fischer equation we know that here you have the real rate of interest real rate of interest is nothing but you have the the normal rate of interest minus here you have the expected inflation rate so if you have the expected inflation rate expected real interest rate playing role so you have r t is equal to iit minus expectation of t pi t plus 1 so here what is more important is that here we are putting a expectation operator with pi t plus 1 which means that it is talking about you are expecting in current period about future inflation so expectation of t pi t plus 1 which means that you are expecting in the current period about future inflation so once you have future inflation then that matters a lot so we it can be also like here you have expectation of t minus 1 pi t so r t is equal to i t minus expectation of t minus 1 pi t can also be linked which means that if you are going to think about the real interest rate then the subtraction of the normal interest rate with inflation it is the expected not the actual so that means that there is some kind of stochastic element attached increase in price period from t to t plus one not known in period t this is what we have increase in price level from t to not known for period t and it is about the expectation so expectation is happening in period t about the pi t plus one so fischer equation what happened that because of this expectation it also become the expected real interest rate so your expected real interest rate is nothing but the nominal interest rate minus the expected inflation that the consumer is expecting in current period about the future inflation so maybe you can think about the current inflation based on the expectation from the past so maybe this can be linked with the adopting expectation scenario so adopt expectation will be coming after this so this is how it works the second is about the phillips curve so phillips curve is coming from the supply side so phillips curve how it works so here you have the current inflation and here as i told that this is coming from here expectation of t pi t plus 1. so here you have expectation of t minus one pi t here which is nothing but the previously expected inflation here we have a phi y t y t minus y bar and this is nothing but your output gap how much is inflation responds when output fluctuates around its natural level so this is the natural level of output and this is the actual output how much is the deviation natural level output means the output achieved at the full employment equilibrium and there is no deviation happening so this is the most ideal scenario you can see so yt bar represents the most ideal output but in reality in actuality depending upon the rate of interest and certain parameters it may not be the same to achieve the same level of output so deviation will attract some change in the policy rate and inflation and this is what we are trying to understand here and vt is nothing but here you have the supply shock random or so it is having the same like aggregate demand the epsilon that we had assumed so it is having the same the the phi shows the sensitivity of inflation with respect to output around the natural level which means that when economy is booming your y t will be greater than y t bar which means that here you will have the the output rises above the natural level which means that this is the natural level output your economy is booming if it is doing good then it will be y t minus y t bar and if the economy is not going up if it is not moving up and if it is in radiation then it will be just opposite to this so y t minus y bar that we have this will be y t greater than y t bar boom scenario you will have the higher inflation scenario the central bank will also react in the same way if a y t less than y t bar you have this slow down in the economy so this will create a very favorable scenario for the lowering the interest rate then the central bank will think about reducing the interest so output gap has lot of importance second thing about the output gap it also talks about the unemployment scenarios right so unemployment scenario can be linked with your output gap if it is higher if your white is greater than yt bar then it means that you are creating more output demand of goods and services are higher and then then it will also bring more ah favorable scenario for the economy right so we can think from the perspective of unemployment increasing and decreasing so there is a very famous law so there above equation can be linked also with the with the okun's law that shows the inverse relationship between output and employment so if y is greater than y bar unemployment will be lower if y t is less than y bar unemployment will be higher which means that it is having some kind of inverse relationship with a pi t right so here y t y t minus y t bar is linked with the with the ocon's law which means that it is also talking about the inverse relationship between output and unemployment output unemployment will be linked with this when the economy is booming output rises above its natural level which means that here you have more implement of labor everyone will be getting wages everyone will be happy unemployment will be lower so from such theory perspective also we discuss that if the economy is booming everyone is having good scenario there is not so much increase in the social welfare cost and the social welfare amount is not increasing which means that unemployment insurance benefit if it is not increasing then this creates more matching scenarios which means their form will be posting vacancies and the individuals will be also getting job so if your y t greater than y t bar then this creates that kind of scenario so ultimately will be having a less of unemployment but if you have output gap increasing which means that y t is less than y t bar then this is this is creating us more unemployment less matching happening the economy companies are posting jobs individuals are not applying and at that time if the central bank or the if the government has gone for increasing the unemployment insurance then there will be again matching efficiency decreasing and labor market tightness that we discuss in that way so this will further ah decrease the the output and increase the unemployment so it is also linked with this when the output unemployment is below natural rate and vice versa so this is how we mention about ad of the expectation this is coming directly from the fischerian equation so here we had the fischer equation expectation of t pi t plus 1 so here what we say that expectation of t pi t plus 1 is nothing but pi t which means that the individual's expectation depend upon the individual's future expectation depends upon the immediate a past or the current period so this is the underlying idea behind this adaptive expectation that you are just assimilating the previous period information to predict about the current period or future period to predict ah or using current information for prediction about the future so this is how it link with this then here we have the finally the monetary policy rule that we discuss about so lets combine everything all the equations if you go for solutions substituting one to another then we finally arrive at this particular equation so which is the nominal interest rate it is equivalent to pi t right which is inflation plus rho which is the natural rate of interest plus theta pi pi t minus pi t star plus theta y y t minus y t bar and this particular equation is coming by combining all demand then we had fischer equation demand for goods and services then we had fischer equation then we had the phillips curve then we had the adapted expectation so combining all those we are getting this particular equilibrium this particular equation talk about the dynamic adjustment because here you have the t plus 1 and t so here you have the one period ahead we are talking about when we are expecting in the current period about future right so it involves some dynamic or the inter temporal scenario so this also speaks about the dynamic systems here we have i t is equal to pi t plus rho plus theta uh pi here you have a pi t minus pi t star plus theta y y t minus y t bar so this this is how we say so normal interest rate set each period by the central bank and here you have part here we have the row which is nothing but the natural rate of interest now this part t star is nothing but the central bank inflation target so party star here central bank inflation target as i mentioned about that in case of most of the countries about inflation targeting mechanism countries have gone for deciding about the the normal rate of inflation so in case of india as i mentioned at for the mpc it is four plus minus two so four percent you can understand so this is about four percent so this is decided by the rbi the central bank here you have a theta y which is linked with the this is the coefficient attached with the output gap theta pi is the coefficient attached with the inflation gap so this is what we have the inflation gap right so how much inflation is deviating from the central bank target plus how sensitive is the nominal interest rate with the output gap so these two parameters theta pi and theta y play very important role they indicate how much central bank allows the interest rate target to respond to fluctuations in inflation and output so here we which means that with the nominal interest rate which is nothing but the policy rate how this policy rate is sensitive to the inflation gap and the output gap so this is how we are how much it is deviating if we have a party equivalent to the policy target rate of the central bank then this will be zero this pi tau will be zero so this it means that it it is zero almost right now here if you do not have any output gap then this will also be zero so if this is zero then this will also be zero so in most of the cases what you will have is that your natural rate of interest is nothing but i t minus pi t which means that the equilibrium rate of inflation and the number interest rate whatever is the difference that will be your natural rate of interest that we always mention they indicate how much the central bank allows the interest rate target to respond larger the value of theta pi if theta pi is greater which means the deviation is happening it is much larger the more responsive the central bank is to the deviation and inflation from target so if it is higher than the central bank will also react by the same way it is having direct relationship if it is higher then the central bank will also increase by the same amount so if one if the theta pi appears to be 1.2 then one percent increase in inflation beyond the the inflation target will be by increase by the size of the theta pi so 1.2 the larger the value of theta y the more responsive the central bank is to the deviation of the output from its natural level so this is how it and it is also linked with the the opens law that i mentioned that at equilibrium how much you have the employment taking place and how much it plays very important role so this is how we talk about so for the central bank whether it is federal fund reserve or the reserve bank of india theta pi and theta y play very important role and these two concepts are really important so if you are thinking about i t is equal to pi t plus rho so here what it mentions if you just try to understand measure how much the central bank adjusts the interest rate when inflation deviates from its target this output gap you have how much the central bank adjusts the interest rate when output deviates from its natural rate so this is how we try and understand so theta pi will be high relative to theta y if the central bank considers fighting inflation more important than fighting unemployment so this is how we can interpret the coefficient in the real life in real life scenario this is how it looks like that your inflation the federal fund rate of the u.s economy it will be around pi plus 2. so this is the federal fund rate taylor rule of the federal fund rate that the federal federal reserve bank of u s always consider so they consider theta pi and theta y at 0.5 both same gdp 2 percent is the send federal bank federator bank target so they consider 2 percent which is also the natural rate of interest right so nominal federal funded target is this right now gdp gap that we they consider by this you can also kind of can calculate gdp gap by as i told i think in some sessions that you can take the you can go by filtering mechanism you can take the deviation from the actual so any data will have the cyclical and trend if you subtract actual minus actual data if you subtract trend from actual data whatever is dual amount that you are going to get that acts as an gdp gap so percentage so according to eller rule the real central banks policy rate minus inflation this is what should respond to inflation and gap so in case of us economy sensitive 2 percent if you have the scenario where pi is also 2 then this becomes 0 we have to only deal with gdp gap so if pi is equal to 2 then this will also disappear which means that the central bank will be hovering about the real interest rate around two percent so this is how the real federated equals two percent when inflation is two percent and gdp is is at its natural level in most of the scenario in williamson book what they mention about this is the actual and this is the predicted with the taylor rule and they see a marginal deviation not much but yes in certain situation they do not go for they do not have the similar kind of kind of trend that we often find so this is how it looks like so overall what i hope it is clear that when we are talking about the decision about the policy rate then what all factors are important first is the demand supply scenario which means that we are talking about the inversions between output and rate of interest then we superimpose the condition of the fischer equation the real rate of interest will matter why reality rate of interest will matter because individuals who are living in the economy they will be thinking about how much they gain really from saving in the bank so if they are getting above the inflation it is all good for the central bank if they are getting less than the inflation then thats not good and individuals will have doubt about the central banks credibility about the inflation targeting so all the central banks they always think about moving around the taylor rule or they apply the taylor idea from this perspective and that's why it is very important to understand the john taylor idea to at least come out with the appropriate policy rate so if you want you can refer the man cube book and also the taylor and i will be continuing further with recent developments non conventional in next session so i am stopping it here i hope it has helped you understand the monetary policy context in a much better way we will be having further discussion in the next session and i am stopping it now thank you thank you so much for your attention [Music] [Music] [Music] you