Overview:
• Cagan model as a demonstration of the central role of expectations in macroeconomics
• How does inflation get started? The rise, fall and resurrection of the Phillips curve as an example of inductive economics
• Motivation of the central role of expectations and uncertainty in macroeconomics: The Lucas (1973) island model
• Preview of the rest of the course
by Prof. Burda
more helpful content:
https://www.youtube.com/@macronotes3647/videos
#macroeconomics #analysis #cagan #model #roleofexpectations #inflation #centralbank
So welcome to what to lecture number nine today we’ll explore uh some of the implications of the sadrowski model for inflation and in particular High inflation High inflation that we don’t observe very often in the in the real world but we do observe it and we’re observing it in several countries uh
Today uh that’s the Kagan model and I’ll discuss the revise renew review the stuff that we did last week and I’ll talk about the role of um of the future in the present that’s one of the most important insights of the Kagan model is that the expectations of the future influence the current
Equilibrium the currently observed price level and therefore the currently observed inflation rate therefore surprises to uh to information in Period uh the current period will affect these variables even though they’re not observed in real time so the role of expectations anticipations whether they’re rational or not is a different question but their importance
Is under is Undisputed in in macroeconomics and we’ll explore the role of expectations in general in macroeconomics and this will be the segue to the second part of the course which deals with short-run fluctuations so next week I’ll talk about fluctuations of the the economy uh
Measured its GDP or measured in terms of the consumption that agents have chosen to to uh to to um undertake or investment they’re undertaking in relation to some long-run Trend and these fluctuations we call the business cycle and that’s probably the most important dimension of interest to the second half
Of the course which is the business cycle and how to understand it the first part has been of course economic growth and understanding the the separation of price and price level from the real goings-on in the in the economy last time we did a lot of important
Stuff we used the palm tree again maximum principle to look at a different set of issues namely the role of money and we took the sadrowski model as an excellent springboard into this issue the idea of money entering the utility function indirectly for the reasons that I’ve spoken about that it helps us
Undertake transactions helps us to make transactions more efficiently therefore if we can if we can enjoy more real purchasing power in the form of money it makes us better off but of course that has a cost and the cost shows up in the inflation rate and the inflation rate plus the opportunity cost
Of of holding real assets because we’re holding our some of our wealth in the form of money so it may not seem like a very intelligent thing to do especially if inflation is high but it does give us utility so the Kagan model will is a is a derivation of that
And I’ll talk about that I’ll talk about how inflation gets started I’ll talk about the Phillips curve which is probably the most infamous most famous example of inductive economics around I’ll talk about the the conclusion from the Phillips curve that I’m just looking at an empirical stylized fact is
Not enough we have to have some microeconomic foundations and one of those foundations we’ve already sort of looked at in the OLG model and you can you can adjust that model to allow for labor Supply we can come very close to that to understanding why anticipations and deviations of anticipations from from
The real realization of those variables can cause economies to deviate from their long-run levels and this is what we have called in the past the Lucas Island model I will not go into too much detail today but it will come back uh later on in the course
So the Kagan model is a way of thinking about hyperinflation which is a situation when the rate of growth of the price level is Extreme an arbitrary definition says when the price level uh increases by 50 or more per month we have a situation we call hyperinflation it’s a
Very arbitrary definition but clearly when prices are rising at that rate you really pay a huge price to it for ignoring the inflation rate at any period of time in fact even in the the height of the the Weimar Republic it was very important to spend the money
Quickly which just means you don’t want to hold real balances given the evolution of the price level that you anticipate it seems to be a recurrent problem we have high inflation in in countries like Venezuela and turkey in recent years the recent decades we’ve had countries in Eastern Europe
Including the Ukraine and Croatia and Serbia that had sporadically High inflation I gave you the example of Bulgaria I’ll talk about it again the Kagan model is an implication of sadrowski okay so it basically shows that the demand for money in real terms taking the nominal money supply dividing
By the price level is really a function of people’s anticipation of the opportunity cost of the real opportunity cost of holding that money which to a large component is the inflation rate for that reason High rates of money growth that are anticipated in the future will show up in the present
Because High rates of money growth in the future will be associated with higher rates of inflation and high rates of inflation in the future impact my demand for money today and therefore the price level today for this reason it’s not easy to defeat inflation because you have to convince
The aid economic agents that are holding the money to hold more of it in a sense please expose yourself to this risk of inflation and if if agents aren’t willing to do that it’s because they don’t believe that the the promise of lower inflation will be realized therefore the expectation of inflation
Is a crucial element of the demand for money and it’s also a statement about the credibility of promises that the government may make or the Central Bank may make concerning the path of money in the future so we’ll have to ask the question what drives those inflationary expectations let’s revise and review the
The situation in Germany in 1922 this was the the year of the hyperinflation one might say of course it extended into 1923 but the the inflation really started going in 1922 the price level was if you normalize it to having a value of one in January
Within a year it was 16 times higher so that’s a situation one can hardly imagine in the current environment but if you went to Zimbabwe in 2007 or eight you would have observed exactly the same type of evolution however in Zimbabwe in 2008 we we had really a situation that
One observed in Germany in 1923 so the the the notion of a rising rapidly Rising price level is not enough it’s actually an accelerating uh level of of prices which means the inflation rate is increasing rather dramatically so again these are not this is not a measure of inflation that I’m showing
You this is a measure of the price level the price level Rose by 75 fold um what I said before is not quite right the currency the supply of currency increased by 16 fold and the price level increased by 75 fold within the year of 1922 and this is nothing compared to
What happened in the following months and again thinking of inflation as a hyperinflation is a situation where the price level is is literally increasing by 50 or 100 percent every month you can see that this was definitely realized in the year 1923 and the inflation rate that you can
Derive from that is is shown to the right okay and towards the end the price level is rising so fast that the money has no value in terms of purchasing power it has value as as um as heating um fuel or fuel for a fireplace or for uh to make toys or
Um building blocks or the one of the interesting aspects of hyperinflation is that in the postal system the stamps are no longer actually printed with the with the value they’re actually stamped in in the moment that the stamps are bought this turns out to be a very economical way of doing
Business but it’s a bit tricky because because of the potential for counterfeiting is increased and again in German a billiona billion is a trillion so we’re talking about 10 to the 12th power the situation we saw in many other hyperinflation episodes in the night in the 20th century
Now you can see the the pictures are quite suggestive people carrying their their paychecks home in a wheelbarrow a central Banker is pushing um huge stacks of money around it it sounds a bit absurd the question is how do you get to that and you can get to the same
Way that Zimbabwe got to it in in 2000 uh in the 2000 decade leading up to 2008 or the hyperinflation in Germany the years leading up to 1922 namely a very large pressure point placed on the central bank to create money to make loans to the central government
To pay their bills and these loans have to be of course put on the balance sheet of the Central Bank and the central bank has as liabilities the the paper uh that it uh sort of prints to uh to represent or to pay out the loans that it’s making to the central government
So in Weimar Germany this was a A desperate measure given the strikes in the in the uh and the Aurora and the uh the tsarland basically to to pay the workers by in state Enterprises because tax revenues were falling in Zimbabwe it was a similar situation when the Zimbabwean
Government nationalized many farms and didn’t provide for uh adequate adjustment of production there was a large shortfall in revenues for the government and the government needing to pay its Army to pay its police to pay its uh other functionaries had to resort to printing money um in a big way
Then again the the situation is quite quite dramatic now Philip cabin Kagan has generally considered to be one of the most interesting analysts of this of this phenomenon he wrote a very important dissertation on the subject at the University of Chicago with Milton Friedman as his advisor he was also a
Professor at Brown in the Columbia University he was in the Council of economic advisors and his work simply writing down the price level and the money supply Evolution from many interesting countries and and episodes um and proposing a framework to think about that was a was a real contribution um
His dissertation when a part of his dissertation appeared in an important book that Milton Friedman wrote in the 1950s trying to reassert the the notion of monetary um the importance of monetary Aggregates in uh in understanding the long-term evolution of the price level remember we’re always talking about the
Long term in the short term many other things will happen we’ll see later on in this course but um at that time analysts had had really spent too much focusing on the too much energy focusing on the short run and not enough thinking about the long run namely um
What is the consequence of excessive monetary growth for the price level in the long run and we know that if if there’s a a thin hope for monetary neutrality it implies that central banks that create money an excessive rate will not be able to to avoid the the consequences in the long
Run although it may take a while for that to happen so this is a definitive work um it’s on the reading list so if we think about um the sidrosky model we can basically um understand the following one of the first order conditions was at the at that the agent the representative agent
Holds real money to the extent that the the margin utility of holding that money is equal to the opportunity costs of doing so which would be the the nominal interest rate and the nominal interest rate is the real interest rate plus um the rate of growth and the price level
And the real interest rate in the Kagan model turned out to be the subjective rate of time preference the the stripped down version that we looked at Kagan in his original paper uh sorry in um and sadrowski in his original paper looked at Capital so it’d be the marginal product of capital instead
If you substitute uh into the first order condition that we had in the sidrowski model we end up getting the condition that the marginal product of holding real balance is equal to the opportunity cost that I just said and if you substitute our assumed isoelastic formula for the the
Subutility of Agents over real balances the first derivative of that function is equal to M raised to the minus gamma and Gamma is a positive parameter so you can see that immediately we have a a an invertible function and the implied demand for real balances so real balances will be a negative function
Of the sum of the subjective discount rate of our household in the sadrowski model plus the inflation rate that the household is facing again this is a model with perfect foresight so the agent knows what the inflation rate is going to be and therefore the higher the sum of
Those two is the lower the agent will choose to hold real Is wealth or her wealth in real balances we say that this is a very robust result this is well known and has been empirically verified in many countries and around the world that the demand for cash and bank accounts
I.E forms of holding wealth that involve a sacrifice of a nominal interest rate response negatively to that nominal interest rate and therefore it responds negatively to both in patience and inflation okay now if you take take logarithms of both sides we have something that looks like a an elasticity of money demand
Actually some people call this the semi-elasticity it’s not quite correct but it’s often referred to to as the elasticity of my demand um you know one percent uh change in in those right hand side variables lead to a to a an eight percent reduction in real holding Holdings of money which
Means given the price level you would reduce your nominal Holdings or given your nominal Holdings an increase in the price level would accomplish the same the same outcome now if you you convert that model to the discrete time um we’ll have the inflation rate measured now as tomorrow’s price level
Divided by today’s price level minus one and that’s the inflation rate without the percentage formulation so it’d be if you want to make that percentage terms you’d have to multiply it by a hundred but that would imply something like um the um the nominal rate of um
Of interest on the right hand side is an argument to that same function and if you take logs of that we can approximate it and again this is an approximation that is used frequently in monetary economics we end up getting a the logarithm of the real money supply on
The right hand side you can see that it’s the the difference between the logarithm of money supply in nominal terms minus the log of the price level but that is a negative function of the change in the logarithm of the price level that is expected between today and
The next period so today’s money demand depends on tomorrow’s price level relative to today’s price level so it’s that’s the the role of future expectations in a current um demand for money this is called the Kagan money demand equation so you know you can derive it many different ways we
Saw how it arises naturally from the sidrowsky model but it could also be um James Tobin and William baumel were able to derive something like that from a an inventory transactions demand for money type of theory but here we’re using the the sadrowski model is the motivator so utility over real balances
Even though it involves a sacrifice involves a negative demand for money and the negative a positive demand for money that depends negatively on the inflation rate that’s expected to occur over the future okay so you can see that this is an interesting possible theory for the
Price level today if you go back and ask the question what is determined today well the Central Bank supposedly determines the money supply today and the price level tomorrow is determined by expectations of the price level tomorrow so all that’s left to move is the price level today so we can actually um
Think of this as a determination of the price level today and that’s what Kagan and other people who have studied hyperinflations have have come to believe and come to to argue that expectations of the future determine the present price level okay and to see that we just need to rearrange that equation
And solve for the price level today in the logarithms as a function of today’s money supply which is presumably determined by the central bank um and this is again a presumption that means the central bank would if if wanted could actually control the the aggregate supply of Bank liabilities
That are held by the public this is a question that always arises in a hyperinflation um Banks Bank deposits tend to tend to tend to drop dramatically if not go to zero because people are running around paying in cash because Banks already take a couple of days to do the transaction so
It doesn’t seem like much of a good business model for banks it’s not a good business model for banks to be doing because they won’t get any customers customers can’t wait two or three days to to make it a bank transfer so people tend to go into into cash or to highly
Fungible liquid means of payment so today’s price level depends on today’s money supply determined by the Central Bank Plus the expectation of the future price level and uh Kagan basically said this could be the basis for a a more elaborate way of thinking about the price level today if you just lead
This equation by one period again this is a world in this particular case of perfect foresight the tomorrow’s price level is going to depend on tomorrow’s money Supply Plus the next days expected price level okay so we have a recursive situation in which we can take the latter equation substitute it in the
Former and we see that the price level today is dependent on two money supplies one today and one tomorrow and the price level in on the day after tomorrow okay but there’s no reason to stop there you can do this add infinitum and you can end up writing the price level today
As the in infant as a sum of money supplies from zero to to capital T appropriately weighted by a term that is the elasticity of money demand divided by the elasticity of money demand plus one so it’s like it’s like a discount Factor it functions like a discount Factor
Because it means that that this geometric average um uh the the weights are declining um geometrically as the power of of time and then you’ve got this leading term which is the price level in um in t plus cap t plus one in case I think this is the the tail
That that Wags the dog if you like it’s the last it’s the last term of this of the price after you’ve accounted for all the intervening logs of future logarithms of future money supply now if you let cap T go to Infinity you end up having two terms you have one is
The an infinite weighted sum of future expected money supplies and current money supply of course and then you have this this leading term which is a single term and it really we don’t really know what’s going to happen um it could it could in some sense the price level could grow faster than
Um One Plus ETA divided by ETA or 1 over ETA and that would imply um a second term that’s actually infinite and that would kind of mean the price level today is infinite which means that the money is worthless today um this is often called a bubble component because it implies that this
This price level keeps rising at some rate that doesn’t have any sort of uh Moorings it’s just Rising on its own um if we don’t think this is a a tenable situation or a sustainable situation in the long run we basically assert that at some point that bubble will probably burst and if
It does um then you have a zero value for that term and therefore you can really focus on the intervening future money supplies as of period t Okay so the the lesson of the Kagan model is not the current money supply but future expected Mutual money supplies uh matter that’s a very
Important Insight because if you if you again if you return to that and think about it it means that the the anticipation of future monetary policy will impact the current price level and if a central bank can credibly argue that the the money supply will not grow
At a at a higher rate and remember first differences of the log of money supply are the monetary growth rate so convincing the public that the Central Bank means is serious when it talks about controlling monetary growth would be one way of getting the price level under control in Period t
Now this whole goes goes through on in a world of uncertainty the interesting thing about this is we haven’t we’ve assumed that agents have perfect knowledge of the of the future Evolution the price level that’s nonsense but it’s a good way to fix ideas because it shows the importance of the expectations but
If if we had a world of uncertainty it’s pretty feasible to it’s pretty pretty plausible that households would try to to um avoid the mistakes especially those involved with a high rate of inflation by making a lousy forecast so we’ll try to do as best they can and they won’t be
Consistently fooled this is often um thought of as a form of the rational expectations hypothesis one one version is a strong version the strongest version is that agents actually have access to our model and a weaker version would be that agents just don’t make systematic mistakes they don’t they don’t consistently
Underestimate the price level and therefore if they make a mistake in this period they’re going to try to avoid it in the future periods and they may even try to reassert the real terms of trade that they had before the surprise took place so the way of formulating this as I said
Takes various guises and one way to do it is just to say that it’s just the conditional expectation of Agents given their available information this is called the the strong or stronger form of rational expectations and we would think of the ET as being the expectations operator a linear operator
In the sense of probability Theory based on the model okay so the model is the is the data generating function for the price level and the price levels is a random variable and in that case um the model basically goes through the model is log linear so all the
Operations that I took that I performed on the certainty the certainty version of the model apply um when the model involves uncertainty because in this log linear form the expected value of the price level tomorrow is going to be a linear function of the logarithm of the
Price level in The Next Period and the log of the money supply today so the same recursion can be applied and the price level today is equal to the conditionally expected weighted average of future logarithms of money supply and current money Supply Plus some leading term that we called
The bubble or the non-fundamental solution most important Insight of this whether in a world of certainty or uncertainty is the current price level the current price level which I say price is the price of all Goods adjust immediately to clear the market supply demand money are equal and this
Is very similar to the Samuelson model that we had in the overlapping generation sense where the the generation was a 25-year period or a 20-year period or a 30-year period okay so the again the inside of Kagan is to understand a picture like this which is why did the the price level of
Bulgaria first way to Spike the way it did and that’s easy to understand if you understand that Bulgaria had a planned economy and released a few prices along the way until the mid-1990s but it was in the middle of a transition to a from a socialist planned economy to a
Market economy but more importantly it was it was funding its its budget deficits which were Rising rapidly by accessing Central Bank credit and the central bank credit was paid out in the form of banknotes because the Bulgarian banking system was fairly primitive at the time and you can see that at the
Time the price level was already starting to adjust even though the inflation rate was rather was rather low and you see this also in the fact that bulgarians were reducing their real Supply their real Holdings of money so M over P the Orange Line already started dropping rapidly
Um precipitously if you like even before the spike of the inflation so in some sense people in Bulgaria are already reducing their money Holdings because they were anticipating that at some point the price level would rise and they would be exposed to a very large increase in the price level
Um in my my own trips to Bulgaria I noticed and I was actually there around 1994 I noticed that that a lot of the shelves were empty and I know the Bulgarian economy was producing goods and services they just weren’t producing them for for to be sold in stores and their
People were holding back with some perhaps anticipation that prices would go up or people were buying the goods and and hoarding them so this is two SIM two sort of symptoms of a of a high inflation episode but most importantly the the spike of the price level occurred very quickly and then the
Bulgarian government reformed the central bank and reformed monetary policy they actually went on a sort of currency board with the the Deutsche Mark at the time which meant that to the extent that Bulgaria could actually maintain this currency board which means that if you had Leva you
Could go to the to the central bank and get Deutsche marks at a fixed exchange rate having a fixed exchange rate is like having a a peg to the external value of your currency and that of course can get expectations of inflation down to the extent that people
Believe that the monetary policy of Bulgaria will follow that that rigorous course and in fact you see after the reforms the real money supply the real money demand which is equal to money supply in this model started Rising immediately after inflation uh peaked and decline dramatically
Okay so we still have to ask the question are these people uh are they really rational are they really believing um in Evolutions that are on average correct um or do they have do they make systematic errors and the evidence is we see similar patterns in many countries recently in
Turkey 2019 you see a similar evolution of the price level and accelerating evolution of the price level increasing inflation and a reduction in demand for money and a reduction in the real measured demand for money so it it’s a the model has a certain amount of predictive power the question Still Remains
Why would the Central Bank do this the central bank is Not By Nature out to print lots of money that’s a very expensive operation uh during most severe hyperinflations one of the big items in the balance of payments or the balance of trade that is in deficit is
The import that contributes to the deficit is the import of the paper that’s been printed by usually Swiss or German companies the banknotes as ludicrous as that seems so Central Bank seems unlikely to do that on its own usually it has to be sort of coerced to do it because the
Government needs the the funding and the central bank can deliver the funding because it has the Monopoly rights to create the means of payment so you know there are two possibilities one possibility the Central Bank says no we’re not going to do that you might say
That the the after the reichs bank was was reformed and became the Renton Bank bank in 1924 that they committed to a very strict monetary policy and they were forbidden to lend to the government this would be a case of where the central bank can say no to the
Government and just like the European Central Bank could say no to buying a Securities in the open market we call this Central Bank dominance it’s only one possibility but it could be the case of the central bank can say no and if the if the fiscal Authority
Has a deficit it has to go to the capital markets and raise money by issuing bonds the central bank has no commitment to buy those bonds and therefore the the borrowing capacity of the central of the of the central fiscal Authority is limited in that case the price level becomes a
Function of expected Mutual future money supply is decided by the um the monetary policy Authority but it can well be the case as I say in the last line that um the central bank is not independent the Central Bank might be coerced into um printing money funding the the Central Bank the central
Government’s deficits okay suppose if the central bank is not dominant and again it because I say this is not a an accident that we have these hyperinflations it seems like the government has been somehow forcing the central bank to do its business and I told you already um Napoleon
Founded the bank de France and Adolf Hitler tried to take over the the reichsbank because it’s a great way to finance adventurous Wars and um it’s not an accident that these types of situations often lead to high inflation or hyperinflation so fiscal dominance is the alternative to monetary dominance that would mean
That basically the fiscal Authority imposes will on the the monetary Authority and the people understand that and they see future deficits and the price level would react commensurately this is a situation that we would have in high inflation environments not in something we observed today at least that’s the current thinking
So to summarize the underlying problem is central bank finance of government budget deficits hyperinflation usually arises for that reason and fiscal deficits can be related to Wars they can be related to us to to real terms of trade change I think if it can also be related to the
Um to government cause disasters if you think about the the problems of Zimbabwe they were really homegrown they the nationalization of of the Farms was a big mistake in an economic sense even though it might have appealed to some senses of people’s sense of social justice it meant that Zimbabwe lost a
Very important source of of its real economic well-being and because it couldn’t replace it the central bank was forced by the the the government of Zimbabwe to to print tons of money to pay civil servants and finance a very large budget deficit things get worse if inflation Rises suddenly and the taxpayers
Try very hard to avoid paying their taxes and doing so they actually increase the the deficit because the revenues of the government fall and this is called the tonsi effect um meaning that high inflation and Rising inflation can re lead to Heart larger deficits which lead in turn to to larger
Um in to larger increases in the money supply to finance the the the growing government deficit so in a sense both of these might be endogenously and simultaneously determined a good example of this was Bolivia and the early 1980s this is a while ago but uh Bolivia was a extremely um
Successful growing uh country in the 1970s because the price of copper was rise and the price of oil was rise and the price of tin was rising and the government uh uh ran the state-owned Enterprises and they made lots of money and then what happened um
In in the early 1980s was the price of copper and the price of zinc and the price of 10 and the price of oil all started to fall in real terms and this meant that Bolivia’s sort of business model was collapsing and we see a very
Sharp rise in in the inflation rate in Bolivia and I think you can call Bolivia hyperinflation after 1980 82 or 80 80 um is certain maybe even 1981 this is the rate of change percent per annum um in the price deflator the GDP deflator the the Pasha index for
The the price level measured on GDP in Bolivia and this is an annual rate of change so these are really extreme changes and you can see that you can anticipate this that already in 1981 the government’s deficit increased immensely the government surplus with a minus sign
In front of it is the deficit status of 1981 the the deficit Rose to ultimately almost half of GDP because the collapse of the the government Enterprises meant they had huge deficits and they the government worked these these workers in the in the copper mines and the Tim mines were basically paid by
The central bank and commensurately M2 which is a measure of monetary Aggregates including checking accounts and savings accounts Rose very sharply and you can see that at these high rates of inflation the Kagan model is a pretty good predictor of what’s going on at the same time GDP was already kind of
Was was not growing anymore by 1980 and it was actually shrinking because of this collapse of of the relative prices of these primary Commodities that Bolivia had actually done quite well with the 1970s and it just shows up immediately in this gaping government funding deficit which the government basically could not issue
Bonds who’s going to hold a Bolivian Bond with the government that’s not credible so the central bank took over and printed money so to summarize fiscal deficits are a prime candidate not a misbehaving Central Bank central banks don’t get any utility from printing lots of money it’s usually
Coming from pressure from the central government and we see this again and again we see it in Argentina and we see it in Turkey in burgeoning and inflation situations you always look to the government as a Cause there may be some other things that could happen sometimes a government may
Try to maintain an exchange rate and the Central Bank may be instructed to buy lots of uh foreign currency and in doing so it expands its balance sheet and for some time could also have a inflationary impact this is a rather rare situation but it could also be um
A cause of of high inflation but um you know governments usually don’t do that for fun usually there’s a reason for maintaining the exchange rate may have to do with trying to avoid the political consequences of of an appreciating exchange rate but as we saw in the case of China China actually monetized
Or the Chinese Central Bank bought a lot of dollars in the Years between 1990 and 2010 and because the economy of China was growing so fast this did not translate into any sort of significant rise of inflation okay so what does this take as this
Takes us now to to the the transition to the rest of the course because we’ve talked about the long run we’re also interested in the shorter run we’re interested in fluctuations um and we’re interested not just in the steady state which is has driven a lot of our analysis but we’re also
Interested in the Dynamics so starting next year we’ll speak of this we’ll we’ll speak more about or talk more about Cycles as opposed to long-term trends and we’ll talk about the dynamic interaction of inflation and output but we already have the tools to talk about that so we’re
We’ll be in pretty good shape I’ll give you a graphical tool to work with and then we’ll talk about how to make make sense of the graph make sense of the Curves in the graph so you’ll have something to hang on to for a quick answer and you’ll have something to to
Chew on to understand why the curves shift or why they have certain slopes to get to get to a to an understanding of inflation one has to understand where it came from and I think the recent experiences is instructive um in the United States and and Germany
Over the past uh 40 years inflation has been rather low actually uh coming off the 1980s um but recently we’ve had a rise in inflation if you go back another 20 years you see that inflation also Rose for a period of time it’s always instructed to think about where this came from
Ultimately this course will develop some theories about why firms set prices that can lead to higher prices in the future as a short-run reaction to situation in at the present but um most important thing I’d like to talk about now is how expectations matter and how they adjust
Which is motivating why we have we have thought so much about inflation because inflation is a little bit like an oil tanker it takes a little bit of time to get going but once it gets moving has quite a bit of inertia it’s hard to it’s
Hard to change these are just these are just kind of insights that that people have acquired over the past hundred years so the first time we ever encountered inflation was the really I mean was the demise in in the modern industrial world was the demise of Bretton Woods in 1971.
Okay and up until then we’d had some situations where inflation would be relatively high but not really high but or it’s been very very low or even negative um and just by observation we were able to see um that certain variables move in certain ways with with the inflation rate
Inflation is high other variables may be high others may be low again this is what we call inductive reasoning I mean we have we have some observations on on reality and we’d like to make some sense of them think of Kepler and the planets that was my example I gave earlier
So aw Phillips looked at data on nominal wages wages in pounds sterling in a period when the price level in England or the United Kingdom was relatively stable okay and he found that discovered that in periods when interest when when inflation measured as the rate of change of nominal wages was high the
Rate of unemployment was relatively low and vice versa this is not a perfect relationship but it looked pretty good from from where he was sitting he saw this sort of as a as an observation and it it kind of made sense to him that in periods when the labor Market’s tight
Workers have a pretty good situation where they they’re free to change their job negotiate better wage deals with their bosses and inflation measured as a change of wages not prices but the rate of change of nominal wages would would be stronger or be higher similarly when unemployment is high as Karl Marx noted
It’s easy to pick up cheap labor and workers have less bargaining power so the rate of growth of wages in nominal terms should be lower okay so remember wages are a part of the the economy’s cost structure taken as a whole it’s about two-thirds of the
Economies value added so a change in the wages for the whole economy for the macro economy is an important source of pressure for the prices uh for the evolution of prices in the economy and that’s why one would suspect that a good theory of wage inflation is a pretty
Good theory of price inflation okay so aw Phillips this guy basically a fascinating fellow sheep farmer ran his own Cinema for a while crocodile hunter went to study Engineering in the UK in in the way the very tough time to be a to be a young man at the time he was
Conscripted to fight in World War II and it’s a prisoner in the Japanese POW Camp for about three and a half years during that period he developed a certain affinity for economics and eventually after doing his degree he went on to to study economics and wrote some interesting papers he
Also became a member of the the order of the British Empire which is a fairly respectable thing I think Mick Jagger has that but not everybody his most important Discovery was this relationship it’s not the only thing he did but it was he just kind of discovered this relationship a lot of
People would claim that Irving Fisher also discovered it in the United States in the 1930s there’s a nice paper where he says he claims the same thing for the uh for U.S data and this is these are both in periods when Unemployment uh just Traverse quite a range of values and the
Inflation rate was rather low but still fairly volatile and variable and it made sense for him to look at wage inflation and you know the Phillips Phillips one of the other things he did was develop this machine which is a hydraulic machine based on the the national income
And product account so based on y equals c plus I plus G Plus x minus Z is a can be thought of as a you know it’s it’s an identity of course but if you think about the the causal relationships that we can imagine to
Assign to the to see an eye and G um you can think of this as a um a system of equations and that’s what we do in macro but you can also think of this as a as a system of pipes connecting various um levels of of water in a hydraulic system
And being an engineer Phillips was um was sort of pretty pretty obsessed with this idea and was able to put it into a machine which you can find in many museums around the world and I’ve seen this I saw this at the LLC when I was
Visiting there and it was even a back room actually now it’s it’s in the in the the science museum in London there’s a version there are several versions of the United States there’s one in New Zealand and Phillips basically showed you can it’s an analog computer effectively it
Was able to track the evolution of the components of GDP just on the basis of fluid mechanics so it’s a kind of a cool idea and it was even described in uh in some some of the press reports at the time but this is what I want to talk
About this was Philip’s contribution to our to our field Phillips basically said that we’ve got this negative relationship between a nominal rate of change the rate of change of wages in percent per annum okay um and unemployment in the UK economy and he took a period when the British
Currency was not uh was not um freely issued like it like it was in the post Bretton Woods the night the post-1971 period This is a period when inflation got as high as maybe nine percent and sometimes it was negative this is because the UK was pretty much
On the gold standard which meant that the supply of gold determined roughly the amount of transactions medium in the economy this is not exactly the case because the bank of England cheated a little bit but they couldn’t cheat systematically in the sense of creating a new credit and
New money every period in increasing amounts so that was not allowed back then and still in all Phillips finds a negative relationship and it’s a it’s kind of a log log linear relationship he described as such in his famous paper in 1958 economica okay so naturally if you
Look at this you see wow this must be something there I mean the tight labor markets inflation is rising in nominal terms which kind of violates all your predisposed Notions of of money neutrality why should the unemployment rate in any way depend on the rate of change of a nominal variable in pounds
Well if you think that pounds aren’t being created in ever increasing amounts maybe there’s something real going on there but it must be anchored by people’s expectations of inflation so already Phillips was thinking maybe in these terms but he didn’t write down that model but he certainly said we
Shouldn’t use this as a basis for policy if you read the paper he’s actually a bit circumspect but the the negative relationship is definitely there okay so in tight labor markets wages are rising fast and when the unemployment’s really high and depressed economies wages might even be falling and there’s some deviations of
Course okay so a lot of economists at the time thought this was the Magic Bullet that would help us connect the real economy that we’ve started studied in the first half of the course with the business Cycles in the second namely all we can we can imagine is you know you
Can accept higher rates of inflation you just have to accept them uh higher rates of inflation means low unemployment yay the unemployment’s low good for the economy and if we want we can we can elect some Republicans and we can slide back down to the to the 1959 uh point if
We want that was that was the conce conception of the of the profession in the 1960s so there’s a fair amount of optimism that we can actually my you know sort of Master this uh this this this animal and in 1959 Dwight Eisenhower was president Republican fairly conservative
A general did a great job of building the highways in the United States but he also believed that government should be strict and should run should run surpluses when possible you shouldn’t have deficit spending so it was kind of a political thing and unemployment was high and then Kennedy
Got elected and he cut taxes and did a lot of military spending and a lot of social programs were initiated by him and were followed up by his successor Lyndon Baines Johnson and as a result the movement from the 1959 point to the 1969 point is simply a
Huge expansion of the U.S economy the Vietnam War the Great Society and a lot of a lot of spending beyond beyond your means in 1969 Richard Nixon was elected and Richard Nixon promised lower inflation because inflation was high like it is in the United States now and
Richard Nixon promised that he would do whatever it took to get inflation down again and his notion was all we have to do is cut back on government spending increase taxes and everything would just slide down the Phillips slope and we’d be back to where we started again
Okay so this notion of a trade-off was criticized a lot at the time um although it was politically expedient for the the Democrats who were in power in the 1960s so it was it was a good time for the United States economic growth was had never been higher people were hiring
You know buying lots of cars and two cars in every garage and two chickens in every pot it was a great time and this seemed to be like a Vindication for Keynes because Keynes basically said all we have to do is put our foot on the accelerator increase spending cut taxes
And we can move the economy to a higher um sort of higher level of economic activity and Welfare and at the same time we can um we’ll have to accept a bit of higher inflation but that’s kind of euthanasia for the people who have lots of money
They can suffer a little bit of loss of purchasing power that was the logic that Keynes was pushing now at the same time this criticism was coming from uh not necessarily the right wing but just coming from a class of Economist who thought that the money supply was being
Ignored in this analysis and the monetary fundamentals of of inflation were being ignored so much that eventually inflation would come back and and bite Us in in the in the rear end that was the the notion that Milton Friedman said he said this monetary nature of inflation will come back and
Get its revenge at some point in the future and he made a very controversial uh address to the American economic Association in 1967 he said basically this he said there is a temporary but not a permanent trade-off between inflation and unemployment and there’s no such thing as a permanent trade-off
So the notion of riding down the Phillips curve or riding up the Phillips curve as Kennedy and Johnson did in the 1960s in the United States and other countries by the way also I think Helmut Schmidt famously said he would rather have four percent um inflation of four percent unemployment
Um that’s a long time ago but uh that type of thinking connecting a nominal variable with a real variable seemed to Milton Friedman to be a rather dangerous thing and Milton Friedman and his famous address in 1967 which was published in 1968 he said it was the unanticipated a
Part of inflation that was mattering not the inflation itself so getting inflation up to six percent is may look like you’re doing it to purchase lower unemployment but in the long run there’s no reason to believe that the rate of unemployment a real variable would have anything to do with the rate of
Inflation the rate of which Milton Friedman thought was in the long run correlated with the rate of growth of the monetary aggregate okay and he went on to argue that basically the unemployment rate is the outcome of of real variables he called it the general equilibrium involving the
Characteristics of demand and supply for labor the demand for Commodities that are complements or substitutes Market imperfections shocks variability and supply and demand the costs of gathering information for the unemployed people and for unemployed people and for firms to to find workers the cost of Mobility Etc so when this was published Milton
Friedman was criticized roundly as being uh you know some sort of fear monger and we should just ignore him and turns out that Milton Friedman was completely right so in in 1969 Richard Nixon was elected president and he said okay my fellow Americans I’m going to increase the tax surcharge I’m
Going to cut spending we’re going to get out of Vietnam all these sort of ideas would reduce the government’s claim on GDP and therefore reduce aggregate demand we’ll see later next year where that would we could actually think of how that would matter and therefore we would just slide right down the Phillips
Slope and we’d move back to the ike Eisenhower years of the 1950s well he tried that and it didn’t work in fact another bunch of other things happened that caused the Phillips curve to basically uh collapse in its in the form that people thought in the 1960s
That it existed and um you can see that there’s definitely still a negative correlation between changes in unemployment and changes in inflation but the the level of that relationship had shifted and it shifted fairly persistently for the next decade until um several years of a deep recession and
If you go back and plot the same data for the United States today it looks surprisingly like the old Phillips curve of the 1960s but it gives us the warning that maybe a shift of some of the determinants of the Phillips curve that we hadn’t thought about could be absolutely relevant for understanding
How it works so that’s the point of the the second half of the course is understanding why that Phillips curve shifted um and why it shifted back and how a similar experience can be observed in other industrial countries of Europe and and Asia and one of the most important things is
Indeed the real economy is independent of the evolution of inflation in the long run so it’s kind of a Vindication of Friedman’s critique that indeed there is kind of a slow-moving long-run equilibrium of the labor market and of other markets and what we’re observing is basically people moving along some
Relationship in which firms are willing to produce at higher rates of inflation and workers are willing to work at higher inflation rates wage and price inflation rates but not consistent with the long run okay so we’ll use this as an as a foundation for macrodynamics in general expectations are a key element of
Macroeconomic fluctuations we’ll see not only is just in the in the context of the Ramsay model we saw the expectations of the long-term future important but here short-term changes of expectations can matter as well um Keynes emphasized this when he talked about animal spirits the collapse the systematic collapse of investment because
Entrepreneurs get pessimistic about the future hobbler schumpeter Fisher all these guys talked about the role of expectations in the future and these may not be rational but in our course and in our thinking we try to ground our our own Thinking by saying well let’s just assume that
Agents are as smart as we are and they can figure this out and if they can then it’s important to to use the theory to think about how expectations are formed just in terms of the OLG model we can get some some idea of how this works so
I’ll make an important modification in that agents when they’re young don’t have a fixed endowment of the consumption good that they sell to the old people but rather they have to work and working means they have to supply their labor and their labor is compensated at some rate some wage rate
And this wage rate is nominal so it’s in terms of the money that they will use when they’re older and um price at which they purchase consumption today is also in terms of money so money serves as function of facilitating exchange and it also is a common denominator for measuring value
Of Labor and the value of of goods today and the goods of goods tomorrow okay so we’ll just make this very simple modification to the OLG model and see how far it gets us okay so agents still live two periods when they’re young they Supply labor that’s painful but it
Enables them to buy consumption Goods today with money they acquire but also tomorrow with money that they will save into the second period and be subject to the possibility of the price of money in terms of goods changes the price of goods in terms of money changes okay so
Um when agents are young they work and work is painful work creates disutility okay so you this utility will just subtract utility of consumption uh from utility consumption will subtract the disutility of work uh working has this slight Advantage the essential Advantage if you’re an agent if you don’t work you can’t consume
Either today or tomorrow so you’re going to do some work okay and you earn a WT for every unit of L you work um there should be a subscript on the L and every period the agent every every period young people are working for paper money
At nominal wage WT and they can buy real they can buy real Goods CT at price level PT okay now what happens when you’re old you have some money you’ve saved um to to uh transact in the future and this money is subject to this uh this uh the
Possibility that inflation goes up okay so if you spend your money today you don’t have you know exactly what the price level is today in this model and you’re subject to only the risk that prices will rise in the future and if it’s a certainty model you know exactly
What price is going to be but you they may be higher and therefore you may not be so interested in working tomorrow the reason is that the government is injecting new cash into the economy so we unlike the last version of the OLG model we had a fixed supply of money now
We have a money that’s growing at a rate mu which means that people who have money when they’re old will get like an extra transfer proportional to their cash Holdings and we’ll call that mu t plus one that’s the rate of growth of money between t and t plus one
So the households now choose their consumption when young consumption when old their labor Supply went Young and the cash Holdings that they will acquire I.E not spend on consumption today to allow them to consume tomorrow so the money is purely a vehicle for savings as in the Samuelson model it’s not used
Strictly speaking for transactions today in this model it’s used for transactions tomorrow so the households maximize this object utility net of the disutility of work and subject to a budget constraint which we can easily write down is just two different equations that we can combine into one by eliminating MD
Because money is really only used to facilitate transactions in the second period and we’ll assume specialized forms of the utility function um CT C1 T is a typo so just eliminate that from the slide and this is just a generalized form of the utility function and Gamma and Nu are assumed to be
Non-negative if they take the value 0 then it’s a linear form and if they’re if we’re close to one then we have the isoelastic form that’s logarithmic so in general this is called the isoelastic specification for utility because if you take the elasticity gamma and mule respectively the
Elasticities of utility respect to the arguments C and L but um as you can see when Gamma or mu get close to one uh these this are these um these functions get very very large at the same time they get large with a limit so they don’t go to Infinity but
You can’t just plug in gamma equals one because you’d be dividing by zero or mu Nu equals one so if you let the respective parameters go to one you can apply lopital’s Rule and you end up getting that these are the logarithmic functions so that’s kind of a fun idea
Logarithmic function is very popular as you’ve already seen with with Leopold in his section so households need to work how much do they work well utility is more General than the log so we don’t have a we’re not going to have the logarithmic magic remember the logarithmic function has the property
Um when it’s defined or defined defines utility over consumption that the proportions of your budget spent on various elements are constant that turns out to be a very robust and problematic feature because we noticed that budget Shares are not constant so utility is probably not logarithmic but in any case
This is going to give us a bit of response higher or lower elasticity of substitution than one okay so to find the elasticity inner temporal substitution as being the inverse of gamma okay so this is a following the notation in some famous textbooks and therefore Sigma is going
To range between 0 and infinity if it’s equal to zero then you have something like a leonty of preferences over consumption over time in the special case of gamma going to one we have logarithmic utility okay so this Theory will imply that cash and Advance money demand can be sensitive to
The rate of return on on money we already showed that earlier okay and if we substitute uh into the problem and look at the maximization problem we can actually get first order conditions um that are real relatively intuitive okay so by substituting we eliminate um C1 so basically we’re choosing C2 old consumption
And our labor Supply today and that will implicitly through the budget constraint imply how much I can consume today so we’ve just instead of using a LaGrange approach we can just eliminate consumption today okay so we have a case of uh we’ll consider the case of certainty so people
Know for sure money growth in the future and they know inflation uh this just focuses ideas the most interesting part of this model is allowing all these things to be uncertain the first order conditions um when you substitute for C1 back in even though you’ve you’ve eliminated in the
Maximization problem you end up getting that C2 is a function of C1 they’re related then that relationship is going to depend on the elasticity of substitution one over gamma and that’s going to depend in turn on the the path of the rate of increment of of the money supply relative to the
Inflation rate so it’s like a real return on holding money um with the real return coming from the government paying you more money based on what you had to start with labor Supply is going to be related to C1 and you can see this is a complex relationship so it’s really not you
Can’t really say anything yet because you have to substitute but labor Supply today will be correlated with um in an inverse way with with um wages today relative to C1 depending on what C1 is and we haven’t solved for C1 so to do that we have to combine it with
The budget constraint and then we’ll have three results we’ll have a we’ll have a labor Supply Choice we’ll have a consumption uh in the first period and we’ll have consumption in the second period and all these are hanging together or sort of whole sort of moving together in some way that’s governed by
These first order conditions and the budget constraints so that’s the important thing you can’t say anything more about this until you’ve solved for the level of C1 C2 and L as a function of the exogenous variables on the right hand side and that’s why we we do this
Exercise so getting there is a little bit of a bit of exercise so you can take ratios and eliminate C1 again and express C2 in terms of Labor Supply today okay so you see those are kind of uh catares paribus will be positively related because both new and Gamma are
Positive okay so think of think of you know if you’re going to have more consumption tomorrow and today it better be it better be worth it okay so that’s one way of thinking about it um if you substitute um for C1 you end up getting the first order
Condition for l in terms of C2 and then you can substitute for C2 and then we can eliminate both levels of consumption from this equation now we can actually solve for labor Supply in the first period of life okay and you’ll see that it does depend
On only things that are exogenous to the age from the agent’s perspective the real wage the inflation rate and the rate of growth of of the money supply um from the perspective of period t so a little bit of algebra which I’m going to show you on the slides you can actually
Eliminate or you can solve for L as a function of all these things and a bit of simplification you already see that we’ve got L now as a function of the real wage function of money growth and of price growth and if we express it in terms of the elasticity of substitution
We see that labor Supply in the first period depends on the inflation rate that’s expected it depends on the money growth rate that’s expected and it also depends on the real wage today okay now those objects are known with certainty then we can say with certain the impact on current labor Supply it
Might be the case of course that agents have to form expectations so if you take the logarithms of this expression and take approximations of that you could show that the labor Supply today will depend on the expected rate of inflation in the future and it depends on the
Expected uh if the price level today can’t be observed it depends on the expected price level today that’s the Lucas Island model and it also depends if essentially on the this the sign of the exponent on the real wage which is going to be related to the elasticity of substitution uh inner temporal
Substitution as well as the uh the the disutility of uh labor and um in the utility function and you can see that as long as Sigma times Nu is less than one we’ll have a and sigma is greater than one will have a positive response of Labor Supply today to the real wage
Which is kind of what we’d expect but you can see it’s complicated because if agents are have a lot of um disutility of of supplying labor if if new takes a large value that could actually flip the sign of this relationship okay so using that we can actually
Derive the other two we can derive consumption in terms of the real wage and we can derive and labor Supply and we can derive consumption tomorrow as a function of the real wage and labor Supply and then we’re done so basically we see that current wages um current consumption depends on present
And pastoral wages it depends on current and future inflation and real monetary growth so all these things jointly determine uh can determine the paths of those variables so even in the in the world of overlapping Generations we have potential for fluctuations and think about if we reduce the period to to a
Quarter then suddenly you have much more room for Action so in a world of certainty or real a perfect foresight you may not have regrets but in reality you do have regrets you have uncertainty so mistakes are part of the story of generating the cycle and in Lucas’s Island model oversupply of Labor
Misperception of the price level is a key explanation of the Phillips curve even so in periods when unemployment is low agents have underestimated the price level and work too hard for what real wage they perceive to be high but wasn’t high at all yeah so you don’t know what’s going to
Happen with the money supply in this model you don’t know what’s going to happen in the future interest rates or the future transfer policy of the government you don’t know what inflation is going to be you don’t even know what the real wage is going to be all these
Things are possible sources of uncertainty that can affect the behavior of the economy in the short run okay so that’s going to be the basis for understanding the short-run behavior of the macro economy and you subject that economy to shifts in demand and Supply this will be a source of
Expectational mistakes which could be thought of as one of the Prime determinants of the business cycle okay so just to summarize macroeconomics in the long run we’re interested in the steady state we’re interested in the long-term trends in the short run we’re interested in Dynamics so we’ll spend the rest of the
Semester talking about Dynamic interaction of inflation and output and we’ll have to understand how shocks disturbances that surprise us can lead to under Supply or over over Supply or un deficient demand or excessive demand for goods and services in the beginning you know we the Keynesian approach was to take uh
Take a very sort of naive view of people’s expectations in recent years we’ve become more refined um Robert Lucas said we have to design models that are robust to to changes in policy and um and this is a very fundamental idea which will be driving the rest of this course is which Which
Models do we want to look at which kind of models we think about that show how agents can make mistakes and still recover from those mistakes and the recovery process from these mistakes are what we call the business cycle okay so we talked about slutsky before
The the next part of the course tomorrow we’ll talk next week we’ll the next year we’ll talk about the Asad model as a source of understanding um a very very primitive undergraduate level way of understanding so if you don’t remember how that works check out the appropriate chapters we’ll end up
Thinking about how these shocks these mistakes are culminated into Cycles because it’s not just enough to have a shock a one-time shock but you want to see how the economy adjusts to that shock over time so that’s going to be partially um a way of transmitting or trans
Ferring shocks that are purely random in the sense of this time series White Noise serially uncorrelated constant variance means zero shocks into something like this so we’ll show in January how these random shocks can be actually propagated into a cycle that looks like very similar to what we’d see if we
Looked at the data for inflation or for output growth so this is what I call slutsky’s Vision it’s basically the idea that that’s enough to generate a business cycle these types of unanticipated shocks that get propagated over time through the economic uh Theory so my vision of slutsky here’s
My vision of the holidays have a happy holiday and I’ll see you next year here are the key Concepts to remember and have a nice vacation thank you