I start the recording, and here we go.
It is the lecture on the fiscal theory of the price level,
as I already said.
It is a lecture in the program MSC on economics,
but there may be participants from other fields as well.
That's fine with me.
Welcome to everybody who would like to attend this lecture.
Now, of course, I start with an introduction,
monetary policy and the price level.
And I would like to start this introduction
by immediately pointing out the central questions which
we address in various forms during this lecture,
namely, how is the price level determined in an economy,
and how is inflation determined in an economy.
These are actually the same question.
Determination of the price level and determination of inflation
has a slight technical difference which we
don't need to bother about now.
But basically, it's the same question, of course,
when the price level changes because it's determined
differently, or it's determining causes change somehow,
then obviously we have some type of inflation,
be it positive or negative.
So inflation is just the percentage change
of the price level, and basically the question
how the price level is being determined
is the same as the question how inflation is determined.
So these are the guiding questions
throughout the matter.
Now, you all have had your undergraduate studies,
and I think you may have learned more or less what
I have summarized on this slide in terms
of determination of the price level
and determination of inflation.
So what we typically teach in economics
and undergraduate studies is the following.
There is some central bank in an economy which
controls the money supply.
There are various ways of doing that,
but a particularly important way of doing that
is by means of open market operations.
Open market operations, as you may recall,
means buying or selling assets on capital markets
in order to expand or shrink the supply of high-powered money.
Clearly, when a central bank sells an asset, which it has
on its balance sheet, then it receives money
from the person purchasing the asset.
And since money is always what is outside the central bank
system, money is always the liability of a central bank,
the amount of money is being reduced when a central bank
sells assets.
Similarly, or just conversely, when a central bank
buys assets, like most central banks in the world,
a lot of the world, let's say, are currently doing,
then by buying assets, they pay with newly created money.
They just, in some sense, print the money in the moment
in which they buy something on capital markets
so they expand the money supply.
And to express that somewhat more exactly,
they expand the supply of high-powered money,
which we typically call the monetary base, or M0.
Now, the monetary base is not exactly
what we call money in the daily sense of the word.
But the monetary base is something
which allows the banking system in our economy
to create other forms of money, which we collect
in broader monetary aggregates like M1 or M3.
And you have learned in your undergraduate studies,
I suppose, that there is something
which is called a money multiplier,
or at least we teach you that there
is something like money multiplier.
I will go ahead and question this teaching
in a couple of minutes in this lecture.
But that's typically how macroeconomics undergradates
lectures, monetary theory is taught,
that we teach you there is a monetary base created
by the central bank.
And then in a particular process of lending and borrowing,
this monetary base can be broadened
to include other forms of means of payments of money, which
we then call it 1M3.
And there is some kind of relationship,
some kind of fixed relationship between the monetary base
and the broader monetary aggregates, such that more or less
there is covariational, positive correlation
between the size of the monetary base
and the size of broader monetary aggregates.
Now, if we have changes in the supply of money,
changes in the supply of money used for transactions, M1
or even M3, so not only M0, not only the monetary base,
but also these types of money which we use in daily life,
if we have changes in the supply of money,
then you have been taught that these changes induce changes
in the price level via the quantity equation, which
you certainly recall from your undergraduate studies.
M times V, and V is the velocity of money
is equal to nominal income, price level times real income.
Y and M is, of course, the supply of money.
This is actually not exactly trivial
or it doesn't really follow from this quantity equation
that changes in the money supply.
So a change in M on the left hand side of this equation
leads to a change in the price level
because obviously it is also possible
that V, the velocity of money changes.
So say the velocity of money prints
when the money supply expands.
That could be that there's no things on the right hand side
of the equation.
Or it is possible that real income changes.
Say real income increases due to increases in nominal money.
Then it is also not necessarily the case
that the price level increases.
But in most of your undergraduates,
you have been taught that money is neutral in the long run.
Typically, we speak in macroeconomics lectures
much about short run non-neutrality of money.
And in the short run, money may have real effects
on income, on consumption, on investment,
perhaps even on velocity.
But in the long run, typically, macroeconomic models,
let's say, mainstream macroeconomic models
are structured in such a way that in the long run,
money is neutral with respect to real variables.
And the velocity is a real variable and real income
is a real variable.
So from the quantity equation, it
would follow that the change in the money supply,
nominal money, has to lead to change in price level.
And therefore, we would have some type
of inflation or deflation if nominal money increases
or decreases.
Now, actually, I will not make the point
that anything of that is true in this lecture.
So I will not argue that the quantity equation is true.
But I will argue that perhaps we do not
have embodied the complexities of money creation
in a sufficient manner in order to use the quantity equation
in such a sense that we say, well, an increase in money
increases the price level.
It may still be true in the long run.
I actually believe it is true in the long run.
But the short run is perhaps a much more interesting
and intricate thing to study.
And we will see that the short run, at least,
it is often not the case that with increases
in the size of nominal money, the price level increases.
And then the question is, why is this not the case?
And what actually does increase?
Is the quantity equation useful in the first place?
We will actually study models which do not
have a quantity equation.
We will study models in which there
is no transactions demand for money, which
is at the heart of the quantity equation.
And we will actually study models
in which there is no money, which
is some kind of attempt to explain the price level
completely independently of money.
This is basically the heart of the fiscal theory
of the price level, that the theory aims
at explaining developments of the price level
without resorting to monetary aggregates.
As the cause of these price level fluctuations.
And therefore, it can be helpful to formulate models
in which money is non-existent.
Yet, we still have a price level which can change.
And we will then resort to fiscal variables
as the determinants of the price level.
That's basically the aim of the fiscal theory
to establish such causal links between fiscal variables
and the price level.
And make very clear that movements of the price level
need not have monetary costs.
Obviously, I will not claim that the price level is determined
just by fiscal variables.
That is completely independent of monetary variables.
And no reasonable proponent of the fiscal theory
of the price level would claim something like that.
It is just for the clarity of our thinking
that we look at models in which money is non-existent.
Not because we want to claim that money doesn't have
any influence of price level.
Certainly has some influence.
But not everything which happens at the price level
is well traced back to monetary developments.
And there may actually be situations
in which fiscal variables are perhaps more important,
or at least as important as monetary variables
for explaining the price level.
I already said that the quantity equation
is perhaps too simple to capture all the complexities which
exist in reality between money and its various forms
of appearance, going from high part money
from the monetary base to broad concepts of money.
And the process of money creation
by something which in your undergraduate studies
we have called the money multiplier.
And for that reason, what I want to do in the next slides
is that I first give you some kind of empirical impression
that the quantity equation is actually
doing a bad job when explaining what we observed
in terms of monetary aggregates and developments
of the price level or developments of inflation
in the last years or at least five years, if not longer.
And then to explain to you in a more sort of institutional way
how actually the monetary aggregates develop,
how they interact with each other
or with certain types of economic activities,
and why the quantity equation while not being in any way
false, in some sense the quantity equation
is trivially correct equation because it
can be seen just as the definition
of the velocity of money.
While this equation is not exactly false,
it perhaps makes it more difficult to understand
the correct way of how the relationship
between monetary aggregates and the price level
is because the quantity equation maps
are thinking in such a very restricted equation,
such a very easy restriction which
restricts our thinking and perhaps makes us shut our eyes
with respect to other properties of the economic system
and particular of the workings of the financial system.
So the question which I will raise first
is, therefore, is this kind of economic theory
which we have taught you in other graduating studies
in line with empirical facts?
And then the rest of the lecture I will ask,
well, if that is not the case, and I will show you
that there are at least substantial pieces of evidence
which suggest that it is not in line with empirical facts.
If it is not the case, what is wrong with the theory?
And in order to understand what's wrong with the theory,
it is helpful to get a better understanding of how money
is created and what actually happens with money
in our financial system.
That will be the second part of today's lecture.
OK, let us first have a look at the central bank balance
sheet both in the US and in the eurozone
after the financial crisis.
I start here with the asset side of the central bank
balance sheets in the Federal Reserve System.
Because I had told you that in undergraduate studies
you have learned the money supply is created
by means of open market operations,
that is to say, by buying or selling assets
to expand or shrink the supply of high-powered money.
So here we see in a time series how the Federal Reserve
System in the United States has purchased assets
over a long range of years.
Actually, basically from 2007 onwards,
the trend of the asset side in the central bank balance sheet
is increasing at least till 2014.
Then we have a plateau phase, or it
looks almost like a plateau phase here between 2014
and 2018, so no substantial decrease.
Even though it is true that between 2014 and 2018,
beginning of 2018, even between 2014 and 2018,
there has been a slight decrease of assets.
So the Federal Reserve System has,
much unlike the European Central Bank,
sold off some of its assets in this period of approximately
four years, and that has increased the pace of asset
sell-offs between 2018 and the beginning of 2019.
But then suddenly with COVID, the asset purchases
increased substantially, as you can see here.
So basically, between 2007 and 2020,
we see a huge increase of assets
on the asset side of the central bank's balance sheet
in the United States of America.
And in order to appreciate how big this increase in assets
is, watch out for the scale of the y-axis in this diagram
here.
This is millions of US dollars.
So two millions here means two million millions,
which is two trillions of US dollars.
So the scale here is actually trillions of US dollar,
where a trillion is 1,000 million US dollar.
Sorry, I sometimes get confused with the big numbers.
A trillion is a million million US dollar.
OK, so we see that the Federal Reserve System used
to have a rather constant-looking asset side
of its balance sheet in 2007 and 2008 of approximately $1
trillion of assets.
And then in response to the financial crisis
and the economic depression which followed severe recession,
the United States suffered as a consequence
of the financial crisis of 2008, 2009.
The balance sheet was expanded such
that the volume of assets roughly doubled.
So already, this year is a tremendous increase
in central bank assets.
The number of assets held by the central bank almost,
no, not only almost, it clearly doubled
in a very short amount of time.
And then in the wake of the financial crisis
and until approximately 2014, December of 2014,
the already doubled size of assets as of 2009,
doubled once again to 4 trillion assets.
So in 2014, the Federal Reserve System
was holding approximately four times the amount of assets
it had held seven years earlier in 2007 or 2008.
So it's a massive expansion of assets.
And we will see in a few minutes that this, of course,
goes hand in hand with a massive expansion
of high-powered money in the United States of America.
Then, as I said, for years of a slight reduction of assets,
followed by somewhat stronger reductions,
assets fell below 4 trillion here.
And then came COVID and, again, a huge expansion
of the assets held by the Federal Reserve System.
Here is an analogous graph of what the Euro system has
been doing.
The Euro system is meant to indicate
that it is the Euro CMP in central bank
and all the national central banks abbreviated
and CB.
You may know that in the Eurozone,
the European Central Bank and the National Central Bank,
like the Baca de Talia, Bank de France, Deutsche
Bünders Bank, and so forth, they form the system
of European central banks, ESCB, European system of central banks.
So Euro system can also be abbreviated as ESCB.
And this comprises the European Central Bank
and all the national central banks of the Euro system.
And what you here see in this graph
is the total value of assets held by the Euro system
since it was created in 1999.
So I don't only go back to 2007, 2008 here,
as I did in the graph for the Federal Reserve System,
but I go back all the way to 1999
when the Euro as a currency was created
and the Euro system established.
And then you see that the amount of assets held by the Euro
system was approximately something
below 1 trillion euros prior to 2005.
It increased then over 2,000, perhaps 4, 5, 6,
and very strongly in the financial crisis up to 2008.
And then there were some downs and ups and downs and ups
again.
And the latest up is actually not yet included in the data.
It's going up, up, up, up, up again,
because what I have here is always the balance sheet
per 31st December of each year.
So I do not yet have the balance sheet data
for 31st of December 2020, naturally,
because this is still in the future.
I here end with the 31st of December
in 2019, which is the most recent data available.
Actually, I should perhaps inform you here
that I have just today updated my slides
to incorporate, to include the most recent data which
are available.
There's nothing more recent than what I show you here
for the Euro system.
If you have downloaded my slides prior to today, so yesterday
or even earlier, then you will see
that the old set of slides, these graphs
were not yet updated and some other information was also
not yet included in the set of slides.
So if you want to go through the slides again,
perhaps use them for exam preparation
or for student contributions, then
download the slides again from Stine,
please, since there have been changes.
And in general, that may happen often
that I do modifications to the slides that I have uploaded
to Stine as new information comes in
or as when I prepare for lecture, I think perhaps
I should change something.
So it's not an exception, but perhaps rather the rule
that I will present you in the lecture slides, which
do not correspond one-to-one with the slides
that you have downloaded just a day before the lecture.
Perhaps it is wiser that you download slides after the lecture
rather than prior to them.
OK, so that's the Euro system's development
of the asset side of its balance machines.
And we see that the Euro system also
reacted to the financial crisis of 2007, 2008
with an increase in assets, reduced the asset slightly
already in 2009, increased again a little bit in 2010.
And then there was, of course, the sovereign debt crisis
in the Euro zone, which the United States of America
did not experience and did not have any trouble at this time.
So there was, again, a huge increase in assets
in the Euro system, which led already in 2012
to a peak in asset holdings of about $3 trillion, which
is more than three times the amount the Euro system has
held, say, at the beginning of this century in 2002
or something like this.
So also a great expansion of assets and debt, as we would see,
goes hand in hand with an increase in the monetary
base.
Then assets were reduced again as the sovereign debt crisis
seemed to come down, or people hoped
that it had come down, pretended that it had come down.
But then the conviction spread out
that perhaps not all is good in the Euro zone.
And countries need more support, and the European Central Bank
started in 2015, actually.
It's expanded as a purchasing program
where the amount of assets purchased
by the European Central Bank and National Central Bank,
so the amount of assets actually held,
because these are holdings here, by the Euro system increased,
again, by a tremendous amount going from, well,
this was the peak here of $3 trillion.
We were down below $2.5 trillion in 2014,
but then it increased to almost $5 trillion in 2018
and has not settled down in 2019,
will increase again considerably in 2020.
So also a great increase in assets held by the Euro system.
What is interesting about the Euro system's balance sheet
is that the instrument used to increase
the assets of the Euro systems changed over time.
You will find the legend on the next slide
to read what kind of components make up
the assets of the Euro system, but I can tell you already,
this year, for instance, is gold and gold certificates
and these kind of things, which also increased over time
or had some fluctuations over time.
But obviously, the big increase in asset holdings
is not due to gold, and it's not due to this blue here,
which I forgot what it was, and it is due partially
to increases in this light blue here,
which are actually loans to banks in the Euro system.
These are in particular so-called long-term refinancing
operations of the European Central Bank,
so-called ETROs or TELTROs, targeted long-term refinancing
operations, of which there were two big waves,
as you can see here, where these kind of loans to the troubled
banks of the Euro zone were increased by a great amount
and later than decreased again, because these refinancing
operations usually terminate after a maximum of three years.
So these were transitory increases in assets held
by the Euro system, but they, not all of them,
but mostly they went back to where they came from
and have stayed constant since 2015.
When in 2015, as I already told you,
the European Central Bank changed its market operations
and now purchased a great amount of government bonds
on the open market.
And this is this violet area here,
the holdings of government bonds, which the ECB started in 2015.
It has expanded since to yield asset holding
in terms of government bonds of almost 3 billion,
3 trillion, excuse me, 3 trillion euros worth.
And it is even more today, because as I said,
the COVID-19 extra purchase program, PEPP,
is not yet included in this type of data.
Here is the legend.
You see the balance sheet, just to give you an example,
as it was at the end of 2018.
And the violet here is described in technical terms
by the European Central Bank as securities of euro area
residents denominated in Europe.
These securities are overwhelmingly
like government bonds.
There are also some other type of securities
like corporate bonds, covered bonds,
but mostly it is government bonds.
Today about 2.3 trillion euros of government bonds
and the rest is other types of assets
the European Central Bank and the National Central Bank
acquired from euro area residents.
And as I said, the slide blue here
is lending to euro area credit institutions related
to monetary policy operations denominated in Europe.
This is the other big item on this balance sheet here.
You see the sum of all the items on the balance sheet
is 4.7 trillion in 2018, of which almost 3 trillion
of the 4.7, so really the biggest part,
is assets purchased under the purchasing programs,
so-called EAPP, expanded asset purchasing program.
And the next important issue, the next important position,
sorry, in 2018 was still the Eltus and Teltus
of the European Central Bank.
So the specific loans given to banks in the euro system
to improve their shaky economic position.
OK, and so what we have seen here, sorry, yes,
what we have seen here is the asset side
of the balance sheet of the European Central Bank
and of the Federal Reserve System
as two of the major banks in the bird economy.
And the reasoning we taught you in undergraduate studies
would actually suggest that by doing market operations
at a great, great scale, the supply of high-powered money
would increase in a similar way.
And then by the money multiplier, real money,
I mean, nominal money in terms of transactions money,
like a one or a three, also increases by a great amount
and that translates then in huge inflation.
And here now you see the inflation rate in the euro zone.
This is the so-called harmonized index of consumer prices,
which I have used here to compute an inflation rate.
Harmonized index of consumer prices.
I computed the inflation rate for this harmonized index
of consumer prices.
And you see that not much is going on in terms of inflation.
Actually, inflation levels in the year 2000s until 2007,
approximately, were basically at least as high, if not higher,
than inflation levels in the subsequent years,
despite of the fact that in the years since the financial
crisis, there has been this huge increase in the balance
sheet of the European Central Bank
and thereby in money, either high-powered money
or we will have a look at that soon,
other forms of broad money aggregates.
Despite of the fact that the money increased,
despite of the fact that assets and as we
see monetary base and other aggregates increased greatly,
the inflation rate does not reflect
these enormous changes in the central bank's assets sheets.
And this suggests that perhaps our thinking is,
and the way at least you learned it in undergraduate studies,
at least too easy, if not wrong.
It does not seem to be the case that there
is some kind of automatic increase in the price level
or automatic rise in inflation if the central bank increases
its holdings of assets and increases the supply of money
in the way in which the quantity equation suggests
this given constant velocity and constant,
or approximately constant, real income.
Now, you may ask, is this an exception?
Is this perhaps due to a depression
we've had in the eurozone during this over debt crisis
and after some of the eurozone countries still
having troubles finding bank to growth paths,
to growth of the GDP?
Is perhaps the case that real GDP contracted
while the money supply increased?
And well, would this actually solve the problem that,
no, it would not.
We would need to see a strong increase in real output
in order to prevent the price level from increasing,
given constant velocity.
But clearly, we have not seen such a strong increase in output
as we have seen an increase in assets
purchased by the European Central Bank
and National Central Banks.
So that the question remains, why don't we
see an increase in the price level?
Why do we have very, very moderate degrees
of inflation, which actually falls below zero sometimes?
Not permanently, fortunately, so far.
No deflation on a permanent level so far.
But clearly, there are occurrences,
or more of them here also, in the financial crisis,
where very briefly, we have negative inflation.
That is to say, we have deflation in the eurozone.
Is that an exception?
No, it is not.
Here, we look at the inflation experience
of the United States of America.
And here, I use the CPI inflation rate
from July 2007 to October 2020.
And you see this inflation rate is rather constant, actually.
At least there is no upward trend in inflation,
or no persistent increase in inflation
in response to the extraordinary monetary measures which
the Federal Reserve system has enacted
in the wake of the financial crisis 2007, 2008, 2009.
It's not so clear when you date exactly the financial crisis.
The beginning of the financial crisis
with the first banks collapsing was actually already 2007.
But the crisis increased in importance and size
during 2008, mainly.
And the main recession then was in 2009.
So this is why I sometimes use these dates, 2007, 2008,
2009, without being very precise there.
In any case, we have seen that the Federal Reserve system has
increased its asset holdings and never expanded its money
supply, but there is not really a dramatic increase
in inflation.
Quite to the contrary, inflation is, if anything,
perhaps more stable than it used to be,
and perhaps even on a lower level than it used to be,
at least during the years 2008 and 2009, where inflation
was clearly above 2%.
Whereas here, inflation fluctuates quite nicely
around 2% in the years from 2017 to 2020,
with a drop in inflation due to COVID.
OK, so broadly speaking, I think it's
fair to summarize these two graphs
by saying that the development of inflation rates in the US
and in the eurozone between 2015 and 2019
is broadly similar.
However, recall, we have almost constant inflation
in these years, 2015.
No, perhaps, sorry, I was starting 2015 now.
2015, we have in the US first rise in inflation
from almost 0% to 2%.
So here, a clear increase in inflation.
And then basically, until the beginning of 2020,
a constant level of inflation, and compare this
to the development we had in the eurozone, 2015 is here,
as first an increase in inflation,
and then more or less a constant level of inflation, perhaps not
quite as constant as in the United States,
and then a decrease starting in 2020.
I will show you another picture which
makes this point perhaps even more visible than my explanation
here, but just following what I've just said on the two
graphs, it should already be heard
that despite the different scaling of the two graphs,
it seems to be the case that the inflation development
in the eurozone and the United States of America
is not all that different during 2015 to 2019.
Now, why do I focus now on 2015 and 2019?
I do this because 2015 to 2019 was the period of time
where the European Central Bank greatly purchased assets,
and in particular, government bonds,
in forms of open market operations.
We've seen this here.
2015 to 2019, this is this increase here.
Basically, this is end of 2014.
So in 2015, this increase in net assets happened.
So the euro system was really going
into open market operations at that time,
and really expanding the supply of high-powered money
available to banks, and thereby expanding the money
supply in the economy and in the banking,
in the commercial banking system of the eurozone.
Whereas, sorry, wrong way, whereas between 2014 and 2019,
the Federal Reserve System did not at all acquire new assets.
Rather, they sold off new assets.
First, as I said, very, very slowly,
then even a little bit more strongly.
So between 2015, this here basically
is the beginning of 2015.
And the end of 2019, in these five years,
the US Federal Reserve has done exactly the opposite
of what the European Central Bank has
been doing, which increased its assets greatly, which more
than doubled its assets greatly, while the Federal Reserve
System at least slightly reduced assets
and sold off government bonds.
And yet, the development in terms
of inflation between 2015 and 2019
is broadly the same in the US and in the eurozone.
Here you have it all in one graph.
These are the same data, just in a different graph.
Does the inflation rate in the United States of America
and in the euro area between 2015 and, well, end of 2019
is here, end of 2019 is here.
So basically, you can see more or less
the same development in the eurozone
and in the United States of America.
Of course, there are minor differences.
There is a phase here where the euro area inflation actually
fail, despite purchases of government bonds
at a greater scale, whereas inflation
rose in the United States of America,
despite government bonds being sold off
by the Federal Reserve System.
But apart from these type of more or less secondary
deviations in the development of the inflation rate,
the broad development in the US seems
to be the same as in the eurozone,
even though central bank policy attempts
to control the money supply to steer the money supply
in a certain way, either increase it or decrease it,
was extremely difficult.
That raises, of course, questions
of whether our perception of what happens in money markets,
what happens in the control of the money supply,
what happens in terms of developments in the macro
economy, the relationship between supply of money
and the price level, whether these concepts are correct
or it is approximately correct, or if they are perhaps
approximately incorrect, just a tiny little bit correct.
These are the questions we want to go
in the course of the lecture.
I have three hours of lecture to give to you today,
and I have already spent quite some time on that.
What I will do now is that I will summarize basically what
you have already learned from the graphs just again
in order to have it neatly pinned down on one slide.
And then I will make a break.
I suggest perhaps 10 minutes time for you to have a coffee
or to relax or something like that.
And we will meet again to continue for another 45
minutes after this break.
OK, note the following things.
The EuroSystems public sector purchasing
program, which is the program by which the EuroSystem purchases
government bonds, started in 2015.
At this point in time, the inflation
measured by the standard harmonized index of consumer
prices.
The inflation in the euro area was already rising, right?
Inflation was already rising before the EuroSystems
started its great purchases of government bonds.
From January onwards, inflation was on the rise,
and well, EuroSystems purchases began approximately here
in March.
No, actually, I think it was announced in March,
and purchases began in May, which is possibly even here.
When the EuroSystems enacted its purchases of government bonds,
so increased the money supply, the inflation rate,
and the euro is actually decreased.
That's actually the next remark here, which should read,
I just note that there's no mission here,
from May 2015 to April 2016, euro area inflation
fell despite large asset purchases, right?
This is approximately May 2015 to April 2016,
where despite of the big, extremely big purchases
of assets by the European Central Bank
and the National Central Banks, the inflation rate
was completely unoppressed by that in the euro zone,
and fell from approximately 0.6 or something like this
to something which is negative, right?
OK, now let's compare that with what
happened in the United States.
HICP inflation rate in March 2015
was virtually equal to the CPI inflation rate in the US.
You know that in the US, quantitative easing
had just ended.
So the US was not buying bonds anymore,
but rather they were slowly selling off bonds.
So in March 2015, inflation rates in the US
and in the euro zone were almost the same, basically 0%, 0%
here, right?
But then the development was completely different.
Shortly after net purchases had begun in the euro zone,
inflation rates fell, whereas at the same period in time,
basically US inflation rose despite sending off assets.
This is the next sentence here.
US CPI inflation rose sharply during 2015,
although there were no net purchases of assets by the Fed.
Quite to the contrary, there were net sell-offs of assets.
From mid 2016 then to mid 2019, inflation rates in the euro
area and in the US moved surprisingly parallel.
Although the central bank's balance sheets
moved in opposite directions, the Fed selling off assets,
the euro system purchasing assets.
From mid 2016, approximately here, all the way to 2019,
there's a largely parallel movement of inflation rates
in the United States of America and in the euro zone,
despite different monetary policy.
Yes, and then last thing to note,
after the outbreak of COVID-19, both central banks
increased net purchases.
So here, both central banks were doing the same thing.
But now, surprisingly, inflation moves
in the opposite direction.
So it's difficult to make sense out of that, I would say.
Inflation often moves exactly in the opposite direction
of what we would expect given certain open market operations
by a central bank.
And sometimes, it may actually happen
that two central banks do exactly the same thing.
And inflation and the two currency areas
does exactly the opposite thing.
So the question which I would like to raise before breaking
is, do we as academics, scientists, future scientists,
or do the central banks actually have any idea how
the price level is determined?
That is the central question of this lecture.
And I will continue this type of empirical demonstrations
after the break, which would be in 10 minutes time.
Please be back in time for that.
Thank you very much.
Bye.
Thank you.
Thank you very much.
Thank you.
OK, I hope you are all back.
Let me continue by first asking you
if there are any questions concerning what I have
presented to you today so far.
I think I did not see anything coming in.
No.
All right, good.
So the question is, do we actually
know what happens when price or the price level forms
and how price level is determined?
Good.
Let us go to the process of money creation
and the way in which it is typically
taught at an upgraded level in order
to understand what perhaps inhibits
our deeper understanding of the relationship
between money and the price level.
A good reference to what I'm going to present now
in a more formal way is this article here
by McLee, Radia, and Thomas, Money Creation
in the Modern Economy, which you find in the quarterly journal
of the Bank of England in 2014.
We start out with what we already had, namely
the Fisher equation, the quantity equation,
m times the velocity of money is identically equal to p times y.
I've written this here with an identical equal sign
in order to emphasize that this equation is actually always
true because essentially it just defines
what the velocity of money is.
So one question we may consider is,
what actually determines p?
Is this really a constant?
We usually teach this in undergraduate economics,
or does it depend on something?
Does it depend on economic data, like say interest rates
or something like that?
How is it determined?
What we teach you in undergraduates
is what I would like to call a fairy tale.
It is only decently related to what happens in reality,
as you will see shortly.
This is the fairy tale of the so-called money multiplier,
and its derivation is typically done as follows.
We have m as money used for transaction purposes.
So this is the m, which we find here in equation 1,
the quantity equation.
This quantity of money we can decompose into currency,
so bank notes basically and coins,
and deposits, demand deposits, which we have at banks
which we use when we pay by bank transfer,
by credit card, by checks, for instance,
Americans, I think, still pay by checks.
So it's currently currency and bank deposits,
and typically what we teach is then that households
hold a fraction, small c, of their money stock, m,
as currency, and the rest of their money
they hold as a bank deposit.
So 1 minus c, the fraction 1 minus c of total household
money is held on banks, and a fraction c
is held as currency.
Banks, on the other hand, have to hold reserves,
which we denote by r at the central bank.
And often it is the case that the central bank
or the banking authority which shapes banking regulation
requires r to be a fraction of the demand deposits.
So bank reserves are required to be
proportional to demand deposits.
The higher deposits r at the bank,
the more reserves the bank has to hold at the central bank.
Let's call this fraction theta.
High power money, the monetary base,
is therefore given by what I denote here as h,
the amount of currency issued by the central bank,
and the reserves.
Why is this so?
Well, because on the balance sheet of the central bank,
you will see that these are the liabilities of the central bank.
On the one hand, the central bank has issued bank notes,
and the bank note basically is a liability
of the central bank because it is a claim any citizen who
holds a bank note has against the central bank.
Even though we are not used anymore
to go to the central bank and ask the central bank
to satisfy this claim, but we just
content ourselves with trusting in the value of money
using this claim for paying somebody else
and not going to the central bank.
Actually, we are not allowed anymore to go to the central
bank and receive anything in exchange for that.
But in principle, the origins of the systems,
it was the case that with the bank note,
say in the 19th century, with the bank note,
you could go to the central bank and request
that you receive gold in exchange for this bank note
so that the claim you have against the central bank
is satisfied by deliverance of a certain amount of gold,
precious metal, in exchange for your certificate
for your bank note.
OK, so that's a liability.
The bank notes are liability of the central bank.
And the reserves, which commercial banks hold
at the central bank, are also a liability of the central bank
because obviously the banks then have claims
against the commercial banks.
I mean, the commercial banks have
claims against the central bank.
They can request that the central bank transfers
reserves, which bank A has, to somebody else
where this typically is also a bank.
Where does it say that bank B, at least modern economies,
typically your reserve money is not transferred to private
agents, but it's just transferred to other banks.
But that's not so important.
Important is that bank A, which holds reserves
at the central bank, has a claim against the central bank
and may request that the reserves are transferred
to somebody else, to another bank.
So the reserves are a liability of the central bank.
So currency is a reliability of the central bank related
to money, and reserves is a liability of the central bank
related to money.
These two together, the sum of these C plus R
is the monetary base.
This is so-called high-powered money.
And we know from the assumption that we
have made that reserves are a fraction theta of deposits.
So we can also write high-powered money as C plus theta times
D if we believe in this logic, which we typically
teach you in other grades.
Nice.
We also know that currency is a fraction of money.
And deposits is the remaining fraction of money.
So currency is C times M, and deposits
is 1 minus minus C times M. So we
know that high-powered money is C times M plus theta times 1
minus C times M. And then it is easy to solve the equation
for M. And we get M, the actual amount of money
used for transactions, say M1, is equal to the monetary base
H divided by C plus theta times 1 minus C.
This ratio here, 1 over C plus theta 1 minus C
is greater than 1.
And that is called the money multiplier.
Now, is it trivial to see that this thing here
is greater than 1?
Yes, indeed, that is trivial to see,
because we know that if theta is equal to 1,
then we have the numerator C plus 1 minus C.
So the numerator would then just be 1.
But theta is smaller than 1, because obviously, banks
are not required to hold all their deposits as reserves.
It is much smaller than 1.
So this is C plus less than the complement of C.
And therefore, the denominator of this ratio here
is smaller than 1.
And therefore, the hold ratio is greater than 1.
And it is called in undergraduate economics
the money multiplier.
Now comes the actual fairy tale.
The fairy tale goes like that.
Banks need deposits to lend out a fraction of these deposits
to new debtors.
So what we typically tell you when
we present the multiplier story to other graduate students
is that there are people who have money, private agents who
have money, and they bring this money to the banks
or they deposit this money there.
You may say they save the money on a bank account.
So the bank receives a deposit.
And can then take the money which
is deposited with the bank to lend it out to somebody else
or, to be more precise, to lend out just a fraction of this
money to other people, debtors, people who take up a loan.
And the fraction which the bank can lend out
is, of course, 1 minus theta of the deposits,
because the fraction theta of the deposits,
the bank has to hold as a reserve at the central bank.
So the commercial bank has to hold fraction theta times
deposits at the central bank.
And the rest, 1 minus theta times the deposits,
may be lent out to debtors.
Well, what do the debtors do when they receive a loan?
Let's say, just to structure our thinking,
it isn't necessarily so.
But let's say the debtors deposit the money they lend.
They borrow from a commercial bank.
They deposit this with some other bank.
So this other bank also receives a deposit.
And it can then lend out a fraction, 1 minus theta
square, of the initial deposit of the first deposit
the first customer was doing.
The second bank receives a deposit of size 1 minus theta
times d.
And it can then lend out 1 minus theta squared times d
to a third, 2 to a second debtor.
And the second debtor, of course,
deposits the money again with another bank.
And this bank, again, lends out a fraction 1
minus theta of the new deposit, which
would be 1 minus theta squared, 1 minus theta
to the power of 3 of the initial deposit.
So the story we tell you is that there
is a customer, A, who receives somehow,
and we never explain how, one unit of high-powered money.
He keeps the C units as cash and deposits 1 minus C units
with bank number 1.
So I start now numbering the customers and the banks.
Customers have alphabetical letters, A, B, C.
Banks have numbers 1, 2, 3.
So let's say customer A has one unit of high-powered money,
which somehow drops from the sky.
Helicopter money or something like that.
This receives one unit of high-powered money.
And then splits this into C units
as cash and 1 minus C units as deposits with bank 1.
Bank 1, then, according to this logic,
must hold reserves of 1 minus C, which is the deposit, times
theta.
So this is the reserve at the central bank.
So bank 1 can lend out only 1 minus C times 1 minus theta
to customer B. Customer B then chooses
to hold a fraction C of this amount here, this loan, which
he has taken up at bank 1, as cash.
So he holds C times 1 minus C times 1 minus theta as cash.
And therefore, 1 minus C squared times 1 minus theta
as deposits with bank 2.
So bank 2 has received deposits,
which are 1 minus C squared times 1 minus theta times
1 unit of high-powered money.
And on this bank, 2, of course, has
to hold reserves, which would be theta times exactly
this amount of deposits here.
So up to this step, we have that currency
is being held in the magnitude of C times 1.
This was the initial unit of high-powered money,
plus 1 minus C, 1 minus theta.
This was sort of what the first loan generates
in terms of new currency.
Deposits, which would be 1 minus C times
exactly the same amount here.
And reserves, which would be 1 minus C times theta
times this amount here.
Bank 2, then, you can imagine the process continues,
can lend 1 minus C squared times 1 minus theta squared
to customer C. And customer C chooses
to hold a fraction small c of this amount as cash.
And a fraction 1 minus C of this amount as deposit.
So the new deposit will be 1 minus C
to the power of 3 times 1 minus theta squared.
That's the new deposit with bank 3,
which is the bank of customer C.
And on these deposits, bank 3, again, holds reserves.
And these reserves will be a fraction theta
of the deposits, which is 1 minus 3 to the 3 times 1
minus theta squared.
Now, this gets a little messy if you do this over and over
again.
But three steps, like we have done them here,
suffice actually for seeing how this thing builds up.
If we repeat this process infinitely often,
then we find that the amount of currency
is small c times this infinite sum here
over 1 minus C to the power of i, 1 minus theta
to the power of i.
This is C times 1 minus C squared, 1 minus theta
squared for customer C. And it was C times 1 minus C, 1
minus theta.
So both raised to the power of 1 for customer B.
And it was just C times 1 minus C to the power of 0,
1 minus theta to the power of 0.
So both is 1 for customer A. So you
can verify the correctness of this formula here.
Currency is small c times this infinite sum here.
This infinite sum is, of course, using
the formula for a geometric series equal to 1
over 1 minus this term here, which
is raised to the power of i.
So 1 minus 1 minus C, 1 minus theta.
And this thing multiplied by C, which
is the term in front of the sum, it
gives me, if I simplify the expression down here,
C over C plus theta times 1 minus C. In the same way,
we can calculate what deposits are.
And that's very easy because deposits
is just the complement of currency.
Currency was C times this infinite sum.
Deposits is 1 minus C times this infinite sum.
So it is 1 minus C divided by C plus theta times 1 minus C.
And then we can compute very easily what reserves are.
Reserves are a fraction theta of deposits.
So just multiply this expression for deposits,
which we have computed by theta, and there you are.
This is exactly the same thing as what I have written down here.
So repeating this process of lending and borrowing
infinitely many with infinitely many customers,
with infinitely many banks, each customer has a separate bank,
we arrive at these type of quantities for currency,
deposits, and reserves.
And we know, of course, currency plus reserves
is high powered money.
And currency plus deposits is money.
So we find M is equal to currency plus deposits.
And that is then simply 1 over C plus theta times 1 minus C
per unit of high powered money because we started out
with one unit of high powered money.
Obviously, if we have H units of high powered money,
then the money we use, M, is equal to H over C plus theta
times 1 minus theta.
So this is the same formula we had already derived here.
M is equal to H divided by C plus theta times 1 minus theta,
or H multiplied by the money multiplier.
So this whole process, which I have just described,
is just an illustration of why there is a money multiplier
in the way in which we teach it in other graduate studies
and why high powered money is being inflated in some way
to a broader monetary aggregate.
In this case, this is actually M1, currency plus demand
deposits is M1, by this money multiplier.
It observed that this money multiplier here
implies that as long as the customer's decision
to have a certain split between currency and deposits
is not changed, so long the C here is constant,
and as long as the reserve requirement is constant,
we would expect that high powered money
is exactly proportional by this factor of proportionality here
to M1.
Well, and as I already said, high powered money is C plus R,
and that is equal to 1.
You can verify that C plus R is equal to 1 just
by adding this and this here, and then you
immediately see C plus 1 minus C theta divided by C plus 1
minus C times theta is equal to 1.
OK.
So this way of viewing the process of money creation
suggests that the central bank steers the quantity of money,
so money needed for transactions, M,
by controlling currency, which is
issued by the central bank, and reserves.
Reserves are not issued by the central bank,
but reserves are controlled by setting the reserve
requirements theta, which is something the central bank is
entitled to do.
The problem with all this fairy tale
is that this model of money creation
has little to do with reality.
One reason for that, not the only one,
is that the central bank can only
control the required reserves.
The central bank can determine this theta here,
which is the percentage of deposits,
which banks are required to hold as reserves.
But today, most reserves which banks hold at the central banks
are so-called excess reserves.
One flaw of the analysis we have done
is that the R in our little model
here is both required reserves and excess reserves.
And this we have not properly taken into account
when setting up this model here.
Now, let us confront the model with reality
because I claimed that this model of money creation
has little to do with reality.
We look again at the Federal Reserve System's balance
sheets, expressed in millions of US dollar.
And I have just picked two years of which
we know that the balance sheet was looking very different,
2006 and 2017.
So the Federal Reserve System was holding gold or gold
certificates, which did not change.
It's actually a small amount relative to the whole volume
of the balance sheet.
There were certain securities purchased
under agreements to resell.
That was a small amount here that has gone down to zero,
but it was a small amount first place.
So it's not a great change.
And then there are US government securities.
US government securities basically
means government bonds.
In 2006, the Federal Reserve System
was owning almost $800 billion of US government bonds.
And that has increased until 2017 to $2.5 trillion,
so $2,500 billion US dollars worth of government bonds.
So that's a great increase in government bonds.
And that's a very sizable share of the total increase
in assets, as we see it here in total volume, which
increases from $800 billion to $4.4 trillion or $4.5 trillion.
It was, however, not only government bonds in the US
Federal Reserve System, which led to the inflation,
to the expansion of the balance sheet of the central bank
of the Federal Reserve System, you
see there are also mortgage-backed security, which
is a debt instrument which is not so popular with the European
Central Bank.
We don't really find it at prominent positions
in the ECB's balance sheet.
But as you see in the Federal Reserve System,
that's a very important position.
There were no mortgage-backed securities in 2006,
but there are almost $2 trillion mortgage-based securities
in 2017.
So these are the two positions in the balance sheet, which
are accountable for the huge increase in the balance
sheet of the Federal Reserve System,
because the other positions down here
are, again, of just lesser importance.
Investment in foreign currencies have hardly changed,
and they are a small position.
Other assets have changed.
Actually, they have tripled, but that's still a small position
compared to the numbers we have here.
Now we have seen this increase in assets already in the graphs
I presented earlier in this lecture.
Now let's look at the other side of the balance sheet
of the Federal Reserve System at the liabilities side.
So on the liability side, you find,
as the first position, Federal Reserve notes.
So these are bank notes.
And you see that the amount of bank notes between 2006 and 2017
has roughly doubled from almost $800,000 to almost $1.6 trillion.
Sorry, about $800 billion to $1.6 trillion
to get the numbers right.
There's also another increase, which is sizable.
Security sold under repurchase agreements.
Not quite as sizable as here, but it is, indeed, sizable.
And then there are bank deposits, which go up greatly,
from the $19 billion, which we have here,
to $1.9 trillion, which we have here.
So that is more than 100 times, so the amount in 2017,
is more than 100 times the amount in 2006.
There's a great, great increase here,
and we know that Federal Reserve notes, bank notes,
which is currency, and reserves, is high-powered money.
So that's the monetary base here.
There's also this particular issue of security
sold under repurchase agreements,
which is not part of the monetary base.
That has also increased, no doubt about that.
But we ignore that now,
because it actually doesn't really enhance
our understanding of what happened here.
It's completely sufficient to see that the monetary base,
high-powered money, has increased by great amount
in the United States, so in the Federal Reserve system.
Roughly speaking, we have 800 billion
of high-powered money in 2006,
and these two positions up, it's basically 800 billion.
And here we have, roughly speaking,
3.5 trillion U.S. dollars in terms of high-powered money.
Let me add that the reserves we see here in 2006
are mostly required reserves.
So this is what banks had to hold
as the ratio, theta of their deposits.
But the 2017 position here is basically excess reserves,
and these excess reserves,
they have increased from virtually zero
to this huge amount which we have in 2017.
Here the numbers are again, just the same numbers,
but presented in a different way
to make perhaps a little bit more suggestive
of what I want you to learn in this part of the lecture.
High-powered money was 800 billion in 2006,
and it was 3.5 trillion in 2017, or the end of 2017.
So it is fair to say that high-powered money
in the United States in these 11 years here
has more than a quadrupled.
This is more than four times the amount in 2017
than it was in 2006.
If our money multiplier story were approximately correct,
then we should see a similar increase
in money used for transactions.
I don't have M1 here, but I use M3.
We see money stock M3 in the US was 7 trillion in 2006,
and it was 14 trillion in 2017.
So the money stock has only doubled,
even if I take the broad definition of M3,
has only doubled, even though high-powered money
has quadrupled.
So there is apparently not a constant money multiplier
at work in explaining these numbers here.
Now, how does this relate to the price level?
We see that the money stock has doubled,
and the price level from 2006 to 2017
increased from 203 to 249.
So this is an increase of 50% and not an increase of 200%.
This here would be an increase of 200%.
That's an increase of 50%.
No, not 50% of 25%, sorry, of 25%.
So that's a great difference, obviously.
The price level also does not develop proportionally
to the money stock, which is at odds with the quantity equation.
So these numbers here indicate to us
that the simple reasoning you have
in taught in undergraduate economics,
and let me say it's not your fault
that you were taught this type of content,
that the simple economic reasoning we
taught you in undergraduate studies
is wrong along some very important dimensions.
The story of the money multiplier
does not seem to be correct.
It is grossly refuted by the data.
And the story of the quantity equation
also does not seem to be correct, at least not
in a period of time, which extends over 11 or even 12
years here, 2006 to 2017 is, I think, 12 years.
So that's not just explained by saying, well,
this is a short-term effect.
11 or 12 years is already quite close to the long run.
And still we don't see the effect
of the increase in the money stock reflected
in the same way in the price level.
There is some increase in prices, no doubt,
but by far not as much as the increase in the money stock
would imply, and by far not as much as the increase
in the monetary base would suggest
if the money multiplier were a constant.
So the conclusions we can draw up to here
is that there seems to be no constant money multiplier.
And therefore, it is unclear if the central bank actually
controls the stock of money.
Plus, it seems to be the case that there
is no constant velocity of money.
And therefore, it is unclear how the price level is determined.
Let us do the same type of analysis of the euro system.
Again, the balance sheet, this time for years 2006 and 2018.
There are gold certificates.
They have increased.
I pointed that already out when I explained
the graph or the asset side of the balance sheet to you.
It's not a great increase, though,
compared to the increase in the total volume of the balance
sheet.
You see here the increase is about $200 billion.
But here we have an increase in the order of magnitude of $3.6
trillion.
So that's a small increase in mechanic art.
Main refinancing operations have gone down, actually,
from $330 billion to virtually nothing.
Long-term refinancing operations.
These are those electrodes, which I have already mentioned,
have increased.
These were other types of attempts
by the central bank to increase the money supply.
And I won't concentrate on them now.
But I would like to point out that there
has been a substantial increase in these electrodes
between 2006 and 2018.
And then there are the securities.
And as I said, the securities are mostly government bonds.
But they also include other securities
like covered bonds or corporate sector
bonds, which the European Central Bank or the National
Central Banks have acquired on the open market.
They have increased from virtually nothing
to $2.9 trillion in 2018.
And then there's, again, a smaller position
about investments in foreign currencies.
Has increased a little.
And other assets have also increased a little bit.
But nothing as sizable as the increase in government bonds
or better in assets purchased on the open market, which
leads to this enormous increase in the size of the Eurosystems
balance sheet, as far as the asset size of the balance sheet
is concerned.
Now to the liability side, which, of course,
mirrors the asset side.
So the numbers down here are, of course,
the same as the numbers on the asset side of the balance
sheet.
We see that bank notes have increased.
Circulation of bank notes has increased greatly
between 2006 and 2018.
So that's, again, basically a doubling of bank note
circulation, much the same as we saw it in the Federal Reserve
balance sheet.
And then there are bank deposits, reserves.
Again, and these have not only doubled,
they have increased by a factor of 10 or more.
So here, again, in 2006, the 174 billion euros of bank reserves
were basically required reserves.
But banks were forced, compelled to hold.
And here, much of that is actually
excess reserves, which banks hold at the European Central
Bank or the National Central Banks,
but are not required to hold there.
We'll talk about the interest rate on these excess reserves
in the next lecture, actually, because it's negative.
Still banks hold reserves there.
Then there are liabilities to non-banks.
That's a position which I also mentioned because it
has increased greatly.
But it is not so important for our current purposes
because it doesn't count to the monetary base.
The monetary base is the sum of these two numbers in 2018
and these two numbers in 2006.
So we see that the monetary base was much, much smaller
in 2006 than in 2018.
And then there are also other items.
And there's also an increase, which
is not so important for our current purposes
and total capital and so forth.
This does not matter.
Much important are the yellow entries in this little table.
Summarizing these numbers here, high-powered money was.
That's not true.
Where am I?
Is this a coincidence?
Is that 802 is the same as with the US system?
Let's check.
So if we add this up, this is indeed a 2 here and a 0 here.
And again, OK, so I was confused.
But that's a funny coincidence that it is high-powered money.
And euro is exactly the same number
as it was in dollars in the US Federal Reserve system.
I didn't notice this early on.
But that's, of course, just a coincidence.
So we had 800 billion euros high-powered money
at the end of 2006.
And we have more than 3 trillion at the end of 2018.
So that's slightly less than a tripling of high-powered money
in this period of 12 or 13 years.
And the money stock, M3, has by far
not expanded at the same rate of growth.
We see M3 was 7.7 trillion end 2006.
And it was 12.3 trillion in 2018.
So that is not even 50% of the initial M3 money
stock, which is the increase in M3 money.
There's no doubling.
By far, no doubling.
There's certainly no tripling of money stock M3.
As for the price level, we had a price level
in terms of the harmonized index of 87 in end 26.
And we had 104 in end 2018.
So there is a little increase in the price level.
But the increase in the price level
is by far not as strong as the increase in M3.
And the increase in M3 is by far not as strong
as the increase in high-powered money.
So that, again, we may conclude there
seems to be no constant money multiplier.
Because if there were, then the increase here
should be mirrored by an increase of similar size
in money stock M3.
But we don't see a similar size.
We see a much smaller increase in actual money
than the central bank has generated new high-powered money.
And therefore, again, it is unclear
if the central bank controls the stock of money.
And there seems to be no constant velocity of money.
The quantity equation cannot be used in an easy way
to establish a causal link between money
and the price level in the way in which we teach it
in other gradients studies.
Because we still have a sizable increase in M3,
even though it is less than 50% growth rate.
This growth rate is much greater than the growth rate
we have here for the price level increase in terms
of the harmonized index, where we have perhaps 20% increase
roughly in the price level, rather than almost a 50%
increase in the money stock.
So it is unclear how the price level is determined.
And this is why we want to study this question in more detail.
Now, knowing that whatever you have
learned in other graduate studies
does not do a great job when explaining
those numbers, which we have seen in recent years
in major economies of the Western bird.
Good.
I think I will stop here for today.
Next lecture, I will try to correct the fairy tale
and point out what is wrong with our concept of money creation,
the way we teach it to undergraduates.
Before I actually finish the lecture,
let me ask if there are any questions.
I didn't see anything coming in.
No, apparently there is nothing.
If you still have questions you would like to ask,
then please indicate that now, perhaps anybody
who would like to ask a question or comment on something
I have said could just quickly send me a yes.
And I know that something is coming.
And if nobody sends a yes in the next seconds,
then I conclude that there is no question that
needs to be answered and no comment that participants
would like to give.
So there is probably nothing coming.
Therefore, I thank you for your attention.
I hope you found the lecture interesting.
And we meet again next time.
Recall no student contribution is
necessary for today's lecture, but student contributions
will start next lecture with the deadline in 14 days from now.
Thank you very much, and see you or not see you next week.