# macroeconomics summary

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Macroeconomics summary chapters 1 to 8
Macroeconomics for E&BE (Rijksuniversiteit Groningen)
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Macroeconomics summary
2 - Aggregate output is measured as the gross domestic product GDP; The value added by all
domestic ﬁrms, disregarding domestic ﬁrms operating abroad. All value added in an economy
consists of the value of the ﬁnal good - the value of inputs (intermediate goods). It can also be computed as the sum of all incomes: Labour income and capital income or proﬁt
income. Aggregate income and production are always equal. Nominal GDP is the sum of quantities of ﬁnal goods produced
times their current price. This increases over time not only due to
increased production, but also because of price increases due to
inﬂation. If we want to measure the change in production we need
the real GDP: The sum of the quantities of ﬁnal goods times
constant (instead of current) prices. We use a reference / base
year to construct prices. On the right, we see that the 2 intersect in 2010. This is thus the
base year, because real and nominal GDP are then equal. Nominal GDP is also known as GDP in current prices/euros. Real GDP is also known as GDP in terms of goods, GDP in
constant euros, GDP adjusted for inﬂation, or GDP in ‘year’ prices. Real GDP per person is the ratio of real GDP to the population of a country. GDP growth is computed in the growth of real GDP, with expansions and recessions. Hedonic pricing takes into account the changed quality of goods and thus the changed value,
because a computer in 2000 is not the same as one in 2017, leading to diﬀerent values. Employment is the number of people who have a job, unemployment is the number of people who
don’t and are looking for one. Together they form the labour force. L = N + U.
Unemployment rate is the unemployment / labour force. u = U / L Those who aren’t looking for a job are not counted as in the labour force, so when some stop
looking for jobs due to high unemployment, the number of unemployed people oﬃcially falls:
These are discouraged workers. This decreases the participation rate, deﬁned as the labour force
divided by the total population of working age. Inﬂation is a sustained rise in the price level: The general level of prices. The inﬂation rate is the
rate at which price level increases. Deﬂation is the opposite. If we see the nominal GDP increase faster then the real GDP, it must be
because prices increase. The GDP deﬂator is the nominal GDP / Real GDP. The GDP deﬂator is an index number and gives the rate at which the
general level of prices increases over time - It gives the rate of inﬂation. Rearrange the equation and we see nominal GDP = GDP deﬂator * real GDP
The GDP deﬂator gives the average price of output (production). The consumer price index gives
the average price of consumption, so the cost of living. These 2 are often diﬀerent because some
of the goods produces are sold abroad, or to governments/ﬁrms. The consumer price index also consists of goods made abroad and imported, inﬂuencing cost of
living as well. In Europe, the CPI is the HICP. Real wage is measured in goods rather than euros, and if it would equal price increase there’s
pure inﬂation. But this doesn’t exist, because not all wages rise proportionally, inﬂuencing income
distribution. Also, people might automatically move up in their tax brackets when they’re not
adjusted for inﬂation: The bracket creep. So aggregate economic activity has 3 dimensions: Output growth (GDP), unemployment and
inﬂation. Okun’s law suggests that when output growth is high, unemployment will decrease. It takes about
1,5% of GDP growth to keep unemployment constant. This is because population grows, and the
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output per worker also grows. To keep unemployment constant, with a 0,5% population growth
and 1% productivity growth, we need 1,5%
output growth. The Philips curve explores the relation between
unemployment and inﬂation, stating that when
unemployment becomes too low, the economy
will overheat and put an upwards pressure on
inﬂation. It has been deﬁned as a relation
between the change in the rate of inﬂation, and
the unemployment rate. We see that higher unemployment leads to a
decrease in inﬂation on average. Aggregate output is determined by 3 main
factors. In the short run, a few years, changes
in demand determine output growth. In the medium run, a decade, supply
determines the output. This consists of the
capital stock, the level of technology and labor force size. In the long run, a few decades or more, the savings rate, education and government determine
output. Short - demand, as a result of consumer conﬁdence for example.
Medium - supply, as a result of capital stock and the labor force.
Long - education, government, saving. 3 - GDP is composed of:
-Consumption, C. (55%)
-Investment, I, sometimes ﬁxed investment, is the sum of non-residential investment (ﬁrms
-Government spending, G, purchases by all levels of government. This excludes government
transfers such as beneﬁts, and interest, making G smaller than government spending. (21%)
-Net exports, X - IM, is exports minus imports. The result is the trade balance, either a trade
surplus or deﬁcit. -Inventory investment, the production exceeding sales, leading to a positive or negative amount.
Some goods are sold a year later than produced, thus the diﬀerence between production and
sales.
Z = total demand for goods. We make some assumptions: All
ﬁrms make 1 good, which can be used by consumers for
consumption, ﬁrms for investment and by governments. This
means we only look at the supply and demand of this market. We also assume ﬁrms will supply any amount at a given price P, meaning we can focus on
demand when determining output.
Lastly we assume the economy is closed, so X = IM = 0 The equation than becomes the following: Consumption depends mainly on disposable income, Yd, which is after tax and transfers. Thus
the consumption function is C = C(Yd) meaning consumption is a function of disposable income. This is a behavioural equation because it captures some aspect of behaviour,
namely consumers’. More speciﬁc is the function on the right, a linear equation
determined by the propensity to consume, which gives the eﬀect an
additional euro has on consumption 0 < C1 < 1, and by C0, which is
the consumption people make when income is 0. They still need to
eat, so they’ll use savings or borrow. C0 may change because
borrowing becomes easier or they become more optimistic. Seen
on the right, the equation has a vertical intercept at C0 and the
slope of C1.
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Disposable income Yd = Y - T where T is the paid taxes - received
transfers. Replacing Yd in the equation for consumption gives:
Investment will be treated as an exogenous variable, meaning contrary to endogenous variables,
it’s independent of other variables and given. Government spending describes ﬁscal policy together with T, and we take both as exogenous. Taking these 3, we now know Z = C + I + G becomes
The demand for goods Z depends on income Y, taxes T,
investment I and government spending G. Assuming ﬁrms don’t hold inventories and inventory investment = 0, equilibrium in the goods
market requires that production equals the demand for goods: Y = Z
This is an equilibrium condition, and together with the identities (3 stripes), and behavioural
equations (consumption function) form all 3 equations. In equilibrium, production Y equals demand. Demand depends on income Y, which equals
production. Y denotes both income and production, because GDP equals the total income
earned in an economy. Production value = income.
We can rewrite the equilibrium equation
We can C1Y to the left side and reorganise the right
We divide both by (1 - C1)
The term (C0 + I + G - C1T) is the given consumption, investment,
government spending and taxes (tax - transfers). These are all the
parts of demand that don’t depend on output: the autonomous spending, independent of output. If the government is running a balanced budget taxes equal government spending, and if T = G.
Because the propensity to consume C1 is smaller than 1, G - C1T is positive and thus
autonomous spending is positive. 1/(1 - C1) is always greater than 1, because C1 is smaller than 1. This is the multiplier, the number
that multiplies autonomous spending. The larger the propensity to consume C1, the larger the
multiplier. Both changes in consumption and autonomous spending change output by more than its direct
eﬀect. This is because an increase in C0 increases demand, leading to an increased production,
and because production equals income Y, and income increases consumption. When we plot production as a function of income, we get a 45 degree line: They are always equal. Then plot demand as a function of income. Demand depends on income
and autonomous spending. Autonomous spending is the intercept with the Yaxis, where Y = 0. The slope of the line ZZ, denoting the relation
between income and demand, is equal to the
propensity to consume C1. In equilibrium production equals demand, Y = Z, so
at the intersect of ZZ and the 45 degree line
depicting income Y / demand Z / production Y. Distributing prohibited | Downloaded by David Seidell ([email protected])
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When demand increases by 1 billion, production also
increases by 1 billion, from A to B. Because income
equals production, income grows with BC, which is
just as long as AB. Then comes the 2nd round: The increase in demand
CD, which equals AB times the propensity to
consume. So 1 billion * C1. This second round increase in demand Z increases
production Y, which equals income Y, so income
increases with DE. These rounds keep going, until they approach a limit.
This limit is the multiplier: 1 / (1-C1)
The initial increase in demand triggers successive
increases of production and income, leading to more
demand etc. All these circles together equals the
multiplier. The dynamics of adjustments formally describes the
adjustment of output to demand over time, as it takes a while for ﬁrms to adjust production. Saving is the sum of private saving and public saving.
Private saving S = Yd - C so the disposable income minus consumption. This can be rewritten
as S = Y - T - C so savings equals income minus taxes (disposable income) - consumption. Public saving (T - G) equals taxes (tax - transfers) minus government spending, which can either
result in a budget surplus or deﬁcit, respectively a positive or negative public saving. We know production Y equals demand, which is C + I + G. We can rearrange to ﬁnd the equation for private saving. Subtract T from both sides and move C
to the left, get Y - T - C = I + G - T. The left side is private saving: So S = I + G - T. Thus investment = saving + the government surplus. I = S + (T - G). Saving equals investment: Saving S and public saving T -G. The IS-relation stands for investment equals saving, because what ﬁrms invest must be equal
what government and people save. So besides production = demand we also have saving =
investment in equilibrium. So we know saving S = Y - T - C Income - tax - consumption. We know C is more complex so
S = Y - T - C0 - C1*(Y - T) We can rearrange this: S = -C0 + (1 - C1)*(Y - T)
The propensity to save is 1 minus the propensity to consume, so (1 - C1), and propensity to save
+ propensity to consume = 1. In equilibrium the sum of private and public saving must thus equal investment. Thus when we take the saving from above and add T G we get private and public saving. Together, they equal investment.
private
public
When we solve for Y, output, we get the following
Which is again the equilibrium When people save more, they consume less, decreasing output.
Because saving S = -C0 + (1 - C1)*(Y - T) is a function of income,
which again equals on output, saving more will cause consumers to save less: The paradox of
saving. In equilibrium, investment equals public + private saving: I = S + (T - G) because I, G and
T are exogenous our saving cannot change in equilibrium condition. In the long run however,
saving is possible of course. Distributing prohibited | Downloaded by David Seidell ([email protected])
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4 - Financial markets
Money is used for transactions and pays no interest: Either currency or deposit accounts. Bonds pay a positive interest i, but can’t be used for transactions. The proportion you should choose between holding money and bonds depends on 2 things:
-Your level of transactions: Enough money to live, not having to sell bonds for groceries.
-Interest rates on bonds: More interest means holding more bonds. Money market (mutual) funds pool funds of many people and buy (government) bonds.
The demand for money in an economy, M’d, depends on the overall
level of transactions and interest rate. The overall level of transactions
is roughly equal to the nominal income. So we can write M’d
= \$Y (which is the nominal income) * L(i) which is a decreasing
function of the interest rate. The - sign means L(i) has a
negative eﬀect on the demand for money: Higher interest
means lower demand for money. This is shown on the right: For a given level of nominal income, the
demand for money is downward sloping: With higher interest, demand
is lower. When looking at the supply of money, ﬁrst we assume there’s only
currency, supplied by central banks. In the real world there’s also
deposit accounts supplied by banks, but we disregard this for now.
Supply is M’s, and in equilibrium supply equals demand: For a given supply M’s, a income Y and interest rate i, equilibrium
occurs at point A. Let’s say nominal income increases to Y’, which
increases the level of transactions thus increasing the demand for
money at any interest rate. The demand curve shifts out right,
increasing equilibrium to A’ and interest rate to i’. An increase in nominal income leads to an increase in interest
because the demand for money exceeds supply at the initial
interest rate. The increased i decreases the money people want to
hold, re-establishing the equilibrium demand so it again equals
supply. An increase in supply on the other hand leads to a decrease in the
interest rate; this increases demand for money, so it equals supply. A central bank changes money supply by buying or selling bonds. If
it buys bonds and pays for them by creating money, it increases
M’s. If it sells bonds and removes the money it receives from
circulation, it decreases supply. These are open market transactions because the central bank
inﬂuences money supply in the open market for bonds. Let’s take the balance sheet of a central bank. Its assets are the bonds it
holds in its portfolio, its liabilities are the stocks of money in the economy.
Open market operations lead to equal changes in assets and liabilities. An expansionary open market operation increases money supply: It buys
1 million worth of bonds and thus increases its assets, while also
increasing the amount of money in the economy, its liabilities. A contractionary open market operation decreases the money supply, by
selling 1 million worth of bonds and thus decreasing its assets. This
contracts 1 million worth of money from the economy, which it will then
destroy, decreasing its liabilities and money supply. Let’s take a one-year bond of \$100, meaning a promised payment of \$100 one year from now. If
you buy the bond for a price \$pB today and hold it for a year, the rate of return is (100 - \$pB) / \$pB The rate of return is the interest rate, thus the interest rate: If the price is \$90, the interest rate is 100 - 90 = 10 / 90 = 11,1% So the interest rate is what you get one year from now minus what you pay for
the bond today, divided by the price of the bond today. Distributing prohibited | Downloaded by David Seidell ([email protected])
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Thus for a one year bond paying \$100 with a given interest rate we
can ﬁgure out the price: The price equals the ﬁnal payment divided by 1 + the interest rate.
The higher the interest rate, the lower the price today. If bond markets
go up, the price of bonds goes up, meaning interest goes down. With an expansionary open market operation, the central bank thus buys bonds increasing money
supply and increasing bonds prices. This in turn decreases bonds’ interest rate. A contractionary open market operation will decrease money supply, decreasing bonds’ price and
increasing bonds’ interest rate. In practice, central banks choose an interest rate, deciding to increase it by decreasing money. Besides currency, money is also supplied by private banks: Deposit accounts. Financial intermediaries are institutions that receive funds and use these to buy ﬁnancial assets or
make loans. Their assets are the ﬁnancial assets they own + loans they made, their liabilities are
what they owe to those they received funds from. People and ﬁrms can at any time withdraw funds or use a debit
card to pay with what’s in their account, meaning a banks’
liabilities equals the value of their deposit accounts. Banks hold reserves: To make sure there’s enough cash for
people to withdraw, and regulations require them to hold a certain
proportion of their deposit accounts in reserve. Of the banks’ assets that aren’t reserves, roughly 70% are loans
and 30% are bonds. Central bank money is the money it has issued, and these are a
central banks liabilities. Not all this central bank money is held by
the public as currency: Some is used as reserves by banks. The demand for central bank money = demand for currency by
the public + demand for reserves by banks. Supply of central bank money is under the central banks’ control, and the equilibrium interest rate
is such that supply of central bank money and demand are equal. The demand for central bank money consists of currency demand by the people and
reserves by banks. For simplicity, we assume people only hold deposit accounts, so the
demand for deposit accounts is given by M’d = \$YL(i), meaning demand for deposit
accounts will go down when interest goes up, and goes up when transactions goes up. The larger the amount of deposit accounts, the more reserves banks must hold. If we let the greek
letter theta denote the reserve ratio, the demand for reserves by banks H’d =
So the demand for reserves is proportional for the demand to deposit accounts,
and the amount for deposit accounts in turn depends in interest and nominal
income. Demand for central bank money, equivalently demand for reserves by
banks, is equal to the the reserve ratio times the demand for money by people.
H is the supply of central bank money, H’d demand. In equilibrium the 2 are equal so:
The demand for central bank money is given, for a given level of
nominal income. As interest is higher, demand is lower as people
hold less deposit accounts and more bonds, thus banks need less
reserves. Again, decreases in money supply will increase interest,
while increased money supply decreases interest rates.
By controlling the supply of central bank money, central banks
determine bonds’ interest rates. In the US, the Federal Reserve determines interest by adjusting
central banks money supply. In Europe, the ECB sets a reﬁnancing
rate (reﬁ) at which banks borrow from the ECB when short on funds:
They thus directly set a interest rate which inﬂuences the rates banks
charge their own costumers. In the US the Fed intervenes in the
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federal funds market, the ECB sets the rate at which banks borrow directly. Decreasing the interest rate hits a zero lower bound; a central bank can’t decrease interest below
0%, the liquidity trap. While people want to hold more money as interest rate decreases, when it
hits zero people become indiﬀerent between holding money and bonds. They want to hold at
least the amount they need for transactions, and from there the demand for money becomes
horizontal: Because bonds and money pay the same interest they’re indiﬀerent. When interest rates are 0, increasing the money supply won’t have any eﬀect: The rates remain 0.
When interest rates are 0, banks too are indiﬀerent between holding reserves and bonds: Both
pay 0, so when interest rates are 0 and the central bank increases money supply, banks will hold
more reserves and people more deposit accounts. 5 - The IS-LM model
Remember that production Y equals demand Z, and Y = C(Y-T) + I + G
We assumed that interest doesn’t aﬀect demand and mainly investment I.
Investment primarily depends on the level of sales of a ﬁrm (low sales means little
investment) and the interest rate. These two eﬀects are captured in the equation:
Here, investment depends positively on production and negatively on interest.
Because we assumed there’s no inventory investment, production equals sales. The new equilibrium becomes this. This is our expanded ISrelation, we can now look what happens to output when interest
rate changes. An increase in output leads to an increase in demand both
through its eﬀect on income and investment. The demand relation ZZ equals output at point A, where the
equilibrium level of output Y is given. When interest rates change,
increasing to i’. This leads to lower demand and lower investment,
making ZZ intersect at point A’ where equilibrium output is Y’. We can ﬁnd equilibrium output for
any value of interest rate,
corresponding higher i with lower Y.
This relation is the IS curve: The
relation between interest and output,
represented by a downward sloping
curve. The IS curve can be shifted by taxes:
When T increases, Y decreases,
shifting the IS curve inwards. The
same is true for G or consumer conﬁdence. Returning to ﬁnancial markets, where nominal income and interest rates determine the demand
for money. Income positively, interest negatively. Supply M we’ll take as determined by the CB. Now lets rewrite it as a relation between real money (in terms of goods), real income (in terms of
goods) and interest rate. Remember: nominal GDP = real GDP * GDP deﬂator \$Y = YP Real GDP = nominal GDP / GDP deﬂator Y = \$Y/P So nominal income divided by the price levels equals real income Y. Dividing both sides of
the money supply equation gives: So real money supply (in goods) depends on real income, and interest. This is the LM-
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relation: A relation between the liquidity preference (the amount of currency people want to hold)
and the money supply. In deriving the LM curve, we can either take monetary policy as a choice of M, money stock, or i,
interest rate. Lets say we think of monetary policy of choosing nominal money supply and thus
through M/P, the real money stock. If real incomes then increase,
interest rates must also increase in such proportion that money
demand remains equal to supply: The increases interest rates
must oﬀset increased income so that the money stock remains
equal to demand. For a given money supply, increased income
leads to increased interest. This is the traditional thought: The central bank chooses the
money stock and lets interest rates adjust. In reality, central
banks choose an interest rate they want to achieve and adjust
money supply to achieve this. This makes the LM curve simple,
namely horizontal at a chosen level of interest by the central
bank. The IS-relation follows interest rates and output, determining
the goods-market equilibrium. The LM-relation follows interest rate and output, determining the
ﬁnancial market equilibrium. Equilibrium in ﬁnancial markets is along the LM curve,
equilibrium in goods market along the IS curve.
Both markets are in equilibrium at point A.
When governments engage in ﬁscal
contraction or consolidation they
reduce budget deﬁcit, contrary to a
ﬁscal expansion. They increase taxed
but keep G constant. This has no
eﬀect on the ﬁnancial markets, but
does decrease disposable income,
either by reducing G or increasing T.
The decreased Y shifts the IS curve inwards, because it decreases both
consumption and investment. Now, suppose the central bank decreases i by increasing
money supply M: A monetary expansion, contrary to
contraction or tightening. This won’t shift the IS curve, but
it will change the LM curve: This will decrease. When i is lower, both
investment and output/demand increase, increasing both consumption and
investment without the IS line itself shifting. Fiscal policy, taxes, and monetary policy, interest rates and money supply
can be used together in a monetary-ﬁscal policy mix, or simply policy mix.
E.g. in a recession, both can be used in the same direction: Expansionary
ﬁscal policy (decreasing T) shifts the IS curve outwards. Expansionary monetary policy (interest
rate decrease) shifts the LM curve down. These both lead to higher output.
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6 - Financial markets II
Nominal interest rates are expressed in currency: E.g. one year government bonds 4,2% means
every euro now is worth 1,042 euro’s a year from now. If the nominal interest rate for year t is i’t,
borrowing one unit this year requires paying 1 + i next year. Real interest rates are expressed in terms of goods. Real interest for year t is r’t, so borrowing one
basket of goods now requires you to pay 1 + r’t baskets next year. The one-year real interest rate R’t = Where 1 + r’t is the real interest rate. This thus equals (1 +i’t), which
is the nominal interest rate. P’e t + 1 denotes the expected price of
goods next year. P’t is the current price. So basically the real interest rate is the nominal
interest rate * (current prices / expected future prices). We denote the expected inﬂation between t and t+1 by Pi’e t+1. The expected rate of inﬂation equals the expected change in euro price / euro price of
this year. We can place this formula in the formula for the real interest rate: Real interest rate = Nominal interest rate / expected rate of inﬂation So 4% nominal interest rate and 3% inﬂation means real interest rate is 1,04 / 1,03 =
0,97% A less exact measure is the following:
This would give 4 - 3 = 1%
When expected inﬂation equals 0, nominal and real interest rates are equal. In the IS relation, what matters for consumption and investment is the real interest rate,
whereas the CB sets the nominal interest rate. To set the real interest rate that it wants, it
must account for expected inﬂation. Real interest = interest - inﬂation
Again comes the liquidity trap: Real interest rate can not be lower than the negative of inﬂation,
because nominal interest rate can’t be lower than 0. Thus r = i - inﬂation implies that when i = 0,
the zero lower bound the CB can set, real interest R = -inﬂation. Bond holders require a risk premium to compensate for the risk of default. The higher this
probability for default, p, the higher the premium and thus the higher the interest rate. i is the
nominal interest rate on a risk-less bond, i + x on a risky bond. To
get the same expected return the following equation must hold:
The left hand side is the return on a risk-less bond. With the probability 1 - p of no default, and the interest of the bond
(1 + i + x). So the decrease because of p should equal the increase because
of x, oﬀsetting the risk p with a premium x, making the return equal for both
types of bonds. Rearranging gives:
So the risk premium = the interest rate times the change for default / the
change of payment. If the interest rate on a risk-less bond is 4% and probability of default p =
2%, the risk premium x = 1,04*2 / 0,98 = 2,1% is the risk premium. Apart from direct ﬁnance, borrowing directly to the ultimate lenders, much takes place through
ﬁnancial intermediaries who receive their funds from investors and lend these to others: E.g.
Banks, mortgage companies, and hedge funds. Consider a bank with 100 assets, 80 liabilities and capital 20. The liabilities may be demand
deposits and interest-paying deposits. The assets may be reserves (central bank money), loans,
and government bonds. The capital ratio is capital / assets so 20%. The leverage ratio is assets to
capital, so 5. This is the most important relationship. A higher leverage ratio means higher proﬁt but also higher risk of bankruptcy. If the expected rate
of return on assets is 5% and return on liabilities 4%, it has a expected proﬁt of 100*0,05 - 80
*0,04 = 1,8. This is 1,8/20 = 9% proﬁt per unit of capital. If the capital ratio wouldn’t be 20 but 10,
the expected proﬁt per unit of capital would be 14%: Higher leverage is higher proﬁt per unit. The downside is that higher leverage implies a higher risk that assets become less valuable than
liabilities, making a bank insolvent. Distributing prohibited | Downloaded by David Seidell ([email protected])
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If investors doubt banks’ assets, they will take their funds out of the bank. The bank needs funds
to repay investors, but asking money back from borrowers is hard, and selling loans to other
banks means selling them at ﬁre sale prices, far below their value because of diﬃculties to assess
it’s quality. For demand deposits, against which cheques can be given out, is vulnerable to bank runs forcing
them to close. The shortage in cash is liquidity, and the lower the liquidity of assets, the higher the
risk of ﬁre sales and insolvency leading to bankruptcy. Narrow banking restricts banks to holding liquid and safe government bonds. This means not
banks but ﬁnancial intermediaries now make loans, shifting the problem but not solving it. The
federal deposit insurance guarantees demand deposits to a certain ceiling meaning people don’t
have to redraw their cash when fearing default. This risks moral hazard as banks leverage more. Another solution is liquidity provision where central banks lend to a bank against the value of its
assets, avoiding ﬁre sales so the may weather a bank run. The IS-LM model had one interest rate, determined by the central bank. We now know there’s
nominal and real interest rates, and the policy rate set by the CB diﬀers from those faced by
borrowers. This makes the new IS equation: LM stays the same, controlling nominal interest
rate. In IS, the presence of expected inﬂation
Pi’e, and risk premium x are now present. Spending decisions depend on the real interest
rate r = i - Pi’e, nominal minus inﬂation, rather
than the nominal rate. And x captures worries about liquidity and solvency. So the interest rate in
the LM equation, i, no longer equals that of the IS relation, r + x. The policy rate is the nominal
rate of the LM equation, the borrowing rate is the IS
rate. Because CB can choose the nominal i to achieve
the desired real interest r, we rewrite it:
So the CB chooses the real policy rate r, but the real
interest rate relevant for spending decisions is the
borrowing rate: R + x: nominal interest + inﬂation + risk premium. Again, the CB faces the zero lower bound and a liquidity trap. In the
case on the right, it decreases policy rate enough to oﬀset the
decrease in spending because of the IS shift. It sets the nominal rate
at a low enough level that the real policy rate actually becomes
negative, stimulating spending. Because the real policy rate can
never be larger than the negative of inﬂation, it faces problems when
inﬂation is low. If inﬂation is 0,5%, it can’t decrease the real interest
rate below -0,5% and may be unable to stimulate the economy. The Case-Shiller index maps the US housing prices. The low
interest rates of the 2000s pushed up demand for houses.
Mortgage lenders engaged in subprime mortgages, lending to
risky borrowers. When house prices started going down in
2006 their mortgage often became underwater (mortgage
value exceeding house value). As borrowers defaulted, lenders
made losses. Banks were highly levered because they underestimated the
risk. Their managers were enticed to go for high returns, and
ﬁnancial regulation was avoided through structured investment
vehicles. These SIVs didn’t appear on banks balance sheet and
didn’t require banks to hold capital. When these SIVs dropped in value like housing prices, banks
guarantee to provide funds for SIVs meant questions arose about the solvency of banks
themselves. In the 90s and 00s securitisation grew: The creation of securities based on a bundle of assets, to
diversify portfolio of mortgages away from one particular part of the country for example.
Mortgage-based security MBS is a title to the returns from a bundle of mortgages, increasing
supply of funds and again decreasing the cost of borrowing. Distributing prohibited | Downloaded by David Seidell ([email protected])
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Senior securities have ﬁrst claim on the returns from the bundle, junior securities get what’s left.
Collateralised debt obligations CDOs are very risky junior securities. Securitisation meant that banks sold mortgages instead of keeping them on their balance sheet.
This meant they no longer had incentives to make sure the borrower could repay. Rating agencies
missed this risk, because MBSs were hard to asses. These became known as toxic assets, and
only sellable at ﬁre sale prices. In the 90s and 00s banks more and more depended on borrowing from other banks and investors
than demand deposits. Wholesale funding is ﬁnancing the purchase of assets through short termdebt from other banks/investors. Structured Investment Vehicles were entirely funded through
this. Although holders of demand deposits were protected by deposit insurance, investors
weren’t. When they worried about the value of assets held by the banks or SIVs, the redrew their
funds. High leverage, illiquid assets and liquid liabilities resulted in a major ﬁnancial crisis. Banks
stopped lending to each other or to anyone else, transforming it into a macroeconomic crisis.
This increased interest rates at which people and ﬁrms could borrow (decreasing investment), and
decreased conﬁdence leading to decreased consumption. Some European banks were exposed to the US housing market through Mortgage Backed
Securities and Collateralised Debt Obligations they owned: Securities whose underlying assets
were US housing mortgages. Trade decreased because of less trade credit provided by banks and less consumption. The US
interest rates spilled over to the European market as well. In the IS-LM model, the IS curve shifted inwards. Policy responses included increasing federal deposit insurance, and the Fed put in place liquidity
facilities to borrow from the Fed. It increased the set of assets institutions could use as collateral,
the assets a borrower pledges when borrowing from a lender. The government introduced the Troubled Asset Relief Program to increase banks’ capital: The
government acquired shares and thus provided funds for large US banks. From 2007 the Fed decreased the policy interest rate, until it hit 0 in 2008. It then turned to
unconventional monetary policy, buying other assets to directly aﬀect the rate faced by
borrowers. Fiscal policy included the American Recovery and Reinvestment act with tax reductions and
spending increases. The budget deﬁcit skyrocketed to 9% of GDP in 2010. Europe started cleaning up banks’ balance sheets much later, and the ECB didn’t start
unconventional monetary policy until 2015. It’s buying government bonds. Fiscal policy depended on each country’s room for expansionary policy: The higher the debt at
the start of the crisis, the less room a country has for increasing government spending to oﬀset
the shift of the IS-curve. This meant countries like Italy were unable to stimulate their economies. 7.1-The labour market
The population of working age are potentially available for employment, the labour force is those
working or looking for work, while the rest is out of the working force. The participation rate is the
ratio of labour force to the population in working age. The unemployment rate is the ratio
unemployment to the labour force. For a given unemployment, a labour market can either be very active or sclerotic. Flows between
3 groups are recorded: Out of the labour force /
unemployment / employment. There are 3,7 million
separations, 3 million of which are job changes, the other
people moving out of the labour force or becoming
unemployed. 80% are quits, leaving a job for an alternative,
and 20% are layoﬀs. Because we’re looking at monthly ﬁgures, we can calculate
the duration of unemployment. There’s 1,7 million
unemployed, if we divide this by the amount of people
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leaving unemployment each month through either dropping out of the labour force or
employment, we ﬁnd the average amount of months people spend unemployed. Many out of the labour force are discouraged workers who will take a job if they can ﬁnd one,
which is why economists sometimes focus on the employment rate: The ratio of employment to
the population available for work. When unemployment is high, workers face 2 problems: Employed workers have a higher change
to lose their jobs & unemployed have a lower change at ﬁnding a job, expecting to remain
unemployed for longer. Wages can be set through collective bargaining, between ﬁrms and unions, but usually through
individual bargaining. 2 facts stand out across institutionally diﬀerent countries:
-Workers are typically paid higher than their reservation wage, the wage that would make them
indiﬀerent between work and unemployment. -Wages are higher when unemployment is lower. Bargaining power depends on how costly it is for the ﬁrm to replace a worker, and how hard it is
for the worker to ﬁnd another job. So it depends ﬁrst on the nature of the job; how much skills are
required. Second, it thus depends on the labour market conditions; low unemployment means
stronger bargaining power for employees. When workers are indiﬀerent (reservation wage) their productivity won’t increase. Eﬃciency wage
theories are theories linking productivity/eﬃciency of workers to their wage. A low unemployment
makes it more attractive for workers to quit, thus meaning ﬁrms have to increase wages to kook
them. The aggregate nominal wage W depends on the expected price level P’e, the
unemployment rate u, and a variable Z. Higher unemployment decreases wages,
while the other variables have a positive eﬀect.
with it. Not W, but nominal wage / price of goods is important: W / P. Firms too care about the wage they pay relative to the price they receive for their goods: They’ll
receive more money and are thus willing to pay more. The variable Z is a catch-all variable, e.g. unemployment insurance: The payment of
unemployment beneﬁts to workers losing their job. Workers are willing to accept any wage, no
matter how low, if there’s no alternative income. Thus unemployment insurance has a positive
eﬀect on W: Wages increase with higher beneﬁts. Minimum wage increases too increases wages, as does employment protection which makes it
harder to lay-oﬀ workers. This increases their bargaining power. The prices set by ﬁrms depend on their costs, depending on production function. If we assume
the only factor of production is labour, we can write the production function Y = AN
Y is output, N is employment and A is labour productivity (output per worker). If we assume labour
productivity to be constant, Y = N, thus only depending on the employment. P = (1+m)W takes into account the mark-up m. If markets are perfectly competitive there’s no
markup and prices equal costs W. If we divide both sides of the wage determination by price level we get:
The higher the unemployment rate, the lower the real wage chosen by
ﬁrms. This wage-setting relation is drawn on
the right.
The price determination was P = (1 + m)W, so the cost of
labour + the markup ﬁrms charge. If we divide both sides
by the wage level W, we get:
The ratio of the price level to the
wage implied by the price-setting
behaviour of ﬁrms equals one plus
mark-up. Reversing this, we get the following:
Thus, the real wage (W / P) is related
to
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the prices set by ﬁrms. An increase in mark-up leads ﬁrms to increase their prices, this is the price
setting relation drawn in the ﬁgure above. Both the price setting relation, the real wage equals the
prices set by ﬁrms, and the wage-setting relation, real wages are dependent on unemployment
and other factors, are drawn in this ﬁgure. The equilibrium between both is given by:
The equilibrium unemployment rate U’n, is such that the real wage chosen in wage
setting is equal to the real wage implied by price setting. This is the natural rate of
unemployment: The unemployment at which the real wage of price
setting is equal to the real wage at wage setting. There’s nothing
natural about it though: If we increase unemployment beneﬁts, we increase wage, shifting
op the WS curve as seen on the right. This will change the natural
rate of unemployment, increasing it to U’n. If we decrease antitrust regulation, the markup
m will increase thus increasing prices and
decreasing real wage. This will shift down the
PS curve to PS’, increasing the natural rate of
unemployment to U’n. Because it turns out to not be natural but
rather a result of the structures of the economy,
the structural rate of unemployment would be a
better name. For a given production function and labour force, the employment rate
determines the level of output. So associated with a natural rate of unemployment is a natural
level of output. In the short run however, the price level is often diﬀerent from what the wages
were set at. Thus in the short run output is still determined by monetary and ﬁscal policy mostly.
In the medium run, the factors determining unemployment and output are indeed the wage level
and the markup. 8 - The Phillips curve
A.W. Philips found a clear negative reaction between inﬂation and unemployment: When
unemployment was low, inﬂation was high. It was later labelled the Phillips curve, and implied a
country could choose between high inﬂation and high unemployment. In the 70’s however, both
high inﬂation and high unemployment appeared in most OECD countries, and a new relation
appeared: Between the unemployment and the change in inﬂation rate. The nominal wage W depends on the expected price level P’e (positively), the
unemployment rate (negatively) and the variable Z (e.g. beneﬁts and bargaining). The price set by ﬁrms P is equal to the nominal wage W + the
markup. Replacing the nominal wage W by its expression we get:
We see that the real price level is a function of the expected price level. If
the expected price increases, the wage increases. Because the costs for a
ﬁrm depend on the wage level, this in turn increases prices. We can give F the following equation: A function of unemployment and
other factors. Then we can put it all together to show a function: Price level is a relation between the expected price level and
unemployment. Plotting it all as inﬂation is year t, we get the
equation on the left. Inﬂation is a function of expected inﬂation, the
markup, z, and unemployment. The original Phillips curve made sense in the 60’s, ﬁnding a clear
relation between low unemployment and inﬂation. In the 60’s, wage
setters calculated expected inﬂation as given on the left: The expected
inﬂation in a year t is independent of the inﬂation rate the year before. In 70’s the relation broke
down. Wage setters changed the way their expectations about inﬂation were formed, because it
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became more persistent. Wage setters began taking into account the
inﬂation in the previous year, thus now using the formula on the right. Expected inﬂation for a year was equal to the ﬁrst part, again independent
oﬀ the current inﬂation, and Pi’t-1, which is the inﬂation in the current year.
Current inﬂation thus became a variable in calculating expected inﬂation. The higher Ø, the more
important current inﬂation became. By 1975, people roughly assumed inﬂation in next year would
be equal to current inﬂation. Thus Ø is equal to 1. Let’s substitute the function of expected inﬂation
Pi’e into the determination of inﬂation. When Ø is
equal to 0, we get the original curve: The relation
between merely inﬂation and unemployment
remains. When Ø is positive, last year’s inﬂation becomes a factor in next year’s
inﬂation. As Ø becomes really large and eventually equal to 1, we get
the following equation (after moving last year’s inﬂation to the left): The change in inﬂation (Pi’t - Pi’t-1) is a result of the markup, z, and
unemployment. High unemployment doesn’t determine the inﬂation, but
the change in inﬂation. Low unemployment doesn’t immediately mean high inﬂation; it just means
an increase in inﬂation. This is what happened in the 70’s: As Ø increased to
1, people started taking into account last years
inﬂation and the relation between unemployment
and inﬂation disappeared. It was replaced by a
relation between the unemployment rate and the
change in inﬂation rate. This is shown on the right:
The red line is the
equation on the left. The
change in inﬂation is
roughly 3% - 0,5* unemployment. Thus when
unemployment is higher than 6%, inﬂation will
decrease. This is also known as the modiﬁed Phillips curve, the
expectations-augmented Phillips curve, or the
accelerationist Phillips curve (Because low U accelerates inﬂation). Because it is simply right, we
call it the Phillips curve, and the original Phillips curve is the one with inﬂation being a result of U. The natural rate of unemployment u’n is the rate at which expected inﬂation is equal
to inﬂation, thus the left side of the equation becoming 0. Solving this for u’n gives
the next equation. Thus, the higher the markup or other factors aﬀecting wages Z,
the higher the natural rate of unemployment. Rearranging a bit gives the equation on the left. The change in inﬂation depends on the diﬀerence between the
actual and natural unemployment rate. When the actual
unemployment rate is higher than the natural unemployment rate, inﬂation will
decrease. When unemployment is lower than natural, inﬂation increases.
Thus the natural rate of unemployment is also the unemployment rate needed to keep inﬂation
constant; the non-accelerating inﬂation rate of unemployment NAIRU. So we know the natural rate of unemployment depends on the markup and Z. The European
average of 10% in the past 25 years, whereas inﬂation hasn’t decreased consistently. So this
appears to be the natural rate. Europe’s labour market rigidities are often blamed for this. The
generous system of unemployment insurance, employment protection, minimum wages and
extension agreements: A agreement by a subset of ﬁrms and unions can be extended to the entire
sector. This means even non-unionised ﬁrms are included in collective bargaining, increasing
unions’ bargaining power because they don’t have to compete with non-union ﬁrms.