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Intermediate Macroeconomics Topic Summarisations

Topic Summarisations

Expenditure and Interest Rates

IS-LM

IS-LM is a stylised, simplistic, closed-economy model.
It can be used to explore the effects of fiscal policy, monetary policy, and shocks.
In explaining output, it also explains consumption and investment.
Price inflation and employment are absent. Assumes prices are fixed.
IS is the inverse relationship between expenditure and how it is affected by the interest rate.
IS is based on analysing the demand for goods, but not the supply of goods.
LM is the monetary policy relationship.
There are three varieties of LM:
- Classic LM: based on money demand and supply
- Fixed interest
- Monetary policy rule: the Central Bank increases the interest rate as output increases
  - Most realistic.

Derived from four components:
- The definition of national income
- A simple consumption function
- A simple investment function
- Assumption of government expenditure as exogenous
IS shifts down if:
- Government expenditure decreases
- The real exchange rate appreciates
- World income decreases
IS shifts up if:
- The real exchange rate depreciates
- Government expenditure increases
- World income increases

Classic LM

The LM curve provides a second relationship between output and interest rates.
The classic LM curve is based on two relationships:
- The demand for money
- The supply for money
Money demand is assumed to depend on output and the interest rate.
Money supply is assumed to be exogenous and fixed by the Central Banks.
The money supply curve shifts left as money supply falls and right as money supply increases.
The LM curve is just the money demand function but with the real money supply treated as exogenous and fixed by the Central Bank.
The LM curve shows combinations of output and the interest rate at which money demand equals money supply, treating the money supply as exogenous.
If income increases, the money demand curve shifts out. With a fixed money supply, this shift needs to be offset by a rise in interest rates. Thus, the LM curve slopes up
If the Central Bank increases the money supply, the LM curve shifts out.
The intersection of IS and LM determines output and the interest rate.
An increase in the nominal money supply shifts out the LM curve. The shift in the LM curve moves the economy down the IS curve to the new equilibrium. Thus, output rises and the interest rate falls.
An increase in expenditure shifts out the IS curve. The shift in the IS curve moves the economy up the LM curve to a new equilibrium. Thus, output and the interest rate increase.

Fixed Interest Rate

In reality, Central Banks conduct monetary policy by choosing the interest rate, not the money supply.
- IN ACTUALITY, the Central Bank can either fix the money supply or the interest rate, but not both.
- IN THIS MODEL, If it fixes the interest rate, the Central Bank sets the supply of money to match the demand for money at the chosen interest rate and adjusts the money supply to match whenever money demand changes.
An increase in income shifts out the demand for money relationship.
- The Central Bank increases the money supply to ensure that it intersects the new money demand curve at the selected interest rate.
An increase in expenditure shifts out the IS curve. The economy moves along the flat LM curve.
- LM curve is flat as policymaker is willing to supply any amount of money at the interest rate they have committed themselves to.
- The LM curve becomes horizontal when the interest rate is very low.
- In this case, increasing the money supply will have no effect on output.
- However, QE can still be used as, via the Portfolio Substitution Effect, it can lower interest rates on financial assets.
- Plus, if the LM curve is horizontal, fiscal policy has a large impact on output, so policymakers are granted options when interest rates are very low.
Output increases by times the increase in expenditure. The Central Bank increases broad money to accommodate the increased demand for goods.
- The higher the marginal propensity to consume, the greater the sensitivity of output to an increase in expenditure.
An increase in the money supply shifts down the LM curve. Policymakers increase broad money and the economy moves down the IS curve. Output increases by times the reduction in the interest rate.

Monetary Policy Rule

A monetary policy rule describes how the Central Bank sets the interest rate in order to hit its policy targets. The most prominent monetary policy rule is the Taylor Rule.
Here, we care less about where the LM curve is on the X axis, and more about its slope.
The Taylor Rule assumes that the targets of the Central Bank are to keep inflation close to the inflation target and output close to equilibrium output.
- If inflation is above target, the policymaker increases the interest rate. This reduces demand and brings inflation back down towards the target.
- If output is above equilibrium output, the policymaker also increases the interest rate. This reduces demand and brings output down towards equilibrium.
- Note that, as prices are assumed to be fixed, no variables or parameters affect inflation in the closed economy model.
Equilibrium output comes from the supply side of the economy. It emerges from the behaviour of workers and firms.
- Thus, equilibrium output is external to the IS-LM model.
Policymakers want output to be equal to equilibrium output because equilibrium output is the sustainable, average level of output.
- In addition, the Phillips Curve implies that inflation is only stable if output equals equilibrium output.
A fiscal expansion will increase output and increase the interest rate.
A more aggressive monetary policy response implies a smaller increase in output and a larger change in the interest rate following a fiscal expansion.

IS-LM and Covid-19

We can use IS-LM to analyse the impact of Covid-19.
We can only give a partial analysis as IS-LM does not analyse the supply side of the economy. Thus, the impact of the pandemic on employment, wages, productivity, and similar issues is beyond the scope of the model. We will use the Fixed Interest Rate version of the model.
To model the pandemic, we assume:
- Consumption and investment fell sharply in late February-March 2020; they then gradually increased back to pre-pandemic levels.
- Government expenditure rose in late February-March 2020 due to increased expenditure on health and social care and other responses to the pandemic. But this increase did not entirely offset the reduction in consumption and investment. It then gradually fell back to pre-pandemic levels.
- The interest rate fell sharply in late February-March 2020. It then gradually increased to its pre-pandemic level.
This implies:
- The IS curve shifts down in late February-March 2020. It then gradually shifts up.
- The interest rate line shifts down in late February-March 2020. It then gradually shifts up.
The observed reduction in output implies that the shift in IS was stronger than the shift in LM.
We can show the immediate impact and the recovery from the pandemic.
In the initial impact, output and the interest rate fell.
In the recovery, IS and the interest rate curves shifted up. Output and the interest rate gradually increased.

Summary

The IS-LM model is a simple and flexible model of output, money, and interest rate.
We can use it to analyse the impact of monetary and fiscal policy.
It can generate simulations of the impact of Covid-19 that resemble simulations by the Bank of England, Office for Budgetary Responsibility, the IMF, and others, which are based on more sophisticated models.
But the IS-LM model is too simple: it assumes that output is determined by output, and it ignores the supply side of the economy.
Thus, it ignores inflation, employment, wages, and other essential variables.
- E.g., money financing in a closed economy IS-LM model would not cause inflation and the government would not need to increase taxes. However, in the AD-AS model, this would cause inflation.
IS-LM can give useful back-of-the-envelope insights, assuming inflation is low and stable.
But serious macroeconomic analysis needs to use a more sophisticated model.
The Ricardian Equivalence argument highlights another weakness of IS-LM: it is not based on optimising behaviour.
- Government borrowing must be repaid – a government does this by increasing future taxes.
- Households know that their taxes will increase in the future.
  - They may respond to this by reducing current consumption in order to save and use these savings to pay increased taxes in the future.
- If so, the impact of a fiscal expansion that is financed by increased borrowing may be offset by a reduction in consumption.

Money and Central Banks

The Banking System

A stylised representation of the banking system involves:
- The Central Bank
- Commercial Banks
- The Private Sector, i.e., households and non-bank firms, including Pension Funds and Insurance Companies.

A Stylised Banking System
Central Banks		Commercial Banks		Private Sector
Assets	Liabilities	Assets	Liabilities	Assets	Liabilities
Assets	Reserves	Reserves	Deposits	Deposits	Loans
	Currency	Loans	Equity	Currency
		Other Assets		Other Assets

The Central Bank:
- Monopoly issuer of currency: no other body can legally issue currency.
- Hold reserves owned by Commercial Banks: only Commercial Banks can hold deposits at the Central Bank. Changes in reserves are one of the main routes through which the Central Bank can affect the economy.
- Holds financial assets such as government bonds.
Commercial Banks:
- Own bank reserves held at the Central Bank.
- Hold deposits owned by the Private Sector.
- Hold other financial assets, including government bonds.
- Issue loans to the Private Sector.
- Act as intermediaries between households and firms that save and those that borrow.
  - This is different from the issue of whether Commercial Banks can create money.
  - Commercial Banks have always created (broad) money.
  - When a bank issues a loan, they credit the account of the borrower.
  - Since (broad) money is the sum of currency and deposits, this increases the (broad) money supply.
  - Commercial Banks do not need to receive deposits in order to make loans – they can just create them.
- Are central to monetary policy as only they can hold deposits at the Central Bank.
The Private Sector:
- Holds currency issued by the Central Bank.
- Owns deposits held at Commercial Banks. This is by far the most important component of the broad money supply.
- Holds other financial assets, including governments bonds.
- Hold loans issued by Commercial Banks. This is the main source of credit in the UK, especially for households.
Currency used to be central to economic transactions. It is now less important. This has weakened the direct link between the Central Bank and the Private Sector.
- Central Bank Digital Currencies (CBDC) may re-establish this link.
Currency is relatively small and stable.
Reserves held by Commercial Banks are larger and more volatile: over the past 15 years, changes in reserves are closely associated with QE.
- Reserves are currently close to £850bn, having fallen as a result of asset sales by the Central Bank.
Deposits held at Commercial Banks are in turn larger than reserves.
- Deposits are currently close to £2.2tn. These are less closely associated with QE.
Commercial Banks are central to the banking and monetary systems, so understanding the profitability of Commercial Banks is essential.
- The profit of Commercial Banks is the sum of the interest received on reserves, loans, and other assets, less the interest paid on deposits.
- The rate of profit of Commercial Banks is the sum of the interest received on reserves multiplied by the share of reserves in their assets, the loans multiplied by the share of loans in their assets, and other assets multiplied by the share of other assets in their assets, less the interest paid on deposits multiplied by the share of deposits in their assets.
The Central Bank controls the interest rate paid on reserves and the amount of reserves and uses these to affect the money supply.
- Note that an increase in the share of reserves in a Commercial Bank’s assets implies a reduction in the sum of the share of loans and other assets in their assets.
- Since the interest received on loans and the interest received on other assets are both greater than the interest received on reserves, this would reduce Commercial Banks’ rate of profit.
- Holding a large share of assets with a lower return reduces the rate of profit.

Money Supply

The different definitions of the money supply are based around:
- Currency (a.k.a., cash, or “notes and coin”)
- Bank reserves
- Bank deposits
We consider:
- Narrow money
  - Currency
  - Bank Reserves
- Broad money
  - Currency
  - Bank Deposits
The narrowest measure is (a.k.a, the monetary base, high-powered money, or Central Bank Money)
- This is the sum of currency and bank reserves.
is the sum of currency and deposits.
Aggregate demand is more closely related to broad money than narrow money since loans – which are closely related to consumption – are a major component of broad money.
Reserves are less risky than loans and other assets as the Central Bank can never default as the monopoly provider of domestic currency.
- The Central Bank can also create money to meet payments.
- Since QE increases the share of reserves in Commercial Bank balance sheets, it reduces risk for Commercial Banks.

Money Creation

Central Banks print currency and issue reserves to Commercial Banks, so the Central Bank creates .
Commercial Banks issue loans to the private sector – and loans lead to deposits – so Commercial Banks create .
The effect of Central Bank asset purchases:
- Prior to 2008, Central Banks mainly purchased assets from Commercial Banks through smaller-scale Open Market Operations (OMO).
- Post-2008, Central Banks mainly purchased assets from the private sector through larger-scale Quantitative Easing (QE).
Changes in have no direct effect on IS-LM.
- However, they may have an indirect effect if the increase in leads to an increase in lending by Commercial Banks and hence an increase in .

Open Market Operations

With OMO, the Central Bank purchases assets held by Commercial Banks.
It pays for this purchase by increasing the reserves of Commercial Banks held at the Central Bank.
= sum of currency and reserves increase.
The purchase increases the share of reserves on the Commercial Bank balance sheet and reduces the share of loans and other assets.
The interest paid on reserves is lower than the interest rate on loans and other assets, so the rate of return earned by Commercial Bank falls.
But this is not the end of the process.
Commercial Banks likely want to increase their rate of return.
They can do this by issuing more loans, since the interest rate on loans exceeds that on reserves.
Commercial Banks issue loans by increasing the deposits held by the Private Sector at Commercial Banks.
The increase in lending increases the share of loans on the Commercial Bank balance sheet and reduces the share of reserves and other assets.
The interest rate paid on loans is higher than the interest rate on reserves and other assets, so the rate of return earned by Commercial Banks increases.
The increase in reserves implies that = sum of currency and reserves increase.
Commercial Banks issue loans by increasing the deposits held by the Private Sector at Commercial Banks, so the increase in loans implies an increase in deposits. Thus, = sum of currency and deposits increase.
QE and OMO share the same mechanism, but QE differs from OMO in terms of scale and purpose.
- With OMO, the Central Bank purchases assets originally held by Commercial Banks.
- With QE, the Central Bank purchases assets originally held by the Private Sector, using Commercial Banks as intermediaries.
- QE purchases are much larger than OMO purchases.
- OMOs are used to keep the interest rate constant, whereas QE is used to lower interest rates.

QE: Bank Lending Channel

With QE, the Central Bank purchases assets held by the Private Sector.
- In effect, Commercial Banks purchase assets from the Private Sector.
- Pension Funds sell assets to Commercial Banks because they offer them a high price for the asset.
- Commercial Banks pay a high price to Pension Funds since they know they can sell them to the Central Bank for an even higher price.
Commercial Banks pay for this by increasing the deposits held by the Private Sector at Commercial Banks.
- As such, the share of deposits held by Commercial Banks on their balance sheets increase; the share of deposits held by the Private Sector on their balance sheets increase; and the share of other assets held by the private sector on their balance sheets decrease.
The Central Bank then purchases these assets from Commercial Banks.
It pays for this purchase by increasing the reserves of Commercial Banks held at the Central Bank.
- As such, the share of assets and the share of reserves on the Central Bank’s balance sheet increase; the share of reserves on the Commercial Banks’ balance sheet increase; and the share of other assets on the Commercial Banks’ balance sheet decrease.
But this is not the end of the process.
The Bank Lending Channel analysed under OMO again occurs:
- The purchase increases the share of reserves on the Commercial Bank balance sheet and reduces the share of loans and other assets.
- The interest rate paid on reserves is lower than the interest rate on loans and other assets, so the rate of return earned by Commercial Banks falls.
- Commercial Banks will likely want to increase their rate of return. They do this by issuing more loans.
- The increase in lending increases the share of loans on the Commercial Bank balance sheet and reduces the share of reserves and other assets.
- Thus, the rate of return earned by Commercial Banks increases.
- Commercial Banks issue loans by increasing the deposits held by the Private Sector at Commercial Banks.
- Thus, the share of loans held on Commercial Banks’ balance sheets increase; the share of deposits held on Commercial Banks’ balance sheets increase; the share of deposits held on the Private Sectors’ balance sheets increase; and the share of loans held on the Private Sectors’ balance sheets increase.
Effect on the money supply:
- The increase in reserves implies that = the sum of currency and reserves increase.
- Commercial Banks issue loans by increasing the deposits held by the Private Sector at Commercial Banks, so the increase in loans implies an increase in deposits.
- Thus, = the sum of currency and deposits increase.
Effect of Central Bank asset purchases on output and the interest rate:
- The LM curve depends on , so LM shifts out.
- Output increases and the interest rate falls.

QE: Portfolio Substitution Effect

Consider a Non-Bank Financial Institution (NBFI), e.g., a Pension Fund (PF).
PFs make predictable payments which they must finance out of returns on their investments.
- Thus, they invest in safe long-term assets that generate high but predictable returns.
The PF has 4 types of asset:
- Deposits at Commercial Banks;
- Old Government Bonds;
- Newly-Issued Government Bonds; and
- Other assets, such as Corporate Bonds, Equity, and Foreign Assets, e.g., U.S. Government Bonds
They have 2 types of liability:
- Pension Liabilities; and
- Net Worth
The Central Bank purchases old Government Bonds in QE, reducing PF holdings of old Government Bonds.
- Thus, PF holdings of bank deposits increase.
The composition of the asset portfolio of the Pension Fund has changed.
The Pension Fund is unlikely to keep this new composition because:
- It has long-term liabilities and prefers to match these with long-term assets.
  - Bank deposits are not long-term assets.
- The return on bank deposits is lower than that on other assets.
QE asset purchases increase the price of, and thus reduce the returns on, Government Bonds.
- Thus, the PF is incentivised to use its increased bank deposits to purchase alternative types of asset, such as corporate bonds.
The QE purchase has increased the price of old Government Bonds and thus reduced their interest rate.
The increased demand for corporate bonds will increase their price and so reduce their interest rate.
Consequently, the PF is likely to increase its holdings of:
- Newly issued government bonds;
- Corporate bonds;
- Equity; and
- Foreign assets.

Money Creation: Commercial Banks Increase Lending

If Commercial Banks issue loans to the Private Sector, deposits held by the Private Sector at Commercial Banks increase - increases.
But there is no change in currency or reserves, so does not increase.
- Note that Commercial Banks have “created money” without any action by the Central Bank.
- And note that the increase in lending has led to an increase in deposits, not the other way round.
The increase in shifts out LM.
Output increases and the interest rate falls.
Suppose you take out a loan:
- When you take out the loan, you acquire an increased asset – the loan is credited to your deposit at your Commercial Bank.
- You also acquire an increased liability – you must repay the loan.
- Thus, deposits increase, and so does .

Money Multiplier

This theory is based on an outdated and unhelpful view of money creation, in which Commercial Banks first need an increase in reserves to increase lending.
The Money Multiplier is the ratio of to .
Money Multiplier theory assumes that the Money Multiplier is constant.
If that were correct, would be a constant multiple of .
Thus, the Central Bank could control through its control of .
This theory is not correct since the money multiplier is not constant.
Add more detail with ‘Money Creation in the Modern Economy’.
Why it’s wrong:
- Money Multiplier theory assumes that Commercial Banks want to issue as many loans as possible and are only constrained by the need to keep a reserve ratio set by the Central Bank.
- However, Commercial Banks are risk averse and are reluctant to make risky loans.
- Many Central Banks do not have a reserve ratio, relying on the risk aversion of Commercial Banks.
- When this fails, e.g., in 2008, they put prudential limits on the amount of risk that Commercial Banks take on, not the amount of lending.
IS-LM assumes an increase in leads to an increase in and thus shifts the LM curve to the right.
- This does not require the money multiplier to be constant – it just needs to be positive.
The Classic LM can be critiqued on the grounds that the ability of the policymaker to control the supply of is limited and contingent.

Tiered Reserves

Arguably, the policy of paying interest on all bank reserves has inhibited lending by Commercial Banks.
The alternative of tiered reserves has been proposed.
This distinguishes between required reserves – set by the Central Bank – and excess reserves, where total reserves are equal to the sum of required and excess reserves.
The proposal is that the Central Bank pays interest on required reserves but not excess reserves.
In this case, the profit of Commercial Banks is the same as before, but substitute the interest received on reserves with the interest received on required reserves.
This implies a lower rate of return for Commercial Banks and an increased incentive to increase lending.

Monetary Policy and Covid-19

Central Banks have responded to the Covid-19 pandemic by cutting interest rates.
It is unlikely, but decreasingly so, that they will raise rates within the next 12 months.
The Bank of England has increased QE purchases to £435bn. As a result, and have both increased.

Government Borrowing

Government Revenue and Expenditure

The Government has expenditures and revenue. It must also pay interest on debt.
Expenditure covers purchases of goods and services, i.e., items such as public spending on consumption and investment.
If the Government has debt of B, it must pay interest of iB.
To finance this, the Government raises taxes and borrows.
In some circumstances, the Government can also finance expenditure by printing money.
The primary deficit is real government expenditure minus real taxation revenue; or real government expenditure as a proportion of GDP minus real government tax revenue as a proportion of GDP.
- To find the above as a proportion of GDP, divide the variables by national income.
The total deficit is the primary deficit plus interest payments.

The Government Budget Constraint

If there is a deficit, the Government must cover the gap by borrowing. This increases debt.
The Government budget constraint is the equitable sum of tax revenue and the change in debt to the sum of government expenditure and the interest paid on debt.
In order to reduce debt, the primary surplus must exceed interest payments.
The Government budget constraint implies that the sum of real tax revenue as a proportion of GDP and the change in debt as a share of GDP is equal to real government expenditure as a proportion of GDP plus real interest paid on debt as a proportion of GDP.
Debt as a share of GDP depends on the Primary Deficit and the difference between the interest rate and economic growth.
The primary deficit is often a more useful concept that the overall deficit:
- Debt is driven by the primary deficit.
- Plus, the overall deficit is driven by the primary deficit and by debt.
- Thus, the overall deficit can only be brought down by reducing the primary deficit.
If economic growth exceeds the interest rate, an economy can run a primary deficit without increasing debt as a share of GDP.
- Economic growth reduces the denominator of the primary deficit as a share of GDP.
We can calculate the equilibrium debt ratio, denoted by b*.
This is the stable debt ratio implied by the growth rate and the interest rate when the change in real debt is equal to zero.
This implies that the stable debt ratio is equal to the ratio of real government expenditure less real tax revenue over real GDP growth less the real interest rate.
- Debt sustainability is an equilibrium issue. It assumes constant growth and interest rates. It cannot be used to discuss annual budget changes.
- The analysis assumes that higher g does not lead to higher y, i.e., higher government expenditure does not increase the growth rate. This is highly dubious.
- A lot of the debate around debt is around Piketty’s ‘r > g’, where r is the interest rate. To link our analysis to those debates, note that we replace i with r in the formulae if there is inflation.

Money Financing

The Central Bank can increase the Monetary Base to finance Government spending.
Allowing for money financing, the Government budget constraint implies that the sum of government expenditure and interest payments on debt is equal to the sum of real taxation revenue as a proportion of GDP, the change in debt as a proportion of GDP, and the change in the monetary base as a proportion of GDP.
In turn, the change in real debt as a proportion of GDP is equal to the primary deficit less the money supply as a proportion of GDP multiplied by the rate of growth of the money supply plus real debt as a proportion of GDP multiplied by (the real interest rate less the real rate of GDP growth).
Thus, a primary deficit that is financed through creation does not require increased borrowing, assuming zero inflation.
If the Government increases spending, so the primary deficit increases, and the Government finances this by ordering the Central Bank to increase the Monetary Base, and we assume that the Central Bank sets a fixed interest rate, so we have a flat LM curve, the LM curve shifts out and national income increases.
The impact of a fiscal expansion does not depend on how the expansion is financed.
Nothing would change if we assumed instead that the increase in Government expenditure was financed by increased borrowing.
However, in this latter case, debt would increase and thus debt payments would increase.
Therefore, the Government may be less likely to increase expenditure if this has to be financed through borrowing.
Thus, money financing enables the Government to achieve different macroeconomic policy outcomes.
- However, the mechanics of money financing assumes that the Government can direct the behaviour of the Central Bank.
Pros of money financing:
- Provides an alternative source of funding to the bond market, particularly for projects that the bond market does not favour, e.g., long-term projects that gradually increase productivity and hence increase the growth term in the change in debt equation.
- There are concerns that QE has increased inequality by boosting the prices of financial assets, held largely by the rich. Money financing can be seen as an extension of QE in which the Central Bank issues reserves in order to finance investment in social capita and infrastructure, which is more likely to benefit those who do not own financial assets.
Cons of money financing:
- Excessive reliance on money financing leads to increased inflation, with well-known cases of hyperinflation including Zimbabwe and Venezuela.
- If money financing is used to finance unproductive but politically favoured projects, then the growth term in the change in debt equation may fall.
During the pandemic, QE purchases by the Bank of England mirrored issuance of new debt by the UK government.
- Debt is not cancelled and does not disappear when the Bank of England purchases a bond.
- The Bank of England receives interest payments on the bond and receives payment when the bond matures.
- The Bank pays these funds back to the government.

The Open Economy

Exchange Rates

Capital mobility measures how responsive investment flows are to interest rate differentials.
- Our explanation of UIP assumes no costs to swapping one currency for another sometime in the future.
  - If there are costs, these would need to be deducted from the expected returns from a foreign investment, reducing the expected return.
- As a result, the incentive to invest abroad is reduced as foreign interest rates rises are reduced.
- If there are transaction costs, capital mobility is not perfect.
The nominal exchange rate, denoted as E, is the rate at which one currency can be exchanged for another.
We define the nominal exchange rate between country A and country B as the amount of country A’s currency that must be paid to purchase one unit of country B’s currency.
Thus, the nominal exchange rate is the price of foreign currency.
- For example, the nominal exchange rate of the pound against the euro is the number of pounds it costs to buy 1 euro.
We refer to country A as the domestic economy and the currency of country A as the domestic currency.
The domestic currency depreciates if the price of foreign currency increases.
Thus, an increase amount of domestic currency is needed to purchase a unit of foreign currency.
- For example, a depreciation of the pound against the euro implies that the number of pounds needed to buy a euro increases.
Thus, a depreciation of the nominal exchange rate means that E increases.
Our definition of E is always pound Sterling first, foreign currency second, e.g., GBPEUR.
Exchange rates are more volatile than, e.g., output, employment, and inflation, with substantial shifts in short time periods.
We denote the real exchange rate as R.
The real exchange rate of the domestic economy is defined as equal to the effective nominal exchange rate of the domestic economy multiplied by the world price level (the foreign price level converted into domestic currency), over the domestic price level.
- Thus, the real exchange rate is equal to the world price level relative to the domestic price level.
So, the real exchange rate measures relative prices in terms of domestic currency.
The real exchange rate also measures (inversely) relative prices in terms of foreign currency.
A depreciation of the real exchange rate means that R increases.
A depreciation of the real exchange rate occurs if:
- The nominal exchange rate depreciates, i.e., E increases.
- The foreign price level increases, i.e., P^w increases.
- The domestic price level decreases, i.e., P decreases.
The rate of depreciation of the real exchange rate is the proportional change of the real exchange rate.
The rate of depreciation of the real exchange rate is equal to the rate of depreciation of the nominal exchange rate plus the world inflation rate minus the domestic inflation rate.

Exports, Imports, and the Current Account

Imports depend on the price of foreign goods in terms of domestic currency, relative to the price of domestic goods.
- The relative price of foreign goods in terms of domestic currency is the real exchange rate.
We assume that the demand for imports is higher when the relative price of imports is lower, so imports are higher when R is lower.
A depreciation in R leads to a reduction in imports.
The demand for imports is equal to the sensitivity of imports to income multiplied by national income less the sensitivity of imports to the real exchange rate multiplied by the real exchange rate.
Exports depend on the price of domestic goods in terms of foreign currency relative to the price of foreign goods.
- The relative price of domestic goods in terms of foreign currency is the inverse of the real exchange rate.
We assume that the demand for exports is higher when the relative price of exports is lower, so exports are higher when R is higher.
A depreciation in R leads to an increase in exports.
The demand for exports is equal to the sensitivity of exports to world income multiplied by world income plus the sensitivity of exports to real exchange rate multiplied by the real exchange rate.
The Current Account is the difference between exports and imports.
The Current Account is in equilibrium when it is equal to 0. This gives a vertical current account equilibrium line.
- This line shifts left towards a current account surplus as R appreciates (decreases) or world income decreases.
- This line shifts right towards a current account deficit as R depreciates (increases) or world income increases.
If the economy is in Current Account equilibrium, but the real exchange rate depreciates, imports will fall, and exports will increase.
- At the existing value of output, the economy will move into Current Account surplus.
- To restore Current Account equilibrium, imports must increase, which requires higher output.
We next extend the IS curve to incorporate the open economy. National income is now equal to the sum of consumption, investment, expenditure, and the current account.

The Capital Account

The capital account (CP) is the sum of cross-border financial transactions that do not involve the public sector.
We analyse the capital account using the Uncovered Interest Parity (UIP) relationship. This is the relationship between the domestic interest rate, the change in nominal exchange rate expected in the next period, and the foreign interest rate.
If an investor is risk-neutral, they are indifferent between a certain return of the domestic interest and a certain return from an overseas investment.
The return from the overseas investment is uncertain because the investor does not know next year’s exchange rate when making this decision.
- This is the Uncovered Interest Rate Parity (UIP) condition. It is essentially a no-arbitrage condition.
Arbitrage occurs when an investor can, or expects to, gain higher returns from an investment rather than from an alternative.
- If the expected return from investing abroad were higher than the certain return from investing in the domestic economy, investors would only invest abroad.
- This is not an equilibrium – in equilibrium, risk-neutral investors must be indifferent between investing in the UK or the US.

Equilibrium

Equilibrium is where variables are constant, are expected to remain constant, and expectations are correct.
In macroeconomic equilibrium, the exchange rate is constant and expected to remain constant.
The capital account is equal to capital mobility multiplied by the domestic interest rate in the current term less the foreign interest rate in that same term.
- Note that this is only true in equilibrium.
Out of equilibrium, the capital account will also depend on expected exchange rate movements.

Balance of Payments

The Balance of Payments (BoP) is the sum of the current account and the capital account.
The BoP is always zero.
The FE curve shows combinations of output and interest rates at which the Balance of Payments equals zero.
In equilibrium, the sum of the current and capital accounts is the FE curve.
- Remember: out of equilibrium, the capital account also depends on expected exchange rate movements.
We now assume perfect capital mobility. This means capital mobility is close to infinity.
- Thus, the FE curve simplifies to domestic interest = foreign interest, and the FE curve is horizontal.
When capital mobility is very small, the FE curve slopes up, and there is a balance of payments surplus. When capital mobility is very large, the FE curve slopes down, and there is a balance of payments deficit.
- Check this.
We implicitly assumed perfect capital mobility when using UIP.
Since in equilibrium, the UIP condition simplifies to domestic interest = foreign interest.
The BoP is always in equilibrium, but the current and capital accounts are not necessarily in equilibrium.
- The capital account is only in equilibrium if interest rates are equal to the world interest rate.
  - We assume this holds in the flex-price Mundell-Fleming model.
- This assumes the capital account is in equilibrium in this model.
- This also implies that the current account is in equilibrium in our analysis.

Open Economy Macroeconomic Policy

The Mundell-Fleming Model

In the open economy, macroeconomic equilibrium occurs when the economy is simultaneously on the IS, LM, and FE curves.
- We only consider cases where the macroeconomy is in equilibrium.
- This implies that variables are constant and are expected to remain constant.
- Thus, we assume expected exchange rates are the same as current exchange rates, and domestic interest is the same as world interest.
The Mundell-Fleming model is an extension of the IS-LM model to the open economy.
- MF uses Classic LM, and the interest rate is equal to the world interest rate.
  - In the flex-price Mundell-Fleming model, the money supply is exogenous, and thus is not explained by the model.
  - Thus, someone has to set the money supply. The model assumes this is done by a monetary policymaker.
- The LM curve in the open economy is the same in the closed economy.
LM is a relationship between domestic output and the interest rate.
- With the interest rate determined by the world interest rate, LM determines domestic output.
The Mundell-Fleming open economy IS-LM model considers fixed and flexible nominal exchange rates, but we will only consider flexible exchange rates.
The three relationships (IS, LM, FE) are used to determine output, interest rate, and exchange rate.
- These are all endogenous variables in the flex-MF model.
If the exchange rate is flexible:
- The FE curve fixes the interest rate.
- The LM curve determines output.
- The IS curve determines the exchange rate.
The position of the economy is determined by the intersection of the LM and FE curves.
The real exchange rate will adjust to ensure the IS curve also passes through this point.
The equilibrium exchange rate is defined as the exchange rate that ensures that the IS curve passes through the point where the LM and FE curves intersect.
- If R is less than the equilibrium exchange rate, the real exchange rate must depreciate (R increases). This shifts the IS curve right, so IS, LM, and FE all intersect.
- If R is higher than equilibrium exchange rate, the real exchange rate must appreciate (R decreases). This shifts the IS curve left, so IS, LM, and FE all intersect.
Taken together, we can summarise the Mundell-Fleming model as:
- The interest rate is determined by the world interest rate;
- Output is determined by the LM curve;
- The exchange rate is determined by the IS curve.
Because of perfect capital mobility, and in equilibrium, the FE curve fixes the domestic interest rate to be equal to the world interest rate.
- Given this, the LM curve determines output.
- Government expenditure only enters the IS curve.
- The exchange rate also only enters the IS curve, which determines the exchange rate given output and the interest rate.
  - Graphically, the IS curve must go through the point where the FE and LM curves intersect.
- An increase in government expenditure does not shift the FE or LM curves.
  - It therefore does not affect output or the interest rate.
- The IS curve must still intersect the point where the FE and LM curves intersect – this point has not changed.
  - Thus, the increase in government expenditure must be offset by an exchange rate appreciation.
In Mundell-Fleming, a recession can only be caused by two things:
- A reduction in the world interest rate; and
- A reduction in the money supply.
Note:
- Fiscal policy does not influence output or the interest rate.
- Monetary policy does not influence the interest rate.

	Domestic interest rate i	Domestic income Y	Real exchange rate R
World interest rate i^w	+	+	+
World income Y^w	0	0	-
Money supply M/P	0	+	+
Government expenditure G	0	0	-

The model has three endogenous variables: I, Y, and R.
And 4 exogenous variables: i^w, Y^w, M/P, and G.

Macroeconomic Policy with Flexible Exchange Rates

Fiscal Policy

There are 3 endogenous variables in the flex-price Mundell-Fleming model:
- Interest rates;
- Output; and
- The real exchange rate.
Because of perfect capital mobility, interest rates are equal to the exogenous world interest rate.
The endogenous variables in the LM curve are interest rates and output.
- Thus, if the interest rate is determined by the world interest rate, output is thus determined by the LM curve.
The IS curve is a relationship between all 3 endogenous variables.
- If interest rates and output are determined through the FE and LM curves, the IS curve must then determine the real exchange rate.
The equilibrium values of output and the interest rate are not affected by fiscal policy.
- Thus, output and interest rates do not change following a fiscal expansion.
However, the fiscal expansion does load to an exchange rate appreciation.
- Thus, in the new equilibrium, output and interest rates are unchanged but the exchange rate has appreciated.
Diagrammatically, nothing happens:
- A fiscal expansion shifts out the IS curve.
- But the exchange rate appreciation shifts in the IS curve.
- These shifts exactly offset each other.
Why a fiscal expansion under perfect capital mobility and flexible exchange rates does not change output or the interest rate but does cause the exchange rate to appreciate:
- The equilibrium values of output and the interest rate are not affected by fiscal policy, but the equilibrium value of the exchange rate is.
- Thus, output and interest rates do not change following a fiscal expansion, but the fiscal expansion does lead to an exchange rate appreciation.
The equilibrium point is where the LM curve cuts the FE curve.
- The exchange rate will adjust so that the IS curve intersects this point.
A fiscal expansion does not shift either the FE or the LM curves.
- Thus, a fiscal expansion does not change the equilibrium point.
- Everything else equal, the fiscal expansion shifts out the IS curve.
- However, the IS curve has to intersect the unchanged equilibrium point.
- Thus, the exchange rate has to adjust to offset the impact of the fiscal expansion on the IS curve. This implies an appreciation.

Monetary Policy

A monetary expansion (increase in the money supply) shifts out the LM curve to intersect the FE curve at a higher level of output.
The economy moves to a new equilibrium with the same interest rate but higher output.
The exchange rate depreciates – this shifts out the IS curve to intersect with the FE and new LM curves.
- An excess supply of home currency caused by falling interest rates depreciates the domestic currency, raising net imports and shifting out the IS curve.
The depreciation reinforces the impact of monetary policy on output.
Why a monetary expansion under perfect capital mobility and flexible exchange rates increases output, does not change the interest rate, and causes the exchange rate to depreciate:
- The domestic interest rate is set by the world interest rate and is independent of the money supply.
- Domestic output depends on the interest rate and the money supply (the LM curve determines output in the Mundell-Fleming model), so a monetary expansion increases output.
- The real exchange rate depends on the money supply, with a positive coefficient.
- Thus, a monetary expansion leads to a depreciation.

Increase in the World Interest Rate

The FE curve shifts up.
The economy moves to a new equilibrium with increased output and interest rates.
The exchange rate depreciates – this shifts out the IS curve to intersect the LM curve and the new FE curve.
- The impact of investment from higher interest rates is more than offset by the boost to demand resulting from the exchange rate depreciation and which causes IS to shift out.
Effect on UK economy of Fed reduction of policy rate:
- The simple Mundell-Fleming model with perfect capital mobility imply this would reduce interest rates, reduce output, and lead to an appreciation of the pound.
- This did not happen – the Mundell-Fleming model is overly simple and lacks realism.
Effect on foreign economy of a domestic recession:
- Output and the interest rate would not be affected, but the exchange rate would depreciate.

Increase in World Income

The equilibrium values of output and the interest rate are not affected by world income.
Thus, output and interest rates do not change following an increase in world income.
The exchange rate appreciates.
Thus, in the new equilibrium, output and interest rates are unchanged but the exchange rate has appreciated.
Diagrammatically, nothing happens:
- An increase in world income shifts out the IS curve.
- But the exchange rate appreciation shifts in the IS curve.
- These shifts exactly offset each other.

Aggregate Demand and the Labour Market

Aggregate Demand

Aggregate demand is a relationship between the output gap and the inflation gap.
- We use the output gap as a measure of the business cycle.
- We find the output and inflation gaps by equating aggregate demand and aggregate supply.
The following analysis of aggregate demand builds on the IS-LM model.
The IS curve is a negative relationship between output and the interest rate.
As opposed to the simple, stylised IS relationship in Topic 1, we will instead use the real interest rate rather than the nominal interest rate, and we assume a relationship between the log of output and the interest rate.
We alter the IS curve to:
- Add a demand shock;
- Use the real interest rate r rather than the nominal interest rate i;
- Assume a relationship between log output and the interest rate.
A demand shock is a change to aggregate demand that was not expected.
- They can come from unexpected changes to government expenditure, so policymakers can create demand shocks.
- They might also come from unexpected changes to consumption or investment.
The equilibrium level of output is denoted as Y*.
The equilibrium real interest rate is denoted as r*.
There are no shocks in equilibrium.
The output gap is log(Y) – log(Y*).
- This is the proportional distance between actual and equilibrium output.
In equilibrium, the output gap is zero.
- If the output gap is zero and then a shock makes the output gap non-zero, equilibrium is only restored when the output gap is again zero, since only then expectations are correct.
We are only explaining he output gap, not output.
- An unexpected fiscal expansion will shift out AD, but anticipated changes in government expenditure will have no effect.
We denote inflation as pi.
- Inflation in period t is the proportionate change in the price level compared to the previous period.
It is approximately equal to the change in the log price level.
The real interest rate in the current period is equal to the nominal interest rate in the current period less the expected inflation rate in the next period.
- Expected inflation affects the AS curve but not the AD curve.
We assume that policymakers use a monetary policy rule that is more sophisticated than that previously considered.
We assume policymakers have an inflation target of pi = pi^T and wish output to be at the equilibrium level.
- A reduction in the inflation target will shift the AD curve to the left.
- Intuitively, a lower inflation target implies interest rates are higher for any given value of inflation, leading to lower aggregate demand.
We represent the interest rate chosen by policymakers using the Taylor rule.
The Taylor rule states that policymakers raise the interest rate if:
- Inflation is too high; or
- Output is too high.

Aggregate Supply

We analyse the labour market, considering labour demand and supply. We do this for:
- Competitive labour markets, to see the forced that drive employment and wages.
- Non-competitive labour markets, to understand how this leads to unemployment.
We will then:
- Show how sticky prices lead to an AS curve that slopes up in the short run; and
- How flexible wages and prices lead to a vertical AS curve.
We begin with the competitive labour market. Here, labour market outcomes are determined by the intersection of labour demand and labour supply relationships.

Labour Demand

The production function is Y = F(L).
L is labour input purchased by the firm.
The marginal product of labour MPL is the derivative of output with respect to employment – it is the slope of the production function.
We assume diminishing returns to labour, so MPL > 0.
Firm profit is equal to the price level multiplied by output less the wage bill multiplied by labour input purchased.
The real wage is defined as the wage bill divided by the price level.
At a given capital stock, the more labour is being used, the smaller the marginal product of labour becomes.
Firms choose employment to maximise profit, subject to the production function.
We assume that the goods market is competitive – the employment choice of the firm does not affect the price.
The optimality condition is when the price level multiplied by the derivative of output with respect to employment, less the wage bill, is equal to 0.
This implies that the marginal product of labour is equal to the wage bill over the price level, a.k.a., the real wage.
- This is the labour demand relationship.
Labour demand determines the real wage:
- Firms offer a fixed wage, independent of employment.
- Labour supply determines employment as the number of workers willing to work at the wage offered by firms.

Labour Supply

The utility function of a worker is the function of consumption and labour input purchased.
We assume the derivative of the utility function with respect to consumption is greater than 0 and the derivative of the utility function with respect to labour input purchased is less than 0.
The worker’s budget constraint is equivalence of the price level multiplied by consumption to the wage bill multiplied by labour input purchased.
Consumption, then, is equal to the real wage multiplied by labour input purchased.
The budget constraint implies the derivative of the worker’s utility function with respect to labour input purchased is equal to the real wage.
The budget constraint alongside the decision to maximise L gives the upward-sloping labour supply curve.

Competitive Labour Market

If the labour market is competitive, the real wage adjusts to equate the demand and supply of labour.
In a competitive labour market, labour demand equals labour supply.
The real wage is the real marginal cost of labour in a competitive labour market.
- Note that the real marginal cost of labour is not he same as the real marginal cost of output.
The equilibrium wage is denoted as w* - at this wage, labour demand equals labour supply.
If w > w*:
- Unemployed workers would be willing to work for a lower real wage than currently paid.
- Thus, the real wage falls to w*.
If w < w*:
- Firms would be willing to pay a higher wage than currently paid.
- Thus, the real wage rises to w*.
Excess supply of labour drives real wages down.
Excess demand of labour drives real wages up.
Why the real wage reflects the workers’ dislike of working and the firm’s ability to pay:
- The real wage reflects labour demand and labour supply.
- This is most obvious in a competitive labour market but is also true in a non-competitive labour market.
- The labour supply curve shows the maximum number of hours a worker will choose to work for a given wage.
- As workers dislike work, they must be paid more to induce them to supply more labour.
- Thus, the wage reflects the workers’ dislike of working.
- The labour demand curve comes from equating the revenue earned by a firm from employing an additional worker to the input cost of labour purchased by the firm.
- The firm’s ability to pay reflects revenue, so the wage reflects the firm’s ability to pay.

Unemployment

The ONS measures a worker as being unemployed if they:
- Do not have a job;
- Have been actively seeking work in the past four weeks; and
- Are available to start work in the next two weeks.
In a competitive labour market, all workers who wish to work can get jobs, so there would be no measured unemployment.
Thus, the unemployment data is a challenge to competitive labour markets.
We might explain involuntary unemployment by observing how, in a competitive labour market, the real wage will fall if labour supply exceeds labour demand.
In an imperfectly competitive labour market, this may not happen – the wage may be above the competitive wage.
If it is, labour supply will exceed labour demand, and there will be involuntary unemployment.
Thus, we can explain involuntary unemployment if the wage is above the competitive wage.
Involuntary unemployment can be explained via the following:
- There is bargaining over the wage between employers and a trade union;
- A legal requirement, for example a minimum wage; or
- The firm may choose to offer a higher wage in order to increase effort or to reduce labour turnout.
With each of these, the wage will be above the competitive wage, labour supply will exceed labour demand, and there will be involuntary unemployment.
Involuntarily employed workers will be measured as unemployed by the ONS.
Wage bargaining is complicated. We will use a stylised and unrealistic simplified model.
In this model, the union chooses the wage to maximise its utility, subject to the labour demand curve.
The union chooses the wage at the point where there is a tangency between the labour demand curve and the union indifference curve.
As the labour demand curve moves in and out, this gives a relationship between employment and wages. This can be described as the Trade Union Supply Curve.
How payroll tax would affect employment if the real wage was chosen by a trade union:
- In much the same way as in a competitive labour market.
- The tax shifts the labour demand curve to the left.
- The wage chosen by the union will fall.
- Thus, employment and real wages fall.
The strengths and weaknesses of the Monopoly Union model:
- Strengths:
  - It can explain unemployment; and
  - It is simple.
- Weakness:
  - It is highly unrealistic and can give rise to ill-founded policy implications.
- Recent debates about declining worker bargaining power and firm monopsony power do not fit into this framework.
- There are better explanations of unemployment than simply attributing it to unions.

Aggregate Supply and Business Cycles

Sticky Prices

Sticky process lead to an upward-sloping AS curve in the short-run.
Sticky prices are the basis of New Keynesian DSGE models.
- These are the most widely used models of the business cycle used in Central Banks and academic research.
- These models assume that firms cannot always change price.
In our simple version of the model, there is a fixed probability that a fir can change price in any period.
This analysis is based on a classic paper by Mankiw: The Inexorable and Mysterious Tradeoff Between Inflation and Unemployment.
- Mankiw’s notation is consequentially used here.
Assume a 50/50 chance that firms can change price.
- I.e., the probability of a firm being able to change price lambda = 0.5.
Also assume that firms are identical, apart from the fact that, in any period, 50% of firms can change price and 50% cannot.
p denotes the log of the price level.
x denotes the log of the price chosen by firms that are able to change price.
p* denotes the log of the price that firms would choose if they could change price in every period.
All firms that can change price will choose the same price.
- lambda = 50% of firms can change their price in this period. They all the same price: x_t.
- lambda(1 – lambda) = 25% of firms were able to change their price in the previous period, but cannot change price in this period. In the previous period, these firms all chose the same price: x_t-1.
- lambda(1 – lambda)² = 12.5% of firms were able to change their price two periods ago but were not able to change price since then. Two periods ago, these firms all chose the same price: x_t-2.
- lambda(1 – lambda)³ = 6.25% of firms were able to change their price three periods ago but were not able to change price since then. Three periods ago, these firms all chose the same price: x_t-3.
- And so on and so forth.
Again, assume lambda = 0.5. The price that firms choose are as follows:
- Assuming that firms’ preferred price in period t is p*_t.
- lambda = 50% of firms can change their price in this period. Their preferred price in this period is p*_t.
- lambda(1 – lambda) = 25% of firms can change price in this period, but will not be able to change price in period t + 1. Their preferred price in period t + 1 will be p*_t₊₁. Firms don’t know this in period t, so they use the expected value E_tp*_t₊₁.
- lambda(1 – lambda)² = 12.5% of firms can change price in this period, but will not be able to change price in either period t + 1 or t + 2. Their preferred price in period t + 2 will be p*_t₊₂. Firms don’t know this in period t, so they use the expected value E_tp*_t₊₂.
- And so on and so forth.
However, if we instead assume prices are not sticky and are flexible, firms can always change price. Thus, lambda = 1.
If prices are flexible, firms always choose their current preferred price.
The IS-LM model analysed previously assumed that prices are fixed.
We fit fixed prices into the IS-LM model by defining the price level as the price level in the current period.
Thus, New Keynesian models lie between two extremes:
- Prices are fixed (IS-LM model)
- Prices are flexible (lambda = 1), i.e., the Real Business Cycle (RBC) model.
To find the firm’s preferred price, we assume:
- There are many firms, all producing different goods using the same technology;
- The demand for a firm’s output depends on the price it sets relative to other firms; and
- This demand function has a constant elasticity.
The preferred price for a firm is then the equivalence of the equilibrium price level less the price level to the log of the market-up of price over marginal cost plus the log real marginal cost.
We next assume that marginal cost is higher when output is higher. This is the key link between inflation and the business cycle.
As the output gap rises, output increases, so employment increases.
If the labour market is competitive:
- Real wages have to rise in order to induce workers to supply more labour.
- This increases real marginal cost.
If wages are chosen by unions:
- Real wages rise because the labour demand curve shifts out.
- In response to this, unions increase the real wage.
- This increases real marginal cost.
Thus, these assumptions are consistent with a range of different models of the labour market.

Aggregate Supply

As aforementioned, the AS curve slopes up when the economy is out of equilibrium, but it is vertical when it is in equilibrium.
In this model, equilibrium means:
- All firms set their desired price, so p_t = p*_t;
- Output is at equilibrium, so the output gap is zero; and
- Expectations of inflation are correct.
Equilibrium does not imply that prices are constant.
But it does imply that inflation is constant.
Next, we introduce productivity shocks.
These shocks shift the AS curve.
A positive productivity shock:
- Increases productivity;
- Which reduces marginal cost;
- Which reduces inflation.
Note that the AS curve cuts the vertical axis where inflation equals expected inflation when there are no shocks.
If there are no shocks and the output gap is positive, inflation must exceed expected inflation.
With shocks and a positive output gap, inflation can be less than expected inflation if the productivity shock is sufficiently positive.
If expected inflation falls, inflation can fall even if the output gap is positive. This is the self-fulfilling aspect of inflation expectations.

The Business Cycle

Inflation and the output gap are determined by the intersection of the Aggregate Demand and Supply relationships.
In equilibrium, there are no shocks: inflation equals the inflation target equals expected inflation.
We model the business cycle as follows:
- The economy is in equilibrium;
- Then, it is hit by a temporary shock that lasts for one period;
- In the period it hits, this shock moves output and inflation away from equilibrium.
We consider the case where expectations of inflation are anchored: expected inflation always equals the inflation target.
In this case, the economy returns to equilibrium immediately after a shock ends.
This gives useful insights into business cycles but does not capture the persistent effects of shocks over time that characterise the business cycle.
We analyse anchored expectations because it is simple.
With anchored expectations:
- A positive demand shock leads to:
  - Higher output; and
  - Higher inflation.
- A positive productivity shock leads to:
  - Higher output; and
  - Lower inflation.
- The shocks last for one period.
- After this, the economy immediately returns to equilibrium.
Negative aggregate demand and productivity shocks have the opposite effects.
In the case of anchored expectations, expected inflation will not always equal the inflation target.
- Expectations are only correct in equilibrium.
- If citizens understand how the economy works, then they know that shocks will change inflation.
- Thus – is it sensible to assume that expectations do not change when shocks occur?
Our analysis with anchored explanations implies that business cycle expansions and contractions last for one period only.
- In reality, they last for several years.
- There are two ways to adjust our model to make expansions and contractions last for multiple periods.
  - Firstly, allow for non-anchored expectations.
    - With these, expectations change when there are shocks.
    - This gives rise to persistent deviations of output and inflation from equilibrium.
  - Or, adapt the model to incorporate lags into price-setting or wage-setting.
    - With these, the impacts of shocks take time to work their way through wages and prices.
    - This generates more persistent deviations of output and inflation from equilibrium.
Note:
- Demand shocks increase output and increase inflation;
- Productivity shocks increase output and reduce inflation.
The impact of these shocks depends on the stickiness of prices.
- A shock that shifts the aggregate supply curve to the right will increase output and decrease inflation. These changes are larger if prices are flexible.

Business Cycles with Flexible Prices

If prices are instead flexible and not sticky, the AS curve:
- Is vertical; and
- Is shifted by productivity shocks.
When prices are flexible:
- A positive aggregate demand shock increases inflation but does not affect output;
- The impact of an aggregate demand shock on inflation is larger when prices are flexible;
- A positive productivity shock leads to higher output and lower inflation; and
- The impact of a productivity shock on output and inflation is stronger when prices are flexible.
If prices are flexible then firms can always change price, so lambda = 1.
- Thus, the AS curve simplifies to the output gap equals the productivity shock.
So, if prices are flexible and not sticky, the AS curve:
- Is vertical; and
- Is shifted by productivity shocks.
In conclusion, if prices are flexible:
- Demand shocks do not affect output;
- Demand shocks have a larger impact on inflation; and
- Supply shocks have a larger impact on both inflation and the output gap.
The AS becomes flatter when prices are less flexible. In this case, the impact of a demand shock on the output gap is larger and the impact on inflation is smaller.

Modelling the Covid-19 Pandemic

The main facts to explain here are:
- A large fall in output; and
- A small change in inflation.
Our explanation is based around:
- A large negative aggregate demand shock; and
- A large negative aggregate supply shock.
Adverse supply shocks include:
- Workers sick or self-isolating;
- Reduced productivity due to employees working from home;
- Lost output due to job losses and increased corporate failures; and
- The Job Retention Scheme, which enabled large numbers of workers to step away from the workplace.
Adverse aggregate demand shocks include:
- Reduced consumption; and
- Reduced investment.
Adverse demand shocks were partially offset by:
- Reduced interest rates and increased QE; and
- Increased government expenditure.

Current Policy Issues

The current UK macroeconomic environment is dominated by a large negative supply shock that is:
- Pushing up inflation; and
- Pushing the economy towards a recession.
Without intervention, the economy shifts towards a negative output gap and higher inflation.
Note that monetary policy is rather passive in response to a supply shock, since:
- Higher inflation increases the interest rate; and
- Lower output reduces the interest rate.
Faced with an adverse supply shock, there are no good fiscal policy options.
- Policymakers could expand aggregate demand:
  - This would help prevent a recession; but
  - This would push inflation further above the target.
- Or, policymakers could reduce aggregate demand.
  - This would help move inflaton towards the target; but
  - This would make a recession worse.
Note that this discussion is separate from the debate on the “growth agenda” – the attempt to increase productivity growth and, through this, increase the equilibrium level of employment.

The Labour Market

Job Matching

There are unemployed workers in the labour market searching for employment.
Firms with unfilled vacancies are also searching for workers.
A job match is formed when an unemployed worker is hired by a firm with an unfilled vacancy.
The matching process is described by a matching function.
Job matching is not perfect, so some unemployed workers do not find jobs, and some vacancies remain unfilled.
Assume the number of unemployed workers is u.
And the number of vacancies is v.
Labour market tightness theta, a key variable in the search model, is equal to v over u.
- This is the number of available jobs per unemployed job seeker.
Unemployed workers find a job at rate f – f equals job matches h over the number of unemployed workers u.
The average duration of unemployment is 1/f.
We assume a proportion tau of workers leave employment in each period – this is the separations rate or job destruction rate.
Vacancies are filled at rate q. q = job matches over the number of vacancies.
The average duration of a vacancy is 1/q.
An increase in the efficiency of job matching (m) causes the job finding and vacancy filling rates to both increase.
- If the efficiency of job matching increases, both firms and workers find matches more rapidly.
Vacancies are pro-cyclical (i.e., have a positive correlation with output).
Unemployment is anti-cyclical.
- Post-2008, unemployment rose and vacancies fell.

The Equilibrium Rate of Unemployment

The labour market is dynamic.
But these dynamics are complicated to analyse.
We assume that the labour market is in equilibrium.
Thus, we analyse the determinants of unemployment, vacancies, and wages in equilibrium.
The rate at which workers enter unemployment is the inflow rate I, where n = 1 – u is the employment rate.
The rate at which workers leave unemployment is the outflow rate O; O = fu.
In equilibrium, the inflow and outflow rates are equal – I = O – so tau(1-u) = fu.
This implies that the equilibrium unemployment rate is tau over tau plus f.
The equilibrium unemployment rate is higher when:
- tau is higher – when the probability of becoming unemployed is higher; or
- f is lower – when the probability of leaving unemployment is lower.
There are marked differences between US and European labour markets.
- In the US:
  - Employed workers are much more likely to become unemployed; but
  - Unemployed workers are much more likely to find a job.
The marked differences in f and tau do not imply marked differences in equilibrium unemployment rates because a high separations rate is matched by a high job finding rate.
An increase in the efficiency of job matching (m) increases f and thus reduces equilibrium unemployment.
If country A has a higher value for labour market tightness than country B, but the rate of job destruction is the same across both countries, country B has a higher equilibrium unemployment rate as a tighter labour market implies a higher job finding rate.

The Beveridge Curve

The Beveridge Curve is a negative equilibrium relationship between unemployment and vacancies.
The Beveridge Curve will shift out if:
- m decreases – job matching becomes less efficient; or
- tau increases – the probability of becoming unemployed increases.
Along the Beveridge Curve, the inflow rate equals the outflow rate.
However, this analysis ignores an important issue.
Our analysis has assumed there are only two labour market states: workers can either be employed or unemployed.
In reality, there are four labour market states: workers can be employed, unemployed, inactive, or self-employed.
- The numbers inactive or self-employed are much larger than the numbers unemployed.
We will stick to the assumption that there are only two labour market states (employed or unemployed), but we need to be aware of the weakness of that assumption.
If the equilibrium rate of unemployment increases, the Beveridge Curve does not shift out.
- The economy is on the Beveridge Curve in equilibrium, so unemployment equals equilibrium unemployment along the Beveridge Curve.
- If equilibrium unemployment increases, the economy shifts down along the Beveridge Curve.

Unemployment, Vacancies, and Wages

A Search Model

Each firm has a single job slot for a single worker.
Jobs are either filled or vacant.
If the job is filled, output is y.
We assume, for simplicity, that output is constant.
If output is constant, the wage will be constant.
And so will be theta, f, and q.
The lifetime profit of a firm with a currently filled job slot is denoted as J.
And the lifetime profit of a firm with a current vacant job slot is denoted as V.
In the current period, output is y and the cost of labour is w.
With probability (1 – tau), the job remains filled filled and productive in the next period.
- If so, discounted future profit in that period is again J.
With probability tau, the job match breaks down in the next period.
- If so, discounted future profit in that period is V.
Firms must pay a real cost of gamma to post a vacancy.
With probability q, the next vacancy is filled, and the job becomes productive in the next period.
With probability (1 – q), the vacancy remains unfilled.
We assume the profit of a firm with a current vacancy is zero.
The value of a firm with a productive job match is positive, J > 0, even though the value of a vacancy is zero, V = 0.
This is because a firm with a productive job match does not have to incur the cost of hiring a new worker.

The Vacancy Creation Curve

Higher wages lead to less employment and more unemployment, similar to the labour demand curve.
- If workers find jobs at a lower rate, more workers are unemployed.
- Thus, there is more unemployment and less employment.
Since output is fixed, y is an inverse relationship between theta and w.
- This is the vacancy creation curve.
The Vacancy Creation Curve will shift out if:
- m increases – job matching becomes more efficient, so vacancies are filled faster.
  - In this case, vacancies get filled more easily, so the cost of recruiting a worker decreases.
  - As such, the firm posts more vacancies.
  - In addition, labour market tightness increases.
- gamma decreases – the cost of posting a vacancy falls.
- tau decreases – the probability an employed worker becomes unemployed falls.
The Vacancy Creation Curve shifts out if the rate of job destruction falls.
- Posting a vacancy is similar to making an investment: firms incur short-run costs and get long-run benefits.
- If the rate of job destruction falls, on average, firms get the benefits of a filled job match for longer, so the benefits of posting a vacancy increase, leading to increased posting of vacancies.
An increase in the efficiency of job matching leads to an increase in labour market tightness (for a given wage).
- If matching efficiency m increases, a vacancy is more likely to be filled, so the cost of hiring a worker goes down and the Vacancy Creation Curve shifts out.

Wage Bargaining

A firm and a worker bargain over the wage.
This occurs in every period.
We represent the bargained wage as the wage that maximises the utility of an employed worker less the utility of an unemployed worker, multiplied by the firms’ bargaining power parameter phi, multiplied by the lifetime profit of a firm with a currently filled job slot, to the power of 1 less the firms’ bargaining power parameter.
When phi = 1:
- Workers have full bargaining power; and
- The wage maximises the objective of workers.
When phi = 0:
- Firms have full bargaining power; and
- The wage maximises the objective of firms.
The objective of a firm in the wage bargain is to maximise the value of a job match.
- This implies a low wage.
The objective of a worker in the wage bargain is to maximise the utility of an employed worker less the utility of an unemployed worker, i.e., the value of being employed compared to the value of being unemployed.
- This implies a high wage.
To find the wage, we maximise the bargain with respect to the wage.
The total surplus from a job match S is equal to the value of being employed compared to the value of being unemployed plus the lifetime profit of a firm with a currently filled job slot.
The worker gets a share phi of the surplus from the job match, and the rest goes to the firm.
The worker earns a wage w. We assume they consume this and gain utility of w.
Thus, utility from consumption is assumed to be linear.
With probability (1 – tau), they are employed in the next period.
- If they are employed, they have utility L in that period.
With probability tau, they are unemployed in the next period.
- If they are unemployed, they have utility U in that period.
An unemployed worker consumes real unemployment benefits paid to unemployed workers b and gain (linear) utility of b.
With probability f, they find a job in this period and become employed in the next period.
- If they are employed, they have utility L in that period.
With probability (1 – f), they do not find a job in this period and remain unemployed in the next period.
- If they are unemployed, they have utility U in that period.
The reservation wage is defined as w^R.
- This is the wage at which workers are indifferent between employment and unemployment.
Thus, L = U when w = w^R.
- This is the minimum a worker must be paid to make them willing to work.
The reservation wage is a weighted average of the wage and unemployment benefits.
The weight on unemployment benefits is higher when:
- The probability an employed worker loses their job (tau) is higher; or
- The probability an unemployed finds a job (f) is lower.
If phi = 0:
- w = b;
- Workers have no bargaining power; and
- Firms set the wage as low as possible.
If phi = 1:
- w = y + gamma multiplied by theta.
- Firms have no bargaining power; and
- The worker sets the wage as high as possible.
If theta increases, the wage increases.
- There is an upward-sloping relationship between w and theta due to wage-setting.
The Wage-Setting Curve will shift out if:
- b increases – unemployment benefits increase, i.e., income of unemployed workers increase.
- gamma increases – the cost of posting a vacancy increases.
There is involuntary employment.
- This arises when workers who are unemployed would like to have a job.
Thus, the utility of the employed is higher than the utility of the unemployed.
This means that there is involuntary unemployment if L > U.
- Since w > w^R, it follows that L > U.
Thus, there exists involuntary unemployment.
The wage depends on the cost of posting a vacancy.
- If the worker and firm do not reach an agreement in the wage bargain, the job match is dissolved.
  - The firm then has a vacancy.
- Thus, the benefit to the firm of reaching an agreement is higher if the cost of posting a vacancy increases, so frms agree to a higher wage in the bargain.

The Complete Model

We have three relationships:
- The Beveridge Curve
  - A relationship between unemployment and vacancies.
  - Shows labour market equilibrium where the inflow from employment to unemployment equals outflow from unemployment to employment.
- The Vacancy Curve
  - A relationship between the wage and labour market tightness that reflects the optimality condition of firms.
  - It captures the incentive to post vacancies.
- The Wage Setting Curve
  - A relationship between the wage and labour market tightness that reflects the outcome of worker-form wage bargaining.
Note:
- The Beveridge Curve does not determine labour market tightness.
- An increase in bargaining power does not shift the Beveridge Curve.
  - Instead, it will move the economy to a new position on the curve.
We can combine these to find the complete model.
We do this in two stages:
- On a diagram with the wage and labour market tightness as axes.
  - Draw the vacancy creation and wage setting curves.
  - Their intersection gives the wage and labour market tightness.
- On a diagram with vacancies and unemployment as axes.
  - Draw the Beveridge Curve.
  - Take the value of labour market tightness from the first diagram and draw the job creation line – the slope of this is the value of theta.
  - The intersection of the Beveridge Curve and the job creation line gives unemployment and vacancies.
We will highlight the workings of the model by considering four cases:
- m increases – job matching becomes more efficient;
- tau increases – the probability of becoming unemployed increases;
- gamma increases – the cost of posting a vacancy increases; and
- b increases – unemployment benefits increase.

Job Matching Becomes More Efficient

If m increases:
- The matching function becomes more efficient;
- The Vacancy Creation Curve shifts out; and
- Intersects the Wage Setting line at a higher wage and a higher theta.
- The increase in theta implies that the job creation line rotates up.
- There is also an inward move of the Beveridge Curve;
- The rate of unemployment is lower; and
- Vacancies will rise or fall depending on which curve shifts most.

The Probability of Becoming Unemployed Increases

If tau increases:
- The job separation rate (or the rate of job destruction) increases;
- The Vacancy Creation curve shifts down; and
- Intersects the Wage Setting line at a lower wage and a lower theta.
- The reduction in theta implies that the job creation line rotates down;
- This reduces vacancies and increases unemployment.
- Also, the Beveridge Curve shifts out;
- This increases vacancies and unemployment;
- Unemployment increases; and
- The impact on vacancies is ambiguous.

The Cost of Posting a Vacancy Increases

If gamma increases:
- The cost of posting a vacancy increases;
- The Wage Setting Curve shifts up; and
- The Vacancy Creation Curve shifts down.
- This results in a lower theta.
- The wage will rise or fall, depending on which curve shifts more.
- The reduction in theta implies that the Job Creation Line (JCL) rotates down;
- Thus, unemployment is higher and vacancies are lower.