Exchange Rates and Monetary Policy

Question 1

What is the formula for the Real Exchange Rate?

Answer 1

RER = P*S/P
RER =  ((aN/aT)/(aN*/aT*))^gamma

Question 2

Explain what happens to the RER if the productivity of the tradable sector abroad improves?

Answer 2

This is modelled by a fall in the aT* variable. By the RER formula this causes an depreciation in the RER. This happens because the rise in productivity abroad drives up wages abroad. This increases the price of non-tradables abroad relative to tradables. The RER depreciates since now home currency buys less in real terms abroad.

Question 3

Explain how a shift in demand towards tradables affects the RER?

Answer 3

The RER is depreciates. The shift in preferences changes the optimal output of tradables and non-tradables. The increase in demand for tradables increases the price of tradable relative to non-tradables and deprecaites the RER.

Question 4

What is the difference between absolute and relative PPP?

Answer 4

Absolute PPP ————> RER~~1
Relative PPP ————-> RER ~~ Constant

Absolute PPP is a long run. Relative PPP holds in the short run/medium run. The RER can be constant when inflation differentials are compensated for by movements in the nominal exchange rate.

Question 4

What is the difference between absolute and relative PPP?

Answer 4

Absolute PPP ————> RER~~1
Relative PPP ————-> RER ~~ Constant

The RER can be constant when inflation differentials are compensated for by movements in the nominal exchange rate. Relative PPP holds in long-run and in countries with high inflation.

Question 5

What evidence is there for relative PPP?

Answer 5

Evidence suggest a half-life of 3 years. This means that half of the difference in PPP dissapears in 3 years (speed of convergence). The variance of nominal rates is much higher than inflation differentials.

Question 6

What explains the volatility of the RER?

Answer 6

Most of the volatlity can be explained by deviations from the law of one price for tradables. ~~0.95. Exchange rate pass through is quite low to tradables goods.

Question 7

What does the Cournot Model tell us about the effect of an exchange rate depreciation on quantities?

Answer 7

A depreciation makes domestic firms more competitive. Foreign producers lower their production.

Question 8

What is exchange rate pass through? How is it related to the mark-up charged by firms?

Answer 8

Exchange rate pass through is a measure of the elasticity of domestic prices to changes in the exchange rate. The higher the mark up the lower the pass through.

Question 9

Describe the classical approach to monetary policy?

Answer 9

The classical approach to MP assumes that prices are fully flexible, the exchange rate is fixed, and the money supply is endogenously determined.

Money is neutral and only effects the price level. There is no room for monetary policy to influence real variables. The economy is always in full employment.

Question 10

Desrcibe the goods market in the IS-LM model?

Answer 10

Y = C (Y - T, R) + I(R) + G + TB(P*E/P, Y - T)

Consumption - depends negatively on R
Investment - depends negatively on R
TB - depends negatively on RER

The higher the interest rate the lower output (downward IS curve).

Question 11

Describe the money market of the IS-LM model.

Answer 11

M/P = L(Y,R)
real money supply = real money demand. In equilibirum every point Y, R is on the LM curve and equates demand to supply of money. If R increases, then demand for money is lower but output must be higher to maintain the same demand for money.

Demand for money is increasing in output and decreasing in the interest rate.

R plotting against Y (upward LM curve).

Question 12

Using the IS-LM model describe monetary policy under a fixed exchange rate regime.

Answer 12

INEFFECTIVE.

Expansionary monetary policy reduces the nominal interest rate. From the IS equation this raises output. However, it increases demand for foreign currency putting downward pressure on the exchange rate. In order to maintain the nominal rate, the CB reduces the intrest rate. No effect.

Question 13

Using the IS-LM model describe the effects of monetary policy under flexible exchange rates.

Answer 13

HIGHLY EFFECTIVE

CB increases the nominal supply of money. This shifts the LM curve outwards. The interest rate falls to maintain equilibrium in the money market. Output increases. The nominal exchange rate depreciates which leads to a fall in RER due to sticky prices. This raises TB and shifts the IS curve outwards.

Question 14

Using the IS-LM model describe the effects of fiscal policy under fixed exchange rates.

Answer 14

HIGHLY EFFECTIVE

If G increases due to a fiscal expansion, then output increases and the IS curve shifts outwards. The interest rate increases due to higher demand for money transactions. The exchange rate experiences upward pressure. The CB lowers the policy rate by increasing the supply of nominal money. This shifts the LM curve outwards.

Question 15

Using the IS-LM model describe the effects of fiscal policy under flexible exchange rates.

Answer 15

INEFFECTIVE.

The government increases G. The IS curve shifts outwards which increases the intrest rate. The domestic rate is now above the world rate. This increases the demand for domestic currency and appreciates the curreny. Exports are more attractive and the trade balance goes into deficit. The IS curve falls back.

Question 15

Using the IS-LM model describe the effects of fiscal policy under flexible exchange rates.

Answer 15

INEFFECTIVE.

The government increases G. The IS curve shifts outwards which increases the intrest rate. The domestic rate is now above the world rate. This increases the demand for domestic currency and appreciates the curreny. Exports are more attractive and the trade balance goes into deficit. The IS curve falls back.

Question 16

What is a liquidity trap?

Answer 16

A liquiduity trap occurs when almost everyone prefers holding cash. In this situtation, monetary policy is ineffective. The liquiduity trap can happen in deflationary period when the real interest is bounded.

r = i - inflation

Question 17

Describe deflationary spirals and solutions to them?

Answer 17

A deflationary spiral is a situation where decreases in the price level lead to lower production, which in turn leads to lower wages and demand, which leads to further decreases in the price level.

Possible solutions include expansionary fiscal policy, quantitative easing, forward guidance, raise inflation target.

Question 18

Why can R=!R*?

Answer 18

There can be differences between the domestic rate and the international rate because of movements in the expected exchange rate.

Question 19

What is the formula for Uncovered Interest Rate Parity (UIP) condition?

Answer 19

1 + i_t = (1+i_t*) * E_t[e_t+1]/e_t

The domestic rate is equal to the international rate multiplied by the expected movement in the nominal exchange rate. This means that if the domestic rate increases this can be compensated for by a depreciation in the currency - keeping returns equal in both countries.

Question 20

Describe the Dornbush Over-Shooting Model.

Answer 20

The DOM is defined by five key equations.

1. The goods market which equates output to its natural rate and the deviation of the RER from its natural rate (depreciation increases output through the TB).
2. The RER formula
3. The money market - real money supply negatively related to interest rate.
4. UIP
5. Price adjustment - positive output gap increases inflation.

Question 21

Describe how to solve the Dornbush Overshooting Model?

Answer 21

1. Combine the IS equation with the RER
2. Combine this equation into the price adjustment equation. This gives you how prices evolve as a function of the RER and natural RER.
3. Combine money supply with UIP.
4. Solve for this for nominal exchange rate growth.

Question 22

Describe the impact of an unanticipated monetary expansion using the Dornbush Over-Shooting Model.

Answer 22

At the time of the shock the e scheldue shifts upwards. Prices are sticky so the nominal exchange exchange rate depreciates (over-shoots) and causes a real depreciation. Ouput increases. The UIP condition holds so the lower-interest rate must leave room for an appreciation over time. In the long run, RER, output, and interest rate are unchanged.

Question 23

Describe the effects of an unanticipated monetary expansion.

Answer 23

The exchange rate jumps at the time of the announcment. The size of the jump depends on how far away the expansion is.

Question 24

Describe the effects of a shock to demand for exports.

Answer 24

This depreciates the natural RER. The price scheldule shifts outwards. There is an immediate depreciation of the nominal rate.This keeps prices and output constant. The economy adjusts to real shocks.

Question 25

Describe the effects of monetary and real shocks under a fixed exchange rate regime.

Answer 25

Under a fixed exchange rate the economy can easily adjust to monetary shocks because the CB can move the nominal money supply. Under real shocks the exchange rate can’t adjust so prices need to adjust. The economy can’t adjust to real shocks.

Question 26

Descibe the Barro-Gordon Model.

Answer 26

The Barro-Gordon Model is made up of five equations.

1. Output as a function of natural rate(positively) and real wage (negatively).
2. Wage determination - wages in t are determined by expecation of prices in period before.
3. Inflation
4. Loss function
5. Inflationary bias

Question 27

How do you solve the Barro-Gordon Model?

Answer 27

1. Combine the output, wage determination, and inflation equations. This gives you output as a function of expected inflation and inflation.
2. Using this output inflation equation you combine the loss function with the inflation bias and output from part

Question 28

What does the Barro-Gordon model predict under perfect commitment?

Answer 28

Under perfect commitment, workers have rational expecations. This leads to a commitment of inflation at zero. Output is at the natural rate.

Intuition - the CB commitment creates so possibility of deviation to achieve higher output. Therefore, optimal choice of inflation is zero.

Question 29

Describe the intuition of the Barro-Gordon Model under no commitment.

Answer 29

The timing under no commitment is different. In this case, expectations about wages are set before the government choses inflation. This creates an incentive for the government to increase inflation and achieve higher output. However, workers are rational and are not fooled in equilibrium so they anticipate this. Thus, we see higher than optimal inflation and output stays at the natural rate.

Question 30

What happens to the predictions of the model when you have conservative central bank?

Answer 30

There will be lower inflation and less response to shocks.

Question 31

How do you modify the model under a fixed exchange rate regime?

Answer 31

You can add a cost function to the loss funtion. This captures the fact if if the peg is abonded inflation increases and results in a cost.

Question 32

Describe the Barro-Gordon predictions for abonding the peg.

Answer 32

1. Compute the loss function under positive inflation and under no inflation. The inflation to use is the inflation from no commitment. If the peg is maintained then inflation is zero.
2. Compute the cost of abonding peg when expectations are optimistic.
3. Compute the cost of abonding the peg when expectations are pessimisitic.

Question 33

What determines whether the economy is in an optimistic equilibrium.

Answer 33

If the cost of abonding the peg is high relative to the temptation to increase inflation.

Question 34

Explain the meaning of the sign on the coefficient which captures the foreign effect of policy on the domestic loss function.

Answer 34

A postive sign captures the positive spill over effect from fiscal expansion abroad. For example, fiscal expansion increases the interest rate which appreciates the foreign currency and causes a real depreciation at home. This expands output through increasing the trade balance.

A negative sign captures monetary policy spillovers. If the MP expands abroad this reduces the interest rate and causes a real appreciation at home.

Question 35

How do you solve the policy coordination model.

Answer 35

1. Take derivatives with respect to inflation and solve for inflation.
2. Take expectations —> inflation expecation =0
3. Solve for inflation uses FOC.

Question 36

What does the policy coordination model predict?

Answer 36

Monetary Policy —> too much monetary policy without coordination.

Fiscal Policy —–> too little without coordination.

Question 37

What are the benefits of Optimal Currency Areas?

Answer 37

(1) Trade Benefits
(2) Commitent
(3) Stabalisation Policies
(4) Feedback

Question 38

Explain the three equations of the Cagan Model.

Answer 38

Money Demand —-> decreasing function of the expected inflation rate because higher expected inflation leads to higher interest rate and higher opportunity cost of holding money (assume stable output and real interest rate beacuase of volatility).

Seigniorage ——> the government finances the deficit by printing money in real terms. Seigniorage is a real value.

Adaptive Expectations —–> workers adapt expectations gradually at speed b based on previous inflation and expectations.

Question 39

Explain how to solve the steady state of the Cagan Model.

Answer 39

Inflation is constant. Use the quiotient rule to differentiate money demand equation with respect to time. Solve to find that the steady state money demand. This states that seigniorage is eqaul to the “inflation tax”.

Question 40

Explain the dynamics of the Cagan Model.

Answer 40

Money grows at rate sigma. You can use this definition to write seignorage as a function of the growth rate of money and money demand. Solve this equation to find expected inflation. This gives you combination of expected inflation and sigma which equal mu.