Week 8 A small open economy model Flashcards
What do we mean by small?
Effectively our economy cannot impact the rest of the world- view us as price takers not price makers.
What are our 3 starting assumptions?
- Endowment economy (i.e income is exogenous)
- Two periods
- SOE (so r = r∗)
What does r = r∗?
In a small open economy- the domestic real interest rate is the same as the world real interest rate.
Define a country’s current account balance.
The change in the value of its net claims on the ROW (the change in net foreign assets, NFA)
Is the CA in surplus if positive or negative? What does this mean?
Positive, and it means that the country is a net lender.
If an economy borrows from abroad, when does it have to pay it back?
In the next period.
What does the CA represent?
Trade over time.
How many periods does NX focus on?
A single period
If we assume optimality, what must be true of the current account surplus in period 1?
CA surplus period 1 = CA deficit period 2
What is a government budget surplus?
Taxes- Government spending
What is total domestic saving equal to?
Private saving + Government saving
What preferences does a representative curve have its indifference curve over?
(C + G and C’ + G’) where private consumption and government consumption are perfect substitutes.
- What is the effect on the current account surplus following an increase in current income?
- Why?
- The current account surplus rises with an increase in current income.
- Because consumption smoothing means that as income rises more than expenditure, the current account surplus rises
What is the CA equal to?
CA= Y-C-G
- What is the effect on the current account surplus following an increase in future income?
- Why?
- The current account surplus falls following an increase in future income
- As an increase in Y’ will increase consumption now, thus as CA = Y-C-G, but Y stays the same whilst C and G fall, the CA surplus falls.
- What is the effect on the current account surplus following a change in taxes?
- Why?
There is no impact as Ricardian equivalence holds, private and government savings just change by equal and opposite amounts.
What will happen to the 2 period small-open economy diagram following an increase in interest rates?
An increase in world interest rate will make the BC steeper and it will pivot around the endowment point
- When CA<0, what is the effect of an increase in the real interest rate?
- Why?
- When CA<0, an increase in the real interest rate increase CA (reduces the deficit)
- As increase in the real interest rate reduces consumption and increases savings
- When CA>0, what is the effect of an increase in the real interest rate?
- Why?
- When CA<0, an increase in the real interest rate has an ambiguous effect on the CA
- As for net lenders, an increase in the real interest rate could increase or decrease savings, so as C+G could rise or fall, so could the CA.
What do credit market imperfections allow?
The Home economy the possibility of defaulting on its debts
If a nations debt to the world in the current period is B, what is its CA?
CA= B- B’/1+r’
What is limited commitment?
When a country can default on its debt in either the future or current period.
Can a government post collateral against its debt?
No
What does v represent?
A penalty for defaulting in the future period, which captures the cost the country will suffer from being denied access to “future” credit markets.
What is the limited commitment constraint that implies that a nation’s indebtedness cannot be so large that defaulting will occur?
-B’ ≤ v
Following the introduction of v, what is the first period budget constraint?
C + G ≤ Y + (ν/1+r) − B
If a nation defaults on its debts in the current period, what does B’ =?
B’ = 0
At what point should a nation default on its debt?
When B > v/1+r
What is the effect of the world interest rates on defaulting?
As B > v/1+r, the higher the world interest rate is, default is more likely.
What happens to NX if domestic demand for a good is higher than domestic supply?
Net exports are negative, as these goods are imported.
When goods can be freely traded, what is the new income-expenditure identity?
Y= C + I + G + NX
Does an increase in the world interest rate increase or decrease output?
An increase in the world interest rate increases output and the current account surplus?
What happens to output demand and supply following an increase in government spending?
- Output supply increases a small amount due to the negative wealth effect associated with an increase in govt spending (which means higher taxes)
- Output demand increases as a direct result of the increase in G
What are the effects of an increase in technology?
- The direct effect is an increase in output supply
- Since interest rates cannot change, output demand increases (via NX)
- As output increases, consumption also rises
- Given that the change in Z is temporary, investment does not change
What are the effects of a future increase in technology?
- With ‘news’ about a future increase in TFP consumption rises
- As does investment
- However, Ys does not shift as current production • technologies have not yet changed
- This implies no effect on current output so NX must fall
- CA falls
What does e denote?
The nominal exchange rate
How do we calculate the value of purchasing a foreign good?
eP*
Eg if I want to buy a book in dollars which is worth £10 and 2 = £1
2x10 = $20
How do we calculate the real exchange rate?
eP*/P
If it is costless to transport goods between foreign countries and the domestic and there’s no trade barriers, when would it be cheaper to buy foreign goods than domestic goods?
When eP* < P
If it is cheaper to purchase foreign goods, what would we expect to happen to the price of domestic goods, and what relationship would this result in?
- We would expect P to fall until P=eP*
- This relationship is called purchasing power parity
- Here, the real exchange rate =1
Does PPP hold?
It depends on the kind of good, for example crude oil is shipped globally for low cost, so could hold. Whereas the cost of going to another country for a haircut is relatively far larger, so the “law of one price” may not hold in this case.
What is PPP also known as
The law of one price.
Would we expect PPP to hold in the long run?
Yes, as if it didn’t consumers would generally purchase the good from the cheaper location. However it is fairly unrealistic in the short-run.
What is an alternative way of writing PPP, what does this imply?
∆ ln et = πt − π∗t
This implies that the rate of depreciation is equal to the difference of inflation between the home country and the foreign country
What is Uncovered interest parity (UIP)?
rt = r∗t + st+1
ie if the UK pays 5% interest and the US pays 6%, it is because the pound is expected to appreciate by 1%.
Does the UIP often hold?
No
What are the 2 types of exchange rate regimes?
- Fixed exchange rates
* Flexible exchange rates
In an open economy, what will a young agent in country a be able to do?
- Sell some of her endowment ya to the old in a, obtaining qa
- Sell some of her endowment to the old in b, obtaining qb
- Then, when old she will be able to purchase output from the young in countries a and b
If a government imposes currency controls, and prevents a young person transferring foreign currency from one period into the next, what will the young person do?
- They will transfer the foreign currency to their home currency whilst they are still young.
- As a result, for a young a agent, qa = ya and qb = 0
What is the nominal value of the b money (euro) compared to a money (dollar)?
et= (pat/pbt)
What is therefore the nominal exchange rate = to?
- et = (Mat/Mbt)(yb/ya)
* The exchange rate is determined by relative money supplies and relative output
After removing currency controls, what is an agents budget constraint when they are old?
ct+1 = c = Πa^−1 qa + Πb^−1 qb
As agents are trying to maximise utility, what must be true?
- Expected inflation rates must be the same across the two countries
- Πa = Πb
After currency controls are removed, what must be true about the 2 currencies?
- The two currencies are viewed as perfect substitutes by the young
- All agents will have q = qa + qb = y
- But any value of qa, qb satisfying the above will be an equilibrium
What is the only market with a market-clearing condition?
- The only market-clearing condition we have is for the world money market (use qa + qb = y )
- Ma + etMb = 2pat Ny
- Any values of e and pa that satisfy the equation above will yield the equilibrium exchange rate.
Why is there indeterminacy?
All the money supplied by each country will be
held, but our model does not tell us by whom
