week 2 Term 2 CA sustainability

Question 1

Answering intuitively can you have a Perpetual Trade Balance Deficit?

Answer 1

If a country is a net debtor no (negative NIIP)

if a country is a net creditor yes (positive NIIP). This is because it can finance the TB deficit with the positive interest.

Question 2

1.How could you model having a trade balance deficit in two periods?

2.Please compute this mathematically and then say what the result says

Answer 2

1. Period 1:
   B1 = (1 + r)B0 + TB1
   B2 = (1 + r)B1 + TB2

We know that B*2 = 0 as the economy ends in period 2 so nothing can be collected.

You sub in the 0 and then divide through by 1+r

Then you plug in for B1 and then have
(1+r)B0 = -TB1 - TB2 / (1+r)

2. This shows that if B*0 is negative it is impossible that TB1 and TB2 can both be negative.

The net foreign asset position (including interest) = present discounted value of future trade deficits.

Question 3

What is B*0

What is B*1

What is (1+r)B*0

Answer 3

The initial NIIP

The NIIP in period 2

Initial NIIP + interest on this NIIP.

Question 4

If we abstract from valuation changes in simple model how do we calculate CA

Answer 4

CA1 = B1 - B0

Question 5

What is the simple model to prove perpetual current account deficits can not be held in two periods?

Answer 5

-CA1 = B1 - B0
-CA2= B2 - B1

-We know B*2 = 0 as world ends in period 2.

• Then plug in for B*1

-Then B*0 = -CA1 - CA2

So in order for country to run a perpetual CA deficit they need to have a positive NIIP at the start.

Question 6

What is another way of calculating the Current Account and what is the intuition behind this?

Answer 6

CA = S1 - I1

Domestic savings that are in excess of domestic investment must be used for purchase of foreign assets.

(The extra savings must go somewhere, it goes abroad).

Question 7

How do we derive CA using the National Accounting Identity

Answer 7

Start off with national account identity:
-Q1 + IM1 = C1 +I1+ G1 +X1

• Add rB*0 (investment income) to both sides

Q1 + IM1 + rB*0 = C1 + I1 + G1 + X1

Then use the fact CA = TB +rB0
and that Q1 + rB0 = Y

Y1 = C1 + I1 + G1 + CA1

Then recall S1 = Y1 - G1 + C1

This then gives
CA1 = S1 - I1

Question 8

What are the three ways to express the current account?

Answer 8

CA = S1 - I1
CA = B1 - B0
CA = Change in NIIP + VC
CA = TB1 + rB*0

Question 9

What is the no-ponzi scheme condition and what is the implication in an infinite economy?

Answer 9

B*T / (1+r)^T (greater than or equaled to 0)

This means your debt cannot grow at a rate faster than the interest rate.

As that would mean rolling over the debt indefinetly and never paying it off.

Question 10

What would it mean if a government’s debt was growing at a faster rate than interest rate?

What about when debt grows slower than interest?

Answer 10

This would mean the debt would be growing at an increasing rate which would make it unmanageable.

This would mean the debt is growing at a decreasing rate.

Question 11

What is the optimality condition?

Answer 11

B*0 / (1+r)^T (is less than or equaled to 0).

This means that a country would never have growth of credit increasing at a faster rate than interest rate as no country would pay it back?

Question 12

What is the transversality condition?

Answer 12

-This condition is derived from the Ponzi- Scheme and the Optimality conditon having to both hold so:

B*0 / (1+r)^T = 0

Question 13

Whhy is the transversality condition useful?

Answer 13

As when you calculate an infinite time-period economy:

B0 = B0/ (1+r)^T - TB1/ (1+ r) - TB2/ (1+ r)^2 - TBT / (1+r)^T

As transversality = 0

Then the first term drops out and it becomes B*0 = - TB1/ (1+ r) - TB2/ (1+ r)^2 - TBT / (1+r)^T

Question 14

1. Intuitively is it possible for a country with Negative NIIP to run perpetual CA deficits in infinite time horizon?
2. Why could this be an issue intuitively?
3. So when is debt only sustainable?

Answer 14

1. We assume trade balance that repays fraction alpha every period.

As CA is negative every period the amount of debt is growing

Therefore TB must also be growing as since the debt is increasing the constant fraction is increasing.

2. As this means that the TB has to grow unboundedly

In order to generate this path to export more, the amount of production has to be growing.

3. Debt is only sustainable if we can produce more and more.

Question 15

In an infinite period model can you run a perpetual trade deficit?

Answer 15

As in two period model NO if you are net debtor / start off with negative NIIP

As B0 = - TB1/ (1+ r) - TB2/ (1+ r)^2 - TBT / (1+r)^T. So if the B0 is negative the RHS cannot hold if it is all negative.

However, if you start off with positive NIIP it is positive.

Question 16

How do we compute the trade balance in an infinite time period economy?

Answer 16

B1 = (1 + r )B0 + TB1

Then solve for B*0

B0 = B1/ (1+r) - TB/ (1+r). Equation 1

Shift this one period forward to get
B1 = B2 / (1+r) - TB/ (1+r). Equation 2

Then sub in equation 1 into equation 2.

This gives
B0 = B2/ (1+r)^2 - TB2/ (1+r)^2 - TB1 / (1+r).

This process can be repeated by shifting forward again for B2 = B3/ 1+r - TB3/1+r

Then sub into that new equation.

Infinitely this gives:
B0 = B(T)/ (1+r)^t - TB1/(1+r) - TB2/ (1+r)^2 …… TB(T)/(1+r)^T

Due to transversality conditon first term cancels out and gives infinite period.

Question 17

How do we compute CA in infinite period economy?

what are the assumptions made?

Answer 17

-We assume that a country has negative initial investment position.
-We assume that the country has perpetually negative CA.
-Every period the country has trade balance surplus that allows it to pay off constant fraction alpha of debt.

B1 = (1+r)B0 +TB1

TBt = -alphaRB*T

where factor alpha is between 1 and 0

Law of motion
B1 = (1+r)B0 +TB1
Sub in the definition TBt = -alphaRB*T

Then create

CAt = rB*t-1 + TBt

then sub in definiton of TBt to get

CAt = r(1- alpha)B*t-1

This shows that the current account will always be negative as alpha is between 1 and 0.

Question 18

Does the infinite time horizon of CA for a country that is net debtor and negative CA in each period satisfy transversality?

Answer 18

1st write law of motion of debt.

Bt* = (1+r-alphar)Bt-1
so for t periods
Bt = (1+r-alphar)^t B0

It follows that Bt*/(1+r)^t

Sub in Btt in that and get ]
(1+r(1-alpha)/ 1+r)^t B0
and the limit of this converges to 0 as 1+r > 1+r (1-alpha).