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The Intertemporal Approach to the Current Account. Professor Roberto Chang Rutgers University January 2007.

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the intertemporal approach to the current account

The Intertemporal Approach to the Current Account

Professor Roberto Chang

Rutgers University

January 2007

slide2
The so called Intertemporal Approach to the Current Account amount to the application of the basic principles behind decision theory to the question of how much an economy decides to borrow or lend internationally.
  • Chapter 2 of Schmitt Grohe and Uribe.
a small economy
A Small Economy
  • Consider the problem of a resident of a small economy that can borrow or lend in international markets.
  • Assume two periods (today vs tomorrow), one nonstorable good in each period.
  • The typical agent in this economy has endowment Q1 in period 1 and Q2 in period 2
slide4
Suppose that the typical agent can borrow or lend from the capital market at interest rate r.
  • Let Bt = asset position at the end of period t. Then:

C1 + B1 = (1+r)B0 + Q1

C2 + B2 = (1+r)B1 + Q2

slide5
However, no agent would hold a positive B2, and negative B2 will not be feasible. Hence B2 = 0.
  • Assume that B0 = 0 here, for simplicity (SU allows nonzero B0). Then the two budget constraints above collapse to

C1 + C2/(1+r) = Q1 + Q2/(1+r) = I

slide6
Suppose that the preferences of the typical agent are given by a utility function U = U(C1, C2)
  • Then the problem is of the same form as before, with (1+r) = price of C1 relative to C2.
slide7

Future C (C2)

A

Q2

O

Q1

Current C (C1)

slide8

Future C (C2)

I (1+r)

The Present Value of

Income:

Q1 + Q2/(1+r) = I

A

Q2

O

I

Q1

Current C (C1)

slide9

Future C (C2)

I (1+r)

A

Q2

Budget Line:

C1 + C2/(1+r) = Q1 + Q2/(1+r) = I

(Slope = - (1+r))

O

I

Q1

Current C (C1)

slide10
As in standard choice problems, we assume that agents in this economy have well defined preferences on consumption today versus consumption tomorrow.
slide11

C2

Equilibrium in Small Economy

A

Q2

B

C2

Q1

C1

O

C1

the current account
The Current Account
  • The current account is defined as the change in international wealth. So, in period 1,

CA1 = B1 – B0

  • But, recall that C1 + B1 = (1+r)B0 + Q1, so

CA1 = rB0 + Q1 – C1

= Y1 – C1

= S

slide13

C2

A

Q2

B

C2

Q1

C1

O

C1

slide14

C2

A

Q2

B

C2

Q1

C1

O

C1

CA Deficit in Period 1

slide15
Note that the consumption choice depends on the present value of income, not on its timing.
  • In contrast, savings and the current account do depend on the timing of income.
slide16

C2

A

Q2

B

C2

Q1

C1

O

C1

CA Deficit in Period 1

slide17

C2

If the Endowment Point is A’ instead of A

the economy runs a CA surplus

A

B

C2

A’

Q2’

C1

O

Q1’

C1

CA Surplus in Period 1

welfare implications
Welfare Implications
  • International capital markets improve welfare.
  • The benefits from access to international markets are bigger the bigger the resulting CA imbalance (relative to autarky)
capital controls
Capital Controls
  • Suppose that residents of this economy are not allowed to borrow abroad.
slide20

C2

Suppose that this is the outcome

under free capital mobility

A

Q2

B

C2

Q1

C1

O

C1

slide21

C2

Capital controls mean that agents cannot

borrow in the world market, that is,

points in the budget set for which C1 > Q1

are not available.

A

Q2

Q1

O

C1

slide22

C2

The resulting budget set is

below and to the left of the

red line.

A

Q2

Q1

O

C1

slide23

C2

The resulting budget set is

below and to the left of the

red line.

A

Q2

Q1

O

C1

slide24
The domestic interest rate must increase so that the domestic market for loans is in equilibrium.
slide25

C2

The domestic interest rate must increase

to rA so that home residents are happy

consuming their endowments.

A

Q2

Slope: - (1+rA )

Q1

O

C1

slide26
Summarizing: if the economy is a net borrower from the rest of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in high interest rates at home.
  • If the economy is a net lender to the rest of the world, capital controls are irrelevant.
slide27

C2

Suppose instead that this is the outcome

under free capital mobility

B

C2

Q2

A

Q1

O

C1

C1

slide28

C2

A prohibition on foreign borrowing

does not affect agents’ choices here.

B

C2

Q2

A

Q1

O

C1

C1

a fall in current income
A Fall in Current Income
  • Suppose that Q1 (initial endowment) falls by some quantity Δ.
slide31

Future C (C2)

I (1+r)

A

Q2

O

I

Q1

Current C (C1)

slide32

Future C (C2)

I (1+r)

A

Q2

O

I

Q1 - Δ

Q1

Current C (C1)

slide33

Future C (C2)

I (1+r)

This is the

new budget line

A

Q2

A’

Q1

O

I’

I

Q1 - Δ

Current C (C1)

slide34

Future C (C2)

Suppose the CA was

originally zero.

Although A’ is now feasible,

C is the new consumption

point.

I (1+r)

A

Q2

A’

C

I

O

Q1 - Δ

Q1

I’

Current C (C1)

slide35

Future C (C2)

Suppose the CA was

originally zero.

Although A’ is now feasible,

C is the new consumption

point.

I (1+r)

A

Q2

A’

C

C1

O

I

Q1 - Δ

Current C (C1)

CA deficit

slide36
The result is that the country runs a CA deficit.
  • Intuition: access to international capital markets allow countries to smooth out temporary shortfalls in income.
  • A possible explanation for current US CA deficits?
slide37
A fall in future income has the opposite effect: it induces international lending and, therefore, a current account surplus.
slide38

Future C (C2)

I (1+r)

A

Q2

Q2 - Δ

A’

O

I

Q1

Current C (C1)

slide39

Future C (C2)

I (1+r)

A

Q2

Q2 - Δ

A’

Q1

I’

I

O

Current C (C1)

slide40

Future C (C2)

Suppose again the CA was

originally zero.

C is the new consumption

point : the CA is now in

surplus.

I (1+r)

A

Q2

C

Q2 - Δ

A’

C1

Q1

O

I’

I

Current C (C1)

CA surplus

transitory vs permanent changes in income
Transitory vs permanent changes in income
  • Suppose that both Q1 and Q2 fall by the same amount.
  • By itself, the fall in Q1 would tend to induce a CA deficits
  • But the fall in Q2 acts in the opposite direction
  • Hence the CA will move little.
slide42
The lesson: transitory changes in income are strongly accommodated by CA surpluses or deficits; the CA is, in contrast, unresponsive to permanent income changes.
an increase in the world interest rate
An Increase in the World Interest Rate
  • Consider an interest rate increase from r to r’ > r.
slide44

Future C (C2)

I’ (1+r’)

r’ > r

I (1+r)

A

Q2

I

O

I’

Q1

Current C (C1)

slide45

Future C (C2)

I’ (1+r’)

r’ > r

I (1+r)

A

Q2

I

O

I’

Q1

Current C (C1)

slide46

Future C (C2)

I’ (1+r’)

r’ > r

I (1+r)

C

Q2

A

C1

I

O

Q1

I’

Current C (C1)

CA surplus

slide47
If the CA was initially zero, and the interest rate increases, the current account must go into surplus.
  • (Exercise: How do we know that consumption does not go to a point like C’ in the next slide?)
slide48

Future C (C2)

I’ (1+r’)

r’ > r

I (1+r)

Q2

A

C’

I

O

Q1

I’

Current C (C1)

slide49
Here we have assumed that the economy was originally neither lending nor borrowing.
  • One consequence is that the economy is always better off if the interest rate changes.
  • This is not the case, however, if the economy was a net lender or borrower at the original interest rate.
slide50
If the economy was a lender at r, an increase in r causes a beneficial wealth effect that reinforces the previous effects.
  • But if the economy was a borrower before the interest rate increase, the increase in r makes it poorer and can cause a welfare loss.
slide51

Future C (C2)

I’ (1+r’)

r’ > r

I (1+r)

A

Q2

C’

C

I’

I

O

Q1

Current C (C1)

net wealth and trade surpluses
Net Wealth and Trade Surpluses
  • Recall that

C1 + B1 = (1+r)B0 + Q1

C2 = (1+r)B1 + Q2 B1 = – (Q2 – C2)/(1+r)

  • It follows that:

(1+r)B0 = B1 – (Q1 – C1)

= - (Q1 – C1) – (Q2 – C2)/(1+r)

slide53
Recall that Qt – Ct = Trade Surplus at t = TBt
  • (1+r)B0 = - TB1 – TB2/(1+r)
  • This says that initial foreign net wealth must equal the discounted value of trade deficits.
algebraic example
Algebraic Example
  • Assume

U(C1,C2) =log C1 + log C2

  • Recall that optimal consumption then requires that

(∂U/∂C1)/ (∂U/∂C2) = 1+r, i.e.

(1/C1)/(1/C2) = (1+r), or

C2 = (1+r)C1

slide55
Combine the last expression [C2 = (1+r)C1 ] with the (present value) budget constraint:

C1 + C2/(1+r) = Q1 + Q2/(1+r) = I

  • C1 + (1+r)C1/(1+r) = I
  • C1 = I/2
slide56
Savings, or the current account, in period 1 are given by:

TB1 = Q1 – C1 = Q1 – (I/2)

But: Q1 + Q2/(1+r) = I, so:

TB = [Q1 – Q2/(1+r) ] / 2

tb q1 q2 1 r 2
TB = [Q1 – Q2/(1+r) ] / 2
  • As expected, the trade balance tends to be positive if Q1 is large, negative if Q2 is large. Why?
  • Here, an increase in the world interest rate r causes an improvement in TB
  • If the trade balance is initially zero, it continues to be zero if Q1 and Q2 change in the same proportion (“permanent shocks have small effects on the trade balance”)
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