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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 l.jpg

The Intertemporal Approach to the Current Account

Professor Roberto Chang

Rutgers University

January 2007


Slide2 l.jpg


A small economy l.jpg
A Small Economy 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.

  • 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


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Future C (C2) by a utility function U = U(C1, C2)

A

Q2

O

Q1

Current C (C1)


Slide8 l.jpg

Future C (C2) by a utility function U = U(C1, C2)

I (1+r)

The Present Value of

Income:

Q1 + Q2/(1+r) = I

A

Q2

O

I

Q1

Current C (C1)


Slide9 l.jpg

Future C (C2) by a utility function U = U(C1, 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 l.jpg


Slide11 l.jpg

C2 this economy have well defined preferences on consumption today versus consumption tomorrow.

Equilibrium in Small Economy

A

Q2

B

C2

Q1

C1

O

C1


The current account l.jpg
The Current Account this economy have well defined preferences on consumption today versus consumption tomorrow.

  • 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 l.jpg

C2 this economy have well defined preferences on consumption today versus consumption tomorrow.

A

Q2

B

C2

Q1

C1

O

C1


Slide14 l.jpg

C2 this economy have well defined preferences on consumption today versus consumption tomorrow.

A

Q2

B

C2

Q1

C1

O

C1

CA Deficit in Period 1


Slide15 l.jpg


Slide16 l.jpg

C2 value of income, not on its timing.

A

Q2

B

C2

Q1

C1

O

C1

CA Deficit in Period 1


Slide17 l.jpg

C2 value of income, not on its timing.

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 l.jpg
Welfare Implications value of income, not on its timing.

  • 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 l.jpg
Capital Controls value of income, not on its timing.

  • Suppose that residents of this economy are not allowed to borrow abroad.


Slide20 l.jpg

C2 value of income, not on its timing.

Suppose that this is the outcome

under free capital mobility

A

Q2

B

C2

Q1

C1

O

C1


Slide21 l.jpg

C2 value of income, not on its timing.

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 l.jpg

C2 value of income, not on its timing.

The resulting budget set is

below and to the left of the

red line.

A

Q2

Q1

O

C1


Slide23 l.jpg

C2 value of income, not on its timing.

The resulting budget set is

below and to the left of the

red line.

A

Q2

Q1

O

C1


Slide24 l.jpg


Slide25 l.jpg

C2 value of income, not on its timing.

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 l.jpg


Slide27 l.jpg

C2 of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

Suppose instead that this is the outcome

under free capital mobility

B

C2

Q2

A

Q1

O

C1

C1


Slide28 l.jpg

C2 of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

A prohibition on foreign borrowing

does not affect agents’ choices here.

B

C2

Q2

A

Q1

O

C1

C1


Some comparative statics l.jpg

Some Comparative Statics of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in


A fall in current income l.jpg
A Fall in Current Income of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

  • Suppose that Q1 (initial endowment) falls by some quantity Δ.


Slide31 l.jpg

Future C (C2) of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

I (1+r)

A

Q2

O

I

Q1

Current C (C1)


Slide32 l.jpg

Future C (C2) of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

I (1+r)

A

Q2

O

I

Q1 - Δ

Q1

Current C (C1)


Slide33 l.jpg

Future C (C2) of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

I (1+r)

This is the

new budget line

A

Q2

A’

Q1

O

I’

I

Q1 - Δ

Current C (C1)


Slide34 l.jpg

Future C (C2) of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

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 l.jpg

Future C (C2) of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

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 l.jpg

  • The result is that the country runs a CA deficit. of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

  • Intuition: access to international capital markets allow countries to smooth out temporary shortfalls in income.

  • A possible explanation for current US CA deficits?


Slide37 l.jpg

  • A fall in of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in future income has the opposite effect: it induces international lending and, therefore, a current account surplus.


Slide38 l.jpg

Future C (C2) of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

I (1+r)

A

Q2

Q2 - Δ

A’

O

I

Q1

Current C (C1)


Slide39 l.jpg

Future C (C2) of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

I (1+r)

A

Q2

Q2 - Δ

A’

Q1

I’

I

O

Current C (C1)


Slide40 l.jpg

Future C (C2) of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

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 l.jpg
Transitory vs permanent changes in income of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

  • 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 l.jpg

  • The lesson: of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in 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 l.jpg
An Increase in the World Interest Rate of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

  • Consider an interest rate increase from r to r’ > r.


Slide44 l.jpg

Future C (C2) of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

I’ (1+r’)

r’ > r

I (1+r)

A

Q2

I

O

I’

Q1

Current C (C1)


Slide45 l.jpg

Future C (C2) of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

I’ (1+r’)

r’ > r

I (1+r)

A

Q2

I

O

I’

Q1

Current C (C1)


Slide46 l.jpg

Future C (C2) of the world, capital controls (no foreign borrowing allowed) eliminate CA deficits and result in

I’ (1+r’)

r’ > r

I (1+r)

C

Q2

A

C1

I

O

Q1

I’

Current C (C1)

CA surplus


Slide47 l.jpg


Slide48 l.jpg

Future C (C2) increases, the current account

I’ (1+r’)

r’ > r

I (1+r)

Q2

A

C’

I

O

Q1

I’

Current C (C1)


Slide49 l.jpg


Slide50 l.jpg

  • If the economy was a lending nor borrowing.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 l.jpg

Future C (C2) lending nor borrowing.

I’ (1+r’)

r’ > r

I (1+r)

A

Q2

C’

C

I’

I

O

Q1

Current C (C1)


Net wealth and trade surpluses l.jpg
Net Wealth and Trade Surpluses lending nor borrowing.

  • 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 l.jpg


Algebraic example l.jpg
Algebraic Example lending nor borrowing.

  • 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 l.jpg


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Tb q1 q2 1 r 2 l.jpg
TB = [Q1 – Q2/(1+r) ] / 2 (present value) budget constraint:

  • 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”)