Transcript The Intertemporal Approach to the Current Account

The Intertemporal Approach to
the Current Account
Professor Roberto Chang
Rutgers University
March 2012
• 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
• 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
• 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
• 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
• 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.
Future C (C2)
A
Q2
O
Q1
Current C
(C1)
Future C (C2)
I (1+r)
A
Q2
The Present Value of
Income:
Q1 + Q2/(1+r) = I
O
Q1
I
Current C
(C1)
Future C (C2)
I (1+r)
A
Q2
Budget Line:
C1 + C2/(1+r) = Q1
+ Q2/(1+r) = I
(Slope = - (1+r))
O
Q1
I
Current C
(C1)
• As in standard choice problems, we
assume that agents in this economy have
well defined preferences on consumption
today versus consumption tomorrow.
C2
Equilibrium in Small Economy
Q2
A
B
C2
O
Q1
C1
C1
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
• 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
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
C2
Q2
A
B
C2
O
Q1
C1
C1
C2
Q2
A
B
C2
O
Q1
C1
CA Deficit in Period 1
C1
• 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.
C2
Q2
A
B
C2
O
Q1
C1
CA Deficit in Period 1
C1
C2
If the Endowment Point is A’ instead of A
the economy runs a CA surplus
A
C2
B
A’
Q2’
O
C1
Q1’
CA Surplus in Period 1
C1
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
• Suppose that residents of this economy
are not allowed to borrow abroad.
C2
Suppose that this is the outcome
under free capital mobility
Q2
A
B
C2
O
Q1
C1
C1
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.
Q2
O
A
Q1
C1
C2
The resulting budget set is
below and to the left of the
red line.
Q2
O
A
Q1
C1
C2
The resulting budget set is
below and to the left of the
red line.
Q2
O
A
Q1
C1
• The domestic interest rate must increase
so that the domestic market for loans is in
equilibrium.
C2
The domestic interest rate must increase
to rA so that home residents are happy
consuming their endowments.
Q2
A
Slope: - (1+rA )
O
Q1
C1
• 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.
C2
Suppose instead that this is the outcome
under free capital mobility
B
C2
Q2
A
O
Q1
C1
C1
C2
A prohibition on foreign borrowing
does not affect agents’ choices here.
B
C2
Q2
A
O
Q1
C1
C1
Some Comparative Statics
A Fall in Current Income
• Suppose that Q1 (initial endowment) falls
by some quantity Δ.
Future C (C2)
I (1+r)
Q2
O
A
Q1
I
Current C
(C1)
Future C (C2)
I (1+r)
A
Q2
O
Q1 - Δ
Q1
I
Current C
(C1)
Future C (C2)
I (1+r)
This is the
new budget line
Q2
O
A
A’
Q1 - Δ
Q1
I’
I
Current C
(C1)
Future C (C2)
Suppose the CA was
originally zero.
Although A’ is now feasible,
C is the new consumption
point.
I (1+r)
Q2
A
A’
C
O
Q1 - Δ
Q1
I’
I
Current C
(C1)
Future C (C2)
Suppose the CA was
originally zero.
Although A’ is now feasible,
C is the new consumption
point.
I (1+r)
Q2
A
A’
C
O
Q1 - Δ
C1
CA deficit
I
Current C
(C1)
• 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?
• A fall in future income has the opposite
effect: it induces international lending and,
therefore, a current account surplus.
Future C (C2)
I (1+r)
A
Q2
Q2 - Δ
O
A’
Q1
I
Current C
(C1)
Future C (C2)
I (1+r)
A
Q2
Q2 - Δ
O
A’
Q1
I’
I
Current C
(C1)
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
O
A’
C1
Q1
CA surplus
I’
I
Current C
(C1)
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.
• 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
• Consider an interest rate increase from r
to r’ > r.
Future C (C2)
I’ (1+r’)
r’ > r
I (1+r)
Q2
O
A
Q1
I’
I
Current C
(C1)
Future C (C2)
I’ (1+r’)
r’ > r
I (1+r)
Q2
O
A
Q1
I’
I
Current C
(C1)
Future C (C2)
I’ (1+r’)
r’ > r
I (1+r)
C
Q2
A
O
C1
Q1
CA surplus
I’
I
Current C
(C1)
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?)
Future C (C2)
I’ (1+r’)
r’ > r
I (1+r)
Q2
A
C’
O
Q1
I’
I
Current C
(C1)
• 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.
• 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.
Future C (C2)
I’ (1+r’)
r’ > r
I (1+r)
Q2
A
C’
O
Q1
C
I’
I
Current C
(C1)
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)
• 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
• 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
• 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
• 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
• 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”)