Intertemporal Approach
to the Current Account
GDP vs. GNP



GDP is value of production/ value of income
produced within a domestic economy.
GNP is value of income earned by residents of
domestic economy.
GNP = GDP + NFP
Net factor payments is income earned from overseas
sources by domestic residents less income earned
from domestic sources by overseas residents.
Current Account

The current account is, conceptually, the amount of
income earned overseas less the amount of income
earned by foreigners from the domestic economies:
CA = NX + NFP.
Current Account =
Balance on Goods
(Goods Exports-Goods
Imports)
+ Balance on Services
(Services ExportsServices Imports)
+ Net Investment
Income
(Investment Income
Earned Overseas –
Investment Income
Paid to Foreigners)
+Net Transfers
(Donations from
Overseas)
Global Imbalance
Current Account
USA
Japan
China
Taiwan
Korea
-0.06
-0.04
-0.02
0
0.02
% of GDP
0.04
0.06
0.08
0.1
Savings



Private Savings is disposable income minus
consumption spending.
SP = (Y + NFP – T – C)
Public savings is the budget surplus (T- G)
Capital investment and the budget deficit can be
financed by domestic savings or net borrowing from
abroad.
SP + KA = I + (G-T)
Capital & Financial Account

The capital account (more accurately the capital &
financial account) records capital inflows into the country.
The account includes the financial account, the capital
account, and change in reserve assets.
Capital
&
Capital
Account
Financial
+ Financial
Account →
Account=
+ Change in
Reserve Assets
(Debt Forgiveness, Patents)
Direct Investment
(FDI of Foreign Companies – FDI by
Domestic Companies)
+ Portfolio
Investment
(Domestic Securities Purchases by
Foreigners – Foreign Securities Purchases
by Domestic Residents)
+ Other Investments
(Deposits in Domestic Banks by Foreigners
– Deposits in Foreign Banks by Domestic
Residents)
-Accumulation of Foreign Exchange
Reserves
Current Account = Negative of Capital
Account

S = Y + NFP – T – C +KA = I + (G-T)
-KA = Y+NFP – I – C – G = [Y - I- C - G] +NFP

Y = C + I + G + NX→ NX = [Y - I- C - G]
-KA = NX + NFP

Intuition: When you buy more from overseas than
you earn overseas from exports or other income, you
must borrow to make up the difference
Hong Kong Current Account & Capital
Account 2001

Net
Goods
Services
Income
Current Transfers
Current Account
Capital Account
Credit
-64970
133468
41175
-13878
95795
Debit
1488982
323087
384595
4719
2201383

-9155
Into HK
Direct Investment
Portfolio Investment
Financial Derivatives
Other Investment
Change in Reserves
Capital &Financial
Account
1553952
189619
343420
18597
2105588
Abroad
96948
185424
88476
Foreign Holdings Holdings of
of Hong Kong
Foreign Assets
Assets
-322045
-9054
312992
39640
-100507
-140147
133783
-327414
-461197
-36530
-97359

Hong Kong had a
96 million dollar
current account
surplus in 2001.
Hong Kong had a
97 million dollar
capital & financial
account deficit.
The difference is
reserve assets.
Current account equals the
accumulation of wealth



Define Net International Investment Position, NIIPt, as
a country’s foreign wealth less foreign owned domestic
assets including stocks, bonds, real estate etc.
NIIPt is end of period wealth accumulateds through
current account.
NIIPt – NIIPt-1 = CAt = NXt + NFPt
Assume that NFP is real investment income (which for
the most part is a reasonable assumption). NFPt =
r∙NIIPt-1
NIIPt = (1+r)NIIPt-1 +CAt
Wealth to GDP ratio

Divide both sides of the wealth accumulation
equation by Yt
NIIPt
NIIPt 1 CAt NIIPt 1  r  NIIPt 1 CAt
 1  r 




Yt
Yt 1
Yt
Yt
1  g Yt 1
Yt

If current account (as a share of GDP) is below
some level it will lead to a loss of wealth
relative to GDP and if the ultimately increasing
debt.
25 years of current account deficits
means US external wealth has turned
to deficit.
USA
15.00%
10.00%
% of GDP
5.00%
0.00%
-5.00% 80 82 84 86 88 90 92 94 96 98 00 02
19 19 19 19 19 19 19 19 19 19 20 20
-10.00%
-15.00%
-20.00%
-25.00%
-30.00%
NIIP
CA
Sustainable current account
A large, perpetually negative current account
is unsustainable as it would result in infinite
debt.
 Sustainable current account is a current
account that would maintain net international
investment position at a constant level
 Define the sustainable current account

npy 
npy  cay 
NIIPt
Yt

NIIPt 1
Yt 1
(1  r )
(g  r)
npy  cay 
npy
1 g
1 g
Sustainable current account
g>r
r<g
npy < 0
npy > 0
cay < 0
cay>0
High growth→, economy can
keep borrowing without debt
growing relative to GDP
High growth →, economy must save
a lot to keep its wealth high relative
to GDP
cay < 0,
cay<0
High interest rates →, economy High interest rates →, economy can
must save to pay interest on
consume interest paymens from the
debt.
rest of the world.
Determinants of the Current Account
Current account is the gap between domestic
savings and the domestic investment and the
budget deficit.
CA = S – I – (G-T)
 Examine the determinants of each in turn.

Consider a firm considering in owning $1 worth
of capital for 1 period.
Cost: 1+r (Either borrow funds for 1 period or
use own savings and lose chance to get
savings.
 Benefit: Can produce MPK extra goods plus
sell any of the capital that hasn’t depreciated
Y
MPK

(1

d
)

 (1  d )
(1-d)
Y
 Firm adds to profits if benefit is greater than
MPKt 1  (1  d )  1  r 
cost. Invest if:

t 1
MPKt 1  r  d
t 1
t 1
Capital has diminishing returns, so
MPK
Y
ΔY
ΔK
r+d
K
MPK
K
Different Growth Paths of Current
Account
Current Account
0.25
0.2
0.15
0.1
Korea
0.05
Taiwan
19
70
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
0
-0.05
-0.1
-0.15
% of GDP
Investment Choice


Increases profits to
invest as long as
MPK > r+d, but
investing pushes down
MPK. Investment will
occur until MPK = r+d.
Firms must invest until
they reach target
capital stock.
Example: Cobb-Douglas
MPK t 1  aK t 1a 1 (Qt 1 Lt 1 )1 a  r  d 
K t 1
 1 


Qt 1 Lt 1  r  d 
 1 
K t 1  

r

d


 1 
It  

r

d


1
1 a
1
1 a
1
1 a

Qt 1 Lt 1
Qt 1 Lt 1  (1  d ) K t
Volatile Investment
Investment is the most volatile part of demand.
A 1% change in technology or increase in
employment will increase target capital stock.
 In any year, investment is one-tenth as large
as the capital stock.

 A 1%
change in the capital stock requires a 10%
change in investment.
Investment Curve
r
Q: Why does the curve slope
down? The greater is
interest rate, the more
profitable capital must be to
invest in it.
Q: What shifts the curve?
Increases in technology and
labor increases profitability
of capital.
I (r )

I
Investment high but falling in Japan
and Korea, Investment high but
increasing in China.
Investment as a % ogf GDP
45
40
35
30
1990-1994
25
1995-1999
20
2000-2003
15
10
5
0
China
Japan
Korea, Rep.
United States
Savings high but falling in Japan and
Korea, savings high but increasing in
China.
Savings as a % of GDP
45
40
35
30
1990-1994
&
25
1995-1999
20
2000-2003
15
10
5
0
China
Japan
Korea, Rep.
United States
Two Consumption Theories
Keynesian: Consumption is dependent on
current income.
 Permanent Income Theory: Consumption
decision is a savings decision so households
take into account future income as well as
outstanding financial wealth.

 People
prefer smooth consumption and save and
borrow to do so.
Why do People Save?


Life Cycle Motives – Income is Not Smooth Across
Time. Households save, in part, to transfer income
from high income periods to low income periods.
Precautionary Motives – Households like to achieve
a buffer stock of wealth in the case of a possible bad
outcome. If households have a buffer stock of
saving, bad outcomes in terms of income don’t result
in really bad outcomes in terms of consumption.
Life Cycle Motives: Two Period Model
To examine life-cycle theory, we use simplest
possible model.
 One good consumed by a household that lives
two periods, C0 and C1.
 Household lives and earns income Y0 and Y21
in each period.
 Household pays taxes in each period T0 and
T1.
 Household can buy/sell bonds, B, at real
interest rate r.

Temporal Budget Constrants

First period,
B0 = Y0 – T0 – C0

Second period,
C1=Y1 –T1+(1+r)B0

1)
2)
Note B can be either > or < 0. If B > 0, household is
a saver. If B < 0, household is a borrower.
Intertemporal Budget Constraint
C
Y

T
1
1
1
 Combine two budget


B
constraints
1 r 1 r
 Present Discounted Value of
Lifetime Income equals
B  Y0  T0  C0
Present Discounted Value of
Lifetime Consumption.
C1
C0 
W
1 r
Y1  T1
W  Y0  T0 
1 r
Consider 3 scenarios

Baseline Y1 = Y2 =YY implies
2 r 

Permanent Consumption Hypothesis
C1=C2
1 r
1 r  2  r 
C
[W ] 
Y  Y


2r
2  r  1 r 
W Y 

Y

1 r  1 r 
Temporary Rise in Income

The propensity to consume is a fraction of the
temporary extra income. The remainder is saved
for the future.
Y
 2r 
Y1  Y  , Y2  Y  W  Y   

Y 
1 r  1 r 
1 r
1 r  2  r  1 r
1 r
C
W 
Y 
 Y 


2r
2  r  1 r  2  r
2r
1 r
1
S  Y    (Y 
) 

2r
2r
Permanent Rise in Income
The propensity to consume is larger when the
increase in consumption is permanent. There is
no need to save a permanent rise in income for
the future.
Y   2r

Y1  Y  , Y2  Y  ,  W  Y   

Y    

1 r
1 r
1 r  2  r

C
W 
Y  Y 

2r
2  r  1 r


S  Y    (Y   )  0

 1 r

Future Rise in Income

Consumption may rise when future income
increases which will also increase W. Savings will
fall as people borrow to enjoy future income

 2r 
today.
Y  Y , Y  Y  ,  W  Y  
Y 


 1 r  1 r
1 r
1  r  2  r 
 

C
W
Y 
Y 



2r
2  r  1  r  1  r 
2r
1
2


S  Y  (Y 
)
2r
2r
Permanent Income Hypothesis

A simplified (and extreme) version of this
theory hypothesizes that consumption is equal
in each period. *
C2
C
C 
W  C 

1 r
1 r
1 r
C
[W ]
2r
*
1
Income Stream & Consumption

Consider three hypothetical increases in income of Δ.
1.
2.
3.


A Temporary Increase – Y1 increase by Δ, but Y2 is
unchanged. This will increase W by Δ.
A Future Increase – Y2 increases by 100, but Y1 is unchanged.
W increases by Δ /1+r≈ Δ
A Permanent Increase – Y1 & Y2 increase by 100. W increases
by Δ(2+r/1+r) ≈2∙ Δ
Cases 1 & 2 increase W by nearly identical amounts. But
current consumption depends only on W. Thus, cases 1 & 2
will increase C1* , C2* by similar amounts.
Case 3 increases W by nearly double the amount.
Income Stream and Savings



In the first case, future income does not rise but
optimal future consumption, C2* does . Current
savings must rise.
In the second case, current income does not rise, but
optimal current consumption. Current savings must
fall.
What happens to savings with a permanent change
in income?
Application: Life Cycle of Saving



Permanent Income Hypothesis suggests that
households like to keep a constant profile of
consumption over time.
Age profile of income however is not constant.
Income is low in childhood, rises during maturity and
reaches a peak in mid-1950’s and drops during
retirement.
This generates a time profile for savings defined as
the difference between income and consumption.
Time Path of Savings
C,Y
S>0
C
S<0
S<0
Y
time
East Asian Demographics
During last 25 years, East Asian Nations had a
sharp decrease in their ‘dependency ratio’.
 Dependency ratio is the % of people in their
non-working years (children & seniors.
 Dependents are dis-savers and nondependents are savers.

East Asian Demographics



Due to plummeting birth
rates, East Asia had a
plummeting ratio of youths
as a share of population
This put a large share of
population in high savings
years.
Share of prime age adults
has hit its peak in most
Asian countries and will fall
over the next half century.
China
Hong Kong
Indonesia
Japan
South Korea
Malaysia
Singapore
Taiwan
Thailand
Change in Age Shares
%Below 15
% Prime Age 20-59
1950-1990
2005-2025
-13.56
0.41
-20.64 NA
-7.26
5.52
-16.72
-4.03
-18
-4.12
-7.7
7.5
-20.22
8.35
-18.82 NA
-14.74
0.25
Interest Rates: Incentives and Effects



A rise in interest rates increases the payoff to savings and
increases the incentive to save. Substitution Effect (Plus
Factor for All)
A rise in the interest rate reduces the amount of savings you
need to do to meet target level of future consumption. Income
Effect (Minus Factor for Net Savers).
A rise in the interest rate reduces the amount of borrowing
you can do and still meet some target lever of future
consumption. Income Effect (Plus Factor for Net Borrowers)
Aggregate Savings & Interest Rates




Interest rates have a positive impact on savings by
borrowers, i.e. borrowers reduce their borrowing.
Interest rates have an ambiguous effect on savings
by savers.
Since there is positive net savings, interest rates
have ambiguous effect on aggregate savings.
Empirically, impact of interest rates on savings are
hard to detect.
Saving Curve
S (r )
r
Q: Why does the curve slope
up? Empirical work
suggests substitution effect
is slightly more powerful
than income effect.
Q: What shifts the curve?
Changes in current income
relative to future income.

I (r )

I