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 Exports-Services Imports)

+ Net Investment Income

(Investment Income Earned Overseas – Investment Income Paid to Foreigners)

+Net Transfers (Donations from Overseas)

Global ImbalanceCurrent Account

-0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

Korea

Taiwan

China

Japan

USA

% of GDP

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

(Debt Forgiveness, Patents)

Financial + Financial Account →

Direct Investment (FDI of Foreign Companies – FDI by Domestic Companies)

Account= + PortfolioInvestment

(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)

+ Change in Reserve Assets

-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

Capital Account -9155Into HK Abroad

Direct Investment 96948 185424 88476Foreign Holdings Holdings ofof Hong Kong Foreign AssetsAssets

Portfolio Investment -322045 -9054 312992Financial Derivatives 39640 -100507 -140147Other Investment 133783 -327414 -461197Change in Reserves -36530Capital &Financial -97359Account

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.

Net Credit DebitGoods -64970 1488982 1553952Services 133468 323087 189619Income 41175 384595 343420Current Transfers -13878 4719 18597Current Account 95795 2201383 2105588

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

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.

1 1

1 1

11

1t t t t t t

t t t t t t

rNIIP NIIP CA NIIP NIIP CAr

Y Y Y Y g Y Y

25 years of current account deficits means US external wealth has turned to deficit.

USA

-30.00%

-25.00%

-20.00%

-15.00%

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

% o

f G

DP

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 account1

1

t t

t t

NIIP NIIPnpy Y Y

(1 ) ( )

1 1

r g rnpy cay npy cay npy

g g

Sustainable current accountnpy < 0 npy > 0

g>r cay < 0High growth→, economy can keep borrowing without debt growing relative to GDP

cay>0High growth →, economy must save a lot to keep its wealth high relative to GDP

r<g cay < 0, High interest rates →, economy must save to pay interest on debt.

cay<0High interest rates →, economy can consume interest paymens from the 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 (1-d)

Firm adds to profits if benefit is greater than cost. Invest if:

11

1(1 ) (1 )t

tt

YMPK d dY

1

1

(1 ) 1t

t

MPK d r

MPK r d

Capital has diminishing returns, so MPK

K K

Y

ΔY

ΔKMPKr+d

Different Growth Paths of Current Account

Current Account

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

% of GDP

Korea

Taiwan

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.

1 11 1 1 1

1

11

1 1

1

1

1 1 1

1

1

1 1

( )

1

1

1(1 )

a at t t t

at

t t

a

t t t

a

t t t t

MPK aK Q L r d

K

Q L r d

K Q Lr d

I Q L d Kr d

Example: Cobb-Douglas

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

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 r

Investment high but falling in Japan and Korea, Investment high but increasing in China.

Investment as a % ogf GDP

0

5

10

15

20

25

30

35

40

45

China Japan Korea, Rep. United States

1990-1994

1995-1999

2000-2003

Savings high but falling in Japan and Korea, savings high but increasing in China.

Savings as a % of GDP

0

5

10

15

20

25

30

35

40

45

China Japan Korea, Rep. United States

&

1990-1994

1995-1999

2000-2003

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 1)

Second period,C1=Y1 –T1+(1+r)B0 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

Combine two budget constraints

Present Discounted Value of Lifetime Income equals Present Discounted Value of Lifetime Consumption.

1 1 1

0 0 0

10

1 10 0

1 1

1

1

C Y TB

r rB Y T C

CC W

rY T

W Y Tr

Consider 3 scenarios

Baseline Y1 = Y2 = Y implies

Permanent Consumption Hypothesis

C1=C2

2

1 1

Y rW Y Y

r r

1 1 2[ ]

2 2 1

r r rC W Y Y

r r r

Temporary Rise in Income

The propensity to consume is a fraction of the temporary extra income. The remainder is saved for the future.

1 2

2,

1 1

1 1 2 1 1

2 2 1 2 2

1 1( )

2 2

Y rY Y Y Y W Y Y

r r

r r r r rC W Y Y

r r r r r

rS Y Y

r 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.

1 2

2, ,

1 1

1 1 2

2 2 1

( ) 0

Y rY Y Y Y W Y Y

r r

r r rC W Y Y

r r r

S Y Y

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 today.

1 2

2, ,

1 1

1 1 2

2 2 1 1 2

( )2 2

rY Y Y Y W Y Y

r r

r r rC W Y Y

r r r r r

S Y Yr r

Permanent Income Hypothesis

A simplified (and extreme) version of this theory hypothesizes that consumption is equal in each period.

** 21 1 11

[ ]2

C CC W C

r rr

C Wr

Income Stream & Consumption

Consider three hypothetical increases in income of Δ. 1. A Temporary Increase – Y1 increase by Δ, but Y2 is unchanged. This

will increase W by Δ.

2. A Future Increase – Y2 increases by 100, but Y1 is unchanged. W increases by Δ /1+r≈ Δ

3. 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

by similar amounts. Case 3 increases W by nearly double the amount.

* *1 2,C C

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

time

C,Y

S>0

S<0C

Y

S<0

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 non-dependents 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.

Change in Age Shares%Below 15 % Prime Age 20-591950-1990 2005-2025

China -13.56 0.41Hong Kong -20.64 NAIndonesia -7.26 5.52Japan -16.72 -4.03South Korea -18 -4.12Malaysia -7.7 7.5Singapore -20.22 8.35Taiwan -18.82 NAThailand -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

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

r( )S r