Consumption & Saving

Chapter 13

East Asian Savings Rates As a region, East Asia

has high savings rates. These high savings rates have helped finance high rates of capital accumulation and growth.

Why have East Asian savings rates been so high? Culture? Luck?

Will it last?

World Rank1 Macao 62.232 Singapore 49.885 Malaysia 39.657 Korea, Republic of 35.658 China 35.559 Thailand 35.30

12 Indonesia 30.5813 Hong Kong 30.2816 Japan 29.5942 Germany 23.3149 Canada 22.0479 USA 16.98

Objectives

Explain high East Asian Savings rates. Calculate Present Value & Annuity

Value of a series of present and future payments.

Calculate Real and Nominal Present Values

Calculate the Multiplier for an open economy.

Consumption in Hong Kong

Per Capita Spending, HK 2000 HK$Food & Non-alcoholic Beverages $13,495.79Alcoholic Beverages $505.85Tobacco $410.34Clothing, Footwear & Other Personal Effects $15,976.16Rent, Rates, Water & Housing Maintenance $19,222.53Fuel & Light $1,973.63Furniture, Furnishings & Household Equipment $9,933.99Household Operation $1,471.36Personal Care $1,316.55Medical Care & Health Expenses $5,560.01Transport & Communications $10,262.83Recreation & Entertainment $7,125.38Education $1,852.34Other Services $17,224.61Total $106,331.37

0

20

40

60

80

100

120

140

1970 1975 1980 1985 1990 1995 2000

FOODDURABLES

NONDURABLESSERVICES

Consumption Shares in HK

Pro-cyclical Consumption

-.10

-.05

.00

.05

.10

.15

1975 1980 1985 1990 1995 2000

Real GDP Real Consumption

Consumption & Hong Kong Business Cycles

% D

evi

atio

n fr

om

Lo

ng

Ru

n T

ren

d

Year

Durables

-.4

-.3

-.2

-.1

.0

.1

.2

.3

.4

1975 1980 1985 1990 1995 2000

Consumer Durables Non-Durables & Services

% D

evi

atio

n fr

om

Tre

nd

Hong Kong Business CyclesConsumer Durables & Nondurables

Consumption Facts

Consumption movements are closely correlated with GDP. In other words, consumption is pro-cyclical.

Consumption volatility is overall somewhat less than output volatility.

The volatility of consumer durables purchases is much greater than the volatility of services or non-durables.

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, C1 and C2.

Money price of goods is P1 and P2. Household lives and earns money

income PY1 and PY2 in each period. Household can buy/sell bonds, B, at

nominal interest rate i.

Temporal Budget Constraints First period, period 0.

B = PY0 – P0C0 1)

Second period, period 1. P1 C1=PY1+(1+i)B 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 Multiply 2) by the

inverse of the budget constraint.

Rearrange terms. Set left side of 2.2)

equal to right side of 2.1).

Rearrange terms of 3). Present Discounted

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

2.1)

2.2)

3)

4)

1 1 1

1 1

PC PYB

i i

1 1 1

1 1

PC PYB

i i

1 1 10 0 01 1

PC PYPY PC

i i

1 1 10 0 01 1

PY PCPY PC

i i

Present Value Many assets can be described as an income stream

paying a certain amount of dollars in each period in the future: $Y1, $Y2, $Y3…..$YN.

Q: How much is the current value of such an income stream? A: Current payments are worth more than future

payments, since current money can be saved at interest.

Value of a Future Payment Consider two payments. I could pay

you $YN in N periods or pay you a smaller value today, .

You put the smaller amount in the bank at interest rate i. After 1 period you will have . After 2 periods you will have .

After N periods you will have The two payments have equal value.

NN

i

Y

)1(

$

2 $(1 )

(1 )NN

Yi

i

$(1 )

(1 )NN

Yi

i

$(1 ) $

(1 )N N

NN

Yi Y

i

Present Discounted Value The present value of a

payoff N periods in the future is the dollar payoff divided by the interest rate raised to the N power.

The present value of a stream of payments is equal to sum of the present values of each payment

31 2 4

0 2 3 4 ....1 1 1 1 1

NN

PV

Y YY Y YY

i i i i i

1N

N

YPV

i

RealIntertemporal Budget Constraint Convert the model to

real terms. Define real income Y. Divide both sides by

P1 . Remember the

definition of the real interest rate.

Real Present Discounted Value of Lifetime Income, W, equals Real Present Discounted Value of Lifetime Consumption.

4.1)

4)

1 1

0 0

1 10 01 1i i

P PP P

Y CY C

0 10 1

0 1

,PY PY

Y YP P

1

0

11 iPP

r

1 10 0 01 1

Y CW Y C

r r

Graph the Budget Constraint

C1

C0

(1+r)∙W

W

Preferences People prefer some combinations of

present and future consumption. More is better. If two combo’s have equal

future consumption, choose the combo with more present consumption.

Smooth over time. Households have diminishing returns to consumption in any period.

Preferences are represented by indifference curves – Smooth sets of combo’s amongst which the household is indifferent.

C1

C0

A B C

C B A

Optimal Choice Preferences represent combo’s the

household would like to have. Budget represents combo’s the household

can have. Optimal choice is to choose the point on the

budget constraint which is part of the highest available indifference curve.

This indifference curve will be exactly tangent to the budget at the optimal point.

Optimal Point

C1

C0

(1+r)∙W

W

* *0 1,C C

Implications

Because of diminishing returns to consumption, will lie in the middle. That is consumption will be smooth over time.

Optimal current consumption will depend only on lifetime present wealth, not on income in any time period.

* *0 1,C C

Income Stream & Consumption Consider three hypothetical increases in income of

$100. 1. A Temporary Increase – Y0 increase by 100, but Y1 is

unchanged. This will increase W by 100.2. A Future Increase – Y1 increases by 100, but Y0 is

unchanged. W increases by 100/1+r≈1003. A Permanent Increase – Y0 & Y1 increase by 100. W

increases by 100(2+r/1+r) ≈200 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

Optimal Point

*** ***0 1,C C

C1

C0

(1+r)∙W

W

** **0 1,C C

* *0 1,C C

W+100 W+200

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?

Annuity Value Just as any stream of future payments has

a present value, so does it have an annuity value.

An annuity is an asset that makes a constant payment every period, for a number of years, N. Such an annuity has a present value.

The annuity value of any amount is the size of the payment of an annuity whose present value is equal that amount.

Present Value of an Annuity Payment

The real present value of an annuity with payment Y.

Off-the-shelf formula for geometric sum

Solve for present value of an annuity Y 5)

2 3

2 3

...1 1 1 1

1 1 1 11 ...

1 1 1 1

Nt N

N

Y Y Y YPV Y

r r r r

Yr r r r

1

2

11

11 1 11 ...

11 1 1 11

N

N

r

r r rr

1

11

11

11

N

Nt

rPV Y

r

Annuity Value of a Present Value If you have some

current lump sum, PV, payment and you want to buy a annuity for T periods.

Q: How big an annuity payment Y can you get.

A: Invert Equation 5)

1

1111

11

N

N

rY PV

r

Permanent Income Theory

The permanent income theory says that households keep consumption smooth consuming the annuity value of their financial wealth, F, plus the present value of lifetime income, W.

1

1111

11

[ ]T

r

r

C W F

Example

The fraction is referred to as the propensity to consume out of wealth.

A household lives for = 40 periods and the real interest rate is .02. In every period they would consume a fraction of their wealth equal to

11.02

4111.02

1

1.0353

11

111

1

1

rN

r

Applications: Wealth Effect Changes in asset prices will change the

current value of financial wealth. The effect of an increase in financial wealth

on consumption is called the wealth effect. According to the PIH, a one dollar increase

in the value of a stock portfolio should lead to an increase in consumption equal to the propensity to consume out of wealth.

Econometricians estimate that the wealth effect to be less than $.05 consistent with our theory.

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.

Consumption & Business Cycles

Consumption fluctuates more over the business cycle than can be accounted for permanent income hypothesis.

Two Explanations for co-movement of consumption with current income Borrowing Constraints Permanent Income Hypothesis

Borrowing Constraints Though dollar changes in financial wealth

may have relatively small effects on optimal consumption, for some people current income matters more.

If your optimal consumption is greater than your income you need to borrow to reach that consumption.

But if you cannot borrow the most you can consume is your income.

In this case, your present income is very important for current consumption.

Borrowing Constraints

C1

C0

(1+r)∙W

W

* *0 1,C C

Y1

Precautionary Savings Many people are buffer stock savers

holding a stock of savings to protect against a rainy day.

When the economy gets worse, the likelihood of a rainy day increases and people tend to save more.

Again this suggests a stronger relationship between current income and consumption than indicated by permanent income theory.

Consumption, Income & the Multiplier Effect

Real consumption is a function of current income which is a function of GDP.

Consumption is a major component of GDP.

There is positive feedback between consumption and GDP which is called the multiplier effect.

Open Economy Multiplier Consumption is a linear function of current

GDP.C = A + mpc ∙Y

Some consumption is imports, so imports are also a function of current GDP.

IM = B + mpim ∙Y (Assume mpim < mpc)

By accounting identity, GDP is a function of consumption and imports

Y = C + I + G – IM + EX

Multiplier Effect

We can calculate the effect of an autonomous increase in demandY = A + mpc ∙Y + I + G + EX – B-mpim ∙Y

Y = A-B + (mpc-mpim) ∙Y + I + G+ EX

Define mpd = mpc-mpim (1-mpd) ∙Y =A – B+ I + G+ EX

1( )

1Y A B I G EX

mpd

Multiplier Effect An exogenous change in demand has

a larger effect on total demand, the larger is the effect of current GDP on consumption of domestic goods.

If budget constraints or precautionary savings are important then mpc may be high and mpd high.

If economy is very open, like HK mpim may be high and mpd low.