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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 Rank
1 Macao
2 Singapore
5 Malaysia
7 Korea, Republic of
8 China
9 Thailand
12 Indonesia
13 Hong Kong
16 Japan
42 Germany
49 Canada
79 USA
62.23
49.88
39.65
35.65
35.55
35.30
30.58
30.28
29.59
23.31
22.04
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
Consumption Shares in HK
140
Per Capita Spending, HK 2000
Food & Non-alcoholic Beverages
Alcoholic Beverages
Tobacco
Clothing, Footwear & Other Personal Effects
Rent, Rates, Water & Housing Maintenance
Fuel & Light
Furniture, Furnishings & Household Equipment
Household Operation
Personal Care
Medical Care & Health Expenses
Transport & Communications
Recreation & Entertainment
Education
Other Services
Total
HK$
$13,495.79
$505.85
$410.34
$15,976.16
$19,222.53
$1,973.63
$9,933.99
$1,471.36
$1,316.55
$5,560.01
$10,262.83
$7,125.38
$1,852.34
$17,224.61
$106,331.37
120
100
80
60
40
20
0
1970 1975 1980 1985 1990 1995 2000
FOOD
DURABLES
NONDURABLES
SERVICES
Pro-cyclical Consumption
Consumption & Hong Kong Business Cycles
% Deviation from Long Run Trend
.15
.10
.05
.00
-.05
-.10
1975
1980
1985
Year 1990
Real GDP
1995
2000
Real Consumption
Durables
Hong Kong Business Cycles
Consumer Durables & Nondurables
.4
% Deviation from Trend
.3
.2
.1
.0
-.1
-.2
-.3
-.4
1975
1980
1985
Consumer Durables
1990
1995
2000
Non-Durables & Services
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
 Second period,
1)
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.
PC
PY1
1 1

B
1 i 1 i
2.1)
2.2)
PC
PY1
1 1

B
1 i 1 i
PC
PY1
1 1

 PY0  P0C0 3)
1 i 1 i
4)
PY1
PC
1 1
PY0 
 P0C0 
1 i
1 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 $YN in N periods or pay you a
smaller value today, (1$Yi) .
 You put the smaller amount in the
bank at interest rate i. After 1 period
$Y
(1

i
)
you will have
. After 2 periods
(1  i )
you will have (1  i) (1$Yi.)
$Y
(1  i)
 $Y
 After N periods you will have
(1  i)
 The two payments have equal value.
N
N
N
N
2
N
N
N
N
N
N
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
PV 
YN
1  i 
N
PV 
Y0 
Y3
YN
Y1
Y2
Y4




....

N
1  i 1  i 2 1  i 3 1  i 4
1  i 
Real
Intertemporal 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.
Y0 
Y0 
PY0
PY
, Y1  1
P0
P1
Y1
1 i
P1
P0
 C0 
1 r 
C1
4.1)
1 i
P1
P0
1 i
P1
P0
Y1
C1
W0  Y0 
 C0 
4)
1 r
1 r
Graph the Budget Constraint
C1
(1+r)∙W
C0
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.
CB A
C1
A
B
C
C0
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
(1+r)∙W
C0* , C1*
C0
W
Implications
 Because of diminishing returns to
*
*
C
,
C
consumption, 0 1 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.
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≈100
3. 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
C1* , C2* only on W. Thus,
cases 1 & 2 will increase by similar amounts.
 Case 3 increases W by nearly double the amount.

Optimal Point
C1
(1+r)∙W
C0*** , C1***
C0** , C1**
C0* , C1*
C0
W
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
PVt N  Y 
Y

1  r 
Y
1  r 
2

Y
1  r 
3
 ... 
Y
1  r 

1
1
1
1
 Y 1 


 ... 
2
3
N
 1  r  1  r  1  r 
1  r 
1
1
1
1  r 

1
1  r 
1
PVt N 
2
 ... 
1
1  r 
N

N



1
1  r 
1
N 1
1
1 r
1
1  r 
N 1
1
1
1 r
Y
5)
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)
YN 
1
1
1
1 r
1
1  r 
N 1
 PV
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.
C
1
1
1
1 r
1
1 r T 1
 [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
1 11 r
1
N 1
1
1 r
1 11.02
1 11.02 
41
 .0353
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 mid1950’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.
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
(1+r)∙W
C0* , C1*
C0
Y1
W
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 demand
Y = A + mpc ∙Y + I + G + EX – B-mpim ∙Y
∙Y + I + G+ EX
 Define mpd = mpc-mpim
(1-mpd) ∙Y =A – B+ I + G+ EX
Y = A-B + (mpc-mpim)
Y
1
( A  B  I  G  EX )
1  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.