Consumption & Savings
Romer Chapter 7
Topics
1. What is savings?
2. Consumption, savings and income
3. Savings and the Interest Rate
4. Uncertainty and Savings
The Data
• Data on Expenditure Categories are typically
obtained from the National Income and Product
Accounts gathered by the statistical authorities.
• USA: Bureau of Economic Analysis, Dept. of
Commerce
– The national income and product accounts provide an
aggregated view of the final uses of the Nation's output
and the income derived from its production; two of its
most widely known measures are gross domestic
product (GDP) and gross domestic income (GDI). BEA
also prepares estimates of the Nation's stock of fixed
assets and consumer durable goods.
Data
• In HK, data is collected by the Census and
Statistics Department: NIPA Tables
• The U.N. maintains statistical databases for a
wide variety of countries UN Main Aggregates
Database
Consumption in HK
• Four consumption
Consumption Shares in HK
categories 140
1. Food 120
100
2. Non-Durables: Clothes,
80
Toys
60
3. Durables: White Goods, 40
Electronics 20
4. Services: Health, Rental 0
1970 1975 1980 1985 1990 1995 2000
FOOD NONDURABLES
DURABLES SERVICES
Source: CEIC Database
2005
Gross domestic product....... 12455.8
Categories of Personal consumption expenditures. 8742.4
Durable goods................... 1033.1
Spending Motor vehicles and parts......
Furniture and household
448.2
equipment.................... 377.2
Other......................... 207.7
Nondurable goods................ 2539.3
Food.......................... 1201.4
Clothing and shoes............ 341.8
Gasoline, fuel oil, and other
energy goods................. 302.1
Other......................... 694.0
Services........................ 5170.0
Housing....................... 1304.1
BEA NIPA Table 2.3.5 Household operation........... 483.0
Electricity and gas......... 199.8
Other household operation... 283.2
Transportation................ 320.4
Medical care.................. 1493.4
Recreation.................... 360.6
Other......................... 1208.4
HK Short-term: Year to year growth
0.4
0.3
0.2
0.1 Durables
NonDurables
0 GDP
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
-0.1
-0.2
-0.3
Theory of consumption best explains non-durables, services and food
consumption. HK NIPA Table 038
Savings
• Output which is not devoted toward current
consumption
Gross Savings = Income – Personal Consumption
Expenditure – Government Consumption Expenditure
2005
Personal consumption expenditures 8742.4
BEA NIPA
Tables Government Expenditure
and gross investment 2372.8
Less Government Investment 397.1
Gross Consumption 10718.1
Gross domestic product 12455.8
Less Gross Consumption 10718.1
Gross Savings 1737.7
As a share of GDP 14.0%
2004 2005
Personal income 9731.4 10239.2
Personal Compensation of employees, received
Proprietors' income
6665.3 7030.3
911.1 970.7
Savings Rental income
Personal income receipts on assets
127.0 72.8
1427.9 1519.4
Personal current transfer receipts 1426.5 1526.6
vs. Less: Personal current taxes
Equals: Disposable personal income
1049.8 1203.1
8681.6 9036.1
Gross Less: Personal outlays
Personal consumption expenditures
8507.2 9070.9
8211.5 8742.4
Durable goods 986.3 1033.1
Savings Nondurable goods 2345.2 2539.3
Services 4880.1 5170.0
Personal interest payments\1\ 186.0 209.4
Personal current transfer payments 109.7 119.2
What’s
Equals: Personal saving 174.3 -34.8
Missing?
Personal saving as a percentage of
disposable personal income 2.0 -0.4
BEA NIPA Tables
Retained Earnings and Depreciation are not counted
in Personal Savings
Gross Saving
2005
Gross saving 1612
Net saving 7.2
Net private saving 319.7
Personal saving -34.8
Undistributed corporate profits 354.5
Net government saving -312.5
Consumption of fixed capital 1604.8
Private 1352.6
Government 252.2
Gross domestic investment, 1683.1
capital account transactions, and net lending,
Bureau of Economic Analysis
1,550
1,600
1,650
1,700
1,750
1,800
1,850
1,900
1,950
19
50
19
52
19
54
19
56
19
58
19
60
19
62
19
64
19
66
19
68
19
70
19
72
19
74
19
76
19
78
19
USA
80
19
82
19
84
Hours per Worker 19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
20
10
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.
Keynesian Consumption Function
• Consumption Function
C = A + mpc×[GDP – TAX]
– C = Household Consumption Expenditure
– A = Autonomous Consumption { Consumption not
dependent on current income}
– mpc = Marginal propensity to consume
• {Fraction of extra income will be spent on consumption}
• mpc will be smaller than consumption to GDP ratio if A is
positive.
Why do Chinese Save so Much?
Why do Americans Save so Little?
45.00%
40.00%
35.00%
30.00%
25.00%
20.00%
15.00%
10.00%
5.00%
0.00%
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
China USA
UN Main Aggregates Data Base
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? Period Saving
• Will it last? 5 Macao SAR of China(Patacas) 2003 55.02%
9 Singapore(Singapore Dollars) 2003 44.89%
12 China(Yuan Renminbi) 2003 42.48%
13 Malaysia(Ringgit) 2003 42.34%
GDP C G
s 22
23
Thailand(Baht)
Republic of Korea(Wons)
2003
2003
33.27%
33.02%
GDP 25 Dollars)
Hong Kong SAR of China(Hong Kong 2003 31.92%
30 Vietnam(Dong) 2003 28.21%
41 Japan(Yen) 2003 25.49%
UN Main Aggregates 55 Canada(Canadian Dollars) 2003 24.30%
Data Base 68 Germany(Euros) 2003 21.43%
108 United States(Dollars) 2003 13.50%
Cultural Reasons
• mpc simply depends on cultural factors and not
economic factors.
• Hayashi, 1989 Japan's Saving Rate: New Data
and Reflections
• Japan: 1960-1990 Savings Rate averaged
about 30%
• Japan 1880-1935 Savings Rate average less
than 15%!
Japanese Gross Saving Rate 1994-2004
Source: CEIC Database
0.32
0.3
0.28
0.26
0.24
0.22
0.2
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Income and Savings
Present Discounted Value
• Life cycle consumption functions assume that
households consider not just the current flow of
income but the present value of lifetime income.
• Consider a stream of income received over
time {y0, y1, …, yT}. This is equivalent in value
to a certain amount of current income,
pvy 0, then Annuity Value is a weighted
average of lifetime income with larger weights
on current income than on income in the far
future.
Permanent Income and Current Income
If Y grows at constant rate
• Yt = (1+g)tY0
(1 g )Y0 (1 g ) 2 Y0 (1 g )3 Y0 (1 g )T Y0
HW Y0 ...
1 r 1 r 1 r 1 r
2 3 T
1
1 g T 1
Y
1
1 T 1 1 1 r
1 g
1 Y0 Y
P 1 r
1 g
1 1 r 1 r
1 1 g
1 r 1
1 T 1
1 r 0
Permanent Income and Current Income
If Y is mean reverting
Yt Y Yt BC , Yt BC Yt 1 tY0BC
BC
W
r 0, C0
T 1
HW T 1 Y Y0BC ( )Y0BC ( ) 2 Y0BC ( )3 Y0BC ... ( )T Y0BC
HW T 1 Y
1
1
1 T 1 Y0
Y Y
P 1
T 1 1
1
1 T 1 Y0
Intratemporal Utility Function
• A household will exist for t = 0,…,T periods then
expire.
• Household will enjoy a stream of consumption
spending {c0, c1, c2,….cT}
• Households preferences over this stream can be
defined by a utility function
U = U(c0, c1, c2,….cT)
• Often a utility function is represented as a weighted
sum of utility in each period (called felicity functions).
Example: Felicity
• Agents get the same utility from consumption
in each period.
• Households lifetime utility is a weighted sum
of the felicity that they receive in each period.
• The per-period utility of the household is called
the felicity function, u(ct).
• Felicity displays diminishing returns from
consumption u’(C) > 0, u’’(C) 0
C
S
au0
After interest rate rise, new steeper
budget constraint is to the left of
previous consumption level.
Household must cut back on current
consumption just to get to affordable
consumption combination. Savings
rise.
au0,au1
Before interest rate rise, optimal c0 < au0.
After interest rate rise, new steeper
budget constraint is to the right of
previous consumption level. New set of
affordable consumption combinations
which make the household better off,
some of which can involve less
consumption in period 1. Savings may
rise or fall.
Income Effect
• Change in interest rates changes the value of your
savings.
– For savers, (i.e. consumption to left of autarky point), a rise
in interest will increase the future value of those savings
increasing lifetime income
– For debtors, (i.e. consumption to right of autarky point) a
rise in the interest rate will increase future costs of paying
debts reducing lifetime income.
• If income goes up, you will have a tendency to
consume more in both periods. If income falls, you
will have a tendency to consume less in both periods
and savings will rise.
Substitution Effect
• A rise in the interest rate will make
consumption today more expensive relative to
consumption in the future.
• A rise in the real interest rate will lead to a
reduction in consumption today relative to
consumption in the future.
How strong is the substitution effect?
• Constant Elasticity Intertemporal Substitution
Utility Function
1
1
1
1
c
u (c ) , 0 u '(c) c
1
1
1 1
c0
c0
1 r c1 1 r
c1
• When ψ = 1, the CEIS felicity is natural log for
all intents and purposes. Natural log felicity is
sometimes referred to as unit elasticity of
intertemporal substitution.
Point Elasticities
• Elasticity is the % change in one variable
caused by a % change in another variable.
• Elasticity of substitution is the % change in the
demand for one variable relative to another.
• Functions with constant elasticities are log
linear.
Income Effect: Borrowers
• For borrowers, households to the right of au, an
increase in the interest rate offers a lower budget
constraint, which allows less present consumption if
we keep future consumption constant.
• Substitution effect and income effect work the same
way. Present consumption drops relative to future
consumption but at any given future income,
affordable present consumption will drop.
– Present consumption of borrowers will drop if real interest
rate rises.
Income Effect Lenders
• For lenders, households to the left of au0, an
increase in the interest rate offers a higher budget
constraint and allows higher present consumption if
we keep future consumption constant.
• Income and substitution effects will work in opposite
ways. A rise in the interest rate reduces current
consumption relative to future consumption, but at
any given future consumption a higher level of
present consumption is affordable.
– Effect of an increase in the interest rate on consumption is
ambiguous.
Effect of Interest Rate on Savings
• Empirically, opinion on the effect of interest
rate on savings varies in a range from zero to
mildly positive.
The Effect of Interest-Rate Changes on
Household Saving and Consumption: A
Survey Douglas W. Elmendorf 1996-27
Uncertainty and Savings
Taiwan, National Health Insurance
• In 1995, Taiwan implemented a scheme
providing national health insurance to all
islanders.
• This program raised coverage rates from 57%
to 97%
• Aggregate gross savings declined in Taiwan.
• Careful study shows this to be concentrated
among low income households who were not
previously covered.
National Health Insurance and precautionary saving: evidence from Taiwan
Shin-Yi Chou , Jin-Tan Liu , James K. Hammitt
Taiwan Gross Saving Rate
(Taiwan National Income Accounts)
0.345
0.335
0.325
0.315
0.305
0.295
0.285
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
Precautionary Savings
• Decision making is taken under certainty.
• Most saving is done under a cloud of
uncertainty about the future.
• Question: How does the uncertainty
environment affect the willingness to save?
• Return to Polonius.
– Assume that β = (1+r) = 1
– If fw0 = tax0 = tax1 = 0, & y0 = y1 then c0 = y0
• Return to the two period life problem. Abstract from
taxes and initial financial wealth.
• When consumption decision is made, the household
knows its current income, y0. However, second
period income is a random variable.
• Assume that there are two equally likely future
outcomes, good and bad. If the outcome is good, the
household will have income y0 + x. If the outcome is
bad, the household will have income y0 – x.
• Expected household income is
.5 *(y0 + X) + .5* (y0 - X) = y0.
Decision making under uncertainty
• Most popular decision making paradigm is
maximize expected utility subject to the
budget constraint.
– Pick three variables, c0, c1,GOOD cBAD
• Expected utility is
– U(c0) + .5 * u(c1,GOOD) + .5*u(c1,BAD)
• Budget constraints
– C1,GOOD = y1 + x + (y0-c0)
– C1,BAD = y1 -x + (y0-c0)
Maximization problem
• Max u(c0) + .5 ∙ u(y1 + x + (y0-c0)) +
+ .5 ∙ u(y1 - x + (y0-c0))
• 0 = u’(c0) - .5 * u’(c1,GOOD)- .5*u’(c1,BAD)
• u’(c0) = E[ u’(c1)]
Under uncertainty, set marginal
utility today equal to expected
marginal utility tomorrow.
Marginal utility function
• Further assume utility is a diminishing function
of consumption.
• This is true if utility is a constant intertemporal
elasticity of substitution function.
• Expected value of marginal utility is greater
than marginal utility of expected value.
Expected Marginal Utility is greater
than Marginal utility of expected value
B: E[u’(y0)]
A: u’(c0)
u’(c)
c
y0 - x y0 y0 + x
Precautionary Savings
• If household sets marginal utility of
consumption today equal to marginal utility of
expected value tomorrow, this would be less
than expected value of marginal utility
tomorrow.
• Must act to increase marginal utility today or
reduce marginal utility in the future (i.e. shift
income toward the future)
• The household will shift income away from
periods of certainty toward periods of
uncertainty or save as insurance.
Precautionary savers & spenders
u’(c) Precautionary
Savers
B: E[u’(y0)]
Precautionary
A: u’(c0)
Spenders
Certainty
Equivalent
c
Optimal Consumption: Borrowing
Constraints c0 = au0
c1
(1+r)(w)
au1
c1*
c0
au0 c0 * w
Buffer Stock Savings
• Borrowing constraints and precautionary
savings interact.
• If short-term income falls sharply and borrowing
constraints hold, then consumption in bad
states may fall dramatically.
• Expected marginal utility of consumption may
be high due to this downside risk.
• Precautionary savings should fall as income
rises because high income people have a
smaller chance of hitting liquidity constraint.
Social Insurance, Financial Credit &
Savings
• Various government programs may reduce the
uncertainty of income.
• Social welfare or health insurance may reduce
the individual unpredictability of insurance and
reduce the need for precautionary savings.
• A more smoothly operating financial system
may also reduce the need for precautionary
savings.
MPC
• Under certainty with perfect financial markets,
the marginal propensity to consume out of
temporary income must be very small (as
shown by the wealth effect in stock markets.
• Propensity to consume increases if large
share of consumers face borrowing
constraints or precautionary motives are large.