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Week 2 Lectures 3 & 4
Saving and Wealth
Reference: Bernanke, Olekalns and Frank - Chapter 2
Key Issues
Definition and Measures of Saving
Saving and Wealth
Motives for Saving Investment and Capital Accumulation
Saving, Investment and the Real Interest Rate
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Saving
Saving = current income current spending
Saving rate = IncomeSaving
Saving is aflow variable
If saving is positive then assets are being accumulated
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If saving is negative then assets are being de-
cumulated or liabilities (debts) accumulatedCapital Gains and Losses
Fluctuations in the market value of assets capital gains
or capital losses have can have an important effect on netwealth
Change in Wealth = Saving + Capital gains Capitallosses
Change in Wealth = W = W W(-1)
W = W(-1) + S + Net Capital Gains
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Assets, liabilities and wealth arestockvariablesWealth
Net Wealth = Value of Assets Value of Liabilities
Balance SheetAssets $ Liabilities $
House (m.v.) 700,000 Mortgage 450,000Car (m.v.) 10,000 Credit Card 3,500Bank Account 3,500Shares (m.v.) 25,000Furniture (m.v.) 15,000Total 753,500 Total 453,500
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Net Wealth = 300,000 m.v. = market valueAsset Pricing
How can we determine the price of a financial asset?
Characteristics of Financial Assets
have monetary payoffs ($X) payoffs arrive in the future (need to discount)
payoffs can be uncertain (risky)
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Simple Example: What is the value today of a (certain)
$100 in the next period?
Present-Value Formula
Suppose the interest rate (r) is 5 percent (0.05)
24.95$)05.01(
100=
+=PV
Some Notation
PV = Price of asset (today)
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100 = payoff of asset
)05.01(1
+= discount factor
Asset Pricing Formula
Xrr
XP
+=
+=
1
1
)1(
Price of Asset (today) = Discount Factor Payoff (tomorrow)
With Uncertainty
Price of Asset (today) =
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Expected Value of [Discount Factor Payoff
(tomorrow)]
Very general formula, but can be specialized to particularassets.
Example: Share Price
Assume (for simplicity) complete certainty
Payoff for a share
Pays a dividend 1D in the next period
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Resale price in the next period is 1P
Payoff = 111 DPX +=
Discount Factor
Let rbe the certain return on an alternative asset (e.g. abank deposit)
r
DPP
+
+=
1
11
0
Simple model for share price
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Complications
Payoff on share is uncertain What is the correct discount factor? Different assetpricing models use different discount factors.
Motives For Saving
1. Life-Cycle Saving
Typically people only work for some fraction of theirlifetime, e.g. might work from age 20 to 60.
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Consume over your entire lifetime, e.g. might expect to
live to 80.
Save during your working life to provide forconsumption during retirement.
Households might also save for other costly items suchas:
House deposit
Education expenses
2. Precautionary Saving
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Saving can be used as a form of insurance againstunexpected declines in income or unexpected increases inconsumption, e.g. temporary unemployment, medicalexpenses
3. Bequest Saving
People save to leave a bequest or inheritance for their
heirs and dependents
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Saving and the Real Interest Rate
We expect the level of saving will increase with higher
real returns to various assets.
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We will focus on the real interest rate ras being most
relevant to the saving decision.
Other things equal (ceteris paribus) we expect saving toincrease with the real interest rate.
S(r)
r
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Saving
Psychology and Behavioral Motives for Saving
Standard macroeconomic model assumes that individualsand households choose a level of saving that maximizestheir long-run welfare
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In reality people may lack sufficient self-control orwillpower to undertake an optimal level of saving.
The consumption benefits of saving arise far into the
future, but costs in terms of forgone consumption areimmediate.
Factors that tend to reduce saving
Availability of consumer credit, e.g. home equityloans
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Demonstration effects. High consumption levels of
our neighbors may influence us to consume more andsave less
Government provision of retirement benefits may leadto less private saving for retirement.Reducing ones
own saving in response to government retirementbenefits may be rational behavior
If people cannot make rational savings decisions whatcan be done?
Compulsory superannuation saving.
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Hard to justify this policy of compulsory saving if webelieve that individuals make fully rational savingdecisions.
Compulsory saving schemes will only increase totalsaving if individuals do not reduce their voluntary savingby an equal amount in response.
Household saving ratio for Australia
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-0.100
-0.050
0.000
0.050
0.100
0.150
0.200
Sep-59
Sep-62
Sep-65
Sep-68
Sep-71
Sep-74
Sep-77
Sep-80
Sep-83
Sep-86
Sep-89
Sep-92
Sep-95
Sep-98
Sep-01
Sep-04
Sep-07
S
/Y
National Saving
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Saving is undertaken by:
Households
Business
Government
National saving measures aggregate saving in aneconomy
National Accounting Identity
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Y = C + I + G + NXAssume NX=0
Y = C + I + G
Saving = Current income current spending
S = Y C G
We excludeIbecause by definition it is spending that
provides for future needs not current ones.
Durable Goods
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In reality not all ofCand G are for immediate needs.
Consumer durables (e.g. cars, furniture, appliances)provide a flow of consumption services over a period of
time.
Government purchases of durable goods (e.g. roads,bridges, schools, other infrastructure) will provide afuture flow of services.
Known as public capital.Private and Public Components of Saving
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Private Saving
Households
Business
Public Saving
Government
S = Y C G
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S = Y C G + T T
T = taxes paid by private sector to governmentless
transfer payments from government to private sectorlessinterest payments from government to private sector
bond holdersTransfer payments: payments the government makes to
the public for which it receives no current goods orservices in returnS = Y C G + T T
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S = (Y T C) + (T G)
S = Private saving + public saving
Private Saving = Y T C
Saving by households and business (i.e. retainedearnings)
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Public Saving = T G
Public Saving is equal to the Budget Surplus
T G = Budget Deficit/Surplus
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Government Budget Balance (cash balance)
-5
-4
-3
-2
-1
0
1
2
3
1
977
1
979
1
981
1
983
1
985
1
987
1
989
1
991
1
993
1
995
1
997
1
999
2
001
2
003
2
005
2
007
%o
fGD
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Investment and Capital Formation
National saving provides the resources for investment.
Investment is the purchase of new capital goods.
Influences on the level of Investment
Cost of capital
Should Tiger Airlines buy an additional plane?
Costs vs. Benefits
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3 Components to Cost of Capital (The following is more
technical than in BOF)
1. Suppose Tiger Airlines have to borrow the funds to
buy the new plane at the nominal interest rate = i
The dollar price/cost of the new plane = KP
(Note: even if they used retained earnings there would be
an opportunity cost = i )
2. Physical depreciation rate on plane =
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3. Over time the price of the plane may rise or fall
(capital gain or capital loss) = KP
Net cost of owning a plane for one year.
Cost of capital = price of capital (begin year)+ interest cost- price of (depreciated) capital (end
year)
Cost of capital = ])[1( KKKK PPiPP ++
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Some Algebra
Cost of capital = ])[1( KKKK PPiPP ++
or
Cost of capital = ])1()1(1[K
K
K
P
PiP
+
or if KK
P
P
is small
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Cost of capital = )(K
K
K
P
PiP
+
Finally let the price of capital goods rise at the general
rate of inflation =
K
K
P
P
Cost of capital = )( +iPK
or since = ir
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Cost of capital = )( +rPK
Summary
Model suggests that two important influences on TigerAirlines investment decision will be:
Price of the capital goods
Real interest rate
Other things equal (ceteris paribus) a rise in the realinterest rate will make investment less attractive.
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Other things equal (ceteris paribus) a rise in the price of
capital goods will make investment less attractive.Cost vs. Benefits
The benefit of a new plane is value of the additionaloutputit provides to Tiger Airlines.
The change in output for an increase in capital is calledthe marginal product of capital (MPK).
Tiger Airlines will invest provided:
Value of marginal product of capital Cost of capital
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Saving, Investment and Financial Markets
In an economy with no access to international capitalmarkets:
National Saving = Investment.
The supply of saving by HH, businesses, and governmentand the demand for saving (for investment) by business
are equated by the financial markets.
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Model
Saving is an increasing function of the real interest rate
Investment is a decreasing function of the real interestrate
r S(r)
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I(r)
S, IInitial Equilibrium
r S
r
I
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Saving and InvestmentNew Technology
r S
r`
r
I`I
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Saving and InvestmentInitial Equilibrium
r S
r
I
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Saving and InvestmentIncrease in Budget Deficit
S`
r S
r`
r
I
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Saving and InvestmentCrowding Out
An increase in the government budget deficit will reduceprivate investment spending
In the above model a larger deficit reduces the supply ofsaving (savings curve shifts inwards) and drives up thereal interest rate. The higher real interest rate makes
investment less attractive and causes a move along theIcurve.
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