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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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