saving lect2 handout

8/7/2019 Saving Lect2 Handout

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Why households save?

UIUC Econ303 Zhao 1

Saving

Why household save?

Income effect is households response to a parallelshift of the intertemporal budget constraint.

An increase of

the present value

of income

c2

c1

Households consume

more in both periods

Substitution effect is households response to a compensated interest rate change,

so that the new budget line is tangent to the old indifference curve

Present value of

income is adjusted

to stay on the same

indifference curve

c1

c2Interest rate increases;

the slope, 1/(1+r), is smaller,

budget line flatter

Households consume lesstoday and more tomorrow

Comparative static analysis: a change of todays income

Changes of y1 only have income effect

An increase of todays income increases household saving.

, but the increase of c1 is less than the increase of y1

A decrease of todays income reduces household saving.

, but the decrease of c1 is less than the decrease of y1


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UIUC Econ303 Zhao 2

Comparative static analysis: a change of future income

Changes of y2 only have income effect

An increase of future income decreases household saving.

A decrease of future income increases household saving.

A permanent income change (both y1 and y2 change at the same time) increases consumption in both periods, but may have no effect on saving.

Increased income will mostly be consumed.

Marginal propensity to consume

Marginal propensity to consume: if household has one

more unit of income, what percentage will be consumedtoday?

Marginal propensity to consume out of temporary income

increase (only y1 or y2 increases) is much less than 1.

Marginal propensity to consume out of permanent incomeincreases (both y1 and y2 increase) is close to 1

Comparative static analysis: a change of interest rate

An uncompensated interest rate change has both income effect andsubstitution effect.

An interest rate change may have positive or negative income effect

depending on how income is distributed in two periods.

Interest rate increases;the slope, 1/(1+r), is smaller

c1

c2

Income point of Jacks dadInterest rate increases:

present value of income is smaller.

Jacks is reduced more than his dads

Income point of Jack

Interest rate increase leads to a positive income effect on Jacks dad (y1 > y2)

If a household has much more income today then tomorrow, this household is

a lender. A higher interest rate means higher return on saving; this household

enjoys an actual increase of available resources.

From point A to point B is substitution effect and from point B to point C is

income effect.

A

B

C

*

c2

c1

y1


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UIUC Econ303 Zhao 3

Interest rate increase leads to a negative income effect on Jack (y2 > y1)

If a household has much more income tomorrow then today, this household isa borrower. A higher interest rate means higher interest payment; this

household enjoys an actual decrease of available resources.

From point A to point B is substitution effect and from point B to point C is

income effect.

A

B

Co

c2

y1

c1

In summary, an interest rate increase will for sure reduce the borrowing of

a borrower; whether it increases the saving of a saver depends on the

relative strength of income and substitution effect.

Compared with before

r = 5%, Jack and his dad: c1 = 26316; c2 = 24868

r = 10%, Jack: c1 = 25359; c2 = 25105

His dad: c1 = 26076; c2 = 25816

Both Jack and his dad consume less in the first period andmore in the second period after an increase of interest rate

Jack borrow less and his dad saves more

Jacks dad consumes more than Jack in both periods

Similarly, an interest rate decrease will for sure increase the borrowing of

a borrower; whether it reduces the saving of a saver depends on the

relative strength of income and substitution effect.


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UIUC Econ303 Zhao 4

Why household save? -- To obtain a smooth consumption path

Computed example

Jacks income difference between periods | y1 - y2 | = 32000

Jacks consumption difference between periods | c1 c2 | = 1448

Jack consumes a bit more in the first period only because he

discounts future more heavily than the market. His subjective

discount rate, =0.9, while the market discount rate 1/(1+r)=0.95.

Households prefer smaller consumption variation. When

income is volatile, households smooth consumptionthrough saving or borrowing.

Smooth consumption path comes from risk aversion

Diminishing marginal utility of consumption = concave utility function

Average of utility from two levels

of consumption is less than the utility

of the average consumption

[u(c1) + u(c2)]/2 < u([c1+c2]/2)

Households should avoid gambling

and buy insurance.

Stock return is higher than bond

return

average

utility

utility of

average

c

u(c)

Consumption being less variable than income is a pronounced empirical fact

both in aggregate data (Macro data) and in individual data (Micro data).

Macro data: GDP is twice as volatile as private

consumption of nondurable goods and services.

Micro data: A worker suffers 40% plus income loss due to unemployment; the

reduction of consumption of a worker after being laid off is less

than 10%.

The inequality is less severe if measured by consumption than

income. The Gini coefficient in the US in 1988 for income is 0.4and for consumption is 0.3.

Lorenz curve of consumption, income and wealth in the US 1990s


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UIUC Econ303 Zhao 5

Saving as a way of buffer income variation

Frequent and short term income variation

due to lost of a job, illness, or other unforeseen events

Households usually build buffer stock in the form of saving account in thebank (more liquid, easy to transform into cash) to prevent a dramatic fallin their consumption when such an unfortunate event does occur. This isprecautionary motive of saving.

Earning variation during life-cycle; age-earning profile is hump-shaped.

At this moment, a 25 year old earns about $25,000. His earning grows ashe gets older and peaks around age 45-50. By then his wage income is abit more than $50,000. As he approaches retirement age his earningdecreases. Once he is retired, his wage earning is 0.

Saving and borrowing plays an important role in reducing the impact ofincome variation over the life cycle on consumption. This life-cyclemotive of saving accounts for a large percentage of total saving ofhouseholds.

Age earning profile in Spain by education group

Saving motives of households at different point of their life-cycle

A typical young household saves little. Their motive for saving ismostly precautionary and for down payments of big-ticket items, such

as car and house.

The saving rate is highest when households reach their peak earning

years and get closer to retirement age.

Households after retirement run down their accumulated assets. Many

of old households do not consume all their accumulated assets.Instead, they leave bequests. Some are accidental (they do not know

that they will be dead tomorrow) and some are intentional. The

bequest motive explains the saving behavior of older households.

Decline of the US saving rate: Aggregate data


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UIUC Econ303 Zhao 6

From the micro data, the saving rate ([income-consumption]/income) for

most of the age group is lower in 1980s than 1970s. The decline is more

dramatic for older householdsFact 1: Increased social security payments and private pension

For households near the retirement age, their future income increases( ). They have less life-cycle incentive to save.

The Medicare provides an insurance for medical expense of theelderly. That further reduces the precautionary motive of saving forpeople close and beyond the retirement age.

The social security in the US is an income redistribution from currentworking population especially the young households to the retired.Since the saving rate of the old and retired households decreased more

than the young households, the saving rate of the society as a wholedecreases.

This also shows up as a disproportional increase of medical expensesin the private consumption boom.

Factor 2: Stock market boom Stock market boom: return on saving increased

For those who enjoy a positive income effect, if the income effect is

stronger than substitution effect, their saving will drop.

Predicts that the saving rate should drop for the mature households.

They are the ones have more income now and less in the future

tomorrow thus a positive income effect.

Hit: Indeed those households saving rate did decrease while the

saving rate of the young households stays the same.

Hit: Households who actually hold stocks, their saving rates did

drop more than the non-stock holders.

Miss: Timing is off. Increase of consumption mainly occurred in

1980s while stock market boom starts 1990s.


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UIUC Econ303 Zhao 7

Stock market: prediction on future earnings

Stock market indicates publics prediction on future

economic outlook

An increase of stock price shows a prevailing optimisticprediction of future income.

Perceived increases of future income will reduce savingnow.

Factor 3: easy credits: a decrease of interest rate on borrowing

The easy credit will encourage the borrower (usually the younger

households (y1


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UIUC Econ303 Zhao 8

Summary

Households save to reduce the consumption fluctuation in theirlifetime.

Changes of household income has only income effect Households save more if current income increases

Households save less if future income increases

Households adjust their saving when the change of income is temporary;households dont adjust their saving when the change is permanent.

Change of interest rate has both income effect and substitution effect.

An increase of interest rate will induce households consume less todayand more tomorrow via substitution effect.

An increase of interest rate has positive income effect on lender andnegative income effect on borrower.

Reminder

Readings

Williamson Chapter 8, Page 246-265 (2nd ed)

Page 263-279 (3rd ed)

Barro Chapter 7

Rainy day blues (optional)

US current account deficit (optional)

saving lect2 handout

Documents