slides inter temporal choice

8/9/2019 Slides Inter Temporal Choice

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Intertemporal Choice

Frederic Lambert

Business Cycles and Stabilization Policies


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Adding a time dimension

So far we have only studied static choices.

Life is full of intertemporal choices: Should I study

for my test today or tomorrow? Should I save or

should I consume now?

We will consider both the households

consumption/saving decision and the firmsinvestment choice.

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Households consumption/savingchoice

We will present a simple model: the Life-

Cycle/Permanent Income Model of Consumption.

Friedman (Nobel winner 1976).

Will allow us to address several key issues: effectsof government programs including Social Security,

government debts and deficits.

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The model

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More on preferences

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Figure 8.2 A Consumers Indifference Curves

Copyright 2008 Pearson Addison-Wesley. All rights reserved.6


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The Budget Constraint - 1 Abstract from labor/leisure tradeoff. Inelastic labor

supply.

Current incomey >0; future incomey >0; initial

wealth a, say inherited from parents.

in the first period, or it can borrow against future

incomey. Interest rate on both savings and on loans is

equal to r. Let s denote saving.

Choice variables: a= wealth at beginning of future

period; c = current consumption; c = future

consumption

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The consumers current-period budget constraint:

The consumers future-period budget constraint:

The Budget Constraint - 2

atysc +=+

srtyc )1(''' ++=

Summing both budget constraints:

That is called the present value budget constraint.

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weyar

tt

r

yy

r

cc

PV=+

+

+

+=

+

+

1

'

1

'

1

'


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Figure 8.1 Consumers Lifetime Budget Constraint



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Present values

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Present values - Examples

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Implications of the Euler equation

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A parametric example

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Comparative statics: The effects of

changes in income and wealth - 1

The effect on consumption of a change in income

(current or future) or wealth depends only on howthe change affects the PVLR.

An increase in current income:

Increases PVLR, so shifts budget line out parallel toold budget line

If there is a consumption-smoothing motive, both

current and future consumption will increase Then both consumption and saving rise because of

the rise in current income

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Figure 8.5 The Effects of an Increase in Current

Income for a Lender



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An increase in future income

Same outward shift in budget line as an increase incurrent income

Again, with consumption smoothing, both current

Comparative statics: The effects of

changes in income and wealth - 2

Now saving declines, since current income isunchanged and current consumption increases

An increase in wealth

Same parallel shift in budget line, so both currentand future consumption rise

Again, saving declines, since crises and yisunchanged (wealth effect)

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Figure 8.7 An Increase in Future Income



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Figure 8.9 Stock Prices and Consumption of

Nondurables and Services, 19852006



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Comparative statics: Changes in

interest rate Income effect: if saver s > 0, then higher interest rate

increases income for given amount of saving. Increases

consumption in first and second period. If borrower s < 0,

then income effect negative.

of consumption in period 1 to consumption in period 2.

Current c becomes more expensive relative to c. This

increases c and reduces c.

Hence: for a saver an increase in rincreases c and mayincrease or decrease c. For a borrower an increase in r

reduces c and may increase or decrease c.

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Figure 8.12 An Increase in the Real Interest Rate

for a Lender



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Figure 8.13 An Increase in the Real Interest Rate

for a Borrower



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Life-cycle hypothesis - 1

We can extend to Tperiods: Franco Modiglianis life-

cycle hypothesis of consumption

Individuals want smooth consumption profile over theirlife. Labor income varies substantially over lifetime,

startin out low increasin until the 50th ear of a

persons life and then declining until 65, with no laborincome after 65.

Life-cycle hypothesis: by saving (and borrowing)

individuals turn a very nonsmooth labor income profileinto a very smooth consumption profile.

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Figure 4.A.5 Life-cycle consumption, income, and

saving

27Copyright 2008 Pearson Addison-Wesley. All rights reserved.


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Case of Japan

Japanese saving rate fell from 23% of personal income in1975 to 14% in 1990 down to 5% in 2000.

Over same horizon, US saving rate roughly flat around 6%. Why? One reason: aging of the population in Japan.

Ratio of Japanese over age of 65 to those of working agerose rom n o n . orecas o

increase further to 38% by 2010 and 50% by 2020.

Estimates by HSBC that demographic shift can account forhalf of the decline in the savings rate.

Effects of inflation, slower growth rates, changes ingovernment debt are other factors contributing to savingsdecline.

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US and Japan national saving rates

29Source: Chen, Imrohoroglu and Imrohoroglu, 2006


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Permanent income hypothesis - 1

Future labor income is uncertain.

Income of an individual household,y consists of a

permanent part,yp and a transitory partyty = yp + yt

Permanent art : ex ected avera e future income

(usual salary) Transitory partyt: random fluctuations around this

average income (bonus)

Permanent meansy andy change. Transitory: onlyy

changes.

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Figure 8.8 Temporary Versus Permanent Increases

in Income



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Application: Ricardian equivalence

What are the effects of government deficits in the

economy?

A first answer: none (Ricardo (1817) and Barro

(1974)). How can this be?

All that matters is present value of governmentexpenditures and taxation. Timing does not

matter. Deficits today imply higher taxes in future.

The answer outside our small model is tricky.

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Ricardian equivalence

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Households problem

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Figure 8.15 Ricardian Equivalence with a Cut in

Current Taxes for a Borrower



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Empirical evidence

Many instances of temporary tax cuts.

President George H. W. Bush (1992): withholding cut.

Pure timing issue. Little effect on consumption. President George W. Bush (2001): tax rebate. Timing

mixed with reduction in tax rates. Modest increases in

President George W. Bush (2007-08): Stimulus rebate.Seems to have mostly led to increased saving, modestconsumption increase.

In its exact form, Ricardian equivalence fails. Evidence thatconsumption does respond to temporary tax cuts, buteffects not substantial.

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The firms investment choice

Why is investment important?

Investment fluctuates sharply over the business

cycle, so we need to understand investment to

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un ers an e us ness cyc e

Investment plays a crucial role in economic

growth

Production function and law of


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Production function and law of

motion for capital Firms current-period production function:

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Firms future-period production function :

Evolution of the firms capital stock:


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Profits

Firms current-period profits:

Firms future-period profits:

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Present value of profits:


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Firms dynamic problem

r

KdNwYIwNYV

INN +

++=

with1

)')1('''()(max

,',

43

IKdK

NKFzYNKzFY

+=

=

=

)1('

)','(''),(


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The Firms Labor Demand

As before, the firmslabor demand schedule

is the marginal product

of labor for the firm,

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w c s ownwar

sloping.

Copyright 2008 Pearson Addison-Wesley. All rights reserved.

The Representative Firms Investment


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The Representative Firm s Investment

Decision

The firm invests to the point where the

marginal benefit from investment equals themarginal cost.

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Marginal cost of investment

The marginal cost of investment is 1, as the

firm gives up one unit of current profits foreach unit it invests, so:

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Marginal benefit of investment

The marginal benefit of investment is the

marginal product of future capital plus thequantity of capital that will be left in the

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uture a ter eprec at on, a scounte acto the present:


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Optimal investment rule

The firms optimal investment rule, obtained

by equating the marginal benefit andmarginal cost of investment:

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O


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Simplified optimal investment rule:

Optimal investment rule

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Optimal Investment Schedule for the


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Optimal Investment Schedule for the

Representative Firm



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A li ti


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Applications

Housing booms and busts

Investment and the stock market

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Time to build and aggregate fluctuations

H i b d b t


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Housing boom and busts

''

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rIB +=

1)(



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The Relative Price of Housing


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The Relative Price of Housing


Residential Construction as a Percentage of


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g

GDP




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Firms change investment in the samedirection as the stock market: Tobins qtheory of investment


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firm should invest more Tobins q= capitals market value divided by

its replacement cost If q< 1, dont invest

If q> 1, invest more



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Stock price times number of shares equalsfirms market value, which equals value offirms capital Formula: q= V/(pKK), where Vis stock market


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va ue o rm, s rm s cap ta , pK s pr ce onew capital

So pKKis the replacement cost of firms capitalstock

Stock market boom raises V, causing qto rise,increasing investment



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Data show general tendency of investmentto rise when stock market rises; but

relationship isnt strong because many otherthings change at the same time


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This theory is similar what we said: Higher MPKf increases future earnings of firm, so Vrises

A falling real interest rate also raises Vas people buystocks instead of bonds

A decrease in the cost of capital, pK, raises q



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10000

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Dow Jones Industrial (left scale)

Private investment/GDP (right scale)

Lags and investment


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Some capital can be constructed easily, butother capital may take years to put in place.

Acknowledging that it may take time to get

g

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the business cycle.See Kydland and Prescott (1982), Time tobuild and aggregate fluctuations,Econometrica

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