Aggregate Expenditure Model Consumption, Saving & Investment
Macroeconomics in the World Economy: Theory and ......Outline 1 Topic 3: Consumption, Saving, and...
Transcript of Macroeconomics in the World Economy: Theory and ......Outline 1 Topic 3: Consumption, Saving, and...
Macroeconomics in the World Economy:Theory and Applications
Topic 3: Consumption, Saving, and Investment
Dennis Plott
University of Illinois at ChicagoDepartment of Economics
http://blackboard.uic.edu
Spring 2014
Plott (ECON 221) Spring 2014 1 / 89
Outline
1 Topic 3: Consumption, Saving, and InvestmentInvestment
Saving
Consumption
The Investment-Saving Curve
Plott (ECON 221) Spring 2014 2 / 89
Goal: Start Modeling Aggregate Demand (AD)
What drives business investment decisions?
Does investment theory accurately match the data?What is the role of inventory?
What drives household consumption?
Does consumption theory accurately match the data?What theories of consumption seem to match the data?What role can the government play in shaping spending?Should a distinction be made between unexpected and expectedchanges and permanent and temporary changes in income?What is the link between consumption and savings?
Plott (ECON 221) Spring 2014 3 / 89
Outline
1 Topic 3: Consumption, Saving, and InvestmentInvestment
Saving
Consumption
The Investment-Saving Curve
Plott (ECON 221) Investment Spring 2014 4 / 89
An Introduction to Investment
Second major component of spending
Includes purchase and construction of capital goods (fixed capital);
inventories; residential structures.
Two reasons why studying investment is important:1 Investment matters more for business cycle fluctuations than
consumption; i.e. much more volatile than consumption. Investmentaccounts for one-sixth of GDP, but more than half of the decline inspending during a recession.
2 Determines long-run productive capacity of an economy; i.e. output ishigher if capital stock is higher.
Plott (ECON 221) Investment Spring 2014 5 / 89
Desired Capital Stock
Firms optimize the amount of capital to have (just like they optimize
the amount of labor to hire).
Remember from Topic 2: For the optimal amount of labor, firms
equate the MPN with the real wage (cost of an additional unit of labor).
For the optimal amount of capital, firms equate the MPK (per period
benefit of one more unit of capital) with the per period cost of an
additional unit of capital.
How does capital evolve: Kt+1 = (1−d)Kt + It
i.e. Capital is increased tomorrow by investing today less depreciation(d).So the desired capital stock is determined by future MPK and expecteduser cost of capital (uc)
What is the cost of an additional unit of capital (user cost of capital)?
Plott (ECON 221) Investment Spring 2014 6 / 89
User Cost of Capital
User Cost of Capital = Expected cost of using an extra unit of capital for aperiod
Capital is long lived – so user costs include not only current, but future costs
Real Interest Rate (Cost of Funds). Firms usually have to borrow to buy
equipment. If you do not borrow and instead use retained earnings, you
give up the interest payments you would have received in you invested
that money instead of buying new equipment. (Assume borrowing rates =
lending rates = r = expected real interest rate).
Depreciation Rate on the Capital (how long the capital lasts) (Percent that
depreciates, on average, per year) (Symbol = d)
Maintenance Rate – How much will it cost (per unit price) to maintain the
equipment. (Symbol = mm)
Real Purchase Price of capital (how much the equipment costs per unit)
(Symbol = pK )
User Cost (per period) = uc = r ·pK +δ ·pK +mm ·pK
Plott (ECON 221) Investment Spring 2014 7 / 89
Desired Capital Stock (Cont.)
First order condition from profit maximization:
P ·MPK f = pK [r+δ+mm]
Benefits of investing are more output tomorrow – so, it is the future
MPK that is important. P is the price of output, pK is the price of
capital. If P = pK , then:
MPK f = [r+δ+mm] = user cost
If User Cost of Capital > MPK f , then MPK f must rise (capital must fall;
i.e., investment must be lower today).
If User Cost of Capital < MPK f , then MPK f must fall (capital must rise;
i.e, investment must increase).
Plott (ECON 221) Investment Spring 2014 8 / 89
The Desired Capital Stock
Graphical representation of the definition of the desired capital stock.
The desired capital stock is affected by changes in future MPK (MPK f )
or the user cost of capital (uc)
K f
uc,MPK f
uc(r,d)
MPK f (Af ,N f )
K f0
uc0
Plott (ECON 221) Investment Spring 2014 9 / 89
Changes in the Desired Capital Stock: Af Increases
As (Af ) increases, MPK f shifts rightward, desired future capital stock,
K f , increases.
K f
uc,MPK f
uc(r,d)
MPK f (Af ,N f )
K f0
uc0
Plott (ECON 221) Investment Spring 2014 10 / 89
Changes in the Desired Capital Stock: r Increases
As r increases (to r1 > r0), User Cost shifts upward, desired future
capital stock, K f , falls.
K f
uc,MPK f
uc(r,d)
MPK f (Af ,N f )
K f0
uc0
Plott (ECON 221) Investment Spring 2014 11 / 89
Changes in the Desired Capital Stock: Tax the Revenues
Suppose now the government starts taxing revenues at rate τk. At optimum:
MPK f (1−τk) = r+δ+mm
Need to Tax Adjust the User Cost, equivalent to User Cost Shifting Up, desired
future capital stock, K f , falls.
K f
uc,MPK f
uc(r,d)
MPK f (Af ,N f )
K f0
uc0
Plott (ECON 221) Investment Spring 2014 12 / 89
Reaching the Desired Capital Stock: Investment
Rationale: Investment decisions today have effects on the capital stock
tomorrow. It takes time to build, install, train workers, etc. This is
especially true with large expenditures (buildings, structures,
assembly lines, etc).
Recall how capital evolves: Kt+1 = (1−d)Kt + It
i.e. Capital is increased tomorrow by investing today (less depreciation).Gross investment is It ; Depreciation is dKt ; Net investment is Kt+1 −Kt
Net Investment = Gross Investment – Depreciation
If K∗ is the desired capital stock then K∗ = (1−d)Kt + It
A change in K∗ produces a change in It . The relationship is 1-to-1.
Investment is the means to achieve the optimal capital stock.
Plott (ECON 221) Investment Spring 2014 13 / 89
Investment (I) and Real Interest Rates (r)
Investment Demand (ID)
I
r
ID(Af ,N f )
Key: As r decreases, desired capital stock increases, investment increases.
Read: Section 4.2 on investment in Abel, Bernanked, and Croushore.
Plott (ECON 221) Investment Spring 2014 14 / 89
Investment: Some Caveats on the Process
Investment takes time to plan.
Investment tends to be "irreversible" (costly to change if you over/under invest).Investment returns are uncertain (returns are in the future – which is unknown).
As economic uncertainty increases, investment decisions can become delayed.
Firms, like individuals, are forward looking. If interest rates fall today, I may not
invest today because I believe interest rates can be even lower tomorrow.
Firms, like individuals, may be liquidity constrained. (The role of banks in the
economy may be important). Liquidity constrained means that the firm is
unable to have access to financial markets – or they have access, but the cost of
funds is prohibitive.
Tax policy can affect investment decisions (investment tax credit . . . )
Correlation between A and Af (if A changes today and it is only temporary and it
was unexpected, then no effect on investment)
Plott (ECON 221) Investment Spring 2014 15 / 89
Other Components of Investment
We have focused on business fixed investment so far.
But Aggregate Investment also includes:
Inventories (unsold goods, unfinished goods, raw materials)Residential Structures (new houses, condos, apartment complexes).
Same principles apply for the decision of how much inventories to
keep or condos to build (i.e. equalize marginal benefit and marginal
cost).
Note: the following topics will be discussed in Topic 9 on the FinancialCrisis:
investment and the banking systemleveragehousing market
Plott (ECON 221) Investment Spring 2014 16 / 89
Investment: The Role of Inventories
Investment is highly procyclical! (remember procyclical means – when
Y increases I increases and vice versa).
Inventories are the most volatile (and procyclical) component of GDP.
Can inventories be a signal of future economic activity?
Yes, can predict recessions (a rapid rise in inventories – unplannedinventories)Yes, can predict expansions (a smooth rise in inventories – plannedinventories).
Plott (ECON 221) Investment Spring 2014 17 / 89
Outline
1 Topic 3: Consumption, Saving, and InvestmentInvestment
Saving
Consumption
The Investment-Saving Curve
Plott (ECON 221) Saving Spring 2014 18 / 89
Measures of Aggregate Saving: Government
Government saving = net government income – government
purchases of goods and services
Sgovt = (T −TR− INT)−G
Government saving = government budget surplus = governmentreceipts – government outlaysGovernment receipts = tax revenue (T)Government outlays = government purchases of goods and services (G)+ transfers (TR) + interest payments on government debt (INT)Government budget deficit = −Sgovt
Simplification: count government investment as governmentpurchases, not investment
Plott (ECON 221) Saving Spring 2014 19 / 89
Measures of Aggregate Saving: Private and National
Saving = current income – current spending
Saving rate = saving/current income
Private saving = private disposable income – consumption
Spvt = (Y +NFP−T +TR+ INT)−C
National saving
National saving = private saving + government saving
S = Spvt +Sgovt
S = (Y +NFP−T +TR+ INT −C)+ (T −TR− INT −G)
S = Y +NFP−C −G
S = GNP−C −G
Plott (ECON 221) Saving Spring 2014 20 / 89
Saving and Investment
Use the private saving definition and the income-expenditure identity to show
the relationship between saving and investment.
Note: with a closed economy (which we assume until Topic 8) NX = 0 and
NFP = 0. The current account (CA) also equals zero since CA = NFP+NX = 0
Spvt = Y +NFP−T +TR+ INT −C
Y = Spvt −NFP+T −TR− INT +C
Y = Y
Spvt −NFP+T −TR− INT +C = C + I +G+NX
S−Sgovt −NFP+T −TR− INT = I +G+NX
S− (T −TR− INT −G)−NFP+T −TR− INT = I +G+NX
S−T +TR+ INT +G−NFP+T −TR− INT = I +G+NX
S = I +NFP+NX
S = I +CA
S = I
Plott (ECON 221) Saving Spring 2014 21 / 89
Saving and Wealth
Wealth
Household wealth = a household’s assets minus its liabilitiesNational wealth = sum of all households’, firms’, and governments’wealth within the nationSaving by individuals, businesses, and government determine wealth
Wealth and saving as stock and flow (wealth is a stock, saving is a flow)
Flow variables: measured per unit of time (GDP, income, saving,investment)Stock variables: measured at a point in time (quantity of money, value ofhouses, capital stock)Flow variables often equal rates of change of stock variables
Plott (ECON 221) Saving Spring 2014 22 / 89
Saving and Wealth
National wealth: domestic physical assets + net foreign assets
Country’s domestic physical assets (capital goods and land)Country’s net foreign assets = foreign assets (foreign stocks, bonds, andcapital goods owned by domestic residents) minus foreign liabilities(domestic stocks, bonds, and capital goods owned by foreigners)Wealth matters because the economic well-being of a country dependson itChanges in national wealth
Change in value of existing assets and liabilities (change in price of
financial assets, or depreciation of capital goods)
National saving (S = I +CA) raises wealth
Comparison of U.S. saving and investment with other countries
The United States is a low-saving country; Japan is a high-saving country
U.S. investment exceeds U.S. saving, so we have a negative
current-account balance
Plott (ECON 221) Saving Spring 2014 23 / 89
Outline
1 Topic 3: Consumption, Saving, and InvestmentInvestment
Saving
Consumption
The Investment-Saving Curve
Plott (ECON 221) Consumption Spring 2014 24 / 89
University of Michigan: Consumer Sentiment1978M1–2013M7
Plott (ECON 221) Consumption Spring 2014 25 / 89
Animal Spirits & Irrational Exuberance
Fluctuations with contagious swings of optimism and pessimism,
called "animal spirits" by Keynes and "irrational exuberance" by
former Fed chairman Alan Greenspan.
Plott (ECON 221) Consumption Spring 2014 26 / 89
An Introduction to Consumption
Major component of spending (approximately 70% of U.S. GDP).
Includes purchases of goods and services by individuals.
Two reasons why studying consumption is important:1 It is the largest component of demand for goods and services in the U.S.2 Deciding how much to consume is linked to how much to save.
Cd = desired consumption; Sd = desired saving.
Assume income is all disposable (Yd = Y ), Y −Cd −G = Sd
Plott (ECON 221) Consumption Spring 2014 27 / 89
Old School Consumption?
Keynesian Consumers (named after a theory of John Maynard Keynes)
C = C +MPC ·Yd (ignoring Taxes and Transfers: Yd = Y )
C = "subsistence" level of Consumption ("wolf point")MPC = marginal propensity to consume
Key: Consumption is based solely on current income.
Based on cross-country and long-run time series data: C ≈ 0 and
MPC = ∆C
∆Y≈ 0.90
Problem: In Micro Data (household data) over short term,
MPC << 0.90
Using household data researchers find the MPC ≈ 0.40
The Keynesian consumption function does not seem to match
short-run (household) data. It does match long-run (country level)
data.
Plott (ECON 221) Consumption Spring 2014 28 / 89
John Maynard Keynes (canes)
In 1936 Keynes published The
General Theory of Employment,
Interest, and Money establishing
Keynesian economics as a major
alternative to the Classical model.
Keynes questioned the classical
view that economies moved
quickly to their long-run
equilibriums.
Stating that "in the long-run, we
are all dead", Keynes argued that
the primary focus of
macroeconomists should be the
short-run.
Plott (ECON 221) Consumption Spring 2014 29 / 89
Old School Consumption?
Drawbacks to Keynesian Consumption Functions (aside from notmatching data):
Does not result from optimizing household behaviorDoes not allow for the role of interest ratesDoes not distinguish between different types of income (one-timeincrease vs. permanent increase)Does not include expectations
Is there another theory which allows us to look at household
consumption behavior?
Yes
FisherLife-Cycle Hypothesis (Modigliani)Permanent Income Hypothesis (Friedman)
Plott (ECON 221) Consumption Spring 2014 30 / 89
A Model of Consumption: Fisher’s Model
Fisher’s model of consumption allows us to look at
individual/household consumption behavior.
Based on the intuition that in your consumption-saving decision you
face a trade off.
Consuming more today means less saving today. Less saving today
means that your resources for future consumption tomorrow are going
to be lower.
Call r the real interest rate (given).
The intertemporal price of 1 extra unit of consumption today is
−(1+ r) less units of consumption tomorrow.
If we understand this simple point we are already half way through!
Plott (ECON 221) Consumption Spring 2014 31 / 89
Set up of the Fisher’s Model of Consumption
Let’s study the decision of an individual (i.e. representative consumer
or household) that lives for two periods; e.g., think of them during
their working age and retirement.
r given.
Current and future income given, wealth given (exogenous).
Define:
y = current income i.e.current wageyf = future income i.e. future wagea = initial assets i.e. wealthc = current consumptioncf = future consumption
Objective: determining the choice of (c,cf )
Plott (ECON 221) Consumption Spring 2014 32 / 89
Relationship between Current and Future Resources
We call the relationship between current and future resources the
(intertemporal) budget constraint.
Key: The amount of c chosen will determine the amount available for
cf
y+a− c are the leftover resources that you carry to period 2 (the
future).
Particularly if you put those resources in a bank you will get
(y+a− c)(1+ r)
Assume that at period 2 you consume everything. It’s the last period.
We have
cf = (y+a− c)(1+ r)+yf
This is the budget constraint. Let’s look at it in the (c,cf ) space
Plott (ECON 221) Consumption Spring 2014 33 / 89
Intertemporal budget constraint
Slopes downward. There is a trade off between current and future
consumption.
c
cf
cf = (y+a− c)(1+ r)+yfIntertemporal Budget Constraint
Plott (ECON 221) Consumption Spring 2014 34 / 89
Present Value of Lifetime Resources (PVLR)
An additional concept: how much are all your resources (current and
future) worth today?
We just need to add the resources up, appropriately discounted.
We call it the present value of lifetime resources = PVLR = y+a+ yf
1+ rYou can check that this is also equal to present value of lifetime
consumption (PVLC = c+ cf
1+ r) (nobody is getting away with
consuming more that he can and nobody wastes resources that go
unconsumed).
PVLR is also the maximum level of consumption that you can get in
the current period.
Plott (ECON 221) Consumption Spring 2014 35 / 89
Intertemporal Budget Constraint
Note the PVLR on the horizontal axis.
c
cf
PVLR
cf = (y+a− c)(1+ r)+yf
PVLR = y+a+ yf
1 = r
Plott (ECON 221) Consumption Spring 2014 36 / 89
Last Piece: Individual Preferences
Our individual consumer, Bender, has utility U(c,cf )
Ignore his (immense) dependence on leisure for this example – makes itsimpler.
(Realistically) Bender likes consumption (both in the present and future)
Assume c, cf are normal goods (if your income increases you want toconsume more).
(Realistically) Bender likes if the level of consumption (c, cf ) remains smoothover time (consumption smoothing, more on this later). No large drops orjumps.
So Bender has regular indifference curves (curves representing the (c,cf )pairs that yield the same utility).
Plott (ECON 221) Consumption Spring 2014 37 / 89
An Indifference Curve for Standard Preferences
c
cf
Plott (ECON 221) Consumption Spring 2014 38 / 89
Optimal Choice of Consumption (Current and Future)
Borrower vs. Lender/Saver
c
cf
Plott (ECON 221) Consumption Spring 2014 39 / 89
Fisher’s Model of Consumption
Objective: determining the choice of (c,cf )
We just did it graphically!
It is the point of tangency we just found. (where the intertemporal rate
of substitution equals 1+ r). (From Micro, some more details in an
example coming up)
This simple set up is good enough for start thinking at consumption
and saving.
Saving = s = y− c
Plott (ECON 221) Consumption Spring 2014 40 / 89
Permanent Income Hypothesis (PIH) & Life-CycleHypothesis (LCH)
Milton Friedman and Franco Modigliani:
Consumers like smooth ConsumptionOptimize "lifetime" utility (over consumption). Pretty much the Fishermodel.
Today, you plan your consumption based upon what you observe today
and what you expect to happen tomorrow.
Constraint: PVLC = PVLR (PVLC = present value of lifetimeconsumption).They like to smooth "marginal utility" across seasons, business cyclesand life cycles.Think about it: Retirement, Job Loss, Summer Vacations, etc.Does much better at matching data – although not perfect.
Plott (ECON 221) Consumption Spring 2014 41 / 89
Franco Modigliani (mo-deel-YAH-nee)
1918–2003
Awarded Nobel Prize in Economics in 1985Work
Life-Cycle Hypothesis (LCH)Modigliani-Miller Theorem: under particular assumptions, it makes nodifference whether a firm finances itself with debt or equity.
Plott (ECON 221) Consumption Spring 2014 42 / 89
Milton Friedman
Awarded Nobel Prize in Economics in 1976
"the most influential economist of the second half of the 20th
century. . . possibly of all of it." – The Economist
http://miltonfriedman.blogspot.comPlott (ECON 221) Consumption Spring 2014 43 / 89
From Micro: An Example of Solving the Model
Again assume households (Bender) maximize U(c,cf ) in a two period
model (current = period 1, future = period 2)
U(c,cf ) = ln(c)+βln(cf )
(log utility for simplification, β = Discount Factor – i.e., how much youlike eating today versus tomorrow)
cf = (y+a− c)(1+ r)+yf
(Budget Constraint; a = Initial Wealth)
or
c+ cf
1+ r= a+y+ yf
1+ r(I just re-wrote the above constraint PVLC = PVLR)
Do some simple constrained optimization: Maximize U(c,cf ) with
respect to (c,cf ) subject to intertemporal budget constraint.
Plott (ECON 221) Consumption Spring 2014 44 / 89
An Example (Continued)
For our example, assume that β= 1 and r = 0 (for simplicity, not
realism).
Solution: c = cf (Households want equal levels of consumption each
period).
Suppose: y = 1, yf = 9, a = 0: What are the optimal (c,cf )?
We know that c is smoothed over time (optimizing behavior).
We also know that cf = (a+y− c)(1+ r)+yf ( budget constraint).
Solving we get c = (a+y+yf )
2= PVLR
LL= 5 ; where LL = length of life.
Plott (ECON 221) Consumption Spring 2014 45 / 89
An Example (Continued)
Period 1 2
Income 1 9
Consumption 5 5
Savings –4 4
Note: expected income increases are already included in today’sconsumption plan:
Only news today (about today or the future) affect our consumptionplan!The fact that income rises from 1 to 9 between periods 1 and 2 is alreadyincluded in my consumption plan!
Unexpected news about income, life spans, etc. WILL effect
consumption decisions.
Plott (ECON 221) Consumption Spring 2014 46 / 89
Unexpected Transitory Increase in Current Income
Example: Suppose today I find out that my current income increases
by ∆= $2. What is the new consumption plan associated with this
transitory (temporary) increase in y?
c = cf = 6 (still smooth consumption across periods)
s =−3,sf = 3
Consumption increases by a little today (and in the future), saving
increases today!
Saving increases today so consumption tomorrow will be higher
(transfer some of the transitory income shock towards the future)
MPC = ∆ctoday
∆ytoday= 1
LL= (in this example) = 0.5
Plott (ECON 221) Consumption Spring 2014 47 / 89
Unexpected Transitory Increase in Current Income
Increase in current income (y+∆= y′ > y). Pure income effect. Increasing incomeincreases both current and future consumption (both normal goods). Bender is alender here.Note that current saving (y′− c′) also goes up when y′ increases. The level of cf
increases for this reason.
c
cf
Plott (ECON 221) Consumption Spring 2014 48 / 89
Transitory Increase in Future Income
Increase in future income (yf +∆(1+ r) > yf ). Pure income effect. I know now
that in period 2 I have ∆(1+ r) more. Increasing future income increases both
current and future consumption (both normal goods).
Note that current saving (y− c′) goes down when future income increases!
c
cf
Plott (ECON 221) Consumption Spring 2014 49 / 89
Unexpected Increase in Permanent Income
Example: Suppose today I find out that my income will permanently
increase by $2 (in both period 1 and period 2). What is the new
consumption plan associated with this permanent increase in y and
yf ?
c = cf = 7
s =−4,sf = 4
Consumption increases more today (and in future) than compared
with the case of a transitory income shock, and saving remains
constant!
MPC = ∆C(today)
∆Y (today)= 1 = (in all examples) = 2
2= 1
With permanent changes in income, consumption and income move 1for 1.
Plott (ECON 221) Consumption Spring 2014 50 / 89
Unexpected Increase in Wealth
Example: Suppose today I find out that my wealth increased by $2
prior to period 1 (a one-time unexpected stock market gain). What is
the new consumption plan associated with this unexpected increase
in a?
c = a+y+yf
2= cf = 6
s =−5(= y− c),sf = 3 (increase in PVLR due to wealth = 2)
Consumption increases today (and in future), and saving falls.
One time increases in wealth are identical to one time (transitory)
changes in current income. Different effect on saving though.
Plott (ECON 221) Consumption Spring 2014 51 / 89
Unexpected Increase in Wealth
Increase in initial wealth (a+∆= a′ > a). Pure income effect. Increasing wealth
increases both current and future consumption (both normal goods).
Note however that current saving (y− c′) goes down when a increases!
c
cf
Plott (ECON 221) Consumption Spring 2014 52 / 89
Some Evidence Consistent with PIH Behavior
Business Cycles are likely to be associated with temporary shocks toincome.
We find consumption to be more stable than income over the businesscycle.And the saving rate is generally procyclical.So, C does not move 1-for-1 with Y .
Micro Studies find the MPC out of income changes to be much less
than 0.9 (C does not track Y one for one).
Micro Studies find a MPC out of changes in wealth of about 0.05.
(Unexpected capital gains in housing/securities are like one time
increases in income).
Household consumption responds more to permanent shocks to
income than to temporary shocks.
Plott (ECON 221) Consumption Spring 2014 53 / 89
However . . .
In contrast to the predictions of the PIH, consumption does vary too much withtemporary income changes.
Suppose a household earns $60,000 (on average) over 40 working years.Total earnings over working years = $2.4 million (do not worry about discounting)Suppose in a recession, that household loses their job for 1 year and because of transfers(unemployment insurance, severance) only earns $20,000 that year.That household’s lifetime income only declined by 0.166% (less than one fifth of onepercent) . . . ($40,000/$2.4 million) because of recession.Being unemployed – even for one full year out of a lifetime – does not effect lifetimeincome all that much!According to the PIH, consumption should not respond that much . . . (household shouldspread that $40,000 over 40 years. Consumption should, at most, decline only$1,000/year).If you prepared for the possibility of job loss, consumption really shouldn’t change at all(just draw down savings).
If the PIH theory is true, consumption of the economy should not respond that muchduring recessions
1 recessions have little effect on our lifetime incomes and2 we should prepare for recessions and as a result, have savings to buffer our low income).
Plott (ECON 221) Consumption Spring 2014 54 / 89
Consumption During Recessions
But Consumption falls during recessions
Not a prediction of the standard permanent income hypothesis (PIH).
If households were smoothing consumption, they should realize that
their lifetime income has not changed that much because of job loss.
Furthermore, they should have saved to prepare for a recession (we all
know that recessions sometimes happen)!
During recessions, aggregate consumption behavior looks more
Keynesian than PIH . . .
Why do I say this? Well, Keynesian behavior says C is a function of only
current Y ; i.e., C = C +MPC ·Yd
As current Y falls (as in a recession), current C falls. However, data
shows that C falls only by about 40% of the Y fall. That implies MPC is
0.40. But, this doesn’t match long term response of consumption to
income changes (too high).
Plott (ECON 221) Consumption Spring 2014 55 / 89
Refinements to Consumption Theory
These are refinements to consumption theory that we will not spendmuch time on (there is a whole consumption literature modelingconsumption behavior more thoroughly to match the data).
Liquidity Constraints (borrowing constraints – maybe consumerscannot smooth income!)Uncertainty (Precautionary Savings)Little is known about preferences (time preference rates – β and riskaversion).Bequests explain a large portion of wealth accumulationPortfolio Choice makes a differenceLarge variation in wealth accumulations across individualsLife Cycle ShocksHome production (including shopping for bargains)
Plott (ECON 221) Consumption Spring 2014 56 / 89
Refinement of PIH Theory (part 1): LiquidityConstraints
Liquidity Constraints refer to the fact that sometimes a household (or a firm) optimally wants
to borrow to smooth consumption (or for investment), but lenders are unwilling to lend to
that household against future streams of income.Why will lenders refuse to lend?
Lender may not believe that the household will pay them back.Lender cannot distinguish between households who want to borrow to smooth consumptionfrom borrowers who want to borrow and then default.
In recessions, in order to smooth consumption, households who receive a negative income
shock either have to draw down saving or borrow. If they are prevented from borrowing,
household will have no choice but to cut their consumption. As a result, C will fall during
recessions.
Liquidity constraints make households look Keynesian when income falls (C falls when Y falls
– for those with no saving and who cannot borrow).
However, when Y is high, households look like PIH households – nothing prevents them from
saving. If Y is temporarily high, households would want to save some of that income.
Liquidity constraints prevent borrowing NOT saving . . .
Plott (ECON 221) Consumption Spring 2014 57 / 89
Liquidity Constraints
Desired consumption is Cd. Note: current and future consumption are
constrained.
c
cf
Plott (ECON 221) Consumption Spring 2014 58 / 89
Refinement of PIH Theory (Part 2): Grasshoppers and Ants
Perhaps the economy is made up of both Keynesian and PIH consumers:
"It was wintertime, the ants’ store of grain had got wet and they were laying it out to dry dry. A
hungry grasshopper asked them to give it something to eat. "Why did you not gather food in
the summer like us?" the ants asked. "I hadn’t time", it replied. "I was too busy making sweet
music." The ants laughed at the grasshopper. "Very well", they said. "Since you piped in the
summer, now dance in the winter."
– An Aesop Fable
The fable is a a story about consumption (eating), saving (storing food) and retirement (winter) . . .
Suppose the population is made up of both economic grasshoppers (Keynesian consumers) and
ants (PIH consumers).
The ants in the parable were forward looking (like PIH theory suggests – they know retirement is
coming and prepare for it).
The grasshoppers eat their current income and do little saving. They behave as if retirement does
not exist. When retirement comes, they do not have enough resources to sustain their
consumption. (we can also think of winter as a recession . . . the grasshoppers do not prepare for
recessions)
As a result, the consumption of grasshoppers will respond to predictable changes in income
(recessions, retirement, etc.)
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Grasshoppers and Ants: Evidence
About 20% of households behave according to Keynesian theories
(increasing consumption with income without regard for future states of
the world).
A full 1/3 of the baby boom generation is "ill prepared" to sustain
consumption through retirement (Bill Gale, Brookings).
Over 20% of households do not own a checking/saving account – (40% have
less than $5k in liquid assets).
Observe "Grasshopper" behavior among households in the population
(consumption responds to both predictable income increases and
predictable income declines). These same households are ill prepared for
retirement.Pseudo-Keynesian behavior important for policy!
Keynesian’s will have large current response to temporary tax cuts.PIH households (who are not liquidity constrained) will have very smallresponse to temporary tax cuts.
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Refinement of PIH Theory (Part 3): Home Production
We measure consumption (as with most macro variables) in dollars.
Expenditure may not be a good measure of consumption when the
value of time changes.
When the value of time is low (unemployment – like in recessions) orretirement, individuals can take action to reduce their expenditure(holding consumption constant).
Clip couponsSearch for bargains across storesMake your lunch at home instead of buying it at a cafeteria.
If home production/search is important, we would expect
EXPENDITURE to fall during a recession. However, CONSUMPTION
may remain unchanged!
Strong evidence for the home production/search theory of
consumption expenditures. The decline in expenditure during
recessions does not mean people are consuming less.
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LCH Diagram & an Empirical Problem
Many economists have studied the
consumption and saving of the elderly.
Their findings present a problem for the
life-cycle model. It appears that the
elderly do not dis-save as much as the
model predicts. In other words, the
elderly do not run down their wealth as
quickly as one would expect if they were
trying to smooth their consumption over
their remaining years of life.
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Refinement of LCH Theory (Part 1): PrecautionarySaving & Bequests
There are two chief explanations for why the elderly do not dis-save to the extent that the modelpredicts.
The first explanation is that the elderly are concerned about unpredictable expenses. Additional savingthat arises from uncertainty is called precautionary saving. One reason for precautionary saving bythe elderly is the possibility of living longer than expected and thus having to provide for a longer thanaverage span of retirement. Another reason is the possibility of illness and large medical bills. Theelderly may respond to this uncertainty by saving more in order to be better prepared for thesecontingencies.
The precautionary-saving explanation is not completely persuasive because the elderly can largelyinsure against these risks. To protect against uncertainty regarding life span, they can buy annuitiesfrom insurance companies. For a fixed fee, annuities offer a stream of income that lasts as long as therecipient lives. Uncertainty about medical expenses should be largely eliminated by Medicare, thegovernment’s health insurance plan for the elderly, and by private insurance plans.
The second explanation for the failure of the elderly to dis-save is that they may want to leave bequeststo their children. Economists have proposed various theories of the parent-child relationship and thebequest motive.
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Consumption and Interest Rates
So far we have focused at changes in income and wealth.
Now let’s analyze what are the consequences of changes in prices.
1+the real interest rate is the price of today’s consumption relative to
future consumption. You forgo 1+ r dollars of future consumption to
consume 1 dollar today.
An increase in the real interest rate produces an increase of the price of
today’s consumption relative to future consumption.
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Consumption and Interest Rates
Increase in real interest rate (r′ > r): Example of income effect
dominating (Saver/Lender). New intertemporal budget constraint.
c
cf
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Substitution and Income Effects: Intuition
Assume current and future consumption are normal goods.
1+the real interest rate is the price of today’s consumption relative to
future consumption: You forgo 1+ r dollars of future consumption to
consume 1 dollar today.
An increase in the real interest rate means an increase of the price of
today’s consumption relative to future consumption.
The fact that you shift away from current consumption (i.e. you increase
your saving) as a consequence of this change in price is the substitution
effect. Cheaper future consumption produces an incentive to consume
less today and save more.But an increase in r also affects income (hence an income effect):
1 An increase in the real interest rate increases interest receipts for a lender.This produces an incentive to consume more today and save less.
2 An increase in the real interest rate increases interest payments for aborrower. This produces an incentive to consume less today and save more.
Plott (ECON 221) Consumption Spring 2014 66 / 89
Intertemporal Substitution in Consumption
Increase in real interest rate: Example of income effect dominating
(Saver/Lender). Step 1: Trace Substitution effect (allow original choice
at new prices).
c
cf
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Intertemporal Substitution in Consumption
Increase in real interest rate: Example of income effect dominating. Step 2:Now increase income to new level. Both current and future c increase.
Note: current saving decreases. See Abel, Bernanke, Croushore textbook foran example where substitution effect dominates (saving increase).
c
cf
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Intertemporal Substitution in Consumption
Increase in real interest rate: Example of the problem for a Borrower. cdecreases.
Note: for a borrower Income and Substitution effects go in the samedirection. When r increases, saving increases.
c
cf
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Recap Consumption and Interest Rates
Assume households are net lenders.
Substitution effect: higher r lowers c. Think of people saving more to reap thehigher return, or people borrowing less because it is more expensive. Higherinterest rate today, makes saving more beneficial (price of future consumptionfalls). Households will switch away from consumption today (i.e., c today falls, cf
tomorrow increases, and s today increases)Income effect: higher r raises c today. For every dollar saved, you get higherincome (if you are a net saver). When richer, you buy more of the things you like.What do you like? Consumption today and consumption tomorrow. As a result,you can save less and get more of both. (c today increases, cf tomorrow increases,and s today falls)Evidence: some studies find the substitution effect stronger, others find they arethe same. My intuition is that higher r has little, if any, effect on currentconsumption (i.e. substitution effect equals income effect).
What if households are net borrowers? – Income effect is opposite as
lender/saver. Higher interest rates make households poorer (they have to pay
higher interest payments). Income effect will say that c today will fall, cf
tomorrow will fall and s today will increase.
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Full Recap of the Fisher/PIH model
Assume current and future consumption are normal goods.
An increase in current income increases current and future
consumption and increases saving.
An increase in future income or wealth increases current and future
consumption but decreases saving.
An increase in the real interest rate decreases current consumption but
increases future consumption and saving for a lender, if the
substitution effect dominates.
An increase in the real interest rate increases current and future
consumption but decreases saving for a lender, if the income effect
dominates.
An increase in the real interest rate decreases current consumption
and increases saving for a borrower. May increase or decrease future
consumption.
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Laibson’s Pull of Instant Gratification
Keynes called the consumption function a "fundamental psychological law". Yet,
as we have seen, psychology has played little role in the subsequent study of
consumption. Most economists assume that consumers are rational maximizers
of utility who are always evaluating their opportunities and plans in order to
obtain the highest lifetime satisfaction.
More recently, economists have started to return to psychology. They have
suggested that consumption decisions are not made by the ultra-rational Homo
economicus but by real human beings whose behavior can be far from rational.
This new sub-field infusing psychology into economics is called behavioral
economics. The most prominent behavioral economist studying consumption is
Harvard professor David Laibson.
Laibson notes that many consumers judge themselves to be imperfect decision
makers. In one survey of the American public, 76 percent said they were not
saving enough for retirement. In another survey of the baby-boom generation,
respondents were asked the percentage of income that they save and the
percentage that they thought they should save. The saving shortfall averaged 11
percentage points.
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Two Questions and Time Inconsistency
1 Would you prefer (A) a candy today, or (B) two candies tomorrow?
2 Would you prefer (A) a candy in 100 days, or (B) two candies in 101
days?
In studies, most people answered (A) to 1 and (B) to 2.
A person confronted with question 2 may choose (B).
But in 100 days, when confronted with question 1, the pull of instant
gratification may induce her to change her answer to (A).
http://www.nobelprize.org/nobel_prizes/economic-sciences/
laureates/2002/kahneman-lecture.html
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Summary: What Effects Consumption
Current Income (Both PIH and Keynesian Theories)
Expectations of Future Income (Only PIH theory)
Wealth
Temporary vs. Permanent Changes
Tax Policy
Interest rates (slightly)
Preferences
The magnitude of the results depend on whether consumers follow
Keynesian or PIH consumption rules and whether or not liquidity
constraints exist!
In our Government Policy Lecture, we will talk about Social Security
Systems and consumer’s expectations of tax changes
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Conclusion: Getting Closer to Modeling Demand
Ctoday = C(y, yf , wealth, taxes, liquidity constraints, consumption rules,
expectations)
Ctoday = C(PVLR, taxes, liquidity constraints, consumption rules,expectations)
We will assume that r does affect C only through the substitution effect.You can extend the model to account for substitution and incomeeffects.
Itoday = I(r, Af , MPK f expectations, investment taxes)
We are moving towards a model of Aggregate Demand:
Y d = Cd(·)+ Id(·)+G+NX
We will get to G & NX later in the course
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Outline
1 Topic 3: Consumption, Saving, and InvestmentInvestment
Saving
Consumption
The Investment-Saving Curve
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From Our Previous Work to Goods Market Equilibrium
In Topic 2 we defined Aggregate Production.
Up to this point in Topic 3 we defined two main components of
Aggregate Spending: Consumption and Investment.
More specifically desired levels of Consumption (Cd) and Investment
(Id).
We now consider the Equilibrium: aggregate quantity of goods &
services demanded equals goods & services supplied (Y ).
Plott (ECON 221) The Investment-Saving Curve Spring 2014 77 / 89
Goods Market Equilibrium
Goods Market equilibrium condition:
Y = Cd + Id +G+NX (1)
Cd is a function of PVLR (Y , Y f , a), tax policy, expectations, r, etc.
Id is a function of r, Af , K , and investment tax policy.
G is a function of government policy.
NX we will model later in the course
Let us take Y (supply) as given.
Let us postpone studying G in detail to later. NX in future lectures.
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Goods Market Equilibrium (Continued)
For given Y , we can re-express (1) as:
Sd = Y −Cd −G = Id (2)
when NX = 0 Desired Saving = Desired Investment
Equilibrium: the resources not consumed by private households or the
government are channeled to firms that use them to finance
investment.
So what links Sd to Id? The real interest rate, r. In equilibrium S = I .
We defined I as negative function of r earlier in Topic 3 by looking at
MPKf = ucf . ↑ r →↓ Id.
We also considered saving and consumption decisions as a function of
r. Assume now substitution effect dominates (true empirically).
↑ r →↑ Sd
Plott (ECON 221) The Investment-Saving Curve Spring 2014 79 / 89
Goods Market Equilibrium (Continued)
I ,S
r
Sd
Id
I0 = S0
r0
Plott (ECON 221) The Investment-Saving Curve Spring 2014 80 / 89
Goods Market Equilibrium (Continued)
I ,S
r
Sd
Id
I0 = S0
r0
r′
At r′ desired investment is higher than desired saving, hence the price of saving (i.e. r) isgoing to increase converging to equilibrium.
If investors want to borrow (I ′) more than savers are willing to lend (S′), this will be bid upthe price of saving (r).
Plott (ECON 221) The Investment-Saving Curve Spring 2014 81 / 89
Example: Increase in output (Y ′ > Y )
I ,S
r
Sd = Y ′−Cd −G
Id
Sd = Y −Cd −G
I1 = S1I0 = S0
r1
r0
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The Investment-Saving (IS) Curve
The IS curve is named as such because it shows the relationship
between saving and investment (holding NX constant to 0).
The IS curve relates Y to r.
For any level of output Y the IS curve shows the value of r for which
the goods market is in equilibrium.
How do interest rates relate to Y ?
As Y increases, desired saving increases, decreasing the real interest ratethat clears the goods market.Alternatively think of IS as: Y = C(r)+ I(r)+G where C and I are negativein r.IS curve is downward sloping in {r,Y }–space.
The IS curve represents demand side of the economy.
Why IS? Because the demand side of the economy can be boiled down
to I = S (when NX is zero).
Plott (ECON 221) The Investment-Saving Curve Spring 2014 83 / 89
Building the IS Curve
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Demand Side Analysis (IS Curve)
Y
r
IS
r0
Y0
Suppose r is set by the Fed (U.S. central bank) at the level of r0 (we willexplore this in depth later in the course). For a given r, we can solve for thelevel of output desired by the demand side of the economy.
Plott (ECON 221) The Investment-Saving Curve Spring 2014 85 / 89
Some Thoughts on the IS Curve
What shifts the IS curve?
Anything that causes desired C, I or G to change (or NX when we modelit).
What shifts IS curve to the right? (i.e., makes Y higher on the demandside of the economy).
Increase in consumer confidence (expectations of future PVLR).Permanent increase in stock market wealth, bonds, and the like.A permanent reduction in income taxes (if households are PIH orKeynesian).A temporary reduction in income taxes (if households are Keynesian orLiquidity Constrained PIH).An expected future increase in TFP (stimulates investment demand).Anything shifting MPK up.An increase in government spending (e.g. war).
Changes in r will NOT cause the IS curve to shift (causes movement
along IS curve).
Plott (ECON 221) The Investment-Saving Curve Spring 2014 86 / 89
Example 1: Suppose Consumer Confidence Falls
Suppose consumer confidence falls. Desired saving increases,
decreasing the real interest rate that clears the goods market at any Y .
The IS curve will shift leftward.
Y
r
IS
r0
Y0
Plott (ECON 221) The Investment-Saving Curve Spring 2014 87 / 89
Example 2: Suppose Future TFP Increases
Suppose future TFP increases. Desired investment increases (MPK goes
up), increasing the real interest rate that clears the goods market at any Y .
The IS curve will shift rightward.
Y
r
IS
r0
Y0
Plott (ECON 221) The Investment-Saving Curve Spring 2014 88 / 89
Example 3: Suppose Population Increases (N goes up next period)
Suppose N f goes up. Desired investment increases (MPK goes up), increasingthe real interest rate that clears the goods market at any Y . The IS curve willshift rightward.
Y
r
IS
r0
Y0
Plott (ECON 221) The Investment-Saving Curve Spring 2014 89 / 89