Transcript Consumption - Vincent Hogan

Consumption
Mankiw Chapter 16
Learning Objectives
1. The limitations of the Keynesian
consumption function
2. The role of interest rates in consumption
3. The influence of age on consumption
4. The permanent income hypothesis
The Keynesian Consumption Function
• Looking at Aggregate Demand (closed economy)
•
Y=C+I+G
• Assuming G is exogenous, this leads to enquiring into
determinants of Consumption and Investment
• Consumption is of particular interest (multipliers, etc)
• Previously we have:
–
C = (1 - s)Y
(0  s < 1)
–
C = C(Y - T)
• We need to model the behaviour of C
Keynes (1936)
• Keynes (1936) made three main assertions:
–
C = C(Y), (not r)
–
0  MPC  1, (where MPC is dC/dY)
–
APC falls as Y increases (APC is C/Y)
• Taken together these imply a Consumption Function of
the form: C = A + bY
– where A and b are positive constants
– APC = A/Y + b
– MPC = b
– and A/Y must fall as Y increases
Keynes C. Fn.
As Y increases, C/Y falls: also dC/dY  C/Y
C
45O
C = A + bY
dC/dY = b
A
0
Y
Empirical Evidence
• Keynes hadn’t have much statistical evidence on
consumption
• Early estimates in the 1940s for the USA and
elsewhere were conflicting.
• Short-medium term annual data (1929-45)
– C = A + bY;
A 0;
b  0.7
• Long-term data (1869-1945)
– C = bY:
A  0, b  0.9
• Which is “right”?
• We need a proper model to answer this.
Contrasting Empirical Evidence
• 1929-45: C = A + bY
• 1869-45; C = b*Y
C
45O
b* 0.9
C = b* Y
C = A + bY
b 0.7
0
Y
Alternative Models
• Clearly the simple Keynes approach is
missing something.
• We look at Three candidates
– Interest rates: Intertemporal Choice model
(Fisher)
– Age: The Life-Cycle theory of (Modigliani, etc)
– Forward looking consumers: The Permanent
Income theory of Consumption (Friedman)
Intertemporal Choice
• Individuals can borrow against future income
to fund consumption now or save now to fund
consumption in the future
– Hence consumption choice is a decision on timing
– Consumption will be influenced by interest rates
• Specifically
– Consumer chooses between consumption in different time
periods
– The “price” of shifting consumption between periods is the
interest rate
• Apply standard consumer choice theory from micro
The Micro of Consumer Choice
• Budget constraint
– Generally we require: PV(C)  or  PV(Y)
• Two periods
– C1 + C2  (1+r)  or  Y1 + Y2  (1+r)
• Many Periods
–
 Ci  (1+r)i  or   Yi  (1+r)i
• Households maximize Utility over expected lifetime
– U (C1, ..., Ci , ... , Cn)
• Notice how this is just a special case of the standard
two good model from micro
Consumer Choice
Indifference Curves represent U = U(C1 , C2 )
C2
0
C1
Budget Constraint
Endowment at E: OB = PV(Y) = y1 + y2  (1 + r)
Slope of AB is  (1 + r)
Y2
A
y2
.E
0
y1
B
Y1
The “Price” of Consumption
• Why is slope AB = - (1 + r) ?
• Suppose (present) savings increase by €100
– i.e. C1 = - 100
• This allows an increase in C2 of 100(1 + r)
– i.e. C2 = +100 (1 + r)
• Slope AB = C2  C1 = 100 (1 + r)/ - 100
–
= - (1 + r)
A Change in r
An increase in r: AB pivots at E  CD
Y2
C
A
y2
.E
0
y1
D
B
Y1
Consumption Choice
• Max U st BC
– Saving is (oy1- oc*1) : future dis-saving is (oc*2 oy2)
Y2
A
c*2
y2
0
c*
E
.
c*1 y1
B
Y1
Change in Income
• Y2 increases: E’  E”, AB  CD, c’1  c”1
Y2
C
A
.
E”
0
c’1
E’
c”1
.
B
D
Y1
A Change in r when saver
• Income effect 1 3; Sub effect 3  2
Y2
C
F
A
2
3
1
y2
0
E
.
3
c11 c21 c 1 y1
D
B G
Y1
Change in R when Borrower
• Inc. effect 1  2; Sub. effect 2  3
Y2
C
A
F
0
.
E
3
1
2
y1 c31 c21 c11 D
G
B
Y1
Lessons of Intertemporal Model
1. Consumers are potentially forward looking
2. The ability to borrow or save means that
consumption can be influenced by future
income
3. Interest rates can influence consumption in
potentially complicated ways
4. Wealth can influence consumption
5. All these factors were absent from the simple
model
Life Cycle Model
• Income shows a marked life-cycle variation
• It is low in the early years, reaches a peak in
late middle age and declines, especially on
retirement
• Smoothing consumption over a lifetime is a
rational strategy (diminishing MUy)
• This implies C/Y will vary during the lifetime
of an individual
Life Cycle Hypothesis
• Two period version
C2
E’: low Y1/Y2  high C1/Y1
A
E”: high Y1/Y2  low C1/Y1
E’
.
C2 *
.
0
Y1’
C1*
E”
Y1”
B
C1
Cons Varies over life-time
Y, C and W over the life-cycle
Y, C
Ct
Yt
18
+W
65
Age
Wt
Age
W
The Life Cycle
• Let retirement age = 65; life expectancy =
75
• Years to retirement = R (= 65 – present age)
• Expected life = T (= 75 – present age)
• Assuming no pension, no discounting:
– CT = W + RY is the lifetime constraint
– C = (W + RY)/T
– C = (1/T)W + (R/T)Y
– C = W + Y
( = 1/T;  = R/T)
Life Cycle Model
• C = W + Y
–
–
–
MPC =  C Y = 
APC = C Y =  (W  Y) + 
clearly MPC < APC
• for a “typical” individual, age 35
– R=30, T = 40
–  = 1/T  0.03;
 (MPC) = RT  0.75
– APC = [0.03 (W  Y) + 0.75] > MPC
• This helps explain the Kuznets data
Empirical Relevance
• This helps explain the Kuznets data
– Recall short term CPC falls with income
– But long term APC is constant
• Here APC > MPC so APC falls with Y
– for fixed W
• In long term W will rise with income
• So APC will be constant
Savings
• Saving and Consumption behaviour may depend on
population age-structure
• Does Social Security displace personal savings?
• What is the effect of Medicare (USA) or Medical Cards
for over 70s (IRL) on Savings?
• Savings and Uncertainty:
– “rational” behaviour: run down wealth to zero
– individual circumstances unpredictable (care
needs)
– individual life expectancy unpredictable
– on average even selfish people will die with W > 0
Lessons of LCH
1. Consumption and income vary over the life
cycle
2. Consumption function should have wealth
and age as variables
3. Elderly save more than is suggested by the
LCH
The Perm Income Hypothesis
• Income has both permanent and transitory
components.
– Y = Yp+ Ytr
• Consumption is more strongly influenced by
permanent component
– Cp = kYp
(0  k  1 )
• Permanent income is the return to all wealth,
human and non-human:
– Yp = rW
Transitory Income
• What happens to Ytr?
– Saved
– Added to wealth
– Consume return on it
• In reality people will consume at least some of
transitory income
– See case studies in book
– PIH does not hold exactly in the real world
Recessions and Booms
• Ytr > 0 in boom, < 0 in recession
– C should be the same (perm inc same)
– Measured C/Y should  be < in boom than in
recession
• Suppose there is a shock to the system
(financial crisis)
– Expect severe long-drawn-out recession
– Yp falls
– C falls
• Current situation: big fall in W
• PIH suggests C will fall
Conclusions
1. Keynesians consumption function is
proximately true but is too simple
2. Interest rates and wealth have a effect
because people can transfers consumption
through time
3. Age and life cycle effects are specific reasons
why the might transfer consumption
4. Transitory should matter less than
permanent income