THE CONSUMPTION FUNCTION

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THE CONSUMPTION FUNCTION. Looking at Aggregate Demand (closed economy) Ep = C + Ip + 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:

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THE CONSUMPTION FUNCTION
• Looking at Aggregate Demand (closed economy)
• Ep = C + Ip + 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)
• or, C = C(Y - T)
• We need to model the behaviour of C
EARLY FORMULATION: 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
GRAPH OF THE BASIC CONSUMPTION FUNCTION
• As Y increases, C/Y falls: also dC/dY  C/Y

C

45O

C = A + bY

dC/dY = b

A

0

Y

EARLY 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.
LONG AND MEDUIM RUN EVIDENCE ON CONSUMPTION
• 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

MODELS OF AGGREGATE CONSUMPTION
• Basic Intertemporal Choice model (Fisher)
• The Life-Cycle theory of Consumption (Modigliani, etc)
• The Permanent Income theory of Consumption (Friedman)
INTERTEMPORAL CHOICE
• Generally we require: PV(C)  or  PV(Y)
• i.e. C1 + C2  (1+r)  or  Y1 + Y2 (1+r)
• or  Ci  (1+r)i  or   Yi  (1+r)i
• Households maximize Utility over expected lifetime
• i.e. Max: U = U (C1, ..., Ci , ... , Cn)
• s.t.  Ci  (1+r)i  or   Yi  (1+r)i(i : 1  n)
INTERTEMPORAL CHOICE

Indifference Curves represent U = U(C1 , C2 )

C2

C1

0

INTERTEMPORAL CHOICE

Endowment at E: OB = PV(Y) = y1 + y2  (1 + r)

Slope of AB is  (1 + r)

Y2

A

.

E

y2

y1

Y1

0

B

INTERTEMPORAL CHOICE

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

.

E

y2

y1

Y1

0

D

B

OPTIMAL C

Saving is (oy1- oc*1) : future dis-saving is (oc*2 - oy2)

Y2

A

c*2

c*

.

y2

E

0

c*1

y1

B

Y1

CHANGES IN Y AND C

Y2 increases: E’  E”, AB  CD, c’1  c”1

Y2

C

A

.

E”

.

E’

0

c’1

c”1

B

D

Y1

A INCREASE IN r : SAVER

Income effect 1 3; Substitution effect 3  2

Y2

C

F

A

2

3

1

.

y2

E

0

y1

Y1

c31

c21

D

B

G

c11

A INCREASE IN r : BORROWER

Inc. effect 1  2; Sub. effect 2  3

Y2

C

A

.

F

E

3

1

2

0

Y1

y1

c31

c11

c21

D

G

B

IMPERFECT CAPITAL MARKETS

Borrowing rate (EB) > lending rate (AE)

C2

A

.

Y2

E

0

Y1

B

C1

CREDIT (BORROWING) CONSTRAINT

.

C2

I”

I’

A

Consumer cannot

borrow more than Y1B

E

Y2

D

0

Y1

B

C1

THE LIFE-CYCLE HYPOTHESIS
• 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
THE LIFE-CYCLE HYPOTHESIS

.

C2

E’: low Y1/Y2  high C1/Y1

E”: high Y1/Y2  low C1/Y1

A

E’

.

C2*

.

E”

C1

B

0

Y1’

C1*

Y1”

THE LIFE-CYCLE HYPOTHESIS

Y, C and W over the life-cycle

Y, C

Ct

Yt

Age

18

65

+W

Wt

Age

W

THE LIFE-CYCLE MODEL
• 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
• i.e. C = (W + RY)/T
• and C = (1/T)W + (R/T)Y
• or C = W + Y ( = 1/T;  = R/T)
THE 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
THE LIFE-CYCLE MODEL
• 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
THE PERMANENT INCOME HYPOTHESIS
• Cp = kYp (0  k  1 )
• Y = Yp+ Ytr
• C = Cp + Ctr
• Permanent income is the return to all wealth, human and non-human:
• Yp = rW
• which implies: Cp = rkW
• NB: C is not related to Ytr i.e. dC dYtr = 0
MEASURING PERMANENT INCOME AND CONSUMPTION (1)
• Are Cpand Yp observable?
• E(Ytr ) = 0
• E(Ctr ) = 0
• which imply that E(Y) = E(Yp ), etc.
• However this is ex ante: ex post, actual measures may reveal more
• (a) in a recession: Y < Yp :  Ytr < 0
• (b) in a boom: Y > Yp :  Ytr > 0
MEASURING PERMANENT INCOME AND CONSUMPTION (2)
• Cross-section measurements of C and Y

C

45o

Ci, Yi.

.

.

.

.

Ci = A + bYi

.

.

Cm

.

0

Y

Ym

MEASURING PERMANENT INCOME AND CONSUMPTION (3)
• Where Yj > Ym, Ytr > 0 and Yj > Ypj

C

45o

Cp =kYp

Cj

Ci = A + bYi

Cm

Ytrj

0

Y

Yj

Ym

Ypj

MEASURING PERMANENT INCOME AND CONSUMPTION (4)
• Aggregate: Ytr > 0 in boom, < 0 in recession
• Measured C/Y should  be < in boom than in recession (Recent experience?)
• Aggregate Ctr = 0: individual Ctr is > or < 0
• Average Ctr = 0 for all income groups
• Measuring Yp:
• Adaptive expectations: Yp = f(Yt, Y t - 1, ...Y t-n)
• Rational expectations: only new information (shocks) change Yp
• Consumption V Consumption Expenditure, which highlights the role of durables (Investment and saving rather than consumption
MEASURING PERMANENT INCOME AND CONSUMPTION (5)
• Also we may express the PYH as an error-correction model:
• Ypt = Ypt-1 + j(Yt – Ypt-1) 0 < j < 1
• which with: Ct = Cpt = kYpt
• gives: Ct = kYpt = kYpt-1 + kj(Yt – Ypt-1)
• Re-arranging: Ct = (k – kj)Ypt-1 + kjYt
• j  0 implies slow adaptation, j  1 implies rapid adaptation
• assume k = 0.9, j = 0.3, so kj = 0.27
• then: Ct = (0.9 – 0.27)Ypt-1 + 0.27Yt or 0.63Ypt-1 + 0.27Yt
• However this is not an explicitly forward-looking model.
• Now suppose C = Cp = kYp, then Yp = 1/k(Cp)
• Thus Ct = (0.63/k)Ct – 1 + 0.27Yt = 0.7Ct – 1 + 0.27Yt
PERMANENT INCOME AND RECESSION
• Y < Yp in short-run (mild) recession
• Suppose there is a shock to the system (financial crisis)
• Pwople expect a severe long-drawn-out recession: i.e. Yp falls, ie. E(Y) falls
• It is possible that initiallyY > Yp
• C (and Cp) will fall
• If people anticipate a fall in Yp, then C/Y may fall
• Current (mid-2009) situation: big fall in W, both the Permanent and Life-cycle theories predict that this will hit C (independently of current measured Y)