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

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The consumption function

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

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

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

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

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

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

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 choice1

INTERTEMPORAL CHOICE

Indifference Curves represent U = U(C1 , C2 )

C2

C1

0


Intertemporal choice2

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 choice3

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

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

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

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

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

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

IMPERFECT CAPITAL MARKETS

Borrowing rate (EB) > lending rate (AE)

C2

A

.

Y2

E

0

Y1

B

C1


Credit borrowing constraint

CREDIT (BORROWING) CONSTRAINT

.

C2

I”

Constraint: ADB

I’

A

Consumer cannot

borrow more than Y1B

E

Y2

D

0

Y1

B

C1


The life cycle hypothesis

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 hypothesis1

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 hypothesis2

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

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 model1

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 model2

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

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

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

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

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

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

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

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)


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