the consumption function looking at aggregate demand (closed economy) ep = c + ip + g assuming g is...

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

45OC

Y0

C = A + bY

A

dC/dY = b

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

45OC

Y0

C = A + bY

b 0.7

C = b* Yb* 0.9

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)


Indifference Curves represent U = U(C1 , C2 )

0

C2

C1


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

Slope of AB is (1 + r)

0

Y2

Y1B

A

.Ey2

y1


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

0

Y2

Y1B

A

.Ey2

y1

C

D

OPTIMAL C

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

oy2)

Y1

Y2

0

A

B

.E

c*c*2

c*1

y2

y1

CHANGES IN Y AND C

Y2 increases: E’ E”, AB CD, c’1 c”1

B

A

Y2

Y10

E’.

.E”

c”1c’1 D

C

A INCREASE IN r : SAVER

Income effect 1 3; Substitution effect 3 2

Y1

Y2

0

A

B

.E

c11

y2

y1

C

D c21 G

F

c31

32

1

A INCREASE IN r : BORROWER

Inc. effect 1 2; Sub. effect 2 3

Y1

Y2

0

A

B

.E

c11y1

C

D

12

c21

3

c31

F

G

IMPERFECT CAPITAL MARKETS

Borrowing rate (EB) > lending rate (AE)

0

C2

C1

.EY2

Y1

A

B

CREDIT (BORROWING) CONSTRAINT

.

0

C2

C1

EY2

Y1

A

B

D

I” I’

Consumer cannot borrow more than Y1B

Constraint: ADB

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


.

0 C1

C2

C1*

C2*

A

B

E’.

E”.

Y1’ Y1”

E’: low Y1/Y2 high C1/Y1

E”: high Y1/Y2 low C1/Y1


Y, C and W over the life-cycle

Age

Y, C

6518

Age

+W

W

Ct

Yt

Wt

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)


– 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) = RT 0.75– APC = [0.03 (W Y) + 0.75] > MPC


• 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 Cp and 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


• Cross-section measurements of C and Y

45o

C

Y0 Ym

CmCi = A + bYi

.. .

. . . .

Ci, Yi .


• Where Yj > Ym, Ytr > 0 and Yj > Ypj

45o

C

Y0 Ym

Cm

Ci = A + bYi

Cp =kYp

Yj

Cj

Ypj

Ytrj


• 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


• Also we may express the PYH as an error-correction model:• Yp

t = Ypt-1 + j(Yt – Yp

t-1) 0 < j < 1

• which with: Ct = Cpt = kYp

t

• gives: Ct = kYpt = kYp

t-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)Yp

t-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 initially Y > 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)

the consumption function looking at aggregate demand (closed economy) ep = c + ip + g assuming g is...

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