The Demand Side: Consumption &

Saving.

Created By:Reem M. Al-Hajji

Agenda.

• Intro.• The “Keynesian” Consumption

Function.• Permanent Income/Life Cycle Theory.• Modification to the Life Cycle Theory.• Saving Ration Explanation.• Conclusion.• Application on Kuwait.

Introduction

Why “Consumption” is important?

• It is the largest category of spending.

• Its marginal propensity to consume is one of the determinant of the multiplier.

• It is more stable than “The Saving Ratio”.

The “Keynesian” Consumption Function

A simple “Keynesian” Consumption Function:

C = A + β*Y

C : The actual consumption.

A : The autonomous consumption.

Β : The marginal propensity to consume.

Y : The current level of income NOT the disposable income.

Does this type of equation is acceptable for consumption

description?

Using statistical tests

How well does the equation in predicting

consumption

Why should we consider another model?

1. This model did fit the data set as shown in (fig.2.4) but it did fail to explain the fluctuations in that period.

2. This model assuming that any change in consumption or in saving ratio is explain by changes in income ONLY.

3. So, to explain the behavior of saving ratio we need to consider other factors.

Adjusting The “Keynesian” Consumption Function

How to adjust the simple “Keynesian” consumption function?

c = α + β*y

c : Log Actual Consumption.α : Log Autonomous Consumption.β : Log Marginal Propensity to Consume and

here it reflects the elasticity of C to Y.y : Log Actual Income.

AYC

Permanent Income / Life Cycle Theory

What is the life cycle theory?

Consumers base their consumption on the expected lifetime income, saving and dis-saving so as to smooth out short-term fluctuation in income.

What is permanent income?

Permanent income is the constant income stream which has the same present value as an individual’s expect lifetime income.

What is the permanent income consumption function?

pkYC

pY

pyc

C : The actual consumption.

k : The average propensity to consume (k<1)

: The permanent income.

c : Log actual consumption.

α : Log k (Log average propensity to consume (Log k<0)

Β : =1

: Log permanent income.py

How to measure permanent income?

1. Permanent Income as Lagged Income:• Taking weighted average of past incomes.• Temporary fluctuations in income will be random

and they will cancel each other over periods.

ptt yc

• If assuming that permanent income is the weighted average of all past incomes:

• Where 0<λ<1.• k(1- λ) is the elasticity of consumption to income.• Then modeling a consumption function with lagged

income could include lagged consumption also.• Note that both equations give different short and long

run consumption function.

1)1( ttt cykc

2. Permanent Income as determined by Rational Expectation:

• Consumers predict income as accurately as possible given the information available.

• Information could be divided into 2 parts:1. Information that already known at time (t-1).2. New information that has become available since

time (t-1).

• Where is “white noise” : random variable with zero mean and uncorrelated info. With time t-1.

ttt cc 1

t

• There is no constant term.• If β = 1 then the probability of consumption to rise or fall

is equal.• In reality, β>1 because that the probability of

consumption is being undertaken not by a constant population but by a population which income per capita is rising over time.

• Note that the importance of interpreting the error term is that if it happened to have a correlation with previous information (C, Y, or itself at time t-1) this theory cannot be correct.

• Since , then the test is not correct.ttt 1

Modifications to The Life Cycle Theory

What are the modifications to the Life Cycle Theory?

• Inflation:– It affects both C and S.– It reduces the real value of any debts denominated in

money.– As debt value decreases, debtors (government and

corporate sector) gain and creditors (personal sector) lose.

– The reduction in real income is referred to as inflation tax (a tax on holding money).

– inflation should be taken into account in calculating consumption function since it is not calculated in the calculation of personal disposable income.

Where is the elasticity of consumption to inflation .

tttt cykc 1)1(

• Error Correction Mechanism:– The standard consumer theory suggest that

in the long run permanent income is proportional to actual income and hence consumption should be proportional to income.

– In the short run, consumption is not proportional to income strictly.

– Error correction Mechanism is built from:• In the long run, there is a target consumption

level that is proportional to income.• In the short run, consumption will not equal the

desired proportional of income (mistakes and shocks always take place).

tttt syc 1

Where s is the saving ratio .

• House Prices and Uncertainty:– Credit liberalization made it easier for consumers to

borrow money.– Savings increase as uncertainty increases.– Including income, saving ratio, inflation, real house

prices, and uncertainty will give us the following consumption function that fits most the changes in consumption:

RHPsyc tttt 1

Explaining The Saving Ratio

How to calculate the “Saving Ratio”?

• Using the last form of the consumption function, we end up with that:– The contribution of inflation to consumption in any one

year is defined as ( ), where is the mean value of inflation.

– Subtracting it from c we get what is the consumption when inflation if equal to its mean and then we can calculate what is the saving ratio when inflation is at its mean.

– Similarly we can obtain the saving ratio following the same procedure with all other factors (real house pricing and uncertainty).

– Note that our consumption function is unlikely to provide a complete account of factors that affect both consumption and saving ratio.

)( )(

Conclusion

To conclude:

• The simple Keynesian consumption function:

• The logarithmic form of the Keynesian Consumption Function:

C = A + β*Y

c = α + β*y

• Permanent Income/Life Cycle Theory:

• Logarithmic Form of Permanent Income:

pkYC

pyc

• Permanent Income with Lagged Income:

• Permanent Income with Rational Expectation:

ttt cc 1

1)1( ttt cykc

• Modification to the Life Cycle Theory:– Inflation:

– Error Correction Mechanism:

– House Prices and Uncertainty:

tttt syc 1

RHPsyc tttt 1

tttt cykc 1)1(

• Although the results showed some consumption functions that were used in serious applied macroeconomics, it remains oversimplified in a number of respects:

The lag structure still relatively simple. The equation were stated for total consumption

while separated equations are normally be estimated for durable and non-durable consumption.

There are more factors that should be included (e.g. demographic changes and income distribution changes).

Application on Kuwait

Fig. 1. Income and Consumption, 1970-2007

0

5000

10000

15000

20000

25000

30000

35000

Years

KD

mil

lion

Consumption Income

Kuwait GDP and House Consumption, 1970-2007:

C = 799.02 + 0.3 Y

Where A (autonomous consumption) = 799.02, and the β (marginal propensity to consume) = 0.3.

The Simple Keynesian Consumption Function

Fig. 2. Prediction from Simple Keynesian Consumption Function

0

2000

4000

6000

8000

10000

12000

Actual C C=799.02+0.3Y

The Logarithmic Form

c = -0.6 + 1.05 y

Where α (log A) = -0.6, and the β (the elasticity of consumption with respect to income) = 1.05.

Fig. 3. Prediction from Logarithmic consumption Function

0.00.51.01.52.02.53.03.54.04.5

Actual Log C c = -0.6 + 1.05 y

Permanent Income As Lagged Income

Ct = 564.95 + 0.37 Ypt

Where α (autonomous consumption) = 564.95, and β (marginal propensity to consume) = 0.37.

Fig. 4. Prediction of Permanent Income with Lagged Income

0

2000

4000

6000

8000

10000

12000

14000

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

Actual C Ct = 564.95 + 0.37 Ypt

The logarithmic form of Permanent Income As Lagged Income

ct = -0.66 + 1.08 ypt

Where α (log A) = -0.66, and the β (the elasticity of consumption with respect to income) = 1.08.

Fig. 5. Prediction of Logarithmic Con. Function wiht Lagged Income.

0.00.51.01.52.02.53.03.54.04.5

Actual Log C ct = -0.66 + 1.08 ypt

Permanent Income As Lagged Income: with all past income

Ct = 38.5 + 0.105 Ypt + 0.8 Ct-1

Where the α (autonomous consumption) = 38.5, β (marginal propensity to consume) = 0.105, and λ (how much does the previous consumption affect the current one) = 0.8.

Fig. 6. Prediction of Con. Fun. with Lageed Income and Lagged Consumption

0

2000

4000

6000

8000

10000

12000

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

Actual C Ct = 38.5 + 0.105 Ypt + 0.8 Ct-1

Logarithmic Form of Permanent Income As Lagged Income: with all past

income

ct = -0.15 + 0.33 ypt + 0.68 ct-1

Where α (log A) = -0.15, β (elasticity of consumption to lagged income) = 0.33, and λ (elasticity of current consumption to the previous (lagged) consumption) = 0.68.

Fig. 7. Prediction of Logarithmic Con. Fun. with Lagged Income and Lagged Consumption

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Actual Log C ct = -0.15 + 0.33 ypt + 0.68 ct-1

Permanent Income as determined by Rational Expectation

Ct = 1.08 Ct-1 + εt

Where β > 1 because that every generation is becoming wealthier than the previous one.

Fig. 8. Prediction of Rational Expectation Consumption Function

0

2000

4000

6000

8000

10000

12000

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

Actual C Ct = 1.08 Ct-1 + εt

Logarithmic Form of Permanent Income as determined by Rational Expectation

ct = 1.01 ct-1 + εt

Where β (elasticity of current consumption to the lagged consumption) = 1.01 getting close to 1 is called the random walk and εt is the white noise ( a random variable with zero mean and uncorrelated information with time t-1.

Fig. 9. Prediction of Rational Expectation using the Logarithmic Form

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Actual Log C ct = 1.01 ct-1 + εt