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  AY

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.
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?
C  kY
c    y
p
p
C : The actual consumption.
c : Log actual consumption.
k : The average propensity to
consume (k<1)
p
: The permanent income.
α : Log k (Log average
propensity to consume (Log
k<0)
Y
Β : =1
p
: Log permanent income.
y
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.
ct     y
p
t
• If assuming that permanent income is the weighted
average of all past incomes:
ct  k (1   ) yt   ct 1
• 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.
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).
ct   ct 1   t
•
Where  t is “white noise” : random variable
with zero mean and uncorrelated info. With
time t-1.
• 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  t    t 1  t , then the test is not correct.
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.
ct  k (1   ) yt   ct 1    t

Where
is the elasticity of consumption to
inflation.
•
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).
ct     yt   st 1    t
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:
ct     yt   st 1    t   RHP   
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:
C = A + β*Y
• The logarithmic form of the Keynesian
Consumption Function:
c = α + β*y
• Permanent Income/Life Cycle Theory:
C  kY
p
• Logarithmic Form of Permanent Income:
c    y
p
• Permanent Income with Lagged Income:
ct  k (1   ) yt   ct 1
• Permanent Income with Rational Expectation:
ct   ct 1   t
• Modification to the Life Cycle Theory:
– Inflation:
ct  k (1   ) yt   ct 1    t
– Error Correction Mechanism:
ct     yt   st 1    t
– House Prices and Uncertainty:
ct     yt   st 1    t   RHP   
• 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
Kuwait GDP and House Consumption,
1970-2007:
35000
25000
20000
15000
10000
5000
20
06
20
03
20
00
19
97
19
94
19
91
19
88
19
85
19
82
19
79
19
76
19
73
0
19
70
KD million
30000
Years
Fig. 1. Income and Consumption, 1970-2007
Consumption
Income
The Simple Keynesian Consumption
Function
C = 799.02 + 0.3 Y
Where A (autonomous consumption) = 799.02,
and the β (marginal propensity to consume) =
0.3.
12000
10000
8000
6000
4000
2000
Fig. 2. Prediction from Simple Keynesian Consumption Function
Actual C
C=799.02+0.3Y
20
06
20
03
20
00
19
97
19
94
19
91
19
88
19
85
19
82
19
79
19
76
19
73
19
70
0
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.
19
70
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
Fig. 3. Prediction from Logarithmic consumption Function
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.
14000
12000
10000
8000
6000
4000
Fig. 4. Prediction of Permanent Income with Lagged Income
Actual C
Ct = 564.95 + 0.37 Ypt
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
0
1970
2000
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.
19
70
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
Fig. 5. Prediction of Logarithmic Con. Function wiht Lagged Income.
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.
12000
10000
8000
6000
4000
Fig. 6. Prediction of Con. Fun. with Lageed Income and Lagged Consumption
Actual C
Ct = 38.5 + 0.105 Ypt + 0.8 Ct-1
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
0
1970
2000
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.
19
70
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Fig. 7. Prediction of Logarithmic Con. Fun. with Lagged Income and Lagged
Consumption
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.
12000
10000
8000
6000
4000
Fig. 8. Prediction of Rational Expectation Consumption Function
Actual C
Ct = 1.08 Ct-1 + εt
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
0
1970
2000
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.
4.5
4
3.5
3
2.5
2
1.5
1
0.5
19
70
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
0
Fig. 9. Prediction of Rational Expectation using the Logarithmic Form
Actual Log C
ct = 1.01 ct-1 + εt