social cost of living indices with applications to · pdf filesocial cost of living indices...
TRANSCRIPT
�����������
����� ��������� �
Social Cost of Living Indices with
Applications to Thailand
�������������
���
�����������������
�� ����������
SOCIAL COST OF LIVING INDICES WITH
APPLICATION TO THAILAND
by
N. Kakwani*
School of EconomicsThe University of New South Wales
Sydney 2052 Australia
Email: [email protected]
Abstract
This paper develops new social cost-of-living indices. The indices are defined in termsof social cost functions which are derived from two alternative classes of socialwelfare functions. The most important attribute of the proposed social cost-of-livingindices is that they allow us to choose the degree of inequality aversion in the society.The application of the methodology developed in the paper to the Thai data shows thatthe price changes during period from 1986 to 1995 have adversely affected the poormore than the rich.
_____________________________________________________________________
* I would like to thank Professor Murray Kemp for his helpful comments.
1
1. Introduction
We are often interested in making welfare comparisons between individuals
in different price situations.
The theory of the cost of living index has been developed to give a precise
meaning to price indices which are widely computed to make cost of living
comparisons. Many economists have contributed to the development of the theoretical
foundation of consumer price indices, the most important being those of Hicks (1946),
Pollak (1983, 1990), Diewert (1976, 1990), Samuelson and Swamey (1974), Konüs,
A.A. (1924).
Most of the literature on the theory of the cost of living index is focused on
the comparison of the welfare of a single consumer in different price situations.
However the cost of living indices defined for a single consumer do not take into
account the effect of price changes on real income inequality which always exists in
the real world. Muellbauer (1974) has shown that the price changes in the United
Kingdom since 1974 have had an inequality increasing bias. He used the Atkinson
(1970) inequality index in conjunction with the linear expenditure system to define a
real index of expenditure inequality.
To take into account the effect of price changes on income inequality, we
need to develop social cost of living indices which are defined for many individuals in
the society. An obvious social cost of living index is a simple average of the
individual cost of living indices. This index is called a democratic price index (Prais
(1959) and Muellbauer (1974)).
The construction of any type of social cost of living index should be derived
from a social welfare function which incorporates the value judgements of the society.
2
The democratic cost of living index does not explicitly use a social welfare function.
In this paper, we define social cost of living indices in terms of social cost functions
which are derived from some specific social welfare functions.
Pollak (1981) proposed a social cost of living index which is defined as the
ratio of the total expenditure required to enable each individual to attain his or her
reference indifference curve at comparison prices to that required at reference prices.
He calls this index as a Scitovsky-Laspeyres group cost of living index. Prais (1959)
refers to this index as plutocratic price index. We demonstrate in this paper that this
index has an implicit social welfare function which assumes that the society is
inequality-neutral in its attitude. It means that the index is completely insensitive to
changes in income inequality caused by price changes.
In the present paper we derive social cost of living indices on the basis of two
alternative classes of social welfare functions. The first class of social welfare
functions is utilitarian in which every individual has the same utility function. The
class of social-cost-of living indices is derived using a homothetic utility function
proposed by Atkinson (1970).
The second class of social cost-of-living indices is derived from a class of
social welfare functions (proposed by Kakwani (1980)) which takes into account the
interdependence of individual utilities, i.e., the utility of an individual depends not
only on his or her consumption but also on the consumption of others in the society.
1These indices capture the idea of relative deprivation suffered by individuals with
different income levels.
1 Sen’s (1973, 1974) social welfare function is a particular member of this class.
3
The most important attribute of the proposed social cost-of-living indices is
that they allow us to choose the degree of inequality aversion in the society. The
higher the degree of inequality aversion, the greater the importance the society
attaches to income inequality. We compute the social cost-of-living indices for
alternative values of the inequality-aversion parameter.
The methodology developed in the paper is applied to compute social cost of
living indices in Thailand. The indices were computed annually covering the period
from 1986 to 1995. Two sources of data are utilized. The first source is Thailand’s
socioeconomic survey 1990 conducted by Thailand’s National Statistical Office.
These data are used to compute the social weights developed in the paper. The second
source is the price data which were obtained from the Department of Business
Economics, Ministry of Commerce, Bangkok, Thailand.
2. Individual Cost of Living Indices
Suppose q is a quantity vector, consumption of which provides utility which
contains everything that is relevant to a representative consumer. We assume that u(q)
is the utility level that the consumer can attain if he or she consumes the consumption
vector q. The conventional treatment of consumer behaviour is to maximize the utility
function u(q) subject to the constraint p′q = x, where p is a column vector of market
prices and x is income. The solution to this maximization problem yields a system of
n Marshallian demand equations q = q(x,p).
The maximum attainable utility is then obtained by substituting demand
equations q = q(x, p) into the utility function u(q) to obtain
( )[ ] ( )u u x x= =q p p, , )Ψ (1)
4
which is called the indirect utility function.
Solving (1) for x gives the cost function
( )x e u= ,p (2)
which is the minimum cost of attaining utility level u at the price vector p.
If the utility function u(q) is continuous, increasing and concave in q, then the
cost function in (2) has the following properties.
(i) ( )e u,p is increasing in u for every p
(ii) ( )e u,p is (positively) linearly homogeneous in p for every u, i.e.,
( ) ( )e u e u, ,λ λp p= for λ > 0 .
(iii) ( )e u,p is concave in p for every u.
This cost function is the basis for measuring the cost of living indices.
Suppose the price vector p changes to p* , then a true cost of living index
measures the relative cost of buying a given level of utility at the new prices p*
compared to that at the old prices p.
The Laspeyres-Konüs index is then defined as (Diewert 1983).
( ) ( )( )LK x
e u
e u=
,
,
p *
p(3)
where u is the base period utility level enjoyed by an individual with income (or total
expenditure) x.
LK(x) is the true cost of living index of an individual with income x. It can be
calculated only if we completely know the cost function. In practice it is difficult to
estimate the cost function accurately. A practical solution is to assume that the price
5
elasticities of substitution are zero. Using Taylor’s expansion, and utilizing the
property of the cost function that ∂∂
e
pq
ii= , we can write
( ) ( ) ( )( )e u e u
p p
pv x
i i
iii, ,
*
p * p= +−
∑ (4)
where ( ) ( ) ( )v x p q x q xi i i i= , being the consumption of ith commodity by an
individual who has income x. The terms of higher order of smallness in (4) have been
ignored because of the assumption of zero substitution elasticities. Utilizing (3) into
(4) gives
( ) ( )L xp
pw xi
ii
n
i= ∑=
*
1(5)
where ( )w xi is the share of the ith commodity in the consumption of the individual
with income x. L(x) is the Laspeyres price index of the individual with income x.
3. Group Cost of Living Indices
Since there are always many consumers in a society, the single-person cost of
living indices are of limited value. We consider below the two well-known group-
cost-of-living indices.
The Democratic Consumer Price Index
The democratic cost of living index proposed by Prais (1959) is defined as the
average of the price indices of each individual in the society.
Since there are many individuals in the society, we assume that income x of an
individual is a random variable following a probability distribution. If f(x) is the
6
probability density function of x, then the democratic consumer price index from (3) is
obtained as
( ) ( ) ( )( ) ( )DCPI LK x f x dx
e u
e uf x dx= ∫ = ∫
∞ ∞
0 0
,
,
p *
p(6)
To make the index in (6) operational, we assume that the elasticities of
substitution are zero. Thus utilizing (4) into (6) gives
LDp
pwi
ii
n
i= ∑=
*~
1(7)
where
( ) ( )~w w x f x dxi i= ∫∞
0(8)
is the average of the individual budget shares of the society. LD may be called
Laspeyres-Democratic index (Diewert 1983).
LD can be given an interesting interpretation. To do so, let us define
( ) ( )
( )w
v x f x dx
xf x dxi
i
=∫
∫
∞
∞0
0
(9)
which is the ratio of average expenditure of the society on the ith commodity divided
by the average total expenditure. wi is the ith commodity average budget share of the
society. wi will generally be different from ~wi . If the ith commodity is an essential
good such as food, wi(x) will be higher for the poor than for the non-poor. And,
therefore, for such commodities ~wi > wi but if the ith commodity is a luxury good,
then ~wi < wi .
We may write (7) as
7
( )
( )
LDp
pw
p
pw w
Lp
pw w
i
ii
i
ii
n
i
n
i i
i
ii
n
i i
= − ∑∑ −
= − ∑ −
==
=
* *
*
~
~
11
1
(10)
The first term in (10) given by Lp
pwi
ii
i
n= ∑
=
*
1 is in fact the Laspeyre’s index for an
average consumer in the society (because wi s are the budget shares of a consumer
who has an average income µ). This index is most commonly used to measure the cost
of living index - in almost every country.
The second term in (10) will be positive (negative) if the prices of necessary
(luxury) goods increase at a faster rate than the prices of luxury (necessary) goods.
Thus, the second term in (10) indicates whether the price changes affect the poor more
than the rich. Thus, the LD index is sensitive to the changes in real inequality in the
society as a result of price changes.
Multiplicative Democratic Cost of Living Indexes
Diewert (1993) proposed multiplicative democratic cost of living indexes
which are denoted by MDα and may be written as
( ) ( ) ( ) ( )[ ] ( )log log , * log ,MD x e u e u f x dxα α= −∫∞
p p0
where α(x) is the weight attached to the cost of living index of an individual with
income x. Since Diewert (1993) does not indicate how one should determine α(x), we
may assume that α(x) = 1 for all x. Diewert’s index is then written as
( ) ( ) ( )[ ] ( )log log , * log ,MD e u e u f x dx= −∫∞
p p0
(11)
8
Again assuming that the price substitution elasticities are zero, we can use
Taylor’s expansion to write
( ) ( ) [ ] ( )log , * log , log log*e u p e u p p p w xi ii
n
i= + −∑=1
(12)
where the terms of higher order of smallness have been ignored (because of the
assumption of zero substitution elasticities).
Substituting (12) into (11) gives
( ) [ ]log log log ~*LMD p p wi ii
n
i= −∑=1
(13)
where LMD may be called Laspeyres-Multiplicative-Democratic index. It will be
useful to write (13) as
( ) ( ) ( )log log log *LMD LT LT= + (14)
where
( ) [ ]log log log*LT p p wi ii
n
i= −∑=1
(15)
and
( ) [ ]( )log * log log ~*LT p p w wi ii
n
i i= −∑ −=1
(16)
Equation (14) shows that the index LMD is decomposed into two indexes, viz,
LT and LT*. The index LT is the cost of living index for an average consumer in the
society. This index is completely insensitive to changes in income inequality in the
society. But the second term in (14) measures the effect of price changes on income
inequality. This term will be positive (negative) if the prices of necessary (luxury)
goods increase at a faster rate than the prices of luxury (necessary) goods. Thus, the
LMD index is sensitive to changes in inequality in the society as a result of price
changes.
9
The index LT looks similar to Tornqvist’s (1936) price index but it differs in
one important respect. It uses the average budget share wi only for the base year,
whereas in the case of Tornqvist’s index, the averages of budget shares of both base
year and terminal years are utilized. The index LT may be called the Laspeyre-
Tornqvist index because it is based on only the base year budget shares.
The Plutocratic Cost-of-Living Index
Pollak (1981) proposed a group cost of living index which is defined as the
ratio of the total expenditure required to enable each individual to attain his or her
reference indifference curve at comparison prices to that required at reference prices.
He calls this index the Scitovsky-Laspeyres group-cost-of-living index. Prais (1959)
refers to this index as a plutocratic price index. This index in our notation may be
written as
( ) ( )
( ) ( )PCPI
e u f x dx
e u f x dx=
∫
∫
∞
∞
,
,
p *
p
0
0
(17)
Again assuming the substitution elasticities equal to zero, we can substitute (4) into
(17) to obtain
Lp
pwi
ii
n
i= ∑=
*
1(18)
where wi defined in (9) is the average budget share of the ith commodity. L in (18) is
in fact the Laspeyres’ index for a consumer at the average income. As noted above,
the index L which is widely used to measure inflation in almost every country, is
10
completely insensitive to changes in real inequality caused by price changes. Thus, in
this respect, the Plutocratic cost of living indices is inferior to the Democratic indices.
4. Social Cost Function
The group cost of living indices discussed in the previous section were
obtained by aggregating the cost of living indices of individuals. The aggregation
procedures were defined on an ad hoc basis. The construction of any type of group
cost of living index should be based on a social welfare function. In this section we
define the true social cost of living indices in terms of social cost function.
Suppose ~u is the aggregate welfare of the society which is obtained by
aggregating the levels of utilities enjoyed by the individuals in the society. Then the
social cost function denoted by ( )e u~,p is defined as the minimum money income if
given to every individual will allow the society to enjoy ~u level of social welfare at a
given price vector p . If the price vector p changes to p *, then every individual
should receive the minimum income of ( )e u~,p * in order that the society enjoys the
same level of welfare.
The social cost of living should have the following properties.
1. ( )e u~,p is an increasing of function ~u for all p .
2. ( )e u~,p is increasing and concave in p for every ~u .
3. ( )e u~,p is (positively) linearly homogeneous in p for every ~u , i.e.
( ) ( )e u e u~, ~,λ λp p= .
We may now define the true social cost-of-living-index (TSCLI) as
11
( )( )T
e u
e u=
~,~,
p *
p(19)
Note that if all prices increase by the same proportion, that is p p* = λ , then T
must be equal to λ. This is a necessary requirement of a price index and is satisfied by
T in view of the fact that ( )e u~,p is (positively) linear homogeneous in p, i.e.,
( ) ( )e u e u~, ~,λ λp p= .
The social cost function ( )e u~,p must be a function of the individual cost
functions ( )e u,p such that the three properties given above are satisfied. To derive
( )e u~,p , we utilize the concept of “the equally distributed equivalent level of income”
(Atkinson 1970). ( )e u~,p may be interpreted as the equally distributed equivalent level
of income, the level which, if received by every individual, would result in the same
level of social welfare as the present distribution. Like Atkinson, we assume that the
social welfare function is utilitarian and every individual has exactly the same utility
function. Further suppose ( )[ ]g e u,p is the utility enjoyed by an individual in the base
period whose income is x (which is equal to ( )e u,p in the base period) where g(x) is
increasing in x and is concave, then the social welfare function will be
( )[ ] ( )W g e u f x dx= ∫∞
,p0
(20).
( )[ ]g e u~,p will be the average welfare enjoyed by the society if every individual in it
receives an income level of ( )e u~,p . This, obviously, should be equal to W in (20).
Thus, we have
( )[ ] ( )[ ] ( )g e u g e u f x dx~, ,p p= ∫∞
0(21)
12
which gives the relationship between the cost functions of individuals in the society
and the social cost function.
Since ( )′ >g x 0 for all x and ( )e u,p is an increasing function of u, the social
cost function ( )e u~,p will also be an increasing function of ~u . Thus, the social cost
function defined in (21) will satisfy property 1 as given above. Property 2 that the
social cost function is increasing and concave in p is also satisfied in view of the
assumption that g(x) is an increasing and concave function in x.
The third property, that ( )e u~,p is (positively) linearly homogeneous in p for
every ~u , will be satisfied only if it is assumed that g(x) is a homothetic function in x.
A class of homothetic functions is given by (Atkinson 1970)
( )
( )
g x ABx
xe
= + ∈≠
= ∈=
−∈
−∈
1
1 1
1
,
log ,
(22)
where ∈> 0 is a measure of relative risk-aversion, which is constant for this utility
function. Note that the social cost function ( )e u~,p in (21) is invariant with respect to
(positively) linear transformation of g(x).
The social cost function in (21) takes into account the inequality of income in
the society. Following Atkinson (1970), the inequality in the society is defined as
( )A
e u= −1
~,p
µ(23)
where
( ) ( )µ = ∫∞e u f x dx,p
0(24)
is the mean income of the society in the base period.
13
The inequality measure A can be made operational if we utilize the utility
function (22). The inequality measure so obtained will be scale independent because it
is based on a class of homothetic utility functions. The only unknown parameter will
be ∈, which is interpreted as a measure of the degree of inequality aversion or the
relative sensitivity to income transfers at different income levels. As ∈ rises, more and
more weight is attached to income transfers at the lower end of the distribution and
less weight to transfers at the top. If ∈ = 0, it reflects an inequality-neutral attitude in
which case the society does not care about the inequality at all.
5. A New Class of Social-Cost-of-Living Indices
We may now derive a class of social-cost-of living indices. To make these
indices operational, we need to assume that the price elasticities of substitution are
zero. Using the Taylor’s expansion we can write
( )[ ] ( )[ ] ( ) ( )[ ] ( ) ( ) ( )g e u g e u g p g p q x g x g pi ii
n
i i, , *p * p= + −∑ ⋅ ′ ′=1
(25)
where use has been made of the property that ( )∂∂
e u
pq
ii
,p= and the terms of higher
order of smallness have been omitted because of the assumption of zero substitution
elasticities. Substituting (25) into (21) gives
( )[ ] ( )[ ] ( ) ( )[ ]( ) ( ) ( ) ( )g e u g e u
g p g p
g pq x g x f x dx
i i
ii
n
i~, ~,
*
p * p= +−
′∑ ∫ ′=
∞
1 0(26)
Substituting (19) into (26) gives a class of social cost of living indices in terms
of the utility function g(x). To make these measures empirically operational, we
substitute the utility function g(x) given in (22) into (26).
14
Thus, we obtain a class of social cost of living indices
( )( ) ( )
( )T
p
pw x x f x dx
x f x dx
i
ii
n
i
∈ =
∑ ∫
∫
∈≠
−∈
=
∞−∈
−∈∞
−∈*
,
1
1 0
1
1
0
1
1
1
[ ]= −∑
∈==
exp log log ~ ,*p p wi i ii
n
11 (27)
where exp stands for exponential and ~wi , the average of the ith commodity shares of
all the individuals in the society.
When we substitute ∈ = 0 into (27), we obtain T(0) equal to L as given in (18).
L is the Laspeyres index for a consumer at the average income level. As pointed out,
∈ = 0 implies that the society is unconcerned with the issue of inequality. This index
is completely insensitive to how the price changes affect the poor or rich individuals
in the society. When ∈ = 1, we obtain T(1) equal to LMD, the Laspeyres-
Multiplicative-Democratic index derived in (13). As we have demonstrated, this index
is sensitive to changes in income inequality. As ∈ increases further, the weight given
to the poor increases and the index becomes more and more sensitive to the welfare of
the poor. When ∈ approaches infinity, the social cost of living T(∈) becomes
( )Tp
pw pp
i
ii
n
i=
∑ ⋅
=
*
1
where w(p) is the ith commodity share in the consumption basket of the poorest
person in the society. T is in fact the Laspeyres index of the poorest person in the
society. This is the extreme situation. ∈ = 2.0 probably provides a more reasonable
social cost of living index. Still we emphasize that the choice of ∈ depends on the
15
kind of society for which the index is being computed. If a society has a high degree
of inequality, then a higher value of ∈ may be considered more appropriate.
6. Social-Cost-of-Living Indices when Social Welfare Functions
Are Interdependent
In the previous section we derived social-cost-of-living indices from a class of
social welfare functions in which the utility or welfare of an individual depended only
on his or her own income or consumption. In this section we derive a class of social-
cost-of-living indices which take into account the interdependence of individual
utilities. The utility of an individual depends not only on his or her income but also on
theincomes of others in the society. Such a social welfare function captures the idea of
relative deprivation suffered by individuals with different income levels; the lower a
person is on the welfare scale, the greater is his or her sense of deprivation with
respect to others in the society.
Sen (1974) proposed a social welfare function in which the relative deprivation
suffered by a person is captured by taking into account the proportion of persons who
are richer. Kakwani (1980) proposed a generalization of Sen’s social welfare function
which allows one to make a judgement about the society’s degree of aversion to
inequality. The social cost function based on this social welfare function may be
defined as
( ) ( ) ( ) ( )[ ] ( )e u k e u F x f x dxk~, ,p p= + −∫
∞1 1
0(28)
where F(x) is the probability distribution function and is the proportion of people in
the society who have income less than or equal to x.
16
It is important to point out that the social cost function in (28) will always
satisfy the three desirable properties of a social cost function mentioned earlier.
Assuming that the substitution elasticities are zero, we may utilize (4) in (28)
to obtain
( ) ( ) ( )( )
( ) ( )[ ] ( )e u e u kp p
pw x x F x f x dx
i i
ii
n
ik~, ~,
*
p * p= + +−
∑ −∫=
∞1 1
1 0
which yields
( )( ) ( )[ ] ( )
( )[ ] ( )T k
p
pw x x F x f x dx
x F x f x dx
i
ii
k
i
n
k*
*
=⋅ −∫∑
−∫
∞
=∞
1
1
01
0
(29)
which is a new class of cost of living indices based on an interdependent social
welfare function.
The parameter k can be interpreted as a measure of inequality aversion. In
particular, k = 0 implies an inequality-neutral attitude of the society. For k = 0, T*(k)
is equal to L, the Laspeyres index of a person at the average income. As pointed out,
this index is insensitive to any effect of price changes on income inequality. This
index, which is used by almost all countries in the world, clearly, is not desirable
when the society is concerned about inequality.
It can easily be demonstrated that (Kakwani 1980)
( )[ ] ( ) ( )2 1 10x F x f x dx G−∫ = −
∞µ (30)
and
( ) ( )[ ] ( ) ( )2 1 10v x F x f x dx Ci i i−∫ = −
∞µ (31)
17
where µ is the mean income of the society and G is the Gini index which is a well-
known measure of inequality, ( ) ( )v x p q xi i i= is the expenditure of a person with
income x on the ith commodity in the base year price, then µi is the mean expenditure
of the society on the ith commodity and Ci is the concentration index of the ith
commodity.2
Let us now substitute k = 1 into (29) and utilize (30) and (31), then we obtain
( )( )
( )T
p
pw C
G
i
ii i
i
n
*
*
1
1
11=
−∑
−=
(32)
where wi is the ith commodity budget share at the average income of the society, i.e.,
wii=
µµ
. This equation can further be simplified as
( )( ) ( )T L
G
p
pw Ei
ii i
i
n*
*
11
1 1= −
−∑=
(33)
where Ei = Ci - G.
Note that L measures the effect of price change when there exists no income
inequality in the society. The second term in (33) is the correction for income
inequality. In fact, it measures the change in the Gini index as a consequence of
changes in prices. If this term is positive, it implies that the price increases have an
inequality increasing bias and if negative, the inequality decreasing bias.
Ei is the elasticity index proposed by Kakwani (1980). The ith commodity is
luxury (necessity) if Ei is greater (less) than zero. If the prices of necessities (luxuries)
increase faster than those of luxuries (necessities), the second term in (33) will be
2 For a detailed discussion of concentration indices, see Kakwani (1977, 1980a).
18
positive (negative). Thus, the sign of the second term in (33) tells us whether or not
the price changes have an adverse effect on the poor or the rich.
The social cost of living index T*(k) can be computed for any value of k. The
larger the value of k we choose, the greater is our concern for the poor.
7. Social Cost of Living Indices for Thailand
In this section, we utilize the methodology developed in the paper to compute
the social cost of living indices for Thailand. The indices were computed annually
covering the period from 1986 to 1995. The social weights developed in the paper
were computed using the socioeconomic survey (SES) data for 1990. The price
indices of various goods and services were obtained from the Department of Business
Economics, Ministry of Commerce, Bangkok, Thailand.
The National Statistical Office (NSO) of Thailand conducts the
Socioeconomic Surveys on a regular basis. The surveys cover all private non-
institutional households residing permanently in municipal areas, sanitary districts and
villages. However, they exclude that part of the population living in transient hotels,
rooming houses, boarding schools, military barracks, temples, hospitals, prisons and
other institutions (see Report of the 1990 Household Socioeconomic Survey, NSO,
Thailand).
The NSO Thailand provided us with unit record data giving expenditures on a
wide variety of goods and services for 13186 households. Since we could obtain a
very detailed disaggregation of goods and sources, the matching of the data from the
two sources was not a problem.
19
To estimate the social weights accurately from the sample households, we
needed to estimate the weight attached to each sampled household to enable the data
provided by these households to be expanded to obtain estimates for the defined
population. For instance, if N is the number of households in the population and n is
the sample of households selected in the survey, then the weight attached to every
household will be N/n. This weight is not correct because it is based on the
assumption that every household in the population has exactly the same probability of
being selected. The weight given to each household must be determined by the
probability of selection within a stratum adjusted to take account of non-responding
households. We estimated these weights using the sample design used in the survey.
The population weights were determined by multiplying the population household
weights by the household size. Thus, the social weights estimated in the paper relate to
individuals rather than households.
The social cost of living indices and inflation rates are presented in Tables 1
and 2 for different values of inequality aversion parameters. Table 1 is based on the
utilitarian social welfare function whereas Table 2 is computed on the basis of the
interdependent social welfare function.
It may be recalled that when the inequality aversion parameter is zero, the
society is completely inequality neutral. The higher the inequality aversion parameter,
the greater the importance society attaches to inequality. It can be seen that the
inflation rate from Table 1 in the 1987-88 period is 3.8 per cent when the inequality
aversion parameter is equal to zero. When the inequality aversion parameter is equal
to 2.0, the inflation rate is 5.2 per cent. It means that during the 1987-88 period, the
changes in prices have affected the poor individuals much more than the rich
Table 1: Social cost of living Indices and Inflation Rates in Thailand
based on utilitarian social welfare function
'Social cost of living indices Inflation rate
Inequality aversion parameter equal to Inequality aversion parameter equal to
Year 0 0.5 1 1.5 2 0 0.5 1 1.5 2
Based on per capita expenditure
1986 100 100 100.0 100 100 - - - - -
1987 102.4 102.5 102.5 102.6 102.6 2.4 2.5 2.5 2.6 2.6
1988 106.3 106.8 107.2 107.6 107.9 3.8 4.2 4.5 4.9 5.2
1989 110.7 111.5 112.1 112.6 113.0 4.2 4.4 4.6 4.7 4.7
1990 116.4 117.2 117.7 118.2 118.5 5.1 5.1 5.0 5.0 4.9
1991 122.8 123.5 124.1 124.5 124.9 5.5 5.4 5.4 5.4 5.3
1992 127.4 128.3 128.9 129.4 129.7 3.8 3.9 3.9 3.9 3.9
1993 131.9 132.3 132.6 132.7 132.9 3.5 3.2 2.8 2.6 2.4
1994 137.4 138.1 138.4 138.6 138.7 4.2 4.4 4.4 4.4 4.4
1995 144.3 145.3 145.8 146.1 146.2 5.0 5.2 5.3 5.4 5.4
Table 2: Social cost of living Indices and Inflation Rates in Thailand
based on interdependent social welfare function
Social cost of living indix with k equal to Inflation rates with k equal to
Year 0 1 2 3 0 1 2 3
Based on per capita expenditure
1986 100 100 100 100 - - - -
1987 102.4 102.6 102.6 102.6 2.4 2.6 2.6 2.6
1988 106.3 107.3 107.9 108.2 3.8 4.6 5.1 5.4
1989 110.7 112.3 113.1 113.5 4.2 4.7 4.8 4.9
1990 116.4 118.0 118.7 119.1 5.1 5.1 5.0 4.9
1991 122.8 124.5 125.3 125.8 5.5 5.5 5.6 5.6
1992 127.4 129.5 130.4 130.9 3.8 4.0 4.1 4.1
1993 131.9 133.0 133.5 133.8 3.5 2.8 2.4 2.2
1994 137.4 139.2 139.7 140.1 4.2 4.6 4.7 4.7
1995 144.3 147.0 147.8 148.4 5.0 5.6 5.8 5.9
S o c i a l c o s t o f l i v i n g i n d ic e sT h a i l a n d 1 9 8 6 t o 1 9 9 5
8 0
1 0 0
1 2 0
1 4 0
1 6 0
1 9 8 6 1 9 8 7 1 9 8 8 1 9 8 9 1 9 9 0 1 9 9 1 1 9 9 2 1 9 9 3 1 9 9 4 1 9 9 5
I n e q u a l i t y n e u t r a l c o s t o fl i v in g i n d e x
I n e q u a l i t y a v e r s e c o s t o fl i v in g i n d e x
individuals and consequently, the real inequality in the society has increased as a
result of price changes.
If we look at the entire period from 1986 to 1995, we find that the overall price
index has increased by 44.3 per cent when the inequality aversion parameter is equal
to zero but when it takes value equal to 2, the prices have increased by 46.2 per cent. It
means that the prices in the 1986 to 1995 period have increased more in favour of the
rich than the poor (Table 1).
Table 2 based on the interdependent social welfare function shows much larger
adverse effects of price changes on the poor. The index when k = 3.0 has increased by
48.4 per cent between 1986 and 1995 whereas when k = 0, the increase is only 44.3
per cent. This means that an inflation rate of 4.1 per cent is attributed to the inequality
increasing bias of price changes.
The graph shows that the inequality neutral social cost of living index is lower
than the inequality averse cost of living index every year. This means that the price
changes have a monotonically inequality increasing bias. The poor have been
becoming relatively worse off over the 1986 to 1995 period. This conclusion is, of
course, valid only if the nominal income of the poor has been increasing at the same
or at a slower rate than that of the rich.
8. Concluding Remarks
In this paper we have developed a new methodology to compute social cost of
living indices. These indices indicate whether or not the price changes have a
favourable (or unfavourable) impact on the welfare of the poor. The application of this
22
methodology to the Thai data shows that the price changes have adversely affected the
poor more than the rich.
Thailand has a very high income inequality. It has been increasing more or less
monotonically (Kakwani, 1997). The government of Thailand has been deeply
concerned with the increasing trend in inequality. To formulate policies to reduce
inequality, it is important to know the causes of the increase in inequality. This paper
provides a useful link between the price changes and income inequality. It is hoped
that Thailand’s Department of Business Economics will publish the social cost of
living indices developed in the paper on a regular basis so that greater attention is
focused on the issue of inequality.
To make our methodology empirically operational we have assumed that the
substitution elasticities are zero so that the welfare losses associated with increases in
prices tend to be exaggerated. From the theoretical point of view, it is correct to say
that our estimates are biased. But many empirical studies have indicated that the bias
is small enough that it can probably be neglected [Braithwait (1975), Christensen and
Manser (1974) and Manser (1975)].
However, it must be emphasized that our methodology can be extended to take
into account the substitution effect but this will require estimating a demand system.
The estimation of demand systems from the household surveys is problematic.
Moreover, various demand systems will yield different estimates of the substitution
bias, thus creating a problem of selecting a specification which best explains the data.
So, it is very likely that the errors in the estimation of complete demand systems are
larger than the size of substitution bias.
23
Our empirical results assume that all households in Thailand face the same
prices of various commodities. This is an unrealistic assumption because there do
exist regional price differences in Thailand (Kakwani and Krongkaew, 1997).
Fortunately, the information on regional prices is available and it will be a worthwhile
exercise to improve the empirical results presented in this paper.
24
REFERENCES
Atkinson, A.B. (1970), “On the Measurement of Inequality”, Journal of EconomicTheory 2, 244-63.
Braithwait, S.D. (1975), “Consumer Demand and Cost of Living Indexes for the U.S.:An Empirical Comparison of Alternative Multi-Level Demand Systems”, BLSWorking Paper 45, June.
Christensen, Laurits R. and M. E. Manser (1974), “Cost of Living Indexes and PriceIndexes for U.S. Meat and Produce: 1947-1971”, National Bureau ofEconomic Research, Conference in Research in Income and Wealth, 40,Household Behaviour and Consumption.
Diewert, W.E. (1983), “The Theory of the Cost-of-Living Index and the Measurementof Welfare Change”, in W.E. Diewert and C. Montmarquette (eds), PriceLevel Measurement, Ministry of Supply and Services Canada, 163-225.
Diewert, W.E. (1980), “The Economic Theory of Index Numbers.Diewert, W.E. (1993), “Group Cost of Living Indexes: Approximations and
Axiomatics”, Chapter 11 in W.E. Diewert and A.O. Nakamura (eds), Essays inIndex Number Theory, 1, Elsevier Science Publishers, B.V., 287-316.
Diewert, W.E. (1976), “Exact and Superlative Index Numbers”, Journal ofEconometrics 4, 115-145.
Diewert, W.E. (1990), Price Level Measurement, Amsterdam: North-Holland.Hicks, J.R. (1946), Value and Capital, Oxford: Clarendon Press.Jorgenson, D.W. and D.T. Slesnick (1983), “Individual and Social Cost-of-Living
Indexes”, Price Level Measurement, Proceedings from a ConferenceSponsored by Statistics Canada.
Kakwani, N. (1987), “Economic Growth and Income Inequality in Thailand”,presented at the Final Workshop on Establishment of Key Indicators Systemfor the 8th Plan and Monitoring and Evaluation, National Economic andSocial Development Board Bangkok.
Kakwani, N. and M. Krongkaew (1987), “Poverty in Thailand: Defining, Measuringand Analyzing”, presented at the Final Workshop on Establishment of KeyIndicators System for the 8th Plan and Monitoring and Evaluation, NationalEconomic and Social Development Board Bangkok.
Kakwani, N. (1980), “On a Class of Poverty Measures”, Econometrica 48, 437-46.Kakwani, N. (1977), “Applications of Lorenz Curves in Economic Analysis”,
Econometrica 45, 719-27.Kakwani, N. (1980a), Income Inequality and Poverty: Methods of Estimation and
Policy Applications, Oxford University Press, New York.Konüs, A.A. (1924), “The Problem of True Cost of Living”, translated in
Econometrica 7, 1939, 10-29.Manser, M.E. (1975), “The Translog Utility Function with Changing Tastes”, BLS
Working Paper 33, January.Muellbauer, J. (1974), “Recent U.K. Experience of Price and Inequality: An
Application of Cost of Living and Real Income Indices”, Economic Journal,84, 32-55.
25
Pollak, R.A. (1983), “The Theory of the Cost-of-Living Index”, in W.E. Diewert andC. Montmarquette (eds), Price Level Measurement, Ministry of Supply andServices Canada, 5-78.
Pollak, R.A. (1981), “The Social Cost of Living Index”, Journal of Public Economics15, 311-336.
Prais, S.J. (1959), “Whose Cost-of-Living”, Review of Economic Studies, 26, 126-134.Samuelson, P.A. and S.Swamy (1979), “Invariant Economic Index Numbers and
Canonical Duality: Survey and Synthesis”, American Economic Review 64,566-93.
Sen, A.K. (1974), “International Bases of Alternative Welfare Approaches:Aggregation and Income Distribution”, Journal of Public Economics 4, 387-403.
Tornqvist, L. (1936), “The Bank of Finland’s Consumption Price Index”, Bank ofFinland Monthly Bulletin 10, 1-8.