2 This body of literature always uses the term "real" with the meaning "deflated". cf. Ch. I, Section B, §11.
The basic principles are quite similar to those underlying the
comparison of GNP over several years for a country. Because of inflation
and changes in the price structure, in order to compare real changes in
output or in expenditures, one must devise a way to determine real prices
or, more explicitly, one must value each item of total output with the
same yardstick. When inter-country comparisons are concerned, the prob
lems are even more acute because the price structure can be very different.
The Gilbert and Kravis approach consists of breaking down total
GNP for two different countries into equivalent groups of products. Then
within each group a certain number of items are selected. These items
must be identical in the two countries, hence all sorts of difficulties
related to quality differences arise. A distinction is drawn between
economic (cost) differences that are measurable and non-economic differ
ences (related to know-how or skill) that are not measurable.
The next step consists of gathering price or quantity data for
these identical items. Here another question arises; should the factor
costs or the market prices be chosen? It all depends upon the major
concern: whether it is to obtain the relative real cost of production
or the relative real worth for the purchaser. Factor costs will corres
pond to a relative productivity comparison, while market prices will
correspond to a relative expenditure comparison. The OEEC studies of
Gilbert and Kravis use the first valuation. Once the relative prices are
gathered they are used in order to revalue the expenditures in each group
of products in equivalent prices and then to aggregate them in comparable
sums.
Obviously the two countries P and R produce or consume differ
ent relative quantities and Qr and face different relative prices P^
and P . Hence the so-called index number problem is present.
We will obtain two values for the internal purchasing power
used as weights, i.e. EP EP IPPQr EPrQr (Paasche) (Laspeyres)
and two values for the corresponding quantity comparisons according to
which country’s relative prices are used as weights, i.e.
EQPPP E(fpP
ZQPPr EQrPr
(Paasche) (Laspeyres)
These two indices are often geometrically averaged to obtain the Fisher
index.
Gilbert and Kravis affirm that the differences between the
Paasche and the Laspeyres are not a consequence of a difference in the
pattern of taste but are due to the fact that the countries compared
experience different levels of development. They assume that as countries
reach similar levels of real income, their price structure will become
similar. This is indeed a very bold but necessary statement.1
/
(b) Multilateral Comparisons
A serious limitation of the earlier PPP studies has been partly
overcome in the last study by Kravis, Kenessey, Heston and Summers.
Indeed, the earlier attempts had to be restricted to binary comparisons;
a country was chosen as a base to which the other countries were compared;
then if the other countries were compared between themselves using the
results yielded by their comparisons to the base country no consistency
1 This is more or less equivalent to stating that the two countries are
at different levels of the same indifference map. cf. assumption 2,
was present, (i.e. Fisher’s circular test1 was not met).
In A System of International Comparisons of Gross Produet and
Purchasing Power, Kravis et.al. affirm that they perform multilateral
comparisons which are base-country invariant and which meet Fisher’s
circular test. Their method named "country product dummy method" permits
them to deal with missing price data at the most detailed level of the
comparison and at the same time to incorporate in the study the informa
tion carried by all the price data of all the countries. The method was
developed by Summers (1973) who proves that the coefficients of the
country dummies in a regression of the logarithms of all the available
prices (P) against dummies for all the countries (X^,) except one and
against dummies for all the items (Y^) in a specific category are the
PPP relative to the country without dummy.2 Furthermore, he argues that
PPP meets the requirements of country-base invariance, additive consist
ency, the circular test and the factor reversal test. From an economet
ric point of view, a rather abundant use of dummy variables is usually
not advisable. In fact, a very similar problem had already been studied
by Kloek and Theil (1965). They developed a method based on limited
information theory and were able to construct a single comparable index
of total expenditure for the six members of the European Coal and Steel
Community. From a theoretical point of view, Summers’ method is
questionable as it is replacing the missing price data for a certain
1 q(Q2»Q1) ^CQ-^Qq) = q(Q2,Q0) and
p(P2 »Pi) p(Pr P0) = P(P2 ,P0) where q(Q2 »Q1) is the quantity index
between country (or period) 2 and 1 and p(P2 ,P^) is the corresponding price index etc.
His equation is the following:
ln P 3, X + + 3 aj 1 al n-1 n is number of countries, j = 1 , .. A is number of items, a = 1, .., A. X -1 + Y-. Y . a,n-1 1 lj + y ay aA Aj.+ v
country by some average of the experience of all the other countries
included in the comparison, thereby imposing on the country some hybrid
foreign price structure. Hence we are back to the same basic theoretical
criticism of overlooking the difference in taste.
(c) Extension of the PPP method with non-monetary indicators
We must note that the PPP approach was a monetary approach.
However, an application of the PPP method using non-monetary indicators
was developed by Beckerman (1966). This study is very similar to Heston’s
(1973) and differs only in the following respect.1 The dependent
variables used in the regressions are not exchange rate GNP, but are the
’real consumption’ data estimated by various PPP studies. They are re
gressed against several non-monetary indicators. Then the coefficients
yielded by the multiple regression are used to predict 'real consumption’
for other countries on the basis of their scores on the selected non
monetary indicators.
This method combines the monetary and the non-monetary approaches.
However, the main problem faced by the author concerns the small number
of existing purchasing power parity studies available at the time.
2
These equations are based on the data for nine developed western countries
plus four other observations for Japan, USSR, China and India. As these
are mainly developed countries, the author does not have a very represent
ative sample of countries in order to carry out predictions for a larger
group of developed and less developed countries. Several equations also
Heston's method was discussed earlier.
2 Beckerman also uses for each country two observations corresponding to two different years but does not include a dummy in order to
isolate the variations due to the time trend in the pooled regressions as he assumes that the observations are independent because they are five years apart.
had to be derived in order to predict the level in various countries.
If PPP studies were available for a larger and more representative
sample of countries, this method would offer a very valuable short-cut
to the estimation of PPP consumption in various countries.
(d) Criticism of the PPP methods
The PPP methods can be criticised on two levels: first on
pragmatic grounds and second on theoretical grounds.
First, the PPP studies are very lengthy and expensive to
undertake. They also involve a lot of corrections, adjustments,
definitions that are judgmental and arbitrary. Hence there is room for
a lot of personal bias, and the nationality of the investigator might be
reflected in the choice of the basic basket of goods chosen.
However, these are not very serious shortcomings. On the other
hand, the PPP methods face more ominous criticism on theoretical grounds.
Indeed, it was shown that the PPP methods always yield Paasche-type and
Laspeyres-type indices and the justification for presenting two such
indices is as follows: the exact index is assumed to be bracketed by
them. Furthermore, some average of the two indices offers a sort of
approximation to this exact index. Unfortunately it was shown in the
section on the theory of index numbers that the Paasche and the
Laspeyres quantity indices provides lower and upper bounds to the exact
index only under very restrictive assumptions which were then spelled
out. The question is now to appraise how realistic these assumptions
are. Hence we will first discuss the likelihood of a common indifference
map for all the countries and then raise the question of homotheticity
of the utility function.
Common indifference map
An exact index exists only if the various countries have the
same tastes, i.e. if they share the same indifference map or the same
to their budget constraints and their relative prices.
This is a very restrictive assumption. Indeed, if we accept
the existence of national tastes embedded in a national utility function,
we know that the national tastes in the USA are very different from the
national tastes in Mali; these two countries could not possibly share
the same indifference map. Of course tastes might be similar in similar
countries; for instance the EEC countries might have very resembling
utility functions. So if we are comparing very similar countries, the
assumption of a common indifference map for practical purposes should not
distort the results too much. However, if we are comparing a whole range
of countries from the very poor to the highly developed ones, the
assumption becomes quite unrealistic.
Homotheticity of the utility function
Such a condition implies unit income elasticity for all goods
as the budget constraint shifts upward, i.e. as income increases. More
explicitly, it means that, when faced by the same relative prices, if
the average citizen of a rich country consumes twice as much of any one
commodity as the citizen of a poor country consumes, he will also
choose to consume twice as much for instance of any other commodity;
twice as much bread as well as twice as many cars etc.
Such a consumption pattern definitely goes against the
empirical evidence given by the Engel’s curves. We know that, as people
become richer, they consume relatively more of certain goods, so defined
as luxuries, and relatively less of other goods, so defined as necessities.
Since the Engel's path which shows all the points of tangency between
the price lines and the various indifference curves as the budget con
straint shifts to higher levels is not a straight line, this provides a
Fortunately, Samuelson has also developed the theory in the
case of non-homotheticity1 and we can thus relate it to the results of
the PPP studies.
Non-homotheticity
As a consequence of the introduction of non-homotheticity, we
believe that the assumption of a common indifference map for all
countries becomes much more acceptable for the following reasons. It is
now consistent with the actual pattern of consumption for the various
countries ranked along their level of development. Thus Gilbert's and
Kravis's statement that the various countries do not really exhibit
difference in the pattern of taste, but represent different levels of
development, becomes more sensible when the existence of luxuries and of
necessities is acknowledged.
It would now be interesting to turn to some empirical studies
and to examine them in the light of these findings. Unfortunately, a
straightforward application of Samuelson's theory cannot be carried out
unambiguously. Indeed, Samuelson's demonstration is based on two commod
ities, one being a necessity and the other a luxury. When we consider
actual inter-country comparisons, we have to classify the commodities
into necessities and luxuries and weight them with their prices in order
to obtain total expenditure on necessities and total expenditure on
luxuries. First, an index problem immediately appears. Which price
structure is relevant? Should we use each country's own prices? Secondly,
commodities are usually classified into necessities and luxuries with
the help of national surveys, i.e. with reference to the same group of
people. In an article commemorating the centenary of Engel's Law}
Houthakker (1957) presented a comparative study of household expenditure
patterns for 25 different countries; however, all his elasticities
were calculated from regressions based on national series.1 On the
other hand, Samuelson's demonstration rests on a classification of the
commodities into necessities and luxuries based on cross-country con
sumption patterns. Since this does not refer to the same group of people,
the meaning of such classification becomes somewhat different. What
causes the tilt of the cross-country Engel’s path? The fact that some
goods are necessities and others are luxuries for the various countries,
(i.e. we assume one common indifference map for the various countries),
or the fact that tastes are really different in different countries,
(i.e. we actually have a specific indifference map for each country but
we are linking together along the Engel's path the respective indiffer
ence curves where each country stands at this specific time). In Table
2.2, we will present various necessities-luxuries classifications based
on a number of national surveys and cross-country surveys. We will also
refer to pure income elasticities when the price elasticities have been
taken into account and to approximate income elasticities when the price
effect has not been isolated.
The last major difficulty in applying Samuelson’s theory to
empirical data is precisely linked to the above distinction between pure
and approximate income elasticities. Indeed, as prices and income change
simultaneously, it is very difficult to isolate the pure income effect.
As purchasing power parity studies have to collect price data, they are
in a better position to value the pure income elasticities by also
including prices as independent variables in their regressions. Unfort
unately, with the exception of food and education, the two PPP studies
included in the above table do not show much agreement.
Table 2.2
Various Approximations of Income Elasticities
I. Houthakker - National Surveys of 25 Countries
Approximate Income Elasticities
Low Average High
Income Inelastic:
Food .43 .57 .69
Housing
(incl. fuel and light) .48 .81 1.11
(not incl. furniture)
Income Elastic:
Clothing 1.05 1.31 1.77
Misc.
II. a) Gilbert and Associates b) Kravis, Kenessey et.al.
Cross country - 9 European countries and the USA
Cross country - 1 0 countries
Pure income Pure income
Elasticities Elasticities
Income Income
Inelastic: Inelastic:
Food .54 Food .63
alcohol, bev. .77 supply and opera- ^
tion of housing
tobacco .88 purchased transport .58
Clothing .84 Education .78
Housing .81
Income
purchase of trans- ^ Elastic:
port equipment meat 1.21 Education .75 beverage 1.18 Income tobacco 1.15 Elastic: Clothing 1.40 non-alcoholic bev. 1.13
Housing (rent and ..
footwear 1.01 fuel) i * J
furniture 2.10 house furnishings 1.12
fuel and light 1.19 purchase of trans- ^
Table 2.2 (Cont’d)
Income Inelastic: