British and American Exports: A Study Suggested by the Theory of Comparative Costs.
Part II
Author(s): G. D. A. MacDougall
Source: The Economic Journal, Vol. 62, No. 247 (Sep., 1952), pp. 487-521
Published by: Wiley on behalf of the Royal Economic Society
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THE ECONOMIC JOURNAL
SEPTEMBER 1952
BRITISH AND AMERICAN EXPORTS: A STUDY
SUGGESTED BY THE THEORY OF COMPARATIVE
COSTS. PART I.1
C. ELASTICITY OF SUBSTITUTION
IN Section B of this paper we dealt with observed facts about
the prices and quantities of British and American exports of a
large number of manufactures in a given period of one or five
years, and made some speculations about the possible effects of
errors in the data used. We reached the conclusion that, in the
years 1934-38 for example, where the relative price of product A
was 1% lower than the relative price of product B, the relative
quantity of product A tended to be at least 31 % greater than
that of product B, and quite possibly 4-41-% greater when
allowance is made for bias due to errors of observation. We
made no examination of changes over time. It would, therefore,
be a bold step to conclude from the facts observed that, in prewar
conditions, a 1% fall in a typical product's relative price
would tend to lead to a 4-41% (or even to a 3 %) rise in its
relative quantity. In view, however, of the difficulties involved
in most methods hitherto used for measuring elasticities in
international trade,2 it seems that this possible alternative
approach, which might perhaps be called the " commodity
comparison" method, should be further explored. A similar
type of cross-section analysis is, after all, used when conclusions
are drawn about income elasticity of demand from family budgets
observed in a given period; although admittedly one set of consumers
may be more likely to behave like another set, given the
conditions of the latter set, than one manufactured export is
to behave like another.
1 Part I appeared in the ECONOMIC JOURNAL for December 1951. The whole
article was largely completed before the author took up a temporary appointment
in government service.
2 See Orcutt, op. cit.
No. 247-vOL. LXII. K K
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488 THE ECONOMIC JOURNAL [SEPT.
The " Commodity Comparison
Method
Although the commodity comparison method of estimating
elasticities in international trade is open to special objections,
it avoids certain other difficulties involved in the use of time
series.
(1) The latter method often suffers from a paucity of
observations. For example, Mr. Chang's estimate of the
elasticity of substitution between British and American
exports of manufactures in the inter-war years 1 was based
on fifteen observations (for the years 1924-38) compared
with between 86 and 171 observations in each of the calculations
described above.2
(2) In the time series method the range of relevant
price variation (after allowance has been made for income
changes) is often small in relation to the errors of observation-in
many cases only 5 % or 10%.3 For example, the
standard deviation of the ratio of the U.S. to the U.K.
export price indices of manufactures over the period 1922-38
was only 7-8% of the mean, even before allowing for trend
or for world income, which, according to Professor A. J.
Brown,4 was highly correlated with relative prices. In the
calculations described above, the errors may be greater but
the range of price variation is much larger. For example,
the standard deviation of the 109 relative prices (U.S.:
U.K.) used in the calculation for 1934-38 was 40% of the
mean.5
(3) Mr. Orcutt has shown 6 that most time series analyses
I Tse Chun Chang, " A Statistical Note on World Demand for Exports,"
Review of Economics and Statistics, May 1948.
2 Mr. Kubinski's method (" The Elasticity of Substitution between Sources of
British Imports, 1921-38," Yorkshire Bulletin of Economic and Social Research,
January 1950) is based on an examination of 289 commodities imported into the
U.K., but the number of observations in each correlation calculation is never more
than eighteen (for each of the years 1921-38).
Messrs. D. J. Morgan and W. J. Corlett (" The Influence of Price in International
Trade: A Study in Method," Journal of the Royal Statistical Society,
1951) give the results of a few calculations with as many as forty-five observations
(for the years 1870 to 1914), but the great majority of their calculations are based
on less than twenty observations.
See also Orcutt, op. cit., footnote 7, where it is argued that, in the time series
method, the effective may be substantially less than the actual number of observa-
tions.
3 See Orcutt, op. cit., p. 121.
4 Oxford Studies in the Price Mechanism, p. 95.
5 The standard deviation of the 109 relative prices, U.K. : U.S., was 57%
of the mean. 6 Op. cit., pp. 125-6.
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1952] BRITISH AND AMERICAN EXPORTS. PART II 489
of inter-war data can at best show the consequences of
relatively small changes in prices since the range of relative
price variation was small., He has also given reasons for
supposing that elasticities are greater for large than they
are for small price changes, mainly because of the cost and
trouble to the buyer of shifting from one source of supply
to another. The commodity comparison method described
above shows the extent to which relative quantities may
vary when there are substantial differences in relative
prices (at least as between different commodities at one
time).
(4) According to Mr. Orcutt, the time series method may
tend to give estimates of relatively short-run elasticities
and underestimate the long-run elasticities. If this is so,
the commodity comparison method may give a closer
approximation to long-run elasticities, i.e., to probable
changes in relative quantities resulting from changes in
relative prices if time were allowed for the consequences
to work themselves out. This is, of course, an advantage
only if it is desired to estimate long-run elasticities. Since
the general pattern of relative export prices of British and
American manufactures in our sample did not change greatly
between 1934 and 1938, it may be that the regression
coefficients for the later thirties give a fair idea of relatively
long-run elasticities of substitution.
These apparent advantages of the commodity comparison
method may justify its use, despite its limitations, at least as
a complement to the time series method.' The last three of the
four advantages just mentioned would lead one to expect higher
elasticities than are obtained by the time series method. But,
like the latter, the commodity comparison method may also tend
to underestimate elasticities for a number of reasons. That
connected with errors of observation was discussed in the last
section, and there are two others that must now be explained.
1 Mr. Orcutt has also shown (op. cit., pp. 122-3) that, over time, supply
and demand schedules are likely to move up and down together, and that
this probably leads to an underestimate of elasticities of demand calculated
from observed time series. We shall see later that, in the method described in the
present article, there are schedules somewhat similar to demand and supply
schedules and that these are not the same for each product, but there is no obvious
reason why they should vary up and down together. This cannot, however, be
counted as an advantage of the commodity comparison over the time series
method, since Mr. Orcutt's criticism does not seem to apply to time series
calculations using relative price and quantity indices. (See also footnote 1
to p. 491.)
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490 THE ECONOMIC JOURNAL [SEPT.
Further Possible Bias in the Commodity
If we take the plunge and attempt to use the results of the
commodity comparison method as some indication of what
might happen to the relative demand for British and American
exports of a particular product when relative prices change,
we must assume that, for each product, there is a relationship
between relative price and relative quantity demanded. Using
our diagram measuring relative prices vertically and relative
quantities horizontally on a double logarithmic scale, we have
"demand substitution curves" for each product. Let us
assume that these are straight lines and, for the moment, that
they all have the same slope, which we wish to discover. There
is, however, no reason why they should coincide. When, for
example, British and American prices are equal (even after
adjustment for " quality " differences) the relative quantities
demanded may vary; Britain may have an advantage in one
imperfect market, America in another. We thus get a series of
demand substitution curves lying between D1D1 and D2D2 in
the following diagram:
' D 4 /DD D
0~~~~~
Relative Quantity, U.S.:U.K.
We can also think of " supply substitution curves " for each
product, showing the relative quantities supplied at various
relative prices.' These, likewise, are unlikely to coincide, because
of diffSerences in national factor endowmaents. When, for examnple,
1 This is, of course, a simplification, since there may be an infinite number of
pairs of prices that will give the same price ratio, and these different pairs of
prices will normally lead to different ratios of quantity supplied unless the two
national supply curves are related in a special way, e.g., if they are parallel
straight lines on a double logarithmic scale, i.e., with equations of the typo:
log q _ log a1 + b log p
log q-log a2 + b log p
where p and q are relative price and relative quantity, and a1, a2 and b are constants.
The two curves in this case have the same (constant) elastieity.
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1952] BRITISH AND AMERICAN EXPORTS. PART la 491
British and American prices are equal, Britain may supply much
more of product A than the U.S., and much less of product B.
We thus get a series of supply substitution curves lying between
S1S1 and S2S2 which we assume for the time being to be upward
sloping.
The observed points will lie at the intersection of the supply
and demand substitution curves for each product, i.e., within the
shaded area. It is fairly clear (and this is demonstrated in
Appendix B) that a regression line fitted to such points, so as to
minimise the sum of the squares of the deviations in a horizontal
direction, will tend to have a slope steeper than D1Dj, and
thus underestimate the true slope of the demand substitution
curves for each commodity.' The fact that negative rather than
positive slopes are obtained for the regression lines means,
presumably, that the position of the demand substitution curves
varies less from product to product than the position of the
supply substitution curves, i.e., broadly, that differences in comparative
national advantages in the imperfect markets for the
various commodities have a less important effect than differences
in national factor endowments on the position of the curves.
This does not seem altogether unreasonable.
We must now remove the assumption that the demand
substitution curves are parallel. It seems almost certain that
some will be flatter than others, e.g., where the market is more
perfect or the product less heterogeneous. To isolate this point,
let us suppose that, where British and American prices are equal,
the ratio of the quantities demanded is the same for each product;
i.e., if either country has an advantage, it is the same in the
market for each product. The various demand substitution
1 According to our conventions the nearer the curve to the horizontal t
the slope (see footnote 1 to p. 711 of Part I).
When a supply substitution curve is well to the right, i.e., when national factor
endowments are such that America supplies far more of the product than
Britain at the same price, it is possible that the demand substitution curve will
also tend to be well to the right, i.e., that the demand for the American product
will be far more than that for the British product at the same price. This might be
so, because America's inevitably large share in the market has made her products
better known to importers. Similarly, supply substitution curves towards the
left may tend to be associated with demand substitution curves towards the left.
In other words, high demand substitution curves may tend to be associated with
low supply substitution curves and vice versa. If this is the case, the calculated
regression line may tend to overestimate the true slope of the demand substitution
curves for each commodity for reasons similar to those given by Mr. Orcutt
(op. cit., p. 123), where he shows that, in so far as demand and supply curves tend
to move up and down together, the calculated regression line will tend to underestimate
the true slope.
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492 THE ECONOMIC JOURNAL [SEPT.
curves will all pass through the point Z in the following
diagram:
Relative Quantity, U.S.:U.K.
The steepest is D1D1, the flattest D2D2, the mean slope is that
of DmDm.
The observed points will lie within the shaded area. It is
fairly clear (and this is also demonstrated in Appendix B) that
the regression line fitted to such points will tend to have a slope
steeper than Dm;Dm, and will thus underestimate the true average
slope of the demand substitution curves for the various
commodities.
The various demand substitution curves will, in fact, both
have diserent slopes and cut the equal price axis at different
points. The calculated slope will thus be steeper than the true
average slope for both of these reasons.
This conclusion depends, however, on the assumption that
the supply substitution curves slope upwards. If they are
horizontal there is no bias, and if they are downward sloping the
bias is in the other direction. This would necessitate downward
sloping export-supply curves for individual British and American
manufactures. It might be argued that, in the thirties at least,
these curves did not slope appreciably upwards, since, inter alia,
there was generally excess capacity and since exports were only
a fraction of total output. For similar reasons it might be
argued that the curves did not slope downwards and that, even
in the long run, this would be unlikely where exports were not a
large part of total output. The reader may make his private
guess, but, for the purpose of this article, it seems safer to
make no adjustment to our figures for the possible bias just
discussed.
1 The slope of D vDm is the arithmetic mean of the individual slopes.
reasons for choosing this form of average see footnote 2 to p. 496.
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1952] BRITISH AND AMERICAN EXPORTS. PART II 493
"Product " and " Total " Elasticities of Substitution
A "product" elasticity of substitution of, say, -4 between
British and American exports of individual manufactures would
not necessarily mean, of course, that the elasticity of substitution
between the two countries' total exports of manufactures was as
high as -4, because of the different patterns of exports. Suppose,
for example, that the total market for British and American
exports together were fixed for each product, and that there were
only two products, the U.K. exporting 99 yards of cloth and 1
radio, the U.S. 99 radios and 1 yard of cloth. A 1% fall in the
British price for each product relative to the American would
then increase the ratio of British to American exports of cloth by
4% (from 99 to about 103 times), but this would raise the quantity
of Britain's cloth exports to only about 99 04 yards, while American
exports fell to approximately 0-96 yards ( 103). Britain's
exports of cloth would then rise by only 0-04% and, since the
weight given to her radio exports is very small, her total volume
index of exports would also rise only slightly. Similarly,
America's volume index would fall only slightly, and the ratio
of the two volume indices would change by only a small fraction
of 1%.
To get some idea of the importance of this factor, a calculation
was made, covering the 109 products mentioned above for the
years 1934-38, of the change that would result in the ratio of
the two countries' export-volume indices for the 109 products
if there were a small uniform percentage change in the price
ratio for all products caused either by a uniform change in all
the prices of one country or by this combined with a different
uniform change in all the prices of the other. It was assumed
that the total market for each good, for U.S. and U.K. exports
taken together, remained the same or changed in the same
proportion. It was found that, assuming a uniform " product "
elasticity of substitution for each commodity, the corresponding
" total " elasticity of substitution (relating to price and volume
indices) would be 0-614 times as large. Thus, if the product
elasticity of substitution is taken as (a) -3-6 (the calculated
regression coefficient), or (b) -4 to -4- (allowing for bias due
to errors of observation), the total elasticity would be (a) -2-2
or (b) -2-5 to -2-8.
Similar calculations can be made for other years or groups
of years, or for other pairs of countries. To find the total elasticit
of substitution on the assumptions stated it is necessary tQ
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494 TIXE ECONOMIEC JOURNAL [SErT.
multiply the product elasticity of s
where Va and Vb are the values of the two countries' exports of
each product, and A and B the proportions of the market (in
terms of quantity) held by each of them (A + B = 1). The
formula may perhaps be called an index of similarity of exports.
Where the pattern of exports is exactly the same in the two
countries the index is unity, where the exports are entirely
different it is zero. Details are given in Appendix C.
Indices of similarity were calculated for the 109 British and
American exports of manufactures for each of the years 1928
to 1938. These are shown in column (2) of Table VIII, together
with the results of multiplying the indices by the corresponding
regression coefficients (called " product elasticities of substitution
" in the table). The resulting " total elasticities of substitution
" are in column (3). Apart from year-to-year fluctuations,
they show a steady increase throughout the period, rising
from under II at the beginning to over 2 at the end.
TABLE VIII
British and American Exports of 109 Manufactures
Total elasProduct
Index of ticity of
elasticity of similarity. substitution
substitution.1 | (1) X (2).
(1) (2) (3)
1928 . . . . . 2 501 0-472 1-2
1929 . . . . . 2601 0*572 1-5
1930 . . . . . 2599 0 542 1-4
1931 . . . . . 2713 0*656 1.8
1932 . . . . . 2 602 0 647 1-7
1933 . . . . . 2*826 0 683 1-9
1934 . . . . . 3 241 0.561 1.8
1935 . . . . . 2*958 0*679 2-0
1936 . . . . . 2 934 0.611 1-8
1937 . . . . . 3128 0 701 2-2
1938 . . . . . 3-134 0*660 2-1
1934-38 . . . . 3624 0 614 2-2
1 As in column (3) of Table V. Before allowing for bias due to errors of
observation.
The assumption that the total market for each product
remains constant, or changes in the same proportion, tends,
however, to understate the total elasticity of substitution.
Suppose, for example, that America had roughly the same share
in the Anglo-American export market for both silk and rayon
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1952] BRITISH AND AMERICAN EXPORTS. PART II 495
stockings (two products that are, in fact, included separately
in the calculations described above). A relative fall in all
American prices would induce foreign buyers to substitute
American for British silk stockings, and American for British
rayon stockings. It would also, probably, induce them to
substitute American silk for British rayon stockings and American
rayon for British silk stockings. But there is no obvious reason
why the total market for either silk or rayon stockings should
increase relatively to the other. If, however, America had a
larger share in one market than in the other, the matter would
be different. If, for example, America had the bulk of the market
for silk stockings, and Britain the bulk of the market for rayon
stockings, there would be much more scope for substitution of
American silk for British rayon stockings than for the substitution
of American rayon for British silk stockings, since exports of
both these last two products would be small. It seems likely,
therefore, that the total market for silk stockings (America's
speciality) would increase in relation to the total market for
rayon stockings (Britain's speciality). The increase in America's
total exports relative to Britain's would then be greater than it
would have been had the total silk-stocking market not expanded
in relation to the total market for rayon stockings. This means
that the total elasticity of substitution will tend to be a greater
fraction of the product elasticity than that given by the formula
described above.
This formula showed that if, as had been suggested earlier,
the product elasticity of substitution were -4 to -4k, the total
elasticity would be -2'5 to -2-8. After what has just been
said, we may perhaps hazard a guess that the total elasticity
might be of an order approaching -3.1 This is about ten times
as high as the figure of -03 obtained by Mr. Chang for the pre-
1 It is perhaps not necessary to remind the reader that we are talking of
elasticity of substitution and that this may differ from the elasticity of demand for
British or American exports. If we assume that the world import market for
manufactures and the prices charged by our competitors remain constant, a given
elasticity of substitution between British and all other exports of manufactures
would mean an elasticity of demand for British exports four-fifths as great, since
Britain supplied about one-fifth of the world's exports of manufactures before the
war. The elasticity of demand would, however, be greater in so far as the world
import market for manufactures was increased as a result of lower British prices,
British manufactures being substituted both for manufactures produced in
importing countries and for non-manufactures. Any changes in the definition
of elasticity of demand so as to allow, for example, for price reactions by
our competitors or for income changes would give correspondingly different
results.
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496 THE ECONOMIC JOURNAL [SEPT.
war elasticity of substitution between British and American
exports of manufactures.1
The assumptions are, of course, still unrealistic. Allowance
should be made for elasticities of demand by third countries for
the exports of America and Britain together that vary from
product to product; this also would lead to varying changes in
the size of the total markets. Allowance should also be made
for product elasticities of substitution that vary from product
to product,2 for varying changes in price according to elasticity
of supply and so on. Further adjustments of this kind might
tend to increase or to decrease the value of the total elasticity,
but the author has been unable to think of any obvious reasons
for such bias.
Changes over Time
The calculations described so far have all referred to one
year or to an average of years. Some calculations have also
been made for changes over time using the figures obtained for
the 109 products. These may be of some use in attempting to
assess short-run elasticities of substitution in particular periods.
Suppose, for example, we wish to examine the effects on relative
quantities of British and American exports of the large changes
in relative prices that took place after Britain left the gold
standard in September 1931. The published price and volume
indices of exports of manufactures by themselves tell us relatively
little. We find, for example, that, between 1930 and 1932,
the American price index for exports of manufactures rose by
23% in relation to the British (in terms of dollars), while the
American volume index fell relatively by 42%.3 This suggests
an elasticity of substitution of over -2X.4 Similarly, between
1 Chang, op. cit., p. 112. Based on the years 1924-38. Mr. Chang appears to
compare total U.K. exports (which were mainly manufactures and semi-manufactures)
with U.S. exports of semi-manufactures and manufactured goods only.
Professor A. J. Brown (op. cit., p. 95) has given reasons for the low figure obtained
by Mr. Chang.
2 Some reasons are given in Appendix C for thinking that the assumption that
each product elasticity of substitution is equal to the arithmetic mean of the
product elasticities does not introduce any bias into the derivation of the total
elasticity. This provides some justification for taking the arithmetic rather than
any other mean of the product elasticities as the magnitude we wish to find.
(See footnote 1 to p. 492.)
3 Using the indices for U.S. exports of " finished manufactures" and U.K.
exports of " articles wholly or mainly manufactured." These are not wholly
comparable, but this does not matter, since the figures are used here for illustrae
tion only.
4 log 0 58 -02366 = -2-63.
log 1-23 0-0899
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1952] BRITISH AND AMERICAN EXPORTS. PART I 497
1932 and 1934, America's price index fell relatively by 27%,
while her volume index rose relatively by 23%; this suggests
an elasticity of substitution of only --. But it would be rash
to rely on single observations of this type. We have reason to
think, moreover, that American exports of manufactures are
more sensitive than the British to cyclical fluctuations, since
they contain a higher proportion of capital goods and of durable
consumer goods for which the income elasticity of demand is
high. This may account for part of the relative fall in American
exports between 1930 and 1932, when activity was rapidly
declining throughout the world. Then again, there might have
been changes, between 1932 and 1934, in the imperfection of the
world market that worked to the disadvantage of U.S. exports,
for example, the Ottawa Agreements and the general spread of
discriminatory practices. This might account in part for the
comparatively small relative rise in American exports between
1932 and 1934.
More useful results may perhaps be obtained if we examine
changes in individual products. A comparison was therefore
made of changes, (a) between 1930 and 1932 and (b) between
1932 and 1934, in the relative quantities and relative prices of
the 109 products mentioned above. In this way we can obtain
109 observations of short-period changes instead of only one
(and there is also a substantial range of variation in relative
prices). We can largely eliminate the complications that arise
from the different patterns of British and American exports of
manufactures, except in so far as there are differences within
the commodity classifications used. We can isolate, in a general
way, the effects of changes in the imperfections of the world
market that work to the disadvantage of one country. Thus,
in comparing 1932 and 1934, we plot the relative price index for
each product in 1934 (1932 1) against the relative quantity
index on a double logarithmic scale. The regression line cuts
the horizontal axis, indicating no change in relative price, at a
point where the relative quantity index is 0-72 (A in Fig. 3).
This suggests that, where the relative price of a commodity
remained unchanged between 1932 and 1934, there was a fall
of 28% in the American quantity relative to the British quantity.
This may give some indication of the extent to which imperfections
of the markets changed to the disadvantage of the U.S.; 2
I log 1 23 0 0 0899 -0-66
log O-73 - -0-1367 06.
2 In the case of nearly one-third of the 109 products, the American relative
quantity fell despite a fall in the American relative price.
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498 THE ECONOMIC JOURNAL [SEPT.
although the later analysis (pp. 500 et seq. and Appendix D) shows
the need for caution in drawing such a conclusion. The correlation
coefficient is -0-62, and the slope of the regression line is
2*0. This suggests that, after allowing for the shift to America's
disadvantage, a change of 1% in relative price of a product was
accompanied by a change of 2% in relative quantity; in other
words, that the product elasticity of substitution was -2.1 A
similar calculation for 1930-32 gave a correlation coefficient of
-057 and an elasticity of -15.
Changes in Relative Prices and Quantities
of U.S. and U.K. Exports of 109 Manufactures
1932-34
2-0
= r=-O62r 1= 06
A ND__ _ __ _ _ _
1.0
O8s t ~~~~08 -
0-6
.05
0-2 0-3 04 0-6 0-8 1 2 3 4 5
Q = Relative Quantity U.S.: U.K. 1934 (1932 = 1)
FIG. 3
These elasticities are considerably lower than those obtained
by the other method, before allowing for downward bias. This
may be partly because they can only show the comparatively
short-run consequences of changes in relative prices, whereas
the other method may give a better idea of long-run consequences.
Even, however, when similar comparisons were made of changes
over longer periods, relatively low figures were obtained. Thus,
a comparison of 1929 and 1937, again for the 109 commodities,
gave a correlation coefficient of only -045 and an elasticity of
-18. A comparison of the four years 1928-31 against the five
years 1934-38 gave a correlation coefficient of -048 and an
elasticity of -17. These lower elasticities cannot be explained
by the difference between long-run and short-run elasticities,
unless it is thought that more than eight years are required for
the full effects of price changes to be felt. It may be that they
are biased towards zero more than the results of the earlier
calculations, one important reason being that the range of variaThe
equation of the regression line is:
log q = -20 log p + log 0-72,
where q and p are indices of relative quantity and price (1934: 1932)
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1952] BRITISH AND AMERICAN EXPORTS. PART 1I 499
tion in relative prices is much smaller. In general, one is hardly
surprised to find rather a poor relation between relative price and
relative quantity changes over a period of eight years, since so
many things have happened, other than price changes, to affect
the relative quantities demanded. The implications of the type
of analysis just described prdbably deserve further examination,
but this is not attempted here, as the present article is concerned
primarily with the cross-section type of analysis.
Conclusions on Elasticity of Substitution
This concludes the discussion of elasticity of substitution.1
It cannot be too strongly emphasised that any numerical results
that may be obtained by this or by other methods cannot be used
to make precise forecasts. It is, however, useful to gather
together all evidence that may provide some background for
those who have to make forecasts and decisions, to consider as
carefully as possible what the evidence means and what it does
not mean, to examine possible biases and so on. Practical
judgments about, for example, the effects of exchange-rate
variations or the degree of difficulty involved in restoring international
equilibrium do not depend upon a knowledge of whether
elasticities of substitution are, say, -2-3 or -2-7, but they do
require a knowledge of whether they are of the order of -0-03,
or -0-3, or -3 or -30. Such judgments also, of course, require
a knowledge of, or at least a view on, many other things (which
will vary from time to time), such as the flexibility of supply,
the reactions of producers and of their governments to changes
in the prices charged by their competitors, the extent to which
demand for the goods of competing nations is determined by
supply of currency, speed of delivery, etc., rather than by price,
and so on. Practical judgments of this type inevitably involve
an act of faith; no one can work out the full implications on the
world economy of an important change in the economic policy
of a major country; no one can foretell the actions and reactions
of millions of producers and consumers and of governments
throughout the world. But this does not render futile the attempt
to establish the likely order of magnitude of, for example, the
elasticity of substitution between the exports of various countries,
nor does it rob such a concept of all meaning.
1 Another type of analysis of the figures for the 109 products would be the
correlation, for each product, of relative prices and relative quantities in the
eleven years 1928-38, i.e., 109 correlations with eleven observations each. This
analysis, which would be similar to that made by Mr. Kubinski for imports into
the U.K., has not been attempted.
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500 THE ECONOMIC JOURNAL [SEPT.
This paper has suggested one method by which some relevant
evidence can be collected and applied it to the particular case of
American and British exports of manufactures, mainly in the
years between the wars. There are doubtless difficulties involved
in the method described other than those mentioned in this paper,
and it is hoped that these will be explored by others. But it
does seem fairly clear that there was some inverse relation between
relative price and relative quantity and that variations in the
former were associated with comparatively large variations in
the latter. While it is dangerous to apply the results obtained
to future changes, I believe that the evidence gives some grounds
for thinking that, at least in conditions resembling those of the
later thirties (an important proviso), changes in the relative
prices of British and American exports of manufactures should
lead to comparatively large changes in the relative quantities
demanded in third markets, at least after a period of years.
D. EXPORTS AND FACTORS OTHER THAN PRICE
Apparent American Disadvantage in the Imperfect World Market
It will have been noticed that, according to the regression
line in Fig. 2,1 which referred to the years 1934-38, the U.S.
tended to export little more than half as much of a commodity
as Britain when she charged the same price and that she exported
as much only when her price was 16% below the British. As
Table IX shows, this was rather typical of the individual, years
1933-38. When prices were equal, the U.S. tended to export
between one-half and two-thirds as much as Britain and exported
as much only when her price was 10-20% lower. For the earlier
years, 1928-32, the regression lines show the U.S. in a more
favourable relative position; when prices were equal she tended
to export roughly 80-90% as much as Britain, and she sold as
much when her price was some 5-10% lower. For the years
before 1928, allowing for lack of comparability, the figures tell
roughly the same story, at least from 1924 onwards. (The
results for 1948 show a striking improvement in the relative
position of the U.S. compared with 1937 and, though the comparison
is dangerous, there seems to have been a similar improvement
between 1913 and the early 1920s.)
The figures for the years between the wars suggest that, in
the period 1933-38 and, to a lesser extent, between 1924 and
1932, the U.S. had, on balance, a comparative disadvantage in
the imperfect world market as the result of such factors as Imperial
1 In Part I.
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1952] BRITISH AND AMERICAN EXPORTS. PART la 501
Preference, discrimination against dollar goods, differences in
transport costs, stronger commercial ties between Britain and
overseas markets, greater selling efforts by British exporters,
etc. But before jumping to this conclusion we must consider
other possible reasons for the low figures in Table IX.
TABLE IX
Particular Values shown by Regression Lines
Relative Relative
No. of quantity price
mNo.factu . (U.S.: U.K.) (U.S.: U.Kmanufactures. when price when quantity
equal. equal.
(1) (2) (3)
1913 1 . . 32 0-48 0-80
1922 . . . . . 86 1-01 1.01
1923 . . . . . 86 0 95 0 97
1924 . . . . . 86 0-82 0 90
1925 . . . . . 86 0-87 0 94
1925 . . . . . 97 0-81 0-91
1926 . . . . . 97 0-83 0-92
1927 . . . . . 97 0-78 0*90
1928 . . . . . 97 0-85 0-93
1928 . . . . . 109 0 90 0-96
1929 . . . . . 109 0-87 0 95
1930 . . . . . 109 0 79 0.91
1931 . . . . . 109 0-86 0 94
1932 . . . . . 109 0-84 0 93
1933 . . * * * 109 0-57 0-82
1934 . . . . . 109 0-51 0-81
1935 . . . . . 109 0-69 0-88
1936 . . . . . 109 0-59 0-83
1937 . . . . . 109 0-67 0-88
1938 . . . . . 109 0-61 0-85
1934-38 . . . . 109 0-53 0'84
1937 . . . . . 118 0 50 0 79
1948 . . . . . 118 1-10 1-06
Commonwealth countries 1937 115 0-22 0 54
Non-Commonwealth countries
1937 . . . 115 1-36 1-16
Mid-1912 to mid-1913 for U.S.
(1) One possible explanation is that different methods
of valuing exports in the two countries led to an artificial
relative under-valuation of American exports. If this was
so, regression lines based on the corrected figures would be
above the lines we have obtained. They would show the
U.S. exporting a higher fraction of the British quantity
when prices were equal. There are two obvious corrections
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502 THE ECONOMIC JOURNAL [SEPT.
that should be made. First, U.S. exports are relatively
under-valued because freight charges up to the Canadian
border are not included in the recorded value of certain
exports to Canada. This under-valuation probably represented
about 1% of the value of U.S. exports to all countries
before the war,' but may have been a smaller percentage
of the value of manufactured exports, which tend to have a
relatively high value per ton. Secondly, U.S. exports are
in general valued f.a.s. (free along side), while U.K. exports
are valued f.o.b. (free on board), the difference being the
cost of loading. It is unlikely that this normally involved
a difference of more than 1% of the value of manufactured
exports. It is hard to discover any other important reason
for American under-valuation, but the possibility should
not be ruled out.
(2) A second possibility is that British exports were,
on average, of a higher quality than the American, and that
appropriate corrections would therefore raise the regression
line.2 This is a matter on which it is difficult to express
an opinion.
(3) It has been shown above that the true average
slopes of the lines are probably flatter than the calculated
slopes because of errors of observation (other than a general
tendency for the quality of one country's exports to be
higher) and possibly for other reasons. The true regression
lines would probably cut the equal-price and equal-quantity
lines at different points, and this might reduce or eliminate
the apparent American disadvantage. (This is discussed in
Appendix D.)
For these reasons it seems unwise to conclude from the figures
that, at least before 1933, the U.S. had a comparative. disadvantage
in the imperfect world market. For the later prewar
years the presumption is stronger that this was the case,
even allowing for possible errors. According to the regression
line for the years 1934-38, the U.S. exported as much as the
U.K. when her price was 84% of the British. It is hard to
make allowance for the errors under (3) above, but it is suggested
1 Balance of International Payments of U.S. (Department of Commerce).
It is pointed out in Foreign Commerce and Navigation of the United States for 1946
that similar inaccuracies may occur in connection with ocean shipments.
2 The correction would shift the observed points, on a double logarithmic scale,
upwards and to the left at an angle of 450 to the horizontal. Since the regression
lines obtained all have a slope flatter than -1, they would clearly be shifted
upwards.
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1952] BRITISH AND AMERICAN EXPORTS. PART II 503
in Appendix D that this might well raise the figure to 861%.
A 2% allowance for under-valuation of U.S. exports (as in (1)
above) would raise the figure farther to 88%. Thus we are left
with a price margin of some 12%. If this cannot be explained
by a higher average British quality ((2) above) and by immeasurable
errors under (1) and (3) above, we may conclude that the
U.S. had a comparative disadvantage in the later period.
That this was so is suggested in a more simple manner by the
figures in columns (2) and (3) of Table X. These are, in fact,
unweighted quantity and price index numbers for the products
TABLE X
Geometric Means and Medians
Unweighted geometric Medians.
No. of means.
m anu- -_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
factures. Relative Relative Relative Relative
quantity price quantity price
(U.S.: U.K.). (U.S.: U.K.). (U.S.: U.K.). (U.S.: U.K.).
(1) (2) (3) (4) (5)
1913 1 . 32 0*69 0 90 0 55 0-89
1922 . . . 86 1.42 0-84 1-075 0-88
1923 . . . 86 1-14 0 90 1-04 0 94
1924 . . . 86 088 0-96 0-85 1-035
1925 . 86 1-03 0 93 0-89 0-98
1925 . 97 1.02 1090 0-89 0 95
1926 . . . 97 1.00 0-92 099 0-98
1927 . . . 97 0-98 0.91 0-85 0 98
1928 . . . 97 1.05 092 1.01 0.99
1928 . * * 109 1-18 0 90 1-17 0-96
1929 . . . 109 1-13 0 90 1.10 0-96
1930 . * * 109 1-07 0-89 0-92 0-925
1931 . . . 109 094 097 0-98 099
1932 . . . 109 0*66 1-17 0-56 1-17
1933 . . . 109 0*57 1.00 0 45 1-03
1934 . . . 109 0-62 0 94 0 59 0.995
1935 . . . 109 0.59 1-05 0 50 1-02
1936 . . . 109 0-64 0*97 0 55 1-02
1937 . . . 109 0-76 0-96 0-58 0.99
1938 109 0-78 0-92 0 63 0 95
1934-38 . . . 109 0-69 0 93 0-58 1.00
1937 . . . 118 0-65 0.91 0-58 0 97
1948 . . 118 1-37 0-87 1.33 0-91
Commonwealth countries
1937 . . 115 0-235 0 97 0*24 0-96
Non-Commonwealth
countries 1937 . 115 1-61 0-92 1.53 0.95
1 Mid-1912 to mid-1913 for th
in our sample. But, instead of comparing one year with another,
they show for each year, or period of years, indices for the U.S.,
the U.K. being taken as unity. For the years 193438 taken
as a whole, the recorded U.S. price was, on average, 93 % of the
British, but the U.S., instead of exporting more than Britain,
as might have been expected, exported, on average, only 69%
No. 247-vOL. LxII. LL
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504 THE ECONOMIC JOURNAL [SEPT.
as much.' If we assumed that a 2% correction is adequate for
under-valuation of U.S. exports ((1) above) this would raise
the 93% to 95%; the general picture would not be materially
altered. If we further assumed that British products were as
much as, say, 10% better in quality than the American, this
would further raise the average U.S. price to around 105% of
the British, but it would also reduce the average U.S. quantity
to around 63% of the British. Such a low American export
could be explained by 5% higher prices only if there were an
elasticity of substitution of more than 9,2 and this seems
improbable.
If median relative quantities and prices are used (columns
(4) and (5) of Table X), the result is less convincing, but, despite
all the uncertainties, it seems not unlikely that, in the later
thirties, the U.S. tended to export less of a commodity than
Britain when the price was equal. It also seems likely that,
in the earlier years, any American comparative disadvantage in
the imperfect world market was smaller or non-existent. These
tentative conclusions may not, however, apply to the whole
range of manufactures; it should be remembered in particular
that, for statistical reasons, the products in our sample include
very few in the important field of machinery.
The figures in Table X confirm the striking improvement
in the relative position of the U.S. between 1937 and 1948, though
it is not easy to assess the relative importance of various possible
causes. While British exporters were out of the market during
1 These are geometric means. The arithmetic means are, of course, larger, and
the harmonic means (i.e., the reciprocals of the arithmetic means of relative price
and quantity, U.K.: U.S. instead of U.S.: U.K.) are smaller. The various means
are as follows:
Arithmetic. Geometric. Harmonic.
Relative quantity, U.S.: U.K. . 4-75 0-69 0 03
Relative price, U.S.: U.K. . . 1-03 0 93 0-86
The arithmetic and harmonic means of relative quantity are greatly influenced by a
few extreme cases which have a much smaller effect on the geometric mean.
Nevertheless, the large difference between the arithmetic and harmonic means
shows the need for caution in the use of the geometric mean. The differences
between the various means of relative price are much less marked because the range
of variation is much smaller in relative price than it is in relative quantity.
As a form of check on the geometric means, the medians were also calculated
and these are shown in columns (4) and (5) of Table X. The general picture is not
very different, and the use of medians instead of geometric means does not greatly
affect the arguments in the text.
2 log 063 =-5
log 1-05
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1952] BRITISH AND AMERICAN EXPORTS. PART II 505
the war and early post-war years, American manufacturers doubtless
built up goodwill and a preference for American models and
qualities, and at the same time gained a lead in the development
of new types of products. They were handicapped after the War
by discrimination caused by dollar shortage, but this was limited
by U.S. government loans and grants. On the other hand, the
large change in the figures may reflect in part merely the inability
of British exporters, in 1948, to meet demand at a given price.
Imperial Preference
It is tempting to try to discover how far the apparent disadvantage
of the U.S. in the imperfect world market in the later
thirties can be accounted for by Imperial Preference and how
far the increase in preferences resulting from the Ottawa AgreeRelative
Prices and Quantities of U.S. and U.K. Exports
of 115 Manufactures in 1937:
(a) to Commonwealth Countries
(b) to Non-Commonwealth Countries
26
b) Non-Commonwealth Countries 2.0 I
Mean- -'*Mean 10C
058
(a) Commonwealth Countries 0
0.5
0 4
0I1 02 0-3 0-4 06 08 1 2 3 4 8 10
Relative Quantity U.S. U.K.
U.S. recorded prices raised by 3% to cover
freight to Canadian border.
FIG. 4
ments accounts for the apparent change to America's disadvantage
after 1932. It is shown in Appendix E that, after
Ottawa, the margin of preference on U.K. goods entering British
Commonwealth markets was, on average, of the order of 10%,
so that, as roughly one-half of British exports went to Commonwealth
countries, the margin represented about 5% of the total
value of British exports. The increase in the margin resulting
from the Ottawa Agreements must have been considerably less
than 5%. The reader may care to make his private deductions
about the effects of Imperial Preference, but, in view of the
difficulties described above, it does not seem that trustworthy
conclusions can be drawn from the figures so far given.
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506 THE ECONOMIC JOURNAL [SEPT.
A more fruitful approach is to consider separately British
and American exports (a) to Commonwealth countries (excluding
the U.K.) and (b) to non-Commonwealth countries (excluding
the U.S.). This has been done, for 115 commodities, for the year
1937.1 Owing to the labour involved, similar calculations were
not made for other years. The two regression lines are shown
in Fig. 4, and the main results are given in Tables IX and X.
It will be seen from Table X that American prices were, on
average, 92% of the British for exports to non-Commonwealth
countries and 97% for exports to the Commonwealth.2 This
latter figure should perhaps be raised to about 100% to cover
-under-valuation of U.S. exports to Canada.3 Other possible
corrections for relative under-valuation or quality differences
need not concern us here, since they would probably apply in
more or less equal degree to exports both to Commonwealth and
to non-Commonwealth countries. We are concerned only with
the fact that average relative prices were some 8% lower in
trade with non-Commonwealth countries than they were in trad
with the Commonwealth. There was, on the other hand, a very
large difference in relative quantities. The U.S. exported, on
average, 161% as much to non-Commonwealth countries as
Britain and only 231% as much as Britain to Commonwealth
countries. In case these figures are biased by quality differences,
it is safer to say that the relative quantities (U.S.: U.K.) were,
on average, about 6.9 times as great for non-Commonwealth
countries as they were for Commonwealth countries.4 Such
a large difference could be explained by the 8% difference in
relative prices only if we assumed an " elasticity of substitution "
as high as -23.5 This is unlikely, and it therefore seems almost
1 For statistical reasons, it was impossible to obtain figures for the 171 or for
the 109 commodities covered by the previous analyses.
2 The geometric means are used in this paragraph and the next, but the argument
is unaffected if the medians are used instead.
3 Railway freight to the Canadian frontier not included in the recorded value
of U.S. exports has been estimated at $34 million in 1937 (The Balance of
International Payments of the United States in 1937, p. 28). This is 4% of U.S.
exports to the British Commonwealth (excluding the U.K.), which totalled $827
million. Since the percentage for manufactures may have been smaller, and since
there may have been offsetting factors, it seems reasonable to round up our
observed figure of 97% to 100%.
4 A comparison of the values of British and American exports of all manufac
tures to Commonwealth and non-Commonwealth countries shows a much smalle
discrepancy.
log 6-9 23
log 0.92 -23.
This is a sort of " spatial " elasticity of substitution. Questions of bias
discussed, as the figure is purely illustrative.
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1952] BRITISH AND AMERICAN EXPORTS. PART II 507
certain that a large part of the difference is to be explained by
factors other than price.
Of these, Imperial Preference seems to provide only a partial
explanation. The margin of preference was about 10% of the
value of British exports to the Commonwealth, so that if, as the
figures suggest, the prices of British and American exports to the
Commonwealth were, on average, the same excluding import
duty, then American prices, including duty, were some 110%
of the British. In non-Commonwealth countries they were
92% of the British, i.e., relative prices (U.S.: U.K.) were about
16% lower in non-Commonwealth countries than they were in
Commonwealth countries.L But, even allowing for this, the
large difference in relative quantities could be explained solely
by prices, including duty, only if we assumed an elasticity of
substitution of at least - J1.2 It therefore seems likely that
factors other than preferential duties were important.
An examination of the two regression lines may give some
indication of the relative importance of Imperial Preference and
other factors. It will be seen from Fig. 4 that the line for Commonwealth
countries was far to the left of that for non-Commonwealth
countries. Whatever corrections may be necessary,
1 0.92 . 1.10 = 0.84. It is assumed that the rate of duty on British and
American goods in non-Commonwealth markets was the same. See also next
footnote.
2 log 6-9 1
log 0584
This is an understatement for two reasons:
(a) Where duties are ad valorem, relative prices to Commonwealth countries,
including duty (but excluding transport costs, the difference in which is small for
most manufactures), would be:
I + tc +ta- 1 ta
1 + to 1 + t#
where t, is the rate of common tariff and ta the r
goods. Where t. is 0 1 (10%), the relative price is t
not zero. Where duties are specific, relative prices, including duty, would be:
I + EC, + T_'
p + T. + T, P Pp?T.+T ___,_.,
p + T, 1 + CZac
p
where T. and T, are the common and additional specific
and British price. Where = 041 this will again be less than 1 1.
(b) Relative prices of exports to non-Commonwealth countries, including
duty, would be greater than 92% in so far as there are specific duties.
Relative prices to non-Commonwealth countries would thus be less than 16%
lower than relative prices to Commonwealth countries, and the elasticity of
substitution required to explain the difference in relative quantity would be
higher than -11.
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508 THE ECONOMIC JOURNAL [SEPT.
this seems to indicate a substantial difference in the relative
advantages of America and Britain in these two markets at a
given f.o.b. price ratio. According to the regression lines, U.S.
exports to non-Commonwealth countries were 136% of the
British when recorded prices were equal while her exports to
the Commonwealth were only 22% of the British. It is suggested
in Appendix D that, even allowing for corrections, it may still
be fairly safe to say that, where British and American prices were
equal in both markets, relative exports (U.S.: U.K.) were four
times as great for non-Commonwealth as for Commonwealth
countries.1
Now the margin of Imperial Preference was about 10% of
the value of British exports to Commonwealth countries. Where
British and American prices in Commonwealth markets were
equal, including duty, the American price, excluding duty, was,
therefore, on average, 9% less than the British price, excluding
duty.2 Assuming a product elasticity of substitution as high
as -5, the relative quantity (U.S.: U.K.) was about 60% higher
when prices were equal, including duty, than it was when prices
were equal excluding duty.3 If, therefore, the relative quantities
were about four times as great in non-Commonwealth markets as
they were in Commonwealth markets when prices, excluding
duty, were equal, they were still about 4 _ 21 times as grea
1.6 2
when prices, including duty, were equal. There is thus still a
margin of this order to be explained by factors other than Imperial
Preference. The latter, in fact, explains directly only a comparatively
small part of the relative advantage of the U.K. in
Commonwealth as compared with non-Commonwealth markets,
1 According to the regression lines the U.S. exported the same amount as
Britain to non-Commonwealth countries even when her price was 116% of the
British, but the same amount to Commonwealth countries only when her price was
54% of the British. It is argued in Appendix D that the last figure may well be
too low and the first too high.
2 When duties are ad valorem, and prices are equal, including duty:
pa(' + to + ta) = Pb(l + tQ)
where Pa, Pb are the American and British prices, excluding duty, tc the common
rate of tariff and ta the additional rate on U.S. goods (transport costs are ignored).
I.e.,
Pa 1+ tc 1 +tc
Pb 1 + to + ta 1-1 + to
which is greater than 1.1 s.e., greater than 091. In so far as th
exceeds 091, the argument in the text is strengthened.
3 Antilog (-5 log 0 91) = 1-6.
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1952] BRITISH AND AMERICAN EXPORTS. PART II 509
It would seem that factors such as commercial ties of Britain
with the Commonwealth and of the U.S. with certain nonCommonwealth
countries were considerably more important;
although Britain's ties with the Commonwealth may, in part,
have been indirectly fostered by the preferential duties. If the
elasticity of substitution was less than -5, the importance of
preferential duties was, of course, smaller.
It is interesting to speculate about the effect of preferential
duties on the volume of Britain's export trade. Before the
war, Commonwealth countries probably took around 37-38%
of their imports of manufactures from Britain,1 i.e., the ratio
of British to foreign exports of manufactures to Commonwealth
countries was about 0.6.2 If the preferences had been removed
and prices, excluding duty, had remained the same, the ratio
of British to foreign prices, including duty, would have risen by
something like 10%. Assuming a total elasticity of substitution
of -3 (the highest figure we dared to suggest for the total elasticity
between British and U.S. exports of manufactures to all countries)
the ratio of 0-6 would have fallen by about one-quarter,3 i.e.,
to 0 45, so that Britain's proportionate share would have fallen
from about 37 ?% to about 31 %.4 If the total market had
remained the same, the quantity of Britain's exports to Commonwealth
countries would thus have fallen in the ratio 37 : 31,
i.e., by about 17%, and, if her trade with other countries had
been unaffected, her exports to all countries would have fallen
by about 9%. Assuming a total elasticity of substitution of
-2, the figure would be about 6%. In view, however, of the
many indirect repercussions and of the danger, emphasised
above, of using calculated elasticities, too much significance
should not be attached to these results, which suggest that
preferential duties safeguarded less than 10% of Britain's total
exports.5 It should be remembered, too, that they take no
account of other preferential arrangements such as preferential
import quotas.
1 This is a rough calculation based on value; it is assumed that the figure for
volume is the same.
2 371=06.
63
3 -3 log 1.1 = -0-1242, the antilog of which is 0 75.
4 39- 0 45.
5 This is not, of course, the same as the percentage of U.K. exports enjoying
preference, which was considerably higher. Table XI shows that more than
one-half of U.K. exports to Commonwealth countries enjoyed preference, i.e., over
one-quarter of all U.K. exports.
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510 THE ECONOMIC JOIURNAL [SEPT.
E. GENERAL CONCLUSIONS
The studies described in this article (including Part I which
appeared in the EcoNoMIc JOURNAL for December 1951) have
ranged over a rather wide field; one thing led to another. It
is hoped that they have illustrated, among other things, the
usefulness of tackling problems of international trade through
a study of individual commodities. The article is intended to
be partly a study of method, but some of the results may be of
more general interest.
It seems that the labour theory of value, crude as it is, does
help to provide some explanation of British and American export
trade in manufactures in an imperfect world market and to
illustrate the importance of tariffs in limiting international
commerce. It reminds us that a country can compete in certain
lines, even with a rival whose general level of productivity is
much higher. (This does not, of course, mean that a high and
rapidly rising level of productivity in, say, the U.S. may not
aggravate the problem of international disequilibrium. For
example, knowledge of the high American standard of living
may increase any tendency of other countries to try to live
beyond their means; high productivity, reflected partly in the
ability to supply the latest products, creates a large demand for
a country's exports; a more rapid growth of productivity than
in other countries may mean continuous pressure on the international
exchanges unless money wages also increase at an
abnormally high rate; and so on.)
The fact that American weekly wages in manufacturing,
which were about twice the British before the war, are now
about 31 times as high suggests that, despite changes in relative
productivity, there may be important opportunities for British
exporters in many new lines. Figures in Tables IX and X,
however, are consistent with the common view that the war
resulted in a substantial improvement in the relative position of
the U.S. in the imperfect world market. Some allowance must
be made for this fact in any estimate of British export prospects
unless it is offset by special selling efforts by British exporters, by
discrimination against American goods or in other ways.
Leaving labour costs and turning to prices, a similar picture
emerged. There was a fairly clear inverse relation between
relative prices of British and American exports and the relative
quantities exported, variations in the former being associated
with comparatively large variations in the latter. The range
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1962] BRITISH AND AMERICAN EXPORTS. PART la 511
of relative prices showed, incidentally, the doubtful value of
such statements as: " before devaluation . . . British goods
had been 25% higher in price than American."l It seems likely
that some British prices are usually higher than the American,
some lower. The important question is how many are higher,
how many lower, and by how much. Even if British and American
prices were, according to some form of average, equal, this would
not necessarily result in international equilibrium.
The results obtained suggested a possible method of estimating
the elasticity of substitution between the exports of two countries
by using data for a number of commodities in one period instead
of data for one commodity (or group of commodities) in a number
of periods. Although open to certain objections, this approach
seems to avoid some of the difficulties connected with the more
normal time series method.
A method was also suggested of using the " product "elasticity
of substitution so obtained to estimate the " total" elasticity
of substitution between groups of exports, which will normally
be a lower figure. The calculations, allowing for possible bias,
suggested a very much higher elasticity of substitution between
British and American exports of manufactures than that obtained
by Mr. Chang. An alternative method was also suggested of
estimating short-period elasticities at particular times of rapid
change.
Finally, the data for individual products were used in an
attempt to estimate the importance of factors other than price
in determining relative exports. The, tentative conclusion was
reached that, in the later thirties, the U.S. had on balance a
comparative disadvantage in the imperfect world market, at
least in the products studied. There was, however, a striking
difference between Commonwealth and non-Commonwealth
markets, the U.S. having a substantial disadvantage in the
former and a substantial advantage in the latter. It seemed
unlikely that more than a small part of this difference could be
directly attributed to Imperial Preference, leaving the major
part to be explained by commercial ties and other non-price
factors. The importance of such factors in determining relative
shares in export markets is not, however, inconsistent with a
high price elasticity of substitution. A purchaser may be prepared
to buy from A rather than B, even though A's price is,
say, 5 % higher; but if the margin rises to, say, 7 % or 8% he ma
quickly switch the bulk of his custom to B.
1 The Time8, September 23, 1949.
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512 THE ECONOMIC JOURNAL [SEPT.
It is hoped that the validity of the methods suggested in
this article will be examined by others and that they may possibly
be of some use in the study of other problems of international
trade.
G. D. A. MACDOUGALL
Nuffield College,
Oxford.
APPENDIx B
Other Possible Bias in the Calculated Slopes of the Regression
Lines
Let the true demand substitution curve for product R be
X1 - Ar + BrX2 . . * * * (1)
where X, and X2 are the logarithms of rel
relative price respectively. (It is assumed in this Appendix
that there are no errors of observation.) Ar and Br are not the
same for each product. For product R, Br is the slope of the
demand substitution curve, Ar the value of X1 when X2 0,
i.e., the logarithm of the relative quantity when the British and
American prices are equal.
Equation (1) may be re-written
(x, + Xj)-(ar + A) + (br + B)(x2 + X2) * (2)
where X1, X2, A and B are means and xl, x2, ar, br deviations
fromn them.
i.e., xi = Bx2+ ar + brx2 + X2br + (A-Xl + BX2) (3)
Multiplying through by x2, and summing, we get
Zx1x2 B2x22 + arX2 + ZbrX22 + X22brX2 . (4)
(Zx2 multiplied by the constant expression in
brackets in (3) is zero)
Let b be the regression coefficient obtained by the method
of least squares from the observed data (minimising the sum of
the squares of the deviations of the logarithms of relative quantity).
Then
b-_1X2 B arX _- + a2 +brx2 - 2brX2
b R2 + ZX2 2 + ZX22 + 2ZX22 (5)
The second, third and fourth terms on the right-hand side of
(5) will tend to be positive if the supply substitution curves
slope upwards.
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1952] BRITISH AND AMERICAN EXPORTS. PART II 513
The second will tend to be positive because a positive value
of a, denotes a demand substitution curve towards the right,
and this will tend to mean a relatively high relative price (since
the supply substitution curves slope upwards), i.e., a positive
value of x2. Similarly, negative values of a, and x2 will tend to
go together.
The third term is a weighted average of the br's, the weights
being the x22's. A positive br denotes a steeper than average
slope, and it is with these commodities that the large x22's will
tend to be found, since a large x22 denotes a relative price which
is well below, or well above, the mean. Similarly, a negative
br will tend to be associated with a small x22. Thus, while the
unweighted average of the be's is zero, the weighted average will
tend to be positive.
The fourth term will tend to be positive for the following
reasons. When X2 > 0, i.e.; broadly, when the majority of
the relative prices are greater than unity, a positive br (i.e., a
steeper than average slope) will tend to mean a positive x2 (i.e.,
a higher than average relative price) and YbIx2 will tend to be
positive. The fourth term will thus tend to be positive. When
X2 < 0, a positive br will tend to be associated with a negative
x2, and 2brX2 will tend to be negative. Again, the fourth term
will tend to be positive.
Thus, from (5), b will tend to be greater than X, i.e., the
calculated slope will tend to be steeper than the mean of the
true slopes of the demand substitution curves if (i) the true
curves are parallel but not coincident, or (ii) the true curves are
not parallel but all cross the equal price line at the same point,
or (iii) the true curves are not parallel and do not cross the equal
price line at the same point.
If, however, the supply substitution curves are horizontal,
it will readily be seen that these sources of bias disappear, and
if they are downward sloping the bias is in the other direction.
APPENDIX C
Relation between the "Product " and the " Total " Elasticities
of Substitution
(on the assumptions given on p. 493.)
If the quantitative shares of America and Britain in the
exports of a commodity are A and B respectively (A + B = 1),
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514 THE ECONOMIC JOURNAL [SEPT.
the ratio of a small proportionate change in A to an accompanying
smal proportionate change in A will be
A
A' d 1A A dA 1-A
If, therefore, there is a small proportionate change K in the
ratio of America's to Britain's exports of each commodity, there
will be a proportionate change of KBn in America's share in the
total market for British and American exports of commodity n.
If that total market changes in the ratio 1: (1 + L) for each
commodity, the quantity of America's exports of commodity n
will change in the ratio 1: (1 + KB1X)(I + L). It can be shown,
similarly, that the quantity of British exports will change in
the ratio 1: (1 - KAn)(l + L).
The volume indices of American and British exports will then
change in the ratios of, respectively 2
1: (1 ?L) Va(l + KB) and I (I + L)Vb(l -KA)
where VJ/ and Vb are the values of America's and Britain's expor
of each commodity.
The proportionate change in the ratio of the American to the
British volume index will be
EVbEVa(l + KB) - I
E VaYVb(i -KA) ***
= [EVbEVaB + EValVbA]
I Val Vb - KE VaVbA
I VaB +VbA]
K E Va ? E Vb i(dividing numerator and
I _KE VbA denominator by VaE Vb.)
Vb
Since K is small, this equals
K[EV+ ZV.bA .(2)
If, now, the price of each American export changes in the
ratio I: ma, and the price of each British export in the ratio 1: Mb,
/ A
d UIn At Afoml
dA (I - ) I-A = (I-- A)2.
2 Usig the formula 2 P"q-.
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1952] BRITISH AND AMERICAN EXPORTS. PART II 515
the price ratio for each product will chan
Mb
It is evident that the ratio of the price indices of the two countries
will also change in the ratio 1: m. In other words, the pro-
Mb
portionate change in the price ratio for each product and in the
price-index ratio will be ma -1. Let us call this P.
mb
The product elasticity of substitution will then be K, and the
total elasticity of substitution will be
K [ VaB + E2VbA]
-P L V a +Z VbI
The term in brackets has been called the index of similarity
of exports. If the two countries have no exports in common
it is zero. The first term is zero because, when America exports
a product, Britain does not; hence, when Va is not zero, B is
zero. The second term is zero for similar reasons.
When the (value) pattern of exports is exactly the same, the
index is unity. Va is constant, and the index may be re-written
IVb(l -A) + ETVbA -1.
2Vb N2Vb
Where K is not the same for each product, the proportionate
change in the ratio of the American to the British volume indices
Will be
E;VaKB + z VbKA
IVa + Vb
r EVa,B+ I VbA] +[V,Bk + E
L zVa YiVb Lzva z vb
where K is the (arithmetic) mean of K, and k the deviation
from it. The first set of terms is the same as (2) with K substituted
for K. An examination of the second set of terms
suggests no obvious reason why they should be biased away
from zero, so that the assumption that K is the same, for each
commodity, as the arithmetic mean of the individual K's does
not seem to introduce any bias into the derivation of the total
elasticity.
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516 THE ECONOMIC JOURNAL [SEPT.
APPENDIX D
Errors in the Intercepts of the Regression Lines on the Equal
Quantity and Equal Price Axes
Using the notation of Appendices A and B, let the true
demand substitution schedule for commodity 1 be
xi/ 1 Ar + BrX2'
i.e., (X1 + X1 - 1 -el) (A + ar) +
(B + br)(X2 + X2-E2 -e2).
Summing and dividing by N (the number of observations), we
get
X1I -A + BX2 + ? N2 + >(ar + BZX2 BYe2 +X22br
- 2Eb,Yb Ex- + Eel) + (El BE2) - 2
The terms in the first bracket are necessarily zero. Those
in the second are zero, assuming that the errors of observation
are unbiased (the case of biased errors is dealt with on pp. 501-2).
The last term tends to zero, since there seems no reason to expect
correlation between br and e2. We are thus left with
A-X1 BX2 2.
'A is the average intercept on the equal
of X1 when X2 - 0) that we wish to discover. The equation
of the regression line we find by the method of least squares is
(X1 -X1)- b(X2 -X2)
X, X1 (X1 - bX2) + bX2.
The intercept on the equal-price axis that we find is thus
a ==1 - bX2 .(2)
Hence
A - a = X2(b - B) N (3)
Since we assume that the true average slope is flatter than
the observed slope, and since both b and B are negative,
(b - B) > 0. When X2 > 0, the first term on the right-hand
side of (3) is thus positive and, when X2 < 0, it is negative.
But, assuming upward sloping supply substitution curves, when
X2 > 0, steep slopes of the demand substitution curves (i.e.,
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1952] BRITISH AND AMERICAN EXPORTS. PART II 517
positive br's) will tend to be associated with high relative prices
(i.e., positive x2's), and therefore the second term will tend to be
negative. Similarly, when X2 < 0, the second term will tend
to be positive. We therefore cannot say whether the calculated
intercept on the equal-price axis is biased to left or to right. If,
however, the supply substitution curves are horizontal or downward
sloping, we can say that the calculated intercept will be
biased to the left when X2 > 0, and to the right when X2 < 0.
In any case it will be unbiased when X2 - 0, i.e., when average
relative price is unity.
For exports to Commonwealth and non-Commonwealth
countries, X2 equals -00128 and -00357 respectively. If
the supply substitution curves are horizontal, the last term in
(3) tends to zero, so that
A a + X2(b-B) . . . (4)
Assuming B's of -3, -4 or -5, the intercept for exports to
Commonwealth countries falls from the calculated figure of
022 to 021, 0-20 or 019, while that for exports to non-Commonwealth
countries falls from the calculated figure of 1 36 to 1 26,
1.16 or 1 07. The ratio of the intercepts falls from the calculated
figure of 6-2 to not less than 51.
If the supply substitution curves are downward sloping,
both intercepts will tend to fall further, and the ratio may also
fall further, but there seems to be no way of estimating the
probable amount.
If the supply substitution curves are upward sloping, the last
term in (3) tends to be positive, since X2 is negative in both cases.
A lower limit for the true value of the intercept for exports to
non-Commonwealth countries is thus given by (4), i.e., 1 07 for
a true B of -5. The corresponding figure of 0-19 for exports
to Commonwealth countries will tend to be raised by the positive
last term in (3), but, as X2 is not greatly below zero, we may
perhaps guess that the true intercept is not greatly in excess of,
say, 025, even after allowing for the correction necessitated by
underestimation of U.S. exports to Canada. If this is correct,
the ratio of the true intercepts is thus at least 4.
There may have been quality differences and differences in
methods of valuation that applied equally to exports to each
group of countries, but, provided these were not too large, and
provided the true slopes for the two groups of countries were not
very different, it does not seem unreasonable to assume that,
when price (corrected where necessary) was equal, relative
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518 THE ECONOMIC JOURNAL [SEPT
quantity (U.S.: U.K.) was probably -at least four times as great
for non-Commonwealth as it was for Commonwealth countries.
We now turn to the intercept on the equal quantity axis,
i.e., the value of X2 when X1 = 0. The intercept we wish to
find is
I A X +X - EbrX2
B B + NX2+N
The calculated intercept is
_ a kl+ 2b - b +2
Hence I- = - XI + Eb2
Now - < 0 and tends to have the opposite sign
from X2 if the supply substitution curves slope upw
sign if they slope downwards and to be zero if they
For exports to the Commonwealth, X1 < 0 and X2 < 0.
Hence I > i if the supply substitution curves are upward sloping
or horizontal, while if they are downward sloping no conclusion
can be drawn. For exports to non-Commonwealth countries,
X1 > 0 and X2 < O. Hence I < i if the curves are downward
sloping or horizontal, while if they are upward sloping no conclusion
can be drawn. Hence the statement, in the footnote
to p. 508, that the figure obtained for relative price where the
quantity of exports was equal may well be too low for exports
to Commonwealth countries and too high for exports to nonCommonwealth
countries.
For exports to all countries in 1934-38, X1 < 0 and X2 < 0
If the supply substitution curves are horizontal, and B = -5,
the antilogarithm of I works out at 0 864. If the supply substitution
curves slope downwards, the true figure is lower, but
if they slope upwards it is higher. Hence the figure of 861%
on p. 503.
APPENDIX E
Imperial Preference I
It was stated in the text that the average margin of
enjoyed by U.K. exports to British Commonwealth countries
1 This appendix is almost wholly the work of Miss Rosemary Orton. Much
valuable help was obtained from London representatives of Dominion Govern-
ments.
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1952] BRITISH AND AMERICAN EXPORTS. PART la 519
before the war, but after Ottawa, was of th
was based on a calculation for, 1937 (or the financial year 1937-38)
covering countries that took 97 % of U.K. exports to the Common
wealth.1 The main sources used were the trade returns and,
where necessary, the tariff lists, of the various countries.
For each product imported into a Commonwealth country
from the U.K., the percentage margin of preference is the
difference between the duty that would have been paid had the
product been American and the duty actually paid on the U.K.
product, expressed as a percentage of the value of the imports
from the U.K., excluding duty. The average percentage margin
of preference on all imports from the U.K. is the average of the
percentage margins of preference on the various products weighted
according to the value of imports of each product from the U.K.
This is the same as the difference between the duty that would
have been paid on the total of imports from the U.K. had the
goods been American and the duty actually paid, expressed as a
percentage of the total value of imports from the U.K.
The average percentage margin of preference for each country
is shown in column (5) of Table XI. It will be seen that the
average of these figures, weighted according to U.K. exports
to each countryin 1937 (column (1)), was 9-10%. This represents
the difference between the duty that would have been paid on
all U.K. exports to Commonwealth countries had they been
American and the duty actually paid, expressed as a percentage
of the value of all U.K. exports to Commonwealth countries.
The method of calculation used tends to overstate the average
margin of preference in so far as the existence of preference
presumably tends to increase the proportion of U.K. exports
enjoying higher preferences and to reduce the proportion enjoying
lower preferences or none at all. Likewise, it might be expected
to increase the proportion of U.K. exports sent to countries
granting the higher average preferences. If the various margins
of preference were weighted according to the pattern that exports
would have taken without preference, or according to the value
of U.S., rather than U.K., exports to Commonwealth countries, one
would expect the final figure to be lower, though this tendency
might, of course, be offset by other factors.
The notes to Table XI describe only some of the difficulties
involved in the calculations. The main purpose of the table
is to help to show how the final figure of 10% was reached. The
1 Defined for this purpose as countries classified as " British " in the U.K.
trade returns.
No. 247-voL. LXII. MM
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520 THE ECONOMIC JOURNAL [SEPT.
results obtained for the various countries, although shown for
convenience with some degree of precision, are subject to a
considerable margin of error. The following broad picture is,
however, probably correct and may be of some interest:
Of U.K. exports to Commonwealth countries, one-third went
to Canada, Australia and New Zealand, which gave an average
preference of around 20%; one-third went to India and South
Africa, which gave an average preference of around 5%; onesixth
went to Eire, which on balance gave little preference, or
to territories giving no preference at all; one-sixth went to
miscellaneous countries, which gave various rates of preference
averaging about 10%.
It is hoped to publish more details at a later date.
No account has been taken of preference given through
import quotas or by any method other than import duties.
TABLE XI
Margins of Preference 1937
(1) (2) (3) (4) (5)
% of total % of % average % average
U.K . ex- imports margin of margin of
Country. poritish % of trade from U.K. pref erence preference
British cvrd giepe- on goods on all imcountries.
ference.4 given pre- ports from
f erence. U.K.
New Zealand . . 8-0 100 0 88-90 25-27 23-24
Canada . . . 10-9 99-7 88 23 20
Southern Rhodesia . 1-2 99.5 96 19-20 19
Australia . . . 14*9 100-0 90 l 19l 17 1
British Guiana . . 05 99-8 93 18-19 17
Channel Islands . . 2-2 59-1 73-86 18-39 15-29
Jamaica . . . 0-8 99-9 83 15 12-13
Trinidad and Tobago . 1.0 99-4 64 19 12
Burma. . . . 1-3 98-6 62-93 10-21 9-13
Northern Rhodesia . 04 99-8 93-97 9-11 9-10
Malta . . . .5 100-0 71 12 8
Cevlon . . . 1-6 97-2 70-86 8-21 7-8
Federated Malay States . 1*2 97-9 44-58 11-19 6-8
India . . . . 14-2 96-0 50 12 6
Union of South Africa . 1635 99-3 39-43 5-8 2-4
Straits Settlements . 3-4 100.0 24 13 3
Gibraltar . . . 04 100 0 5-7 24-48 2
Hong Kong . . 1-3 100.0 5 2 15 1
Eire * * . 86 99-3 10 13-312 1-2 s
Territories granting no
preference " . . 82 100-0 0 - 0
Total of above countries 971 98.6 6 55-57 6 15-18 5 9-10
Taken directly from the official Year Book.
2 Takes no account of additional duty of 10% on certain U.K. goods.
a Allows for additional 10% duty on certain U.K. goods.
4 Refers to imports from the U.K. that were covered in this calculation.
Weighted average.
Nigeria (including British Cameroons), Gold Coast (including Togoland) most of British East
Africa, Anglo-Egyptian Sudan, Palestine, Aden, New Guinea and Papua.
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1952] BRITISH AND AMERICAN EXPORTS. PART n 521
GENERAL NOTES ON TABLE XI
Column (1).
Calculated from Annual Statement of Trade of the U.K.
Columns (2)-(5)
Calendar year 1937 for New Zealand, Northern and Southerni Rhodesia, Trinidad and Tobago,
South Africa, Eire, British Guiana, Malta, Jamaica, Hong Kong; financial year 1937-38 for the
rest.
In calculating the preference margins it was sometimes necessary to give upper and lower
limits for a small percentage of items for which it was impossible to reconcile the classifications in the
trade returns with those in the tariff lists. Several trade returns contained, for example, items such
as " other foods " and " other textile manufactures ". It was impossible to find either the exact
amounts given preference or the amount of preference, if any, conceded. This kind of difficultv
accounts both for many of the percentages in Column 2 being less than 100 and for the outside
limits in columns 3, 4 and 5 which take the place of precise figures. It also, together with rounding,
accounts for the apparent slight inconsistencies between the last three columns.
WEIGHTING
A. To obtain average figutres for each country.
The percentage margin of preference for each product was weighted by the value of imports from
the U.K. as follows:
(a) Australia, Canada, Jamaica, Trinidad and Tobago, South Africa, India. Value of
imports on which preference was granted.
(b) New Zealand, Northern and Southern Rhodesia, British Guiana, Malta, Eire, Blong
Kong. Value of imports originating in the U.K. Since the qualification for preferential rates
is that a certain percentage of an article's value should be the result of British labour (the
percentage varying with the importing country), the figures given in columns (3) and (5) may
be slightly above their true value.
(c) Channel Islands, Burma, Federated Malay States, Gibraltar, Ceylon, Straits Settlements.
Value of U.K. exports as given in U.K. Annual Statement of Trade, Vol. IV. This will also give
an upward bias to the figures in columns (3) and (5), since the U.K. figure includes all goods
which in the U.K. have " undergone operations " which do not " leave them essentially
unchanged."
In the Canadian trade returns imports are attributed to the country from which they are consigned.
The margins of preference on the separate items were weighted by the value of imports
under the preferential tariff and then expressed as a percentage of the total value of imports consigned
from U.K. (as opposed to the total value of imports originating in U.K. for other countries).
The figures for Canada in columns (3) and (5) are therefore, relatively, underestimates.
B. To obtain average figures for all British countries.
For consistency the figures for each country were weighted by total exports of U.K. produce and
manufactures to each country (column (1)).
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