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Cambridge Journal of Economics 1987,11, 197210
The deviation of production prices from
labour
values:
some methodology and
empirical evidence
Pavle Petrovic*
Introduction
The empirical proposition that relative prices of commodities are predominantly deter
mined
by
the relative quantities
of
labour time required
for
their production was put
forward by Ricardo. He stated that a
1 %
fall in profits would change relative production
prices by only
1 %
(Works,
I,
p.
36) and, as the change in profits does not usually exceed 6
or 7%, Ricardo ended up with the
'93%
labour theory of value' (Stigler, 1958). Being an
empirical proposition, it
calls
for evidence which will support or refute
it.
There
is
hardly
any empirical work dealing directly with the extent
of
discrepancies between relative
production
prices
and relative labour
values,
the
one
exception being Shaikh
(1984),
while
conclusions drawn, indirectly, from some other empirical work suggest huge deviations
(Burmeister, 1984). Large deviations are also suggested by numerical examples derived
from a twocommodity hypothetical model (Barkai, 1967).
The aim of this paper is to provide evidence on deviations of production prices from
labour values
in an
actual economy. Besides testing Ricardo's
1%
rule,
the
results
obtained can be also used to assess the empirical significance of Marx's proposition that
total profit equals total surplus value, even though this
is
known
to be not
true
in
general.
1
The paper consists
of
three parts.
In the
first part various linear price models
are
defined, and a number of relations which will be used in the empirical investigation are
derived. The second
part,
the main
one,
deals
with empirical results concerning deviations
between relative prices and labourvalue ratios. Ricardo's 1% rule is tested, employing
first
the value
of
total
output
as
the unit of measurement and then
the
prices,
one
for
each of
47 sectors that are considered. As the deviations obtained have varied when different
numeraires were used, the question of which one to choose arises. Following Ricardian
tradition one would look for an 'invariable standard of value' as the unit of measurement.
•University of Belgrade.
I
am grateful to Dj. Suvakovic and anonymous referees for many comments and
suggestions.
I
have also benefited from the comments by M. Landesmann,
L. L.
Pasinetti and B. Schefold.
The usual disclaimer applies.
1
See various attempts
to
solve
the
socalled transformation problem. Pasinetti (1977) gives some
references.
0309166X/87/030197+14S03.00/0
C
1987 Academic Press Limited
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198 P. Petrovifc
Samuelson (1983) derived such a standard for the model we were using, so we calculated
and employed it as a numeraire commodity. An alternative solution, and in our view the
proper one, is to look at all possible exchange ratios i.e. 1081 in the 47 sectors model we
have been considering. We then examine the generality of the results, which refer to the
Yugoslav economy in 1976 and 1978. Alternative estimates of the deviations between
prices and values based on procedures used by Shaikh (1984), are also reconsidered.
Finally, the third part examines the effects of deviations between production prices and
labour value ratios on some aggregates, particularly on the relation between total profit
and surplus value.
1.
The price models
The model used for the empirical analysis is an inputoutput model with fixed capital,
the framework that has often been employed for price calculations.
1
The following
expressions will be used (with the notation explained below):
V = V(A + D + G) + (1 +
s)
wL (1)
P° = P°(A + D + G) + tvL + rP°B (2)
P» = P
m
(A +D+G) + r^PB (3)
P
1
= P\A +D + G) + tvL + P'Br (4)
P
1

= kL (5)
We are
primarily interested in the relation between labourvalue ratios or value prices (1),
that is prices proportional to labour embodied,
2
and production prices (2). We shall also
consider how the distance between the value prices and production prices changes when
the profit rate increases from the actual level to the maximal one; thus, production prices
with the profit rates above the actual
one will
be calculated, including the case
in
which the
profit
rate is
equal
to
its maximum
(3).
Further, instead of
a
uniform profit rate
one can
use
different rates of profit across sectors arising from different risks in production (Krelle,
1977) or from nonproportional growth (Pasinetti, 1981). For the price calculations, the
latter approach is adopted, so that profit rates across sectors are proportional to sectoral
longrun growth rates (4). Finally, the prices that are proportional to current labour are
defined (5) for comparison with value prices, that is prices that are proportional to both
current and past labour.
The individual symbols have the following meaning:
V
=
(v,),
P° = (p°), P =
U>7),
P
1
= (/>,'), /* = (Pf) and P
a
= (p°),
i
= 1,. . .,»
are the row vectors of the following prices: value prices, production prices, prices with
maximal profit
rate,
prices with different profit rates across sectors, prices proportional to
current labour and actual prices;
•£
= ('j)j
i
= l,..
,n
is the row vector of labour coefficients where /, denotes the input of
labour in manyears required per unit of production in sector i;
3
A =
(a
tJ
),
i,j— 1,.
• Jt
is
' See, for example, Brody, 1970; Kyn et al., 1970; Yefimov and Movshovitch, 1973; Carter, 1970 and Fink,
1981.
2
It can be shown that the value prices denned by (1) are proportional to labour values.
1
Reduction of heterogeneous labour to unskilled worker equivalents is performed by using weights which
are ratios between the average net wage rate for
a
given qualification and the average net wage rate for unskilled
workers.
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Production prices and labour values
199
the square matrix
of
technical coefficients where
a
tj
denotes the amount
of
ith commodity
used
per
unit
of
output
in
sector
j;
D =
{d
tj
),
i,j=
1,...,
n is the
square matrix
of
depreciationoutput coefficients where
d
tj
denotes
the
annual depreciation
of the ith
capital good
in
thej'th sector;
G=gT%~
l
is
the square matrix ofgovernment consumption, where column vector^
=
(£,),
i
= 1,.. .ji
denotes
the
government consumption basket normalised such that
P
a
g= 1;
T=(t[),i=l,.. .,n is the row vector where t, denotes the number ofgovernment consump
tion baskets paid, through taxes,
by
sector
i,
while JC=(x
t
),
i= 1,...,« is the
diagonal
matrix where
x,
denotes the output of the ith sector; X=(x
t
), i =
1,.
..,«is the correspond
ing column vector;
A
= L(I
—
A
—
D
—
G)~
'
is the row vector A
=
(A,),
i
= 1,..
.,« where
kj
is the labour value of
commodity
i; it is
also known
as
the vertically integrated labour coefficient (see Pasinetti,
1973);
B
=
(b
i]
),i
x
j=
1,. .
.,nis the square matrix of capital coefficients where
b
(
j
gives the amount
of
the j'th
commodity tied
up per
unit
to
output
in
sector^'.
It
includes both fixed
and
inventory capital
i.e. the
matrix
B
=
K+In where K=(kij)
and
/M
=
(in,y),
ij,= \,.. .ji
are
the
square matrices
of
fixed capital coefficients
and
inventory capital coefficients
respectively;
H
=
B(I—A
—
D
—
G)~
i
= (h
ij
) i,j=\,..
.,n is the
square matrix
of
integrated capital
coefficients where
h
t]
gives
the
amount
of
good
i
tied
up
directly
and
indirectly
(in
other
sectors)
per
unit
of
output
in
sector./ (see Pasinetti, 1973);
f =
{r
l
),
i
=
1,.. .,« is the
diagonal matrix where
r, is
the profit rate
of
the
ith
sector. Profit
rates across sectors
are
proportional
to the
sectoral longrun growth rates,
i.e.
r =
n
1
v
where fi
2
is a scalar and
v
=
(v
(
),
i= 1,..
.,n diagonal matrix with growth rates
v,
on the main
diagonal;
s,
w, r,
r
nai
and
k
are the following
scalars:
rate of surplus value, wage rate, maximum profit
rate and markup.
Solutions
of
equations (l)(4) turn
out to be
positive characteristic vectors:
V, P°, P",
and
P
l
with characteristic roots: 1/1
+s, \\r,
1/r,^,,
and l///
2
respectively.
Combining expressions (1) and (2) one can obtain the relation between relative prices of
production
and
relative value prices.
1
P°J
»i
v
l
1

1

r
P°h,
w
k
{
rP
0
/:,
TU
k.
(6)
where column vectors h
t
and
hj
are the vectors of integrated capital coefficients while scalars
/., and
?.)
are integrated labour coefficients
for
commodities
i
and j respectively.
It
follows
from
(6)
that deviation between
the
relative prices considered
is due to the
difference
in
corresponding integrated capitallabour ratios, that is, the fact that
1
A
similar result is obtained
by
Shaikh (1984).
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200 P. Petrovi*
p°h,
p°hj
where the total tied up capital P°h, is aggregated
at
production prices.
1
Accordingly,
when direct capital labour ratios are uniform across sectors (and therefore integrated ones
as well) there will be no discrepancies between value and production prices (see also
Samuelson, 1983). An alternative invariance condition
to
secure V=P°
=
P" can
be
derived following the corresponding proof in the circulating capital model (Pasinetti,
1977,
p. 79):
P"
=
r
MI
P"B(/
 A 
D

G)~'
V = (1
+
s)
wL (I
 A 
D

G)~
1
therefore
V =
/"" implies
(1
+
s)
wL (I
 A 
D

G)~
•
=
!•„,„( 1
+s)wL(IADGy
1
B(IADG)
i
and multiplying by
(/
—
A
—
D
—
G) one gets:
L
=
r^AS.
2
(7)
The condition obtained (7) differs from the one in circulating capital model i.e. P
L
= V;
therefore small discrepancies between production and value prices, in the fixed capital
model, do not imply that value prices are close to labour coefficients.
The choice of numeraire commodity affects the size of the deviation of production
prices from value prices so the distance between them will vary with various numeraire
commodities. One way to deal with this problem is by finding an 'invariable standard of
value',
that is a composite commodity the value of which will remain unchanged with
variations in profit rate, and use it as
a
numeraire. S raff a (1960) defined such a (standard)
commodity for the circulating capital model and
fixed
capital model with joint production,
while Samuelson (1983) defined it for the durable capital model we are using. In the latter
case,
a standard commodity turns out to be the righthand characteristic vector X* of the
matrix H?
r
m
HX*
=
X*
(8)
We can now proceed to Ricardo's 1% rule. In his example {Works,
I,
pp. 3336) he
calculates the change in price of commodity i (cloth) relative to that of commodity
7
(corn)
caused by
a
fall of profit rate from 10% to 9% as:
pflp
9
.
5995/5500
'
'
n

1
= '
1
= 
0009
p
w
,lp
lO
j
6050/5500
that is, approximately
1
%.
As we are going to compare value and production prices where
corresponding profit rates are equal
to
zero and r% respectively, Ricardo's 1% rule
corresponds to:

1
(9)
'
The
result that differences
in
integrated capital—labour ratios
is
what matters
has
also been shown
in the
circulating capital model
by
Parys (1982).
2
Samuelson (1983) gives
an
alternative proof of this result and calls
it the key
theorem.
3
One should note that
in
our calculations depreciation coefficients
dy
are fixed,
i.e.
independent
of
r,
so
that
the problem of existence of a standard commodity,
put
forward
by
Samuelson (1983),
has
been avoided.
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Production prices and labour values
201
The expressions we have derived so far contain the coefficients given in physical terms,
while the actual data are denominated
in
current prices.
It
is well known that when
proceeding from actual inputoutput data one can only derive ratios of value prices and
production prices to actual prices'
e.g.
v
t
vjVX
.
= 1,. . .,n
and
ft
=
p^PX
From (10) and (11) the deviation
of
production prices from value prices can
be
determined:
p° _p°!P°X
1
'•••'"
(12)
v,
The last expression will be used to test Ricardo's 1% rule (see 9) when the numeraire is
total output. In the same manner one can obtain production pricevalue price deviations
when the standard commodity X* is used as the numeraire:
P°IP°X*
._
vjVX*
''
1
'""
(13)
Since deviations of production prices from value prices are affected by the choice of unit
of measurement, we need to obtain relative prices for different numeraires. This can be
done by combining the results we have already obtained, that is (10) and (11):
P°IP°X IP?IP°X
=P
?/p°
.
= i
vjVXl vjVX »>,'' '""" (
14
)
Expression (14) gives these deviations taking the first commodity as numeraire; the same
procedure can be applied when other commodities are taken as numeraires.
As has been pointed out, it is possible to derive various price ratios (1014), but not the
relative prices themselves, for example
V^VJVXOT
p°=p
IP°X,
i
= 1,.. .,n. A possible
way to get rid of price ratios is to obtain seaors' outputs evaluated in terms of an appropri
ate price system. For production prices the procedure is as follows:
P°X
=
Ip,x,
=
1.
(15)
In the same manner one can obtain t),x,,p™x
(
and so on, for all other types of prices. An
alternative expression for (6) can now be derived (see also Shaikh, 1984).
r P°h
tXl
ft
o
v
f
f
*/
* +—;—
Pi
x
i \ tO A
t
X
P°X
( r
P°HX\
V
to AX ) (16)
1
Cf. Kyn ei al. 1970; Fink 1981. The result can be provided for our model as well.
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202 P. Petrovifi
Setting P°X
= 1
and VX=
1
it is possible to obtain
a
loglinear relation between output
across sectors evaluated at production and value prices:
lnp°x,
=
lnf.x,
—
lnz, (17)
where
z,
=
r P°HX
1
+
w
AX
The data used are from the Yugoslav economy
in
1976 and 1978, and 47 sectors are
considered.
1
2.
Deviations of relative prices from labour—value ratios
The empirical results obtained enable
us
to assess the extent
of
discrepancies between
various relative prices and labourvalue
ratios.
To that end
we
use the rootmeansquare
percenterror (RMS%E)
2
as well as Ricardo's l°
/0
rule. As the deviations change with
the numeraire,
we
shall first review empirical results when total output
is
taken as the unit
of measurement [VX
=
P°X=
1],
and afterwards those for others numeraires.
Value
of
total output
as a
numeraire
Deviations between relative prices and labourvalue ratios measured
by
the RMS°
o
Es are
given in Table
1.
Table 1.
P>
p
Oi
lv p
02
lv
p/v
p
L
lv
p
l
/v
p
l
lp°
•„,,
=
2403
r,
=
0694v,
3853
4610 747 369
•„,
=
2856
r, =
0873v,
4046
4415 868 445
The distance between production prices and value prices increases with increases in the
profit rate: RMS°
O
E approximately doubles when the profit rate is doubled. Thus devi
ations increase considerably when the profit rate moves from its actual values (41 and
1
An explanation of the data used as well as the empirical results that are not reported are available to readers
on request.
1
A suitable measure
of
distance between
two
vector
of
prices
is
rootmeansquarepercenterror
(RMS°
0
E). When production and value prices are considered, it is equal to:
1976
RMS%
1978
RMS%
E
E
r = 410%
608%
r = 519%
662%
r= 1007
1483
r=1007
1266
r=1503
2224
r= 1504
1877
where
s
denotes the standard of value. In order to calculate it one needs only price ratios [(p°/u),] and that is all
that can be empirically determined. For definitions of various measures see Pindyck and Rubinfeld (1983, pp.
362365).
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Production prices and labour values
203
519%)
to 10% and
15%,
and
particularly when
it
reaches maximum values
(2403%
and 2856%). RMS%Es (3853
and
4046)
are
then about
six
times larger than those
corresponding to production pricevalue price deviations (608 and 662%).
Prices with different profit rates across sectors (P
1
) exhibit somewhat larger deviations
from value prices than production prices do, and are quite close to production prices.
Prices proportional to direct labour coefficients (P
1
) are calculated
to
see whether they
are
a
good approximation
for
value prices and,
via
them,
for
other
prices,
especially actual
ones.
It
turns
out
that these prices exhibit
the
largest deviations from value prices, so
it
would be misleading
to
use labour coefficients
in
order
to
estimate value
or
actual prices
(see Table 2).
Comparisons
of the
results between
the two
years show that
the
discrepancies from
value prices, taking into account equal profit rates, are somewhat smaller
in
1978 than
in
1976.
Deviations of various types of calculated prices from actual prices can
be
assessed by the
values of RMS%E given
in
Table
2.
Table 2.
1976
1978
RMS%E
v\p°
1184%
11 80
P°
11
11
If
•11
•01
P
O1
/P°
1446
1287
P
02
19
16
If
67
53
P"
34
36
If
•80
•45
f
10
10
If
•66
15
P
L
lf
4881
4774
The smallest deviations occur
for
production prices calculated
on the
basis
of
profit
rates across sectors varying
with
longrun growth
rates,
followed
by
production prices and
value prices, although
all
three stand
at
almost
the
same distance from actual prices.
On
the other hand, prices proportional
to
labour coefficients deviate
the
most from actual
prices, a result we have already commented
on.
Let
us
now examine more closely production pricevalue price deviations by applying
Ricardo's
1%
rule. This states that
a 1%
change
in
profit rate will cause
a
change
in
relative prices
of at
most
1%. In the
same manner
we
could speak
of
a
2%
rule when
relative prices change by up to
2%.
By
applying equation
(9)
across sectors
it
is
possible
to
discover
the
number
of
sectors
in
which
the
deviations
of
production prices from value
prices is less than the profit rate
(or
twice the profit
rate).
Results are given in Table 3.
Table 3.
1976
Number of sectors
°
0
of total number
°
0
share in total output
1978
Number of sectors
°o of total number
%
share in total output
l%rule
<M1%
32
681%
724%
052%
32
681%
708%
2%
rule
082%
42
894
933
0104%
44
936
973
Others
over 82%
5
106
67
over 104%
3
64
27
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204 P. Petrovi*
In both years, 32 sectors, with a share in total output that exceeds 70%, satisfy the 1%
rule.
On the other hand, only five sectors in 1976 and three in 1978 with shares in total
output equal to 67 and 27% do not satisfy the 2% rule. Thus this evidence supports the
2%
rule, although most of the sectors satisfy the 1% rule as well. Comparisons done
between value prices and production prices with profit rates of
10
and 15% (P
01
and P
02
)
also confirm the 2% rule, because only five to six sectors in
1976
and three to four in 1978
do not satisfy it.
The extremes of production pricevalue price deviations are
1 2080
(38.
Water supply)
and 09382 (47. Other productive services) in 1976, while in 1978 they are
12396
(1.
Electricity) and 09312
(47.
Other productive services).
The
effects
of
change
in the numeraire
Let us
see
now whether changes in units of measurement considerably affect production
pricevalue price deviations. To this end, the outputs of each of
47
sectors is used as a
numeraire. Again RMS%E
(
, i= 1,.. .,47, (that is, one for each numeraire), is used to
measure the
deviations.
The values obtained for RMS%E, vary from 569%
(33.
Tobacco
production) to 1644% (38. Water supply) in 1976, and from 608% (31. Beverages) to
1826%
(1.
Electricity) in 1978. For more than 2/3 of numeraires, the values of RMS%E
(
are larger than those previously obtained with total output as numeraire (6 08% and
662%). It follows that the choice of numeraire can significantly change the extent of the
deviations
we
are analysing.
Deviation of production from value prices for a given commodity consist both of a
change in its price and a variation in the unit of measurement. So it is not surprising that
greater discrepancies are obtained when, for example, the price of electricity is used as
numeraire, for that price exhibits large variations. It is, therefore, tempting to look for a
numeraire whose value, denominated in production and value prices, will be unchanged,
that is for an 'invariable standard of
value'.
The observed deviations could then be attri
buted solely to commodities whose prices
we
are analysing, and not to
a
change of unit of
measurement. The standard commodity has already been denned [see eqn (8)] for the
model
we
are using, so it can now be employed as the unit of measurement.
1
Correspond
ing ratios between relative prices:
p°lP°X*
and
vJVX*
are obtained and the results are
summarised in Table 4.
As one can see, the discrepancies between production and value prices have hardly
changed when the standard commodity, rather than total output, has been used as
numeraire. The
two sets
of results are almost the same in
1976,
while in
1978
deviations are
somewhat larger when the standard commodity is taken as the numeraire. Anyhow, the
2%
rule
is
still valid. Let us note that
the
similarity of the results obtained in the two cases
does not stem from the closeness of the two composite commodities—X and X*, respect
ively used
as
the numeraires. The deviations between them, measured by RMS%E,
2
are
equal to
20197%
in 1976 and to 19669% in 1978.
The
use
of
a
standard commodity
as
numeraire gave us
a
variation in the exchange ratio
between a given commodity and the standard one caused by the switch from value to
1
This is the procedure that Pasinetti (1977, p. 18) suggests. _
2
As a matter of fact one can obtain only the composite commodities denominated in some prices, e.g. X* =
P,X*. But, by employing RMS%E, we can eliminate prices:
and obtain deviations between the composite commodities themselves.
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Production prices and labour values 205
Table 4.
1976
Number of sectors
% of total number
% share in total output
1978
Number of sectors
% of total number
% share in total output
RMS%E
l%mle
32
681%
726%
30
638%
696%
1976
600%
2%
rule
42
894
933
42
89 3
943
Others
5
106
67
5
107
57
1978
725%
production prices. But in an actual economy, various commodities exchange for each
other and not for a standard commodity. The relevant question is, therefore, how all
exchange ratios between commodities (that is relative prices) are affected by the change
from value to production prices.
Investigating this is straightforward in a twocommodity case (see Barkai, 1967), but it
becomes cumbersome in the 47 sector case since instead of
one,
we now have to consider
1081 relative prices,
1
and of course the same number of deviations. We already obtained
these deviations when each of the 47 commodities was used as numeraire but now we have
to remove some in order to avoid repetitions. Having done that, all 1081 deviations are
used to calculate RMS%E and are distributed into groups satisfying the
1
% rule, 2% rule
and others. The values obtained for RMS%E are 782% in 1976 and 813% in
1978,
while
the distribution is given in Table 5.
Table 5.
Percentage
of total
number
of relative
prices
l%rule
2% rule Others
1976 4940 7697 2303
1978 5254 8326 1674
Thus about half the total number of relative prices have changed by up to
1
% when the
profit rate changes by
1
%, while approximately 4/5 of relative prices satisfy the 2% rule.
Compared with the cases where total output and a standard commodity are, respectively,
the units of measurement, we have now obtained somewhat larger deviations, although
the evidence still supports the 2% rule.
' This is the number of pairwise combinations of 47 elements without repetitions
47
47x46
2
' 1x2
•= 1081.
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206 P. Petrovi6
The distance between production and value prices also depends on the actual rate of
profit. For the Yugoslav economy in the two years under consideration the profit rate on
gross stock of capital was
41
% and 52%, about onesixth of the corresponding maximal
rates
(2403%
and 2856%). These rates, together with the 2% rule, result in the '90%
labour theory of value'.
Generality of the results obtained
These empirical results relate to one economy in two separate years, so the question of
their general relevance may be posed. It has been shown [see eqn (6)] that the deviations
depend on differences in integrated capital labour ratios and on the profit rate. One
should therefore check if these parameters in the Yugoslav economy are typical for other
economies as well.
Differences in capital labour ratios across sectors can be measured by the coefficient of
variation, and the results for the Yugoslav and US economies are given in Table 6.
Table 6.
Coefficients
of variation
Capitallabour ratios
Integrated Direct
Yugoslavia
1976 4277% 971
1978
4071%
9569
US"
60% 114
'Leontiefs data, Shaikh, 1984, p. 75.
It should be noted first that for Yugoslavia variations decrease slightly between 1976
and
1978;
this result is in accordance with the one previously obtained which showed price
deviations also decreased. On the other hand, comparison of the coefficients for these two
economies shows that variations of direct capitallabour ratios are not very different, so
that Yugoslav data can be taken as representative. Further, variation in integrated capital
labour ratios is about half that of direct capitallabour ratios. Thus it is not possible to
deduce from large variations in capitallabour ratios that deviations of relative prices from
relative labourvalues will be large since integrated ratios are what matter. This also
explains why larger deviauons were expected from the twocommodity hypothetical
model (Barkai, 1967) since there the difference between direct capitallabour ratios is
considered instead of the difference between integrated ones. Profit rates in Yugoslavia
also appear representative.
1
Alternative estimates
Shaikh (1984) provided estimates of actual pricevalue price deviations in the US
economy and used Marzi's and Varri's results, which referred to the Italian economy, to
i
Profit rates may
be
estimated
via
real interest
rates;
see Barkai (1967,p.423)and Carter
(1970,
p.
154)
who
give estimates for the UK and US economies while Krelle (1977, p. 306, fig. 9) provides data on West
Germany.
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Production prices and labour values 207
analyse production pricevalue price deviations. In order to measure the distance between
the two sets of relative prices both the average absolute percentage deviation and the
correlation coefficient were employed. The former measure (which is similar to the
RMS°
0
E that we used) varied around 20%, where from it was concluded that the devi
ations are moderate (see Shaikh,
1984,
p.
78). However, Shaikh's analysis heavily relied on
the second measure, that is the correlation. The rationale put forward for this procedure is
that the variation in prices of production, and therefore in actual prices, is dominated by
variations in value prices, and that a high correlation between them can express this
formally.
1
Although our empirical results do support those obtained by Shaikh, it turns
out that his suggested procedure is inappropriate.
It can be shown that, owing to the data denominated in current prices, one can only
obtain price ratios between calculated and actual prices: p.
jp".,
vjp' and so on. Of course,
the correlation between these two sets of price ratios does not represent the correlation
between value and production prices. One should eliminate actual prices and a possible
procedure, previously explained (15), results in a loglinear relation (17) between
sectors' outputs evaluated in production (p°x,) and value prices
(v,x,).
That relation can
now be used for empirical estimation.
Shaikh (1984) used it to estimate the relation between actual prices and value prices in
the US economy in 1947 (192 sectors) and in 1963 (83 sectors) and obtained very high
correlation (R
2
) of
9581
% and
9483%.
Corresponding results for the Yugoslav economy
in 1976 and 1978 were 9866% and 9896%.
2
This relation could be estimated using production prices, and also prices with maximal
profit rate, instead of actual prices; the corresponding coefficients of determination for the
Yugoslav economy are given in Table 7.
These coefficients indicate the presence of a high correlation both in the case of produc
tion and value prices, and in the case of prices with maximal profit rate and value prices.
As,
according to Shaikh (1984, p. 71), prices with maximal profit rate 'bear no relation to
labour times', that is to value prices, it follows that the procedure which suggests a high
correlation between them tells us very little.
Let us add that Wolf (1979, p. 335) reported, as a subsidiary result, the coefficients of
determination (R
2
) between the production and value prices for the US economy. The
' Shaikh, 1984,
p.
64. Our value price corresponds to Shaikh's direct
price;
he often uses the term value for
direct price.
3
Shaikh's estimates for the US economy are:
1947 lnp'x, =  000095 + 096809 In
v
i
x
l
(00895) (64625)
K
2
=95
81%;
1963
In
p'xi =  00138 + 099078 In
v
l
x
i
(094715) (38 08)
R
2
= 9489%;
Note: t ratios are in brackets.
The estimates for the Yugoslav economy
we
have obtained, are:
1976 ln/>'x, =  016727 + 095446
In
v
l
x
i
(57626)
R
2
= 9866%;
1978
In
p'x, =  003988 + 096287 In v,x,
(65597)
R
1
= 9896%.
The correlation is very high in both economies, and the estimates of the slope, which are significantly
different from
zero,
are
almost equal
to
each other. Let us note that somewhat different normalisation rule has
been applied by Shaikh,
i.e.
(l/n)Eu,x,=
1
compared with ours Ii/pr, =
1.
See also
Shaikh
(1984,
p.
84).
But the
difference affects neither correlation nor estimate of the slope in the simple regression; only the intercept will
change.
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208 P. Petrovifc
Table
7.
Coefficients
of
determination
(R
2
)
Inp x, lnp
1976
\nv,x,
9978%
9319
1978
lnt;,jc,
9978 9395
values are 097,093,092 and
091
in 1947,1958,1963 and 1967, respectively. These high
R
2
values led him to conclude that the two sets of prices were empirically close to each
other.
1
However, the same criticism mentioned above would also apply to this case.
3.
Aggregate effects of discrepancies between production prices and labour
value ratios
The relevant aggregates to compare are total surplus value and total profit, where the
former belongs to the value regime and the latter to the production price regime. As is well
known, Marx stated that the origin of profit is surplus value, that is, unpaid labour, and
that profit is merely redistributed surplus value. It has, however, been shown that, while
keeping total value of output unchanged (that is VX
—
P
f>
X= 1), the sum of profits differs
from the total surplus value. This, of
course,
brings into question Marx's explanation of
the origin of profit. By comparing these aggregates, we can see whether Marx's prop
osition survives at an empirical level.
2
The calculated price ratios enable us to determine
total profit and total surplus value evaluated at the corresponding prices, and the ratios
between latter and the former are:
1976:1036; 1978: 1055.
As one can see, these deviations are quite small.
The second wellknown objection to Marx's value analysis refers to his determination
of the average profit rate as the ratio between total surplus value and capital denominated
in value prices, instead of the ratio between total profit and capital denominated in pro
duction prices (r). As can now be expected, the empirical deviations, given in Table 8, are
very small:
Table 8.
Marx's
r
Their ratio
1976 42% 41 1024
1978 53% 519 1033
Wolf provides estimates of these two profit rates for the US economy. The ratios of these
rates for 1947, 1958,1963 and 1967 are 1115, 1195, 1204 and 1203, respectively
(Wolf,
1
Wolf made extensive calculations of production and value prices in the US economy in order to obtain
various aggregates and ratios. However, since these were of secondary interest to him, he did not report the
results on prices. Also, regressors were not explained, although they seem to be deviations of calculated prices
from actual ones.
2
In the sense that Stigler (1958) put it for Ricardo's theory of value.
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Production prices and labour values 209
1979,
p. 335, Table 2). The ratios obtained are somewhat higher than ours but still
indicate moderate discrepancies.
By employing an indirect procedure in relation to the US economy Shaikh has esti
mated that the ratio between surplus value and actual profit is equal to 1064 and the
ratio between Marx's profit rate and actual rate is 107 (Shaikh, 1984, pp. 57 and 58).
The indirect procedure employed assumes, among other things, a circulating capital
model. Shaikh suggested that the inclusion of fixed capital would reduce these
deviations.
The values of most of other aggregates are also hardly affected by the deviations of
production prices from value prices. For example, the value of the consumption basket
denominated in prices with maximal profit rate (P"c) and value prices (Vc), while
VX=P
m
X=
1,
will differ by 99% in 1976 and 64% in 1978.
Conclusions
Contrary to what might be expected from indirect evidence and twocommodity hypo
thetical examples, the evidence we have provided supports Ricardo's empirical prop
osition that relative production prices are mainly determined by labourvalue
ratios.
The
results obtained indicate that a
1 %
change in profit rate will cause most relative prices to
change by less than 2%, while half of them will change by less than 1%. As actual profit
rates are of
the
order of
5%,
we end up with
a
'90% labour theory of value'. Let me stress
that these results are independent of the choice of numeraire commodity, for we have
considered the changes in all possible exchange ratios: 1081 in the 47sector model.
Certainly when various numeraire commodities are used the deviations observed have
varied. They are somewhat smaller when total output and a standard commodity are
used as numeraire commodites. These two composite commodites produce quite similar
results concerning deviations.
The evidence refers
to
an actual economy but the variations in integrated capitallabour
ratios and in the profit rate—the factors that determine the deviations considered—turn
out to be of the same order of magnitude as in other economies. The results obtained
therefore have general significance.
Our findings contradict those implied by other empirical evidence that stresses vari
ations in capitallabour ratios. Large observed or expected variations in these ratios are
put forward as an argument for expecting huge relative pricelabour value deviations.
But, as has been shown in this paper, widely differing capitallabour ratios do not signifi
cantly affect the deviations we are analysing. This is partly because integrated capital
labour ratios are what matter and these ratios are less variable than direct capitallabour
ratios.
We have also
seen that an increase
in
the profit rate substantially increases the deviations
considered between production prices and value prices so that, contrary to what stems
from the procedure that employs correlation for the measure of deviations (Shaikh 1984,
Wolf 1979), discrepancies between labourvalue ratios and production prices with
maximal profit rate are large.
The aggregate effects of the deviations between production prices and labour—value
ratios are small,
so
one can accept as empirically valid Marx's proposition that the sum of
profits is equal to total surplus value.
An important implication of the small deviation obtained between relative prices and
labour values is that the price effect on the wage—profit curve will be insignificant, and the
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210 P.Petrovifc
curve will
be
close
to a
straight line. Corresponding empirical evidence
on the
shape
of
wageprofit curve
is,
however, beyond the scope of
this
paper.
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