The labour theory of value and the prices in China: methodology and analysis.
Everlam Elias Montibeler (Universidade Federal de Mato Grosso Do Sul), César Sánchez (Universidad
Nacional Autónoma de México, Universidad Complutense de Madrid).
Resumo
Este trabalho examina a relação entre valores e preços para China. Utilizando as matrizes insumo-produto
chinesas de 2002 e a metodologia desenvolvida por Shaikh (1984) são estimados os diferentes tipos de
preços. Concluiu-se em primeiro lugar, e em linha com o que foi obtido em outros estudos, a existência de
desvios, inferiores a 20%, entre os diferentes tipos de preços. Em segundo lugar, e em consonância com
resultados de trabalhos similares, se detectou que o requerimento de trabalho, comparado com os
requerimentos (aço, petróleo, etc.) são os que melhores explicam a determinação de preços. Propõe-se
uma metodologia para ponderar o tamanho do sector na análise de regressão. Este teste determinou que os
preços são proporcionais ao valor. Além disso, analisamos se uma má especificação possível pode causar
um viés considerável no impacto de valores para os preços do mercado. Nosso estudo mostra que esse
viés é de pouca importância. Finalmente, foi estimado os valores médios da taxa de lucro, mais-valia e
composição orgânica. É interessante notar que os níveis das taxas de lucro na China são maiores que as
apresentadas em estudo similar para outros países (Estados Unidos, Grécia, Espanha).
Abstract
This paper examines the relationship between values and prices in China. From the information of inputoutput table from 2002 and using Shaikh`s methodology (1984) are counted the different types of prices.
We concluded first and in line with what was obtained in other studies, a distance between the different
types of prices, less than 20%. Secondly, and briefly reviewing some criticisms of these kind of studies, it
appears that labor requirements confronted with the requirements of steel, oil, etc., are the ones that
explain better market prices. Is proposed a way to weight the size of the sector in the regression analysis.
This test determines that prices proportional to the value. In addition, we analyze whether a possible
misspecification may cause a considerable bias in the impact of values to market prices. Our study shows
that this bias is of little importance. Finally, we estimate the average values of the rate of profit, capital
gain rate and organic composition. It is interesting to note that profit rate levels in China are higher than
those shown in other studies for other countries (United States, Greece, Spain).
KEY WORDS: China Economy, Prices Deviation, Labor Theory of Value.
JEL: B41, B50, P16
1. Introduction
In the classics there is developed the idea that prices of commodities are determined by the amount of
work (Meek, 1980). This idea is taking a gradual approach. Since Smith we have the notions of labor
commanded and, on the other side, the efforts, that involves producing goods. Ricardo is more accurate
and develops the idea that the value of a commodity is determined by the direct and indirect labor
incorporated in it. Marx theory not only develops the idea of Ricardo but includes the total labor (direct
and indirect) as social labor and work not only as the direct producer labor. In addition, Marx integrates
his value-labor theory (LTV, hereafter), his theory of the surplus value, absent in the understanding of
Ricardo (Carcanholo, 2002).
Since the eighties, the idea of calculating empirical values has emerged from the proposal of Shaikh
(1984). The author uses for the U.S. the input-output framework and Leontief data to estimate values and
direct and indirect labor requirements. These total requirements, standardized and expressed in money are
called direct prices, and also calculated Sraffian production prices and regression analysis and of distance
measures between the different prices, finding in general, values that approached quite well at current
prices (market). Ochoa (1984, 1989) again for U.S. and based on Shaikh methodology, calculates values,
direct prices, marxist production prices and sraffianos production prices using input-output tables (IOT,
hereafter) for several years, including measures of fixed capital in the estimations. Chilcote (1997)
updates the IOT for more recent years and OECD countries, in addition to examining the so-called
"alternative values” (inputs other than labor which for some authors could also be explanatory such as
labor). Chilcote deepens as Ochoa in various ways of calculating the production prices gradually adding
different aspects: fixed capital, capital turnover, capacity utilization, etc. In this way producer prices are
conceptually closer to market prices. Both authors use different measures of distance, and conclude that
direct prices are quite close to production prices and even more to market prices. Cockshott y Cotrell
(1994), with IOT information from United Kingdom, consider the different kinds of prices and confirm
that the base values as electricity, petroleum, chemistry and agriculture do not explain better the current
prices than the estimated by labor. Guerrero (2000) following Chilcote, applies the methodology for
Spain finding that direct prices are closer to production ones if incorporating to the calculation fixed
capital, turnover etc. Guerrero also makes a thorough theoretical analysis of the calculated and developed
categories in this kind of studies and confirms that vertically integrates value capital compositions
explain almost totally deviations between direct prices and production ones, idea theorized by Marx in
volume III. On the other hand Tsoulfidis and Manitis (T&M hereafter) have applied this same
methodology to Greece with information from IOT from 1970. Tsoulfidis along with other authors has
extended this type of study to Korea, Japan, Canada and China. In the case of China, the central
difference in our study with that of Mariolis and Tsoulfidis (2009, with IOT from 1997 with 38 sectors) is
that incorporates data about fixed capital stock.
The structure of the research is as follows. After the introduction in the second section we will describe
the data and methodology used in this research. First, sources, data and adjustments made (2.1) and, right
away, the mathematical formalization and details of the determination of the different prices (2.2). In the
third section the empirical results are displayed, showing the different distance indicators among direct
prices, production prices, sraffianos ones and market ones (3.1). Immediately after comparing our results
of China to the proximity between prices found in the U.S., Greece and Spain. We will find very similar
results which reinforces the notion that current prices gravitate around the values raised by the LTV (3.2).
The fourth section addresses some specific replicas of LTV. Particularly that which suggests that human
labor is not the only one to explain the current prices as other prices aroused from requirements of
electricity and steel could supply the role of LTV (4.1). Another criticism that emerged recently in this
kind of work argues that the sector size can create a false correlation in regressions between values and
prices (4.2). In this section is shown how to create and incorporate a rank variable with vector size in
regression analysis does not become statistically significant values to explain current prices. On the other
hand, has also been raised that the regressions used may involve a bias in the estimates calculated, since
they omit the impact of vertically integrated compositions in the Shaikh prices model (4.3). It will be
exemplified empirically that this bias is minor in nature, since the explanatory variables of this model
imply a weak covariance. In the fifth section will appear under the different prices, levels of the key
variables in China: profit rate, rate of surplus value and composition of capital. Finally some conclusions
will be drawn.
2. Data and methodology
2.1 Sources and limits of statistics.
IOT for China are available for the period 1987-2005. These Tables are not published for every year,
although it certainly has been increasing the level of disaggregation in which they are presented.
Choosing to work with the Table of 2002 has been for several reasons: because it is a stable year in the
growth of China, because the data are deeply analyzed by other authors such as Holz (2006) and because
it will serve to better compare the results with other papers on deviations between prices (Greece and
Spain).
Most of the literature estimated the prices and productivity of China's economy has encountered problems
getting a reliable source for estimating capital stock. Beyond the statistical problems on the capital stock
we also had to face the problem of information on the labor force employed by each production sector.
This is because the China official statistical department publishes a very little detailed methodology and
unclear about how they are distributed and paid workers in the countryside and the city. Much of this
research was to estimate the statistics on labor and capital stock in China. For data on capital stock and
labor, were used the outstanding papers of the econometrist Gregory C. Chow (1993, 2002, 2006) as well
as Carsten A. Holz´s (2006) who made pioneering estimates of the amounts of capital stock in China. The
IOT were obtained from the National Bureau of Statistics China (NBSC).
2.2. Methodology for calculating the different prices
Labor values are calculated according to expression one:
  ao ( I  A  D) 1
(1)
Where A is the technical coefficients matrix (39 sectors)1 and D depreciation coefficients matrix, I
identity matrix and ao row vector of labor requirements2. Let`s explain how we can obtain ao. Labor
requirements represent direct labor required per production unit for j sector. However, the meaning of this
concept is still more complicated, as far as it includes reducing the concrete to abstract labor3. This,
theoretically, should be done weighing in some way the preparation of the workforce (in study years,
experience…), but due to the lack of this information, for now, we are forced to “reduce it” by wages
rates. Thus, the abstract labor (Tai) is the product of three components: the number of workers per sector
(Tci), the annual working hours on (ii) and the relative salary rate (zi); more specifically, this last measure
is the ratio of average salaries for each sector among the lowest ones, which are agricultural.
Tai  Tci  ii  z i
(2)
For the calculation of (1) should be obtained before:
a 0  Ta  pb 
Therefore:
1
A  T  pb  1
Where Tci and Tai are row vectors and T transactions matrix, A technical coefficients matrix, divided by
the gross production column vector invested and diagonalized (pb). Similarly, obtaining the depreciation
of fixed capital matrix, D, can be done as followed:
D  K  IL 
(3)
Depreciation matrix is the result of multiplying capital requirements square matrix (K) to produce one
unit of i for j sector, for the inverse of average life of capital goods column vector (IL) diagonalized. This
average was obtained following Holz estimation, Holz (2006: 162).
On the other side,
K  f ky
T
fj 
(4) and
1
 fbcfi
 fbcfi
(5)
Matrix (K) is the product of gross fixed capital formation participations row vector (f) y ratio
capital/sector product row vector (ky). Following this argumentation the estimation of direct and indirect
labor (values) from prices matrix and no quantities ones end in [λ*i], this is, the quantity of total labor the
monetary unit of sector i.
Normalizing by the equation (6):  
U T pb
 pb
This is, assuming that: U T pb   pb (7)
Where U is a unit column vector and therefore (UT pb) represents the sum of sales at sectors market
prices. Then, direct prices are:
d= λ ·α
(8)
Production prices are defined following:
p  p( A  D  B)  rp ( K  A  B)
(9)
Where p is production prices row vector, B salary goods requirements for workers square matrix and r
profit rate. We can rename and simplify the equation (9).
p  p( N )  rp ( M ) ,
where:
N  A D B ; M  A  K  B

H   A  K  B  ( I  A  B  D) 1

H  M I  N 
1


Thus, the preceding eigenvalue equation defines the relation:
 p  p H  
1
p  p H 
r
(10)
Following Perron-Frobenius we know the highest eigenvalue establishes the highest profit rate R (this is
R=r) and the associates left eigenvector of H, prices production without normalization, p*. As the former
U T Pb
case, we normalize using (11),  
and obtain price production normalized:
p * Pb
p   p*
(12)
Where p is marxist production prices row vector. We should highlight the two different ways of obtaining
B, following Chilcote (1997) and Guerrero (2000) or T&M (2002). If S and C are defined as salary
column vector and consume one both obtained by IOT. We can define:
UT S
x T
(13)
U C
Where x is, clearly, the proportion of consumption that is spent as salary. Then, we can define (14),
c  x C as row vector expressing consumption of salary goods for each sector. If we also define the
weight of employment in each sector as the following column vector (15), tcw  Tc  U T Tc  1 , this
weighting can be used for (16), E  c (Tcw) T , this is the consumption square matrix in salary goods. The
last step is, as in the case of, A, D and K, expressing it in terms of gross production unit production:
B  E  pb  1
(17)
Sraffian prices can be obtained: s  sB  sD  (1  rs )sA
(18)
This, like Marxist production prices, is an eigenvalue equation, where:
1

 s*  s * H     1 s*  s * H s 
 
(19)
In which H s  A ( I  D  B) 1 . Similarly, we must normalize but now with (20),  
s   s*
U T pb
, thus:
s * pb
(21)
Where s is Sraffian prices row vector.
3. Empirical results
It is often mistaken empirical studies as mere statistical cumulus devoid of theory. However, in scientific
practice not all theoretical attempted is a scientific study and the same goes for empirical studies if they
are not supported by a theoretical model to contrast. The central hypothesis of these studies is to verify
the assertion that the values movements are determining prices movements. The methodology to get the
various prices involves the use of categories and concepts of the LTV that, due to its complexity in some
cases, are necessarily simplified in order to be estimated (vrg, reduction from complex to simple labor).
This type of study attempts to contrast a hypothesis as above within the broad LTV and under a very
specific model like Shaikh prices model (detailed in section 4.2). This is the context of empirical support
in this study.
3.1. The close proximity between values and prices in China, 2002
Next, in table (1), we present the distance measures that are usually shown in the literature. The Mean
Absolute Weighted Deviation (MAWD) between direct and market prices is 14.19%, while the distance
between direct and production ones is just 9.07%. The proximity between production and Sraffian prices
and market ones is even higher, 16.55% y 18.13% respectively. This is valid for the others distance
indexes, Mean Absolute Deviation (MAD), Normalized Vector Distance (NVD) and even with indexes:
“d”, Variation Coefficient, CV y θ proposed by Steedman & Tomkins (1998), who suggest to use these
parameters (d, CV, θ) because they are independent of numeraire. As shown, these measures do not alter
the previous conclusions, direct prices and production are closer to market prices. It is interesting to note
that in China there is a greater proximity between (d,p) regarding (d,m), comparing with other studies
such as Ochoa`s (1989) for United States and Cockshott & Cotrell (1998) for United Kingdom4.
{Insert Table 1. Here}
Guerrero (2000) points out that in deviations among prices there is a in which, whether they are
calculated by the method that uses only circulate capital such as the one that adds capital stock, the results
are not very different. In exchange for profit estimates, it is observed a significant difference. Also, when
it comes to measuring the deviations between p, m and d, the initial hypothesis is that deviations between
p and m are greater, and this can be found for the case of China in this paper (see Table 1) as well as in
Tsoulfides and Marioles (2009). In the same way, the regression analysis (Table 2) between prices shows
the following order of determination: the direct price growth determines the movement of production
ones (98%) and the latter determine the market prices (95%). However, prices proportional to the value
determine the movement of market prices very significantly (96%). This is confirmed statistically by the
greater robustness of the t calculated for the elasticity of models and for the joint explanation with F-test
– note the greater robustness (d,p) and (d,m), in that order. Sraffian prices explain satisfactory market
prices; however, production prices and direct ones do better from the Marxist perspective.
{Insert Table 2. Here}
{Insert Figure 1. Here}
Figure 1 shows the dispersion of the different prices expressed in neperian logarithms, related to direct
prices (45º line). Each point represents a sector of the 39 used in China's TIO. It is slightly more dispersed
the cluster of points of market prices than production prices. But in general there is a good fit for different
prices. This means, in other words, the labor time direct plus indirect, expressed in money, is a useful
variable to explain to the production prices (Marxist and Sraffian) and market prices.
3.2. International Comparison: China, USA, Greece and Spain
Given the empirical research in recent years can make international comparisons of the distances between
these types of prices. With this purpose we will use data from 1970 from Greece (T&M 2002) and USA
(Ochoa 1989) for comparison with our results for 2002 for China and 2000 for Spain. In a general way
can be seen in the Table 3 that although there is a time lag between the countries compared, deviations in
the indices used do not exceed 26%, meaning, that for Marxist prices theory, the determination values →
direct prices → production prices → market prices, is a valid general scheme to explain the prices system
in modern economies (Table 3).
{Insert Table 3. Here}
4. Some critics to the LTV.
If empirical support based on a theory and a specific model requires continuously analyze the relationship
between theory, categories and results, it is normal and necessary that contrast methods are also
continually reviewed (such as usually happens in natural sciences). Regression analysis and correlation
between prices have been the place of criticism of several authors. Without attempting to analyze all these
criticisms, we will briefly discuss some of them.
4.1 Comparing the labor values with other base values
Smith (1965: 47), Ricardo (1954: 22) and Marx (1990: 129) argued that the relative prices of
commodities are determined by the time of labor employed in production. In particular, for Marx, the
only value-creating factor is expressed as price is human labor. But the view that the labor value theory
determines the prices, is and has been persistently attacked because drives into analyzing capitalism on
the exploitation between social classes. Such critics argue that prices of goods could be measured by other
variables that refer to other theories of value, for example, wheat, steel, energy, etc. (see Guerrero 1997:
61-66). In this direction, Roemer (1981) and Hogdson (1982) suggest that the LTV would not be formally
the only theory that could explain the prices. However, these approaches miss a crucial question: What is
the only factor of production that is present in every processes of direct and indirect production of all
commodities?
{Insert Table 4. Here}
In Table 4 the DAMP between direct prices estimated from the different productive factors is presented
in ascending order of deviation, so between the LTV direct prices and market prices, the minimum
deviation found is 15.13%. The maximum deviation is established when using the farm inputs vector
(333.45%). On the other hand, in correlation of the direct prices of each "sector and alternative value" and
market prices we have that it is stronger with job requirements than with any other alternative productive
factor. The same findings throw the robustness of the t of the estimates of labor requirements and the joint
F-test. It should be noted that although estimates of alternative theories of value are statistically different
from zero, most robust estimator is the labor one an elasticity of 0.977 and greater individual significance
(33.55).
4.2. The relationship between prices and the size of each sector.
Might be expected that there is a necessary partnership between sectorial prices analyzed. Then, direct
prices and production ones would be correlated simply because small production sectors have small
prices d and p and sectors with higher production would have d and p prices proportional to the size. If
true, then the correlations obtained in regression analysis could hide a spurious component by the size of
sector, vgr. Kliman (2002) and Díaz and Osuna (2009). This is a second critique of the LTV. To advance
an answer, we must remember that in econometrics temporal series, it is customary to monitor the effect
of the trend in the regression between two variables as in model (I). Then, if both series grow over time, it
is possible to isolate this component by incorporating a trend variable (t) as in model (II), of this way it
would be proves the relationship between Y and X excluding the underlying trend (as in well know
keynesian regression of consumption function explained by income). Returning to this idea, is similarly
possible in the cross-sectional analysis (III, between p and d, vgr.), approach to create a variable that
identifies the order of sectors sizes. This rank (R), orders each sector from lowest to highest according to
their level of production and incorporates it shaping the cross-sectional model (IV).
Yt= ˆ 1+ ˆ 2 X2t + ut
(I)
Yt= ˆ 1+ ˆ 2 X2t+ ˆ t + u’t
(II)
pi= ˆ 1+ ˆ 2 di + vi
(III)
pi= ˆ 1+ ˆ 2 di+ ˆ 3 Ri +v’i
(IV)
Figure 2 shows the correlation between prices: m, p, d and variable rank. The dispersion between these
variables in turn shows some unusual items that are modeled in the regressions of Table 5.
{Insert Figure 2. Here}
Model 1 and 2 of Table 5 shows how the inclusion of the rank variable, does not makes irrelevant the
direct prices to explain market prices. The models have a residue with homoskedastic and normal
distribution. Should be noted that all multiple models 2, 4 y 6 (where they are present more than one
explanatory variable), there appears not to be multicollinearity according to the determinant of the matrix
of explanatory variables, which does not approach zero and although are not reported of varianceinflating factor (VIF) they did not turn out to be high. This way, being models 1 and 2 significant,
according to F-test, the direct price elasticity is also statistically significant individually. Can be stated
then for model 2, that with a 1% growth in direct prices, market prices will grow by 0.72%5, discounting
the effect of the sector size. A similar result is obtained with models 3 and 4, variable rank, again, is little
significative for production prices explaining market prices. It is interesting to note that the hierarchy of d
on p is maintained since the elasticity in model 4 is 0.625. In model 5 the explanation of p by d is not
affected by rank, in fact, this variable is not significant. Finally, model 6 explains production prices by
direct prices, Vertically Integrated Composition and variable rank. These variables are significant, but the
impact of proportional prices is also a unitary elasticity, even weighing the impact of other variables.
{Insert Table 5. Here}
In short, it seems that by including a variable that controls the size of the sector the relationship between
different prices remain significant. This suggests that the critique of spurious correlation is either small or
of no significant amount.
4.3 The effect of an omitted variable in the relationship between values and prices
Another critique of LTV arises from the possibility of bias of the estimates in the regressions among
prices. To understand the problem let us consider the Shaikh production prices model (1984 y 1990: 103112). Assuming any price (pc), they shall consist of the amount of wages, wage workload (wL) plus
profits (π) and material costs (M).
pc  wL    M
These material costs are in turn composed of the same items:
pc  wL    wL(1)   (1)  M (1)
Where the superscript (1) indicates another stage of production. The other materials from other stages in
turn used other wages, profits and materials. Thus the price of a commodity can be viewed as the sum of
wages and earnings integrated.
pc  W T  T
Where,
W T  w ( L  L(1)  L( 2)  ...  L( n ) )
 T     (1)   ( 2)  ...   ( n )
Consequently, above expression reduces to:
pc  w (1  Z ) where Z 
T
WT
Being Z the integrates quotient profit-wage, w salary rate and Λ values.
If we relate two prices i and j:
pc i  wi (1  Zi )
pc j  w j (1  Z j )
pcij 
pi
wi (1  Zi )

 ij zij
p j w j (1  Z j )
Any kind of relative prices depends on the product of relative values and relative integrated quotients
profit-wage. This works for any kind of price. But here Shaikh introduces a fundamental requirement in
the formation of production prices: He assumes that profits are equal to the product of profit rate (r) by
the total advanced integrated capital (KT).
  r KT
Then,
zi 
That is why now:
r KT
w LT
K iT
LT
z ij  iT
Kj
r K iT
)
w LTi
pij 
 pij  ij zij
r K JT
 j (1 
)
w LTj
i (1 
LTj
Simplifying with logarithms:
ln z ij  ln pij  ln ij

ln pij  ln ij  ln z ij
By normalizing the production prices and direct ones and evaluating econometrically the previous model,
in general, empirical studies contrast:
ln pi   '0   '1 ln d i  ui (i)
However, considering all the variables could be adjusted:
ln pi  0  1 ln di   2 ln zi  vi (ii)
There arises the need to assess whether there is bias in that ’1 violates the LTV due to the exclusion of zi.
To this end, we consider also estimates:
ln pi   0  1ln zi  wi (iii)
ln zi   0 1 ln di   i (iv)
Although the bias and consistency of an estimator should be evaluated by the expected value and the limit
of the probability in an equation6, is possible to find a relationship between ’1 and 1 using models (i-iv)
estimated by OLS. Can be shown of (i-iv) and coefficient rd2,z that7:
 '1   1  1rd2,z  1  1
Always for sample values, if the coefficient of determination ( rd2,z ) is null, also will be coefficient δ1 and,
for this reason,  '1  1 , this is, there is no bias, however if, rd2, z  0 there will be a difference established
by the previous equation. Coefficient rd2,z , as well as the estimated 1 are of moderate size, so the bias
will be small. After all, at the sectorial level the huge direct prices in agriculture or services need not be
associated with higher levels of vic (vertically integrated composition). At a theoretical level, the values
of different sectors should not have a relationship with their vic. If the vector d is a vector proportional to
the values, then it should not be associated either with the vic. In a log-log model the elasticity obtained in
(i) and (ii) will be very close to unity, however, this is an empirical question. For the previous models has
the following variances and covariance’s matrix of variables (Table 6).
{Insert Table 6. Here}
With this information we can calculate the elasticities of the models (i-iv) y and rd2,z .
 '1 
Cov(ln p, ln d ) 1.298231
Cov(ln p, ln z ) 0.078864

 1.048570 1 

 3.664684
var(ln d )
1.238096
var(ln z )
0.021520
1 
Cov(ln z, ln d ) 0.056776

 0.045857
var(ln d )
1.238096
1 
rd2, z 
[Cov(ln d , ln z )]2
 0.120985
var(ln d ) var(ln z )
Cov(ln p, ln d ) var(ln z )  Cov(ln p, ln z ) Cov(ln z, ln d )
 1.001710
var(ln d ) var(ln z )  [Cov(ln z, ln d )]2
Then the bias can easily be deduced:
 '1   1  [1   1   1 rd2, z ]  1.001710  [0.04686]  1.048870  bias : ( '1 1 )  0.04716
Therefore, the important conclusion is that no matter the size of the effect of ln z in ln p, if the association
among ln z and ln d is weak, the bias between 1 y  '1 will be small in that measure. These observations
on the regression analysis recognize the need to further development of improved econometric
estimations. However, is shown that traditional empirical work based on a theoretical model such as
Shaikh's (1984) is still useful to explain the relationships among them8.
5. The level of fundamental variables in China
The calculations of the main Marxist variables: rate of profit, surplus value and composition of capital,
have specific behaviors when compared internationally with other researches. However, they follow the
guidelines outlined by the Marx theory. The rate of profit (r '), the rate of surplus value (s') and the capital
composition are defined as:
pu ,i ( I  A  D) pb
T
s' 
pu ,i  B  pb
T
pu ,i  K  pb
T
ccs 
pu ,i  B  pb
T
pu ,i ( I  A  D) pb
T
r'
pu ,i  K  pb
T
pu ,i  K  ( I  A  D) 1
T
ccvi 
pu ,i  B  ( I  A  D) 1
T
T
Where pu ,i are the row vectors of the various unit prices “i”, which indicates the various prices: d, p, s y
m. The other matrices and their orders have been defined above. We estimated the simple organic
composition (ccs) and a version of the vertically integrated composition (vic), with the aim to relate
immediately r’=s’/ccs and observe the levels of profitability rate based on the known s' and ccs, but also
to compare the ccs and vic (which presents a better inter-sectorial homogeneity).
{Insert Table 7. Here}
The fundamental variables in direct prices and production ones are almost identical, the differences are
only slightly higher between market prices and direct ones, as concluded above (column 5 and 6 of table
7). The rate of return (r ') in value appears to be higher than shown in current prices. It should be
remembered that in 2002 China's economy was expanding rapidly (in real terms grew by over 8%, Holz
2006: 113). Profitability levels are relatively high, between 51% and 58% if considered only the fixed
capital, but past relationships are maintained by adding the variable capital where levels change between
31% and 37%. With the limitations involved in comparing different IOT is interesting to note that with or
without weighting fixed capital, the profit rate of China is greater than that shown for other countries
around the same year with the same methodology and measurement of r'. In Spain, for example, with of
an IOT disaggregated to 65 sectors in 2000 the return is: 16.09%, 17.29% and 13.38% for market prices
direct ones and production ones respectively (Sánchez and Nieto, 2010). On the other hand, in Korea with
of an IOT disaggregated to 27 sectors in 2000 and for the same price, returns are 11.6%, 13.6% and
13.3% (Tsoulfidis and Rieu, 2006). In contrast, when comparing rates of surplus value (s'), whereas in
China these are between 96% and 100% in Spain are between 66 and 76% and in Korea between 73% and
86%. In short, China has a higher profit rate, based on a lower composition level (a measure of technical
change) but with a higher level of exploitation. This is interesting because following proposal of
Emmanuel (1972); Carchede (1991) and Shaikh (1998)-for whom the law of value operates at
international level - high profit rates are poles for attracting capital. Reflection of the high mobility of
international capital and the strong attraction of Foreign Direct Investment (FDI) are the poles of higher
rates of profit. Is not by chance that, in recent years, China has received a large amount of investment.
Investment in mainland China has already exceeded 100 billion dollars and the total investment amount
(Hong Kong, Macao and Taiwan) in 2008 surpassed 170 billion dollars in 2009.
6. Conclusions
The results of the close proximity between prices in China’s case agree to other recent papers. The
weighted average absolute deviation between direct and market prices is 15.13%, while between direct
prices and production ones is only 9.07%. These results are not modified by changing the measure of
deviation or distance. The meaning and order in the vicinity is not significantly affected. It seems that for
one of the largest economies in the world, the force of attraction that have values to different prices is
quite strong, in particular, changes in values determine the variations in current prices by 97%. The
regression analysis between the different prices also shows this conclusion, in line with what has been
found in several countries like USA, Greece, Korea, Spain, etc...
Since Shaikh and Ochoa (1984) empirical studies, some doubts have been raised about the use of
correlation and regression analysis to assess the relationship between values and prices. Without
intending to answer to all approaches made so far, this papers deals with three aspects: the validity of
other alternative theories of value, the effect of the sector size in the regressions and the magnitude of bias
involved in excluding a variable in the model Shaikh for prices. As in the research’s Cockshott and
Cotrell (1995, 1997 and 1998), assessing other direct requirements to explain market prices, electricity
requirements, the chemical industry, oil, etc. have no higher goodness of fit and increased robustness in
their regressions. In this direction, the idea that the labor theory of value can be replaced by another
theory of value steel empirically remains in doubt. On the other hand, has been argued that sector size
could cause a false correlation, since it would necessarily have a direct association between the different
prices as those are related by the effect of physical production. Analogous to the use made of the trend in
the econometric analysis of time series, we propose the use of a variable in ascending order of production
levels; this variable has been appointed rank. The use of an instrument as the rank variable does not
make the goodness of fit previously found significantly modified. In the case of the relationship between
direct and market different prices, include the rank variable, the estimator that measures the direct price
effect on market prices does not become insignificant. Even when evaluating the regression between
prices of production explained by direct prices, the variable rank, is not significant as discussed above,
this study found greater closeness between these different prices. Finally, it could be argued that omitting
a relevant variable in the model that explains the different prices of production, like vertically integrated
compositions, there may be a bias in the estimated elasticity. This is just true to the extent the direct prices
are related to them. Theoretically there is no relationship between the various sectorial values and vic, in
any case, the correlation for a sample is very sparse, which makes the bias to be small. In the case of
China, this bias found was smaller as the coefficient of determination between ln p and ln vic is only 12%.
A final point to emphasize is that China seems to show a relatively high rate of profit as the range of this
measured with different prices lies between 51% and 58% only fixed capital weighted. But, even taking
into account circulating capital the range goes down between 33% and 37%. In short, profitability in
China (2002) is well above profitability found with very similar methodologies in countries like Korea
(2000) and Spain (2000), below 18% for different prices. Again, it appears that the LTV has the empirical
explanatory power to assess the dynamism in an economy like China.
Apendix I
Deviation measures
If we deal, for example, with direct prices (d) and production ones (p), mean absolute deviation between
them is:
n
pi  d i
i 1
di
DAM  

1
n
(1)
This measure assumes that a sector has the same weight as others, so may be more useful to ponder the
weight of each sector in the production (q). The weighted average absolute deviation is then defined as:
n
DAMP  
i 1


pi  d i  qi
 n

di
  qi
 i 1






(2)
The normalized vector distance is used by Ochoa (1989) and is defined as:
n
DVN 
( p q
i
i 1
i
 di qi ) 2
(3)
n
( p q )
i 1
i
2
i
A weighted measure (in addition to DAMP) is the Theil index of inequality, although based on a price
vector. In d case:
 pi

  n

pi
n
~
pi  n  d i   
~
i 1
  ln
Theil   d i  ln  ~     n

i 1
 d i  i 1  d   d i

i
n
 i 1 
 d
i
 
i 1








(4)
Gini coefficient:
It is the most popular measure for inequality and therefore deviation, but it should be noted here that it is
just an indicative measure, since the formulation is built for ungrouped data (Milanovic, 1997), however,
is calculated as it conceptually involves variation and correlation coefficients.
  ( , ) 
 1 
G     CV   

 3
1  (1 / n) 
(5)
pi
is written in ascending order and is associated with a vector that indicates that order (η),
di
subsequently we obtain the correlation between them.
Vector  
Coefficient of variation is the quotient between of standard deviation and mean deviation.
 (
C.V . 
  )2
n
i

(6)
The distance Steedman y Tomkins (1998), is defined as:
 
d  2  sen    2(1  cos ( ))
2
(7) showing that: tan ( )  C.V .
Defined  as a vector (see last Gini coefficient) and U unit vector, the angle measured in degrees can be
deduced as:
   arccos
( 'U )
 '  U 'U
(8)
Notes
¹The IOT originally of 42 sectors was reduced to 39, eliminating those non-mercantile.
2
For simplicity reasons, A is weightened as annual rotation. Must be warned that, even deviation between values and prices
should not be notably altered, levels of fundamental variables can suffer modification.
3
A proposal of reduction to simple labor, based in Brody (1970), is developed in Guerrero (2000), However, such as raised by
this latest study, disaggregated information is needed on labor which is currently not yet available.
4
It is interesting to note that in China there is a greater proximity between (d,p) and (d,m), when comparing with other studies
like Ochoa’s (1989) for U.S and Cockshott & Cotrell’s (1998) for United Kigdom. Further details in section 3.2.
5
The confidence interval for the estimated elasticity of 0.724 is, in fact,: [0.60, 0.84].
6
When it comes to seeing the relationship of sample value to their population value, the relations are simplified. In fact, the
expected value, i.e. the average value with infinite sampling of β1’ in (i) is: E(β1’)= β1+β2˙δ1, while the consistency of the
same is the limit of the probability when the sample size grows indefinitely: plim (β1’)= β1+β2˙δ1. In both concepts the
important aspect is the size of the Cov (ln z, ln d) because the latter determines the value δ1. What is made with models (i-iv)
is simply to find a relationship of OLS estimation of the coefficients β1 and β1’. It should also be noted that the standard
deviation of β1 'is greater and so the estimator is inefficient.
The estimator β1 can be inferred directly of the normal equations of OLS in a model with two explanatory variables.
7
8
For example, Valle (2010) and Frölich (2011) show the total validity of the measures correlation and distance between values
and prices, from the viewpoint of dimensional analysis (DA). This type analysis has unfortunately been neglected in
economics, still quite useful for checking the consistency of an equation, an instrument used quite frequently in economic
modeling and corroboration. Discussion about correlation and measure distance between values and prices is undetermined,
and, therefore, the relation between these two variables was unverifiable empirically has been superseded (Díaz y Osuna,
2009). Valle and Frölich show that correlation between two non-homogeneous vectors is an impossible operation. Focusing
just in the correlation coefficient, the relationship between sectorial p and d must be value like Corr (pu·q, du·q), where prices
vectors are “unitarian” multiplied by its quantities, this is, Corr (p, d) calculated in this paper. While Corr(pu , du) must be seen
as an impossible operation more tan undetermined. Of course, when dealing with sector producing more than one good and
with information in money and no in physical quantities, discussion terms are a Little bit modified but not in conclusion and
sense: only homogeneous variables can be correlated. Because of this, correlation coefficient is not modified by the units
measure change in unitarian prices such as is determined by (DA). This way, continues being valid and precious for economic
theory empirical corroboration between values and prices.
Tables, Pictures and Graphics
Table 1 - Deviation measures among prices
Deviation
(d,m)
(d,p)
(p,m)
(s,m)
1. MAD
14.19
12.01
16.54
18.50
2. MAWD
15.13
9.07
16.55
18.13
3. NVD
23
8.7
25.5
22.9
4. Theil
2.03
0.76
2.94
3.16
5. Gini
10.7
8.9
13.
14.1
6. C.V.
19.25
15.53
23.25
24.58
7. d
18.99
15.39
22.79
24.04
8. θ (degrees)
10.89
8.82
13.08
13.81
Measures
Note: Where; d = direct prices, p = production prices, s = sraffian production prices y m = market prices. Deviation measures are defined in the Appendix.
Table 2 - Simple log-log regressions among prices
mi = f(di)
Models
F
R2
ln mi = 0.64 + 0.97 ln di + ui
1122.29
96.81%
2537.38
98.56%
747.49
95.28%
715.46
95.08%
t (0.82) (33.50)
pi = f(di)
ln pi = -0.59 + 1.04 ln di + ui
t
mi = f(pi)
ln mi = 0.99 + 0.91 ln pi + ui
t
mi = f(si)
(-2.43) (50.37)
(2.54)
(27.34)
ln mi = 1.24 + 0.89 ln si + ui
t
(3.18) (26.74)
Note: Being n=39 sectors and k=2 number of estimator, critical value t α/2 with freedom degrees n-k=37≈40, so t5%/2=2.02. As we know, in these models, critical
value of F 5% significance is F(k-1), (n-k) ≈F1,40= t25%/2 = 4.08. Thus, to be larger t and F values calculated than critical values are statistically significant: the
explanatory variables used and the model in general.
Figure 1 - Dispersion of different prices related to direct prices.
Table 3 - Deviation and correlation between values and prices: China, USA, Greece and Spain
Direct prices/market prices
Production prices/market prices
Direct prices/production prices
(d,m)
(p,m)
(d,p)
China
USA
Gr
Sp
China
USA
Gr
Sp
China
USA
Gr
Sp
2002
1970
1970
2000
2002
1970
1970
2000
2002
1970
1970
2000
DAM
14.1
10.3
23.1
12.2
16.5
12.5
14.3
18.8
12.01
16.9
18.7
19.0
DAMP
15.1
11.1
21.6
11.0
16.5
13.1
15.4
18.9
9.07
17.8
18.1
19.0
DVN
23.0
12.7
25.1
13.2
25.5
15.3
20.4
20.6
8.7
18.3
23.0
20.5
R2
97.8
97.8
94.2
97.8
94.9
98.6
93.9
95.8
94.3
97.1
97.1
95.4
Note: Data for USA are from Ochoa’s (1989) with 71 sectors, data for Greece are from T&M’s (2002) with 35 sectors and to Spain from Sánchez and Nieto’`s
(2010) with 65 sectors.
Table 4 - Deviation and regression of the labor value and "base values" on market prices
Independent
MAWD %
(d,m)
Variable
Models
F
R2
1122.29
96.81%
79.50
68.83%
106.171
74.68%
9.446
20.79%
11.062
23.51%
ln mi = 0.280 + 0.977 (ln di ) + ui
Labor
15.13
t
(0.825)
(33.500)
ln mi = 227 + 0.706 (ln di ) + ui
Electricity
35.46
t
(2.548)
(8.916)
ln mi = 140 + 0.806 (ln di ) + ui
Chemistry
37.14
t
(1.762)
(10.304)
ln mi = 571 + 0.256 (ln di ) + ui
Oil
61.13
t
(4.666)
(3.073)
ln mi = 725 + 0.067 (ln di ) + ui
Farm
333.45
t
(7.052)
(3.325)
Note: For alternative bases values, the first estimator is 109 RMB.
Figure 2 - Dispersions between prices and la variable rank
29
ln m
28
27
3
35
21
539
420
26
25
251
12
29
14
6
26
16
19
17
7
22
31
30
18
10
8
1115
13
28
3637
32
9238
3334
24
27
23
24
30
29
ln p
28
27
21
20
35
539
43
34
33
27
24
23
26
25
24
40
Rank
30
20
335
21
39
20
45
34
33
24
23 27
10
0
24
25
26
1
25
12
629
14
19
16
7 26
17
8
10
30
18
13
15
3637
22
9
31
11
32
238
28
1
25
12
629
14
19
16
7 26
17
810
30
18
37
13
15
36
22
93211
2382831
34
33
27
24
23
1
1225
29
14
6
26
16
19
17
22 7
31
30
18
10
8 37
1115
2813
36
32
38
92
27
ln d
34
2433
2327
28
29
30
24
25
21
35
520
39
3
4
1
1225
29
614
26
16
19
717
22
31
30
18
810
37
11
15
13
28
36
32
238
9
3
35
21
39
20
45
26
27
ln m
28
29
33
24
2327
24
25
251
2912
14
6
26
16
19
17
22 7
31
30
18
10
8
37
1115
13
28 36
32
238
335 9
21
39
20
45
34
26
27
ln p
28
29
30
Table 5 - Different price regressions including the variable rank and VIC
(below p. values)
Dependent variable
Mod.1
Mod.2
Mod.3
Mod.4
Mod.5
Mod.6
ln(m)
ln(m)
ln(m)
ln(m)
ln(p)
ln(p)
0.646
6.849
1.777
9.408
0.266
-2.13
0.414
0.00005
0.0304
0.0001
0.8766
0.8154
0.977
0.724
0.982
1.01
<0.0001
<0.0001
<0.0001
<0.0001
Independent variable
Constant
ln (d)
ln (p)
0.936
0.625
<0.0001
<0.0001
ln (vicr)
1.02
<0.0001>
Rank
Dummy
0.027
0.033
0.006
-0.001
0.00004
0.0001
0.3196
0.0048
0.447
0.808
0.579
-0.03
<0.0001
0.0007
<0.0001
<0.0001
0.968
.9884
0.9658
.9802
0.9860
0.999
Adjusted R
0.967
.9874
0.9639
.9785
0.9852
0.999
F (k-1, n-k)
F(1,37)
F(3,35)
F(2,36)
F(3,35)
F(2,36)
F(4,34)
F-statistic
1122.2
1000.2
508.7
496.6
1269.8
217624
<0.0001
<0.0001
<0.0001
<0.0001
White
0.8807
0.6862
0.7315
0.6475
0.1345
0.4469
Breusch-Pagan
0.6891
0.9032
0.7184
0.2750
0.4281
0.3253
Koenker
0.6891
0.9181
0.7837
0.2524
0.2902
0.2366
0.18929
0.25521
0.165189
0.7598
0.4756
0.9670
-
2338594.4
-
R2
2
<0.0001
Homoskedastic
Normality
Chi-squared
Multicollinearity
Determinant X’X
1781802.1 861720.9
3069527.5
590067.2
Note: The variable dummy, controls outliers for model 2 in sectors: 3, 11 y 28, for model 3: just in sector 3, for model 4: 3 and 11 and for model 6: the sector
11. All econometric estimates have been developed in Gretl, free software, designed and supported by Allin Cotrell.
Table 6 - Variances and covariances matrix of the variables: p, d and z (in logarithms)
Ln p
Ln d
Ln z
Ln p
1.381137
1.298231
0.078864
Ln d
1.298231
1.238096
0.056776
Ln z
0.078864
0.056776
0.021520
Table 7 - Marxist Fundamental Variables
Market
prices
Direct
prices
Production
prices
(1)
(2)
(3)
Sraffa
production
prices
(2)/(3)
(2)/(1)
(4)
Profit rate % (r’)
51.24
56.18
56.02
58.45
1.002
1.096
Surplus rate% (s’)
100.41
96.82
96.21
102.24
1.006
0.964
Simple organic composition
(ccs)
1.9593
1.7231
1.7173
1.7492
Vertically integrated
composition (vic)
2.2609
0.882
1.005
1.9884
1.9817
2.0185
1.003
0.876
Bibliography
Carcanholo, R. A. 2002. Ricardo e o fracasso de uma teoria do valor. Curitiba, In: VII Encontro Nacional
de Economia Política, Anais do VII Encontro Nacional de Economia Política.
Chilcote, E. 1997. Interindustry structure, relative prices and productivity: an input-output study of the
U.S. and O.E.C.D countries, theses doctoral no posted, New York, New School for Social Research.
Cockshott, P., Cottrell, A. and Michaelson, G. 1995. “Testing Marx: some new results form UK data”,
Capital and Class, vol. 55, Spring, pp. 103-29.
Cockshott, P. and Cottrell, A. 1997 “Labour time versus alternative value bases: a research note”,
Cambridge Journal of Economics, vol. 21, pp. 545-49.
Cockshott, P. and Cottrell, A. 1998. “Does Marx need to transform?”, in R. Bellafiore (Ed.) Marxian
economics: A Reapparasal, vol. 2 Basingstoke, McMIllan st Martin´s Press.
Chow, G.C. 1993. Capital Formation and Economic Growth in China, Quarterly Journal of Economics
vol. 108. pp. 809-42.
_________ 2006. New Capital Estimates for China: Comments, China Economic, Review 17, pp. 186-92.
Chow, G.C. and Kui-Wai Li 2002. “China’s Economic Growth: 1952-2010”, Economic Development and
Cultural Change, vol. 51, 247-56.
Díaz-Calleja, E.; Osuna, R. 2009. “From correlation to dispertion: geometry of the prices- value
deviation”, Empirical Economics, vol. 36(2), pp. 427-440.
Frölich, N. 2010. “Dimensional analysis of price-value deviation”. Chemnitz University of Technology.
http://www.boeckler.de/pdf/v_2010_10_29_froehlich.pdf
Guerrero, D. 2000. Teoría del valor y análisis insumo-producto, manuscrito, 158 pp.
Hogdson, G., Capitalism, Value and Explotation, Oxford, Martin Robertson, 1982.
Holz, C.A. 2006. “Measuring Chinese Productivity Growth, 1952-2005”, disponible en SSRN:
http://ssrn.com/abstract=928568
Kliman, A. 2002. “The law of value and laws of statistics: sectoral values and prices in the US economy,
1977-1997”, Cambridge Journal of Economics, vol. 26, pp. 299-311.
Mariolis, T. y Tsoulfidis, L. 2009. “Decomposing the Changes in Production Prices into ‘CapitalIntensity’ and ‘Price’ Effects: Theory and Evidence from the Chinese Economy”, Contributions to
Political Economy.
Marx, K. 2002. El Capital, Libros, I, II y III, Madrid, S. XXI.
Meek, Ronald. 1980. Smith, Marx y después: Diez ensayos sobre el desarrollo del pensamiento
económico, Madrid, Ed. Siglo XXI.
Milanovic, B. “A simple way to calculate the Gini coefficient, and some implications”. Economics
Letters, vol. 56, issue 1, 1997, pp. 45-49.
Ochoa, E. 1984. “Labor Values and Prices of Production: An Interindustry Study of the U. S. Economy,
1947-1972”, Ph. D. dissertation, Department of Economics, New School for Social Research, New York.
Ochoa, E. 1989. “Values, prices and wage-profit curves in the U.S. economy”, Cambridge Journal of
Economics, vol. 13, pp. 413-429.
Roemer, J. Analytical Foundations of Marxian Economic Theory. Cambridge University Press, 1981.
Shaikh, A. 1984. “The Transformation from Marx to Sraffa: prelude to a critique of the neo-ricardians”, in
E. Mandel and A. Freeman (eds.), Ricardo, Marx, Sraffa: The Langston memorial volume, London,
Verso, pp. 43-84.
Shaikh, A. 1990. Valor, acumulación y crisis, Bogotá, Tercer Mundo Editores.
Tsoulfidis, L. 2008. “Price-Value Deviations: Further Evidence from Input-Output Data of Japan”.
International Review of Applied Economics.
Tsoulfidis, L. and Paitaridis, D. 2008. “On the Labor Theory Value: Statistical Artefacts or
Regularities?”, Research in Political Economy.
Tsoulfidis, L. and Rieu, D. 2006. “Labor Values, Prices of Production and Wage-Profit Rate Frontiers of
the Korean Economy”, Seoul Journal of Economics.
Tsoulfidis, L., Maniatis, T. 2002. “Values, prices of production and market prices: some more evidence
form the Greek economy”, Cambridge Journal of Economics, vol. 26, pp. 359-369.
Steedman, I. and Tomkins, J. 1998. “On measuring the deviation of prices from values”, Cambridge
Journal of Economics, vol. 22, no. 3, pp. 379-85.
Valle, A.1994. “Correspondence between labour values and prices: a new approach”, Review of Radical
Political Economics, vol. 26, no 2, pp. 57-66.
Valle, A. 1991. Valor y precio: una forma de regulación del trabajo social. Facultad de Economía,
UNAM, México.
Valle, A. 2010. “Dimensional analysis of price-value correspondence: a spurious case of spurious
correlation”. Investigación Económica. UNAM. México.