Empirical Applications of Marxism - A Reading List

I've decided that if I want use data from the National Income and Products Account (NIPA) to explore Marxist and Sraffian economics, I need a more detailed understanding. I should read, sometimes again, at least these references, which are mostly Marxist:

• Applications
• Cockshott, W. Paul and A. F. Cottrell (1997) "Labour Time versus Alternative Value Bases: A Research Note," Cambridge Journal of Economics, Volume 21, Number 4, p. 545.
• Cockshott, W. Paul and Allin Cottrell (2003) "A Note on the Organic Composition of Capital and Profit Rates", Cambridge Journal of Economics, V. 27: 749-754.
• Cockshott, W. Paul and Allin Cottrell (2005) "Robust Correlations Between Prices and Labour Values: A Comment", Cambridge Journal of Economics, V. 29: 309-316
• Han, Z. and B. Schefold (2003). "An Empirical Investigation of Paradoxes: Reswitching and Reverse Capital Deepening in Capital Theory", Cambridge Journal of Economics, V. 30: 737-765.
• Izyumov, Alexei and Sofia Alterman (2005) "The General Rate of Profit in a New Market Economy: Conceptual Issues and Estimates", Review of Radical Political Economics, V. 37, N. 4 (Fall): 476-493.
• Kliman, Andrew J. (2002) "The Law of Value and Laws of Statistics: Sectoral Values and Prices in the US Economy, 1977-97", Cambridge Journal of Economics, V. 26: 299-311
• Kliman, Andrew J. (2005) "Reply to Cockshott and Cottrell", Cambridge Journal of Economics, V. 29: 317-323
• Mohun (2005) "On Measuring the Wealth of Nations: the US Economy, 1964-2001",Cambridge Journal of Economics, V. 29: 799-815
• Mohun (2006) "Distributive Shares in the US Economy, 1964-2001",Cambridge Journal of Economics, V. 30: 347-370
• Moseley, Fred (1988) "The Rate of Surplus Value, The Organic Composition, and the General Rate of Profit in the U.S. Economy, 1947-67: A Critique and Update of Wolff's Estimates", American Economic Review, V. 78, N. 1 (March): 298-303
• Ochoa, Edward M. (1989) "Values, Prices, and Wage-Profit Curves in the U. S. Economy" Cambridge Journal of Economics, V. 13, No. 3, September 1989, pp. 413-429.
• Petrovic, P. (1991) "Shape of a Wage-Profit Curve, Some Methodology and Empirical Evidence", Metroeconomica, V. 42, N. 2: 93-112.
• Podkaminer, Leon (2005) "A Note on the Statistical Verification of Marx: Comment on Cockshott and Cottrell", Cambridge Journal of Economics, V. 29: 657-658
• Shaikh, Anwar (1984) "The Transformation from Marx to Sraffa", in Ricardo, Marx, Sraffa (Edited by E. Mandel and A. Freeman), Verso
• Shaikh, Anwar M. and E. Ahmet Tonak (1994) Measuring the Wealth of Nations: The Political Economy of National Accounts, Cambridge University Press
• Venida, Victor S. (2007) "Marxian Categories Empirically Estimated: The Philippines, 1961- 1994", Review of Radical Political Economics, V. 39, N. 1 (Winter): 58-79.
• Weisskopf, Thomas E. (1979) "Marxian Crisis Theory and the Rate of Profit in the Postwar U.S. Economy", Cambridge Journal of Economics, V. 3 (December): 341-378
• Weisskopf, Thomas E. (1979) "Marxian Crisis Theory and the Rate of Profit in the Postwar U.S. Economy", Cambridge Journal of Economics, V. 3 (December): 341-378
• Wolff, Edward N. (1979) "The Rate of Surplus Value, The Organic Composition, and the General Rate of Profit in the U.S. Economy, 1947-67", American Economic Review, V. 69, N. 3 (June): 329-341
• Wolff, Edward N. (1988) "The Rate of Surplus Value, The Organic Composition, and the General Rate of Profit in the U.S. Economy, 1947-67: Reply", American Economic Review, V. 78, N. 1 (March): 304-306
• Methodology
• Pasinetti, Luigi L. (1973) "The Notion of Vertical Integration in Economic Analysis", Metroeconomica, V. 25: 1-29.
• Pasinetti, Luigi L. (1977) Lectures on the Theory of Production, Columbia University Press
• Raa, Thijs Ten (2005) The Economics of Input-Output Analysis, Cambridge University Press
• Steedman, I. and J. Tomkins (1998) "On Measuring the Deviation of Prices from Values", Cambridge Journal of Economics, V. 22: 379-385

The Wage As The Independent Variable

1.0 Introduction
Piero Sraffa, in his critique of neoclassical theory, described a system of prices in which capitalist earn the same rate of profits in every industry. One can derive, in the pure circulating-capital version of this system, a trade-off between wages and the rate of profits.

The shape of this wage-rate of profits curve depends on the (possibly composite) commodity chosen for the numeraire. It is a straight line when Sraffa's standard commodity is used for the numeraire. If the wage-rate of profits curve were a straight line for all other numeraires, the labor theory of value would be be exactly true as a theory of relative prices, abstracting from deviations between market prices and prices of production and from the theory of joint production. This theorem of mathematical economics raises an empirical question. How far does the wage-rate of profits curve vary from a straight line for various numeraires?

P. Petrovic ("Shape of a Wage-Profit Curve, Some Methodology and Empirical Evidence", Metroeconomica, V. 42, N. 2 (1991): pp. 93-112) explored this question for 1976 and 1978 data from Yugoslavia. Petrovic found that the empirical wage-rate of profits curve never deviated much from a straight line, no matter what numeraire was chosen.

I was only able to partially replicate Petrovic's results with 2005 USA data. The 2005 USA wage-rate of profits curve drawn with a numeraire in the proportions of net output is indeed quite close to a straight line. But the 2005 USA wage-rate of profits curve can be quite convex or quite concave, depending on the choice of the numeraire. My methodology differed from Petrovic's in that I introduced a normalization of the numeraire quantity to fix the maximum wage at unity for each numeraire.

My estimate of the rate of profits in the USA is higher than I expected. I am beginning to think that my approach is too simple. Perhaps I need to account for depreciation, fixed capital, and the distinction between productive and unproductive labor. I may post more analyses in this series before revisiting my past results.

2.0 Derivation of the Wage-Rate of Profits Curve
Consider an economy in which each of n commodities are produced from labor and inputs of those n commodities. Let a_{0, j} be the person-years of labor used in producing one unit of the jth commodity. Let a_{i, j} be the physical units of the ith commodity used in producing one unit of the jth commodity. The direct labor coefficients are elements of the n-element row vector a₀. The remaining input-output coefficients are the entries in the nxn Leontief input-output matrix A, which is assumed to satisfy the Hawkins-Simon condition.

The Sraffa prices equations, in which wages are paid out of the surplus, are:

p A (1 + r) + a₀ w = p

where p is a row vector of prices, w is the wage, and r is the rate of profits. After some manipulation, one has:

a₀ [ I - A (1 + r)]^-1 w = p

The Hawkins-Simon conditions guarantees the existence of the matrix inverse for rates of profits between zero and some maximum rate of profits. Let e be a column matrix representing the numeraire. Multiply on the right by the numeraire:

a₀ [ I - A (1 + r)]^-1 e w = p e = 1

The wage-rate of profits curve is then:

w = 1/(a₀ [ I - A (1 + r)]^-1 e)

3.0 Empirical Results

Figure 1 shows the range of convexities, depending on the numeraire, of the wage-rate of profits curve in the USA in 2005. The straight-line wage-rate of profits curve is constructed using Sraffa's standard commodity as the numeraire.

Figure 1: Wage-Rate Of Profits Curve For Selected Numeraires

I examined a numeraire for each of the 65 industries in the 2005 Use Table. The numeraire corresponding to each industry consists solely of the output of that industry; the output of all other industries is zero in this non-composite numeraire commodity. The quantity of the selected numeraire commodity is set to ensure the maximum wage, corresponding to a rate of profits of zero, is unity. In other words, the numeraire quantity is normalized such that its embodied labor value is one thousand person-years, the unit in which the BEA measures labor.

Figure 1 shows wage-rate of profits curves for two of these 65 numeraires. The wage-rate of profits curve for the numeraire consisting solely of output of Warehousing and Storage industry has the highest positive displacement from the straight-line wage-rate of profits curve. The wage-rate of profits curve for the numeraire consisting solely of output of the Petroleum and Coal Products industry is the furthest below the straight-line wage rate-of profits curves. The wages-rate of profits curves for all other numeraires are closer to the straight-line wage-rate of profits curve.

The remaining wage-rate of profits curve shown in Figure is drawn for a numeraire in the proportions of positive quantities in the net output (final demand) quantities in the 2005 Use Table. (Final demand quantities are net of the circulating capital goods replaced out of gross output; they still include, however, depreciation charges against fixed capital.) Among the components of final demand, imports and nondefense consumption expenditures from the Federal government can be negative. Thus, the final demand for the output of an industry can be negative, if, for example, more of that industry's output is imported than exported. The following industries have negative quantities in final demand:

• Forestry, fishing, and related activities
• Oil and gas extraction
• Wood products
• Nonmetallic mineral products
• Primary metals

Finally, Figure 1 shows a point for the year 2005. Wages, in numeraire units, are calculated from data on employee compensation, full time equivalent employees, and net output. The data on full time equivalent employees is included with data on gross output and was used to calculate labor values. I did not make any correction here for negative quantities in final demand. Compensation of employees is a component in Value Added in the Use Table. The other two components of Value Added are Taxes on production and imports, less subsubsidies and Gross operating surplus. The actual wage is 0.575 of the net output of a thousand person-years. The corresponding rate of profits is 53.3%. The wage, when net output is used as the numeraire lies 0.0766 numeraire units above the straight line wage-rate of profits curve, close to the maximum difference along these two curves of 0.0773 numeraire units.

Theoretically, the wage-rate of profits curve for numeraires other than the standard commodity can be of any convexity. Furthermore, the convexity can differ over different ranges of the rate of profits. One might find surprising how close the wage-rate of profits curve is to a straight line when net output is chosen as a numeraire. The rate of profits can be increased by an increase in productivity, which moves the wage-rate of profits curve outward. The rate of profits can also be increased by a decrease in the wage, that is, by increasing the exploitation of the workers.

If The Workers Were Able To Live On Air

"In so far as the development of productivity reduces the paid portion of the labour applied, it increases the surplus-value by lifting its rate; but in so far as it reduces the total quantity of labour applied by a given capital, it reduces the number by which the rate of surplus-value has to be multiplied in order to arrive at its mass. Two workers working for 12 hours a day could not supply the same surplus-value as 24 workers each working 2 hours, even if they were able to live on air and hence scarcely needed to work at all for themselves. In this connection, therefore, the compensation for the reduced number of workers provided by a rise in the level of exploitation of labour has certain limits that cannot be overstepped..." -- Karl Marx, Capital, Vol. 3, Part 3, Chap. 15, Sect. 2

Introduction
A maximum rate of profits arises in a model of the production of commodities by means of commodities. This maximum rate of profits is an upper limit on the rate of profits in any sublunary capitalist economy, where the workers produce commodities to consume and thereby reproduce their labor power.

This maximum rate of profits would be easily seen if the economy were a giant farm producing one commodity, corn, from inputs of labor and seed corn. The surplus would be the difference between harvested corn and the quantity of seed corn which needs to be set aside to continue production next year. The ratio of this surplus to the quantity of seed corn is the maximum rate of profits. The maximum rate of profits cannot be achieved because of the need to pay wages to the workers eats into this surplus.

Some of the simple lessons of the corn economy generalize to actual more-or-less capitalist economies, such as in the United States of America (USA). One can use the mathematics of eigenvalues and eigenvectors to set out the theory in this case.

2.0 The Standard System
Consider an economy in which each of n commodities are produced from labor and inputs of those n commodities. Let a_{0, j} be the person-years of labor used in producing one unit of the jth commodity. Let a_{i, j} be the physical units of the ith commodity used in producing one unit of the jth commodity. The direct labor coefficients are elements of the n-element row vector a₀. The remaining input-output coefficients are the entries in the nxn Leontief input-output matrix A, which is assumed to satisfy the Hawkins-Simon condition.

This data determines Sraffa's standard system, in which the gross output, the net output, and capital goods have specific properties. Let q* be an n-element column vector denoting the gross quantities output in each industry, that is to say, the gross output in the standard system. The column vector A q* represents the physical quantities of capital goods needed to produce the gross output in the standard system. Let y* be an n-element column vector denoting the net quantities output in each industry in the standard commodity. The net output is available to be divided up between wages and profits after replacing the capital goods needed to reproduce the gross output. Net output and gross output, in any proportions, are related as follows:

y* = q* - A q* = (I - A) q*

In the standard system, the ratio between gross output and the quantity of capital goods needed to produce the gross output is invariant among commodities:

q* = (1 + R) A q*

Or:

A q* = [1/(1 + R)] q*

As a matter of fact, [1/(1 + R)] is the maximum eigenvalue of A. The standard system is scaled such that the amount of labor employed in the standard system is unity:

a₀ q* = a₀ (I - A)^-1 y* = 1

y* is the standard commodity.

One chooses the maximum eigenvalue to ensure, under the Hawkins-Simon condition, the existence of a standard commodity in which all components are non-negative and at least some components are strictly positive. The commodities which enter the standard commodities are called "basic". They enter directly or indirectly into the production of all commodities. Those commodities with zero entries in the standard commodity are called "non-basic". Either non-basic commodities do not enter into the production of any other commodity. Or they enter into the production only of non-basic commodities. For each non-basic commodity, there exist some commodity such that the non-basic commodity does not enter, either directly or indirectly, into the production of that commodity.

To explicate the concept of a commodity entering indirectly into the production of another commodity, consider the output of the Motor Vehicles, Bodies And Trailers, And Parts industry, one of the 65 industries in the 2005 Use Table for the USA available from the Bureau of Economic Analysis (BEA). 0.18 units of the output of the Primary Metals industry enter (directly) into the production of each unit produced by the Motor Vehicles, etc. industry. (A quantity unit of any industry is one hundredth of the quantity output of each industry in the year 2000, where the quantity unit in each year is a chain index.) 0.15 units of the output of the Mining, Except Oil And Gas, industry is an input into each unit produced by the Primary Metals industry. Since Mining, Except Oil And Gas, enters into Primary Metals, and Primary Metals enters into Motor Vehicles, etc., then Mining, Except Oil And Gas, enters indirectly into the production of Motor Vehicles, etc. (0.040 units of Mining, Except Oil And Gas, also enter directly into each unit output of Motor Vehicles, etc..) Any number of steps can separate the indirect production of one commodity by another.

Summary of Some Empirical Results
I've implemented the above mathematics with 2005 data for the USA. Sixty two industries in the USA in 2005 are basic and enter into the standard commodity with positive components. The three non-basic industries are

• Hospitals and Nursing and Residential Care Facilities
• Federal General Government
• State and Local General Government

I think the non-basic property of the general government industries is an accounting convention. The industries Federal Government Enterprises and State and Local Government Enterprises are basic and enter into the standard commodity with positive values.

The maximum rate of profits in the USA in 2005 was approximately 106.4%.

OCC Varies Less Among Vertically Integrated Industries (Part 2)

I gave a hostage to fortune in the first part. That part notes the empirical claim that the Organic Composition of Capital (OCC) varies less among vertically integrated industries, as compared to non-vertically integrated industries. But I did not demonstrate this claim with actual data. This part retrieves this hostage by presenting empirical results.

The first part explained how to calculate the OCC for both non-vertically and vertically integrated industries, given Leontief Input Output tables. I performed these calculations with the Leontief Input Output table obtainable from the 2005 Use Table and other data available from the Bureau of Economic Analysis (BEA). Figure 1 shows these distributions of the OCC among the 65 industries aggregated by the BEA. Notice that the OCC does indeed seem to be more dispersed for non-vertically integrated industries.

Figure 1: Distribution of Ratio of OCC to Sum of Unity and Rate of Exploitation

In both cases, the distributions seem to be skewed and from a non-Gaussian distribution. Taking common logarithms yields the distributions shown in Figure 2. Table 1 presents summary statistics for these distributions. The absolute value of the coefficient of variation in the distribution of the OCC is indeed decreased by vertical integration. So these results replicate, for 2005 United States of America (USA) data, Shaikh’s and Petrovic’s earlier results for the USA in 1947 and Yugoslavia in 1976 & 1978, respectively.

Figure 2: Distribution of Common Logarithm of Ratio of OCC to Sum of Unity and Rate of Exploitation

Table 1: Logarithm of Ratio of OCC to Sum of
Unity and Rate of Exploitation

Statistic	Non-Vertically Integrated Industries	Vertically Integrated Industries
Number Industries	65	65
Mean	-0.0326576	-0.0770277
Standard Deviation	0.396980	0.225224
Coefficient of Variation (Absolute Value)	12.16	2.924

I suppose this analysis could be improved by performing formal statistical tests. In particular, one might use the Kolmogorov-Smirnov goodness of fit test to determine if the distributions of the OCC after a logarithmic transformation are Gaussian. I don’t know how to formally test for a change in the coefficient of variation. But, since the mean is so close to zero anyway, one might use an F test to contrast the variance in the distributions of the (transformed) OCC. I don’t plan on pursuing this line soon, though.

OCC Varies Less Among Vertically-Integrated Industries (Part 1)

1.0 Introduction
Anwar Shaikh claims that one can expect the Organic Composition of Capital (OCC) to vary less among vertically integrated industries than among non-vertically integrated industries. Shaikh shows his claim holds for the United States of America in 1947. Petrovic demonstrates the claim for Yugoslavia in 1976 and 1978.

This post lays out the theory formulating this empirical claim. Results replicating Shaikh's and Petrovic's test of the theory in new data are left for Part 2. I have yet to test the theory, and Part 2 remains unwritten for now.

2.0 Vertical Integration

Consider an economy in which each of n commodities are produced from labor and inputs of those n commodities. Let a_{0, j} be the person-years of labor used in producing one unit of the jth commodity. Let a_{i, j} be the physical units of the ith commodity used in producing one unit of the jth commodity. The direct labor coefficients are elements of the n-element row vector a₀. The remaining input-output coefficients are the entries in the nxn Leontief input-output matrix A, which is assumed to satisfy the Hawkins-Simon condition. The challenge is to express an empirical claim about the variability of the OCC in terms of this empirically-observable data.

Let q be an n-element column vector denoting the gross quantities output in each industry. The column vector A q represents the physical quantities of capital goods needed to produce this gross output. Let y be an n-element column vector denoting the net quantities output in each industry. The net output is available to be divided up between wages and profits after replacing the capital goods needed to reproduce the gross output. Net output and gross output are related as follows:

y = q - A q = (I - A) q

Or:

q = (I - A)^-1 y

The jth column of (I - A)^-1 represents the gross output in a vertically integrated industry producing a net output of one unit of the jth commodity. This interpretation becomes apparent when one considers a net output vector consisting of one unit of the jth commodity:

y = e_j

where e_j is the jth column of the nxn identity matrix.

The above analysis of vertically integrated industries allows one to specify the amount of labor and the capital goods employed in each vertically integrated industry. Consider the n-element row vector v defined as:

v = a₀ (I - A)^-1

The jth element of v represents the labor (in person-years) employed in a vertically integrated industry producing one unit of the jth commodity net. This element is the labor directly and indirectly embodied in one unit of the jth commodity. v is the vector of labor values for this economy. The capital goods used in producing any gross output vector is found by pre-multiplying that vector by the Leontief input-output matrix A. Define the matrix H such that each column is the product of A and the gross output of a vertically integrated industry producing a net output of one unit of the corresponding commodity:

H = A (I - A)^-1

Luigi Pasinetti calls the columns of H "the vertically integrated units of productive capacities." A column "expresses in a consolidated way the series of heterogeneous physical quantities of commodities which are directly and indirectly required as stocks, in the whole economic system, in order to obtain one physical unit of [the corresponding commodity] as a final good."

3.0 The Organic Composition of Capital
According to Karl Marx, the labor value of a commodity is the sum of the labor embodied in the capital goods used in the production of that commodity, the labor value of the labor power used in the production of that commodity, and the surplus value:

v_j = c_j + w_j + s_j

where

• c_j is constant capital expended in producing one unit of the jth commodity
• w_j is variable capital (that is, the labor value of capital spent on the wages of workers) expended in producing one unit of the jth commodity
• s_j is the surplus value obtained in producing one unit of the jth commodity.

For Marx, the labor value of constant capital appears unchanged in the product. The source of profits is the appropriation by the capitalists of surplus value produced throughout a capitalist economy.

The OCC is defined to be the ratio of constant capital and variable capital, both expressed in labor values:

occ_j = c_j/w_j

where occ_j is the OCC for the jth industry. Marxist economics would be much less problematic if the OCC were invariant across industries. The rate of exploitation e is another important parameter in Marxist economics. The rate of exploitation is the ratio of surplus value to variable capital in each industry:

e = s_j/w_j

The equality of the rate of exploitation across industries follows from an assumption of competitive labor markets, inasmuch as workers are free to transition among industries in seeking work. The OCC in each industry can be expressed as a function of the rate of exploitation and the ratio of constant capital to the remaining labor value of the product:

occ_j = (e + 1) c_j/(w_j + s_j)

The rate of exploitation can be treated as a nuisance parameter in exploring the empirical question raised in this post.

Consider non-vertically integrated industries, each producing a gross output of one unit of each commodity. The jth industry in this case employs a_{0, j} person-years of labor. That is, the labor value of the product from newly applied labor is merely the corresponding direct labor coefficient:

w_j + s_j = a_{0, j}

The columns of A represent the capital goods needed in each of these industries. The labor embodied in the capital goods for the jth industry is the dot product of the row vector expressing the labor values of a unit of each commodity and the column vector denoting the quantities of these capital goods. Thus, one has:

c = v A

On the other hand, consider vertically integrated industries, each producing a net output of one unit of each commodity. The amount of labor directly employed in the jth vertically integrated industry is v_j. The labor value c^*_j embodied in the capital goods for the jth vertically integrated industry are easily found:

c^* = v H

where the elements of c^* are the desired labor values.

The above observations can be brought together to summarize the empirical claim of interest here. The OCC in each non-vertically integrated industry is proportional to the ratio of the labor value of the capital goods used in that industry and the labor directly employed in that industry:

occ_j/(e + 1) = c_j/a_{0, j}

The OCC in each vertically integrated industry is also proportional to the ratio of the labor value of the capital goods used in that industry and the labor employed in that industry:

occ^*_j/(e + 1) = c^*_j/v_j

where occ^*_j is the OCC in the jth vertically integrated industry. The proportionality constant is the same function of the rate of exploitation in the above pair of equations. The empirical claim is that the expression on the right hand side varies less among industries for vertically integrated industries than among non-vertically industries. That is, the coefficient of variation is less among vertically integrated industries. Perhaps one should take a variance-stabilizing transformation, such as natural logarithms, before calculating the coefficient of variation.

References

• Luigi L. Pasinetti (1973) "The Notion of Vertical Integration in Economic Analysis", Metroeconomica, V. 25: pp. 1-29 (Republished in Pasinetti 1980)
• Luigi L. Pasinetti (Editor) (1980) Essays on the Theory of Joint Production, Columbia University Press
• P. Petrovic (1991) "Shape of a Wage-Profit Curve, Some Methodology and Empirical Evidence", Metroeconomica, V. 42, N. 2: pp. 93-112
• Anwar Shaikh (1984) "The Transformation from Marx to Sraffa", in Ricardo, Marx, Sraffa (Ed. by E. Mandel and A. Freeman), Verso

2005 USA Labor Values

Figure 1 and Table 1 list industries in order of declining labor values, as of 2005. Industries are as aggregated in the North American Industry Classification System (NAICS), and labor values are in units of person-years per $1,000 output. Table 1 also shows direct labor coefficients for each industry. Direct labor coefficients are the full time equivalent staff hired in each industry. Labor values for each industry are the sum of direct labor values and the labor embodied in the inputs purchased by that industry. For example, the labor embodied in the commodities produced by "Food Services and Drinking Places" includes the labor embodied in commodities purchased by such establishements from the Construction; Real Estate; Miscellaneous Professional, Scientific and Technical Services; and Wholesale Trade industries.

I can think of other analyses to do with this and related data, such as some measure of average wage in an appropriate numeraire. For example, one might examine the rate of exploitation, the variation in the organic composition of capital by industry, and the differences between prices and labor values.

Figure 1: 2005 Embodied Labor Values

Industry	Embodied Labor Values (Person-years per Thousand $ Output)	Direct Labor Coefficient (Person-years per Thousand $ Output)
Social Assistance	0.0219	0.0185
Food Services and DrinkingPlaces	0.0200	0.0157
Forestry, Fishing, and Related Activities	0.0192	0.0103
Transit and Ground Passenger Transportation	0.0174	0.0138
Administrative and Support Services	0.0172	0.0136
Educational Services	0.0169	0.0134
Amusements, Gambling, and Recreation Industries	0.0152	0.0122
Other Services, Except Government	0.0152	0.0112
Hospitals and Nursing and Residental Care Facilities	0.0146	0.0107
Warehousing and Storage	0.0141	0.0127
Wood Products	0.0141	0.00537
Apparel and Leather and Allied Products	0.0139	0.00840
Retail Trade	0.0137	0.0106
Accomodation	0.0133	0.00986
State and Local General Government	0.0129	0.00971
Furniture and Related Products	0.0128	0.00651
Printing and Related Support Activities	0.0119	0.00719
Textile Mills and Textile Product Mills	0.0119	0.00548
Other Transportation and Support Activities	0.0111	0.00908
Construction	0.0110	0.00623
Federal Government Enterprises	0.0105	0.00803
Ambulatory Health Care Services	0.0103	0.00727
Fabricated Metal Products	0.0102	0.00555
State and Local Government Enterprises	0.00996	0.00525
Truck Transportation	0.00989	0.00539
Motor Vehicles, Bodies and Trailers, and Parts	0.00963	0.00226
Waste Management and Remediation Services	0.00923	0.00492
Plastics and Rubber Products	0.0922	0.00410
Machinery	0.00920	0.00399
Misc. Professional, Scientific and Technical Services	0.00914	0.00501
Miscellaneous Manufacturing	0.00903	0.00450
Nonmetallic Mineral Products	0.00898	0.00444
Paper Products	0.00895	0.00302
Food and Beverage and Tobacco Products	0.00890	0.00247
Computer Systems Design and Related Services	0.00888	0.00627
Computer and Electronic Products	0.00880	0.00340
Electrical Equipment, Appliances, and Components	0.00880	0.00393
Information and Data Processing Services	0.00869	0.00339
Other Transportation Equipment	0.00847	0.00349
Air Transportation	0.00841	0.00352
Performing Arts, Spectator Sports, Museums, Etc.	0.00831	0.00512
Motion Picture and Sound Recording Industries	0.00821	0.00371
Federal General Government	0.00812	0.00430
Wholesale Trade	0.00811	0.00526
Insurance Carriers and Related Activities	0.00805	0.00372
Rental and Leasing Services and Lessors of Intangible Assets	0.00784	0.00243
Water Transportation	0.00780	0.00159
Farms	0.00778	0.00264
Legal Services	0.00758	0.00512
Management of Companies and Enterprises	0.00757	0.00469
Publishing Industries (Includes Software)	0.00751	0.00317
Primary Metals	0.00736	0.00237
Rail Transportation	0.00686	0.00326
Support Activities for Mining	0.00656	0.00263
Fed. Reserve Banks, Credit Intermediation, Etc.	0.00635	0.00408
Mining, Except Oil and Gas	0.00623	0.00329
Chemical Products	0.00621	0.00160
Broadcasting and Telecommunications	0.00598	0.00188
Securities, Commodity Contracts, and Investments	0.00542	0.00246
Pipeline Transportation	0.00524	0.000922
Funds, Trusts, and Other Financial Vehicles	0.00514	0.000918
Real Estate	0.00326	0.000687
Petroleum and Coal Products	0.00325	0.000274
Utilities	0.00294	0.00133
Oil and Gas Extraction	0.00250	0.000507

Numeraire-Free Tests Of The Labor Theory Of Value

A reminder to my self - the following article belongs on this list.

• Mariolis, Theodore and George Soklis (2011) "On Constructing Numeraire-Free Measures of Price-Value Deviation: A Note on the Steedman-Tomkins Distance" Cambridge Journal of Economic, V. 35, N. 3: 613-618.