Failing to Empirically Render Visible What Was Hidden

Figure 1: Wage Share versus Ratio of Rate of Profits

1.0 Introduction

Consider the theory that Sraffa's standard system can be used to empirically predict distribution and prices in existing economies. Although individual commodities might be produced with extremely labor-intensive or capital-intensive (at a given rate of profits?) processes, large bundles of commodities chosen for technical characteristics, such as net output or wage goods, would be expected to be of average labor intensity. And the standard commodity formalizes the idea of a commodity of average capital intensity.

The data I looked at rejected this theory as a universal description of economies around the world.

2.0 Theory

The standard system is here defined for a model of an economy in which all commodities are produced from labor and previously produced commodities. The technique in use is characterized by the Leontief input-output matrix A and the vector a₀ of direct labor coefficients. The gross output, q, of the standard system is a (right hand) eigenvector of the Leontief input-output matrix, corresponding to the maximum eigenvalue of the matrix:

(1 + R) A q = q,

where R is the maximum rate of growth (also known as the maximum rate of profits). The maximum rate of profits is related to the maximum eigenvalue, λ_m, by the following equation:

R = (1λ_m) - 1

From previous empirical work, I know that the maximum rate of profits is positive for all countries or regions in my data. The standard system is defined to operate on a scale such that the labor employed in the standard system is a unit quantity of labor:

a₀ q = 1

The standard commodity, y, is the net output of the standard system:

y = q - A q

In the standard system, such aggregates as gross output, the flow of capital goods consumed in producing the gross output, the net output, the commodities paid in wages, and the commodities consumed out of profits all consist of different amounts of a single commodity basket, fixed in relative proportions. Those proportions spring out of the technical conditions of production in the actual economy.

Prices of production represent a self-reproducing system in which tendencies for capitalists to disinvest in some industries and disproportionally invest in other industries do not exist. In some sense, they arise in an economy in which all industries are expanding so as to maintain the same proportions. Such prices can be represented by a row vector, p, satisfying the following equation:

p A(1 + r) + a₀ w = p,

where r is the rate of profits and w is the wage paid out of the net product. The adoption of the standard commodity as numeraire yields the following equation:

p y = 1

One can derive an affine function for the wage-rate of profits. (Hint: multiply both sides of the first equation above for prices of production above on the right by the standard commodity.) This relationship is:

w = 1 - (r/R)

Prices of production in the standard system can easily be found for a known rate of profits.

p = a₀ [I - (1 + r) A]^-1 [1 - (r/R)]

If wages were zero, the rate of profits would be equal to its maximum in the standard system. If the rate of profits were zero, the wage would be equal to unity. The wage represents a proportion of the net output of the standard system. It declines linearly with an increased rate of profits.

The gross and net outputs of any actually existing capitalist economy cannot be expected to be in standard proportions, particularly since some (non-basic) commodities are produced that do not enter into the standard commodity. But do conclusions that follow from the standard system hold empirically? in particular, the average rate of profits, the proportion of the net output paid out in wages, and market prices are observable. Given the average rate of profits for the economy as a whole, the proportion of the standard commodity paid out in wages can be calculated. Is this proportion approximately equal to the observed proportion of wages? Do the corresponding relative prices of production calculated with the standard commodity closely resemble actual relative market prices? This post answers the question about wages. The empirical adequacy of prices of production is left to a later post.

3.0 Results and Discussion

I looked at data on 87 countries or regions, derived from the GTAP 6 Data Base, compiled by the Global Trade Analysis Project at Purdue. (I had help extracting the database and putting it in a format that I can use.) GTAP 6 data is meant to cover the year 2001. The data covers up to 57 industries. (Not all industries exist in each country.)

For each country or region, I calculated:

• The observed proportion of the net output paid out on wages.
• The observed rate of profits, as the proportion of the difference between net output and wages to the total prices of intermediate inputs.
• The maximum rate of profits for the standard system.
• The ratio of the observed rate of profits to the maximum rate.

Figure 2 shows the distributions of the observed and maximum rate of profits.

Figure 2: Distribution of Actual Rate of Profits and Maximum in Standard System

Four countries or regions in the data had an actual rate of profits exceeding the theoretical maximum rate of profits: The rest of North America, Uruguay, Belgium, and Cyprus. The rest of North America is a region consisting of Bermuda, Greenland, and Saint Pierre and Miquelon. The four countries and regions are excluded from the linear regression and statistics given below.

Figure 1 shows the results of a linear regression of the wage on the ratio of the rate of profits. If, for each country or region, the standard system were empirically applicable to that country or region the intercept of the regression line would be near one, and the slope would be approximately negative one. But the 99% confidence intervals of the intercept and slope do not include these values. In this sense, the theory is rejected by the data.

Figure 1 points out the twelve countries with the wage furthest away from the prediction from the standard system. Why might the theory be off for these countries and the four excluded from the regression? Perhaps the net output is not near standard proportions. This possible variation of between the proportions of the standard commodity and the actual net output is abstracted from when plugs the observed rate of profits into the wage-rate of profits function for the standard system. I have looked at wage-rate of profits curves, drawn with the observed technique in use and the observed net output as numeraire. And countries far from the theory generally stick out as having wage-rate of profits curves with extreme curvatures.

Another possibility is that the industries in an economy are not earning nearly the same rate of profits, not merely because of barriers to entry but because of the economy not being in equilibrium. Prices of production, for any numeraire do not prevail.

Another possibility is that the Leontief matrix and the vector of direct labor coefficients do not capture the economic potential of the country or region. For example, the calculation of the rate of profits abstracts from the existence of land and fixed capital. Most interestingly, suppose the country or region does not characterize an isolated economic system. A region in the data combines several countries for which data is difficult to get. And the above analysis highlights several of these regions: the rest of North America, Central America, and the rest of Middle East (which consist of all of the Middle East besides Turkey). Or the country under consideration might be small and heavily dependent on imports and exports. You might notice Hong Kong and Singapore, which are important international ports. Think also of small countries that provide off-shore banking facilities. Recent events have alerted me to Cyprus serving this purpose for the countries that were formerly in the Soviet Union. I do not know much about Ireland, but recent discussion of how Apple shields its profits makes me wonder about the reported profits for its economy.

I do not know what to fully make of this analysis. The empirical use of the standard commodity seems to be more of a heuristic than the application of a claimed universal law. And the failure of its application seems to point out aspects of the deviating countries that seem of economic interest.

Appendix: Data Tables

Table 1: Descriptive Statistics for Rate of Profits (Four Countries Removed)

Statistic	Maximum Rate of Profits	Observed Rate of Profits	Ratio of Observed Rate To Maximum
Sample Size	83	83	83
Mean	84.852	48.623	0.591
Std. Dev.	26.088	14.898	0.138
Coeff. of Var.	0.307	0.306	0.234
Skewness	-0.374	-0.044	0.623
Kurtosis	0.326	0.591	0.134
Minimum	8.623	5.495	0.356
1st Quartile	66.195	39.947	0.476
Median	86.242	47.385	0.575
3rd Quartile	104.139	58.124	0.662
Maximum	144.818	84.822	0.967
Interquartile Range/Median	0.440	0.384	0.323

Table 2: Descriptive Statistics for Wages (Four Countries Removed)

Statistic	Wage in Standard System	Observed Wage
Sample Size	83	83
Mean	0.409	0.431
Std. Dev.	0.138	0.085
Coeff. of Var.	0.338	0.198
Skewness	-0.623	-0.397
Kurtosis	0.134	-0.597
Minimum	0.033	0.246
1st Quartile	0.338	0.360
Median	0.425	0.453
3rd Quartile	0.524	0.491
Maximum	0.644	0.597
Interquartile Range/Median	0.438	0.289

Update (16 September 2014): The analysis reported above is based on Leontief input-output matrices which include investment as a sector. Apparently, it is common in Computational General Equilibrium (CGE) models to treat investment as endogenous, in some sense. I plan on redoing the analysis with this sector removed and with disaggregated investment included in final demands.

The Temporal Single System Interpretation and Marx's History of Political Economy

I associate the Temporal Single System Interpretation (TSSI) of Marx's Capital most notably with Alan Freeman and Andrew Kliman. The TSSI must be addressed today by those grappling with the mathematics of the Transformation Problem, with how prices and labor values are related. But I think the TSSI makes much of Marx's work incomprehensible.

Whatever else Marx was, he was very well read. And he had many comments on the political economy of his predecessors and contemporaries. You can see this most obviously in Theories of Surplus Value, the so-called fourth volume of Capital. But, really, you can find such comments throughout Marx's work, extending back even to the Economic and Philosophical Manuscripts of 1844.

Arguably, Marx was not trying to create a scientific theory of capitalist economies¹, although he did extend classical political economy along these lines. Rather Marx thought that even the best work of British political economy - that is, David Ricardo - took too much for granted. How does capitalism create the illusion that labor is a commodity, freely bought and sold on the market like any other commodity? Why do so many come to believe that profits are a return to capitalists for the contribution of capital to production? How did the institutions of capitalist economies emerge from a feudal past? These are central questions for Marx. He addressed them through a process of immanent criticism.

I am not sure that Marx was always fair to Smith and Ricardo. He often castigates them for not recognizing distinctions that Marx himself created. (On the other hand, I can see the point of arguing that Ricardo was not clear on the difference between relative natural prices and a notion of absolute value that he was struggling to develop.) Marx's unfairness, if that is what it is, strengthens my point. Does he argue that Ricardo should have been developing the sort of supposedly dynamic concepts essential to the TSSI? Or does he accept that Ricardo has adopted an approach consistent with TSSI, with his difficulties being located elsewhere? On the other hand, a dual system interpretation, in some formulation or other, has no problem with understanding the differences between market and natural prices and Smith's idea, for example, that natural prices act as centers of gravitational attraction for market prices.

One can find many proponents of the TSSI writing in a style drawing on Hegel, whether on his head or right-side up. But I am not aware of any detailed work by such proponents exploring Marx's comments on, say, William Petty, Francois Quesnay, Adam Smith, Ricardo, with an emphasis on if or how they disagreed with the TSSI.

Footnotes

1. I recognize a tension here with the empirical work I have been presenting in the last couple of weeks.

Estimates Based On Labor Values More Precise Than Those Based On Direct Labor Coefficients

Table 1: Variations Across Countries

1.0 Introduction

This post is an empirical exploration of a simple labor theory of value as a theory of price. The precision of estimates of labor values is compared with the precision of estimates based on direct labor coefficients. The question of the accuracy of the labor theory of value is left to later posts.

I think of precision and accuracy in terms of darts. Suppose all your dart throws cluster together. Then they are precise, even if that cluster is not near the bulls eye. But if they are also in the bulls eye, then your throws are accurate, as well.

2.0 Direct Labor Coefficients and Labor Values

Labor values are calculated in the manner I find most straightforward, from a pure circulating capital model. Each industry in a modeled country, in the year in which the country is observed, produces a flow of a single commodity. Inputs for each industry consist of labor power and a flow of commodity inputs. The quantity of labor directly used, per unit output of the industry, constitutes the direct labor coefficient for that industry.

The labor value embodied in a commodity consists of all labor directly or indirectly used as an input for producing it. In the model, all inputs into production can be reduced to an infinitely long, dated stream of labor inputs. For example, the input into the industry for wearing apparel includes labor directly employed in the given year, as well as some labor directly employed in the textile industry in the previous year. (In calculating such dated labor inputs, one abstracts from changes from technology, at least in the approach that I am using. The same technique is assumed to have been used forever in the past.) Inputs directly used in the textile industry include outputs of the industry for wool and silk worm cocoons. Thus, the labor inputs into the industry for wearing apparel include some labor directly employed in that industry two years ago, as well as some labor employed three years ago in the industry for bovine cattle, sheep and goats, and horses. Given that the technique for the economy is viable, the sum of the infinite sequence of labor inputs constructed in the way outlined converges to a finite sum. I know that the techniques for all countries that I am considering are viable, based on previous empirical work.

3.0 Source of the Data

Labor values are found, for each of one of 87 countries or regions, as calculated from a Leontief matrix and vector of direct labor coefficients for a country. Each Leontief matrix was derived from a transaction table. The transactions tables, in turn, are derived from the GTAP 6 Data Base, compiled by the Global Trade Analysis Project at Purdue. (I had help extracting the database and putting it in a format that I can use.) GTAP 6 data is meant to cover the year 2001. The data covers up to 57 industries. (Not all industries exist in each country.)

Quantities of each commodities, including labor power, are measured such that a unit of each commodity can be purchased with one billion dollars at prices observed when the data was taken. With this choice of units, and the adoption of one billion dollars as the numeraire, observed market prices are unity for each produced commodity.

4.0 Results and Discussion

Figures 2 and 3 show direct labor coefficients and labor values, as calculated from the data. Each point in, say, Figure 2, represents the direct labor coefficient in a specific country for the industry with the label on the X axis. Many points are plotted for each industry, since that industry exists in many countries.

Table 2: Direct Labor Coefficients By Industry

Table 3: Labor Values By Industry

The labor value for each industry, in a given country, exceeds the corresponding direct labor coefficient. I was surprised to see that any direct labor coefficients or labor values exceed unity. The largest labor coefficient and labor value is for the industry producing oil seeds in Greece. Looking at the transactions tables, I see value added includes rows for a value-added tax, as well as income for labor, returns to capital, and rents on land. In Greece, the value-added tax for oil seeds is negative. Perhaps the government of Greece has decided that, for example, the olive oil industry is important to them for cultural reasons. And they subsidize it. So this most extreme point on my graph points to something of economic interest.

The labor values, for example, for a specific industry constitute a sample, with each country contributing a sample point. For the labor values for that industry, one can calculate various statistics, including the sample size, the mean, the standard deviation, skewness, and kurtosis. The sample size will never exceed 87, since Leontief matrices were calculated, in the analysis reported here, for 87 countries.

The coefficient of variation is a dimensionless number. It is defined as the quotient of the standard deviation to the mean. Since the coefficient of variation is dimensionless, it does not depend on the choice of physical units in which to measure the quantities of the various commodities.

Figure 1, at the top of this post, shows the distributions of the coefficient of variation, for labor values and direct labor coefficients, across countries. The variation in labor values tends to be smaller and more clustered than the variation in direct labor coefficients. Consider two theories, where one states that prices in a country tend to be proportional to labor values. The other theory is that prices tend to be proportional to direct labor coefficients. This post is an empirical demonstration that the first theory is more precise.

Even If The Workers Could Live On Air

The Maximum Rate Of Growth Around The World

Consider a model of an economy in which all commodities are produced from inputs of labor and previously produced commodities. And suppose the commodities needed as inputs in the production of commodities are described through a Leontief input-output matrix in which no commodity can be produced with (unassisted) direct labor alone. Consider the special case in which wages are zero. In a sense, this special case can be seen as a description of a futuristic economy in which all production is automated, and robots are used to produce robots.

In the theory, the input-output relations determine a finite maximum rate of profits, corresponding to the maximum eigenvalue of the Leontief matrix. This maximum rate of profits is also the maximum rate of growth that arises in the Von Neumann growth model. A composite commodity, proportional to the associated eigenvector, arises from the Leontief matrix. Along the Von Neumann ray, the output of the economy each year consists of an evenly expanding output of this standard commodity, as Piero Sraffa called it. The standard commodity, in some sense, is a generalization of "corn" in David Ricardo's corn model (which was expounded in his 1815 Essay on the Influence of a Low Price of Corn on the Profits of Stock). The commodities with positive quantities in the standard commodity are known as basic commodities, once again in Sraffa's terminology.

As this post demonstrates, this is an operational model. The graph above is based on an eigenvector decomposition of Leontief matrices. Each Leontief matrix was derived from a transaction table for a country or region. The transactions tables, in turn, are derived from the GTAP 6 Data Base, compiled by the Global Trade Analysis Project at Purdue. (I had help extracting the database and putting it in a format that I can use.) GTAP 6 data is meant to cover the year 2001. Quantities of each commodities are measured such that a unit of each commodity can be purchased with one billion dollars at prices observed when the data was taken.

The graph above and the table below show the maximum rate of profits or growth for each country or region for the snapshot yielding the data. The actual rate of profits for prices that allow for the smooth reproduction of the economy falls below the maximum, sometimes considerably, because the workers do not live on air. The larger the proportion of the net output of the economy paid out in wages, the lower the corresponding rate of profits. At any rate, prices of production fall out, given some information on the distribution of income and production conditions.

Along with calculating the maximum rate of profits, I found the standard commodity and identified which commodities are basic for each country or region. For example, the commodities produced by the following industries are basic commodities in the United States: Cereal Grains; Vegetables, Fruits, Nuts; Crops; Bovine Cattle, Sheep and Goats, Horses; Animal Products; Raw Milk; Coal; Oil; Minerals; Bovine Meat Products; Meat Products; Dairy Products; Sugar; Food Products; Beverages and Tobacco Products; Textiles; Wearing Apparel; Wood Products; Paper Products; Publishing; Petroleum, Coal Products; Chemical, Rubber, Plastic Products; Mineral Products; Ferrous Metals; Metals; Metal Products; Motor Vehicles and Parts; Transport Equipment; Electronic Equipment; Machinery and Equipment; Manufactures; Electricity; Gas Manufacture, Distribution; Water; Construction; Trade; Transport; Water Transport; Air Transport; Communication; Financial Services; Insurance; Business Services; Recreational and Other Services; and Public Administration, Defense, Education, Health. Which commodities are basic varies among countries, and I typically found a few non-basic commodities in each country.

I think this data is fairly comprehensive, and I hope that I can do further believable analyses with it.

Maximum Rate Of Growth By Country

Country	Rate of Growth (Percent)
Peru	144.8
Turkey	132.5
Rest of Southeast Asia	127.4
Albania	125.3
Uganda	122.5
Zambia	121.6
Rest of Southern Africa Development Community	120.7
Mozambique	119.3
Greece	117.8
Mexico	117.3
Argentina	116.9
Columbia	115.0
France	109.8
Sri Lanka	109.6
Chile	108.8
United States	107.1
Bangladesh	106.4
Zimbabwe	106.3
Rest of Sub-Saharan Africa	105.6
Spain	104.4
Madagascar	104.1
Rest of South Asia	104.1
Venezula	104.1
Japan	103.4
Switzerland	102.5
Italy	101.0
Botswana	98.2
United Kingdom	97.7
India	93.8
Indonesia	93.0
Rest of Free Trade Area of the Americas	92.8
Rest of EFTA	92.0
Portugal	91.4
Canada	90.7
Malta	89.3
Rest of the Caribean	88.9
Denmark	88.7
Rest of Central America	88.4
Tanzania	87.7
Rest of South America	87.1
Australia	87.1
Rest of Europe	86.2
Brazil	85.6
Sweden	85.2
Rest of North Africa	84.3
South Africa	83.5
New Zealand	82.7
Rest of Middle East	82.5
Tunisia	82.3
Taiwan	82.1
Netherlands	81.7
Finland	80.0
Poland	76.8
Germany	76.6
Latvia	75.8
Rest of South African Customs Union	75.0
Malawi	72.9
South Korea	72.9
Hungary	72.4
Austria	70.3
Luxembourg	67.6
Romania	66.6
Russia	66.2
Lithuania	66.0
Rest of East Asia	64.4
Philippines	64.2
Estonia	62.3
Thailand	61.6
Malaysia	60.5
Vietnam	60.0
Rest of Oceania	57.6
Ireland	55.2
Central America	54.3
Slovakia	54.0
China	53.8
Slovenia	53.7
Croatia	51.1
Czech Republic	47.1
Belguim	46.9
Morocco	45.9
Hong Kong	40.6
Singapore	35.0
Cypress	24.6
Rest of Former Soviet Union	12.7
Uruguay	12.4
Bulgaria	8.6
Rest of North America	4.7

Political Intervention in Faculty Selection at the UIUC

This is a post about the University of Illinois at Urbana Champaign (UIUC)¹. It is not about current events.

In the late 1940s, UIUC attempted to revamp their economics department. They hired many new economists, including, for example, Jacob Marschak and Franco Modigliani². A bunch of economists previously at UIUC resisted these modernizing changes. They ended up calling for political support in the press, complaining about New Deal politics. And the department was purged, in a violation of academic freedom, of these new-fangled economists³.

I thought I knew about this incident originally from reading an Esther Merjam Sent article about why both rational expectations and bounded rationality could have emerged from research at Carnegie Mellon during the 1950s - maybe, "Sargent versus Simon: Bounded Rationality Unbound" (Cambridge Journal of Economics, V. 21, No. 3 (1996): pp. 323-338). Or maybe I am recalling Fred Lee's 2009 book, A History of Heterodox Economics: Challenging the mainstream in the twentieth century. Googling, I find a draft of a paper from Antonella Rancan, who I have not otherwise read.

Footnotes

1. I have many positive impressions of UIUC. As I recall, the first graphical web browser was made there.
2. Modigliani, in a 1944 paper, extended the Hicksian IS/LM interpretation of Keynesianism to include a labor market with sticky wages. This was a critical contribution towards a politically powerful approach that Post Keynesians quarrel with on theoretical grounds (while agreeing, mostly, on short term political implications).
3. Modigliani ended up at Carnegie Mellon, which I guess was once not called that.

Labor Demand In A Fog

Figure 1: Labor Demanded Per Unit Output in a Stationary State

1.0 Introduction

As a Sraffian, I have no problem with open models in which room exists for exogenous political forces to determine distribution. The example here, though, has more indeterminancy than I expect.

2.0 Technology

Consider a simple capitalist economy, composed of workers and capitalists. After replacing (circulating) capital goods, output consists of a single consumption good, corn. The workers are paid a wage, w (in units of bushels corn per person year) out of the harvest. Capitalists obtain the rate of profits, r. The technology¹ consists of an infinite number of Constant-Returns-to-Scale (CRS) techniques. In each technique, a bushel of corn is produced from inputs of:

• l₀ person-years of labor performed in the year of the harvest.
• l₁ person-years of labor performed one year before the harvest-year.
• l₂ person-years of (unassisted) labor performed two years before the harvest-year.

Each technique is determined, given the values of the two index variables s and t. s is a non-negative real number less than or equal to the parameter c. t is a non-negative real number.

l₀(t, s) = A - B + (t + 1)(B - s)/2

l₁(t, s) = s

l₂(t, s) = (B - s)/[2 (t + 1)]

where A, B, and c are positive constants and

c ≤ B ≤ A

In effect, the above has traced out isoquants for a production function, where the quantity of output is a function of dated labor inputs². For a given value of the index variable s, labor inputs in the harvest year and two years before can be traded off. That is, if the amount of labor two years before is lower, then more labor must be expended in the harvest year. Likewise, for a given value of the index variable t, more labor being expended one year before the harvest mandates less labor being expended in the harvest year and two years before. So this specification of technology allows for substitution among inputs, at least in comparing steady states^{3, 4.}

3.0 Choice of Technique

As usual, I consider a competitive, steady state economy in which capitalists have chosen the cost-minimizing technique, at an exogenously specified wage or rate of profits. Consider the function v(r, t, s):

v(r, t, s) = (1 + r)² l₂(t, s) + (1 + r) l₁(t, s) + l₀(t, s)

Take a bushel of corn as numeraire. The condition that all income be paid out to workers and capitalists leads to a wage-rate of profits curve, as a function of the rate of profits and the technique (specified by the values of the two index variables):

w(r, t, s) = 1/v(r, t, s)

A wage-rate of profits curve can be drawn for each technique. The wage-rate of profits frontier, consistent with a competitive steady-state, is the outer envelope (Figure 2) of all these curves. That is, for a given wage, one finds the values of the index variables that maximizes the wage among all techniques. This maximization does not fix s. But, for each value of s, the maximum is found by setting the index variable t equal to the rate of profits r. The equation for the frontier is:

w(r) = 1/(A + Br)

Notice the frontier is independent of the labor input, s, in the first year before the harvest. In this case, each point on the frontier is consistent with a continuum of profit-maximizing techniques. And these techniques vary continuously along the frontier. None of this indeterminancy is apparent by looking at the frontier⁵.

Figure 2: The Wage-Rate of Profits Frontier

4.0 Labor Inputs

The analysis of the choice of technique allows one to plot labor inputs versus selected variables from the price system. In any year in a stationary state, some workers will be gathering the harvest, some will be working on preparing for the harvest one year out, and some will be working on preparing for the harvest two years out. So employment, per the unvarying net output, is the sum of l₀, l₁, and l₂. And these labor inputs can be found from a given rate of profits and a choice of s. From the wage-rate of profits frontier, one can calculate the wage for any given rate of profits. Thus, one has the two dimensions needed to draw the curves in Figure 1. One sees that, for any given wage in an interval from zero to a maximum, the quantity of labor demanded by the firms per unit output is a relation, not a function of the wage. If the relation shown were considered to be a labor demand curve, the curve would have a certain (varying) thickness.

5.0 Capital Inputs

The analysis of the choice of technique also allows one to plot the value of capital goods⁶ versus selected variables from the price system. I define the value of capital per unit output, given the rates of profit and the technique like so:

k(r, t, s) = (1 + r) l₂(t, s) w + l₁(t, s) w

This definition is such that the value of capital advanced, discounted to harvest time, and the wages paid out of the harvest add up to unity:

k(r, t, s) (1 + r) + l₀(t, s) w = 1

Impose the condition here, too, that only cost-minimizing techniques are considered for a given rate of profits. Then one obtains the curves shown in Figure 3. Here, too, the analysis yields an obvious indeterminancy.

Figure 3: Capital Demanded Per Unit Output in a Stationary State

6.0 Conclusion

Does this example undermine Sraffian analysis, as well as introductory textbook labor economics?

Footnotes

1. Notation and numerical values are chosen to be consistent with a past post.
2. I am unsure how to explicitly represent such a production function.
3. With three or more inputs, some complementarity among inputs is possible. I am not sure how to express this formally.
4. I suppose the production function consistent with the data exhibits non-negative marginal returns. I am not sure it would exhibit non-increasing marginal returns. If not, I would like to see either a proof, in the general case with n dated labor inputs, that the shaded violet regions cannot arise, given such conventional properties for a production function. Or, I would like to see a concrete numerical illustration like mine, but with such conventional properties shown to hold.
5. Also, notice the analysis of the choice of technique leads to simpler equations than those in the specification of the technology. This is not an accident.
6. I gather that, for any given value of s, unassisted labor two years before the harvest can be used to produce one of a continuum of capital goods, depending on the value of t. And once one of these capital goods is selected, the minimum dated labor inputs in each of the three years are fixed. Maybe this way of thinking about capital goods makes issues of convexity raised in Footnote 4 of little interest.

References

• Enrico Bellino (1993). Continuous Switching in Linear Production Models, Manchester School, V. 61, Iss. 2 (June): pp. 185-201.
• Christian Bidard (2014). The Wage Curve in Austrian Models, Centro Sraffa Working Papers n. 3 (June).

The Generality Of The Sraffian Analysis Of The Choice Of Technique

Figure 1: Labor Demanded Per Unit Output in a Stationary State

1.0 Introduction

This post illustrates the analysis of the choice of technique in a case in which marginal products cannot be defined, even in the sense of an interval. It is one more example of the falsity of Austrian and vulgar neoclassical teaching. Perhaps this example suggests the possibility of, say, labor demand "functions" that have a certain thickness or cloudiness.

As far as I know, nobody has used an Austrian flow-input point-output technology to make the point about indeterminacy illustrated by this post. Bellino (1993) presents three examples in which a continuously differentiable, smooth wage-rate of profits curve is consistent with multiple technologies, with the resulting non-differentiability of micro-economic production functions. The technology in none of the three is of the structure used here. Bidard (2014) develops tools for an analysis of Austrian production functions that I found key to developing this post.

2.0 A Simple Economy

Consider a simple capitalist economy, composed of workers and capitalists. After replacing (circulating) capital goods, output consists of a single consumption good, corn. The workers are paid a wage, w (in units of bushels corn per person year) out of the harvest. Capitalists obtain the rate of profits, r.

I specify two technologies, in some sense. Each technology consists of an infinite number of Constant-Returns-to-Scale (CRS) techniques. In each technique, a bushel of corn is produced from inputs of:

• l₀ person-years of labor performed in the year of the harvest.
• l₁ person-years of labor performed one year before the harvest-year.
• l₂ person-years of (unassisted) labor performed two years before the harvest-year.

A technology is fully determined here by specifying all possible values of these dated labor inputs.

2.1 First Technology

Let s be, roughly, an element of a set Q, with Q a subset of the real numbers to be fully specified below. A capitalist knows the minimum labor requirements for each technique in this technology, where a technique is indexed by s. These labor inputs are, in obvious notation:

l_1,0(s) = a + b s

l_1,1(s) = c

l_1,2(s) = 1/(s + 1)

where a, b, and c are positive constants, b is less than one, b is the square of a rational number, and:

b - b^1/2 ≤ a,

(In drawing graphs throughout this post, I use values of a, b, and c of 2, 9/16, and 3, respectively.)

2.2 Second (Sekt) Technology

I learned the word "Sekt" from Bidard; maybe he enjoys champagne. Anyways, in this technology, positive labor inputs only occur in the year of the harvest and two years before. The labor inputs one year before the harvest are zero. For convenience, define the following non-negative constants:

A = a - b + B

B = 2b^1/2 + c

C = a - b + D

D = B/2

In this technology, the techniques are indexed by the variable t, where t is from the subset of the real numbers obtained by removing all elements of Q from the real numbers. The labor inputs are:

l_2,0(t) = C + D t

l_2,1(t) = 0

l_2,2(t) = D/(t + 1)

3.0 The Choice of Technique

As usual, I consider a competitive, steady state economy in which capitalists have chosen the cost-minimizing technique, at an exogenously specified wage or rate of profits. For a given wage, the cost of a technique in the first technology is proportional to v₁(r, s):

v₁(r, s) = (1 + r)² l_1,2(s) + (1 + r) l_1,1(s) + l_1,0(s)

The corresponding function, v₂(r, t), for the second technology is:

v₂(r, t) = (1 + r)² l_2,2(t) + l_2,0(t)

The capitalists choose the technique to minimize v₁(r, s) or v₂(r, t), depending on whether such minimization results in an index being selected from Q or not. The wage-rate of profits curve for a given technique in the first technology is:

w₁(r, s) = 1/v₁(r, s)

I hope the corresponding notation for the wage-rate of profits curve for a technique in the second technology is obvious.

The choice of the cost-minimizing technique results in specifying the indices for the technique in the two technologies as functions of the rate of profits:

s(r) = (1/b^1/2)(1 + r) - 1

t(r) = r

After working out this analysis of the choice of technique for the first technology, I could have re-specified the first technology such that the index for the cost-minimizing technique was always equal to the rate of profits, as in the second technology. I worked backwards, in some sense, following Bidard, such that this nice property obtained for the second technology.

The wage-rate of profits frontier is the outer envelope of the wage-rate of profits curves for the techniques. This frontier (Figure 2) can be shown to be:

w(r) = 1/(A + Br)

I do not specify the technology for the frontier. This example has been constructed such that the both technologies have the identical frontier, when they are extended such that the index for the technique can be any real number. Since the technique varies continuously with the rate of profits, no point on the frontier is a switch point. Further, no technique on the frontier appears more than once. So this is not an example of the reswitching of techniques.

Figure 2: The Wage-Rate of Profits Frontier

I conjecture that a continuum of technologies exist with this frontier. Think of each one of these technologies as corresponding to a constant labor input in the first year before the harvest in the interval [0, c]. I guess, given Bidard's paper, this is an obvious idea.

4.0 Labor Inputs

The analysis of the choice of technique allows one to plot labor inputs, given a complete specification of the technology, versus selected variables from the price system. Accordingly, suppose the first technology is specified only when the index for the technique is a rational number. That is, the set Q is the set of rational numbers. And the set from which the index for the technique in the second technology is the set of irrational numbers.

Figure 3 is an attempt to visualize the labor demanded by firms, per unit output, in the harvest year as a function of the rate of profits. Despite appearances, neither curve in this graph is continuous; they both have an infinite number of holes. The upper curve has a countable infinity of gaps, while the lower curve has an uncountably infinite number of holes. Since these curves are discontinuous everywhere, the marginal product of labor in the harvest year is undefined. One might think of the employment for harvesters as leaping up and down between the curves as the rate of profit varies among economies.

Figure 3: Labor Inputs Per Unit Output in Harvest Year

Perhaps this example is an argument for adopting constructive mathematics in economics. But one can still get leaps between technologies with a continuous variation in the rate of profits, given a more straightforward set Q. Anyways, the labor demanded by firms, per unit output, one year before the harvest leaps between zero and the constant c. Figure 4 shows the labor demanded, per unit output, two years before the harvest. These curves are also discontinuous everywhere.

Figure 4: Labor Inputs Per Unit Output Two Years Before Harvest Year

Suppose, as in Austrian and neoclassical capital theory, that the interest rate (that is, supposedly the rate of profits) were a scarcity index for capital. A higher interest rate would indicate the availability of less capital per worker. Consequently, capitalists would supposedly be encouraged, for this sort of Austrian model, to adopt a technique in which more labor is hired during the harvest year and less during succeeding years (for example, two years beforehand). This idea is consistent with, for example, the first technology. Figures 3 and 4 show that, if one focuses solely on the blue lines, at a higher interest rate, firms want to hire less labor in the given year before the harvest and more during the harvest year. But this idea is inconsistent with the possibility of leaping from one technology to another, as illustrated in Figures 3 and 4. So this example provides another logical proof of the incorrectness of Austrian theory.

As a final step, I want to describe how to generate Figure 1, at the top of this post. In any year in a stationary state, some workers will be gathering the harvest, some will be working on preparing for the harvest one year out (except in the case of the sekt technology), and some will be working on preparing for the harvest two years out. So employment, per the unvarying net output, is the sum of l₀, l₁, and l₂. And these labor inputs can be found from a given rate of profits. From the wage-rate of profits frontier, one can calculate the wage for any given rate of profits. Thus, one has the two dimensions needed to draw the curves in Figure 1. And these curves, as usual here, are discontinuous everywhere. One can think of the labor demanded leaping left and right in the figure as the wage varies. So much for textbook teaching about competitive labor markers.

5.0 Conclusion

The above example has demonstrated, once again, the incoherence of vulgar neoclassical theory. If I thought economists cared about the truth or falsity of their claims, I would be puzzled about mainstream teaching about labor markets and about price theory, more generally.

References

• Enrico Bellino (1993). Continuous Switching in Linear Production Models, Manchester School, V. 61, Iss. 2 (June): pp. 185-201.
• Christian Bidard (2014). The Wage Curve in Austrian Models, Centro Sraffa Working Papers n. 3 (June).

Political Philosophers On How To Read The Bible

Some time ago, I read Hobbes's Leviathan, a classic argument for the existence of a social contract. I recently became aware of the existence of Spinoza's Treatise, which argues for freedom of thought, speech, and religion. I was surprised to discover a common theme in these early modern works of political philosophy, which I did not expect. I knew from second-hand literature that both contain rational arguments about what powers secular authorities should and should not be recognized to possess.

But I was surprised to find both philosophers engaged in interpreting the bible. Both Hobbes and Spinoza quote passages warning about false prophets. Spinoza gives naturalistic principles of reading. For example, he thinks philosophical doctrines in the bible should be read with the understanding that the authors were writing to engage the understanding of the common people of the day. I did not expect that Spinoza would cite the Israelites under Moses as the canonical example of a social contract. Spinoza, kicked out of their community by the Amsterdam Jews, writes quite a bit about the New Testament. I guess this excommunication may have had something to do with more than his identification of God with the cosmos, the Creator with the creation. (I tried to read the Ethics, with its geometric proofs, long ago.)

Hobbes and Spinoza have another commonality. They spend quite a bit of time cataloging, explaining, and analyzing human sensations, emotions, and qualities. I resist the idea that certain perspectives on human nature map directly to political positions. Mayhaps, this sort of analysis of the human psyche was part of a naturalizing Enlightenment project.

I suppose addressing the topic of religion makes sense in these books. The political authorities of the day were often claiming to rule in the name of God, I gather. I do not know much about, for example, the Spanish Inquisition, but, from what I understand, the Jewish community in Amsterdam contained many families that had fled Spain. The political situation in England often saw an entanglement of religion and politics, what with the beheading of Charles I, the rule of the puritan Oliver Cromwell, the English Revolution, and so on. So if you are going to write on politics, you might want to explain how the reader need not accept the unargued proclamations of supposed authorities. You might want to explain, also, how your ideas are consistent with religion, rightly understood.

As far as I know, many later writers arguing for liberalism in thought and speech did not feel the need to argue about what secular authority can and cannot be deduced from the Bible. As examples, I do not recall any such themes in either Rousseau or Mill.

Caveat: writers on general philosophy will include matters of epistemology and ethics. How can we come to know what ethical principles to follow, if we can? I gather that Hume is an example of such an argument. I do not know if his characters take authority from Bible verses.

References

• Thomas Hobbes (1651). Leviathan Or The Matter, Forme, & Power Of A Common-Wealth Ecclesiastical and Civill.
• David Hume (1779). Dialogues Concerning Natural Religion [TO READ].
• John Locke (1689). A Letter Concerning Toleration. [TO READ].
• John Stuart Mill (1859). On Liberty.
• Jean Jacques Rousseau (1755). A Discourse on the Origin of Inequality.
• Jean Jacques Rousseau (1762). The Social Contract.
• Benedict de Spinoza (16669-1670). Theological-Political Treatise.

Vagueness With Mathematical Economics

"Mathematics is a study which, when we start from its most familiar portions, may be pursued in either of two opposite directions. The more familiar direction is constructive, towards gradually increasing complexity: from integers to fractions, real numbers, complex numbers; from addition and multiplication to differentiation and integration, and on to higher mathematics. The other direction, which is less familiar, proceeds, by analysing, to greater abstractness and logical simplicity; instead of asking what can be defined and deduced from what is assumed to begin with, we ask instead what more general ideas and principles can be found, in terms of which what was our starting-point can be defined or deduced." -- Bertrand Russell, Introduction to Mathematical Philosophy

Many economists may be under the mistaken impression that casting economics into mathematical models ensures assumptions are explicitly stated. This is manifestly false. Here are some examples of questions about mathematical assumptions that might puzzle some economists:

• What quantity is being conserved in typical models with agents maximizing under constraints?
• Do equilibrium models with rational expectations apply when economic time series are non-ergodic?
• How would the agents in such models learn to estimate model parameters if dynamics are chaotic?
• Do models linearized around an equilibrium apply to models with multiple equilibria? Would not interesting bifurcations arise if the number of equilibria varies with model parameters?
• Have economic models been successfully tested by dimensional analysis? (One of my favorite critiques directs one to question using a measure of capital goods in numeraire units in production functions.)
• Can economic models with utility-maximizing agents handle preferences changing not randomly, but by agents imitating what they see other agents consuming?
• What more general ideas and principles (consider, for example, menu independence and the absence of lexicographic preferences) underlie utility maximization?

Against "Mixed Economy"1

The United States and many other countries are often said to have a "mixed economy". This term is supposed to locate the United States on a spectrum whose ends consist of a planned economy, as in the former Soviet Union, and a laissez-faire economy. But where can an example of a laissez-faire economy be found²? In this post, I argue for dropping the term "mixed economy", since laissez-faire is an unachievable utopia. Any attempt to create such will ultimately devolve to some combination of crony capitalism with social-democratic institutions.

I outline two arguments for my conclusion.

First property rights are not exogenous givens, provided by nature for all times and places. They are defined by law³. Any tweaks to property rights by changes in law benefit some and harm others. Those with wealth and power will want to influence these changes so as, at least, to maintain their place in society. And in a non-stagnant society, changes in law will need to be made. Thus, something that can be called crony capitalism will arise.

Second, under capitalism, labor(-power) and natural resources are treated as commodities, to be traded on markets. But such treatment ignores important dimensions of these commodities, such as the impossibility of separating the worker from the delivery of his commodity. Nobody has yet demonstrated that a society organized around self-regulating markets can exist, and the historical experience is in the negative. Some sort of limits to markets will out of necessity be imposed by society. This is the argument, as I recall it, of Karl Polanyi in The Great Transformation: The Political and Economic Origins of Our Time (1944). Polanyi explains why near laissez-faire forms in the nineteenth century could not survive.

What term could then be used for the economy in the United States? How about "actually existing capitalism"?

Footnotes

1. This post is partly inspired by the nonsense spouted by the challenger in my district to the incumbent in the Republican primary for the United States House of Representatives. This vicious reactionary claimed to be for laissez faire, not crony capitalism, and also whined about the incumbents supposed "liberalism", as demonstrated by his support from the Chamber of Commerce.
2. The "third way" is another term to locate an economy somewhere in the middle of a spectrum. I think this term was originally applied to Sweden, but later expropriated during the Clinton and Blair administrations.
3. I have pointed this out before.

Elsewhere

• Paul Heideman reviews, for Jacobin, Philip Mirowski's book, Never Let a Serious Crisis Go to Waste: How Neoliberalism Survived the Financial Meltdown.
• Robert Skidelsky calls for a reform in how economics is taught.
• Does anybody know the something about the Marxist "critique of value", as developed by certain German thinkers? Apparently, that is the theme of a blog and a book.

A Sophisticated Neoclassical Response To Cambridge Capital Controversies

A Reproduction Scheme (Based on Biddard 1990)

1.0 Introduction

One way of reading the Cambridge Capital Controversy (CCC) is an internal exploration of and debate about neoclassical price theory¹. Both sides agreed to concentrate on the case of perfect competition, with no principal agent problems, no asymmetric information, etc. The Cambridge-Italian critics thought themselves to have demonstrated that neoclassical economists could not consistently with their theory claim that equilibrium prices were indices of relative scarcity. Such a claim is not well-founded in the theory, and economists should turn away from biotechnological determinism and turn toward developing price theories in which class power matters.

In this post, I want to outline the sophisticated neoclassical response, in the 1970s, to the Cambridge-Italian critics.

2.0 General Equilibrium Models of Intertemporal and Temporary Equilibrium

This neoclassical response asserted that price theory was best expressed in terms of General Equilibrium Theory (GET). Capital theory involves production over time. Models of intertemporal and temporary equilibrium have been developed in GET. And these models, it is claimed, are both logically consistent and unaffected by Cambridge-Italian criticism².

2.1 The Arrow-Debreu Model of Intertemporal Equilibrium

The Arrow-Debreu model is a model of disaggregated individuals interacting solely through a single centralized market in existence at the beginning of time. Commodities are distinguished by their physical characteristics, where they become available, when they become available, and the state of the world in which they become available. The givens in the Arrow-Debreu model consist of, roughly:

• Tastes: Each agent can choose the more preferred consumption plan, when presented with any pair of such plans. A consumption plan specifies what commodities the agent consumes at each point in space and time in each possible state. It also specifies what inputs that the agent controls are supplied as inputs into the firms at each point in space and time and for each state.
• Technology: What commodities can be produced for supply for consumption from each possible list of inputs is known by everybody.
• Endowments: A list of commodities available at the beginning of time is given. The specification of endowments includes who owns what. Likewise, the ownership (shares) of the given finite number of firms is known.

Equilibrium is achieved in some sort of no-time before the beginning of time. The centralized market opens, and the auctioneer informs all agents of the prices of all commodities. These commodities include, for example, a contract to buy an umbrella in New York City on 20 June 2015, given it is raining. The agents inform the auctioneer of which contracts they are willing to enter and offer at the given prices. The auctioneer adjusts prices, depending on mismatches between offers and demands, until all markets clear. No transactions are allowed to take place until equilibrium is achieved³.

In an equilibrium, the plans of all agents are pre-reconciled. For any commodity with a positive (spot or forward) price, the quantity supplied equals the quantity demanded. Some goods are not commodities in equilibrium; they have a price of zero. The supply of these goods exceeds the demand.

Once equilibrium has been established, all agents make their promised trades and carry out their plans throughout time.

2.2 The GET Model of Temporary Equilibrium

The idea that all plans are only made in one big market transaction at one instant of time is hard to swallow. This constraint is relaxed in models of temporary equilibrium, as developed by, for example, J. R. Hicks (1946).

In Hicks' model, a market opens at the start of each successive week. If I recall correctly, with a single exception, all markets are spot. That is, supplies and demands are contracted each Monday to be delivered or taken during the following week, but not for later weeks. If an agent plans, for example, to hire labor two weeks hence, they must agree on the wage on the Monday at the start of that week. No market exists in which a worker can be hired for a period of more than one week.

In this model, the plans of agents only need to be consistent in equilibrium for a single week. Supply and demand of both factors of production and commodities for consumption match in the spot market. But these supplies and demands may be based on plans that entail inconsistencies in future weeks. When agents see spot markets failing to clear, say, next week, they revise their plans. And, once again, these revisions and the haggling in the market are assumed to bring about instantaneous market clearing.

The single exception to the requirement that all markets be spot is a market for something like a bond or an annuity. Forward markets exist for all time periods in which one can offer to pay a unit of the numeraire commodity at the start of this week for delivery of a given quantity of the numeraire quantity at the start of, say, the next week. So a whole complex of interest rates exist for the numeraire. An individual's expectations include expectations of movements of future spot prices of all commodities. That is, each individual has expectations for not only future movements in, say, one week interest rates for the numeraire commodity but beliefs about own-rates of interest for all commodities. Nothing in the model brings about consistency among agents of these expectations and beliefs about the future.

This model continues to impose the requirement that no false trading occur. When the markets open on Monday, no transactions can take place until a market-clearing set of prices is found. Only after equilibrium has been achieved do commodities change hands. And production proceeds in each week during the period in which markets are closed.

These models impose very few restrictions on equilibrium, even with specific assumptions on expectations. Perhaps models of temporary equilibrium are better, within mainstream economics, than the Arrow-Debreu model of exploring the formation of expectations.

3.0 Acceptance of Cambridge-Italian Criticisms

These models of general equilibrium may be internally consistent. Both sides of the CCC, however, came to recognize they did not support the beliefs about causal properties still relied on to this day in mainstream applied theory. The faulty and unfounded idea is something like this: compare two equilibria, in which the exogenous (given) data is identical, except the quantity of some given endowment varies across the two cases. Then, if one abstracts from violations of the assumptions of pure competition and is ignorant of price theory, one might expect the price of that endowment to be higher in the case where it is more scarce. Similarly, such an ignoramus would expect the price of commodities produced more intensively with the more scarce endowment to be higher. Despite the short run nature of the models outlined above, such beliefs are unfounded in GET. Here is Christopher Bliss forthrightly acknowledging such:

"Even people who have made no study of economic theory are familiar with the idea that when something is more plentiful its price will be lower, and introductory courses on economic theory reinforce this common presumption with various examples. However, there is no support from the theory of general equilibrium for the proposition that an input to production will be cheaper in an economy where more of it is available." -- Christopher Bliss (1975).

3.1 The Meaning of Quantities, Prices, and Commodities in GET

One issue with GET is remaining clear on the meaning of prices, commodities, and endowments. As with Bliss, I have stated the claim about endowments, prices, and scarcity indices in a timeless, static equilibrium. However, the two disaggregated models outlined above are set in logical time. For example, consider the endowment of a natural resource, such as oil. Only the endowment at the beginning of time is taken as data; the quantities of oil available at the start of the second, third, etc., weeks are different commodities. And these quantities are found by solving the model; they are not taken as given. Likewise, a grade of gasoline produced from oil is a different commodity, depending on which week in which it is produced. Christian Bidard is clear about this distinction between commodities that may be physically identical, but available at different times:

"Intertemporal general equilibrium prices associated with a finite or infinite path of consumption and accumulation have no general properties: the reason being that goods called corn at date t, iron at date t, corn at date t + 1, iron at date t + 1 are formally considered as four distinct commodities of an atemporal economy." -- Christian Bidard (1990).

You might find in GET a statement about the price of one commodity and the quantity of one commodity that goes into the production of that commodity at some more-or-less distant time beforehand. But this is not a statement about the whole vector of prices of physically identical commodities distinguished by the time of their availability. In general, GET theory does not provide simple intuitive propositions about prices and quantities of multiple commodities.

3.2 Steady States

The possibility of a third model might be thought to provide a work-around. Consider the limit, as time increases without bound in the models, of relative quantities and relative prices all referring to that single point in time at infinity. This is a model of a steady-state⁴. Does this background help explain the following from Frank Hahn?:

"It is possible that the outputs produced in an Arrow-Debreu economy in the far distant future are independent of its initial endowments. That would mean that in such an economy the relative scarcities prevailing now would have no influence on the relative prices and rentals in the distant future. This should be enough to persuade the critics that the theory is not committed to a relative scarcity theory of distribution, though they seem to believe it is and that often motivates them in their attacks." -- Frank Hahn (1981).

Christopher Bidard also considers such a limiting process:

"The subscripts refer to the date, the horizontal arrow indicates production by means of inputs and labor and the data in italics are neoclassical theory calls the 'endowments' of the economy. The interesting feature of this scheme is that all inputs a_t, except for the very initial ones a₀, are obtained as the result of previous production. If we admit that the influence of the primitive inputs a₀ vanishes in the long run, we have a pure reproduction process (a mechanical endogenization of labour, identified with a given wage basket, would be useful for a comparison with von Neumann's theory, but the operation is not necessary here)." -- Christian Bidard (1990).

In a simple model of a steady state, one might as well drop time indices off state variables for relative quantities and relative prices. They are invariant over time in such a model. But even so, one cannot apply theorems of static equilibrium to such a model. The logic of steady states is not one of allocating scarce resources. Inputs into production, insofar as they are produced, are not exogenous givens. Rather, they are found as part of the model solution. And the kind of relationships that Bliss says above are without foundation in GET are equally unfounded in models of steady-states.

4.0 Does a Logically Consistent Vulgar Neoclassical Theory Exist?

I consider the beliefs that economics is solely about the allocation of scarce resources and that equilibrium prices are indices of relative scarcity to be vulgar neoclassical doctrines. Beliefs about properties of equilibrium, if you are interested in mathematically formalized Neoclassical models, should be logical conclusions derived from assumptions. And those assumptions should be on the primitives of the model. For example, one might have some assumptions about the tastes, production functions, or patterns of initial endowments.

Here Edwin Burmeister states that no such vulgar neoclassical theory is known to exist, albeit in the context of the analysis of an aggregate market for capital:

"Imposing some set of conditions on the technology ... should be sufficient to assure that real Wicksell effects are always negative. Such conditions would be of interest - especially if they could be empirically tested - since they would validate the qualitative conclusions derived from the one-good models often used in macroeconomics without any theoretical justification for ignoring aggregation problems. Moreover, Burmeister ... has proved that a negative real Wicksell effect is a necessary and sufficient condition for the existence of an index of capital ..., and a neoclassical aggregate production function defined across steady state equilibria such that (i) [consumption per head is a function of the index of capital per head], (ii) [the equilibrium interest rate is equal to the marginal product of the index of capital], and (iii) [This index of capital exhibits declining marginal returns]. Unfortunately, no set of such sufficient conditions is known, but the literature on capital aggregation suggests that they would impose severe restrictions on the technology." -- Edwin Burmeister (1987).

Economists who hold fast to vulgar neoclassical economics may present formal models. But often their mathematics is imprecise, disguising muddle and confusion. It is not a matter of having unrealistic assumpions; it is a matter of having assumptions that do not imply one's conclusions.

5.0 Conclusion

As far as I can tell, most economists do not learn the literature of their subject. Not only do most economists stay ignorant of the view of the English side of the CCC. They also remain ignorant of the most sophisticated neoclassical response. Thus, they ask to see irrelevant empirical evidence⁵ for the existence of reswitching, and do not acknowledge their applied stories⁶ are without foundation in rigorous neoclassical price theory.

Footnotes

1. For the purposes of this post, I bracket out the Sraffian reinterpretation of classical and Marxist economics, the Sraffian claim to have reconstructed a viable alternative price theory, and arguments over the compatibility of this theory with the economics of Keynes.
2. It is not clear that these models cannot be attacked by Sraffians. Do they contain or do they need to contain a market for income in general at each point of time, as in Walras's work?
3. Why this haggling over prices would ever approach equilibrium is unclear in theory.
4. The Turnpike Theorem asserts that intertemporal equilibrium paths starting from appropriately selected initial conditions will spend most of their time around a steady state, even if such a steady state is not the final destination of such a path at a final given final time at which the model ends. On the other hand, the Sonnenschein-Debreu-Mantel theorem suggests any dynamics is possible. Thus, intertemporal paths may have no tendency to approach such steady states, even if they have a local saddle-point stability.
5. I am not sure that all those who ask for empirical evidence of reswitching are clear what they are asking, even though I often use "rewitching" as a synecdoche myself. Anyways empirical evidence exists for Sraffa effects. If Sraffa effects were empirically unlikely, one would be faced with the (unmet) theoretical challenge of outlining a theory to explain this supposed unlikeliness.
6. For example, on the supposed decreasing employment effects, under perfect competition, of a minimum wage above the (what is that) equilibrium real wage.

References

• Christian Bidard (1990). From Arrow-Debreu to Sraffa, Political Economy: Studies in the Surplus Approach, V. 6: pp. 125-138.
• Christopher J. Bliss (1975). Capital Theory and the Distribution of Income, Amsterdam: North Holland Press.
• Edwin Burmeister (1980). Capital Theory and Dynamics, Cambridge: Cambridge University Press.
• Edwin Burmeister (1987). Wicksell Effects, The New Palgrave: A Dictionary of Economics (ed. by J. Eatwell, M. Milgate, and P. Newman).
• Frank Hahn (1981). General Equilibrium Theory, in The Crisis in Economic Theory (ed. by. D. Bell and I. Kristol), Basic Books.
• Frank Hahn (1982). The Neo-Ricardians, Cambridge Journal of Economics, V. 6: pp. 353-374.
• J. R. Hicks (1946). Value and Capital: An Inquiry into Some Fundamental Principles of Economic Theory, 2nd edition, Oxford: Oxford University Press.
• J. M. Grandmont (1977). Temporary General Equilibrium Theory, Econometrica, V. 45, N. 3: pp. 535-572.
• Fabio Petri (2004). General Equilibrium, Capital and Macroeconomics: A Key to Recent Controversies in Equilibrium Theory, Edward Elgar.

John Weeks On "The Unpredictable Outcome Of A General Wage Increase"

John Weeks' book, Economics of the 1%: How Mainstream Economics Serves the Rich, Obscures Reality and Distorts Policy (Verso, 2014) is a popular, polemical work.

"...By what logic do econfakers conclude that wage increases reduce employment and why is it contradicted by reality? The logic, if one might call it such, is from the same full-employment fantasy world as 'supply and demand,' dissected in Chapter 4. As in that discussion, I have to begin with clear specification of the fakeconomics trade-off hypothesis. It does not assert that a wage increase in a specific company will reduce employment. The precise hypothesis is: 'From an initial position of full employment for an economy that produces only one commodity under conditions of perfect competition, an increase in the real wage will reduce employment.'

A rational person might ask: why on earth state a simple proposition (wage up, employment down) in such an absurdly complex manner? They do so because the proposition is not simple. It is valid only under extremely restricted conditions. The hypothesis begins with the economy as a whole, not individual companies or industries. This reason for this will soon be clear. The full-employment caveat is necessary in order to exclude the effect of the most important determinant of the level of employment and unemployment: the total expenditure, public and private, in the economy as a whole (aggregate demand).

As should be obvious, if the analysis begins in conditions of unemployment, an increase in real wages should contribute to an increase in employment by increasing consumer demand. The econfakers exclude this possibility by starting from full employment (maximum output), so any increase in demand could only cause inflation.

But starting at full employment means that the analysis cannot apply at the level of individual companies except as part of the economy as a whole. This implies that the trade-off hypothesis has no relevance to real-world decisions made in companies about employment levels.

Moving on to the next absurdity, allowing the economy only one output is an unavoidable technical requirement. With only one product, either there is no input or the input is the output itself (which is quite strange when you think about it). The following example reveals why the econfakers enter into such contorted illogic. In an economy with an output that has an input different from itself (e.g., wheat and fertilizer), the result of a wage increase in both industries cannot be predicted. A possible logical (and practical) sequence might be as follows: the higher wage prompts farmers to use more fertilizer to raise yields and make labor more productive. Employment in the production of fertilizer increases, with little change in labor used on farms, so total employment expands. In a real economy with thousands of products, the result of increases and decreases in wages can only be known after the event.

This is no abstract, arcane issue. The unpredictable outcome of a general wage increase can be easily demonstrated using what are call 'input-output' tables. These tables are available via the Internet for most countries of the world. They show the flow of inputs through the productive system, which eventually results in what are called 'final products' - those bought by households and governments, and businesses for investment.

Finally, the trade-off hypothesis requires a competitive economy in which no collusion exists among employers or employees. This condition ensures that the demand for labor varies independent of the supply..., which rules out a feedback from higher wages to employment.

What seemed so simple and obvious - lower wages, cheaper labor, more employment - proves impossible to establish as a general rule. At the level of the company, lower wages may allow for lower prices, and the lower wage company takes business away from its rivals. The 'higher wages cause unemployment' accusation is quite different. It alleges a fakeconomics faux law that a general increase in wages for the economy as a whole will reduce employment (and vice versa). This allegation cannot be established in theory, nor is it supported by empirical evidence. It is an ideological construction intended to justify lower wages and higher profits, and to blame unemployment on workers themselves.

In practice the econfakers and those they have indoctrinated trumpet this argument as a law of nature, and use it against all attempts to improve the conditions and hours of work. For example, laws that regulate working hours and require additional pay for overtime allegedly reduce employment because they increase labor costs. The same ideological illogic applies to workplace protection, health and safety legislation, and protection of vulnerable workers. They all raise the cost of employing people. Therefore, they must contribute to unemployment. All attempts to improve the conditions of labor, either through the collective action of workers or legislation are self-defeating. These arguments are wrong, technically, empirically, and morally. In civilized societies all people are paid decently and work in healthy conditions to the extent that the level of economic development allows." -- John F. Weeks (pages 36-38)

Can you see that the middle part of the above quotation is about the application of the Cambridge Capital Controversy to so-called labor markets?

Elements of a Taxonomy of Capital

Here are some ways of classifying capital. This post does not talk much about profit on alienation (buying low, selling high). Nor does it talk about analogies (for example, "human capital", "social capital") extending beyond production and, maybe, even economics. The definitions are my attempt to give an off-hand elaboration of the meaning of terms. I have no objection to those offering more authoritative definitions.

First division:

• Physical capital: Physical goods that are used in the production of commodities for sale on the market.
• Financial capital: Assets that (can be expected to) generate a stream of money payments. Examples: Annuities, stocks, bonds, a deed for rental property.

Second division (A decomposition of physical capital goods):

• Fixed capital: Capital goods used in producing commodities that are not completely used up in one production cycle. Examples: Machinery, dams.
• Circulating capital: Capital goods used in producing commodities that are completely used up in each production cycle. Examples: fuel for machinery, semi-finished goods that are transformed into produced commodities.

Third division (A Marxist decomposition of financial capital?):

• Constant capital: Capital whose value is transferred unchanged into commodities produced with its aid. Includes both circulating capital and the proportion of constant capital used up, in some sense, in a production cycle.
• Variable capital: Capital whose value yields a surplus in the value of a commodity produced with its aid.

Fourth division (The physical analog in Marxism to the above decomposition):

• Means of production: The physical capital goods (commodities) with which commodities are produced.
• Labor power: The ability to labor under the direction of another. Under capitalism, labor power - not labor - is bought or sold.

Fifth division (From volume 2 of Marx's Capital; see diagram above):

• Money capital: Finance that the capitalist intends to use to purchase means of production and labor power or the money which produced commodities realizes when they are sold on the market.
• Productive capital: Capital embodied in means of production and labor power when they are being used to produce commodities.
• Commodity capital: Means of production and labor power or the commodities produced by the same for sale on the market.

Update (10 June 2014): I want to note this passage - more succinct than my writing - from Josh Mason:

"We shouldn't ask what capital 'really' is. It really is a quantity of money in a process of self-expansion, and it really is a mass of means of production, and it really is authority over the production process. But the particular historical questions Piketty is interested in may be better suited to thinking of capital as a claim on the social surplus than as a physical quantity of means of production. Seth Ackerman has some very interesting thoughts along these lines in his contribution to the Jacobin symposium on the book. "

With One Hand Tied Behind My Back

Some economists sometimes say that neoclassical economics will be abandoned when a better theory is available. And they use this as an excuse for not pursuing, say, heterodox economics.

I am tempted to respond that a better theory already exists, for example, some combination of Post Keynesian and institutional economics. But two properties of most varieties of heterodox economics make it difficult for this answer to register for mainstream economists. Before I get to to those properties, let me caveat my answer.

Economists have a number of applied fields. Is heterodox economics developed to such a state that one can say economists would (or should) know how it should impact their work in every applied field? I cannot say how my concerns would apply to, say, transport economics, although I know that work exists there that draws on behavioral economics. Anyways, I doubt that many applied economists are aware of or concerned with how there work fits better with some approaches in heterodox economics. Much applied work seems to me agnostic between paradigms. For example, would you say that most work applying linear programming is Sraffian, even though the historical origins of linear programming are entwined with John Von Neumann's Sraffa-like, classically inspired growth model? How about work with National Income and Product Accounts (NIPA), which, to me, fit comfortably with the classical focus on the generation, distribution, and use of the surplus? Furthermore, I know of some applied fields to which heterodox economists have contributed. I doubt that I can count Walter Isard as a heterodox economist, but I think of economic geography and regional analysis as compatible with Sraffian economics. Wassily Leontief, as far as I am concerned, was a heterodox economist, although, as far as I know, he never commented on the theoretical controversies in which I am interested. I am fairly sure that Bertram Schefold has work in energy economics inspired by Sraffian theory. Is not Amartya Sen's work on the capabilities approach a heterodox contribution to welfare economics? Given Paolo Sylos Labini's importance to the field, I suspect that many models exist in Industrial Organization (IO) that are compatible with a broad definition of Post Keynesianism. To conclude, the connection between applied fields and debates about heterodox economics are not clear to me.

Anyways, heterodox economists tend to emphasize a need for open systems models in economics. This emphasis is the first property of heterodox economics that I want to mention that makes it difficult for mainstream economists to accept the superiority of much heterodox work. Tony Lawson has provided lots of elaboration on the need for an open systems approach to studying human society. But I do not need to go into such philosophy. My favorite approach to price theory takes the distribution of income as given for the most abstract theory of the prices of commodities. Likewise, the composition of final uses is exogenous in Sraffa's theory. The structure of the theory is open to elaborations at lower levels of abstractions that include inputs from other social sciences than economics. Consumption might be explained by a substantive theory, in contrast to the empty formal theory of neoclassical utility-maximization.

Second, heterodox economists tend to be skeptical of the possibility of economic laws applying to all societies across all of human existence. By contrast, Lionel Robbins' definition of economics as the study of the allocation of scarce means among alternative uses is often claimed to be universal. There is nothing in the mainstream about capitalism or how social norms might differ among societies. Contrast, for example, with Luigi Pasinetti's work on structural dynamics, in which the theoretical structure builds in a place for variations in institutions. Or look at suggestions in Sraffa's book that taking one of wages or the rate of profits as the independent variable might be more appropriate at different times or places. Or look at the emphasis on conventions in Keynes' analysis of investment. I could go on.

So, by adopting theories appropriate for the problem domain, heterodox economists have developed theories that are superior to many orthodox theories. But, because of this very appropriateness, mainstream economists are socialized to fail to perceive this superiority.

Dominance of Financial Capital in the United States

Profits by Selected Industry as Percent of Total Profits in the United States

The data for the graph are taken from Use tables for the United States. I am thinking of trying my hand again at some empirical exploration of input-output tables. When graphs for such start looking like those I know how to generate from Java code, I will have begun to start to make some progress. I have found a tool, Apache POI, for Java programs to read Excel spreadsheets.

Need For Engagement With Heterodox Economists

Some brief observations:

• Simon Wren-Lewis is asked to define K. His answer: "It is normally K(t) = δ K(t - 1) + I(t)." In times past, Wren-Lewis has seemed like he genuinely was interested in what heterodox economists have to say. But, with that kind of answer, he really needs lots more study to get up to speed.
• Noah Smith tries to provide an overview of contemporary economics. Many groups of economists I pay attention to do not exist for Smith, and I doubt he knows much about even the recent history of his subject. What would he make of, for example, Philip Mirowski's Machine Dreams?
• Matthew Yglesias alerts his readers to the existence of the Cambridge Capital Controversy. For Yglesias, the central question is the origin of returns to capital and the validity of marginal productivity parables organized around the idea of relative scarcity. I think this is a good account, given how terse this is.

Components Of United States GDP

Table 1: Components, As Percentage Of GDP

I thought I'd expand on a recent graph. I was curious to see how state and federal government spending break down in the United States. To draw the graphs in this post I performed some aggregation from the data:

• Consumption: Listed as "Personal consumption expenditures".
• Investment: Combines "Private fixed investment" and "Changes in private inventories".
• Trade deficit: Combines "Exports of goods and services" and "Imports of goods and services".
• Federal Government: Combines "National defense: Consumption expenditures", "National defense: Gross investment", "Nondefense: Consumption expenditures", and "Nondefense: Gross investment".
• State Government: Combines "State and local government consumption expenditures" and "State and local government gross investment".

I suppose I could find a price index, and plot absolute amounts, rather than percentages of GDP. Then you could see, for example, that GDP in 2009 is actually lower than the 2008 value, as a result of the global crash. Does the breakdown of government spending into consumption and gross investment components reflect the influence of Robert Eisner?

Table 2: Selected Components, As Percentage Of GDP

Some Points Of Agreement

Consider:

• "...there is a crucial distinction between financial capital and capital goods."
• "Interest is not the return to physical capital."
• "Interest is not the 'Marginal Product of (physical) capital'."

These quotes are from Robert P. Murphy. (See here also.) I have written about Murphy before, including his take on Sraffa.

Paradigming Is Easy

Some publishers have made it easy to get an overview of currently existing paradigms in economics, including non-neoclassical paradigms:

• Modern Cambridge Economics: Each book is by an expert on the selected topic. (Previous mention here.)
• Schools of Thought in Economics: From Edward Elgar, each book is edited by an expert and consists of reprints of important papers from that school.
• International Library of Critical Writings in Economics: From Edward Elgar as well, each book is also an edited collection. Many of these are more on a field than on a school, but I like number 21, on the Post Keynesian theory of growth and distribution.
• M. E. Sharpe: I do not have a book series for this important publisher of heterodox economics, including the journal Challenge.

The books in the Edward Elgar series are probably too expensive for most individual purchases. Perhaps you can request some of interest from an academic library. Some of these books are more than a decade old, with articles in the collections going back even more decades. But, by looking at authors and journals, you can can get a hint of where to look for more contemporary work in a school of interest.

Compare and contrast Paul Krugman on this topic.