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.