Subject: Re: Labor and value Date: Mon, 25 Jul 94 10:55:45 +0100 From: wpc-AT-cs.strath.ac.uk Chriss Sciabarra accepts the critique of Bohm Baverk of the labour theory of value. The great weakness of this, and all of the transformation problem arguments is their entirely speculative character. They rest upon a hypothesis - the existence of a uniform rate of profit, which is empirically false, and if Farjoun (Laws of Chaos - Verso) is right, is also mathematically unsound when dealing with stochastic phenomena. When one turns to empirical evidence, the critics of the labour theory of value have none, whereas the advocates of it have an increasing body of well founded statistics on their side. Shaik (in Marx, Ricardo Sraffa, Verso) gives figures for the US economy showing a high correlation between prices and labour values, Ochoa (Cambridge Journal of Economics 13/3) provides reinforcing evidence. I and others have used UK input-output data to obtain very high correlations between prices and values: Although theorists may sometimes be inclined to forget, the equalized rate of profit is NOT a fact. It is, however, an assumption that is absolutely crucial to all theories of Sraffian derivation. Farjoun is able to show, for instance, that many Steedman-type examples, of the sort used to demonstrate the frailty of the LTV, fall apart and become economically meaningless given the slightest deviation from this assumption. What IS a fact, is that the distribution of the rate of profit in capitalist economies is quite wide, and broadly stable over time. Yes, there are forces working in the direction of equalization, but there are complementary forces working in the direction of dis- equalization; and the joint outcome of these forces seems to be an "equilibrium" degree of dispersion of profit rates (with different capitals occupying different places in the distribution at different times) It is therefore not at all obvious that a theory based centrally on the assumption of an equalized rate of profit has any claim to correctness, to the status of a benchmark against which the deficiencies of the LTV may be assessed. The greater the equilibrium dispersion of profit rates, the worse are Sraffian prices as approximations to actual prices -- or even to their "centers of gravity," discounting the effects of short-run supply- demand disequilibria. On the other hand, on the maintained hypothesis of an equalized rate of profit, the greater the dispersion of the value composition of capital, the worse are labor-values as approximations to actual prices. Since both of these distributions are non-degenerate, the question of whether Sraffian prices or labor- values offer the better systematic approximation to actual prices is an empirical one. The evidence to date shows, with remarkable consistency across data-sets drawn from different capitalist economies and different time periods, that the two approximations are *roughly equally good*. It is not the case that labor-values are a crude first approximation, and Sraffian prices a clearly superior second approximation. Shaik has argued that the question of whether prices are closely correlated with values is essentially an empirical one. One can in principle measure the degree of correlation between the two provide that one has independent measures of each. Shaik's method uses input-output table data to estimate labour contents and then measures the correlation between these and prices. He presents results derived from Italian and US input-output tables. These show, as one would expect from value theory, that relative prices are almost entirely determined by labour content. He obtains correlation coefficients of well over 90%. Since we are concerned with producing estimates of s/v for the UK economy, we have repeated his experiments using the UK input-output tables for 1984. The results are summarized below Regression of prices against values ----------------------------------- Equation R^2 max error SDEV err avabs err 1 p = -.055 + 1.024 l 0.955 157 23 13.5 2 p = -.039 + 1.014 l 0.961 65.4 16.5 11.8 3 p = -.046 + 1.024 l 0.976 67 20 15 4 p = -.049 + 1.024 p.p 0.980 57 15 10 \end{tabular} \end{table} The commodity use matrix in Table 4 of the I/O tables was used to provide estimates of total labour content of the outputs of each commodity group. Both direct and indirect labour inputs were calculated using a recursive approximation: Recursion was terminated at a depth of 8 giving answers to 3 significant digits. In the tables, labour input is given in \pounds s. This amounts to measuring the price of the labour power used rather than being a direct measure of the labour used. We tried two alternative methods of going from these figures to estimates of abstract labour. Equation 1 Value/price correlation for all industries assuming uniform wage rates. A dummy wage rate of 1 per hour was assumed to be uniform across all industries. On this assumption the labour content of the outputs of all industries was calculated. The assumed wage rate was unrealistically low, but this is of no significance in computing the correlations since it is equivalent to a uniform scaling factor in our time unit. In this and all other cases, the variables enter the regressions in logarithmic form. Equation 2. As above but excluding the oil industry Within the figures for all industries there was one with a very anomalously high price/value ratio - the oil industry. This is exactly what one would expect from the Ricardian/Marxian theory of differential rent. Non-marginal oil fields could be expected to sell their output at above its value. Excluding the oil industry from the correlation gave estimate 2. Equation 3 Values assuming non-uniform wage rates. In practice wages differ between industries. The actual hourly wage rates for the different industries in 1984 were obtained from the New Earnings Survey and used to convert the monetary figures for direct labour into hours. Again the oil industry was excluded from the final regression. Equation 4 No oil industry, price of production is independent variable. Price of production was computed using the recursive application of formula $ Pprod_n= p'(cpprod_{(n-1)}+ vm)$ to all industries, where $ cpprod_{(n-1)}$ is the $(n-1)$th estimate of the price of production of the constant capital inputs, and $Pprod_n$ is the $n$th estimate of the price of production. Two questions arise in looking at the regression results: (1) is labour value an unbiased predictor of money price? and (2) how efficient is labour value as a predictor of money price? The short story is that, there appears to be a slight bias, but nonetheless the efficiency is very high. In the regression of the log of aggregate price on the log of aggregate labour value, sector by sector, the 'ideal' result for the labour theory of value would be if the constant and slope were zero and one respectively. That would say that labour value is an unbiased predictor of money price. In each case the results were pretty close to this ideal, but the constant seems to want to be slightly negative, while the slope differs slightly from unity. If that result is robust, it says there is a slight bias: labour values give an underestimate of price in the case of larger industries (larger, that is, in terms of total labour content), and an overestimate in the case of smaller industries. On the efficiency of labour value as a predictor of price, there are various indicators. The R2 gives the percentage of the total variation in the log of price (i.e. sum of squared deviations of the log of price about its mean) that is 'accounted for' by reference to labour values. This is pleasingly high, at about 96 to 98 per cent. One can get more information on this by looking at the residuals (actual money price minus predicted money price, industry by industry). The fourth estimate shows that price of production is a slight ly more efficient predictor of actual price than value is. This is in conformity with the modification to value theory presented by Marx in Capital III . We would expect price of production to predict market price more efficiently than value does, but, and this is the significant point, prices of production only introduce a minor correction to the underlying determination of market price by labour content. The correction term due to prices of production is so small that it can for practical purposes be ignored. This is especially the case when constructing estimates of ratios like s/v where each individual term is an aggregate of many different types of commodities. The term v for instance denotes a sum of value that is realized as all of the commodities upon which the wage is spent. Since these will be drawn from many industries, the, already small, random correction terms due to prices of production in each industry, will tend to cancel out. We thus conclude that it is valid to use monetary data from the National Income Statistics to produce estimates of value ratios like s/v. \bibitem[7]{CSO} Input-output tables for the United Kingdom 1984, Central Statistical Office, HMSO, 1988. \bibitem[8]{Roemer} Should Marxists be interested in Exploitation, Roemer, in Analytical Marxism, CUP , 1986. \end{thebibliography} \end{document}
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