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Analysing UK economic data over an extended historical timespan, from the mid- nineteenth to the late twentieth centuries, the authors use ‘quantitative’ or ‘empirical’ Marxist techniques to test key Marxian theses and categories. They argue that Marxian economics has nothing to fear from a confronta- tion with empirical data. Paul Cockshott, Allin Cottrell & Greg Michaelson Testing Marx: Some new results from UK data Introduction Quantitative or empirical Marxism has passed through three main phases in the postwar West.l In the first phase, statistical measurement of the economic indices of Marxist political economy was pioneered by Joseph Gillman (1957) who used National Income figures to obtain estimates of the rate of surplus value, organic composition of capital and rate of profit for the US economy. The measurements presented in this paper draw on his methodology. In his Ph.D. dissertation, Mage (1963) also tackled the rate of profit in the US using methods broadly similar to Gillman’s. This work was not immediately followed up, but in the 1970s a second phase opened as the empirical reality of a falling rate of profit in Britain drew attention from orthodox economists (e.g. Panic and Close, 1973) as well as Marxists. Among the latter the most notable contribution came from Glyn and Sutcliffe (1972). But instead of the ‘classical’ Marxian measures, Glyn and Sutcliffe used surrogates such as the Wage Ratio and the Share of Profits in company product. These measures seemed to show the rate of exploitation to be declining, perhaps in consequence of trade union power. Whereas Gillman had distinguished in his estimates of the rate of surplus value between productive and unproductive 103 104 Capital & Class �55 labour, following Marx, the categories used by Glyn and Sutcliffe aggregated all wage incomes.2 This could mask an actual increase in the exploitation of productive workers behind a change from productive to unproductive labour. This objection was raised by Bullock and Yaffe (1975) who used a comparison of the rates of change of take home pay and of productivity to indicate that the rate of relative surplus value had risen over the same period. The same conclusion was arrived at on different grounds by Bacon and Eltis (1976), whose analyses of the share of purchases by the non-industrial sector, led them to conclude that the main problem of the British economy was the shift from productive to unproductive employment. This, they said was the primary cause of the decline in profitability. The third phase of empirical Marxism (roughly, from the mid-1980s to the present) is exemplified by the work of Shaikh (1984), Moseley (1991) and that collected in Dunne (1991). One of the themes here is a revitalisation of the classical Marxian labour theory of value, along with a reassertion of the relevance of the distinction between productive and unproductive labour. This paper is conceived as a contribution to this ‘third phase’.3 We offer a set of time series for the classical Marxian indices, covering a longer run of history than most other contributions (cf. Freeman, 1991, whose data are drawn from 1950–1986). We also offer some arguments, complementary to those in the existing literature, for the relevance and validity of data of this sort. And we show how the data may be used for the testing of Marxian theses, taking for illustration those concerning the ‘immiserisation’ of the proletariat and the tendency for the rate of profit to fall. Justifying empirical Marxism It is noteworthy that Marx himself did not hesitate to use empirical data to measure the rate of surplus value. He estimated, using the prevailing wage rates, costs of constant capital and final selling price for No.32 yarn, that the rate of surplus value in the Manchester cotton industry in 1871 was 154 per cent, and that the rate in wheat farming in 1815 was just over 100 per cent (Marx, 1970: 219–220). Throughout the first volume of Capital, Marx constantly uses official statistics and factory inspectors’ reports to justify his theoretical claims. When dealing with the production of absolute surplus value he produces statistics Testing Marx 105 comparing the production of absolute surplus labour in industrial England with feudal Romania: when dealing with the concentration of capital he uses Income Tax statistics to document the concentration of wealth. Given the limitations of the then existing official statistics, however, it was not possible to estimate the average rate of surplus value for the whole economy. Only with the publication of National Income statistics in the twentieth century did this become practicable. It may be objected that the National Income statistics are given in price terms not value terms, and that their use for calculating Marxian categories could be invalid. We believe such fears to be unfounded. We argue this on the grounds of dimensional analysis, the artificiality of the objection, and empirical validation of the concepts we use. Dimensional analysis In what follows we will use the standard notation with the set of symbols c , v, s , standing respectively for constant capital, variable capital and surplus value. If one had National Income figures in value terms, these variables would be measured in millions of person hours per annum. This would give them the dimension t x h x t-1 where t stands for time and h for humans. Cancelling the time terms, the resulting dimension is h , or so many million people. This may seem unexpected, but it means that s, c and v measure the number of full-time person-equivalents employed on the production of consumer goods (v), the reproduction of constant capital (c) and on the production of luxuries, new capital goods, etc. (s ). The value variables s , c and v measure the size and activity distribution of the workforce. The main ratios of interest — s'= s/v = rate of surplus value, p' = s/(c+v) = rate of profit on a flow basis, and o' = c/v = organic composition of capital — are all dimensionless numbers. For example s1 is of dimension hxh-1 which cancels out. In the case of actual National Income figures, by appropriate choice of categories we can arrive at a monetary estimate of s in terms of £ million per annum or dimension £ t -1. Similar arguments apply to c and v, but computing the ratios s’, o’ and p’ will again yield dimensionless numbers. Hence on purely dimensional grounds there is no contradiction in estimating these ratios from monetary magnitudes. 106 Capital & Class �55 There are a couple of other interesting ratios: 1. The rate of profit on a stock basis, p' s = s/(k + Tv), where k is the stock of constant capital and T is the turnover time of variable capital; and 2. the organic composition of capital on a stock basis, o' s = k/Tv. The dimension of k in value terms is millions of person hours, or ht. and clearly Tv is also of dimension ht. The resulting dimension of p’ s is t -1. This is what one would expect since the rate of profit in stock terms measures the expansion of capital values per unit time. The organic composition on a stock basis is again a dimensionless quantity. Monetary calculation likewise gives us a rate of profit as per cent per annum, which is t -1, and a dimensionless number for o' s . Since monetary ratios are dimensionally compatible with the value ratios, using the former as an estimate of the latter is legiti- mate provided that the monetary measures s m , v m , and c m are approximated by linear functions of the corresponding value measures s l , v l , and c l with positive slope and intercepts at the origin. But is this the case? Value versus price data Are values linear approximations of prices and vice-versa? This has been disputed by authors basing themselves on Sraffa (Steedman 1975; Hosoda 1993), but we consider that their arguments are unconvincing. It has been shown (Wolfstetter, 1976; Farjoun, 1984; Cottrell, 1993) that the examples purporting to demonstrate profit and surplus value to be anti-correlated rest on highly artificial assumptions. In particular, negative labour ‘values’ can arise only in systems that are inefficient in the sense that they are not on the production possibility frontier. In such circumstances the labour ‘values’ calculated do not correspond to the definition of socially necessary labour. Such occurrences would be highly unstable and improbable in a real capitalist economy. The construction of such forced examples is of little scientific, as opposed to ideological, value. Shaikh (1984) 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. Shaikh’s method uses input-output 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 which 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 per cent. More recently, Petrovic (1987) and Ochoa (1989) have carried out very similar studies (using data from the Yugoslav and US economies respectively), with much the same results. To reinforce this conclusion, we have replicated Shaikh’s analysis using the UK input-output tables for 1984 (Central Statistical Office, 1988). The commodity-use matrix in Table 4 of the input-output 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 the recursive approximation l (n) = c l(n-1) + v m /w, where l (n) is the nth estimate of labour content, c l(n-1) is the (n-1)th estimate of the labour content of constant capital, and w is the money wage per hour. Recursion was terminated at a depth of 8 giving answers to three significant digits. In the input-output tables, labour input is given in £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 (see the discussions of Models A and C below). Table 1: Regressions of price on labour-values and prices of production — UK input-output data, 1984 Model A Model B Model C Model D constant –0.055 –0.034 –0.046 –0.049 (0.027) (0.019) (0.023) (0.017) labour-value 1.024 1.014 1.024 (0.022) (0.016) (0.020) pr. of prod. 1.024 (0.015) T 101.00 100.00 100.00 100.00 R2 0.955 0.976 0.964 0.980 Mean Abs. Error 13.5% 11.8% 15.0% 10.0% Max. Error 157.0% 65.0% 67.0% 57.0% (standard errors in parentheses) Testing Marx 107 108 Capital & Class �55 The results of our regressions are shown in Table 1. The various models differ as follows. Model A: Value/price regression for all industries assuming uniform wage rate. A dummy wage rate of £1 per hour was assumed for all industries. On this assumption the labour content of the output of each industry 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.4 Model B: As above but excluding the oil industry. Among the industries there was one outlier with an 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. Model B shows the result of excluding the oil industry from the sample. Model C: 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. Model D: No oil industry, price of production is independent variable. Price of production was computed using the recursive application of the formula P prod(n) = p' (c pprod(n–1) + v m ) to all industries, where c pprod(n–1) is the (n–1)th estimate of the price of production of the constant capital inputs, and P prod(n) is the nth estimate of the price of production. Interpretation of regression results Our findings, for the case of the UK, are in remarkable agreement with the previous results of Shaikh, Petrovic and Ochoa for the US, Italian and Yugoslav economies. The regressions with labour content as independent variable show an excellent fit (with R2 in the range of 96 to 98 per cent), and a close approximation to the ‘ideal’ result, from the standpoint of the labour theory of value, of a zero intercept and unit slope. In relation to Model B, t (98) = 0.834 for the null hypothesis of a unit slope, with a two- tailed p-value of 0.41, so the hypothesis is not rejected.5 Testing Marx 109 Since the regressions are logarithmic, the errors or residuals (actual minus predicted money price, industry by industry) are in percentage form. As can be seen from Table 1, the mean absolute residuals are fairly small, although even when the oil industry is dropped there are a few other outlier industries where the discrepancy between actual and predicted price is on the order of 60 per cent. It may be that rent factors are important in those industries too. It is noteworthy that Model C, in which the labour content figures are adjusted using New Earnings Survey (NES) data, shows a somewhat less good fit than Model B, in which labour content was figured on the assumption of a uniform wage per unit labour across the industries. It may well be that using the NES data ‘over-corrects’ labour content. The issue here concerns the source of inter industry wage differentials. If these differentials were arbitrary, or reflected differential bargaining power, there would be a case for removing the resulting ‘distortion’ from the labour content estimates via the use of the NES wages data. But if, on the other hand, actual inter-industry wage differentials reflect differential skill levels, then one could argue that the theoretical assumption of a uniform wage-per-unit-labour-input across industries is appropriate, amounting in effect to a reduction to hours of simple labour (cf. Marx 1970, ch.1). The fourth estimate (Model D) shows that the use of price of production as independent variable produces a marginally better linear fit with market prices. This is consistent with Ochoa (1989), and is in conformity with the modification to value theory presented by Marx in Volume III of Capital (Marx 1971, ch.19). But 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 realised as all of the com- modities upon which the wage is spent. Since these will be drawn from many industries the random correction terms due to prices of production in each industry, already small, will tend to cancel out. We conclude from this discussion that there is no serious problem with using price denominated data from the National Income statistics to produce estimates of the classical Marxian value ratios such as the rate of surplus value. 110 Capital & Class �55 Preparation of the series We have constructed four distinct sets of time series for the British economy in Marxian categories. The first runs from 1855 to 1919, the second from 1920 to 1938, the third from 1948 to 1969, and the last from 1970 to 1989. The sets of series are not directly commensurable since they are derived from different sources, which makes it difficult to apply exactly the same empirical definitions of the Marxian categories. The source data for the most recent period were obtained from the CSO databank on magnetic media. Unfortunately, the CSO can not provide continuous time series on magnetic media for the years before 1970. For the years 1948 to 1969 our sources were the annual Blue Books of National Income and Expenditure. These started publication in 1948. For the period 1855 to 1938 we used the historical tables of national income produced by Feinstein (1976). The principal differences in the series centre on the definition of variable capital. One has to decide which categories of labour count as productive labour, whose remuneration should be included in v, and which count as unproductive labour. (Following Gillman, we denote the wages of the latter as u, an expenditure which represents a share of the surplus value produced by productive labour.) The information available differs for each time period. For the earliest period, the only breakdown of income from employment is into wages and salaries. For this period we chose to assume that all salaries were payments to unproductive labour, which, given the social structure of the period, is perhaps not unreasonable. Conversely, all wages were assumed to represent payment to productive labour: this probably overestimates the wages of productive labour, since the incomes of such categories as domestic servants were thereby aggregated into v. For the inter-war years Feinstein provides a breakdown of income from employment by industrial category. For this period, variable capital was taken as wages in Agriculture, Forestry and Fishing; Mining and Quarrying; Manufacturing; Building and Construction; Gas, Electricity and Water; and Transport and Communication. All other labour income was treated as unproductive. It may be argued that this underestimates v as it excludes salaries in productive industries. Some of these salaried workers would be involved in unproductive tasks, such as accounting and marketing, but others, such as gas engineers, would be productive. Testing Marx 111 For the post-1948 figures, the same industry categories were used to obtain v but now salaries for these industries have been included in v, since for the later years the CSO figures no longer treat wages and salaries as distinct. This of course means a certain underestimation of the level of unproductive labour by the contrary argument to that applying to the inter-war years. Further details on the construction of the series can be found in the Appendix. What do the series show? Empirical data on an individual capitalist economy can be used for two types of theoretical investigation. They may be used in a conjunctural analysis whose objective is to arrive at a political strategy to be applied in that country, or they may be used to test the validity of certain general hypotheses of historical materialism against a particular real instance. We gave an example of the latter use of empirical data with our test of the labour-value hypothesis against input-output data. In the next two sub-sections we use our data to examine two other Marxian hypotheses, the immiserisation thesis and the law of the tendency for the rate of profit to fall. Immiserisation [A]s capital accumulates, the lot of the labourer, be his payment high or low, must grow worse. The law, finally, that always equilibrates the relative surplus population, or industrial reserve army, to the extent and energy of accumulation, this law rivets the labourer to capital more firmly than the wedges of Vulcan did Prometheus to the rock. It establishes an accumulation of misery, correspo