A clean, simple computation, no doubt, only that it never works
Friday, 14 May 2010, 08:54
Visible to anyone in the world
What gets accumulated?
To a lay person, the question may seem simple to answer: money. Capitalists accumulate when they grow richer; they decumulate when they become poorer. And that is certainly true, but not entirely. To see what is missing, suppose that the actual holdings of a capitalist haven’t changed but that their prices have all risen by 10 per cent, thus making him 10 per cent richer. Now assume further that the overall price level – measured by the GDP price deflator – has also grown at the same rate of 10 per cent, so that the ‘amount’ of commodities the capitalist can buy with his assets remains the same. The capitalist has certainly accumulated in nominal terms, but this increase was merely a price phenomenon. Since the process has affected neither the ‘productive capacity’ of his assets nor their ‘purchasing power’, from a material perspective he has ended right where he started. For this reason, political economists – conservative and critical alike – insist that when measuring accumulation we ignore the price of capital and concentrate only on its material, or ‘real’, quantity.
There is, of course, nothing very unusual about this insistence. After all, political economy is concerned primarily with material processes, so it seems only sensible that the same emphasis should apply to capital. The only problem is that in order to focus on ‘real’ quantities, we first have to separate them from prices; and surprising at it may sound, in general the two cannot be separated.
Separating quantity from price
To understand the difficulty, let’s put aside the theory for a moment and look at what the statisticians do. Their procedure is straightforward: they assume that the dollar market value of any basket of commodities (MV) is equal to its ‘real’ quantity (Q) times its unit price (P), and then they rearrange the equation. Symbolically, they start from:
1. MV = Q × P
Which is equivalent to:
2. Q = MV/P
These formulae are taken to be completely general. They apply to any basket of commodities at any point in time – from the contents of a supermarket cart pushed by a London shopper in 2008, to the annual output of the Chinese economy in 2000, to the global stock of ‘capital goods’ in 1820. Given data on the market value and price of any set of commodities, calculating its ‘real’ quantity and growth rate is a simple matter of plugging in the numbers and computing the results.
To illustrate, suppose the U.S. Bureau of Economic Analysis wishes to calculate the ‘real’ rate of accumulation in the automobile industry from 1990 to 2000. The statisticians know that, over the decade, the market value (at replacement cost) of the industry’s capital stock (MV) grew by 93 per cent and that 17 per cent of that increase was due to a rise in unit price (P). Based on these data, the statisticians can easily tell us that the ‘real’ rate of accumulation – measured by the rate of growth of Q – was 65 per cent (1.93 / 1.17 –1 ≈ 0.65).2
A clean, simple computation, no doubt, only that it never works. The failure is as general as the formulas. The calculation fails with ‘capital goods’, just as it fails with GDP, private consumption, gross investment or any other collection of heterogeneous commodities. And the reason is embarrassingly simple. Equation (2) above tells us that in order to compute the quantity we first need to know the price. What it doesn’t say is that in order to know the price we first need to know the quantity. . . .
To see the circularity, consider the following facts. An automotive factory is made of many different tools, machines and structures. Over time, the nature of these items tends to change. They may take less time and effort to produce; they may become more or less ‘productive’ due to technical improvement and wear and tear; their composition may change with new machines replacing older ones; they may be used to produce different and even entirely new output; etc. The result of these many changes is that today’s automobile factories are not the same as yesterday’s, or as last year’s. The price index of automobile factories, however, is supposed to track, over time, the price of the very same factories. The obvious question, then, is: ‘How can such an index be computed when the underlying factories – the “things” whose price the index is supposed to measure – keep changing from one year to the next?’
A clean, simple computation, no doubt, only that it never works
What gets accumulated?
To a lay person, the question may seem simple to answer: money. Capitalists accumulate when they grow richer; they decumulate when they become poorer. And that is certainly true, but not entirely. To see what is missing, suppose that the actual holdings of a capitalist haven’t changed but that their prices have all risen by 10 per cent, thus making him 10 per cent richer. Now assume further that the overall price level – measured by the GDP price deflator – has also grown at the same rate of 10 per cent, so that the ‘amount’ of commodities the capitalist can buy with his assets remains the same. The capitalist has certainly accumulated in nominal terms, but this increase was merely a price phenomenon. Since the process has affected neither the ‘productive capacity’ of his assets nor their ‘purchasing power’, from a material perspective he has ended right where he started. For this reason, political economists – conservative and critical alike – insist that when measuring accumulation we ignore the price of capital and concentrate only on its material, or ‘real’, quantity.
There is, of course, nothing very unusual about this insistence. After all, political economy is concerned primarily with material processes, so it seems only sensible that the same emphasis should apply to capital. The only problem is that in order to focus on ‘real’ quantities, we first have to separate them from prices; and surprising at it may sound, in general the two cannot be separated.
Separating quantity from price
To understand the difficulty, let’s put aside the theory for a moment and look at what the statisticians do. Their procedure is straightforward: they assume that the dollar market value of any basket of commodities (MV) is equal to its ‘real’ quantity (Q) times its unit price (P), and then they rearrange the equation. Symbolically, they start from:
1. MV = Q × P
Which is equivalent to:
2. Q = MV/P
These formulae are taken to be completely general. They apply to any basket of commodities at any point in time – from the contents of a supermarket cart pushed by a London shopper in 2008, to the annual output of the Chinese economy in 2000, to the global stock of ‘capital goods’ in 1820. Given data on the market value and price of any set of commodities, calculating its ‘real’ quantity and growth rate is a simple matter of plugging in the numbers and computing the results.
To illustrate, suppose the U.S. Bureau of Economic Analysis wishes to calculate the ‘real’ rate of accumulation in the automobile industry from 1990 to 2000. The statisticians know that, over the decade, the market value (at replacement cost) of the industry’s capital stock (MV) grew by 93 per cent and that 17 per cent of that increase was due to a rise in unit price (P). Based on these data, the statisticians can easily tell us that the ‘real’ rate of accumulation – measured by the rate of growth of Q – was 65 per cent (1.93 / 1.17 –1 ≈ 0.65).2
A clean, simple computation, no doubt, only that it never works. The failure is as general as the formulas. The calculation fails with ‘capital goods’, just as it fails with GDP, private consumption, gross investment or any other collection of heterogeneous commodities. And the reason is embarrassingly simple. Equation (2) above tells us that in order to compute the quantity we first need to know the price. What it doesn’t say is that in order to know the price we first need to know the quantity. . . .
To see the circularity, consider the following facts. An automotive factory is made of many different tools, machines and structures. Over time, the nature of these items tends to change. They may take less time and effort to produce; they may become more or less ‘productive’ due to technical improvement and wear and tear; their composition may change with new machines replacing older ones; they may be used to produce different and even entirely new output; etc. The result of these many changes is that today’s automobile factories are not the same as yesterday’s, or as last year’s. The price index of automobile factories, however, is supposed to track, over time, the price of the very same factories. The obvious question, then, is: ‘How can such an index be computed when the underlying factories – the “things” whose price the index is supposed to measure – keep changing from one year to the next?’
Jay Hanson