Spatial Integration

Cambridge–Cambridge

controversies in capital theory for

econometric practice

its more sophisticated cousins, such as the constant-elasticity-of-substitution (CES) production function) have provided yeoman service in endogenous growth theory in recent years.

II

In this chapter I want to concentrate on another aspect of the Cobb–Douglas (and cousins) when used in applied, econometric work. It arises from the implicit assumption in much econometric specification that the short period and the long period may be collapsed into one. Then, for certain forms of the aggregate production function, exactly the same values of key parameters (and therefore variables) are involved, whether we are considering greater or lesser utilisation of a given stock of capital goods in the short run, that is, movements up or down what Joan Robinson called the utilisation function, or changing capital–labour and capital–output ratios as the result of differential rates of growth of accumulation and the labour force over time; in the latter process, there may not only be more capital per head and per unit of output but also better capital per head and per unit of output. Such a specification, allied with the assumptions of competitive market structures in the economy concerned and static expec-tations about the future courses of the prices of products and of the factors of production (so that the simple marginal productivity implications of cost-minimising and profit-maximising may go through) allows the use of actual ‘real world’ statistics on wages, profits, capital and so on when fitting the specified model. This in turn allows the estimation of key parameters, for example, the exponents of the variables of the function, the elasticity of substitution of capital for labour; and so on.

This methodological point was the basis of the criticism by Joan Robinson (1964) of, for example, Solow’s procedures in his 1963 de Vries Lectures (Solow, 1963). There, for much of the book, he used what she called a butter model in the theoretical sections and in the specifications of his empirical work. (The main objective of his lectures was to develop the-oretical measures of the Fisherian social rate of return on investment in a number of different scenarios. He treated it as a technocratic measure – the potential return to a bit more saving/investment at full employment. He estimated its values in what was then West Germany, and in the USA. As the resulting values were considerably greater than those of near riskless returns on certain financial assets, the inference was that more investment should be encouraged in both countries.)

In the model, butter was both input (B) and output (B) and the para-meters of the model were usually functions of key ratiosonly,B/Land

B/L, where Lwas the potential work force. Ignoring technical progress for the moment, it did not matter whether the thought experiment was con-cerned with running up and down the short-period utilisation function with varying values of B/Land B/L, or whether the changes in the values of B/Land B/Lwere due to accumulation over ‘time’ so that B/Lwas taken to be increasing as deepening occurred – ‘moving down the production function’ as Joan Robinson (1959; 1960) once put it.

As I argued above, the ‘real world’ observations are, by definition, observed points on the existing utilisation functions of each instant of time, since, though in the long run we are all dead, the living are always to be found in the short run. Nevertheless, they were meant to serve as well as observations of long-period values taken from, in effect, the same produc-tion funcproduc-tion, see Figure 9.1.

III

We do not have to go into the intricacies of the capital-reversal and reswitching debates and results (see, for example, Cohen and Harcourt, 2003; Harcourt, 1972; 1995) in order to criticise the conceptual basis of this standard procedure.³In 1963 Robin Matthews, who was then review editor Figure 9.1 Short-period utilisation possibilities doubling up for

long-period accumulation possibilities L

B

0

L B

‘long -period’ accumulation

short-run utilisation

of the Economic Journal, asked me to review Bagicha Minhas’s 1963 book, An International Comparison of Factor Costs and Factor Usesin which he exploited the properties of the famous CES production function, which came from an article written by Minhas jointly with Arrow, Chenery and Solow (1961) (hereafter referred to as ACMS). (I don’t suppose many PhD students have such illustrious research assistants these days.) The previous year I had published a review article – see Harcourt (1962; 1982) – of the late Wilfred Salter’s classic, Productivity and Technical Change (1960).

Salter’s book (which grew out of his early 1950s Cambridge PhD disserta-tion, supervised by Brian Reddaway) was a pioneering account of vintage (putty-clay) models and their application at firm and industry levels. As a result of what I learnt from Salter then (I still learn today), I argued in the review of Minhas – see Harcourt (1964) – that though the data used in Minhas’s study came, of necessity, from existing short-run utilisation func-tions incorporating stocks of existing capital goods of different vintages associated with past accumulation, it was being used to estimate the values of the characteristics of what Salter called the iso-quants of the latest ‘best-practice’ techniques. These were, of course, the most up-to-date ways known in various industries of producing different levels of output (or output per unit of input if we assume that the ex anteproduction function – Salter’s iso-quant – exhibits constant returns to scale, defined by an iso-quant in Q/I(l) and Q/L(i) space, see Figure 9.2). As a result of the choice of technique in each short run, the additions through accumulation at the margins of the stock of existing capital goods reflect the then

‘optimum’ point on the iso-quant.

Minhas and his co-authors were interested in a number of theoretical and empirical possibilities. Paul Samuelson (1948) had shown for the case of two countries which produce the same two commodities, use the same factors of production and have the same production functions in each industry, but different factor endowments, that free trade will equalise their absolute and relative factor prices. He assumed constant returns to scale and that, at any given ratio of factor prices, the chosen ratio in one indus-try is always greater or less than the corresponding ratio in the other.

Minhas et al. showed that if the two commodities are produced with two CES production functions that have different elasticities of substitution of capital for labour, there will always be a critical ratio of factor prices at which their factor intensities are equal, and above (or below) are reversed, requiring, for this case, modifications of Samuelson’s factor–price equali-sation theorem. Minhas was concerned in his book to fit relationships derived from the CES production function to observed data that came from the same industries in different countries. He wanted to estimate the values of the elasticities and to see whether factor reversals occurred within the

observed range of factor prices. He purported to show: that the CES pro-duction functions fitted the data well (if it is assumed that the efficiency of factors used between countries differed neutrally); that the elasticities were usually significantly less than unity (bye-bye, Cobb–Douglas); and that the critical price ratio was within the observed range of factor prices. For our present purposes we note that the ‘real world’ data were interpreted as points around the ‘best-practice’ iso-quant in each industry in different countries. The short period and the long period had again been collapsed into one another, where by long period, I mean the choices available at any moment of time for investment in ‘best-practice’ techniques, that is, the choice is made in the short period, but long-period factors are its dominant determinants.

IV

I followed the review with an article, Harcourt (1966), in which I said in effect: let us grant neoclassical economists every assumption they make in these investigations (I had ACMS and Minhas especially in mind), except that we allow for different vintages of ‘best-practice’ techniques to have been embodied by past bursts of accumulation into the total stocks of capital goods of the utilisation functions, which directly or indirectly had thrown up the data used by Minhas et al. in their estimates of the values of the elasticities of substitution. Will the equations they fitted to such data Figure 9.2 Salter’s ‘best-practice’ iso-quant, assuming constant returns

to scale l

0 i

be ‘good’fits, that is, will they provide unbiased estimators of the elastici-ties of substitution of the ‘best-practice’ iso-quants, which is their claim?

ACMS found a close association between the logarithms of labour pro-ductivity (value added per unit of labour used) and money-wage rates in the same industries in different countries, which was confirmed by the appropriate regressions. If the values added and labour inputs used in their analysis are assumed to be observations from CES production functions, the regression coefficients, say b, in equations of the form:

where qvalue added per unit of labour,wmoney-wage rate and error term, can be shown to be estimates of the elasticity of substitution of capital for labour (see ACMS, 1961, 228–9; Minhas, 1963; Harcourt, 1972, 51–55). But do the estimates of bprovide what is claimed for them?

The answer is ‘no’ as I believe I established in the article, and which I think Solow (1997), in so far as I understand him, accepts. Having argued that all we ever have in the data they used are totals and averages, whereas we are really interested in relationships between marginal quantities, I made up a number of plausible (I hope) stories – Solow has his doubts – and examined how close, qualitatively, the estimates ofbwould be approached by the use of ACMS’s procedures. I then put quantitative orders of mag-nitude on the biases by using Minhas’s data and assuming that some of my stories had generated the data. I found biases both upwards and down-wards, of considerable size, relatively to what was known to be their ‘true’

values.⁴

I shall not discuss the intricacies of the arguments between Anwar Shaikh (1974; 1980) and Solow (1974), because the other contributors to this volume have written extensively on it elsewhere and now here. But I do want to emphasise again the up-frontness of Solow’s account of his proce-dure in his 1957 article. He wrote: ‘It merely shows how one goes about interpreting time series if one starts by assuming that they were generated from a production function and that the competitive marginal product rela-tions apply’ (Solow, 1974, 121).

So he is not arguing that the world is Cobb–Douglas or CES or . . ., only that if we view our observations as ifthey were observations thrown up by Cobb–Douglas et al., these are the orders of magnitude of the parameters which our econometric procedures allow us to estimate (this is where the Fisher, Filipe, Shaikh, Solow, and McCombie debates begin). Solow does add that if the findings implied that the share of wages was 25 per cent and of profits 75 per cent, he would be less willing to trust his findings.⁵

log. qlog · Ab log. w ,

V

Finally, I want to discuss what in one sense is the heart of the matter, already touched upon in the claim that the short period and the long period have been collapsed into one. In the Cambridge–Cambridge capital theory debates there has been much discussion about the significance and rele-vance of the results, especially the phenomena of capital-reversal and re-switching, for economic theory and practice. One claim is that the answers to these queries is essentially an empirical one. Two champions of this view are the late Charles Ferguson and Mark Blaug. Here is Ferguson’s most (in)famous quote on the Cambridge critique in general and these issues in particular. It comes from his 1969 book.

[The validity of the Cambridge, England, criticism of neoclassical theory] is unquestionable, but its importance is an empirical or an econometric matter that depends upon the amount of substitutability there is in the system. Until the econometricians have the answer for us, placing reliance upon neoclassical eco-nomic theory is a matter of faith. I personally have the faith; but at present the best I can do is to invoke the weight of Samuelson’s authority as represented, for example, by the fly-leaf quotation [in Ferguson’s book] (Ferguson, 1969, xvii–xviii).⁶

Blaug, as well as defending the faith, has also often asked what is the like-lihood of capital-reversal and reswitching occurring in practice? Joan Robinson especially has argued that this is a nonsense question. The phe-nomena are discussed in theoretical terms, using either comparisonsof long-period equilibrium stationary states or of steady-state equilibrium growth models. They are therefore concerned with differences – what is the long-period equilibrium stationary state associated with a given value of one of the distributive variables, either wor r, for a given set of possibilities now?

The set may be either a smooth, continuously substitutable, neoclassical pro-duction function or an MIT et al. book of blueprints, with a different set of techniques for producing each commodity on each page, with the values of the coefficients – inputs per unit of output – in each industry ‘changing’ dis-cretely from one page to another. (Joan Robinson’s use of this apparatus in her 1953–54 article led Solow (1955–56, 106) to quip: ‘Everyone who invents linear programming these days seems charmed by it’.) So no process of accu-mulation in actual historical time is being considered. Moreover, the book of blueprints (or the neoclassical production function, the equivalent of Salter’s iso-quant at the level of the economy as a whole) could be expected to change over time due to technical advances, so that time series observations are at besttaken from a particular point on the ex anteproduction function on a particular page of the newest, latest book of blueprints. There is thus no way

this information may be used to test whether capital-reversal or reswitching is contained in any one book of blueprints.

So we are really concerned with a doctrinal debate concerning the coher-ence of neoclassical intuitions about the characteristics and functions of prices (and their relationship to the underlying scarcity theory of value) at a very abstract level of ‘high theory’ (no doubt child’s play for the heavies accustomed to publishing in Econometrica, QJE, Review of Economic Studies,JET, and so on⁷). We are reminded here of Piero Sraffa’s account of the different criteria that theory and statistical practice have to meet.

‘[O]ne should emphasise the distinction between two types of measurement . . . the one in which the statisticians were mainly interested. Second . . . measure-ment in theory. The statisticians’ measures were only approximate . . . the theo-retical measures required absolute precision . . . If we found contradictions, . . . these pointed to defects in the theory. (Sraffa, 1961, 305).

Just as Ricardo was chasing a Will-o’-the-wisp when he searched for an invariable standard of value which would allow him to precipitate out the effects of changes in distribution andtechnical progress from a measure of the surplus available for accumulation over time, so, too, is Blaug’s and Ferguson’s search for empirical findings to provide answers to their ques-tions a similar chase, they are just not there to be found. Stiffcheddar, but there it is.

VI

Or is it? I once suggested an alternative approach, see Harcourt (1966, 233;

1982, 145), which led one of the ACMS gang of four to query whether I was fooling/kidding. It was the following: an article by Salter (1962), pub-lished after his tragically early death, was concerned with an empirical enquiry using a questionnaire to ask businesspeople in different industries how much and what type of investment they would do if they wanted to increase their present capacities by a given amount. My suggestion was to test the ACMS hypothesis by asking this question of businesspeople in the same industries but different economies with different actual (and expected) relative factor prices. The resulting observations, on ACMS’s methodology, could be points on Salter iso-quants. If the same techniques were found to be associated with widely different relative factor prices (with other techniques chosen in between), that would be some evidence of the empirical presence of reswitching in the book of blueprints of the current

‘best-practice’ techniques in a situation in which it would be sensible in principle to test for its presence empirically.⁸

What is to be done? Must we despair, in the light of the implications of the capital theory controversies, concerning the possibility of doing useful work using econometric techniques? I do not believe so, though I do think Joan Robinson’s critique bears on the underlying conceptual foundations of much current econometric work. Basically, the world is still viewed in a Marshallian, even Pigovian manner (when it is not being viewed as the outcome of the decisions of Frank Ramsey’s benevolent dictator). There is a stable (?) long-period equilibrium position ‘out there’ which both con-strains and guides short-run movements as though it were a powerful magnet holding them in check, drawing the short-run values of prices and quantities toward itself and its own corresponding long-period values (or, at least, making the former fluctuate around the latter). So actual observa-tions may be interpreted as coming from (and approximating to) short-period flow equilibrium values, each corresponding to a station on the way to the long-period equilibrium cross.⁹Now certainly this is the structure of Marshall’s theory, but he never claimed that it was even an approximate description of the world. He was describing tendencies towards long-period equilibrium, providing that none of the background fundamentals of the initial situation were allowed to change once the process of observ-ing short-period equilibrium flows was started (theoretically, of course). He made it absolutely clear that in actual historical time, the vital components of the initial position could change, especially knowledge of the best ways of doing things.¹⁰This is where Salter comes into the discussion, arguing that,analytically, it is reasonable to suppose that the arrival of new ideas may be treated as if they arrive discretely, so that the accumulation process may embody the current ‘best-practice’ ideas through investment at the margin of the existing stock of different vintages. This is a far smaller order of abstraction to have to accept than what I take to be implied in cointe-gration procedures.

But suppose we follow another tack, using the seminal ideas of Richard Goodwin¹¹and Michal Kalecki concerning the indissolubility of trend and cycle. Kalecki’s succinct (as ever) statement of the approach is the follow-ing: ‘In fact, the long-run period is only a slowly changing component of a chain of short-period situations; it has no independent entity’ (Kalecki, 1968; 1991, 435).¹²

An implication for theory of the indissolubility of trend and cycle is that the separation of the factors responsible for the existence (uniqueness or multiple) of equilibrium from those responsible for stability (local and global) is unacceptable, an insight becoming more and more recognised by the mainstream with the examination in recent years of path-dependent models (already signalled by Nicky Kaldor in 1934 and Joan Robinson in 1953, probably earlier). This is, of course, matched by Kalecki’s work and

Goodwin’s 1967 classic, ‘A growth cycle’. So the role for Classical/Marxist centres of gravitation¹³in theory may be adjusted to the conjecture that actual observations may be regarded as near enough to those associated with short-period macroeconomic rest states¹⁴ to allow econometric methods to be used to fit them in, say, time series analysis. Here I leave it for the Andrew Harveys of this world to take over.¹⁵

APPENDIX 1 THE MAIN ISSUES AND RESULTS OF