Posts Tagged ‘production functions’

economics as faith (6)

Sunday, October 11th, 2009

Everything you wanted to know about aggregate production functions, but were afraid to ask, is available in a long survey paper. The authors end their survey on a pessimistic note.

This paper has aimed at providing a survey of the dense literature on aggregation in production with a view to drawing lessons for the applied economist. It is difficult to find an optimistic note on which to close. As far back as 1963, in his seminal survey on production and cost, Walters had concluded: “After surveying the problems of aggregation one may easily doubt whether there is much point in employing such a concept as an aggregate production function. The variety of competitive and technological conditions one finds in modern economies suggest that one cannot approximate the basic requirements of sensible aggregation except, perhaps, over firms in the same industry or for narrow sections of the economy”. More recently [1980] Burmeister, also after surveying the literature, concluded: “I am not very optimistic […] I have one revolutionary suggestion: Perhaps for the purpose of answering many macroeconomic questions–particularly about inflation and unemployment–we should disregard the concept of a production function at the macroeconomic level. The economist who succeeds in finding a suitable replacement will be a prime candidate for a future Nobel prize”.

Jesus Felipe and Franklin M. Fisher, “Aggregation in Production Functions: What Applied Economists should Know”, Metroeconomica 54:2-3 (2003), 208-262.

Spanish economist Jose Felipe works for the Asian Development Bank (ADB)in Manila. Franklin Fisher (1934-), we noted yesterday, is Professor Emeritus of Microeconomics at MIT.  A pre-publication (June 2002) draft of their paper is available here.

The references are to A.A. Walters,  “Production and Cost Functions: An Econometric Survey”, Econometrica 31:1-2 January- April 1963), pp.1-66  and to Edwin Burmeister, “Comment”, In Dan Usher (ed.): The Measurement of Capital (University of Chicago Press, 1980), pp. 420-431.

economics as faith (5)

Saturday, October 10th, 2009

Today, two self-explanatory – and rather sad – comments. The first is from an MIT colleague of Paul Samuelson. The second is from an ‘Austrian’ economist.

[A]ttempts to explain the impossibility of using aggregate production functions in practice are often met with great hostility, even outright anger. To that I say … that the moral is: “Don’t interfere with fairytales if you want to live happily ever after.”

Franklin M. Fisher, “Aggregate Production Functions – A Pervasive, but Unpersuasive, Fairytale”, Eastern Economic Journal 31:3 (Winter 2005), pp. 489-491.

Franklin Fisher (1934-) is Professor Emeritus of Microeconomics at MIT.

I don’t see [Paul] Samuelson as someone who traced ideas very deeply or as someone who thought outside the box. I see Samuelson’s technical economics like I see the work of a great chess master. To me, it is questionable whether he contributed to the solution of real economic problems. I admit, however, that I do not know all of Samuelson’s works and you may be able to persuade me otherwise.

I am aware of one sad fact about Samuelson. He apparently knew early on that the “good” econometric results of what became known as neoclassical growth theory using the Cobb-Douglas production function were an artifact. Yet he did not advertise this idea and a generation of lesser minds ended up wasting their time and a generation of textbook writers promoted a false belief he could have easily corrected.

Pat Gunning, Email to the thread “DISC–Scientism”, History of Economics Society, 19 September 2007.

J. Patrick Gunning (1942-) is a member of the ‘Austrian’ school of economics. He currently teaches in the College of Business, Feng Chia University. Taiwan. His home pages are posted here.

economics as faith (4)

Thursday, October 8th, 2009

Robert Solow continued to defend the neo-classical faith in 1974.

Mr. [Anwar] Shaikh’s article is based on misconception pure and simple. The factor-share device of my 1957 article is in no sense a test of aggregate production functions or marginal productivity or of anything else. It merely shows how one goes about interpreting given time series if one starts by assuming that they were generated from a production function and that the competitive marginal-product relations apply. Therefore, it is not only not surprising but it is exactly the point that if the observed factor shares were exactly constant the method would yield an exact Cobb-Douglas and tuck everything else into the shift factor.

Robert M. Solow, “Law of Production and Laws of Algebra: The Humbug Production Function: A Comment” The Review of Economics and Statistics 56:1 (February 1974), p. 121.

Paul Samuelson became a heretic just five years later, in a critical ‘eulogy’ for a deceased Paul Douglas, co-inventor in 1928 of the Cobb-Douglas Production Function.

Why has the freedom to make h differ from 1 – k been rejected the scatter? Because nature really favors constant returns to scale? Nonsense: she has not shown us her petticoat. Profit and wages add up to total PjQj along any fixed ray not because Euler’s theorem is revealed to apply on that ray but rather because of the accounting identity involved in the residual definition of profit: with PQj a trivial … sum of WLj and RCj along any Lj/Cj ray, how can its form of (WLj)^k (RCj)^h give other than k + h = 1? ….

It is a late hour to raise these doubts about the Emperor’s clothes, but not until undertaking the present assignment did this child give the matter of across- industry fitting the careful attention it deserves and does not seem to have received. ….

Why use the words “production function” for such an accounting-tautology … ?

Paul A. Samuelson, “Paul Douglas’s Measurement of Production Functions and Marginal Productivities”, Journal of Political Economy 87:5, Part 1 October 1979), pp. 923-939.

These words of Paul Samuelson could easily have been written by Herbert Simon, but perhaps not by Joan Robinson. Robert Solow and Paul Samuelson led the American side of the ‘Cambridge controversy’ between Cambridge, England and Cambridge, Massachusetts. Anwar Shaikh taught (and teaches) at the New School University in New York City; he was allied with the Cambridge, England side of the controversy.

Regrettably, no ungated version of Samuelson’s paper is available on the web.

Update: We noted that Herbert Simon’s 1979 paper on production functions has been cited only 67 times. This small number of citations might be attributed to the fact that Simon published his paper in an obscure journal, The Scandinavian Journal of Economics. Well, Samuelson’s 1979 paper was published in the JPE – the leading economics journal – and has received even fewer citations – 38  according to Google Scholar. In contrast, Samuelson’s 1962 paper on the same subject, written when he was a true believer, has been cited 270 times. I conclude that most researchers have not yet lost their faith, so ignore heretical writing.

economics as faith (3)

Wednesday, October 7th, 2009

Nobel laureate Herbert Simon carefully explained in a 1979 article that the good fit of production functions to empirical data is a statistical artifact – a result of the fact that the functions reflect  the accounting identity between the values of inputs and outputs. In other words, production functions are nearly tautologies – true by definition! Simon has dealt a fatal blow to neo-classical production functions, by demonstrating their innate uselessness.

Empirical data on the Cobb-Douglas and ACMS [Arrow, Chenery, Minhas and Solow] production functions have been alleged to provide substantial support for the classical theory of the firm–so substantial that further testing of that theory, as distinguished from elaboration of its detail, was no longer necessary. An examination of the evidence suggests instead that the observed good fit of these functions to data … are very likely all statistical artifacts. The data say no more than that the value of the product is approximately equal to the wage bill plus the cost of capital services. This interpretation of the statistical findings is plausible for both interindustry cross-sectional studies and time- series studies, the latter for either a single industry or a whole economy. (p. 469)

Herbert A. Simon,“On parsimonious explanations of production relations”, The Scandinavian Journal of Economics 81:4 (1979), pp. 459-474.

Political scientist Herbert Simon (1916-2001) held professorships in political science, administration, psychology and information sciences and made major contributions to psychology, economics, philosophy of science and computer science (including artificial intelligence). He coined the terms ‘bounded rationality’ and ‘satisficing’, and in 1978 was awarded the Nobel Prize in Economics “for his pioneering research into the decision-making process within economic organizations”.

This article – which ought to be required reading for every student of economics – is conspicuous by its absence from syllabi in virtually every academic institution. According to Google Scholar, the paper has been cited 67 times in the 30 years since it was published, including 4 self-citations by the author himself in subsequent publications. These are few citations indeed for an important paper drafted by a Nobel laureate. Some of my own papers have received more citations, and not one of them can hold a candle to this work.

Why have economists ignored this paper of Simon questioning neo-classical production functions? Could it be because the paper causes us to question – indeed, to throw out – a huge number of mindless empirical studies? Or, is there a fatal error in Simon’s reasoning? If this is the case, why has no-one attempted to point out or correct the error?

economics as faith (2)

Tuesday, October 6th, 2009

This contribution to our series is from Cambridge University economist Joan Robinson (1903-1983).  In a 1954 article – “The Production Function and the Theory of Capital” – she attacked the neo-classical idea that physical capital can be measured and aggregated, touching off what came to be known as the ‘Cambridge controversy’ between Cambridge, England and Cambridge, Massachusetts. This extract is from a short, non-technical paper that she published the following year.

The number of robin-minutes worked per day on his territory rises from a minimum when the cock is alone to a maximum when the pair are feeding the fledglings. Assuming that technical conditions remain constant over the period, we can draw up a schedule showing how output (of grubs caught) per robin-minute varies with robin-minutes worked per day. The advantage to a robin of having a more fertile territory (in terms of grubs per square yard, allowing for infestation by birds of other species who do not recognise the robin’s territorial rights) shows itself in a shorter working day (for total needs are rigid) and more time for singing.

For human production, even of the simplest kind, the function cannot be expressed in work alone. To produce an output to-day, work has to be combined with pre-existing goods, and the valuation of these goods affects the technique of production. From a purely engineering point of view, a steam-hammer is a powerful instrument for cracking nuts and gold the best material for lining drain- pipes. ….

The fallacy at the root of the production function is the idea that it is possible to specify purely technical relations, not involving prices, in a human economy. Even Robinson Crusoe does not provide an example of an economy for which this idea is valid. He looks before and after and plans productive processes that take time to carry through. He cannot build himself a hut unless he has food to eat while he is unable to go fishing, and the price, from his point of view, of future shelter in terms of stocks of food comes into his calculation (along with his evaluation of the trouble involved) of whether it is worth his while to build the hut. Only the robins, living in a timeless present, satisfy the conditions required for the neo-classical analysis of production to make sense.

Joan Robinson, “The Production Function”, The Economic Journal, 65:257 (March 1955), pp. 67-71.

I have come to agree that production functions are useless – or worse – as an aid to understanding the organisation of productive activity, but for a simpler and more obvious reason, one that is not mentioned by Joan Robinson. Joan Robinson’s earlier paper was published in The Review of Economic Studies, 21:2 (1954), pp. 81-106. According to Google Scholar, the 1954 paper has been cited 388 times, whereas the more accessible and brief 1955 paper has been cited only 14 times.

economics as faith (1)

Monday, October 5th, 2009

Some time ago – beginning in July 2007 – I circulated a number of thoughts on production functions to the Thought du Jour list. I have decided to recycle these thoughts, for two reasons. First, to bring them together and make them more accessible, with a single subject line. Second, to reach a larger audience via the blog. The posts might seem a bit wonkish, but none are difficult, I promise. The aggregate production function is the work horse of the economics profession. It is too important a concept to be accepted on faith.

We begin with a quote from Paul Samuelson, one of the most important economists of the twentieth century.

Until the laws of thermodynamics are repealed, I shall continue to relate outputs to inputs — i.e. To believe in production functions.

Paul A. Samuelson, Collected Scientific Papers, 1972, p.174.

I, alas, have lost my faith. Samuelson, we shall see, also lost his in later years.