Posts Tagged ‘production functions’

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the Cobb-Douglas production function

Thursday, May 10th, 2012

The current issue of the Journal of Economic Perspectives (open access) has a 14-page essay on the Cobb-Douglas regression, a popular form of aggregate production function. About time, I thought, that someone writing in a popular journal exposed this work-horse of econometrics for the fraud that it is. I accessed the essay with great anticipation, only to find it full of praise, with very light – almost non-existent – criticism. Here are the essay’s two concluding sentences:

There remain open questions about the scientific value of this procedure in each of the contexts in which it is applied, some of which are variations of the friendly and unfriendly questions raised by Douglas’s initial critics. However, measured by the extent to which it has been embraced, applied, and elaborated upon by subsequent economists, Douglas’s innovative 1927 idea that one could use statistical analysis to uncover meaningful empirical relationships between inputs and outputs, as well as his specific implementation of that idea using the Cobb–Douglas functional form and least squares regression, was an overwhelming success.

Jeff Biddle, “The Introduction of the Cobb–Douglas Regression“, Journal of Economic Perspectives 26:2 (Spring 2012), pp. 223-236.

Michigan State University economist Jeff Biddle took to heart this advice of MIT economist Franklin Fisher:

[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.

Nowhere does Professor Biddle mention the most damning criticism of aggregate production functions (including the Cobb-Douglas variant): their good fit 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, aggregate production functions are almost tautologies – true by definition! This was pointed out independently by two Nobel laureates – Paul Samuelson and Herbert Simon – in articles that were published in 1979, and subsequently ignored by virtually everyone. Here are short quotes from each article:

It is a late hour to raise these doubts about the Emperor’s clothes, but ….

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.

 

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“, Scandinavian Journal of Economics 81:4 (1979), pp. 459-474.

Professor Biddle cites Samuelson’s article, but fails to mention Samuelson’s criticism of the Cobb-Douglas function. Biddle does not even cite Herbert Simon in his essay.

For more posts on this subject, click on the production functions tag.

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Solow on education

Thursday, June 16th, 2011

MIT economist Robert Solow participated in a recent IMF conference on “Macro and Growth Policies in the Wake of the Crisis”. Camilla Andersen interviewed him for the IMF publication Finance & Development, asking “What is needed to put people back to work? The role of education in the economic growth of middle-income and low-income countries is an important issue.”

Here is Professor Solow’s response:

We economists tend to measure education by input, not output. We count how many years people have been in school. Instead of worrying so much about quantities of education, we ought to be thinking about the content of the education. What is it that primary school or secondary school kids in poor and middle-income countries need to know? This is not necessarily what they are being taught.

And by the way, the same holds for advanced countries and the United States. We measure our success in generating an educated population in terms of the fraction of the age group that is in college. I would be very interested in other kinds of postsecondary education that are skills-based and would equip people for the jobs that are likely to be available.

That is going to require that employers be involved in the planning of that sort of education. For the United States, and perhaps for much of the world, that is a wholly new idea.

Camilla Andersen, “Rethinking Economics in a Changed World“, Finance & Development (June 2011).

Anderson interviewed two other Nobel laureates – NYU economist Michael Spence and Columbia economist Joseph Stiglitz – and reports their comments as well.

Schooling is often included as an explanatory variable in models of economic growth, because it is believed to be an important determinant of technical progress.

Robert Solow (born 1924) is famous for the “Solow residual”, known also as “total factor productivity”, which is assumed to be a measure of technical change. More accurately, it is what is left ‘unexplained’ after regressing GDP on inputs, i.e. the residual of an aggregate production function.

TdJ has insisted, in numerous posts, that aggregate production functions – and measures derived from them – can only be understood as faith, not science. These posts are titled “economics as faith”; one of them focuses on attempts to measure technical change.

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natural resources and economic theory

Tuesday, July 13th, 2010

Martin Wolf questions whether it makes sense for theorists to merge natural resources with manufactured capital. This has been the norm ever since neo-classical economics triumphed over classical economics, about a century ago.

In moving from classical to neo-classical economics — the dominant academic school today — economists expunged land — or natural resources [incorporating them into capital]. ….

Yet it would seem to me that this way of thinking by economists is no longer sensible, if it ever was. Land must again be treated as separate from labour and capital.

First, resource scarcity is an increasingly pressing issue. It shows up in concerns over pollution (including global warming), in the discussion of “peak oil” and so forth. The idea that diminishing returns will become a more significant factor in the next century than in the past two seems to me to be compelling, now that modern economic growth has spread across the globe. So we need to return to economic models that incorporate resources, as a matter of course.

Second, in a globalised economy, taxing labour and capital will become increasingly difficult. That leaves land. The Australian government is right to want to extract the full rental value of its mineral resources for the benefit of the Australian people. Similarly, the people of the UK should wish to extract the rental value of London for their own use. The benefits of infrastructure investments that make London more productive would automatically be recouped if land rents were heavily taxed. Meanwhile, the taxation of capital and land [labour!] could be reduced.

Martin Wolf, “Why were resources expunged from neo-classical economics?”, Martin Wolf’s Exchange, 12 July 2010.

Despite the unfortunate typo (“land” instead of “labour”), Martin provides a splendid introduction to an important topic. (The extract above is only a small part of this introduction.)

Martin Wolf’s Exchange is open to all readers, but you must open a free account with FT.com to post a comment.

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labour productivity

Saturday, March 6th, 2010

An op-ed published in today’s New York Times takes the US Labor Department to task for grossly overstating labour productivity, “especially in the nation’s manufacturing sector”.

Productivity measures how many worker hours are needed for a given unit of output during a given time period; when hours fall relative to output, labor productivity increases. In 2009, the data show, Americans needed 40 percent fewer hours to produce the same unit of output as in 1980.

But there’s a problem: labor productivity figures, which are calculated by the Labor Department, count only worker hours in America, even though American-owned factories and labs have been steadily transplanted overseas, and foreign workers have contributed significantly to the final products counted in productivity measures.

The result is an apparent drop in the number of worker hours required to produce goods — and thus increased productivity. But actually, the total number of worker hours does not necessarily change.

Alan Tonelson and Kevin L. Kearns, “Trading Away Productivity”, New York Times, 6 March 2010.

This column has value only as a discussion starter for a basic economics course. Instructors might ask students to look for elementary errors in reasoning, of which there is no shortage.

The basic flaw is glaringly simple. Productivity, it is true, is measured as units of output (in practice, value of output) divided by worker hours. But economists measure output as value-added by capital and labour, not as the value of final products. The output of an automobile assembly plant, for example, is measured as the value of the final output less the cost of all purchased parts and paint that go into a fully assembled vehicle, leaving only the value added by workers and the capital equipment they operate. Whether the intermediate parts are purchased locally or imported from afar does not matter for calculation of output, hence productivity.

If the Labor Department actually measured productivity the mistaken way claimed in this column, that would indeed be news!

Kevin L. Kearns has a J.D. from Brooklyn Law School and is the president of the United States Business and Industry Council, an association of small manufacturers. Alan Tonelson, a fellow at the council, holds “a B.A. with highest honors in history from Princeton University” and is author of The Race to the Bottom: Why a Worldwide Worker Surplus and Uncontrolled Free Trade are Sinking American Living Standards (Basic Books, 2000). Neither of the two is a trained economist – fortunately. Otherwise their column would be very embarrassing for the economics profession.

Thanks to Jan Sendzimir for the pointer.

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innovation is not R&D

Wednesday, December 16th, 2009

But is R&D innovation? John Kay explains.

When we talk about innovation, we visualise men and women in white coats with test tubes and microscopes. Outside many university cities around the world there are biotechnology estates established by governments that believe high technology is the key to a competitive future. The funds that governments provide to support innovation are all too often appropriated by large companies that are better at forming committees to pontificate about what the global village will want in the future than they are at assessing what their customers want today. ….

Last month the [UK's] National Endowment for Science, Technology and the Arts picked up this point. For years research and development scorecards have dutifully recorded how much pharmaceuticals companies spend on the search for new drugs and the expenditure of governments on defence electronics. But a Nesta report, presenting plans for a new innovation index has now recognised that most of the spending that promotes innovation does not take place in science departments. The financial services industry may have been Britain’s most innovative industry in the past two decades – perhaps too innovative – but practically none of the expenditure behind that innovation comes under “R&D”. And the same is true in retailing, media and a host of other innovative industries.

John Kay, “Innovation is not about wearing a white coat”, Financial Times, 16 December 2009.

An ungated version of this column will soon be posted here.

A pilot version of pilot version of NESTA’s Innovation Index can be downloaded here.

Data will be added over the next 12 months, and the Index will be extended to incorporate public sector innovation. NESTA promises then to update the Index each year with new data.

I was excited and eager to learn more, but became very disillusioned by the time I reached page 14 of the pilot report:

The second component is what macroeconomists describe as Total Factor Productivity (TFP). This is the measure of productivity growth that is not accounted for by the growth in factor inputs, such as physical capital or labour quality, and is generally attributed to better ways of doing things, including the broader benefits of technological advances and improved processes. In the approach used in the Innovation Index, in which the private benefits of investments such as R&D are captured separately, TFP includes the spillover benefits of innovation investment.

This methodology shows that between 2000 and 2007, labour productivity grew at an annual average of 2.7 per cent per year. Innovation contributed 1.8 per cent, or approximately two-thirds of the growth experienced.

NESTA, “The Innovation Index: Measuring the UK’s investment in innovation and its effects”, November 2009.

TFP is the residual that is left after regressing output on inputs, i.e. the residual of an aggregate production function. I have discussed all the problems with this methodology in a series of seven thoughts titled “economics as faith”. To locate these posts, type “economics as faith” into the search bar, or click on the “production functions” tag.

The first component of the Index is somewhat better. It consists of adding up all expenditure on R&D (really!), plus all expenditure on design, training, market research, etc. etc.. “However, R&D represents only 11 per cent of the investment in innovation ….” In other words, 89% of all innovation expenditure is excluded from the R&D budgets of private firms. So far, so good. But NESTA then uses “a growth accounting approach … to understand the effect of these [expenditures] on productivity growth.” This requires measures of aggregate productivity, reliance again on “economics as faith”.

I did not look at the third and last component of the Index, “a set of metrics that can be tracked to assess how favourable a climate the UK is for innovation”, so will not comment on that. I also do not know how – or whether – the three components will be combined to form a single index.

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economics as faith (7)

Monday, October 12th, 2009

The data of most economies are filled with apparently inconsistent series. By choosing among them, one can produce almost any estimate of productivity growth imaginable.

Alwyn Young “Gold into Base Metals: Productivity Growth in the People’s Republic of China during the Reform Period”, Journal of Political Economy 111:6 (2003), p. 22.

As Professor Young acknowledges, all growth accounting exercises should be taken with more than a grain of salt. Nonetheless growth accounting is a growth industry for academics. A recent study of China and India reaches new lows, however, in presenting questionable findings without providing the reader with caveats of any kind. The American Economic Association published it last year in their prestigious Journal of Economic Perspectives. Somehow it made it past the editors. I report only on the authors’ adjustment of labour input for skill levels – a glaring example of the general low quality of the piece.

Growth accounting provides a framework for allocating changes in a country’s observed output into the contributions from changes in its factor inputs—capital and labor—and a residual, typically called total factor productivity. ….

This approach is based on a production function in which output is a function of capital, labor, and a term for total factor productivity. …. [L]abor … is adjusted for … skills; we use average years of schooling as a proxy for skill levels and assume a constant annual return of 7 percent for each additional year of education.

Young (2003) provides a useful overview of Chinese statistics on educational attainment …. [H]is analysis of the relationship between earnings and years of schooling finds surprisingly low returns. ….

As noted earlier, our human capital index assumes that each additional year of schooling raises labor force productivity [in China and India] by 7 percent [even though Young (2003, p. 1246) found effects a fraction of that size for China.] This [7%] figure is based on a large number of empirical studies relating wages and years of schooling.

Barry Bosworth and Susan M. Collins, “Accounting for Growth: Comparing China and India”, Journal of Economic Perspectives 22:1 (Winter 2008), pp. 45–66.

The empirical studies alluded to are ‘Mincer equations’ – the regression of wage rates on levels of schooling and (sometimes) experience – and there are literally thousands of these studies. They almost always show that more schooling is associated with higher wages, but this does not prove that schooling increases productivity.

Suppose that schools exist only to screen students for ability, and that school attendance has no effect at all on productivity. In such a world, schooling is privately profitable but socially wasteful. Workers who complete more years of schooling are more productive and enjoy higher wages than workers who drop out of school. But increasing everyone’s consumption of schooling by a year has no effect on productivity or wages! Once there is a large pool of ‘schooled’ workers, employers will find that they have to demand a university degree for jobs that used to require only a high school diploma, because completion of high school no longer signals sufficient intelligence to handle the job. All this is well-known but is disregarded by the authors, who literally pull a 7% figure out of the air and inappropriately apply cross-section regression results to macro models of growth.

Barry Bosworth is Senior Fellow of Brookings Institution in Washington, DC. Susan M. Collins is Dean of Public Policy, Gerald R. Ford School of Public Policy, University of Michigan.

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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.

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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)

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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.

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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?

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