Posts Tagged ‘production functions’

thoughts on economic models

Sunday, July 10th, 2016

A typical, very simple economic model is a demand curve, Dx = f(Px). It states that, other things equal, an increase in the price of x will result in a decrease in demand for x. I other things are not equal, the assumptions of the model do not hold. Suppose, writes blogger Arnold Kling, that x stands for tuition charged by a school, and we observe that demand went up rather than down when tuition increased. What may have happened is that scholarships became more generous, so the full tuition – net of student aid – fell. Other things did not remain equal.

Most economic models contain more variables. Consider the aggregate production function X = f(K,L). The quantity of output is a function of the quantity of physical capital plus the quantity of labour.

[This model] is used to predict that differences in output per worker will be proportionate to differences in capital per worker. When this fails, there are many possible reasons: workers may differ in their human capital; physical capital may not be measured or aggregated correctly; output may not be measured or aggregated correctly; institutional differences may matter. etc.

In fact, the primary use of the aggregate production function model is to examine its failure, which is called

does human (and physical) capital exist?

Wednesday, February 25th, 2015

In the heated bloggers’ debate over human capital, I was surprised by the absence of discussion of how to measure human capital, a point that was crucial in the earlier “Cambridge controversy” over physical capital. Typically, human capital is measured as years of schooling. All this is added up (sometimes with adjustment for levels of schooling – counting a year in High School or University as more than a year in primary school). The sum total is then taken to be a nation’s stock of ‘human capital’, which becomes an input into an aggregate production function for the economy. This seems wrong, to me. Some schools are terrible, whereas others are excellent. How can we take account in differences in the quality of schooling?

Nick Rowe has a clever solution to the problem. “Capital” – whether physical or human – is not really a thing, so it is not necessary (impossible?) to measure it.

We invest in increasing our skills, our strength, our knowledge, etc. It just easier to use the words

the human capital controversy

Sunday, February 22nd, 2015

Back in the 1960s there was a famous debate between economists (led by Joan Robinson and Piero Sraffa) of the University of Cambridge in England and economists (led by Paul Samuelson and Robert Solow) of MIT in Cambridge, Massachusetts. The debate, known as “the Cambridge capital controversy“, was over measurement and aggregation of physical capital. The Cambridge (England) economists argued that aggregate physical capital could not be measured without reference to the rate of return on capital. Cambridge (Massachusetts) generally agreed that the Cambridge (England) side won, though many professors of economics continue to teach aggregate production functions and economic growth theory as though the debate never took place.

A similar debate is now taking place, over human rather than physical capital. Noah Smith (HT Mark Thoma) provides a nice overview for those are interested.

Is “human capital” really capital? This is the topic of the latest econ blog debate. Here is Branko Milanovic, who says no, it isn’t. Here is Nick Rowe, who says yes, it is. Here is Paul Krugman, who says no, it isn’t. Here is Tim Worstall, who says yes, it is. Here is Elizabeth Bruenig, who says that people who say it is are bad.

Noah Smith, “Is human capital really capital?“, Noapinion, 21 February 2015.

Noah Smith offers an alternative view: human capital requires owners to work (give up leisure time) to obtain a return from it, so the more leisure is valued relative to other things, the less valuable human capital is. This will be different for each person. In consequence, you are “entitled to your own modeling conventions and definition of terms. So whether human capital is capital is up to you.”

This is an interesting, complex debate. I am still thinking about it but, as TdJ readers might predict, I am most persuaded by the arguments of Carleton University economist Nick Rowe. Before turning to Branko Milanovic and Nick Rowe, however, I would like to emphasize two points that are not always appreciated by participants in this debate. First, financial capital is not capital in an economic sense. Nick makes this point clearly, but others confuse financial capital with physical capital. Financial capital – stocks, bonds and the like – are just pieces of paper, IOUs. They are claims of lenders, and the loans may even have been made for the purpose of consumption rather than investment.

Second, even if human capital is a useful category of income-producing assets (and I think it is), it is as difficult to measure as physical capital is. In fact, it is probably even more difficult to measure. This does not really matter though, as it is impossible to measure aggregate assets of either asset apart from (only in theory!) the present value of the future income the assets produce. The problems of measurement of human capital are

education and growth

Friday, September 5th, 2014

[G]overnments seem convinced that the best way to [stimulate employment and growth] … is to increase the number of students pursuing degrees in the so-called

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

Solow on education

Thursday, June 16th, 2011

MIT economist Robert Solow participated in a recent IMF conference on

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

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

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

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