## Tuesday, October 4, 2011

### Keynes and Econometrics

Regular readers of this blog will know that I think it's important for students of econometrics to know something about the history of the discipline. So, let's pick a big-name economist at random, and see how he fitted into the overall scheme of things econometric.

John Maynard Keynes completed his B.A. with first class honours at the University of Cambridge in 1904. His B.A. in mathematics, that is. Subsequently, he was placed twelfth Wrangler in the Mathematical Tripos of 1905.

You probably know that Keynes made many important contributions to probability theory and statistics (as well as having some things to say about economics, of course!) His A Treatise on Probability is a classic work that makes seminal contributions to the “subjective” theory of probability used by Bayesians.

He also provided (Keynes, 1911) the first modern treatment of Laplace’s (1774) "first law of errors": if we have an odd number of observations, n, then the value of θ that minimizes the expression  Σ |yi - θ| is the median of the (y) data. An odd number of observations is needed simply to ensure that the median is unique. See, also, Wilson (1923).

So, perhaps you should pause and remember Keynes when you fit an LAD or quantile regression; or when you put on your Bayesian hat and choose the median of the posterior as your Bayes' estimate when you have an absolute error loss function.

A very insightful appraisal of Keynes (1911) has been provided recently by Klein and Grottke (2008). Interestingly, that 1911 paper appeared in the same issue of the Journal of the Royal Statistical Society that carried the obituary for the "father" of regression analysis, Sir Francis Galton, whose centenary is the subject of extensive celebrations among statisticians this year. (See my earlier posts on Galton, here and here.)

Keynes was one of the thirty economists from around the world selected in 1933, by the newly formed Council of the Econometric Society, to constitute the first group of Fellows of the Society. Elected to the Council of the Econometric Society a year later, remained a member of Council until his death in April 1946, and was President of the Econometric Society in 1944 and 1945. According to Patinkin (1976, p.1092), he greeted his elevation to the latter position by noting:
"whilst I am interested in econometric work and have done something at it at different times in my life, I have not recently written anything significant or important along these lines."
Such modesty!

A great deal has been written about Keynes' view of econometrics and his role in its early development. I won't try and do it justice here. However, students of econometrics would benefit from looking at Patinkin's (1976) Presidential address; Morgan (1990); and the recent and very readable discussion by Garrone and Marchionatti (2007).

To give you a taste of his influence on econometrics let's consider just one example. The so-called "Keynes-Tinbergen debate" is a justifiably famous milestone in the history of econometrics. If you're not aware of it, I'd urge you to find out about it, because there is much that was said that is still relevant for econometrics and econometricians today.

Tinbergen, a Dutch econometrician and central planner, was the co-recipient (with Ragnar Frisch) of the first Nobel Prize in Economic Science, in 1969. In essence, the "debate" with Keynes and others centered on the logic of using multiple regression methods to make inferences about the economy. Basic stuff!

Let me quote from Garrone and Marchionatti (2004, pp.2-3):

"Tinbergen's 1939 report for the League of Nations, Statistical Testing of Business-Cycle Theories, represented a fundamental contribution to the contemporary statistical and econometric research on business cycle, an increasingly important subject at that time. It was also an innovative contribution from the point of view of testing procedures. ..... The work was expected both to provide general economic forecasts and to guide government policies to control business cycle. ...... The first volume of the report, on which Keynes chose to focus, contained an explanation of the method of econometric testing. Tinbergen presented it as a synthesis of statistical business cycle research and quantitative economic theory, in the spirit of Econometrica's program. Tinbergen outlined the technical method of multiple correlation analysis by applying it to an economic business cycle theory translated into a parametrised mathematical-economic model. Then he tested for the plausibility of the parameter estimates. Finally, he checked the outcomes generated by the system as a whole to see whether the theory provides a business cycle mechanism or not. The first volume was followed by a second one, entitled Business Cycles in the United States of America, 1919-1932, where Tinbergen applied his method to annual data for the United States and endeavored to construct an economic model of the economic system taking into account all the important factors influencing business cycles in the country in the post-war period."
Masters of understatement, the authors continue:

"Tinbergen's work raised immediately a lively debate........"

In a series of papers and letters, in modern parlance Keynes took issue with matters that seem horribly familiar: simultaneity bias, measurement error, functional form, dynamic specification, structural change, omitted variable bias, spurious correlations, and trending data. Crucially, he questioned Tinbergen's use of inductive logic in drawing conclusions from his empirical analysis.

That all sounds pretty reasonable, but for quite some time history had it that Keynes was "anti-econometrics", and some pretty big names (including future Nobel laureates Paul Samuelson and Lawrence Klein) went even further. Samuelson claimed that Keynes was technically incompetent, and Klein said that Keynes' assessment of Tinbergen's report for the League of Nations was "one of his sorriest professional performances". (Garrone and Marchionatti, 2004, p.3.)

Certainly, Keynes himself was not one to mince words, saying of Tinbergen's efforts:

"Newton, Boyle and Locke all played with alchemy. So let him continue."

[Aside: Newton was in fact obsessed with alchemy. Ironically, Keynes actually acquired many of Newton's writings on the subject!]

However, if you want to get a modern perspective on this important "debate", and Keynes' position, I recommend (1976), Keuzenkamp (1995) and Garrone and Marchionatti (2004). In the end, Keynes emerges with his honour intact - for the most part!

So, whatever you may think of Keynesian economics, just keep in mind that Keynes played a crucial role in the history of econometrics, and his influence is still felt today.

Note: The links to the following references will be helpful only if your computer's IP address gives you access to the electronic versions of the publications in question. That's why a written References section is provided.

References

Garrone, G. and R. Marchionatti (2004). Keynes on econometric method. A reassessment of his debate with Tinbergen and other econometricians, 1938-1943. Working Paper № 01/2004, Department of Economics, University of Torino.

Garrone, G. and R. Marchionatti  (2007). Keynes, statistics and econometrics. Working Paper № 03/2007, Department of Economics, University of Torino.

Keuzenkamp. H. A. (1995). Keynes and the logic of econometric method. Mimeo., Department of Economics and CentER for Economic Research, Tilburg University.

Keynes, J. M. (1911). The principal averages and the laws of error which lead to them. Journal of the Royal Statistical Society, 74, 322–331.

Keynes, J. M. (1921). A Treatise on Probability. Macmillan, London.

Klein, R. and M. Grottke (2008). On J. M. Keynes' "The principal averages and the laws of error which lead to them". Discussion Paper № 07/2008, Institut für Wirtschaftspolitik und Quantitative Wirtschaftsforschung, Friedrich-Alexander-Universität.

Laplace, P-S. (1774). Mémoire sur la probabilité des causes par les évènements. Mémoires de l’Academie Royale des Sciences Presentés par Divers Savan, 6, 621–656. (Translated in S. M. Stigler, Memoir on the probability of the causes of events. Statistical Science, 1986, 1, 364–378.)

Morgan, M. S. (1990). The History of Economic Ideas. Cambridge University Press, Cambridge.

Patinkin, D. (1976). Keynes and econometrics: On the interaction between the macroeconomic revolutions of the inter-war period. Econometrica, 44, 1091-1123.

Wilson, E. B. (1923). First and second laws of error. Journal of the American Statistical Association, 18, 841-851.